au brûlage nucléaire de l'hydrogène. Dans la même veine, le mode stable avec $k = 5$ dispose d'un premier maximum situé bien au dessus de la région d'excitation alors que le premier nœud de sa fonction propre $|\delta T/T|$ tombe à proximité de la base de l'enveloppe; une configuration nettement défavorable à la déstabilisation du mode. Enfin, l'illustration du mode avec $k = 8$ montre un maximum secondaire situé précisément sur la couche de brûlage. Celui-ci demeure toutefois stable en raison de la dissipation radiative devenant importante suite à la multiplication des nœuds dans les fonctions propres et à l'amplitude relative beaucoup plus grande dans les régions supérieures de l'enveloppe.

## 6.3 Discussion et perspectives

Les résultats présentés dans ce bref chapitre suggèrent fortement que des pulsations non-radiales (modes g) puissent se manifester durant la phase post-EHB, ouvrant dès lors la perspective d'appliquer les méthodes de l'astéroséismologie pour sonder la structure de ces objets. Les modèles instables sont les descendants d'étoiles de la branche horizontale étendue (EHB) dotées initialement d'enveloppes relativement massives ($M_{env} \gtrsim 0.0010 M_{\odot}$ sur la ZAEHB). Les modes sont excités par la présence d'une région très active de brûlage en couche résiduel de l'hydrogène à la base de cette enveloppe. Il est d'ailleurs interessant de noter que les instabilités constatées sont de nature très similaires à celles discutées par Kawaler, 1988 (voir également Sienkiewicz, 1980) dans le contexte des étoiles, beaucoup plus lumineuses et chaudes, constituant le noyau central des nébuleuses planétaires. Nos modèles définissent une large bande d'instabilité couvrant l'intervalle de température $76000 K \gtrsim T_{eff} \gtrsim 44000 K$ et sont identifiables aux étoiles naines blanches DAO de faible masse. Les oscillations attendues sont des modes g de faible ordre radial avec des périodes typiques localisées autour de $\sim 80$ s, dépendant toutefois de la température effective et de la gravité de surface des modèles.

Contrairement aux sdB, la confirmation de cette prédiction théorique par l'observation reste à établir. Les objets identifiés comme étoiles post-EHB par Bergeron et al., 1994 et qu'ils serait intéressant d'examiner avec les techniques de photométrie rapide sont au nombre de 6. Ils s'agit concrètement des étoiles HZ 34, GD 651, Ton 353, PG0834+501, Feige 55 et PG0134+181. Bien entendu, il n'est pas – *a priori* – garanti que les étoiles mentionnées aient des progéniteurs avec les masses d'enveloppes adéquates pour développer des pulsations. En effet, puisque la région de l'espace $log g - T_{eff}$ occupée par les modèles instables semble extrêmement fine (les chemins évolutifs avec différentes masses d'enveloppes se chevauchent dans cette région; c.f., figure 6.1), il est presque assuré, du moins au niveau de précision auquel les paramètres atmosphériques de ces étoiles sont connus, que des objets instable coexisteront avec des objets stables. Comptes tenu de l'échantillon encore très restreint d'étoiles de ce type, l'interprétation des futurs résultats observationnels sera difficile. De plus, il est envisageable que des phénomènes n'ayant pas été pris en compte lors des calculs des séquences évolutives viennent influencer l'efficacité du mécanisme en jeu. Par exemple, les vents stellaires, complètement ignorés dans les modélisations actuelles d'évolution EHB et post-EHB, pourraient éventuellement suffire à réduire suffisamment la masse de l'enveloppe riche en hydrogène pour annihiler l'effet déstabilisateur du mécanisme $\epsilon$. De toute façon, quels que soient les résultats des prochaines campagnes d'observation des DAO pulsantes, d'intéressantes contraintes sur les quantités d'hydrogène conservées par une étoile en phase post-EHB devraient être proposées. En attendant, il demeure raisonnable de penser qu'une fraction de ces étoiles pourrait constituer une autre nouvelle classe d'étoiles pulsantes...
<figure><img src="image_116.png" /></figure>
Conclusion

Dans cette thèse — dont l'objectif demeurait l'évaluation, par des moyens exclusivement théo-
riques, du potentiel de l'astéroséismologie pour les étoiles sous-naines de type B — nous avons com-
mencé par présenter, au chapitre 1, après avoir préalablement introduit les motivations et le sujet de
cette recherche, le contexte observationnel et théorique dans lequel baigne l'ensemble du projet. Ce fut
l'occasion de rappeler quelques aspects importants relatifs aux équations mathématiques de la théorie
linéaire décrivant les pulsations stellaires non-radiales (adiabatiques et non-adiabatiques) et sur les
outils numériques (codes de pulsation) qui allaient constituer les instruments de notre exploration.

En parallèle, au chapitre 2, après avoir passé en revue les propriétés générales caractérisant
la classe des étoiles sous-naines de type B, nous avons présenté et discuté les modèles numériques
construits pour décrire ces objets et sur lesquels toute notre démarche allait s’appuyer. Dans le contexte
des pulsations, nous avons relevé qualitativement, à cette occasion, plusieurs éléments de la structure
de ces étoiles qui pouvaient potentiellement déstabiliser certains modes d’oscillation. En particulier,
la présence d’une région convective associée à l’ionisation partielle He$_{II}$/He$_{III}$ semblait, par analogie
avec les étoiles naines blanches pulsantes de type DB, constituer un candidat de choix.

Nous avons ensuite discuté de façon exhaustive, dans le chapitre 3, et ce compte tenu de l'absence
totale d'information portant sur cette question, des propriétés générales des modes de pulsation dans
les étoiles sous-naines de type B. De ce travail de défrichement, conduit quantitativement avec le
code des pulsations adiabatiques, découle une multitude de résultats indispensables à une bonne
compréhension et interprétation des caractéristiques des modes d'oscillation dont les périodes sont
maintenant observées dans certaines sdB pulsantes. Parmi ceux-ci, nous avons notamment déterminé
les valeurs typiques, ainsi que leurs variations en fonction des principaux paramètres stellaires défi-
nissant un modèle, des périodes attendues dans ces étoiles pour les différentes catégories de modes
habituellement rencontrés (modes p, f et g; radiaux et non-radiaux). Nous avons montré qu'à l'instar
des étoiles non-dégénérées, les modes acoustiques (modes p) sont principalement des modes d'enve-
loppe, peu sensibles aux régions profondes de l'étoile, alors que les modes de gravité (modes g)
sont surtout des modes d'intérieur confinés dans la partie radiative du noyau d'hélium. Toutefois,
à l'image des étoiles naines blanches avec lesquelles elles partagent une ressemblance flagrante en
terme de stratification chimique, les sdB ont révélé dans leur spectre de périodes, pour les modes g
et — dans une moindre mesure — pour les modes p, les manifestations d'un phénomène de piégeage
et de confinement des modes dû à la transition chimique entre le cœur en hélium et l'enveloppe riche en hydrogène. Nous avons également montré qu'il est possible, voir parfois souhaitable, d'utiliser des modèles statiques d'enveloppes à la place de structures évolutives pour étudier avec une précision suffisante les comportements des périodes des modes p. Il s'agit d'une conclusion importante pour quiconque souhaiterait, par la suite, utiliser des modèles de sdB pour conduire une étude astéro-séismogique de ces étoiles. Nous avons également, dans ce chapitre, étudié le couplage entre évolution et pulsations (calcul des $\dot{P}$) à l'aide des séquences de modèles évolutifs à notre disposition.

Au chapitre 4, en raison de l'absence – à l'époque – d'évidence observationnelle suggérant l'existence de sdB pulsantes, nous avons entrepris de mener une étude de stabilité sur les modèles de sdB à l'aide du code des pulsations non-adiabatiques. Nous avons ainsi démontré qu'il existe un mécanisme déstabilisateur potentiellement efficace dont l'origine provient, contrairement à nos soupçons préalables portant sur la zone d'ionisation partielle $He_{II}/He_{III}$, d'une région d'ionisation partielle d'éléments atomiques lourds, en particulier de fer (donc un mécanisme $\kappa$). Les calculs ont toutefois montré qu'à métallicité solaire ($Z \sim 0.02$), les quantités de fer présentes dans l'enveloppe riche en hydrogène sont insuffisantes pour déstabiliser les modèles mais qu'elles le deviennent pour $Z \gtrsim 0.04$. Dès lors, nous avons insisté sur le fait qu'il n'était pas nécessaire, pour engendrer des instabilités, de disposer de sur-abondances de fer dans la totalité de l'enveloppe de l'étoile et que les processus de diffusion, fortement suspectés d'exister dans ces étoiles, sont en mesure de produire d'importantes accumulations locales de cet élément dans la région qui déstabilise les modes. Ces constatations nous ont conduit à soumettre la prédiction que certaines étoiles sous-naines de type B devaient développer des oscillations observables; une prédiction qui s'est vue confirmée presque simultanément et de façon indépendante par un groupe en Afrique du Sud.

Au chapitre 5, après avoir introduit l'essentiel de la théorie de l'équilibre diffusif entre lévitation radiative et triage gravitationnel, nous avons raffiné notre étude du mécanisme d'excitation des modes de pulsation en construisant des modèles additionnels tenant compte des profils d'abondance de fer non-uniformes engendrés par ces effets. Ces modèles de seconde génération (par opposition aux modèles avec métallicité uniforme dits de première génération) ont permis de confirmer, en produisant des résultats théoriques quantitativement en accord avec les nouvelles données issues de l'observation, le bien fondé de l'idée proposée pour le mécanisme de déstabilisation. Une comparaison directe entre les propriétés des 12 sdB pulsantes connues à ce jour et les calculs théoriques démontre que les périodes observées dans ces étoiles correspondent aux modes p de faible ordre radial $k$, dont certains appartiennent nécessairement au spectre des pulsations non-radiales. La théorie indique également l'existence d'un domaine d'instabilité dans le plan $log g - T_{eff}$ dont le centre, marquant l'endroit où le mécanisme déstabilisateur est le plus efficace, correspond précisément à la région où sont situées la plupart des sdB pulsantes répertoriées. Nous avons par la suite évalué, sur la base de ces résultats et de ceux du chapitre 3, les possibilités que devrait réellement offrir l'analyse astéroséismologique de ces étoiles; notamment les aspects de la structure des sdB qui pourraient devenir accessibles et ceux qui resteront inabordables. Enfin, nous avons montré qu'il sera tout à fait acceptable, et de toute manière nécessaire, d'utiliser des structures statiques d'enveloppes de seconde génération – par opposition aux modèles évolutifs de première génération – pour l'analyse sismique de ces objets.

Finalement, au dernier chapitre (chapitre 6), fort du succès de l'approche purement théorique pour prédire l'existence de pulsations dans les étoiles sous-naines de type B, nous avons étendu les
calculs de stabilité aux modèles de la phase post-EHB de l'évolution stellaire reliant les étoiles sdB à la séquence de refroidissement des naines blanches. Les calculs ont montré que les modèles traversent une autre région d'instabilité durant cette phase de l'évolution. L'effet déstabilisateur est maintenant un mécanisme é impliquant les processus de fusion nucléaire de l'hydrogène en hélium dans les couches de brûlage résiduel situées à la base de l'enveloppe riche en hydrogène. Les modèles instables ont clairement été identifiés à une fraction des étoiles naines blanches de type DAO pour lesquels 6 candidats ont été suggérés comme pulsateurs potentiels. Il revient donc maintenant aux observateurs de déterminer si les DAO peuvent réellement constituer une autre nouvelle classe d'étoiles pulsantes.

De l'ensemble de ce travail, nous sommes en mesure de formuler plusieurs conclusions importantes. En premier lieu, il est remarquable, dans un domaine où les nouvelles découvertes sont essentiellement de nature observationnelle et presque toujours fortuites, qu'une approche structurée basée principalement sur l'application de méthodes théoriques (pulsations et structures stellaires, diffusion des éléments chimiques) ait conduit à une prédiction vérifiée et à des résultats dont l'accord avec les observations est très satisfaisant. Cela prouve qu'il s'agit d'une approche dont la fertilité n'est pas a négliger en astrophysique, une science plutôt traditionellement orientée vers l'observation. En second lieu, cette étude complète des propriétés des pulsations dans les sdB constitue la première du genre dans un domaine totalement neuf ou tout, ou presque, était à découvrir. Cette thèse, en défrichant notablement le terrain, pose donc les bases indispensables à la compréhension des phénomènes observés dans ces étoiles pulsantes ainsi qu'aux futures tentatives d'application des méthodes de l'astéroséismologie pour sonder la structure de ces objets. En dernier lieu, l'étude présentée, loin de constituer un aboutissement dans le domaine, induit au contraire une multitude de nouvelles et fertiles voies de recherche vers lesquelles il serait intéressant de se tourner...
<figure><img src="image_117.png" /></figure>
Références

Alecian, G., Michaud, G., & Tully, J. (1993). "Radiative accelerations on iron using opacity project data". Ap. J., **411**:882.

Allard, F., Wesemael, F., Fontaine, G., Bergeron, P., & Lamontagne, R. (1994). "Studies of hot B subdwarfs. IX. Cousins BVRI photometry and the binary fraction of hot, hydrogen-rich subdwarfs in the Palomar-Green survey". Astron. J., **107**:1565.

Allard, F., Wesemael, F., Lamontagne, R., Fontaine, G., & Bergeron, P. (1998). en préparation.

Baschek, B. & Norris, J. (1970). "'Neutral-He lines strengths. II. The B-type subdwarf HD 205805'". Ap. J. Suppl., **19**:327.

Baschek, B. & Norris, J. (1975). "The OB-Type subdwarf HD 149382 and the nature of the subdwarf B stars". Ap. J., **199**:694.

Berger, J. (1963). "Radial velocities and spectra of faint blue stars at high galactic latitudes". PASP, **75**:393.

Bergeron, P., Fontaine, G., Lacombe, P., Wesemael, F., Crawford, D. L., & Jakobsen, A. M. (1984). "Studies of hot B subdwarfs. I. Strömgren photometry of the Greenstein-Sargent-Sample". Astron. J., **89**:374.

Bergeron, P., Wesemael, F., Beauchamp, A., Wood, M. A., Lamontagne, R., Fontaine, G., & Liebert, J. (1994). "A spectroscopic analysis of DAO and hot DA white dwarfs: The implications of the prescence of helium and the nature of DAO stars". Ap. J., **432**:305.

Bergeron, P., Wesemael, F., Michaud, G., & Fontaine, G. (1988). "Studies of hot B subdwarfs. VI. Detailed calculations of radiative forces on metals in the envelopes and atmospheres of hydrogen-rich subdwarfs". Ap. J., **332**:964.

Billères, M. (1999). PhD thesis, Université de Montréal.

Billères, M., Fontaine, G., Brassard, P., & Charpinet, S. (1998a). In *Third Conference on Faint Blue Stars*, volume sous presse.

Billères, M., Fontaine, G., Brassard, P., Charpinet, S., Liebert, J., Saffer, R. A., Bergeron, P., & Vauclair, G. (1998b). "Detection of p-mode pulsations in the hot subdwarf B star KPD 2109+4401". Ap. J. Lett., **494**:L75.

Billères, M., Fontaine, G., Brassard, P., Charpinet, S., Liebert, J., Saffer, R. A., & Vauclair, G. (1997). "Discovery of p-mode instabilities in the hot subdwarf B star PG 1047+003". Ap. J. Lett., **487**:L81.

Brassard, P. (1991). "Propriétés adiabatiques des naines blanches pulsantes de type ZZ Ceti". PhD thesis, Université de Montréal.

Brassard, P. & Fontaine, G. (1994). "Computations of static white dwarf models: A must for asteroseismological studies". in I.A.U. Colloq., The Equation of State in Astrophysics. Volume **147**, page 560. Cambridge: Cambridge Univ. Press.

Brassard, P., Fontaine, G., Billères, M., & Charpinet, S. (1998). en préparation.

Brassard, P., Fontaine, G., & Wesemael, F. (1995). "The modeling of energy distributions and light curves of ZZ Ceti stars. I:Basic Theory and semianalytic expressions for the emergent flux". Ap. J. Supp., **96 No 2**:545.

Brassard, P., Fontaine, G., Wesemael, F., & Hansen, C. J. (1992a). "Adiabatic properties of pulsating DA white dwarfs. II. Mode trapping in compositionally stratified models". Ap. J. Supp., **80**:369.

Brassard, P., Fontaine, G., Wesemael, F., Kawaler, S. D., & Tassoul, M. (1992b). "Adiabatic properties of pulsating DA white dwarfs. I. The treatment of the brunt-väisälä frequency and the region of period formation". Ap. J., **367**:601.

Brassard, P., Fontaine, G., Wesemael, F., & Tassoul, M. (1992c). "Adiabatic properties of pulsating DA white dwarfs. IV. An extensive survey of the period structure of evolutionary models". Ap. J. Supp., **81**:747.

Brassard, P., Pelletier, C., Fontaine, G., & Wesemael, F. (1992d). "Adiabatic properties of pulsating DA white dwarfs. III. A finite-element code for solving nonradial pulsation equations". Ap. J. Supp., **80**:725.

Buchler, J. R., Yecko, P. A., & Kolláth, Z. (1997). "The nature of strange modes in classical variable stars". A&A, **326**:669.

Caloi, V. (1972). "Extended horizontal branch loci". A&A, **20**:357.

Caloi, V. (1989). "Evolution of the extreme horizontal branch stars". A&A, **221**:27.

Castellani, V., Degl'Innocenti, S., & Pulone, L. (1995). "The hot end of evolutionary horizontal branch". Ap. J., **446**:228.
Charpinet, S., Fontaine, G., Brassard, P., Chayer, P., Rogers, F., Iglesias, C., & Dorman, B. (1999). "A theoretical overview based on 2nd generation models of pulsating subdwarf B stars". In *11th European Workshop on White Dwarfs*, volume sous presse.

Charpinet, S., Fontaine, G., Brassard, P., Chayer, P., Rogers, F. J., Iglesias, C. A., & Dorman, B. (1997a). "A driving mechanism for the newly discovered class of pulsating subdwarf B stars". *Ap. J. Lett.*, **483**:L123.

Charpinet, S., Fontaine, G., Brassard, P., Chayer, P., Rogers, F. J., Iglesias, C. A., & Dorman, B. (1998). "Asteroseismology of hot B subdwarfs: Recent theoretical results". In *Third Conference on Faint Blue Stars*, volume sous presse.

Charpinet, S., Fontaine, G., Brassard, P., & Dorman, B. (1996). "The potential of asteroseismology for hot, subdwarf B stars: A new class of pulsating stars?". *Ap. J. Lett.*, **471**:L103.

Charpinet, S., Fontaine, G., Brassard, P., & Dorman, B. (1997b). "Gravity-mode instabilities in models of post-EHB stars: Another class of pulsating stars?". *Ap. J. Lett.*, **489**:L149.

Charpinet, S., Fontaine, G., Brassard, P., & Dorman, B. (1997c). "The potential of asteroseismology for hot, B subdwarfs: A new class of pulsating stars?". In *10th European Workshop on White Dwarfs*, page 477. Dordrecht: Kluwer Academic Publishers. I. Isern et al. (eds); Astrophysics and space science library; vol 214.

Chavira, E. (1958). "Estrellas azules en el casquete galactico sur (SGP)". *Bol. Obs. Tonantzintla y Tacubaya*, **No. 17**:15.

Chayer, P., Fontaine, G., & Wesemael, F. (1995a). "Radiative levitation in hot white dwarfs: Equilibrium theory". *Ap. J. Suppl.*, **99**:189.

Chayer, P., Vennes, S., Pradhan, A. K., Thejll, P., Beauchamp, A., Fontaine, G., & Wesemael, F. (1995b). "Improved calculations of the equilibrium abundances of heavy elements supported by radiative levitation in the atmospheres of hot DA white dwarfs". *Ap. J.*, **454**:429.

Cox, A. N., Morgan, S. M., Rogers, F. J., & Iglesias, C. A. (1992). "An opacity mechanism for the pulsations of OB stars". *Ap. J.*, **393**:272.

Cox, J. P. (1974). "Pulsating stars". *Reports on Progress in Physics.*, **37**, no 5:563.

Cox, J. P. (1980). "Theory of Stellar Pulsations". Princeton University Press.

Cox, J. P. & Giuli, R. T. (1968). "Principles of Stellar Structure". New York: Gordon & Breach.

Cunto, W. & Mendoza, C. (1992). "The opacity project – The TOPBASE atomic database". *Rev. Mex. Astron. Astrof.*, **23**:107.

D'Cruz, N. L., Dorman, B., Rood, R. T., & O'Connell, R. W. (1996). "The origin of Extreme Horizontal Branch stars". *Ap. J.*, **466**:359.

Demarque, P. & Eder, J. (1985). "Mass loss on the blue horizontal branch and the origin of the subdwarf B stars". In Philip, A. D., editor, *Horizontal Branch and UV Bright Stars*, page p.91.

Deupree, R. G. & Cole, P. W. (1981). "Mass loss during the core helium flah". *Ap. J.*, **249**:L35.

Dorman, B. (1992a). "Oxygen-Enhanced models fo globular cluster stars. III. Horizontal Branch Sequences". *Ap. J. Suppl.*, **81**:221.

Dorman, B. (1992b). "The structure of horizontal branch models. I. The Zero Age Horizontal Branch". *Ap. J. Suppl.*, **80**:701.

Dorman, B. (1996). "Horizontal Branch Stellar Evolution". page 291. 32nd Liège Astrophysical Colloquium. eds A Noels, N. Grevesse, M. Gabriel & P. Demarque.

Dorman, B., Lee, Y.-W., & VandenBerg, D. (1991). "Application of oxygen-enhanced evolutionary sequences to the horizontal branch of M15". *Ap. J.*, **366**:115.

Dorman, B., O'Connell, R. W., & Rood, R. T. (1995). "Ultraviolet radiation from evolved stellar populations. II. The ultraviolet upturn phenomenon in elliptical galaxies". *Ap. J.*, **442**:105.

Dorman, B. & Rood, R. T. (1993). "On partial mixing zones in horizontal branch stellar cores". *Ap. J.*, **409**:387.

Dorman, B., Rood, R. T., & O'Connell, R. W. (1993). "Ultraviolet radiation from evolved stellar populations. I. Models". *Ap. J.*, **419**:596.

Dziembowski, W. (1971). *Acta Astr.*, **21**:289.

Dziembowski, W. & Pamiatnykh, A. A. (1993). "The opacity mechanism in B-type stars. I - Unstable modes in Beta Cephei star models". *MNRAS*, **262**:204.
Eggleton, P. P., Faulkner, J., & Flannery, B. P. (1973). "An Approximate Equation of State for Stellar Material". A&A, 23:325.

Faulkner, J. (1972). "On the nature of the horizontal branch. II. Extremely blue halo stars: A theoretical viewpoint". Ap. J., 173:401.

Feige, J. (1958). "A search for underluminous hot stars". Ap. J., 128:267.

Fontaine, G., Charpinet, S., Brassard, P., Chayer, P., Rogers, F. J., Iglesias, C. A., & Dorman, B. (1998). "EC14026 stars – Theoretical considerations". In New Eyes to See Inside the Sun and Stars, volume 185, page 367. IAU. F.-L. Deubner et al. (eds.).

Fontaine, G. & Chayer, P. (1998). "The helium abundance puzzle in subdwarf B stars: A theoretical interpretation through mass loss". In Third Conference on Faint Blue Stars, volume sous presse.

Gautschy, A. & Glatzel, W. (1990). "On highly non-adiabatic stellar pulsations and the origin of strange modes". MNRAS, 245:597.

Gautschy, A. & Glatzel, W. (1991). "The secular and thermal spectrum of hydrogen-deficient carbon stars". MNRAS, 253:509.

Gautschy, A. & Saio, H. (1993). "On non-radial oscillations of B-type stars". MNRAS, 262:213.

Gautschy, A. & Saio, H. (1995). "Stellar pulsations across the HR diagram: Part 1". Annu. Rev. A&A, 33:75.

Glatzel, W. (1994). "On the origin of strange modes and the mechanism of related instabilities". MNRAS, 271:66.

Gonzalez, J.-F., LeBlanc, F., Artru, M.-C., & Michaud, G. (1995). "Improvements on radiative acceleration calculations in stellar envelopes". A&A, 297:223.

Greenstein, J. L. (1960). "Stellar Atmospheres". University of Chicago Press. Ch. 19.

Greenstein, J. L. (1966). "The nature of the faint blue stars". Ap. J., 144:496.

Greenstein, J. L. & Sargent, A. I. (1974). "The nature of faint blue stars in the halo. II. Ap. J. Suppl., 28:157.

Greggio, L. & Renzini, A. (1990). "Clues on the hot star content and the ultraviolet output of elliptical galaxies". Ap. J., 364:35.

Heber, U. (1986). "The atmosphere of subluminous B stars. II. Analysis of 10 helium poor subdwarfs and the birthrate of sdB stars". A&A, 155:33.

Heber, U. (1991). "Atmospheres and abundances of blue horizontal branch stars and related objects". In Michaud, G. & Tutukov, A., editors, Evolution of Stars: The Photospheric Abundance Connection, IAU Symposium 145, page 363. (Dordrecht, Kluwer).

Heber, U., Hamann, W.-R., Hunger, K., Kudritzki, R. P., Simon, K. P., & Méndez, R. H. (1984a). "Non-LTE analysis of subluminous hot stars". A&A, 136:331.

Heber, U., Hunger, K., Jonas, G., & Kudritzki, R. P. (1984b). "The atmosphere of subluminous B stars". A&A, 130:119.

Horch, E., Demarque, P., & Pinnsoneault, M. (1992). "The evolution of high metallicity horizontal branch stars and the origin of the UV light in elliptical galaxies". Ap. J. Lett., 388:L53.

Humason, M. L. & Zwicky, F. (1947). "A search for faint blue stars". Ap. J., 105:85.

Hunger, K., Gruschinske, J., Kudritzki, R. P., & Simon, K. P. (1981). "Non-LTE Analysis of subluminous O-stars. IV. Spectral photometry and NLTE analysis of 11 subluminous stars". A&A, 95:244.

Iben, I. J. (1990). "On the consequences of low-mass white dwarfs mergers". Ap. J., 353:215.

Iben, I. J. & Tutukov, A. V. (1986). "On the formation and evolution of a helium degenerate dwarf in a close binary". Ap. J., 311:742.

Iriarte, B. & Chavira, E. (1957). "Estrellas azules en el casquete galactico norte". Bol. Obs. Tonantzintla y Tacubaya, No. 16:3.

Itoh, N., Mitake, S., Iyetomi, H., & Ichimaru, S. (1983). "Electrical and thermal conductivities of dense matter in the liquid metal phase. I - High-temperature results". Ap. J., 273:774.

Kawaler, S. D. (1988). "The hydrogen shell game - Pulsational instabilities in hydrogen shell-burning planetary nebula nuclei". Ap. J., 334:220.

Kilkenny, D., Koen, C., O'Donoghue, D., & Stobie, R. S. (1997). "A new class of rapidly pulsating stars - I. EC14026-2647, the class prototype". MNRAS, 285:640.

Kilkenny, D., O'Donoghue, D., Koen, C., Lynas-Gray, A. E., & van Wyk, F. (1998). "The EC 14026 stars -
VIII. PG 1336-018: a pulsating sdB star in an HW Vir-type eclipsing binary". MNRAS, **296**:329.

Koen, C., Kilkenny, D., O'Donoghue, D., van Wyk, F., & Stobie, R. S. (1997). "A new class of rapidly pulsating star - II. PB 8783". MNRAS, **285**:645.

Koen, C., O'Donoghue, D., Kilkenny, D., Lynas-Grey, A. E., Marang, F., & van Wyk, F. (1998a). "The EC14026 stars - VII. PG 1605+072, a star with many pulsation modes". MNRAS, **296**:317.

Koen, C., O'Donoghue, D., Pollacco, D. L., & Charpinet, S. (1999). "The EC14026 stars PG1219+534, PG0911+456: Successes and New Challenges for the Fe Driving Mechanism". MNRAS, soumis.

Koen, C., O'Donoghue, D., Pollacco, D. L., & Nitta, A. (1998b). "The new EC14026 star Feige 48: A link in its class". MNRAS, soumis.

Ledoux, P. & Walraven, T. (1958). "Handbuch der Physik". Berlin: Springer-Verlag.

Lynden-Bell, D. & Ostriker, J. P. (1967). "On the stability of differentially rotating bodies". MNRAS, **136**:293.

Mengel, J. G., Norris, J. E., & Gross, P. G. (1976). "A binary hypothesis for the subdwarf B stars". Ap. J., **204**:488.

Michaud, G., Bergeron, P., Heber, U., & Wesemael, F. (1989). "Studies of hot B subdwarfs. VII. Non-LTE radiative acceleration of helium in the atmosphere of sdOB stars". Ap. J., **338**:417.

Michaud, G., Bergeron, P., Wesemael, F., & Fontaine, G. (1985). "Studies of hot B subdwarfs. IV. Radiative forces, mass loss, and metal abundances in sdB stars". Ap. J., **299**:741.

Michaud, G., Charland, Y., Vauclair, S., & Vauclair, G. (1976). "Diffusion in main-sequence stars: Radiation forces, time scales, anomalies". Ap. J., **210**:447.

Moehler, S., de Boer, K. S., & Heber, U. (1990). "Hot subluminous stars at high galactic latitudes. II - Physical parameters and distances of 37 sdB stars". A&A, **239**:265.

Montmerle, T. & Michaud, G. (1976). "Diffusion in stars: Ionisation and abundance effects". Ap. J. Suppl., **31**:489.

Moskalik, P. & Dziembowski, W. (1992). "New opacities and the origin of the Beta Cephei pulsation". A&A, **256**:L5.

O'Donoghue, D., Koen, C., Kilkenny, D., Stobie, R. S., Lynas-Gray, A. E., & Kawaler, S. D. (1997a). In *10th European Workshop on White Dwarfs*. Dordrecht: Kluwer Academic Publishers. I. Isern et al. (eds); Astrophysics and space science library; vol 214.

O'Donoghue, D., Koen, C., Lynas-Grey, A. E., Kilkenny, D., & van Wyk, F. (1998a). "The EC14026 stars - VI. PG1047+003". MNRAS, **296**:306.

O'Donoghue, D., Koen, C., Solheim, J. E., Barstow, M. A., Dobbie, P. D., O'Brien, M. S., Clemens, J. C., Sullivan, D. J., & Kawaler, S. D. (1998b). "The EC14026 stars - V. The pulsation periods of PB8783". MNRAS, **296**:296.

O'Donoghue, D., Lynas-Grey, A. E., Kilkenny, D., Stobie, R. S., & Koen, C. (1997b). "A new class of rapidly pulsating star - IV. Oscillations in EC 20117-4014 and atmospheric analyses". MNRAS, **285**:657.

Osaki, Y. (1975). "Nonradial oscillations of a 10 solar mass star in the main-sequence stage". PASJ, **27**:237.

Paczyński, B. (1971). "Evolution of single stars. VI. Model nuclei of planetary nebulae". Acta. Astr., **21**:417.

Paquette, C., Pelletier, C., Fontaine, G., & Michaud, G. (1986a). "Diffusion coefficients for stellar plasmas". Ap. J. Suppl., **61**:177.

Paquette, C., Pelletier, C., Fontaine, G., & Michaud, G. (1986b). "Diffusion in white dwarfs – New results and comparative study". Ap. J. Suppl., **61**:197.

Reif, F. (1965). "Fundamentals of statistical and thermal physics". McGraw-Hill series in fundamentals of physics.

Ritter, A. (1879). *Ann. Phys. Chem. Neue Folge*, **8**:157.

Rogers, F. J. & Iglesias, C. A. (1992). "Rosseland mean opacities for variable compositions". Ap. J., **401**:361.

Rosseland, S. (1949). "The pulsation theory of variable stars". Oxford: Oxford University Press. Ch. 1.

Saffer, R. A., Bergeron, P., Koester, D., & Liebert, J. (1994). "Atmosphere parameters of field subdwarfs B stars". Ap. J., **432**:351.

Saio, H., Baker, N. H., & Gautschy, A. (1998). "On the properties of strange modes". MNRAS, **294**:622.

Saio, H., Wheeler, J. C., & Cox, J. P. (1984). "Very nonadiabatic radial pulsations in luminous helium stars". Ap. J., **281**:318.
Sargent, W. L. W. & Searle, L. (1968). "A quantitative description of the spectra of the brighter Feige stars". *Ap. J.*, **152**:443.

Saumon, D., Chabrier, G., & Horn, H. M. V. (1995). "An equation of state for low-mass stars and giant planets". *Ap. J. Suppl.*, **99**:713.

Sienkiewicz, R. (1980). "Stability of white dwarfs undergoing spherically symmetric steady-state accretion". *A&A*, **85**:295.

Stobie, R. S., Kawaler, S. D., Kilkenny, D., O'Donoghue, D., & Koen, C. (1997). "A new class of rapidly pulsating star - III. Oscillations in EC 10228-0905 and pulsation analysis". *MNRAS*, **285**:651.

Sweigart, A. V. (1997). "Effects of helium mixing on the evolution of globular cluster stars". *Ap. J. Lett.*, **474**:L74.

Sweigart, A. V., Mengel, J. G., & Demarque, P. (1974). "On the origin of the blue halo stars". *A&A*, **30**:13.

Tassoul, M. (1980). "Asymptotic approximations for stellar nonradial pulsations". *Ap. J. Supp.*, **43**:469.

Theissen, A., Moehler, S., Heber, U., & de Boer, K. S. (1993). "Hot subluminous stars at high galactic latitudes. IV - Physical parameters and distances of 18 sdB stars and their spatial distribution". *A&A*, **273**:524.

Thejll, P., Bauer, F., Saffer, R. A., Liebert, J., Kunze, D., & Shipman, H. L. (1994). "Analysis of helium-rich subdwarfs O stars. I. NLTE models, methods, and fits for 21 Palomar Green survey sdOs". *Ap. J.*, **433**:819.

Unno, W., Osaki, Y., Ando, H., Saio, H., & Shibahashi, H. (1989). "Non Radial Oscillation of Stars". University of Tokyo Press.

VandenBerg, D. A. (1992). "Oxygen-Enhanced models fo globular cluster stars. I. Evolutionary Tracks". *Ap. J.*, **391**:685.

VandenBerg, D. A. & Poll, H. E. (1989). "On precise ZAMSs, the solar color and pre-main-sequence lithium depletion". *A. J.*, **98**:1451.

Wesemael, F., Winget, D. E., Cabot, W., Van Horn, H. M., & Fontaine, G. (1982). "The hot subdwarfs revisited". *Ap. J.*, **254**:221.

Winget, D. E., Horn, H. M. V., Tassoul, M., Hansen, C. J., & Fontaine, G. (1983). "The pulsation properties of DB white dwarfs: A preliminary analysis". *Ap. J. Lett.*, **268**:L33.

Zalewski, J. (1992). "Strongly nonadiabatic pulsations and strange modes". *PASJ*, **44**:27.
<figure><img src="image_118.png" /></figure>
# Partie IV

## Annexes
<figure><img src="image_119.png" /></figure>
# Annexe A
## Paramètres Stellaires pour les Séquences Evolutives

Dans cette annexe sont présentées les 7 séquences évolutives constituant notre première source de modèles identifiés aux étoiles sous-naines de type B. Chaque séquence est illustrée par un tableau comprenant un ensemble de quantités physiques qui reflètent la structure des modèles à diverses étapes de la vie de ces étoiles. La signification de chacune de ces quantités est donnée dans le tableau ci-dessous. Ajoutons que les tableaux des séquences sont rangés par ordre de masse d'enveloppe croissante ($M_{\text{env}} = 0.0001, 0.0002, 0.0007, 0.0012, 0.0022, 0.0032$ et $0.0042 M_{\odot}$) et que les principales phases traversées par les modèles au cours de l'évolution sont indiquées (de la ZAEHB à la séquence de refroidissement des naines blanches).

<table><thead><tr><th>Colonne</th><th>Signification</th></tr></thead><tbody><tr><td>#</td><td>Numéro du modèle dans la séquence</td></tr><tr><td>Age</td><td>Age depuis la ZAEHB exprimé en millions d'années</td></tr><tr><td colspan="2"><strong>Paramètres de surface</strong></td></tr><tr><td>log L/L<sub>☉</sub></td><td>Luminosité totale (en luminosités solaires)</td></tr><tr><td>T<sub>eff</sub></td><td>température effective (en Kelvin)</td></tr><tr><td>log g</td><td>gravité de surface (g est en cm.s<sup>-2</sup>)</td></tr><tr><td colspan="2"><strong>Paramètres centraux</strong></td></tr><tr><td>Y<sub>c</sub></td><td>fraction de masse de l'hélium au centre du modèle</td></tr><tr><td>log T<sub>c</sub></td><td>Température au centre (T<sub>c</sub> est en Kelvin)</td></tr><tr><td>log ρ<sub>c</sub></td><td>Densité centrale (ρ<sub>c</sub> est en g.cm<sup>-3</sup>)</td></tr><tr><td>log P<sub>c</sub></td><td>Pression au centre (P<sub>c</sub> est en dixièmes de Pascals)</td></tr><tr><td>log q<sub>cc</sub></td><td>Position de la limite du noyau convectif (log q<sub>cc</sub> = log(1 - M<sub>cc</sub>/M<sub>*</sub>) où M<sub>cc</sub> est la masse du cœur convectif)</td></tr></tbody></table>
Séquence évolutif: $M = 0.4690 + 0.0001 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>4.49</td><td>1.126</td><td>34394</td><td>6.076</td><td>0.896</td><td>8.065</td><td>4.367</td><td>20.270</td><td>-0.119</td></tr><tr><td>2</td><td>23.34</td><td>1.172</td><td>34345</td><td>6.027</td><td>0.726</td><td>8.075</td><td>4.354</td><td>20.244</td><td>-0.164</td></tr><tr><td>3</td><td>39.31</td><td>1.205</td><td>34329</td><td>5.993</td><td>0.611</td><td>8.083</td><td>4.340</td><td>20.223</td><td>-0.198</td></tr><tr><td>4</td><td>58.04</td><td>1.245</td><td>34405</td><td>5.957</td><td>0.476</td><td>8.093</td><td>4.331</td><td>20.208</td><td>-0.224</td></tr><tr><td>5</td><td>71.77</td><td>1.278</td><td>34573</td><td>5.933</td><td>0.366</td><td>8.103</td><td>4.331</td><td>20.205</td><td>-0.243</td></tr><tr><td>6</td><td>81.82</td><td>1.307</td><td>34830</td><td>5.917</td><td>0.274</td><td>8.114</td><td>4.339</td><td>20.213</td><td>-0.256</td></tr><tr><td>7</td><td>89.23</td><td>1.330</td><td>35155</td><td>5.910</td><td>0.204</td><td>8.125</td><td>4.353</td><td>20.230</td><td>-0.207</td></tr><tr><td>8</td><td>94.80</td><td>1.349</td><td>35538</td><td>5.910</td><td>0.149</td><td>8.135</td><td>4.373</td><td>20.254</td><td>-0.270</td></tr><tr><td>9</td><td>98.98</td><td>1.363</td><td>35965</td><td>5.916</td><td>0.108</td><td>8.146</td><td>4.396</td><td>20.283</td><td>-0.169</td></tr><tr><td>10</td><td>102.26</td><td>1.373</td><td>36396</td><td>5.927</td><td>0.082</td><td>8.155</td><td>4.419</td><td>20.313</td><td>-0.275</td></tr><tr><td>11</td><td>104.84</td><td>1.381</td><td>36842</td><td>5.940</td><td>0.059</td><td>8.164</td><td>4.443</td><td>20.345</td><td>-0.160</td></tr><tr><td>12</td><td>106.88</td><td>1.388</td><td>37312</td><td>5.956</td><td>0.044</td><td>8.173</td><td>4.469</td><td>20.379</td><td>-0.278</td></tr><tr><td>13</td><td>108.49</td><td>1.392</td><td>37796</td><td>5.973</td><td>0.032</td><td>8.182</td><td>4.495</td><td>20.414</td><td>-0.155</td></tr><tr><td>14</td><td>109.75</td><td>1.396</td><td>38266</td><td>5.991</td><td>0.023</td><td>8.190</td><td>4.521</td><td>20.447</td><td>-0.169</td></tr><tr><td>15</td><td>111.04</td><td>1.402</td><td>38998</td><td>6.018</td><td>0.014</td><td>8.201</td><td>4.561</td><td>20.500</td><td>-0.135</td></tr><tr><td>16</td><td>112.97</td><td>1.450</td><td>43488</td><td>6.159</td><td>0.000</td><td>8.250</td><td>4.795</td><td>20.803</td><td>-0.045</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>17</td><td>113.09</td><td>1.476</td><td>44894</td><td>6.188</td><td>0.000</td><td>8.246</td><td>4.878</td><td>20.899</td><td>0.000</td></tr><tr><td>18</td><td>113.32</td><td>1.500</td><td>47444</td><td>6.261</td><td>0.000</td><td>8.244</td><td>5.018</td><td>21.068</td><td>0.000</td></tr><tr><td>19</td><td>113.84</td><td>1.494</td><td>47766</td><td>6.279</td><td>0.000</td><td>8.205</td><td>5.119</td><td>21.176</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>20</td><td>119.06</td><td>1.727</td><td>50974</td><td>6.158</td><td>0.000</td><td>8.102</td><td>5.298</td><td>21.380</td><td>0.000</td></tr><tr><td>21</td><td>129.67</td><td>1.926</td><td>58104</td><td>6.187</td><td>0.000</td><td>8.090</td><td>5.473</td><td>21.633</td><td>0.000</td></tr><tr><td>22</td><td>135.42</td><td>2.096</td><td>67152</td><td>6.269</td><td>0.000</td><td>8.065</td><td>5.647</td><td>21.890</td><td>0.000</td></tr><tr><td>23</td><td>138.81</td><td>2.156</td><td>78364</td><td>6.477</td><td>0.000</td><td>8.028</td><td>5.799</td><td>22.119</td><td>0.000</td></tr><tr><td>24</td><td>140.79</td><td>1.990</td><td>85087</td><td>6.786</td><td>0.000</td><td>7.989</td><td>5.914</td><td>22.292</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naine blanche</strong></td></tr><tr><td>25</td><td>141.38</td><td>1.262</td><td>70570</td><td>7.188</td><td>0.000</td><td>8.004</td><td>5.996</td><td>22.420</td><td>0.000</td></tr><tr><td>26</td><td>142.41</td><td>0.675</td><td>56611</td><td>7.392</td><td>0.000</td><td>7.948</td><td>6.075</td><td>22.539</td><td>0.000</td></tr><tr><td>27</td><td>144.58</td><td>0.131</td><td>44663</td><td>7.525</td><td>0.000</td><td>7.855</td><td>6.144</td><td>22.642</td><td>0.000</td></tr><tr><td>28</td><td>148.76</td><td>-0.371</td><td>35057</td><td>7.606</td><td>0.000</td><td>7.762</td><td>6.180</td><td>22.695</td><td>0.000</td></tr><tr><td>29</td><td>156.88</td><td>-0.848</td><td>27469</td><td>7.659</td><td>0.000</td><td>7.660</td><td>6.204</td><td>22.730</td><td>0.000</td></tr><tr><td>30</td><td>176.44</td><td>-1.316</td><td>21446</td><td>7.697</td><td>0.000</td><td>7.532</td><td>6.203</td><td>22.729</td><td>0.000</td></tr><tr><td>31</td><td>228.85</td><td>-1.782</td><td>16708</td><td>7.730</td><td>0.000</td><td>7.362</td><td>6.214</td><td>22.744</td><td>0.000</td></tr><tr><td>32</td><td>323.16</td><td>-2.244</td><td>12985</td><td>7.754</td><td>0.000</td><td>7.177</td><td>6.217</td><td>22.747</td><td>0.000</td></tr></tbody></table>
Séquence évolutives: $M = 0.4758 + 0.0002 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>1.79</td><td>1.156</td><td>31462</td><td>5.898</td><td>0.928</td><td>8.066</td><td>4.353</td><td>20.257</td><td>-0.113</td></tr><tr><td>2</td><td>12.06</td><td>1.184</td><td>31399</td><td>5.866</td><td>0.811</td><td>8.072</td><td>4.348</td><td>20.244</td><td>-0.140</td></tr><tr><td>3</td><td>18.98</td><td>1.200</td><td>31351</td><td>5.847</td><td>0.750</td><td>8.075</td><td>4.342</td><td>20.234</td><td>-0.158</td></tr><tr><td>4</td><td>21.73</td><td>1.206</td><td>31331</td><td>5.840</td><td>0.727</td><td>8.076</td><td>4.340</td><td>20.230</td><td>-0.165</td></tr><tr><td>5</td><td>28.83</td><td>1.221</td><td>31292</td><td>5.823</td><td>0.673</td><td>8.080</td><td>4.333</td><td>20.220</td><td>-0.184</td></tr><tr><td>6</td><td>46.87</td><td>1.259</td><td>31253</td><td>5.783</td><td>0.537</td><td>8.090</td><td>4.321</td><td>20.201</td><td>-0.215</td></tr><tr><td>7</td><td>61.90</td><td>1.294</td><td>31310</td><td>5.751</td><td>0.418</td><td>8.100</td><td>4.317</td><td>20.193</td><td>-0.239</td></tr><tr><td>8</td><td>73.01</td><td>1.324</td><td>31454</td><td>5.729</td><td>0.317</td><td>8.110</td><td>4.322</td><td>20.196</td><td>-0.252</td></tr><tr><td>9</td><td>81.14</td><td>1.350</td><td>31679</td><td>5.715</td><td>0.236</td><td>8.121</td><td>4.333</td><td>20.209</td><td>-0.196</td></tr><tr><td>10</td><td>87.19</td><td>1.371</td><td>31968</td><td>5.710</td><td>0.175</td><td>8.132</td><td>4.350</td><td>20.230</td><td>-0.269</td></tr><tr><td>11</td><td>91.79</td><td>1.387</td><td>32300</td><td>5.713</td><td>0.129</td><td>8.142</td><td>4.371</td><td>20.256</td><td>-0.248</td></tr><tr><td>12</td><td>95.14</td><td>1.398</td><td>32632</td><td>5.719</td><td>0.099</td><td>8.151</td><td>4.391</td><td>20.282</td><td>-0.275</td></tr><tr><td>13</td><td>97.94</td><td>1.407</td><td>33014</td><td>5.730</td><td>0.073</td><td>8.160</td><td>4.415</td><td>20.312</td><td>-0.163</td></tr><tr><td>14</td><td>100.12</td><td>1.415</td><td>33416</td><td>5.743</td><td>0.054</td><td>8.169</td><td>4.440</td><td>20.345</td><td>-0.278</td></tr><tr><td>15</td><td>101.71</td><td>1.419</td><td>33779</td><td>5.757</td><td>0.041</td><td>8.177</td><td>4.462</td><td>20.374</td><td>-0.160</td></tr><tr><td>16</td><td>103.17</td><td>1.424</td><td>34223</td><td>5.775</td><td>0.030</td><td>8.185</td><td>4.489</td><td>20.409</td><td>-0.190</td></tr><tr><td>17</td><td>104.28</td><td>1.427</td><td>34616</td><td>5.792</td><td>0.022</td><td>8.193</td><td>4.512</td><td>20.440</td><td>-0.200</td></tr><tr><td>18</td><td>106.49</td><td>1.439</td><td>36479</td><td>5.871</td><td>0.005</td><td>8.223</td><td>4.622</td><td>20.585</td><td>-0.132</td></tr><tr><td>19</td><td>107.23</td><td>1.495</td><td>39863</td><td>5.970</td><td>0.000</td><td>8.254</td><td>4.819</td><td>20.835</td><td>-0.011</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>20</td><td>107.37</td><td>1.524</td><td>41473</td><td>6.009</td><td>0.000</td><td>8.247</td><td>4.924</td><td>20.956</td><td>0.000</td></tr><tr><td>21</td><td>107.60</td><td>1.522</td><td>43301</td><td>6.086</td><td>0.000</td><td>8.245</td><td>5.045</td><td>21.103</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>22</td><td>108.59</td><td>1.606</td><td>43771</td><td>6.021</td><td>0.000</td><td>8.177</td><td>5.159</td><td>21.215</td><td>0.000</td></tr><tr><td>23</td><td>116.79</td><td>1.833</td><td>47107</td><td>5.921</td><td>0.000</td><td>8.106</td><td>5.336</td><td>21.436</td><td>0.000</td></tr><tr><td>24</td><td>124.78</td><td>2.036</td><td>53333</td><td>5.935</td><td>0.000</td><td>8.100</td><td>5.517</td><td>21.700</td><td>0.000</td></tr><tr><td>25</td><td>129.01</td><td>2.186</td><td>61358</td><td>6.028</td><td>0.000</td><td>8.080</td><td>5.682</td><td>21.946</td><td>0.000</td></tr><tr><td>26</td><td>131.66</td><td>2.202</td><td>72008</td><td>6.290</td><td>0.000</td><td>8.043</td><td>5.839</td><td>22.181</td><td>0.000</td></tr><tr><td>27</td><td>133.08</td><td>1.816</td><td>75458</td><td>6.757</td><td>0.000</td><td>8.015</td><td>5.954</td><td>22.356</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naine blanche</strong></td></tr><tr><td>28</td><td>133.59</td><td>1.160</td><td>63616</td><td>7.116</td><td>0.000</td><td>8.006</td><td>6.023</td><td>22.462</td><td>0.000</td></tr><tr><td>29</td><td>134.52</td><td>0.663</td><td>53340</td><td>7.307</td><td>0.000</td><td>7.956</td><td>6.089</td><td>22.561</td><td>0.000</td></tr><tr><td>30</td><td>136.77</td><td>0.103</td><td>42215</td><td>7.461</td><td>0.000</td><td>7.859</td><td>6.151</td><td>22.654</td><td>0.000</td></tr><tr><td>31</td><td>141.17</td><td>-0.412</td><td>33135</td><td>7.555</td><td>0.000</td><td>7.756</td><td>6.186</td><td>22.705</td><td>0.000</td></tr><tr><td>32</td><td>150.06</td><td>-0.902</td><td>25908</td><td>7.618</td><td>0.000</td><td>7.647</td><td>6.206</td><td>22.734</td><td>0.000</td></tr><tr><td>33</td><td>172.62</td><td>-1.377</td><td>20240</td><td>7.664</td><td>0.000</td><td>7.509</td><td>6.218</td><td>22.752</td><td>0.000</td></tr><tr><td>34</td><td>230.67</td><td>-1.845</td><td>15764</td><td>7.698</td><td>0.000</td><td>7.331</td><td>6.227</td><td>22.764</td><td>0.000</td></tr><tr><td>35</td><td>332.43</td><td>-2.308</td><td>12255</td><td>7.724</td><td>0.000</td><td>7.145</td><td>6.232</td><td>22.772</td><td>0.000</td></tr></tbody></table>
Séquence évolutif: $M = 0.4690 + 0.0007 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>1.01</td><td>1.118</td><td>29299</td><td>5.806</td><td>0.939</td><td>8.063</td><td>4.365</td><td>20.271</td><td>-0.109</td></tr><tr><td>2</td><td>1.11</td><td>1.120</td><td>29315</td><td>5.805</td><td>0.938</td><td>8.063</td><td>4.367</td><td>20.272</td><td>-0.109</td></tr><tr><td>3</td><td>2.22</td><td>1.122</td><td>29308</td><td>5.802</td><td>0.924</td><td>8.064</td><td>4.366</td><td>20.271</td><td>-0.111</td></tr><tr><td>4</td><td>14.18</td><td>1.154</td><td>29195</td><td>5.764</td><td>0.797</td><td>8.071</td><td>4.361</td><td>20.256</td><td>-0.141</td></tr><tr><td>5</td><td>33.89</td><td>1.198</td><td>29063</td><td>5.712</td><td>0.647</td><td>8.080</td><td>4.343</td><td>20.228</td><td>-0.189</td></tr><tr><td>6</td><td>53.93</td><td>1.240</td><td>28985</td><td>5.665</td><td>0.501</td><td>8.091</td><td>4.331</td><td>20.209</td><td>-0.221</td></tr><tr><td>7</td><td>68.48</td><td>1.274</td><td>29015</td><td>5.633</td><td>0.386</td><td>8.101</td><td>4.329</td><td>20.204</td><td>-0.240</td></tr><tr><td>8</td><td>79.11</td><td>1.304</td><td>29137</td><td>5.610</td><td>0.290</td><td>8.112</td><td>4.336</td><td>20.210</td><td>-0.255</td></tr><tr><td>9</td><td>86.89</td><td>1.329</td><td>29345</td><td>5.597</td><td>0.212</td><td>8.123</td><td>4.350</td><td>20.226</td><td>-0.217</td></tr><tr><td>10</td><td>92.67</td><td>1.349</td><td>29620</td><td>5.594</td><td>0.155</td><td>8.134</td><td>4.369</td><td>20.250</td><td>-0.155</td></tr><tr><td>11</td><td>97.02</td><td>1.364</td><td>29953</td><td>5.598</td><td>0.113</td><td>8.145</td><td>4.392</td><td>20.279</td><td>-0.271</td></tr><tr><td>12</td><td>100.26</td><td>1.375</td><td>30373</td><td>5.612</td><td>0.082</td><td>8.155</td><td>4.416</td><td>20.309</td><td>-0.155</td></tr><tr><td>13</td><td>102.86</td><td>1.384</td><td>30780</td><td>5.626</td><td>0.059</td><td>8.164</td><td>4.443</td><td>20.344</td><td>-0.155</td></tr><tr><td>14</td><td>104.83</td><td>1.391</td><td>31070</td><td>5.635</td><td>0.043</td><td>8.174</td><td>4.469</td><td>20.380</td><td>-0.158</td></tr><tr><td>15</td><td>106.42</td><td>1.395</td><td>31471</td><td>5.654</td><td>0.031</td><td>8.182</td><td>4.495</td><td>20.414</td><td>-0.167</td></tr><tr><td>16</td><td>107.67</td><td>1.398</td><td>31874</td><td>5.672</td><td>0.023</td><td>8.190</td><td>4.520</td><td>20.447</td><td>-0.152</td></tr><tr><td>17</td><td>108.71</td><td>1.401</td><td>32306</td><td>5.692</td><td>0.016</td><td>8.198</td><td>4.548</td><td>20.484</td><td>-0.137</td></tr><tr><td>18</td><td>110.80</td><td>1.443</td><td>35829</td><td>5.831</td><td>0.001</td><td>8.247</td><td>4.763</td><td>20.764</td><td>-0.065</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>19</td><td>110.95</td><td>1.474</td><td>37215</td><td>5.865</td><td>0.000</td><td>8.248</td><td>4.860</td><td>20.879</td><td>0.000</td></tr><tr><td>20</td><td>111.16</td><td>1.503</td><td>39313</td><td>5.931</td><td>0.000</td><td>8.245</td><td>4.998</td><td>21.044</td><td>0.000</td></tr><tr><td>21</td><td>111.54</td><td>1.454</td><td>39690</td><td>5.997</td><td>0.000</td><td>8.220</td><td>5.097</td><td>21.155</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>22</td><td>114.88</td><td>1.694</td><td>41010</td><td>5.814</td><td>0.000</td><td>8.121</td><td>5.262</td><td>21.336</td><td>0.000</td></tr><tr><td>23</td><td>125.90</td><td>1.895</td><td>45477</td><td>5.793</td><td>0.000</td><td>8.093</td><td>5.440</td><td>21.585</td><td>0.000</td></tr><tr><td>24</td><td>132.27</td><td>2.074</td><td>51481</td><td>5.829</td><td>0.000</td><td>8.076</td><td>5.609</td><td>21.835</td><td>0.000</td></tr><tr><td>25</td><td>135.89</td><td>2.164</td><td>59779</td><td>5.999</td><td>0.000</td><td>8.044</td><td>5.770</td><td>22.075</td><td>0.000</td></tr><tr><td>26</td><td>138.35</td><td>1.992</td><td>69033</td><td>6.421</td><td>0.000</td><td>8.002</td><td>5.913</td><td>22.292</td><td>0.000</td></tr><tr><td>27</td><td>138.40</td><td>1.828</td><td>56457</td><td>6.235</td><td>0.000</td><td>7.981</td><td>5.884</td><td>22.245</td><td>0.000</td></tr><tr><td>28</td><td>138.40</td><td>1.501</td><td>44146</td><td>6.135</td><td>0.000</td><td>7.972</td><td>5.868</td><td>22.221</td><td>0.000</td></tr><tr><td>29</td><td>138.40</td><td>1.564</td><td>40308</td><td>5.914</td><td>0.000</td><td>7.966</td><td>5.858</td><td>22.205</td><td>0.000</td></tr><tr><td>30</td><td>138.40</td><td>2.269</td><td>49217</td><td>5.555</td><td>0.000</td><td>7.966</td><td>5.858</td><td>22.204</td><td>0.000</td></tr><tr><td>31</td><td>138.40</td><td>3.015</td><td>44599</td><td>4.639</td><td>0.000</td><td>7.967</td><td>5.859</td><td>22.207</td><td>0.000</td></tr><tr><td>32</td><td>138.40</td><td>3.181</td><td>41457</td><td>4.346</td><td>0.000</td><td>7.972</td><td>5.866</td><td>22.217</td><td>0.000</td></tr><tr><td>33</td><td>138.41</td><td>3.033</td><td>54928</td><td>4.982</td><td>0.000</td><td>7.977</td><td>5.873</td><td>22.229</td><td>0.000</td></tr><tr><td>34</td><td>138.42</td><td>2.707</td><td>65074</td><td>5.603</td><td>0.000</td><td>7.980</td><td>5.873</td><td>22.229</td><td>0.000</td></tr><tr><td>35</td><td>138.52</td><td>2.248</td><td>72623</td><td>6.253</td><td>0.000</td><td>7.992</td><td>5.894</td><td>22.262</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naine blanche</strong></td></tr><tr><td>36</td><td>139.02</td><td>1.437</td><td>66280</td><td>6.905</td><td>0.000</td><td>8.003</td><td>5.979</td><td>22.394</td><td>0.000</td></tr><tr><td>37</td><td>139.50</td><td>1.022</td><td>58733</td><td>7.110</td><td>0.000</td><td>7.985</td><td>6.037</td><td>22.482</td><td>0.000</td></tr><tr><td>38</td><td>140.89</td><td>0.469</td><td>48143</td><td>7.318</td><td>0.000</td><td>7.910</td><td>6.114</td><td>22.597</td><td>0.000</td></tr><tr><td>39</td><td>143.63</td><td>-0.077</td><td>38078</td><td>7.456</td><td>0.000</td><td>7.821</td><td>6.166</td><td>22.675</td><td>0.000</td></tr><tr><td>40</td><td>148.82</td><td>-0.575</td><td>30041</td><td>7.543</td><td>0.000</td><td>7.730</td><td>6.187</td><td>22.705</td><td>0.000</td></tr><tr><td>41</td><td>160.53</td><td>-1.057</td><td>23603</td><td>7.605</td><td>0.000</td><td>7.628</td><td>6.198</td><td>22.722</td><td>0.000</td></tr><tr><td>42</td><td>202.53</td><td>-1.530</td><td>18473</td><td>7.653</td><td>0.000</td><td>7.464</td><td>6.211</td><td>22.739</td><td>0.000</td></tr><tr><td>43</td><td>310.93</td><td>-1.999</td><td>14385</td><td>7.687</td><td>0.000</td><td>7.243</td><td>6.220</td><td>22.752</td><td>0.000</td></tr><tr><td>44</td><td>485.62</td><td>-2.452</td><td>11237</td><td>7.711</td><td>0.000</td><td>7.057</td><td>6.223</td><td>22.757</td><td>0.000</td></tr></tbody></table>
Séquence évolutives: $M = 0.4758 + 0.0012 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>1.79</td><td>1.159</td><td>27818</td><td>5.682</td><td>0.928</td><td>8.066</td><td>4.351</td><td>20.255</td><td>-0.113</td></tr><tr><td>2</td><td>12.06</td><td>1.187</td><td>27678</td><td>5.645</td><td>0.810</td><td>8.072</td><td>4.347</td><td>20.243</td><td>-0.139</td></tr><tr><td>3</td><td>18.02</td><td>1.201</td><td>27598</td><td>5.626</td><td>0.758</td><td>8.075</td><td>4.342</td><td>20.234</td><td>-0.154</td></tr><tr><td>4</td><td>20.52</td><td>1.207</td><td>27564</td><td>5.618</td><td>0.737</td><td>8.076</td><td>4.340</td><td>20.231</td><td>-0.157</td></tr><tr><td>5</td><td>25.27</td><td>1.217</td><td>27504</td><td>5.604</td><td>0.699</td><td>8.078</td><td>4.335</td><td>20.223</td><td>-0.170</td></tr><tr><td>6</td><td>37.76</td><td>1.243</td><td>27380</td><td>5.570</td><td>0.605</td><td>8.085</td><td>4.325</td><td>20.208</td><td>-0.200</td></tr><tr><td>7</td><td>55.13</td><td>1.281</td><td>27275</td><td>5.525</td><td>0.470</td><td>8.095</td><td>4.317</td><td>20.194</td><td>-0.229</td></tr><tr><td>8</td><td>67.83</td><td>1.314</td><td>27272</td><td>5.492</td><td>0.361</td><td>8.106</td><td>4.317</td><td>20.192</td><td>-0.248</td></tr><tr><td>9</td><td>77.34</td><td>1.340</td><td>27346</td><td>5.471</td><td>0.277</td><td>8.116</td><td>4.323</td><td>20.198</td><td>-0.261</td></tr><tr><td>10</td><td>84.38</td><td>1.362</td><td>27498</td><td>5.459</td><td>0.209</td><td>8.126</td><td>4.336</td><td>20.213</td><td>-0.247</td></tr><tr><td>11</td><td>88.05</td><td>1.374</td><td>27639</td><td>5.455</td><td>0.172</td><td>8.133</td><td>4.347</td><td>20.227</td><td>-0.217</td></tr><tr><td>12</td><td>92.52</td><td>1.389</td><td>27890</td><td>5.456</td><td>0.128</td><td>8.143</td><td>4.366</td><td>20.251</td><td>-0.155</td></tr><tr><td>13</td><td>94.63</td><td>1.395</td><td>28034</td><td>5.459</td><td>0.112</td><td>8.147</td><td>4.376</td><td>20.264</td><td>-0.162</td></tr><tr><td>14</td><td>95.42</td><td>1.398</td><td>28096</td><td>5.460</td><td>0.104</td><td>8.149</td><td>4.381</td><td>20.270</td><td>-0.152</td></tr><tr><td>15</td><td>97.80</td><td>1.374</td><td>27753</td><td>5.463</td><td>0.154</td><td>8.140</td><td>4.336</td><td>20.218</td><td>-0.152</td></tr><tr><td>16</td><td>100.24</td><td>1.405</td><td>28033</td><td>5.448</td><td>0.116</td><td>8.147</td><td>4.364</td><td>20.251</td><td>-0.128</td></tr><tr><td>17</td><td>102.90</td><td>1.414</td><td>28398</td><td>5.462</td><td>0.083</td><td>8.158</td><td>4.394</td><td>20.288</td><td>-0.136</td></tr><tr><td>18</td><td>105.04</td><td>1.420</td><td>28724</td><td>5.476</td><td>0.063</td><td>8.166</td><td>4.418</td><td>20.319</td><td>-0.148</td></tr><tr><td>19</td><td>105.78</td><td>1.424</td><td>28857</td><td>5.480</td><td>0.056</td><td>8.170</td><td>4.428</td><td>20.332</td><td>-0.140</td></tr><tr><td>20</td><td>110.20</td><td>1.436</td><td>30545</td><td>5.567</td><td>0.014</td><td>8.204</td><td>4.544</td><td>20.484</td><td>-0.140</td></tr><tr><td>21</td><td>112.16</td><td>1.487</td><td>34349</td><td>5.720</td><td>0.000</td><td>8.256</td><td>4.791</td><td>20.804</td><td>-0.037</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>22</td><td>112.26</td><td>1.510</td><td>35292</td><td>5.744</td><td>0.000</td><td>8.249</td><td>4.871</td><td>20.893</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>23</td><td>112.74</td><td>1.537</td><td>35668</td><td>5.735</td><td>0.000</td><td>8.193</td><td>4.999</td><td>21.015</td><td>0.000</td></tr><tr><td>24</td><td>116.87</td><td>1.681</td><td>38587</td><td>5.728</td><td>0.000</td><td>8.147</td><td>5.229</td><td>21.298</td><td>0.000</td></tr><tr><td>25</td><td>126.46</td><td>1.963</td><td>41839</td><td>5.587</td><td>0.000</td><td>8.105</td><td>5.446</td><td>21.597</td><td>0.000</td></tr><tr><td>26</td><td>131.82</td><td>2.141</td><td>46653</td><td>5.598</td><td>0.000</td><td>8.090</td><td>5.618</td><td>21.850</td><td>0.000</td></tr><tr><td>27</td><td>134.87</td><td>2.229</td><td>53968</td><td>5.763</td><td>0.000</td><td>8.061</td><td>5.776</td><td>22.086</td><td>0.000</td></tr><tr><td>28</td><td>136.95</td><td>2.085</td><td>64237</td><td>6.209</td><td>0.000</td><td>8.017</td><td>5.921</td><td>22.305</td><td>0.000</td></tr><tr><td>29</td><td>137.34</td><td>2.295</td><td>77075</td><td>6.316</td><td>0.000</td><td>8.013</td><td>5.966</td><td>22.374</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naturelle blanche</strong></td></tr><tr><td>30</td><td>137.49</td><td>1.909</td><td>75807</td><td>6.673</td><td>0.000</td><td>8.014</td><td>5.990</td><td>22.411</td><td>0.000</td></tr><tr><td>31</td><td>137.84</td><td>1.438</td><td>68481</td><td>6.968</td><td>0.000</td><td>8.002</td><td>6.031</td><td>22.474</td><td>0.000</td></tr><tr><td>32</td><td>138.92</td><td>0.801</td><td>55562</td><td>7.241</td><td>0.000</td><td>7.943</td><td>6.102</td><td>22.580</td><td>0.000</td></tr><tr><td>33</td><td>140.97</td><td>0.234</td><td>44019</td><td>7.404</td><td>0.000</td><td>7.857</td><td>6.155</td><td>22.659</td><td>0.000</td></tr><tr><td>34</td><td>144.95</td><td>-0.289</td><td>34608</td><td>7.509</td><td>0.000</td><td>7.762</td><td>6.187</td><td>22.707</td><td>0.000</td></tr><tr><td>35</td><td>153.71</td><td>-0.787</td><td>27112</td><td>7.583</td><td>0.000</td><td>7.651</td><td>6.208</td><td>22.738</td><td>0.000</td></tr><tr><td>36</td><td>180.61</td><td>-1.266</td><td>21238</td><td>7.638</td><td>0.000</td><td>7.496</td><td>6.222</td><td>22.758</td><td>0.000</td></tr><tr><td>37</td><td>253.88</td><td>-1.704</td><td>16879</td><td>7.677</td><td>0.000</td><td>7.290</td><td>6.231</td><td>22.770</td><td>0.000</td></tr><tr><td>38</td><td>329.71</td><td>-1.979</td><td>14557</td><td>7.695</td><td>0.000</td><td>7.168</td><td>6.234</td><td>22.775</td><td>0.000</td></tr></tbody></table>
Séquence évolutive: $M = 0.4758 + 0.0022 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>4.49</td><td>1.170</td><td>26310</td><td>5.575</td><td>0.893</td><td>8.068</td><td>4.350</td><td>20.251</td><td>-0.117</td></tr><tr><td>2</td><td>19.95</td><td>1.208</td><td>26052</td><td>5.519</td><td>0.741</td><td>8.076</td><td>4.339</td><td>20.230</td><td>-0.160</td></tr><tr><td>3</td><td>24.07</td><td>1.217</td><td>25989</td><td>5.506</td><td>0.709</td><td>8.078</td><td>4.335</td><td>20.224</td><td>-0.162</td></tr><tr><td>4</td><td>37.88</td><td>1.246</td><td>25810</td><td>5.465</td><td>0.603</td><td>8.085</td><td>4.323</td><td>20.206</td><td>-0.201</td></tr><tr><td>5</td><td>55.12</td><td>1.284</td><td>25654</td><td>5.417</td><td>0.469</td><td>8.095</td><td>4.316</td><td>20.193</td><td>-0.230</td></tr><tr><td>6</td><td>67.76</td><td>1.317</td><td>25603</td><td>5.381</td><td>0.360</td><td>8.106</td><td>4.317</td><td>20.191</td><td>-0.245</td></tr><tr><td>7</td><td>77.17</td><td>1.343</td><td>25637</td><td>5.356</td><td>0.274</td><td>8.116</td><td>4.323</td><td>20.197</td><td>-0.222</td></tr><tr><td>8</td><td>84.13</td><td>1.365</td><td>25754</td><td>5.342</td><td>0.206</td><td>8.126</td><td>4.336</td><td>20.213</td><td>-0.269</td></tr><tr><td>9</td><td>89.27</td><td>1.383</td><td>25940</td><td>5.337</td><td>0.154</td><td>8.136</td><td>4.353</td><td>20.234</td><td>-0.204</td></tr><tr><td>10</td><td>93.17</td><td>1.395</td><td>26159</td><td>5.339</td><td>0.117</td><td>8.146</td><td>4.372</td><td>20.258</td><td>-0.168</td></tr><tr><td>11</td><td>94.45</td><td>1.400</td><td>26240</td><td>5.340</td><td>0.107</td><td>8.149</td><td>4.378</td><td>20.266</td><td>-0.147</td></tr><tr><td>12</td><td>96.22</td><td>1.388</td><td>26122</td><td>5.344</td><td>0.130</td><td>8.145</td><td>4.355</td><td>20.241</td><td>-0.162</td></tr><tr><td>13</td><td>97.60</td><td>1.406</td><td>26230</td><td>5.334</td><td>0.109</td><td>8.149</td><td>4.371</td><td>20.259</td><td>-0.128</td></tr><tr><td>14</td><td>99.44</td><td>1.412</td><td>26472</td><td>5.343</td><td>0.086</td><td>8.156</td><td>4.392</td><td>20.285</td><td>-0.137</td></tr><tr><td>15</td><td>101.10</td><td>1.417</td><td>26702</td><td>5.353</td><td>0.070</td><td>8.163</td><td>4.410</td><td>20.309</td><td>-0.150</td></tr><tr><td>16</td><td>102.92</td><td>1.422</td><td>26971</td><td>5.366</td><td>0.054</td><td>8.170</td><td>4.430</td><td>20.335</td><td>-0.159</td></tr><tr><td>17</td><td>104.62</td><td>1.426</td><td>27274</td><td>5.381</td><td>0.041</td><td>8.178</td><td>4.452</td><td>20.364</td><td>-0.169</td></tr><tr><td>18</td><td>106.06</td><td>1.430</td><td>27596</td><td>5.397</td><td>0.031</td><td>8.186</td><td>4.474</td><td>20.394</td><td>-0.160</td></tr><tr><td>19</td><td>107.23</td><td>1.433</td><td>27936</td><td>5.415</td><td>0.023</td><td>8.193</td><td>4.497</td><td>20.424</td><td>-0.156</td></tr><tr><td>20</td><td>108.16</td><td>1.436</td><td>28273</td><td>5.434</td><td>0.017</td><td>8.200</td><td>4.520</td><td>20.454</td><td>-0.156</td></tr><tr><td>21</td><td>110.22</td><td>1.461</td><td>30695</td><td>5.551</td><td>0.002</td><td>8.241</td><td>4.682</td><td>20.667</td><td>-0.107</td></tr><tr><td>22</td><td>110.52</td><td>1.508</td><td>32550</td><td>5.606</td><td>0.000</td><td>8.257</td><td>4.822</td><td>20.841</td><td>-0.001</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>23</td><td>110.66</td><td>1.538</td><td>33896</td><td>5.646</td><td>0.000</td><td>8.252</td><td>4.931</td><td>20.966</td><td>0.000</td></tr><tr><td>24</td><td>110.76</td><td>1.546</td><td>34837</td><td>5.686</td><td>0.000</td><td>8.253</td><td>4.995</td><td>21.046</td><td>0.000</td></tr><tr><td>25</td><td>110.87</td><td>1.537</td><td>35506</td><td>5.729</td><td>0.000</td><td>8.251</td><td>5.045</td><td>21.106</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>26</td><td>111.47</td><td>1.581</td><td>35389</td><td>5.678</td><td>0.000</td><td>8.201</td><td>5.136</td><td>21.196</td><td>0.000</td></tr><tr><td>27</td><td>117.46</td><td>1.829</td><td>36014</td><td>5.461</td><td>0.000</td><td>8.110</td><td>5.324</td><td>21.420</td><td>0.000</td></tr><tr><td>28</td><td>125.59</td><td>2.032</td><td>39069</td><td>5.399</td><td>0.000</td><td>8.102</td><td>5.507</td><td>21.686</td><td>0.000</td></tr><tr><td>29</td><td>129.90</td><td>2.189</td><td>43327</td><td>5.422</td><td>0.000</td><td>8.083</td><td>5.673</td><td>21.932</td><td>0.000</td></tr><tr><td>30</td><td>132.53</td><td>2.225</td><td>51249</td><td>5.678</td><td>0.000</td><td>8.048</td><td>5.829</td><td>22.167</td><td>0.000</td></tr><tr><td>31</td><td>133.88</td><td>2.259</td><td>63259</td><td>6.009</td><td>0.000</td><td>8.015</td><td>5.927</td><td>22.314</td><td>0.000</td></tr><tr><td>32</td><td>134.16</td><td>2.322</td><td>77730</td><td>6.305</td><td>0.000</td><td>8.016</td><td>5.965</td><td>22.374</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naine blanche</strong></td></tr><tr><td>33</td><td>134.45</td><td>1.723</td><td>73670</td><td>6.811</td><td>0.000</td><td>8.013</td><td>6.008</td><td>22.439</td><td>0.000</td></tr><tr><td>34</td><td>135.25</td><td>1.037</td><td>60565</td><td>7.156</td><td>0.000</td><td>7.971</td><td>6.078</td><td>22.545</td><td>0.000</td></tr><tr><td>35</td><td>136.88</td><td>0.444</td><td>48260</td><td>7.354</td><td>0.000</td><td>7.890</td><td>6.140</td><td>22.638</td><td>0.000</td></tr><tr><td>36</td><td>138.37</td><td>0.130</td><td>42093</td><td>7.431</td><td>0.000</td><td>7.840</td><td>6.165</td><td>22.675</td><td>0.000</td></tr><tr><td>37</td><td>142.96</td><td>-0.387</td><td>33064</td><td>7.529</td><td>0.000</td><td>7.741</td><td>6.195</td><td>22.719</td><td>0.000</td></tr><tr><td>38</td><td>153.44</td><td>-0.881</td><td>25894</td><td>7.598</td><td>0.000</td><td>7.626</td><td>6.214</td><td>22.746</td><td>0.000</td></tr><tr><td>39</td><td>187.58</td><td>-1.352</td><td>20329</td><td>7.649</td><td>0.000</td><td>7.460</td><td>6.227</td><td>22.765</td><td>0.000</td></tr><tr><td>40</td><td>270.84</td><td>-1.796</td><td>16084</td><td>7.685</td><td>0.000</td><td>7.250</td><td>6.235</td><td>22.776</td><td>0.000</td></tr><tr><td>41</td><td>348.09</td><td>-2.044</td><td>14063</td><td>7.701</td><td>0.000</td><td>7.141</td><td>6.237</td><td>22.780</td><td>0.000</td></tr></tbody></table>
Séquence évolutives: $M = 0.4758 + 0.0032 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>1.79</td><td>1.164</td><td>25349</td><td>5.516</td><td>0.927</td><td>8.066</td><td>4.349</td><td>20.253</td><td>-0.113</td></tr><tr><td>2</td><td>12.06</td><td>1.193</td><td>25146</td><td>5.474</td><td>0.809</td><td>8.072</td><td>4.345</td><td>20.241</td><td>-0.139</td></tr><tr><td>3</td><td>19.53</td><td>1.210</td><td>25007</td><td>5.447</td><td>0.742</td><td>8.076</td><td>4.338</td><td>20.229</td><td>-0.160</td></tr><tr><td>4</td><td>23.43</td><td>1.219</td><td>24936</td><td>5.433</td><td>0.709</td><td>8.078</td><td>4.334</td><td>20.223</td><td>-0.170</td></tr><tr><td>5</td><td>39.83</td><td>1.254</td><td>24696</td><td>5.382</td><td>0.585</td><td>8.086</td><td>4.321</td><td>20.203</td><td>-0.203</td></tr><tr><td>6</td><td>56.38</td><td>1.291</td><td>24519</td><td>5.332</td><td>0.456</td><td>8.097</td><td>4.314</td><td>20.191</td><td>-0.232</td></tr><tr><td>7</td><td>68.54</td><td>1.323</td><td>24443</td><td>5.295</td><td>0.348</td><td>8.107</td><td>4.316</td><td>20.191</td><td>-0.248</td></tr><tr><td>8</td><td>77.44</td><td>1.351</td><td>24468</td><td>5.269</td><td>0.258</td><td>8.118</td><td>4.326</td><td>20.202</td><td>-0.260</td></tr><tr><td>9</td><td>83.92</td><td>1.374</td><td>24587</td><td>5.254</td><td>0.189</td><td>8.130</td><td>4.343</td><td>20.221</td><td>-0.266</td></tr><tr><td>10</td><td>88.76</td><td>1.391</td><td>24784</td><td>5.250</td><td>0.138</td><td>8.140</td><td>4.364</td><td>20.247</td><td>-0.271</td></tr><tr><td>11</td><td>92.27</td><td>1.404</td><td>25022</td><td>5.254</td><td>0.102</td><td>8.150</td><td>4.386</td><td>20.275</td><td>-0.195</td></tr><tr><td>12</td><td>95.10</td><td>1.414</td><td>25309</td><td>5.264</td><td>0.076</td><td>8.159</td><td>4.409</td><td>20.306</td><td>-0.276</td></tr><tr><td>13</td><td>97.37</td><td>1.422</td><td>25632</td><td>5.279</td><td>0.056</td><td>8.169</td><td>4.435</td><td>20.340</td><td>-0.277</td></tr><tr><td>14</td><td>99.17</td><td>1.428</td><td>25971</td><td>5.295</td><td>0.041</td><td>8.177</td><td>4.461</td><td>20.373</td><td>-0.158</td></tr><tr><td>15</td><td>100.58</td><td>1.432</td><td>26337</td><td>5.315</td><td>0.029</td><td>8.186</td><td>4.487</td><td>20.408</td><td>-0.209</td></tr><tr><td>16</td><td>101.68</td><td>1.436</td><td>26697</td><td>5.335</td><td>0.021</td><td>8.194</td><td>4.512</td><td>20.442</td><td>-0.152</td></tr><tr><td>17</td><td>103.04</td><td>1.443</td><td>27410</td><td>5.374</td><td>0.011</td><td>8.208</td><td>4.563</td><td>20.509</td><td>-0.136</td></tr><tr><td>18</td><td>104.51</td><td>1.497</td><td>30593</td><td>5.510</td><td>0.000</td><td>8.254</td><td>4.795</td><td>20.808</td><td>-0.031</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>19</td><td>104.62</td><td>1.523</td><td>31509</td><td>5.535</td><td>0.000</td><td>8.248</td><td>4.880</td><td>20.904</td><td>0.000</td></tr><tr><td>20</td><td>104.82</td><td>1.543</td><td>33266</td><td>5.610</td><td>0.000</td><td>8.249</td><td>5.011</td><td>21.063</td><td>0.000</td></tr><tr><td>21</td><td>105.30</td><td>1.544</td><td>33416</td><td>5.616</td><td>0.000</td><td>8.208</td><td>5.107</td><td>21.162</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>22</td><td>110.10</td><td>1.778</td><td>33100</td><td>5.366</td><td>0.000</td><td>8.110</td><td>5.273</td><td>21.348</td><td>0.000</td></tr><tr><td>23</td><td>119.68</td><td>1.984</td><td>35363</td><td>5.275</td><td>0.000</td><td>8.105</td><td>5.459</td><td>21.616</td><td>0.000</td></tr><tr><td>24</td><td>124.71</td><td>2.159</td><td>38299</td><td>5.239</td><td>0.000</td><td>8.090</td><td>5.630</td><td>21.869</td><td>0.000</td></tr><tr><td>25</td><td>127.61</td><td>2.242</td><td>44220</td><td>5.405</td><td>0.000</td><td>8.060</td><td>5.787</td><td>22.104</td><td>0.000</td></tr><tr><td>26</td><td>129.19</td><td>2.351</td><td>56443</td><td>5.721</td><td>0.000</td><td>8.026</td><td>5.897</td><td>22.269</td><td>0.000</td></tr><tr><td>27</td><td>129.70</td><td>2.315</td><td>65312</td><td>6.010</td><td>0.000</td><td>8.013</td><td>5.937</td><td>22.329</td><td>0.000</td></tr><tr><td>28</td><td>129.94</td><td>2.225</td><td>78384</td><td>6.417</td><td>0.000</td><td>8.016</td><td>5.975</td><td>22.388</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naine blanche</strong></td></tr><tr><td>29</td><td>130.29</td><td>1.598</td><td>71773</td><td>6.891</td><td>0.000</td><td>8.009</td><td>6.022</td><td>22.461</td><td>0.000</td></tr></tbody></table>
Séquence évolutif: $M = 0.4758 + 0.0042 M_{\odot}$

<table><thead><tr><th rowspan="2">#</th><th rowspan="2">Age</th><th colspan="3">surface</th><th colspan="5">centre</th></tr><tr><th>log L/L<sub>☉</sub></th><th>T<sub>eff</sub></th><th>log g</th><th>Y<sub>c</sub></th><th>log T<sub>c</sub></th><th>log ρ<sub>c</sub></th><th>log P<sub>c</sub></th><th>log q<sub>cc</sub></th></tr></thead><tbody><tr><td colspan="10"><strong>ZAEHB</strong></td></tr><tr><td>1</td><td>1.79</td><td>1.167</td><td>24552</td><td>5.459</td><td>0.927</td><td>8.066</td><td>4.348</td><td>20.252</td><td>-0.113</td></tr><tr><td>2</td><td>12.06</td><td>1.195</td><td>24328</td><td>5.415</td><td>0.809</td><td>8.072</td><td>4.343</td><td>20.239</td><td>-0.139</td></tr><tr><td>3</td><td>19.66</td><td>1.213</td><td>24173</td><td>5.386</td><td>0.741</td><td>8.076</td><td>4.337</td><td>20.228</td><td>-0.160</td></tr><tr><td>4</td><td>23.84</td><td>1.222</td><td>24093</td><td>5.371</td><td>0.707</td><td>8.078</td><td>4.333</td><td>20.222</td><td>-0.162</td></tr><tr><td>5</td><td>39.40</td><td>1.256</td><td>23839</td><td>5.320</td><td>0.588</td><td>8.086</td><td>4.320</td><td>20.202</td><td>-0.203</td></tr><tr><td>6</td><td>55.93</td><td>1.293</td><td>23627</td><td>5.267</td><td>0.456</td><td>8.097</td><td>4.313</td><td>20.190</td><td>-0.229</td></tr><tr><td>7</td><td>68.06</td><td>1.325</td><td>23522</td><td>5.227</td><td>0.348</td><td>8.107</td><td>4.315</td><td>20.190</td><td>-0.247</td></tr><tr><td>8</td><td>77.10</td><td>1.351</td><td>23510</td><td>5.200</td><td>0.266</td><td>8.118</td><td>4.322</td><td>20.197</td><td>-0.224</td></tr><tr><td>9</td><td>83.80</td><td>1.373</td><td>23591</td><td>5.184</td><td>0.197</td><td>8.128</td><td>4.337</td><td>20.214</td><td>-0.251</td></tr><tr><td>10</td><td>88.45</td><td>1.388</td><td>23727</td><td>5.179</td><td>0.151</td><td>8.137</td><td>4.353</td><td>20.235</td><td>-0.204</td></tr><tr><td>11</td><td>91.08</td><td>1.397</td><td>23854</td><td>5.179</td><td>0.124</td><td>8.144</td><td>4.366</td><td>20.251</td><td>-0.202</td></tr><tr><td>12</td><td>93.82</td><td>1.407</td><td>24032</td><td>5.182</td><td>0.099</td><td>8.151</td><td>4.383</td><td>20.273</td><td>-0.153</td></tr><tr><td>13</td><td>96.05</td><td>1.414</td><td>24223</td><td>5.189</td><td>0.080</td><td>8.158</td><td>4.399</td><td>20.294</td><td>-0.185</td></tr><tr><td>14</td><td>98.37</td><td>1.422</td><td>24485</td><td>5.200</td><td>0.061</td><td>8.167</td><td>4.420</td><td>20.322</td><td>-0.153</td></tr><tr><td>15</td><td>100.23</td><td>1.428</td><td>24772</td><td>5.214</td><td>0.046</td><td>8.175</td><td>4.442</td><td>20.351</td><td>-0.160</td></tr><tr><td>16</td><td>101.76</td><td>1.433</td><td>25103</td><td>5.232</td><td>0.034</td><td>8.183</td><td>4.466</td><td>20.383</td><td>-0.232</td></tr><tr><td>17</td><td>102.99</td><td>1.437</td><td>25432</td><td>5.251</td><td>0.025</td><td>8.191</td><td>4.490</td><td>20.415</td><td>-0.252</td></tr><tr><td>18</td><td>103.97</td><td>1.440</td><td>25771</td><td>5.270</td><td>0.018</td><td>8.199</td><td>4.514</td><td>20.446</td><td>-0.156</td></tr><tr><td>19</td><td>105.76</td><td>1.452</td><td>27134</td><td>5.347</td><td>0.005</td><td>8.225</td><td>4.611</td><td>20.575</td><td>-0.133</td></tr><tr><td>20</td><td>106.48</td><td>1.509</td><td>29587</td><td>5.441</td><td>0.000</td><td>8.257</td><td>4.806</td><td>20.822</td><td>-0.013</td></tr><tr><td colspan="10"><strong>Disparition du noyau convectif</strong></td></tr><tr><td>21</td><td>106.58</td><td>1.536</td><td>30526</td><td>5.469</td><td>0.000</td><td>8.251</td><td>4.895</td><td>20.923</td><td>0.000</td></tr><tr><td>22</td><td>106.77</td><td>1.552</td><td>32059</td><td>5.538</td><td>0.000</td><td>8.253</td><td>5.010</td><td>21.064</td><td>0.000</td></tr><tr><td>23</td><td>107.04</td><td>1.504</td><td>32607</td><td>5.615</td><td>0.000</td><td>8.232</td><td>5.087</td><td>21.149</td><td>0.000</td></tr><tr><td colspan="10"><strong>Brûlage en couche de l'hélium – Evolution post-EHB</strong></td></tr><tr><td>24</td><td>109.31</td><td>1.729</td><td>31818</td><td>5.348</td><td>0.000</td><td>8.146</td><td>5.240</td><td>21.313</td><td>0.000</td></tr><tr><td>25</td><td>118.57</td><td>1.952</td><td>32807</td><td>5.177</td><td>0.000</td><td>8.107</td><td>5.429</td><td>21.572</td><td>0.000</td></tr><tr><td>26</td><td>124.15</td><td>2.136</td><td>34868</td><td>5.099</td><td>0.000</td><td>8.094</td><td>5.603</td><td>21.828</td><td>0.000</td></tr><tr><td>27</td><td>127.26</td><td>2.249</td><td>39401</td><td>5.199</td><td>0.000</td><td>8.067</td><td>5.761</td><td>22.065</td><td>0.000</td></tr><tr><td>28</td><td>128.86</td><td>2.407</td><td>49329</td><td>5.432</td><td>0.000</td><td>8.037</td><td>5.869</td><td>22.227</td><td>0.000</td></tr><tr><td>29</td><td>129.38</td><td>2.381</td><td>57341</td><td>5.719</td><td>0.000</td><td>8.023</td><td>5.907</td><td>22.284</td><td>0.000</td></tr><tr><td>30</td><td>129.84</td><td>2.356</td><td>66917</td><td>6.012</td><td>0.000</td><td>8.012</td><td>5.944</td><td>22.341</td><td>0.000</td></tr><tr><td>31</td><td>130.04</td><td>2.204</td><td>78867</td><td>6.449</td><td>0.000</td><td>8.015</td><td>5.980</td><td>22.396</td><td>0.000</td></tr><tr><td colspan="10"><strong>Séquence de refroidissement – Evolution naine blanche</strong></td></tr><tr><td>32</td><td>130.38</td><td>1.581</td><td>71669</td><td>6.906</td><td>0.000</td><td>8.008</td><td>6.027</td><td>22.468</td><td>0.000</td></tr><tr><td>33</td><td>131.30</td><td>0.920</td><td>58375</td><td>7.210</td><td>0.000</td><td>7.957</td><td>6.098</td><td>22.574</td><td>0.000</td></tr><tr><td>34</td><td>133.10</td><td>0.341</td><td>46338</td><td>7.389</td><td>0.000</td><td>7.873</td><td>6.155</td><td>22.661</td><td>0.000</td></tr><tr><td>35</td><td>136.50</td><td>-0.188</td><td>36456</td><td>7.501</td><td>0.000</td><td>7.784</td><td>6.191</td><td>22.713</td><td>0.000</td></tr><tr><td>36</td><td>143.78</td><td>-0.690</td><td>28564</td><td>7.579</td><td>0.000</td><td>7.675</td><td>6.213</td><td>22.746</td><td>0.000</td></tr></tbody></table>
# Annexe B
## Etude Asymptotique des Modes de Pulsation

La théorie asymptotique permet d'obtenir des solutions semi-analytiques au problème des pulsations radiales et non-radiales dans les étoiles. Elle peut donc s'avérer très utile pour clarifier l'étude du comportement des modes d'oscillation. Elle s'appuie sur une approche adiabatique où l'on néglige, de surcroît, la perturbation $\Phi'$ du champ gravitationnel (approximation de Cowling). Le problème se réduit alors à résoudre un système du second ordre dont les variables Lagrangiennes sont $\xi_r$, le déplacement radial, et $\delta P/\rho$ la perturbation de la pression (ou de façon équivalente, le déplacement horizontal $\xi_h$). Il s'agit des 2 équations T1 et T2 dans Tassoul, 1980 (dorénavant, les références aux équations dérivées dans cet article seront précédées par le préfixe T). Pour traiter ce système d'équations analytiquement, M. Tassoul a développé une série d'expansions asymptotiques pour différents types génériques de structures communément rencontrées en physique stellaire.

Le système à résoudre comprend deux équations qui possèdent chacune un certain nombre de points singuliers. Dans la limite asymptotique où l'on considère $\sigma^2 \gg N^2$, $L_l^2$ (modes p) ou bien $\sigma^2 \ll N^2$, $L_l^2$ (modes g), ces points singuliers sont le centre de l'étoile ($x \equiv r/R = 0$), sa surface ($x = 1$), et éventuellement, dans la limite asymptotique des modes g, les zéros de la fréquence de Brunt-Väisälä (à l'interface entre zones convectives et radiatives). Heureusement, les points singuliers des deux équations sont distincts, celles-ci jouent donc un rôle complémentaire dans la description des pulsations. L'idée de la théorie asymptotique est de résoudre le système dans différentes régions de l'étoile en utilisant les équations appropriées pour chacune d'elles, puis de joindre les solutions ensemble pour obtenir les fonctions d'ondes globales et le spectre de période des modes.

### Les modes g

Pour évaluer les solutions asymptotiques des modes g, il est nécessaire de diviser l'étoile suivant le nombre de régions radiatives et convectives. Pour les étoiles sous-naines de type B se trouvant encore en phase de brûlage nucléaire central, la structure générique correspondante est le modèle à deux zones: une zone convective interne (le cœur convectif de l'étoile; voir Chapitre 2) surmonté par une zone radiative. Notons qu'il existe une petite région convective en surface engendrée par l'ionisation de l'HeII en HeIII qu'il faudrait, en toute rigueur, traiter comme une troisième zone dans l'approche asymptotique. Par souci de simplicité et compte tenu du faible impact de cette région sur le comportement des modes g dans les sdB, elle ne sera pas prise en considération. Il existe aussi deux discontinuités dans la fréquence de Brunt-Väisälä qui affectent le comportement des modes g en générant des effets de piégeage. La première, située à la frontière entre le noyau convectif et le cœur radiatif, est un pic engendré par la transition C-O/He; son effet sur les modes g étant peu important en
terme de piégegage, elle ne sera pas, non plus, prise en compte par la suite. La seconde discontinuité, essentiellement responsable du piégeage et du confinement des modes g, sera traitée à la manière de Brassard et al., 1992a. A ce titre, les références futures aux équations de cet article seront précédées par le préfixe B.

Le modèle générique qui s'identifie à la plupart des sdB dans Tassoul, 1980 est le modèle à deux zones avec une région centrale convective et une région externe radiative. Dans la région centrale convective, où l'on considère qu'il n'y a pas de discontinuités, les solutions appropriées sont données par (T80) vers $x=0$ et par (T96) pour $x \le x_1$ (où $x_1 \equiv x_c$ est la position de l'interface entre le cœur convectif et le cœur radiatif). Les conditions de continuité entre ces deux solutions sont directement données par (T117) et (T118) (où $k_i$ est une constante arbitraire dépendant de la normalisation et $k_{11}, k_{12}$ sont des constantes associées à la solution près de $x=x_1$):

$$k_{12} = 0 \tag{6.1}$$

$$k_{11} = k_i \exp \left( \frac{\sqrt{l(l+1)}}{\sigma} \int_0^{x_1} \frac{|N|}{x} dx \right) . \tag{6.2}$$

Dans la région externe radiative, les solutions appropriées pour $x \ge x_1$ sont données par (T97) au premier ordre et pour les variables $S_1$ et $S_2$ utilisées par Tassoul, 1980:

$$S_1 = Q_1(v_{1b})k_{11} + Q_3(v_{1b})k_{12} \tag{6.3}$$

$$= k_{11} \left(\frac{v_{1b}}{3}\right)^{\frac{1}{2}} \left[ J_{-\frac{1}{3}}\left(\frac{v_{1b}}{\sigma}\right) + J_{\frac{1}{3}}\left(\frac{v_{1b}}{\sigma}\right) \right] \equiv S_1^- \tag{6.4}$$

$$S_2 = Q_2(v_{1b})k_{11} + Q_4(v_{1b})k_{12} \tag{6.5}$$

$$= k_{11} \left(\frac{v_{1b}}{3}\right)^{\frac{1}{2}} \left[ J_{-\frac{2}{3}}\left(\frac{v_{1b}}{\sigma}\right) - J_{\frac{2}{3}}\left(\frac{v_{1b}}{\sigma}\right) \right] \equiv S_2^- \tag{6.6}$$

où la condition (6.1) a été utilisée pour supprimer les termes proportionnels à $k_{12}$. Les fonctions $J_n(x)$ représentent les fonctions de Bessel de première espèce et le terme $v_{1b}$ est défini par

$$v_{1b}(x) = \sqrt{l(l+1)} \int_{x_1}^{x} \frac{|N|}{x} dx . \tag{6.7}$$

La solution près de la surface ($x=1$) est donnée par (T82) et au premier ordre, on a

$$S_1 = k_0 v_0^{\frac{1}{2}} J_{n_e+1} \left(\frac{v_0}{\sigma}\right) \equiv S_1^+ \tag{6.8}$$

$$S_2 = -k_0 v_0^{\frac{1}{2}} J_{n_e} \left(\frac{v_0}{\sigma}\right) \equiv S_2^+ \tag{6.9}$$

où $k_0$ est une constante arbitraire, $n_e$ est l'indice polytropique des couches superficielles (proches de la surface) et $v_0$ est donné par

$$v_0(x) = \sqrt{l(l+1)} \int_x^1 \frac{|N|}{x} dx . \tag{6.10}$$
Dans la théorie asymptotique, on considère les modes pour lesquels $\sigma^2 \ll N^2$ (modes avec indice radial $k$ élevé). On peut donc développer les fonctions de Bessel dans la limite où l’argument est grand. De manière générale, cela donne

$$J_n(x) \propto x^{-\frac{1}{2}} \cos \left( x - \frac{n\pi}{2} - \frac{\pi}{4} \right) \qquad (6.11)$$

$$J_{n+1}(x) \propto x^{-\frac{1}{2}} \sin \left( x - \frac{n\pi}{2} - \frac{\pi}{4} \right) . \qquad (6.12)$$

En appliquant ces développements à $S_1^+$, $S_1^-$, $S_2^+$ et $S_2^-$, les solutions dans la région radiative du modèle s’écrivent sous les formes utiles

$$S_1^+ \propto k_0 \sin \left( \frac{v_0}{\sigma} - \frac{n_e \pi}{2} - \frac{\pi}{4} \right) \qquad (6.13)$$

$$S_2^+ \propto -k_0 \cos \left( \frac{v_0}{\sigma} - \frac{n_e \pi}{2} - \frac{\pi}{4} \right) \qquad (6.14)$$

$$S_1^- \propto k_{11} \sin \left( \frac{v_{1b}}{\sigma} + \frac{\pi}{4} \right) \qquad (6.15)$$

$$S_2^- \propto -k_{11} \cos \left( \frac{v_{1b}}{\sigma} + \frac{\pi}{4} \right) . \qquad (6.16)$$

Il est maintenant possible de combiner ces deux ensembles de solutions en présence de la discontinuité dans la fréquence de Brunt-Väisälä située à $x = x_H$. Suivant la procédure de Brassard et al., 1992a, on idéalise (à des fins simplificatrices) le pic de Ledoux par une vraie discontinuité caractérisée par les valeurs de $N$ au dessus ($N^+$) et en dessous ($N^-$) de la discontinuité. Celle-ci est alors paramétrisée par la quantité $\alpha^2 \equiv N^+/N^-$. Les conditions de continuité entre les solutions s’écrivent donc, à $x = x_H$,

$$S_1^+ = \alpha S_1^- \quad \text{et} \quad \alpha S_2^+ = S_2^- , \qquad (6.17)$$

où encore sous la forme plus appropriée

$$\frac{S_2^-}{S_1^-} = \alpha^2 \frac{S_2^+}{S_1^+} \quad \text{et} \quad \left(S_1^-\right)^2 + \left(S_2^-\right)^2 = \frac{1}{\alpha^2} \left(S_1^+\right)^2 + \alpha^2 \left(S_2^+\right)^2 . \qquad (6.18)$$

En utilisant les relations

$$\sigma \equiv \frac{2\pi}{P} , \quad v_{1b}(x_H) = \frac{2\pi^2}{\Pi_{0,l}^{\text{rad}}} - \frac{2\pi^2}{\Pi_{H,l}} \quad \text{et} \quad v_0(x_H) = \frac{2\pi^2}{\Pi_{H,l}} \qquad (6.19)$$

où $P$ est la période et où l'on définit, au préalable, les quantités $\Pi_{H,l}$ et $\Pi_{0,l}^{\text{rad}}$ par

$$\Pi_{0,l}^{\text{rad}} \equiv \frac{\Pi_0^{\text{rad}}}{\sqrt{l(l+1)}} \quad \text{avec} \quad \Pi_0^{\text{rad}} \equiv 2\pi^2 \left( \int_{r_c}^{R} \frac{|N|}{r} dr \right)^{-1} \qquad (6.20)$$

$$\Pi_{H,l} \equiv \frac{\Pi_H}{\sqrt{l(l+1)}} \quad \text{avec} \quad \Pi_H \equiv 2\pi^2 \left( \int_{r_H}^{R} \frac{|N|}{r} dr \right)^{-1} , \qquad (6.21)$$
les conditions de continuité (6.18) s'écrivent alors, en utilisant la propriété cot($-x$) = cot($x$),

$$ \cot \left[ \left( \frac{2P}{\Pi_{H,l}} - \frac{2P}{\Pi_{0,l}^{\text{rad}}} - \frac{1}{2} \right) \frac{\pi}{2} \right] = \alpha^2 \cot \left[ \left( \frac{2P}{\Pi_{H,l}} - n_e - \frac{1}{2} \right) \frac{\pi}{2} \right] \quad (6.22) $$

$$ k_{11}^2 = \frac{k_0^2}{\alpha^2} \left[ \sin^2 \left( \frac{P\pi}{\Pi_{H,l}} - \frac{n_e\pi}{2} - \frac{\pi}{4} \right) + \alpha^4 \cos^2 \left( \frac{P\pi}{\Pi_{H,l}} - \frac{n_e\pi}{2} - \frac{\pi}{4} \right) \right] \quad (6.23) $$

Ces deux équations sont à comparer aux relations (B37) et (B38) de Brassard et al., 1992a. Celles-ci sont essentiellement identiques mis à part le terme de gauche dans l'équation transcendentale (6.22). Cette différence est une manifestation directe de la présence d'un noyau convectif dans les sdB et qui n'existe pas dans les naines blanches. Celui-ci affecte donc directement la structure du spectre de périodes généré par cette équation. Pour le reste, il apparaît ici clairement que les modes g dans les étoiles sous-naines de type B adoptent une structure très proche de celle des modes g dans les naines blanches explorée en détails dans Brassard et al., 1992a. Sans reprendre toute cette étude, on peut noter, pour un modèle sans discontinuité ($\alpha = 1$), que l'équation (6.22) est résolue en égalisant les arguments de chaque cotangeante modulo $\pi$. On retrouve alors le spectre de périodes uniforme évalué par Tassoul, 1980; éq. (T127):

$$ P_{k,l} = \left( k + \frac{n_e}{2} \right) \Pi_{0,l}^{\text{rad}} = \left( k + \frac{n_e}{2} \right) \frac{\Pi_{0,l}^{\text{rad}}}{\sqrt{l(l+1)}} \quad . \quad (6.24) $$

Il est intéressant de remarquer que, contrairement au spectre uniforme dans les naines blanches, la période réduite $P_{k,l}/\sqrt{l(l+1)}$ est indépendante de l'indice non-radial $l$. Pour les sdB, les modes g d'ordre radial $k$ donné ont donc essentiellement la même période réduite. Dans le cas limite inverse où les modes sont parfaitement piégés dans l'enveloppe, le spectre de périodes est donné par la limite $\alpha \to \infty$. Le résultat est alors identique à l'équation (B42), obtenue en cherchant les zéros de la cotangeante de droite dans l'équation (6.22). Le spectre de périodes est alors donné par la relation

$$ P_{i,l} = \left( i + \frac{n_e}{2} + \frac{1}{4} \right) \Pi_{H,l} = \left( i + \frac{n_e}{2} + \frac{1}{4} \right) \frac{\Pi_H}{\sqrt{l(l+1)}} \quad , \quad (6.25) $$

où $i$ représente l'indice radial pour les modes piégés ou, de façon équivalente, le nombre de nœuds dans l'enveloppe de l'étoile. Ici aussi, l'équation (6.25) montre que les modes piégés de même indice $i$ (pour des $l$ différents) ont la même période réduite. A la manière de Brassard et al., 1992a, on trouve, en notant qu'un mode parfaitement piégé doit satisfaire à la fois (6.24) et (6.25), la relation entre l'indice $i$ des modes piégés et l'indice radial classique $k$:

$$ i = k \frac{\Pi_0^{\text{rad}}}{\Pi_H} + \frac{n_e}{2} \left( \frac{\Pi_0^{\text{rad}}}{\Pi_H} - 1 \right) + \frac{1}{4} \quad . \quad (6.26) $$

Bien entendu, cette relation ne représente qu'un cas idéalisé impossible à réaliser en pratique dans la mesure où $k$ et $i$ sont nécessairement entiers alors que $\Pi_0^{\text{rad}}$, $\Pi_H$, $n_e$ sont des paramètres réels indépendants. Le piégeage parfait n'existe donc pas dans nos modèles. On peut toutefois obtenir deux informations intéressantes à partir de cette équation. En premier lieu, la relation entre $i$ et $k$ est indépendante de $l$, ainsi tous les modes g piégés sont de même ordre radial $k$ (pour $i$ donné). En second
lieu, on peut déterminer approximativement l'intervalle $\Delta k$ qui sépare deux modes piégés consécutifs ($\Delta i=1$) avec la relation qui sera utile par la suite

$$ \Delta k \approx \frac{\Pi_H}{\Pi_0^{\text{rad}}} \qquad (6.27) $$

Considérant maintenant l'équation (6.22) pour un paramètre $\alpha$ quelconque, on peut montrer que la condition optimale pour le piégeage (celle qui minimise l'énergie) est obtenue lorsque chaque terme de (6.22) est proche de zéro. Si ces termes sont strictement nuls en même temps, cela correspond au piégeage parfait qui, on vient de le voir, ne peut être atteint en raison des contraintes sur $k$ et $i$. On peut, par contre, obtenir une formulation générale approximative pour le spectre de périodes en développant en série l'équation (6.22) au voisinage des modes piégés (c.a.d., là où les cot $\simeq 0$). En utilisant le développement de cot($x$) au voisinage de $\pi/2$ modulo $\pi$, on obtient au premier ordre

$$ P_{ki,l} = \frac{1}{\sqrt{l(l+1)}} \left[ k + i(\alpha^2 - 1) + \frac{\alpha^2 n_e}{2} - \frac{\alpha^2}{4} + \frac{1}{4} \right] \frac{\Pi_0^{\text{rad}} \Pi_H}{(\alpha^2 - 1) \Pi_0^{\text{rad}} + \Pi_H} \quad . \qquad (6.28) $$

Comme précédemment, $k$ est l'indice habituel associé à l'ordre radial du mode et $i$ est le nouvel indice donnant l'ordre du mode piégé ou, de manière équivalente, le nombre de nœuds présents dans l'enveloppe au dessus de la discontinuité. Cette équation admet les cas limites (6.24) pour $\alpha \to 1$ et (6.25) pour $\alpha \to \infty$, comme il était souhaitable. Encore une fois, il apparaît que la période réduite des modes est indépendante de l'indice $l$ contrairement à la version "naines blanches" donnée par l'équation (B48). De (6.28), l'on déduit l'espacement entre deux modes piégés consécutifs:

$$ P_{i+1} - P_i = \frac{\Delta k + \alpha^2 - 1}{\sqrt{l(l+1)}} \frac{\Pi_0^{\text{rad}} \Pi_H}{(\alpha^2 - 1) \Pi_0^{\text{rad}} + \Pi_H} \quad . \qquad (6.29) $$

En supposant que la valeur moyenne pour $\Delta k$ est donnée par la relation (6.27), on obtient

$$ \overline{P_{i+1} - P_i} = \Pi_{H,l} \qquad (6.30) $$

comme l'équation (6.25) le laissait présager. Ce résultat, tout à fait semblable à ce qui est obtenu pour les naines blanches, montre que l'espacement en terme des périodes réduites entre deux modes piégés consécutifs est constant, indépendant de $l$. Cette constante, $\Pi_H$, dépend de la structure de l'enveloppe du modèle et en particulier de la position $r_H$ de l'interface He/H; elle dépend donc directement de la masse de l'enveloppe de l'étoile. A partir de (6.30) et (6.27), l'écart moyen en période entre deux modes consécutifs est évalué par

$$ \overline{P_{k+1} - P_k} \approx \frac{\overline{P_{i+1} - P_i}}{\Delta k} = \Pi_{0,l}^{\text{rad}} \quad . \qquad (6.31) $$

Un résultat fort semblable à son équivalent pour les naines blanches si ce n'est que la constante $\Pi_0^{\text{rad}}$ est évaluée pour les régions radiatives du modèle et dépend de la position $r_c$ de l'interface entre le noyau convectif et le cœur radiatif de l'étoile.

On a vu que les différences qui peuvent exister entre naines blanches et sdB au niveau de la structure du spectre des modes $g$ sont imputables en grande partie à la présence du noyau convectif
dans ces dernieres. Toutefois, ce noyau convectif ne survit pas à l'évolution de ces objets car, entretenu par les réactions nucléaires centrales de la chaîne triple-α, il meurt avec elles lorsque le carburant vient à manquer. Pour la structure des modes g, cette disparition se traduit par un recentrage vers la structure qui est observée pour les naines blanches, toutes les différences que l'on a pu noter étant gommées. Les équations qui s'appliquent pour ces modèles où le cœur convectif a disparu ne sont donc plus celles présentées auparavant mais directement celles dérivées dans Brassard et al., 1992a.

## Les modes p

Les solutions asymptotiques pour les modes p sont beaucoup plus simples à obtenir dans la mesure où seuls deux points de transition, le centre et la surface, sont à considérer. Si l'on néglige, dans les quantités physiques comme la vitesse adiabatique du son, les discontinuités associées aux transitions chimiques dues à la stratification des modèles, le spectre des modes acoustiques est alors obtenu en joignant les solutions valides près de la surface des modèles à celles appropriées au voisinage du centre de l'étoile. Pour nos objets, il provient directement de l'équation (T65) dans Tassoul, 1980 qui, au premier ordre, donne la fréquence des modes p pour le spectre uniforme

$$ \nu_{kl} \approx \left(k + \frac{l}{2} + \frac{n_e}{2} + \frac{1}{4}\right) \left(2 \int_{0}^{R} \frac{dr}{C_s}\right)^{-1} \quad \text{avec} \quad C_s = \left(\frac{\Gamma_1 P}{\rho}\right)^{\frac{1}{2}} \qquad (6.32) $$

en fonction de l'indice radial $k$ et de l'indice angulaire $l$ (où $\nu_{kl} = 2\pi\sigma_{kl} = 1/P_{kl}$). $C_s$ correspond à la vitesse adiabatique du son et $n_e$, comme pour les modes g, à l'indice polytropique des couches superficielles. La relation montre donc clairement que dans la limite des grandes valeurs de $k$, l'inter-valle de fréquence entre deux modes d'ordres radiaux consécutifs ($\Delta k = 1, \Delta l = 0$) est constant et donné par la quantité

$$ \Delta\nu = \nu_{k+1,l} - \nu_{k,l} = \left(2 \int_{0}^{R} \frac{dr}{C_s}\right)^{-1} . \qquad (6.33) $$

De plus, on remarquera que les fréquences (périodes) augmentent (diminuent) lorsque l'indice angulaire $l$ est accru et qu'elles obéissent à la relation $\nu_{k,l+2} = \nu_{k-1,l}$. Un mode d'indice $l=3$ et d'ordre radial $k$ a donc sensiblement la même fréquence (ou période) que le mode d'indice $l=1$ et d'ordre $k-1$. Cette relation s'applique également entre les modes avec $l=2$ et $l=0$ (pulsations radiales) à la nuance importante qu'il y a un décalage $\Delta k = +1$ entre les modes p radiaux et non-radiaux. Ainsi, le premier mode acoustique du spectre $l=0$ est le mode fondamental (avec $k=0$) alors qu'il s'agit du mode $k=1$ pour les pulsations non-radiales (les modes f, ou modes de Kelvin, n'étant pas des modes acoustiques).
# Annexe C
## Périodes Adiabatiques pour les Séquences Evolutives

Cette annexe comprend l'ensemble des résultats issus des calculs adiabatiques effectués sur les 7 séquences évolutives à notre disposition. Chaque modèle est représenté par un tableau contenant les principales informations (P, la période en secondes; log E<sub>cin</sub>, l'énergie cinétique du mode; et C<sub>kl</sub>, le coefficient de rotation rigide du premier ordre) pour les modes p, f et g (radiaux et non radiaux avec l = 1, 2, 3) jusqu'à l'ordre radial k = 10. Les modes d'ordres supérieurs, même s'ils ne sont pas présentés ici, sont disponibles sur demande.

Les séquences sont classées par ordre de masse d'enveloppe croissante et les modèles dans les séquences par ordre d'âge croissant, depuis la ZAEHB jusqu'au commencement de la phase post-EHB. Au total, 149 modèles sont présentés en autant de tableaux. Pour faciliter la recherche, les pages correspondant au début de chaque séquence sont données dans le tableau suivant:

<table><thead><tr><th>#</th><th>Masse de la séquence</th><th>Nombre de modèles</th><th>Page du premier tableau</th></tr></thead><tbody><tr><td>1</td><td>M = 0.4690 + 0.0001 M<sub>☉</sub></td><td>16</td><td>304</td></tr><tr><td>2</td><td>M = 0.4758 + 0.0002 M<sub>☉</sub></td><td>20</td><td>312</td></tr><tr><td>3</td><td>M = 0.4690 + 0.0007 M<sub>☉</sub></td><td>22</td><td>322</td></tr><tr><td>4</td><td>M = 0.4758 + 0.0012 M<sub>☉</sub></td><td>24</td><td>333</td></tr><tr><td>5</td><td>M = 0.4758 + 0.0022 M<sub>☉</sub></td><td>23</td><td>345</td></tr><tr><td>6</td><td>M = 0.4758 + 0.0032 M<sub>☉</sub></td><td>21</td><td>357</td></tr><tr><td>7</td><td>M = 0.4758 + 0.0042 M<sub>☉</sub></td><td>23</td><td>368</td></tr></tbody></table>

En fin d'annexe, des pages 381 à 394, 14 tableaux supplémentaires proposent, pour chacune des 7 séquences, les valeurs des taux de changement des périodes ($\dot{P}$ = dP/dt; exprimées en secondes par million d'année) pour un échantillon de modes p (notés $p_{l,k}$; où l et k sont respectivement l'indice angulaire et l'ordre radial du mode) et de modes g (notés $g_{l,k}$).
Modèle # 1, M = 0.4690 + 0.0001 M☉, T<sub>eff</sub> = 34395 K, log g = 6.08, âge = 4.49 millions d'années depuis la ZAEHB

<table><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>33.23</td><td>41.44</td><td>34.71</td><td>41.52</td><td>0.0183</td><td>33.58</td><td>41.46</td><td>0.0165</td><td>32.63</td><td>41.41</td><td>0.0148</td></tr><tr><td>9</td><td>36.06</td><td>41.59</td><td>37.80</td><td>41.70</td><td>0.0206</td><td>36.47</td><td>41.62</td><td>0.0184</td><td>35.38</td><td>41.55</td><td>0.0164</td></tr><tr><td>8</td><td>39.40</td><td>41.79</td><td>41.49</td><td>41.92</td><td>0.0237</td><td>39.90</td><td>41.82</td><td>0.0209</td><td>38.60</td><td>41.74</td><td>0.0186</td></tr><tr><td>7</td><td>43.45</td><td>42.04</td><td>46.00</td><td>42.20</td><td>0.0274</td><td>44.05</td><td>42.08</td><td>0.0242</td><td>42.48</td><td>41.98</td><td>0.0216</td></tr><tr><td>6</td><td>48.46</td><td>42.34</td><td>51.63</td><td>42.52</td><td>0.0316</td><td>49.18</td><td>42.38</td><td>0.0280</td><td>47.25</td><td>42.27</td><td>0.0253</td></tr><tr><td>5</td><td>54.80</td><td>42.70</td><td>58.88</td><td>42.92</td><td>0.0372</td><td>55.69</td><td>42.75</td><td>0.0332</td><td>53.24</td><td>42.61</td><td>0.0303</td></tr><tr><td>4</td><td>63.21</td><td>43.13</td><td>68.72</td><td>43.38</td><td>0.0441</td><td>64.34</td><td>43.19</td><td>0.0410</td><td>61.08</td><td>43.03</td><td>0.0383</td></tr><tr><td>3</td><td>74.89</td><td>43.60</td><td>82.26</td><td>43.87</td><td>0.0489</td><td>76.31</td><td>43.66</td><td>0.0507</td><td>71.91</td><td>43.49</td><td>0.0505</td></tr><tr><td>2</td><td>91.48</td><td>44.14</td><td>101.33</td><td>44.45</td><td>0.0466</td><td>93.42</td><td>44.20</td><td>0.0671</td><td>87.19</td><td>44.01</td><td>0.0716</td></tr><tr><td>1</td><td>114.68</td><td>44.90</td><td>129.84</td><td>45.42</td><td>0.0407</td><td>118.15</td><td>44.99</td><td>0.1078</td><td>108.95</td><td>44.68</td><td>0.1068</td></tr><tr><td>0</td><td>148.47</td><td>46.22</td><td>...</td><td>...</td><td>...</td><td>161.00</td><td>46.62</td><td>0.3753</td><td>143.50</td><td>45.91</td><td>0.1949</td></tr><tr><td>1</td><td>...</td><td>...</td><td>461.39</td><td>48.37</td><td>0.4061</td><td>298.33</td><td>47.97</td><td>0.0900</td><td>237.49</td><td>47.69</td><td>0.0131</td></tr><tr><td>2</td><td>...</td><td>...</td><td>686.97</td><td>47.94</td><td>0.4306</td><td>426.36</td><td>47.78</td><td>0.1063</td><td>326.36</td><td>47.62</td><td>0.0294</td></tr><tr><td>3</td><td>...</td><td>...</td><td>914.52</td><td>47.54</td><td>0.4484</td><td>555.19</td><td>47.44</td><td>0.1207</td><td>415.76</td><td>47.33</td><td>0.0417</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1137.51</td><td>47.12</td><td>0.4611</td><td>680.10</td><td>47.05</td><td>0.1309</td><td>501.63</td><td>46.96</td><td>0.0503</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1351.41</td><td>46.73</td><td>0.4698</td><td>799.51</td><td>46.69</td><td>0.1384</td><td>583.24</td><td>46.63</td><td>0.0568</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1562.03</td><td>46.44</td><td>0.4763</td><td>917.77</td><td>46.41</td><td>0.1442</td><td>664.23</td><td>46.38</td><td>0.0620</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1777.09</td><td>46.21</td><td>0.4810</td><td>1039.30</td><td>46.20</td><td>0.1485</td><td>747.79</td><td>46.18</td><td>0.0659</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1996.49</td><td>46.01</td><td>0.4843</td><td>1163.83</td><td>46.00</td><td>0.1515</td><td>833.81</td><td>45.99</td><td>0.0687</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2217.32</td><td>45.83</td><td>0.4868</td><td>1289.70</td><td>45.82</td><td>0.1539</td><td>921.29</td><td>45.81</td><td>0.0709</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2440.21</td><td>45.68</td><td>0.4888</td><td>1417.22</td><td>45.68</td><td>0.1558</td><td>1010.36</td><td>45.67</td><td>0.0727</td></tr></tbody></table>

Modèle # 2, M = 0.4690 + 0.0001 M☉, T<sub>eff</sub> = 34345 K, log g = 6.03, âge = 23.34 millions d'années depuis la ZAEHB

<table><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>36.17</td><td>41.40</td><td>37.77</td><td>41.47</td><td>0.0186</td><td>36.53</td><td>41.41</td><td>0.0168</td><td>35.48</td><td>41.37</td><td>0.0151</td></tr><tr><td>9</td><td>39.25</td><td>41.54</td><td>41.12</td><td>41.64</td><td>0.0207</td><td>39.67</td><td>41.56</td><td>0.0185</td><td>38.46</td><td>41.50</td><td>0.0168</td></tr><tr><td>8</td><td>42.90</td><td>41.74</td><td>45.14</td><td>41.86</td><td>0.0235</td><td>43.39</td><td>41.76</td><td>0.0211</td><td>41.96</td><td>41.68</td><td>0.0190</td></tr><tr><td>7</td><td>47.31</td><td>41.98</td><td>50.04</td><td>42.13</td><td>0.0270</td><td>47.90</td><td>42.01</td><td>0.0244</td><td>46.18</td><td>41.92</td><td>0.0221</td></tr><tr><td>6</td><td>52.75</td><td>42.27</td><td>56.15</td><td>42.45</td><td>0.0307</td><td>53.46</td><td>42.31</td><td>0.0283</td><td>51.34</td><td>42.19</td><td>0.0259</td></tr><tr><td>5</td><td>59.62</td><td>42.62</td><td>63.99</td><td>42.85</td><td>0.0358</td><td>60.48</td><td>42.67</td><td>0.0335</td><td>57.82</td><td>42.53</td><td>0.0309</td></tr><tr><td>4</td><td>68.73</td><td>43.06</td><td>74.64</td><td>43.31</td><td>0.0420</td><td>69.82</td><td>43.11</td><td>0.0416</td><td>66.28</td><td>42.95</td><td>0.0391</td></tr><tr><td>3</td><td>81.42</td><td>43.54</td><td>89.33</td><td>43.80</td><td>0.0454</td><td>82.81</td><td>43.59</td><td>0.0523</td><td>78.00</td><td>43.42</td><td>0.0522</td></tr><tr><td>2</td><td>99.41</td><td>44.08</td><td>110.17</td><td>44.38</td><td>0.0424</td><td>101.37</td><td>44.13</td><td>0.0715</td><td>94.54</td><td>43.94</td><td>0.0744</td></tr><tr><td>1</td><td>124.25</td><td>44.81</td><td>140.85</td><td>45.32</td><td>0.0363</td><td>127.92</td><td>44.90</td><td>0.1165</td><td>118.13</td><td>44.60</td><td>0.1086</td></tr><tr><td>0</td><td>158.64</td><td>46.06</td><td>...</td><td>...</td><td>...</td><td>170.13</td><td>46.44</td><td>0.3479</td><td>154.18</td><td>45.79</td><td>0.1791</td></tr><tr><td>1</td><td>...</td><td>...</td><td>447.88</td><td>48.48</td><td>0.4131</td><td>294.85</td><td>47.99</td><td>0.0957</td><td>238.83</td><td>47.65</td><td>0.0171</td></tr><tr><td>2</td><td>...</td><td>...</td><td>653.61</td><td>48.07</td><td>0.4421</td><td>404.19</td><td>47.90</td><td>0.1149</td><td>310.87</td><td>47.75</td><td>0.0363</td></tr><tr><td>3</td><td>...</td><td>...</td><td>885.16</td><td>47.66</td><td>0.4562</td><td>529.38</td><td>47.57</td><td>0.1258</td><td>391.96</td><td>47.48</td><td>0.0453</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1132.19</td><td>47.21</td><td>0.4653</td><td>667.56</td><td>47.16</td><td>0.1333</td><td>485.79</td><td>47.10</td><td>0.0512</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1374.37</td><td>46.78</td><td>0.4721</td><td>804.76</td><td>46.75</td><td>0.1394</td><td>580.43</td><td>46.71</td><td>0.0568</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1611.12</td><td>46.46</td><td>0.4776</td><td>939.80</td><td>46.44</td><td>0.1447</td><td>674.38</td><td>46.42</td><td>0.0619</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1850.78</td><td>46.22</td><td>0.4819</td><td>1077.10</td><td>46.21</td><td>0.1489</td><td>770.44</td><td>46.20</td><td>0.0659</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2093.27</td><td>46.01</td><td>0.4849</td><td>1216.25</td><td>46.01</td><td>0.1518</td><td>867.99</td><td>46.00</td><td>0.0687</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2335.45</td><td>45.83</td><td>0.4872</td><td>1355.37</td><td>45.83</td><td>0.1540</td><td>965.64</td><td>45.82</td><td>0.0709</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2578.42</td><td>45.68</td><td>0.4892</td><td>1495.07</td><td>45.68</td><td>0.1559</td><td>1063.86</td><td>45.67</td><td>0.0727</td></tr></tbody></table>
<table><caption>Modèle # 3, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 34329 K, log g = 5.99, âge = 39.31 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>38.38</td><td>41.37</td><td>40.07</td><td>41.44</td><td>0.0189</td><td>38.75</td><td>41.38</td><td>0.0167</td><td>37.63</td><td>41.34</td><td>0.0152</td></tr><tr><td>9</td><td>41.67</td><td>41.51</td><td>43.64</td><td>41.60</td><td>0.0207</td><td>42.10</td><td>41.53</td><td>0.0185</td><td>40.80</td><td>41.47</td><td>0.0171</td></tr><tr><td>8</td><td>45.55</td><td>41.69</td><td>47.90</td><td>41.81</td><td>0.0232</td><td>46.05</td><td>41.72</td><td>0.0210</td><td>44.52</td><td>41.64</td><td>0.0192</td></tr><tr><td>7</td><td>50.21</td><td>41.93</td><td>53.08</td><td>42.08</td><td>0.0264</td><td>50.81</td><td>41.96</td><td>0.0243</td><td>48.97</td><td>41.87</td><td>0.0223</td></tr><tr><td>6</td><td>55.98</td><td>42.22</td><td>59.56</td><td>42.40</td><td>0.0298</td><td>56.70</td><td>42.26</td><td>0.0284</td><td>54.43</td><td>42.14</td><td>0.0263</td></tr><tr><td>5</td><td>63.27</td><td>42.57</td><td>67.87</td><td>42.79</td><td>0.0342</td><td>64.14</td><td>42.62</td><td>0.0336</td><td>61.29</td><td>42.48</td><td>0.0315</td></tr><tr><td>4</td><td>72.87</td><td>43.01</td><td>79.09</td><td>43.26</td><td>0.0397</td><td>73.97</td><td>43.06</td><td>0.0418</td><td>70.23</td><td>42.89</td><td>0.0396</td></tr><tr><td>3</td><td>86.27</td><td>43.49</td><td>94.65</td><td>43.76</td><td>0.0423</td><td>87.69</td><td>43.54</td><td>0.0534</td><td>82.58</td><td>43.37</td><td>0.0534</td></tr><tr><td>2</td><td>105.23</td><td>44.04</td><td>116.84</td><td>44.34</td><td>0.0389</td><td>107.34</td><td>44.09</td><td>0.0750</td><td>100.05</td><td>43.90</td><td>0.0762</td></tr><tr><td>1</td><td>131.19</td><td>44.75</td><td>149.23</td><td>45.26</td><td>0.0329</td><td>135.25</td><td>44.84</td><td>0.1238</td><td>125.05</td><td>44.54</td><td>0.1097</td></tr><tr><td>0</td><td>165.87</td><td>45.93</td><td>...</td><td>...</td><td>...</td><td>176.76</td><td>46.31</td><td>0.3234</td><td>162.13</td><td>45.70</td><td>0.1653</td></tr><tr><td>1</td><td>...</td><td>...</td><td>435.14</td><td>48.52</td><td>0.4282</td><td>286.27</td><td>47.97</td><td>0.1082</td><td>232.88</td><td>47.61</td><td>0.0268</td></tr><tr><td>2</td><td>...</td><td>...</td><td>650.14</td><td>48.07</td><td>0.4493</td><td>396.70</td><td>47.86</td><td>0.1208</td><td>300.74</td><td>47.67</td><td>0.0404</td></tr><tr><td>3</td><td>...</td><td>...</td><td>905.51</td><td>47.64</td><td>0.4575</td><td>538.62</td><td>47.55</td><td>0.1259</td><td>396.59</td><td>47.45</td><td>0.0440</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1172.53</td><td>47.19</td><td>0.4656</td><td>689.90</td><td>47.14</td><td>0.1331</td><td>501.02</td><td>47.08</td><td>0.0506</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1430.20</td><td>46.76</td><td>0.4723</td><td>836.54</td><td>46.73</td><td>0.1394</td><td>602.67</td><td>46.69</td><td>0.0566</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1681.06</td><td>46.45</td><td>0.4781</td><td>979.94</td><td>46.43</td><td>0.1448</td><td>702.65</td><td>46.41</td><td>0.0619</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1934.73</td><td>46.22</td><td>0.4829</td><td>1125.42</td><td>46.20</td><td>0.1490</td><td>804.52</td><td>46.19</td><td>0.0659</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2190.41</td><td>46.01</td><td>0.4851</td><td>1272.23</td><td>46.00</td><td>0.1518</td><td>907.51</td><td>45.99</td><td>0.0687</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2445.41</td><td>45.83</td><td>0.4873</td><td>1418.78</td><td>45.82</td><td>0.1541</td><td>1010.45</td><td>45.82</td><td>0.0709</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2701.20</td><td>45.68</td><td>0.4892</td><td>1565.92</td><td>45.68</td><td>0.1560</td><td>1113.93</td><td>45.67</td><td>0.0728</td></tr></tbody></table>

<table><caption>Modèle # 4, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 34406 K, log g = 5.96, âge = 58.04 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>40.85</td><td>41.34</td><td>42.62</td><td>41.41</td><td>0.0192</td><td>41.22</td><td>41.35</td><td>0.0167</td><td>40.02</td><td>41.30</td><td>0.0155</td></tr><tr><td>9</td><td>44.36</td><td>41.47</td><td>46.43</td><td>41.56</td><td>0.0209</td><td>44.79</td><td>41.49</td><td>0.0186</td><td>43.40</td><td>41.43</td><td>0.0174</td></tr><tr><td>8</td><td>48.49</td><td>41.65</td><td>50.96</td><td>41.76</td><td>0.0230</td><td>48.99</td><td>41.67</td><td>0.0210</td><td>47.35</td><td>41.60</td><td>0.0196</td></tr><tr><td>7</td><td>53.45</td><td>41.88</td><td>56.47</td><td>42.02</td><td>0.0259</td><td>54.04</td><td>41.91</td><td>0.0243</td><td>52.07</td><td>41.81</td><td>0.0227</td></tr><tr><td>6</td><td>59.58</td><td>42.17</td><td>63.35</td><td>42.34</td><td>0.0290</td><td>60.28</td><td>42.20</td><td>0.0286</td><td>57.86</td><td>42.09</td><td>0.0269</td></tr><tr><td>5</td><td>67.32</td><td>42.52</td><td>72.15</td><td>42.73</td><td>0.0328</td><td>68.17</td><td>42.56</td><td>0.0340</td><td>65.13</td><td>42.42</td><td>0.0321</td></tr><tr><td>4</td><td>77.49</td><td>42.95</td><td>84.02</td><td>43.20</td><td>0.0375</td><td>78.56</td><td>43.00</td><td>0.0425</td><td>74.58</td><td>42.83</td><td>0.0405</td></tr><tr><td>3</td><td>91.68</td><td>43.44</td><td>100.54</td><td>43.71</td><td>0.0390</td><td>93.09</td><td>43.49</td><td>0.0553</td><td>87.63</td><td>43.31</td><td>0.0549</td></tr><tr><td>2</td><td>111.68</td><td>43.99</td><td>124.24</td><td>44.29</td><td>0.0354</td><td>113.89</td><td>44.04</td><td>0.0799</td><td>106.13</td><td>43.84</td><td>0.0782</td></tr><tr><td>1</td><td>138.85</td><td>44.68</td><td>158.52</td><td>45.19</td><td>0.0296</td><td>143.23</td><td>44.77</td><td>0.1334</td><td>132.65</td><td>44.48</td><td>0.1107</td></tr><tr><td>0</td><td>174.04</td><td>45.79</td><td>...</td><td>...</td><td>...</td><td>183.55</td><td>46.14</td><td>0.2903</td><td>170.64</td><td>45.60</td><td>0.1464</td></tr><tr><td>1</td><td>...</td><td>...</td><td>425.55</td><td>48.52</td><td>0.4450</td><td>278.27</td><td>47.86</td><td>0.1253</td><td>225.24</td><td>47.42</td><td>0.0408</td></tr><tr><td>2</td><td>...</td><td>...</td><td>660.74</td><td>48.04</td><td>0.4525</td><td>400.87</td><td>47.80</td><td>0.1229</td><td>302.20</td><td>47.56</td><td>0.0404</td></tr><tr><td>3</td><td>...</td><td>...</td><td>937.21</td><td>47.62</td><td>0.4578</td><td>556.65</td><td>47.52</td><td>0.1258</td><td>409.35</td><td>47.41</td><td>0.0434</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1220.63</td><td>47.17</td><td>0.4658</td><td>717.81</td><td>47.12</td><td>0.1331</td><td>520.96</td><td>47.05</td><td>0.0504</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1491.64</td><td>46.75</td><td>0.4724</td><td>872.25</td><td>46.72</td><td>0.1394</td><td>628.18</td><td>46.68</td><td>0.0565</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1755.49</td><td>46.44</td><td>0.4800</td><td>1023.24</td><td>46.42</td><td>0.1449</td><td>733.56</td><td>46.40</td><td>0.0619</td></tr><tr><td>7</td><td>...</td><td>...</td><td>2021.61</td><td>46.21</td><td>0.4820</td><td>1176.08</td><td>46.20</td><td>0.1489</td><td>840.70</td><td>46.18</td><td>0.0659</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2287.96</td><td>46.01</td><td>0.4848</td><td>1329.35</td><td>46.00</td><td>0.1517</td><td>948.41</td><td>45.99</td><td>0.0686</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2550.21</td><td>45.85</td><td>0.4868</td><td>1480.93</td><td>45.84</td><td>0.1539</td><td>1055.32</td><td>45.83</td><td>0.0708</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2800.07</td><td>45.76</td><td>0.4877</td><td>1628.28</td><td>45.73</td><td>0.1554</td><td>1160.51</td><td>45.70</td><td>0.0726</td></tr></tbody></table>
<table><caption>Modèle # 5, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 34574 K, log g = 5.93, âge = 71.77 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>42.64</td><td>41.31</td><td>44.47</td><td>41.38</td><td>0.0193</td><td>43.00</td><td>41.32</td><td>0.0166</td><td>41.75</td><td>41.28</td><td>0.0156</td></tr><tr><td>9</td><td>46.31</td><td>41.45</td><td>48.45</td><td>41.53</td><td>0.0207</td><td>46.73</td><td>41.46</td><td>0.0185</td><td>45.27</td><td>41.41</td><td>0.0177</td></tr><tr><td>8</td><td>50.63</td><td>41.62</td><td>53.17</td><td>41.73</td><td>0.0226</td><td>51.12</td><td>41.64</td><td>0.0209</td><td>49.39</td><td>41.57</td><td>0.0199</td></tr><tr><td>7</td><td>55.80</td><td>41.84</td><td>58.91</td><td>41.98</td><td>0.0251</td><td>56.38</td><td>41.87</td><td>0.0243</td><td>54.31</td><td>41.78</td><td>0.0230</td></tr><tr><td>6</td><td>62.18</td><td>42.13</td><td>66.08</td><td>42.30</td><td>0.0278</td><td>62.88</td><td>42.16</td><td>0.0287</td><td>60.33</td><td>42.05</td><td>0.0273</td></tr><tr><td>5</td><td>70.24</td><td>42.48</td><td>75.24</td><td>42.69</td><td>0.0311</td><td>71.08</td><td>42.51</td><td>0.0343</td><td>67.90</td><td>42.38</td><td>0.0327</td></tr><tr><td>4</td><td>80.80</td><td>42.91</td><td>87.57</td><td>43.16</td><td>0.0350</td><td>81.87</td><td>42.95</td><td>0.0430</td><td>77.71</td><td>42.78</td><td>0.0412</td></tr><tr><td>3</td><td>95.52</td><td>43.40</td><td>104.79</td><td>43.67</td><td>0.0359</td><td>96.96</td><td>43.45</td><td>0.0571</td><td>91.26</td><td>43.27</td><td>0.0561</td></tr><tr><td>2</td><td>116.18</td><td>43.95</td><td>129.58</td><td>44.25</td><td>0.0322</td><td>118.56</td><td>44.00</td><td>0.0842</td><td>110.47</td><td>43.80</td><td>0.0796</td></tr><tr><td>1</td><td>144.06</td><td>44.63</td><td>165.26</td><td>45.14</td><td>0.0270</td><td>148.82</td><td>44.72</td><td>0.1419</td><td>138.07</td><td>44.44</td><td>0.1110</td></tr><tr><td>0</td><td>179.57</td><td>45.68</td><td>...</td><td>...</td><td>...</td><td>187.77</td><td>46.01</td><td>0.2580</td><td>176.33</td><td>45.52</td><td>0.1261</td></tr><tr><td>1</td><td>...</td><td>...</td><td>413.97</td><td>48.49</td><td>0.4591</td><td>269.80</td><td>47.70</td><td>0.1421</td><td>217.52</td><td>47.12</td><td>0.0564</td></tr><tr><td>2</td><td>...</td><td>...</td><td>663.69</td><td>48.03</td><td>0.4542</td><td>402.15</td><td>47.76</td><td>0.1240</td><td>303.03</td><td>47.48</td><td>0.0404</td></tr><tr><td>3</td><td>...</td><td>...</td><td>951.50</td><td>47.62</td><td>0.4578</td><td>565.17</td><td>47.51</td><td>0.1256</td><td>415.74</td><td>47.39</td><td>0.0432</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1243.13</td><td>47.17</td><td>0.4656</td><td>731.31</td><td>47.12</td><td>0.1329</td><td>530.96</td><td>47.05</td><td>0.0502</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1519.72</td><td>46.76</td><td>0.4721</td><td>889.25</td><td>46.73</td><td>0.1392</td><td>640.78</td><td>46.68</td><td>0.0564</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1784.84</td><td>46.47</td><td>0.4798</td><td>1041.85</td><td>46.45</td><td>0.1445</td><td>747.71</td><td>46.42</td><td>0.0617</td></tr><tr><td>7</td><td>...</td><td>...</td><td>2031.97</td><td>46.35</td><td>0.4801</td><td>1188.68</td><td>46.29</td><td>0.1483</td><td>852.79</td><td>46.25</td><td>0.0657</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2198.19</td><td>46.41</td><td>0.4807</td><td>1295.84</td><td>46.39</td><td>0.1503</td><td>937.17</td><td>46.32</td><td>0.0688</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2389.53</td><td>46.04</td><td>0.4849</td><td>1392.65</td><td>46.06</td><td>0.1523</td><td>998.40</td><td>46.10</td><td>0.0699</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2646.39</td><td>45.84</td><td>0.4874</td><td>1536.12</td><td>45.84</td><td>0.1543</td><td>1094.65</td><td>45.83</td><td>0.0712</td></tr></tbody></table>

<table><caption>Modèle # 6, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 34831 K, log g = 5.92, âge = 81.82 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>43.86</td><td>41.29</td><td>45.73</td><td>41.35</td><td>0.0192</td><td>44.22</td><td>41.30</td><td>0.0165</td><td>42.92</td><td>41.26</td><td>0.0158</td></tr><tr><td>9</td><td>47.65</td><td>41.42</td><td>49.82</td><td>41.50</td><td>0.0204</td><td>48.06</td><td>41.44</td><td>0.0185</td><td>46.54</td><td>41.38</td><td>0.0179</td></tr><tr><td>8</td><td>52.08</td><td>41.59</td><td>54.68</td><td>41.70</td><td>0.0221</td><td>52.56</td><td>41.61</td><td>0.0209</td><td>50.77</td><td>41.54</td><td>0.0202</td></tr><tr><td>7</td><td>57.41</td><td>41.81</td><td>60.57</td><td>41.95</td><td>0.0243</td><td>57.97</td><td>41.84</td><td>0.0244</td><td>55.83</td><td>41.75</td><td>0.0234</td></tr><tr><td>6</td><td>63.95</td><td>42.10</td><td>67.93</td><td>42.26</td><td>0.0267</td><td>64.63</td><td>42.13</td><td>0.0289</td><td>62.00</td><td>42.01</td><td>0.0277</td></tr><tr><td>5</td><td>72.22</td><td>42.44</td><td>77.33</td><td>42.65</td><td>0.0296</td><td>73.04</td><td>42.48</td><td>0.0346</td><td>69.76</td><td>42.34</td><td>0.0332</td></tr><tr><td>4</td><td>83.04</td><td>42.87</td><td>89.97</td><td>43.12</td><td>0.0330</td><td>84.09</td><td>42.91</td><td>0.0437</td><td>79.82</td><td>42.75</td><td>0.0418</td></tr><tr><td>3</td><td>98.09</td><td>43.37</td><td>107.68</td><td>43.63</td><td>0.0334</td><td>99.56</td><td>43.41</td><td>0.0588</td><td>93.69</td><td>43.24</td><td>0.0571</td></tr><tr><td>2</td><td>119.15</td><td>43.92</td><td>133.19</td><td>44.22</td><td>0.0297</td><td>121.65</td><td>43.97</td><td>0.0882</td><td>113.39</td><td>43.77</td><td>0.0807</td></tr><tr><td>1</td><td>147.40</td><td>44.58</td><td>169.82</td><td>45.10</td><td>0.0250</td><td>152.40</td><td>44.67</td><td>0.1493</td><td>141.66</td><td>44.40</td><td>0.1108</td></tr><tr><td>0</td><td>183.14</td><td>45.59</td><td>...</td><td>...</td><td>...</td><td>189.86</td><td>45.90</td><td>0.2271</td><td>179.52</td><td>45.47</td><td>0.1026</td></tr><tr><td>1</td><td>...</td><td>...</td><td>402.34</td><td>48.46</td><td>0.4706</td><td>261.89</td><td>47.54</td><td>0.1582</td><td>210.76</td><td>46.77</td><td>0.0755</td></tr><tr><td>2</td><td>...</td><td>...</td><td>661.75</td><td>48.02</td><td>0.4551</td><td>401.03</td><td>47.73</td><td>0.1249</td><td>302.42</td><td>47.42</td><td>0.0407</td></tr><tr><td>3</td><td>...</td><td>...</td><td>954.52</td><td>47.62</td><td>0.4577</td><td>567.27</td><td>47.51</td><td>0.1255</td><td>417.57</td><td>47.39</td><td>0.0430</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1247.94</td><td>47.20</td><td>0.4652</td><td>734.87</td><td>47.13</td><td>0.1327</td><td>534.01</td><td>47.06</td><td>0.0501</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1518.49</td><td>46.82</td><td>0.4716</td><td>890.91</td><td>46.78</td><td>0.1389</td><td>643.25</td><td>46.72</td><td>0.0563</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1727.46</td><td>46.79</td><td>0.4876</td><td>1020.62</td><td>46.70</td><td>0.1447</td><td>739.30</td><td>46.60</td><td>0.0626</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1877.96</td><td>46.55</td><td>0.4791</td><td>1102.99</td><td>46.58</td><td>0.1478</td><td>798.00</td><td>46.62</td><td>0.0666</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2119.65</td><td>46.23</td><td>0.4825</td><td>1233.80</td><td>46.22</td><td>0.1496</td><td>882.66</td><td>46.22</td><td>0.0668</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2389.46</td><td>46.02</td><td>0.4852</td><td>1387.80</td><td>46.01</td><td>0.1520</td><td>989.84</td><td>46.00</td><td>0.0689</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2662.51</td><td>45.85</td><td>0.4874</td><td>1544.61</td><td>45.84</td><td>0.1542</td><td>1099.87</td><td>45.84</td><td>0.0710</td></tr></tbody></table>
<table><caption>Modèle # 7, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 35156 K, log g = 5.91, âge = 89.23 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>44.41</td><td>41.28</td><td>46.32</td><td>41.34</td><td>0.0195</td><td>44.77</td><td>41.29</td><td>0.0171</td><td>43.44</td><td>41.24</td><td>0.0162</td></tr><tr><td>9</td><td>48.25</td><td>41.41</td><td>50.47</td><td>41.49</td><td>0.0208</td><td>48.65</td><td>41.42</td><td>0.0191</td><td>47.10</td><td>41.37</td><td>0.0184</td></tr><tr><td>8</td><td>52.75</td><td>41.57</td><td>55.38</td><td>41.68</td><td>0.0224</td><td>53.21</td><td>41.59</td><td>0.0216</td><td>51.39</td><td>41.52</td><td>0.0206</td></tr><tr><td>7</td><td>58.14</td><td>41.79</td><td>61.35</td><td>41.93</td><td>0.0247</td><td>58.67</td><td>41.82</td><td>0.0251</td><td>56.50</td><td>41.72</td><td>0.0237</td></tr><tr><td>6</td><td>64.78</td><td>42.08</td><td>68.80</td><td>42.24</td><td>0.0271</td><td>65.40</td><td>42.10</td><td>0.0297</td><td>62.73</td><td>41.99</td><td>0.0281</td></tr><tr><td>5</td><td>73.17</td><td>42.42</td><td>78.31</td><td>42.63</td><td>0.0299</td><td>73.90</td><td>42.46</td><td>0.0355</td><td>70.59</td><td>42.32</td><td>0.0337</td></tr><tr><td>4</td><td>84.14</td><td>42.85</td><td>91.07</td><td>43.10</td><td>0.0331</td><td>85.05</td><td>42.89</td><td>0.0448</td><td>80.75</td><td>42.72</td><td>0.0423</td></tr><tr><td>3</td><td>99.40</td><td>43.36</td><td>108.97</td><td>43.62</td><td>0.0331</td><td>100.66</td><td>43.39</td><td>0.0606</td><td>94.75</td><td>43.21</td><td>0.0577</td></tr><tr><td>2</td><td>120.77</td><td>43.91</td><td>134.82</td><td>44.20</td><td>0.0293</td><td>122.93</td><td>43.94</td><td>0.0915</td><td>114.63</td><td>43.75</td><td>0.0813</td></tr><tr><td>1</td><td>149.39</td><td>44.57</td><td>171.91</td><td>45.07</td><td>0.0247</td><td>153.79</td><td>44.65</td><td>0.1543</td><td>143.21</td><td>44.38</td><td>0.1105</td></tr><tr><td>0</td><td>185.35</td><td>45.57</td><td>...</td><td>...</td><td>...</td><td>190.39</td><td>45.82</td><td>0.2090</td><td>180.82</td><td>45.43</td><td>0.0911</td></tr><tr><td>1</td><td>...</td><td>...</td><td>399.86</td><td>48.43</td><td>0.4719</td><td>260.92</td><td>47.47</td><td>0.1615</td><td>210.38</td><td>46.64</td><td>0.0809</td></tr><tr><td>2</td><td>...</td><td>...</td><td>660.73</td><td>48.03</td><td>0.4548</td><td>401.10</td><td>47.71</td><td>0.1251</td><td>302.73</td><td>47.40</td><td>0.0412</td></tr><tr><td>3</td><td>...</td><td>...</td><td>952.11</td><td>47.63</td><td>0.4573</td><td>566.50</td><td>47.52</td><td>0.1254</td><td>417.40</td><td>47.38</td><td>0.0431</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1232.46</td><td>47.78</td><td>0.7286</td><td>730.32</td><td>47.17</td><td>0.1327</td><td>531.78</td><td>47.09</td><td>0.0503</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1461.30</td><td>47.11</td><td>0.4716</td><td>865.11</td><td>47.00</td><td>0.1405</td><td>629.30</td><td>46.90</td><td>0.0584</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1619.60</td><td>46.83</td><td>0.4758</td><td>952.99</td><td>46.84</td><td>0.1450</td><td>690.61</td><td>46.83</td><td>0.0639</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1853.27</td><td>46.46</td><td>0.4790</td><td>1080.75</td><td>46.45</td><td>0.1463</td><td>775.10</td><td>46.43</td><td>0.0636</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2121.12</td><td>46.23</td><td>0.4825</td><td>1233.63</td><td>46.21</td><td>0.1494</td><td>881.58</td><td>46.20</td><td>0.0663</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2394.65</td><td>46.03</td><td>0.4852</td><td>1390.67</td><td>46.02</td><td>0.1520</td><td>991.74</td><td>46.01</td><td>0.0689</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2665.97</td><td>45.87</td><td>0.4874</td><td>1546.84</td><td>45.86</td><td>0.1543</td><td>1101.58</td><td>45.85</td><td>0.0711</td></tr></tbody></table>

<table><caption>Modèle # 8, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 35538 K, log g = 5.91, âge = 94.80 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>44.40</td><td>41.26</td><td>46.27</td><td>41.33</td><td>0.0189</td><td>44.74</td><td>41.28</td><td>0.0164</td><td>43.41</td><td>41.23</td><td>0.0161</td></tr><tr><td>9</td><td>48.23</td><td>41.39</td><td>50.41</td><td>41.47</td><td>0.0199</td><td>48.62</td><td>41.41</td><td>0.0185</td><td>47.07</td><td>41.35</td><td>0.0183</td></tr><tr><td>8</td><td>52.73</td><td>41.56</td><td>55.32</td><td>41.66</td><td>0.0212</td><td>53.17</td><td>41.58</td><td>0.0210</td><td>51.35</td><td>41.51</td><td>0.0206</td></tr><tr><td>7</td><td>58.10</td><td>41.78</td><td>61.27</td><td>41.91</td><td>0.0231</td><td>58.63</td><td>41.80</td><td>0.0245</td><td>56.45</td><td>41.71</td><td>0.0238</td></tr><tr><td>6</td><td>64.71</td><td>42.06</td><td>68.71</td><td>42.23</td><td>0.0252</td><td>65.35</td><td>42.09</td><td>0.0293</td><td>62.67</td><td>41.97</td><td>0.0282</td></tr><tr><td>5</td><td>73.06</td><td>42.41</td><td>78.22</td><td>42.62</td><td>0.0275</td><td>73.84</td><td>42.44</td><td>0.0353</td><td>70.51</td><td>42.30</td><td>0.0339</td></tr><tr><td>4</td><td>83.95</td><td>42.84</td><td>90.97</td><td>43.09</td><td>0.0302</td><td>84.97</td><td>42.88</td><td>0.0450</td><td>80.66</td><td>42.71</td><td>0.0426</td></tr><tr><td>3</td><td>99.07</td><td>43.34</td><td>108.86</td><td>43.60</td><td>0.0301</td><td>100.54</td><td>43.38</td><td>0.0614</td><td>94.62</td><td>43.20</td><td>0.0582</td></tr><tr><td>2</td><td>120.10</td><td>43.89</td><td>134.70</td><td>44.19</td><td>0.0266</td><td>122.72</td><td>43.93</td><td>0.0939</td><td>114.45</td><td>43.73</td><td>0.0818</td></tr><tr><td>1</td><td>148.15</td><td>44.53</td><td>171.78</td><td>45.06</td><td>0.0228</td><td>153.23</td><td>44.63</td><td>0.1586</td><td>142.86</td><td>44.36</td><td>0.1095</td></tr><tr><td>0</td><td>183.73</td><td>45.50</td><td>...</td><td>...</td><td>...</td><td>187.83</td><td>45.75</td><td>0.1801</td><td>177.99</td><td>45.44</td><td>0.0558</td></tr><tr><td>1</td><td>...</td><td>...</td><td>378.41</td><td>48.40</td><td>0.4862</td><td>246.58</td><td>47.27</td><td>0.1844</td><td>199.24</td><td>46.20</td><td>0.1170</td></tr><tr><td>2</td><td>...</td><td>...</td><td>643.87</td><td>48.03</td><td>0.4560</td><td>390.64</td><td>47.70</td><td>0.1259</td><td>295.15</td><td>47.36</td><td>0.0414</td></tr><tr><td>3</td><td>...</td><td>...</td><td>932.58</td><td>47.65</td><td>0.4573</td><td>555.09</td><td>47.53</td><td>0.1254</td><td>409.26</td><td>47.39</td><td>0.0429</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1207.94</td><td>47.32</td><td>0.4647</td><td>714.72</td><td>47.23</td><td>0.1328</td><td>521.25</td><td>47.13</td><td>0.0506</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1386.58</td><td>47.31</td><td>0.4722</td><td>824.41</td><td>47.25</td><td>0.1422</td><td>602.78</td><td>47.15</td><td>0.0611</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1561.69</td><td>46.82</td><td>0.4791</td><td>915.56</td><td>46.79</td><td>0.1426</td><td>661.08</td><td>46.77</td><td>0.0609</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1814.69</td><td>46.48</td><td>0.4786</td><td>1057.77</td><td>46.46</td><td>0.1456</td><td>758.31</td><td>46.43</td><td>0.0626</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2082.19</td><td>46.25</td><td>0.4823</td><td>1211.00</td><td>46.24</td><td>0.1492</td><td>865.47</td><td>46.22</td><td>0.0661</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2350.55</td><td>46.06</td><td>0.4851</td><td>1365.23</td><td>46.05</td><td>0.1520</td><td>973.74</td><td>46.04</td><td>0.0688</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2610.39</td><td>45.92</td><td>0.4876</td><td>1515.13</td><td>45.91</td><td>0.1544</td><td>1079.34</td><td>45.90</td><td>0.0712</td></tr></tbody></table>
<table><caption>Modèle #9, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 35965 K, log g = 5.92, âge = 98.98 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>43.92</td><td>41.26</td><td>45.74</td><td>41.32</td><td>0.0185</td><td>44.24</td><td>41.27</td><td>0.0161</td><td>42.92</td><td>41.22</td><td>0.0160</td></tr><tr><td>9</td><td>47.71</td><td>41.39</td><td>49.84</td><td>41.46</td><td>0.0193</td><td>48.08</td><td>41.40</td><td>0.0181</td><td>46.54</td><td>41.35</td><td>0.0183</td></tr><tr><td>8</td><td>52.15</td><td>41.55</td><td>54.69</td><td>41.66</td><td>0.0205</td><td>52.58</td><td>41.57</td><td>0.0207</td><td>50.77</td><td>41.50</td><td>0.0207</td></tr><tr><td>7</td><td>57.45</td><td>41.77</td><td>60.57</td><td>41.91</td><td>0.0222</td><td>57.97</td><td>41.80</td><td>0.0243</td><td>55.81</td><td>41.70</td><td>0.0239</td></tr><tr><td>6</td><td>63.97</td><td>42.06</td><td>67.93</td><td>42.23</td><td>0.0241</td><td>64.61</td><td>42.09</td><td>0.0292</td><td>61.96</td><td>41.97</td><td>0.0284</td></tr><tr><td>5</td><td>72.21</td><td>42.40</td><td>77.33</td><td>42.61</td><td>0.0262</td><td>73.00</td><td>42.44</td><td>0.0353</td><td>69.70</td><td>42.30</td><td>0.0341</td></tr><tr><td>4</td><td>82.95</td><td>42.83</td><td>89.94</td><td>43.09</td><td>0.0287</td><td>84.00</td><td>42.87</td><td>0.0453</td><td>79.73</td><td>42.70</td><td>0.0429</td></tr><tr><td>3</td><td>97.82</td><td>43.33</td><td>107.63</td><td>43.60</td><td>0.0284</td><td>99.38</td><td>43.37</td><td>0.0621</td><td>93.53</td><td>43.19</td><td>0.0585</td></tr><tr><td>2</td><td>118.46</td><td>43.88</td><td>133.18</td><td>44.18</td><td>0.0251</td><td>121.26</td><td>43.93</td><td>0.0955</td><td>113.12</td><td>43.73</td><td>0.0820</td></tr><tr><td>1</td><td>145.90</td><td>44.52</td><td>169.89</td><td>45.06</td><td>0.0218</td><td>151.18</td><td>44.62</td><td>0.1613</td><td>141.09</td><td>44.36</td><td>0.1084</td></tr><tr><td>0</td><td>181.03</td><td>45.47</td><td>...</td><td>...</td><td>...</td><td>184.14</td><td>45.71</td><td>0.1603</td><td>173.47</td><td>45.47</td><td>0.0329</td></tr><tr><td>1</td><td>...</td><td>...</td><td>362.67</td><td>48.38</td><td>0.4946</td><td>236.56</td><td>47.14</td><td>0.1996</td><td>192.39</td><td>45.95</td><td>0.1405</td></tr><tr><td>2</td><td>...</td><td>...</td><td>627.87</td><td>48.03</td><td>0.4564</td><td>381.06</td><td>47.69</td><td>0.1262</td><td>288.23</td><td>47.34</td><td>0.0415</td></tr><tr><td>3</td><td>...</td><td>...</td><td>910.19</td><td>47.68</td><td>0.4571</td><td>542.24</td><td>47.55</td><td>0.1253</td><td>400.14</td><td>47.40</td><td>0.0428</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1163.54</td><td>47.46</td><td>0.4646</td><td>691.82</td><td>47.34</td><td>0.1338</td><td>506.39</td><td>47.22</td><td>0.0517</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1303.68</td><td>47.35</td><td>0.4716</td><td>774.14</td><td>47.34</td><td>0.1422</td><td>566.42</td><td>47.31</td><td>0.0619</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1518.03</td><td>46.80</td><td>0.4738</td><td>888.27</td><td>46.77</td><td>0.1411</td><td>640.12</td><td>46.74</td><td>0.0585</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1775.22</td><td>46.49</td><td>0.4783</td><td>1034.65</td><td>46.47</td><td>0.1452</td><td>741.68</td><td>46.44</td><td>0.0622</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2038.03</td><td>46.27</td><td>0.4823</td><td>1185.38</td><td>46.25</td><td>0.1491</td><td>847.23</td><td>46.24</td><td>0.0660</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2297.71</td><td>46.09</td><td>0.4853</td><td>1334.84</td><td>46.08</td><td>0.1520</td><td>952.27</td><td>46.07</td><td>0.0689</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2533.57</td><td>46.03</td><td>0.4882</td><td>1472.29</td><td>46.00</td><td>0.1551</td><td>1049.85</td><td>45.98</td><td>0.0719</td></tr></tbody></table>

<table><caption>Modèle #10, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 36396 K, log g = 5.93, âge = 102.26 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>43.16</td><td>41.25</td><td>44.94</td><td>41.31</td><td>0.0184</td><td>43.47</td><td>41.26</td><td>0.0160</td><td>42.17</td><td>41.22</td><td>0.0161</td></tr><tr><td>9</td><td>46.88</td><td>41.38</td><td>48.96</td><td>41.46</td><td>0.0191</td><td>47.23</td><td>41.40</td><td>0.0181</td><td>45.72</td><td>41.34</td><td>0.0183</td></tr><tr><td>8</td><td>51.23</td><td>41.55</td><td>53.72</td><td>41.65</td><td>0.0202</td><td>51.65</td><td>41.57</td><td>0.0206</td><td>49.87</td><td>41.49</td><td>0.0207</td></tr><tr><td>7</td><td>56.44</td><td>41.77</td><td>59.51</td><td>41.91</td><td>0.0219</td><td>56.95</td><td>41.80</td><td>0.0243</td><td>54.81</td><td>41.70</td><td>0.0240</td></tr><tr><td>6</td><td>62.85</td><td>42.06</td><td>66.73</td><td>42.23</td><td>0.0237</td><td>63.47</td><td>42.09</td><td>0.0292</td><td>60.86</td><td>41.97</td><td>0.0285</td></tr><tr><td>5</td><td>70.92</td><td>42.41</td><td>75.96</td><td>42.62</td><td>0.0258</td><td>71.71</td><td>42.44</td><td>0.0355</td><td>68.46</td><td>42.30</td><td>0.0342</td></tr><tr><td>4</td><td>81.47</td><td>42.84</td><td>88.37</td><td>43.09</td><td>0.0282</td><td>82.51</td><td>42.88</td><td>0.0456</td><td>78.31</td><td>42.71</td><td>0.0431</td></tr><tr><td>3</td><td>96.07</td><td>43.33</td><td>105.77</td><td>43.60</td><td>0.0278</td><td>97.62</td><td>43.37</td><td>0.0627</td><td>91.88</td><td>43.20</td><td>0.0587</td></tr><tr><td>2</td><td>116.30</td><td>43.88</td><td>130.84</td><td>44.18</td><td>0.0244</td><td>119.08</td><td>43.92</td><td>0.0964</td><td>111.12</td><td>43.73</td><td>0.0821</td></tr><tr><td>1</td><td>143.13</td><td>44.51</td><td>166.94</td><td>45.06</td><td>0.0214</td><td>148.31</td><td>44.62</td><td>0.1627</td><td>138.49</td><td>44.36</td><td>0.1076</td></tr><tr><td>0</td><td>177.70</td><td>45.46</td><td>...</td><td>...</td><td>...</td><td>180.10</td><td>45.70</td><td>0.1500</td><td>168.88</td><td>45.49</td><td>0.0236</td></tr><tr><td>1</td><td>...</td><td>...</td><td>351.75</td><td>48.37</td><td>0.4986</td><td>229.39</td><td>47.08</td><td>0.2071</td><td>187.37</td><td>45.85</td><td>0.1500</td></tr><tr><td>2</td><td>...</td><td>...</td><td>614.00</td><td>48.03</td><td>0.4564</td><td>372.64</td><td>47.69</td><td>0.1262</td><td>281.94</td><td>47.33</td><td>0.0414</td></tr><tr><td>3</td><td>...</td><td>...</td><td>890.53</td><td>47.69</td><td>0.4571</td><td>530.55</td><td>47.56</td><td>0.1253</td><td>391.55</td><td>47.41</td><td>0.0428</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1134.37</td><td>47.51</td><td>0.4650</td><td>674.86</td><td>47.38</td><td>0.1345</td><td>494.27</td><td>47.26</td><td>0.0524</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1269.30</td><td>47.35</td><td>0.4716</td><td>752.54</td><td>47.34</td><td>0.1421</td><td>549.77</td><td>47.32</td><td>0.0618</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1486.71</td><td>46.81</td><td>0.4736</td><td>869.73</td><td>46.78</td><td>0.1409</td><td>626.60</td><td>46.74</td><td>0.0582</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1739.62</td><td>46.50</td><td>0.4783</td><td>1013.87</td><td>46.48</td><td>0.1451</td><td>726.77</td><td>46.45</td><td>0.0621</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1996.83</td><td>46.27</td><td>0.4827</td><td>1161.41</td><td>46.26</td><td>0.1490</td><td>830.09</td><td>46.24</td><td>0.0659</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2250.58</td><td>46.09</td><td>0.4887</td><td>1307.48</td><td>46.09</td><td>0.1520</td><td>932.77</td><td>46.07</td><td>0.0689</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2478.44</td><td>46.05</td><td>0.4886</td><td>1440.58</td><td>46.02</td><td>0.1552</td><td>1027.40</td><td>46.00</td><td>0.0720</td></tr></tbody></table>
<table><caption>Modèle #11, $M = 0.4690 + 0.0001 M_\odot$, $T_{\text{eff}} = 36842$ K, $\log g = 5.94$, âge = 104.84 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>42.17</td><td>41.25</td><td>43.93</td><td>41.31</td><td>0.0188</td><td>42.47</td><td>41.26</td><td>0.0166</td><td>41.20</td><td>41.22</td><td>0.0163</td></tr><tr><td>9</td><td>45.80</td><td>41.38</td><td>47.86</td><td>41.46</td><td>0.0197</td><td>46.15</td><td>41.40</td><td>0.0187</td><td>44.66</td><td>41.34</td><td>0.0186</td></tr><tr><td>8</td><td>50.06</td><td>41.55</td><td>52.51</td><td>41.66</td><td>0.0209</td><td>50.46</td><td>41.57</td><td>0.0213</td><td>48.72</td><td>41.50</td><td>0.0209</td></tr><tr><td>7</td><td>55.16</td><td>41.78</td><td>58.16</td><td>41.92</td><td>0.0228</td><td>55.62</td><td>41.80</td><td>0.0250</td><td>53.54</td><td>41.70</td><td>0.0242</td></tr><tr><td>6</td><td>61.44</td><td>42.07</td><td>65.23</td><td>42.24</td><td>0.0247</td><td>62.00</td><td>42.09</td><td>0.0299</td><td>59.45</td><td>41.97</td><td>0.0286</td></tr><tr><td>5</td><td>69.37</td><td>42.42</td><td>74.26</td><td>42.63</td><td>0.0269</td><td>70.05</td><td>42.45</td><td>0.0362</td><td>66.88</td><td>42.31</td><td>0.0344</td></tr><tr><td>4</td><td>79.73</td><td>42.85</td><td>86.40</td><td>43.10</td><td>0.0295</td><td>80.61</td><td>42.88</td><td>0.0463</td><td>76.51</td><td>42.71</td><td>0.0431</td></tr><tr><td>3</td><td>94.09</td><td>43.34</td><td>103.38</td><td>43.61</td><td>0.0292</td><td>95.36</td><td>43.38</td><td>0.0632</td><td>89.78</td><td>43.20</td><td>0.0586</td></tr><tr><td>2</td><td>114.03</td><td>43.89</td><td>127.86</td><td>44.19</td><td>0.0256</td><td>116.32</td><td>43.93</td><td>0.0967</td><td>108.59</td><td>43.73</td><td>0.0820</td></tr><tr><td>1</td><td>140.46</td><td>44.53</td><td>163.19</td><td>45.07</td><td>0.0222</td><td>144.87</td><td>44.63</td><td>0.1625</td><td>135.35</td><td>44.36</td><td>0.1079</td></tr><tr><td>0</td><td>174.42</td><td>45.50</td><td>...</td><td>...</td><td>...</td><td>176.60</td><td>45.71</td><td>0.1559</td><td>166.76</td><td>45.48</td><td>0.0329</td></tr><tr><td>1</td><td>...</td><td>...</td><td>347.67</td><td>48.39</td><td>0.4927</td><td>227.33</td><td>47.15</td><td>0.1972</td><td>185.13</td><td>45.98</td><td>0.1380</td></tr><tr><td>2</td><td>...</td><td>...</td><td>601.23</td><td>48.05</td><td>0.4554</td><td>365.47</td><td>47.70</td><td>0.1257</td><td>276.61</td><td>47.35</td><td>0.0413</td></tr><tr><td>3</td><td>...</td><td>...</td><td>868.11</td><td>47.71</td><td>0.4569</td><td>517.74</td><td>47.58</td><td>0.1253</td><td>382.42</td><td>47.43</td><td>0.0430</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1092.64</td><td>47.60</td><td>0.4684</td><td>651.03</td><td>47.46</td><td>0.1356</td><td>477.56</td><td>47.34</td><td>0.0539</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1238.53</td><td>47.29</td><td>0.4718</td><td>732.00</td><td>47.28</td><td>0.1411</td><td>533.23</td><td>47.24</td><td>0.0603</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1460.47</td><td>46.81</td><td>0.4737</td><td>854.30</td><td>46.78</td><td>0.1410</td><td>615.36</td><td>46.74</td><td>0.0582</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1706.46</td><td>46.50</td><td>0.4783</td><td>994.63</td><td>46.48</td><td>0.1452</td><td>713.01</td><td>46.45</td><td>0.0622</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1953.59</td><td>46.29</td><td>0.4824</td><td>1136.54</td><td>46.27</td><td>0.1493</td><td>812.46</td><td>46.26</td><td>0.0662</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2186.85</td><td>46.16</td><td>0.4859</td><td>1271.48</td><td>46.15</td><td>0.1528</td><td>907.66</td><td>46.13</td><td>0.0697</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2368.49</td><td>46.18</td><td>0.4887</td><td>1378.40</td><td>46.16</td><td>0.1561</td><td>984.26</td><td>46.14</td><td>0.0732</td></tr></tbody></table>

<table><caption>Modèle #12, $M = 0.4690 + 0.0001 M_\odot$, $T_{\text{eff}} = 37312$ K, $\log g = 5.96$, âge = 106.88 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>41.04</td><td>41.25</td><td>42.75</td><td>41.31</td><td>0.0187</td><td>41.33</td><td>41.26</td><td>0.0166</td><td>40.09</td><td>41.22</td><td>0.0164</td></tr><tr><td>9</td><td>44.57</td><td>41.38</td><td>46.56</td><td>41.46</td><td>0.0196</td><td>44.90</td><td>41.40</td><td>0.0187</td><td>43.45</td><td>41.34</td><td>0.0186</td></tr><tr><td>8</td><td>48.71</td><td>41.55</td><td>51.09</td><td>41.66</td><td>0.0208</td><td>49.09</td><td>41.57</td><td>0.0213</td><td>47.39</td><td>41.50</td><td>0.0209</td></tr><tr><td>7</td><td>53.67</td><td>41.78</td><td>56.59</td><td>41.92</td><td>0.0227</td><td>54.12</td><td>41.81</td><td>0.0250</td><td>52.09</td><td>41.71</td><td>0.0242</td></tr><tr><td>6</td><td>59.78</td><td>42.08</td><td>63.47</td><td>42.24</td><td>0.0246</td><td>60.32</td><td>42.10</td><td>0.0300</td><td>57.83</td><td>41.98</td><td>0.0287</td></tr><tr><td>5</td><td>67.49</td><td>42.43</td><td>72.26</td><td>42.64</td><td>0.0268</td><td>68.15</td><td>42.46</td><td>0.0363</td><td>65.07</td><td>42.32</td><td>0.0344</td></tr><tr><td>4</td><td>77.58</td><td>42.86</td><td>84.10</td><td>43.11</td><td>0.0294</td><td>78.44</td><td>42.89</td><td>0.0465</td><td>74.44</td><td>42.73</td><td>0.0432</td></tr><tr><td>3</td><td>91.57</td><td>43.35</td><td>100.63</td><td>43.62</td><td>0.0290</td><td>92.80</td><td>43.39</td><td>0.0634</td><td>87.38</td><td>43.21</td><td>0.0586</td></tr><tr><td>2</td><td>110.97</td><td>43.90</td><td>124.41</td><td>44.19</td><td>0.0255</td><td>113.18</td><td>43.94</td><td>0.0967</td><td>105.68</td><td>43.74</td><td>0.0820</td></tr><tr><td>1</td><td>136.65</td><td>44.54</td><td>158.86</td><td>45.08</td><td>0.0222</td><td>140.91</td><td>44.64</td><td>0.1627</td><td>131.67</td><td>44.37</td><td>0.1077</td></tr><tr><td>0</td><td>169.84</td><td>45.51</td><td>...</td><td>...</td><td>...</td><td>171.76</td><td>45.72</td><td>0.1531</td><td>161.91</td><td>45.50</td><td>0.0298</td></tr><tr><td>1</td><td>...</td><td>...</td><td>336.70</td><td>48.40</td><td>0.4943</td><td>220.23</td><td>47.14</td><td>0.2002</td><td>179.62</td><td>45.95</td><td>0.1421</td></tr><tr><td>2</td><td>...</td><td>...</td><td>584.80</td><td>48.06</td><td>0.4551</td><td>355.54</td><td>47.71</td><td>0.1254</td><td>269.18</td><td>47.36</td><td>0.0409</td></tr><tr><td>3</td><td>...</td><td>...</td><td>844.04</td><td>47.72</td><td>0.4568</td><td>503.44</td><td>47.59</td><td>0.1252</td><td>371.91</td><td>47.44</td><td>0.0430</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1059.67</td><td>47.63</td><td>0.4689</td><td>631.35</td><td>47.50</td><td>0.1360</td><td>463.15</td><td>47.38</td><td>0.0544</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1203.75</td><td>47.30</td><td>0.4715</td><td>710.95</td><td>47.28</td><td>0.1409</td><td>517.52</td><td>47.24</td><td>0.0599</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1422.36</td><td>46.82</td><td>0.4736</td><td>831.98</td><td>46.79</td><td>0.1409</td><td>599.26</td><td>46.75</td><td>0.0581</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1661.37</td><td>46.51</td><td>0.4783</td><td>968.37</td><td>46.49</td><td>0.1452</td><td>694.19</td><td>46.46</td><td>0.0622</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1899.73</td><td>46.30</td><td>0.4824</td><td>1105.24</td><td>46.29</td><td>0.1493</td><td>790.10</td><td>46.27</td><td>0.0663</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2121.96</td><td>46.19</td><td>0.4861</td><td>1233.79</td><td>46.17</td><td>0.1531</td><td>880.76</td><td>46.15</td><td>0.0700</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2297.25</td><td>46.17</td><td>0.4887</td><td>1336.32</td><td>46.15</td><td>0.1560</td><td>953.83</td><td>46.14</td><td>0.0731</td></tr></tbody></table>
<table><caption>Modèle #13, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 37797 K, log g = 5.97, âge = 108.49 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>39.81</td><td>41.25</td><td>41.46</td><td>41.32</td><td>0.0187</td><td>40.09</td><td>41.26</td><td>0.0165</td><td>38.89</td><td>41.22</td><td>0.0163</td></tr><tr><td>9</td><td>43.23</td><td>41.38</td><td>45.16</td><td>41.47</td><td>0.0195</td><td>43.55</td><td>41.40</td><td>0.0186</td><td>42.15</td><td>41.34</td><td>0.0186</td></tr><tr><td>8</td><td>47.24</td><td>41.56</td><td>49.54</td><td>41.67</td><td>0.0208</td><td>47.61</td><td>41.58</td><td>0.0212</td><td>45.96</td><td>41.50</td><td>0.0209</td></tr><tr><td>7</td><td>52.05</td><td>41.79</td><td>54.88</td><td>41.93</td><td>0.0226</td><td>52.48</td><td>41.82</td><td>0.0249</td><td>50.51</td><td>41.72</td><td>0.0242</td></tr><tr><td>6</td><td>57.98</td><td>42.09</td><td>61.56</td><td>42.26</td><td>0.0245</td><td>58.50</td><td>42.11</td><td>0.0299</td><td>56.09</td><td>41.99</td><td>0.0287</td></tr><tr><td>5</td><td>65.46</td><td>42.44</td><td>70.10</td><td>42.65</td><td>0.0267</td><td>66.10</td><td>42.47</td><td>0.0363</td><td>63.11</td><td>42.33</td><td>0.0344</td></tr><tr><td>4</td><td>75.26</td><td>42.87</td><td>81.60</td><td>43.12</td><td>0.0292</td><td>76.10</td><td>42.91</td><td>0.0466</td><td>72.21</td><td>42.74</td><td>0.0433</td></tr><tr><td>3</td><td>88.83</td><td>43.36</td><td>97.64</td><td>43.63</td><td>0.0290</td><td>90.04</td><td>43.40</td><td>0.0634</td><td>84.78</td><td>43.22</td><td>0.0585</td></tr><tr><td>2</td><td>107.65</td><td>43.90</td><td>120.67</td><td>44.20</td><td>0.0254</td><td>109.80</td><td>43.94</td><td>0.0964</td><td>102.53</td><td>43.75</td><td>0.0818</td></tr><tr><td>1</td><td>132.50</td><td>44.55</td><td>154.16</td><td>45.10</td><td>0.0222</td><td>136.66</td><td>44.65</td><td>0.1626</td><td>127.68</td><td>44.38</td><td>0.1074</td></tr><tr><td>0</td><td>164.87</td><td>45.53</td><td>...</td><td>...</td><td>...</td><td>166.65</td><td>45.74</td><td>0.1518</td><td>156.85</td><td>45.53</td><td>0.0279</td></tr><tr><td>1</td><td>...</td><td>...</td><td>326.35</td><td>48.40</td><td>0.4955</td><td>213.36</td><td>47.14</td><td>0.2026</td><td>174.10</td><td>45.95</td><td>0.1452</td></tr><tr><td>2</td><td>...</td><td>...</td><td>569.66</td><td>48.07</td><td>0.4547</td><td>346.29</td><td>47.72</td><td>0.1249</td><td>262.18</td><td>47.37</td><td>0.0404</td></tr><tr><td>3</td><td>...</td><td>...</td><td>821.19</td><td>47.73</td><td>0.4566</td><td>490.06</td><td>47.60</td><td>0.1251</td><td>362.14</td><td>47.45</td><td>0.0429</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1017.25</td><td>47.72</td><td>0.4679</td><td>607.33</td><td>47.60</td><td>0.1373</td><td>446.41</td><td>47.48</td><td>0.0562</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1159.06</td><td>47.30</td><td>0.4709</td><td>683.49</td><td>47.27</td><td>0.1398</td><td>496.90</td><td>47.22</td><td>0.0586</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1383.68</td><td>46.82</td><td>0.4734</td><td>809.07</td><td>46.79</td><td>0.1405</td><td>582.58</td><td>46.75</td><td>0.0576</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1620.04</td><td>46.50</td><td>0.4782</td><td>944.12</td><td>46.49</td><td>0.1450</td><td>676.70</td><td>46.46</td><td>0.0619</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1855.58</td><td>46.29</td><td>0.4823</td><td>1079.42</td><td>46.27</td><td>0.1491</td><td>771.56</td><td>46.25</td><td>0.0660</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2075.71</td><td>46.18</td><td>0.4859</td><td>1207.30</td><td>46.16</td><td>0.1529</td><td>862.05</td><td>46.14</td><td>0.0698</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2223.95</td><td>46.28</td><td>0.4889</td><td>1295.89</td><td>46.27</td><td>0.1567</td><td>926.50</td><td>46.25</td><td>0.0740</td></tr></tbody></table>

<table><caption>Modèle #14, M = 0.4690 + 0.0001 M⊙, T<sub>eff</sub> = 38267 K, log g = 5.99, âge = 109.75 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>38.58</td><td>41.25</td><td>40.18</td><td>41.32</td><td>0.0187</td><td>38.85</td><td>41.26</td><td>0.0165</td><td>37.68</td><td>41.22</td><td>0.0163</td></tr><tr><td>9</td><td>41.89</td><td>41.39</td><td>43.75</td><td>41.47</td><td>0.0195</td><td>42.20</td><td>41.40</td><td>0.0185</td><td>40.84</td><td>41.35</td><td>0.0185</td></tr><tr><td>8</td><td>45.77</td><td>41.57</td><td>48.00</td><td>41.68</td><td>0.0208</td><td>46.12</td><td>41.59</td><td>0.0212</td><td>44.53</td><td>41.51</td><td>0.0209</td></tr><tr><td>7</td><td>50.43</td><td>41.81</td><td>53.18</td><td>41.95</td><td>0.0226</td><td>50.85</td><td>41.83</td><td>0.0250</td><td>48.94</td><td>41.73</td><td>0.0242</td></tr><tr><td>6</td><td>56.18</td><td>42.10</td><td>59.65</td><td>42.27</td><td>0.0245</td><td>56.69</td><td>42.13</td><td>0.0299</td><td>54.35</td><td>42.01</td><td>0.0287</td></tr><tr><td>5</td><td>63.43</td><td>42.45</td><td>67.93</td><td>42.67</td><td>0.0268</td><td>64.06</td><td>42.49</td><td>0.0364</td><td>61.15</td><td>42.34</td><td>0.0344</td></tr><tr><td>4</td><td>72.95</td><td>42.89</td><td>79.11</td><td>43.14</td><td>0.0294</td><td>73.76</td><td>42.92</td><td>0.0467</td><td>69.98</td><td>42.76</td><td>0.0433</td></tr><tr><td>3</td><td>86.12</td><td>43.38</td><td>94.65</td><td>43.64</td><td>0.0292</td><td>87.27</td><td>43.41</td><td>0.0633</td><td>82.18</td><td>43.24</td><td>0.0584</td></tr><tr><td>2</td><td>104.38</td><td>43.92</td><td>116.93</td><td>44.21</td><td>0.0256</td><td>106.43</td><td>43.95</td><td>0.0959</td><td>99.39</td><td>43.76</td><td>0.0816</td></tr><tr><td>1</td><td>128.47</td><td>44.57</td><td>149.46</td><td>45.12</td><td>0.0224</td><td>132.45</td><td>44.66</td><td>0.1622</td><td>123.73</td><td>44.39</td><td>0.1074</td></tr><tr><td>0</td><td>160.03</td><td>45.55</td><td>...</td><td>...</td><td>...</td><td>161.80</td><td>45.76</td><td>0.1538</td><td>152.31</td><td>45.54</td><td>0.0295</td></tr><tr><td>1</td><td>...</td><td>...</td><td>317.04</td><td>48.41</td><td>0.4953</td><td>207.30</td><td>47.16</td><td>0.2022</td><td>169.09</td><td>45.97</td><td>0.1447</td></tr><tr><td>2</td><td>...</td><td>...</td><td>554.34</td><td>48.08</td><td>0.4541</td><td>337.05</td><td>47.73</td><td>0.1244</td><td>255.22</td><td>47.39</td><td>0.0399</td></tr><tr><td>3</td><td>...</td><td>...</td><td>797.65</td><td>47.75</td><td>0.4565</td><td>476.20</td><td>47.61</td><td>0.1251</td><td>351.99</td><td>47.47</td><td>0.0429</td></tr><tr><td>4</td><td>...</td><td>...</td><td>981.28</td><td>47.77</td><td>0.4688</td><td>585.94</td><td>47.65</td><td>0.1380</td><td>430.80</td><td>47.54</td><td>0.0571</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1124.96</td><td>47.30</td><td>0.4707</td><td>662.79</td><td>47.26</td><td>0.1393</td><td>481.43</td><td>47.21</td><td>0.0578</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1347.03</td><td>46.83</td><td>0.4734</td><td>787.55</td><td>46.80</td><td>0.1405</td><td>567.01</td><td>46.76</td><td>0.0576</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1577.10</td><td>46.51</td><td>0.4781</td><td>919.05</td><td>46.49</td><td>0.1450</td><td>658.69</td><td>46.46</td><td>0.0619</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1805.36</td><td>46.29</td><td>0.4823</td><td>1050.19</td><td>46.27</td><td>0.1491</td><td>750.63</td><td>46.26</td><td>0.0660</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2017.45</td><td>46.19</td><td>0.4860</td><td>1173.61</td><td>46.17</td><td>0.1530</td><td>838.09</td><td>46.14</td><td>0.0699</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2156.02</td><td>46.29</td><td>0.4888</td><td>1256.66</td><td>46.29</td><td>0.1567</td><td>898.75</td><td>46.27</td><td>0.0741</td></tr></tbody></table>
Modèle #15, $M = 0.4690 + 0.0001 M_\odot$, $T_{eff} = 38999$ K, $\log g = 6.02$, âge = 111.04 millions d'années depuis la ZAEHB

<table><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>36.86</td><td>41.26</td><td>38.37</td><td>41.32</td><td>0.0184</td><td>37.11</td><td>41.27</td><td>0.0162</td><td>36.00</td><td>41.22</td><td>0.0162</td></tr><tr><td>9</td><td>40.01</td><td>41.39</td><td>41.78</td><td>41.48</td><td>0.0192</td><td>40.30</td><td>41.41</td><td>0.0181</td><td>39.01</td><td>41.35</td><td>0.0184</td></tr><tr><td>8</td><td>43.71</td><td>41.58</td><td>45.83</td><td>41.69</td><td>0.0204</td><td>44.05</td><td>41.60</td><td>0.0208</td><td>42.53</td><td>41.52</td><td>0.0208</td></tr><tr><td>7</td><td>48.16</td><td>41.82</td><td>50.78</td><td>41.96</td><td>0.0221</td><td>48.57</td><td>41.84</td><td>0.0247</td><td>46.74</td><td>41.74</td><td>0.0242</td></tr><tr><td>6</td><td>53.65</td><td>42.12</td><td>56.96</td><td>42.29</td><td>0.0238</td><td>54.15</td><td>42.14</td><td>0.0297</td><td>51.91</td><td>42.02</td><td>0.0287</td></tr><tr><td>5</td><td>60.57</td><td>42.47</td><td>64.89</td><td>42.69</td><td>0.0261</td><td>61.19</td><td>42.51</td><td>0.0362</td><td>58.40</td><td>42.36</td><td>0.0344</td></tr><tr><td>4</td><td>69.66</td><td>42.91</td><td>75.61</td><td>43.16</td><td>0.0286</td><td>70.48</td><td>42.95</td><td>0.0468</td><td>66.86</td><td>42.78</td><td>0.0433</td></tr><tr><td>3</td><td>82.22</td><td>43.39</td><td>90.47</td><td>43.65</td><td>0.0285</td><td>83.41</td><td>43.43</td><td>0.0632</td><td>78.54</td><td>43.26</td><td>0.0583</td></tr><tr><td>2</td><td>99.60</td><td>43.93</td><td>111.69</td><td>44.23</td><td>0.0250</td><td>101.69</td><td>43.97</td><td>0.0954</td><td>94.99</td><td>43.78</td><td>0.0814</td></tr><tr><td>1</td><td>122.48</td><td>44.58</td><td>142.88</td><td>45.14</td><td>0.0221</td><td>126.50</td><td>44.68</td><td>0.1624</td><td>118.15</td><td>44.41</td><td>0.1069</td></tr><tr><td>0</td><td>152.84</td><td>45.57</td><td>...</td><td>...</td><td>...</td><td>154.37</td><td>45.79</td><td>0.1481</td><td>144.49</td><td>45.60</td><td>0.0229</td></tr><tr><td>1</td><td>...</td><td>...</td><td>299.75</td><td>48.42</td><td>0.4999</td><td>196.01</td><td>47.12</td><td>0.2108</td><td>160.51</td><td>45.91</td><td>0.1544</td></tr><tr><td>2</td><td>...</td><td>...</td><td>530.09</td><td>48.09</td><td>0.4538</td><td>322.24</td><td>47.75</td><td>0.1238</td><td>244.12</td><td>47.40</td><td>0.0392</td></tr><tr><td>3</td><td>...</td><td>...</td><td>763.01</td><td>47.76</td><td>0.4561</td><td>455.65</td><td>47.63</td><td>0.1248</td><td>336.87</td><td>47.48</td><td>0.0426</td></tr><tr><td>4</td><td>...</td><td>...</td><td>934.43</td><td>47.81</td><td>0.4665</td><td>559.25</td><td>47.69</td><td>0.1375</td><td>411.95</td><td>47.57</td><td>0.0568</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1071.31</td><td>47.32</td><td>0.4697</td><td>631.61</td><td>47.29</td><td>0.1386</td><td>459.24</td><td>47.24</td><td>0.0573</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1286.44</td><td>46.86</td><td>0.4732</td><td>752.30</td><td>46.83</td><td>0.1403</td><td>541.78</td><td>46.79</td><td>0.0574</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1506.31</td><td>46.53</td><td>0.4781</td><td>877.93</td><td>46.51</td><td>0.1449</td><td>629.32</td><td>46.48</td><td>0.0618</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1722.14</td><td>46.31</td><td>0.4822</td><td>1002.02</td><td>46.29</td><td>0.1491</td><td>716.33</td><td>46.27</td><td>0.0660</td></tr><tr><td>9</td><td>...</td><td>...</td><td>1918.56</td><td>46.24</td><td>0.4858</td><td>1117.25</td><td>46.20</td><td>0.1529</td><td>798.40</td><td>46.17</td><td>0.0699</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2045.80</td><td>46.29</td><td>0.4876</td><td>1194.25</td><td>46.29</td><td>0.1558</td><td>855.35</td><td>46.27</td><td>0.0734</td></tr></tbody></table>

Modèle #16, $M = 0.4690 + 0.0001 M_\odot$, $T_{eff} = 43489$ K, $\log g = 6.16$, âge = 112.97 millions d'années depuis la ZAEHB

<table><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>28.83</td><td>41.27</td><td>30.00</td><td>41.34</td><td>0.0177</td><td>29.02</td><td>41.28</td><td>0.0160</td><td>28.15</td><td>41.23</td><td>0.0162</td></tr><tr><td>9</td><td>31.28</td><td>41.43</td><td>32.65</td><td>41.52</td><td>0.0184</td><td>31.49</td><td>41.44</td><td>0.0181</td><td>30.48</td><td>41.37</td><td>0.0184</td></tr><tr><td>8</td><td>34.16</td><td>41.64</td><td>35.83</td><td>41.77</td><td>0.0197</td><td>34.41</td><td>41.66</td><td>0.0210</td><td>33.21</td><td>41.57</td><td>0.0209</td></tr><tr><td>7</td><td>37.65</td><td>41.90</td><td>39.71</td><td>42.05</td><td>0.0213</td><td>37.96</td><td>41.93</td><td>0.0250</td><td>36.51</td><td>41.82</td><td>0.0245</td></tr><tr><td>6</td><td>41.96</td><td>42.21</td><td>44.57</td><td>42.39</td><td>0.0230</td><td>42.33</td><td>42.24</td><td>0.0301</td><td>40.57</td><td>42.11</td><td>0.0290</td></tr><tr><td>5</td><td>47.41</td><td>42.58</td><td>50.85</td><td>42.80</td><td>0.0252</td><td>47.88</td><td>42.61</td><td>0.0373</td><td>45.67</td><td>42.46</td><td>0.0349</td></tr><tr><td>4</td><td>54.59</td><td>43.01</td><td>59.34</td><td>43.25</td><td>0.0276</td><td>55.23</td><td>43.05</td><td>0.0483</td><td>52.36</td><td>42.88</td><td>0.0439</td></tr><tr><td>3</td><td>64.41</td><td>43.47</td><td>70.97</td><td>43.73</td><td>0.0279</td><td>65.31</td><td>43.50</td><td>0.0642</td><td>61.54</td><td>43.34</td><td>0.0576</td></tr><tr><td>2</td><td>77.96</td><td>43.99</td><td>87.30</td><td>44.30</td><td>0.0246</td><td>79.49</td><td>44.03</td><td>0.0940</td><td>74.41</td><td>43.84</td><td>0.0797</td></tr><tr><td>1</td><td>95.80</td><td>44.67</td><td>112.35</td><td>45.27</td><td>0.0221</td><td>98.81</td><td>44.78</td><td>0.1641</td><td>92.30</td><td>44.50</td><td>0.1063</td></tr><tr><td>0</td><td>120.54</td><td>45.70</td><td>...</td><td>...</td><td>...</td><td>120.78</td><td>45.89</td><td>0.1308</td><td>112.18</td><td>45.78</td><td>0.0150</td></tr><tr><td>1</td><td>...</td><td>...</td><td>228.19</td><td>48.47</td><td>0.5039</td><td>150.88</td><td>47.09</td><td>0.2244</td><td>125.31</td><td>45.92</td><td>0.1652</td></tr><tr><td>2</td><td>...</td><td>...</td><td>409.82</td><td>48.21</td><td>0.4484</td><td>251.04</td><td>47.85</td><td>0.1206</td><td>191.24</td><td>47.51</td><td>0.0367</td></tr><tr><td>3</td><td>...</td><td>...</td><td>556.09</td><td>48.20</td><td>0.4488</td><td>342.05</td><td>47.93</td><td>0.1242</td><td>257.27</td><td>47.70</td><td>0.0439</td></tr><tr><td>4</td><td>...</td><td>...</td><td>645.13</td><td>47.88</td><td>0.4591</td><td>390.44</td><td>47.86</td><td>0.1316</td><td>292.18</td><td>47.82</td><td>0.0540</td></tr><tr><td>5</td><td>...</td><td>...</td><td>811.48</td><td>47.45</td><td>0.4660</td><td>479.58</td><td>47.38</td><td>0.1339</td><td>349.47</td><td>47.31</td><td>0.0519</td></tr><tr><td>6</td><td>...</td><td>...</td><td>962.79</td><td>47.38</td><td>0.4780</td><td>575.02</td><td>47.16</td><td>0.1402</td><td>418.81</td><td>47.02</td><td>0.0573</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1037.06</td><td>47.13</td><td>0.4764</td><td>618.80</td><td>47.26</td><td>0.1453</td><td>458.08</td><td>47.30</td><td>0.0650</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1190.85</td><td>46.64</td><td>0.4779</td><td>695.35</td><td>46.63</td><td>0.1450</td><td>499.94</td><td>46.61</td><td>0.0624</td></tr><tr><td>9</td><td>...</td><td>...</td><td>1354.97</td><td>46.39</td><td>0.4818</td><td>789.34</td><td>46.36</td><td>0.1487</td><td>564.93</td><td>46.34</td><td>0.0657</td></tr><tr><td>10</td><td>...</td><td>...</td><td>1490.90</td><td>46.44</td><td>0.4859</td><td>873.84</td><td>46.32</td><td>0.1532</td><td>626.91</td><td>46.24</td><td>0.0698</td></tr></tbody></table>
<table><caption>Modèle # 1, M = 0.4758 + 0.0002 M☉, T<sub>eff</sub> = 31463 K, log g = 5.90, âge = 1.79 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>46.76</td><td>40.50</td><td>49.10</td><td>40.45</td><td>0.0175</td><td>47.38</td><td>40.51</td><td>0.0225</td><td>45.72</td><td>40.44</td><td>0.0195</td></tr><tr><td>9</td><td>50.58</td><td>40.47</td><td>53.03</td><td>40.70</td><td>0.0281</td><td>51.00</td><td>40.52</td><td>0.0175</td><td>49.83</td><td>40.44</td><td>0.0137</td></tr><tr><td>8</td><td>55.96</td><td>40.71</td><td>58.28</td><td>40.70</td><td>0.0179</td><td>56.56</td><td>40.69</td><td>0.0207</td><td>54.58</td><td>40.73</td><td>0.0264</td></tr><tr><td>7</td><td>60.71</td><td>40.88</td><td>65.06</td><td>41.04</td><td>0.0331</td><td>61.56</td><td>40.95</td><td>0.0309</td><td>59.32</td><td>40.77</td><td>0.0209</td></tr><tr><td>6</td><td>68.42</td><td>40.99</td><td>71.42</td><td>41.14</td><td>0.0273</td><td>68.93</td><td>41.01</td><td>0.0206</td><td>66.94</td><td>40.99</td><td>0.0258</td></tr><tr><td>5</td><td>76.69</td><td>41.43</td><td>82.47</td><td>41.44</td><td>0.0279</td><td>77.99</td><td>41.45</td><td>0.0431</td><td>73.87</td><td>41.31</td><td>0.0417</td></tr><tr><td>4</td><td>86.48</td><td>41.52</td><td>92.15</td><td>41.90</td><td>0.0405</td><td>87.20</td><td>41.57</td><td>0.0310</td><td>84.51</td><td>41.45</td><td>0.0288</td></tr><tr><td>3</td><td>102.87</td><td>42.16</td><td>109.35</td><td>42.15</td><td>0.0206</td><td>104.60</td><td>42.13</td><td>0.0540</td><td>98.00</td><td>42.10</td><td>0.0795</td></tr><tr><td>2</td><td>115.18</td><td>42.45</td><td>127.58</td><td>43.22</td><td>0.0403</td><td>117.26</td><td>42.60</td><td>0.0729</td><td>111.99</td><td>42.27</td><td>0.0468</td></tr><tr><td>1</td><td>147.19</td><td>43.67</td><td>158.55</td><td>43.22</td><td>0.0183</td><td>155.16</td><td>43.23</td><td>0.1166</td><td>141.32</td><td>43.51</td><td>0.1862</td></tr><tr><td>0</td><td>159.92</td><td>43.31</td><td>...</td><td>...</td><td>...</td><td>164.43</td><td>43.95</td><td>0.2775</td><td>158.29</td><td>43.26</td><td>0.0335</td></tr><tr><td>1</td><td>...</td><td>...</td><td>470.66</td><td>48.17</td><td>0.4075</td><td>302.96</td><td>47.48</td><td>0.0906</td><td>240.56</td><td>46.85</td><td>0.0136</td></tr><tr><td>2</td><td>...</td><td>...</td><td>706.17</td><td>47.64</td><td>0.4318</td><td>435.90</td><td>47.32</td><td>0.1073</td><td>332.20</td><td>46.95</td><td>0.0302</td></tr><tr><td>3</td><td>...</td><td>...</td><td>946.05</td><td>46.87</td><td>0.4501</td><td>571.23</td><td>46.61</td><td>0.1228</td><td>425.16</td><td>46.28</td><td>0.0444</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1162.35</td><td>45.56</td><td>0.4783</td><td>686.22</td><td>45.31</td><td>0.1565</td><td>495.76</td><td>45.08</td><td>0.0848</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1255.79</td><td>45.22</td><td>0.5005</td><td>737.47</td><td>45.27</td><td>0.1612</td><td>535.15</td><td>45.39</td><td>0.0703</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1444.06</td><td>46.05</td><td>0.4755</td><td>853.38</td><td>46.10</td><td>0.1437</td><td>620.73</td><td>46.14</td><td>0.0616</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1674.55</td><td>46.37</td><td>0.4789</td><td>985.45</td><td>46.39</td><td>0.1472</td><td>713.31</td><td>46.40</td><td>0.0652</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1912.62</td><td>46.44</td><td>0.4830</td><td>1121.60</td><td>46.44</td><td>0.1509</td><td>808.62</td><td>46.44</td><td>0.0685</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2156.06</td><td>46.30</td><td>0.4862</td><td>1260.66</td><td>46.29</td><td>0.1537</td><td>905.82</td><td>46.28</td><td>0.0711</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2401.84</td><td>45.93</td><td>0.4884</td><td>1400.95</td><td>45.91</td><td>0.1557</td><td>1003.75</td><td>45.89</td><td>0.0728</td></tr></tbody></table>

<table><caption>Modèle # 2, M = 0.4758 + 0.0002 M☉, T<sub>eff</sub> = 31399 K, log g = 5.87, âge = 12.06 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>49.30</td><td>40.47</td><td>51.87</td><td>40.44</td><td>0.0184</td><td>49.93</td><td>40.49</td><td>0.0232</td><td>48.20</td><td>40.39</td><td>0.0186</td></tr><tr><td>9</td><td>53.48</td><td>40.45</td><td>55.90</td><td>40.66</td><td>0.0264</td><td>53.87</td><td>40.48</td><td>0.0166</td><td>52.66</td><td>40.42</td><td>0.0143</td></tr><tr><td>8</td><td>59.07</td><td>40.71</td><td>61.64</td><td>40.67</td><td>0.0174</td><td>59.71</td><td>40.68</td><td>0.0224</td><td>57.49</td><td>40.72</td><td>0.0275</td></tr><tr><td>7</td><td>64.09</td><td>40.83</td><td>68.60</td><td>41.02</td><td>0.0332</td><td>64.88</td><td>40.90</td><td>0.0298</td><td>62.66</td><td>40.73</td><td>0.0200</td></tr><tr><td>6</td><td>72.37</td><td>40.97</td><td>75.45</td><td>41.10</td><td>0.0249</td><td>72.89</td><td>40.98</td><td>0.0211</td><td>70.67</td><td>40.98</td><td>0.0282</td></tr><tr><td>5</td><td>80.82</td><td>41.39</td><td>87.13</td><td>41.42</td><td>0.0281</td><td>82.13</td><td>41.42</td><td>0.0447</td><td>77.83</td><td>41.26</td><td>0.0409</td></tr><tr><td>4</td><td>91.48</td><td>41.48</td><td>97.11</td><td>41.83</td><td>0.0366</td><td>92.16</td><td>41.52</td><td>0.0303</td><td>89.36</td><td>41.42</td><td>0.0300</td></tr><tr><td>3</td><td>108.29</td><td>42.13</td><td>115.71</td><td>42.12</td><td>0.0199</td><td>110.25</td><td>42.10</td><td>0.0607</td><td>103.04</td><td>42.06</td><td>0.0817</td></tr><tr><td>2</td><td>121.48</td><td>42.37</td><td>134.03</td><td>43.13</td><td>0.0368</td><td>123.46</td><td>42.51</td><td>0.0712</td><td>118.36</td><td>42.21</td><td>0.0453</td></tr><tr><td>1</td><td>153.13</td><td>43.69</td><td>168.03</td><td>43.19</td><td>0.0183</td><td>162.91</td><td>43.30</td><td>0.1904</td><td>147.68</td><td>43.49</td><td>0.1826</td></tr><tr><td>0</td><td>169.18</td><td>43.25</td><td>...</td><td>...</td><td>...</td><td>171.41</td><td>43.59</td><td>0.1861</td><td>167.45</td><td>43.22</td><td>0.0283</td></tr><tr><td>1</td><td>...</td><td>...</td><td>460.63</td><td>48.23</td><td>0.4074</td><td>301.55</td><td>47.43</td><td>0.0918</td><td>242.42</td><td>46.73</td><td>0.0149</td></tr><tr><td>2</td><td>...</td><td>...</td><td>671.12</td><td>47.83</td><td>0.4353</td><td>419.24</td><td>47.46</td><td>0.1093</td><td>324.54</td><td>47.05</td><td>0.0317</td></tr><tr><td>3</td><td>...</td><td>...</td><td>890.90</td><td>47.23</td><td>0.4541</td><td>537.80</td><td>47.00</td><td>0.1250</td><td>402.56</td><td>46.71</td><td>0.0457</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1119.83</td><td>46.21</td><td>0.4683</td><td>662.37</td><td>46.01</td><td>0.1380</td><td>483.39</td><td>45.72</td><td>0.0590</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1271.02</td><td>45.15</td><td>0.5076</td><td>739.89</td><td>45.08</td><td>0.1760</td><td>529.36</td><td>44.99</td><td>0.0937</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1399.39</td><td>45.68</td><td>0.4841</td><td>819.25</td><td>45.71</td><td>0.1500</td><td>590.81</td><td>45.75</td><td>0.0658</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1631.73</td><td>46.24</td><td>0.4816</td><td>952.64</td><td>46.25</td><td>0.1487</td><td>684.23</td><td>46.25</td><td>0.0658</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1880.32</td><td>46.41</td><td>0.4849</td><td>1094.95</td><td>46.41</td><td>0.1519</td><td>783.74</td><td>46.42</td><td>0.0690</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2137.58</td><td>46.37</td><td>0.4878</td><td>1242.50</td><td>46.37</td><td>0.1547</td><td>887.15</td><td>46.38</td><td>0.0716</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2399.31</td><td>46.11</td><td>0.4899</td><td>1392.83</td><td>46.12</td><td>0.1567</td><td>992.68</td><td>46.12</td><td>0.0735</td></tr></tbody></table>
<table><caption>Modèle # 3, M = 0.4758 + 0.0002 M⊙, T<sub>eff</sub> = 31352 K, log g = 5.85, âge = 18.98 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>50.85</td><td>40.46</td><td>53.61</td><td>40.43</td><td>0.0185</td><td>51.49</td><td>40.48</td><td>0.0236</td><td>49.69</td><td>40.35</td><td>0.0175</td></tr><tr><td>9</td><td>55.26</td><td>40.42</td><td>57.64</td><td>40.63</td><td>0.0255</td><td>55.62</td><td>40.45</td><td>0.0151</td><td>54.43</td><td>40.40</td><td>0.0137</td></tr><tr><td>8</td><td>61.03</td><td>40.70</td><td>63.71</td><td>40.65</td><td>0.0161</td><td>61.70</td><td>40.67</td><td>0.0228</td><td>59.28</td><td>40.71</td><td>0.0281</td></tr><tr><td>7</td><td>66.11</td><td>40.79</td><td>70.80</td><td>41.01</td><td>0.0335</td><td>66.86</td><td>40.86</td><td>0.0286</td><td>64.67</td><td>40.69</td><td>0.0183</td></tr><tr><td>6</td><td>74.84</td><td>40.95</td><td>77.83</td><td>41.06</td><td>0.0226</td><td>75.32</td><td>40.95</td><td>0.0200</td><td>73.02</td><td>40.96</td><td>0.0285</td></tr><tr><td>5</td><td>83.37</td><td>41.37</td><td>90.05</td><td>41.39</td><td>0.0271</td><td>84.69</td><td>41.40</td><td>0.0457</td><td>80.17</td><td>41.22</td><td>0.0399</td></tr><tr><td>4</td><td>94.44</td><td>41.44</td><td>100.01</td><td>41.79</td><td>0.0346</td><td>95.05</td><td>41.48</td><td>0.0282</td><td>92.30</td><td>41.38</td><td>0.0284</td></tr><tr><td>3</td><td>111.76</td><td>42.11</td><td>119.49</td><td>42.08</td><td>0.0185</td><td>113.79</td><td>42.08</td><td>0.0627</td><td>106.14</td><td>42.03</td><td>0.0830</td></tr><tr><td>2</td><td>125.05</td><td>42.31</td><td>137.86</td><td>43.09</td><td>0.0354</td><td>126.93</td><td>42.44</td><td>0.0690</td><td>121.96</td><td>42.16</td><td>0.0415</td></tr><tr><td>1</td><td>157.13</td><td>43.68</td><td>173.39</td><td>43.16</td><td>0.0182</td><td>167.21</td><td>43.34</td><td>0.2213</td><td>151.65</td><td>43.46</td><td>0.1789</td></tr><tr><td>0</td><td>174.46</td><td>43.21</td><td>...</td><td>...</td><td>...</td><td>175.77</td><td>43.43</td><td>0.1374</td><td>172.56</td><td>43.18</td><td>0.0253</td></tr><tr><td>1</td><td>...</td><td>...</td><td>457.57</td><td>48.25</td><td>0.4113</td><td>300.58</td><td>47.40</td><td>0.0945</td><td>242.82</td><td>46.65</td><td>0.0166</td></tr><tr><td>2</td><td>...</td><td>...</td><td>667.30</td><td>47.86</td><td>0.4399</td><td>414.04</td><td>47.48</td><td>0.1131</td><td>319.32</td><td>47.07</td><td>0.0348</td></tr><tr><td>3</td><td>...</td><td>...</td><td>897.63</td><td>47.24</td><td>0.4560</td><td>538.10</td><td>47.02</td><td>0.1262</td><td>399.51</td><td>46.74</td><td>0.0463</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1139.67</td><td>46.21</td><td>0.4691</td><td>672.10</td><td>46.03</td><td>0.1383</td><td>488.89</td><td>45.76</td><td>0.0584</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1297.28</td><td>45.12</td><td>0.5116</td><td>754.52</td><td>45.05</td><td>0.1799</td><td>539.15</td><td>44.95</td><td>0.0979</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1428.07</td><td>45.66</td><td>0.4846</td><td>835.02</td><td>45.69</td><td>0.1504</td><td>601.28</td><td>45.72</td><td>0.0661</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1669.34</td><td>46.25</td><td>0.4818</td><td>973.79</td><td>46.25</td><td>0.1488</td><td>698.75</td><td>46.25</td><td>0.0658</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1926.66</td><td>46.42</td><td>0.4853</td><td>1121.31</td><td>46.43</td><td>0.1521</td><td>802.05</td><td>46.43</td><td>0.0690</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2192.40</td><td>46.39</td><td>0.4882</td><td>1273.84</td><td>46.39</td><td>0.1548</td><td>909.05</td><td>46.39</td><td>0.0717</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2462.29</td><td>46.13</td><td>0.4900</td><td>1428.92</td><td>46.13</td><td>0.1568</td><td>1017.98</td><td>46.14</td><td>0.0736</td></tr></tbody></table>

<table><caption>Modèle # 4, M = 0.4758 + 0.0002 M⊙, T<sub>eff</sub> = 31331 K, log g = 5.84, âge = 21.73 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>51.47</td><td>40.45</td><td>54.27</td><td>40.43</td><td>0.0188</td><td>52.10</td><td>40.48</td><td>0.0237</td><td>50.30</td><td>40.34</td><td>0.0172</td></tr><tr><td>9</td><td>55.97</td><td>40.42</td><td>58.34</td><td>40.62</td><td>0.0250</td><td>56.33</td><td>40.44</td><td>0.0149</td><td>55.12</td><td>40.40</td><td>0.0139</td></tr><tr><td>8</td><td>61.78</td><td>40.70</td><td>64.53</td><td>40.64</td><td>0.0160</td><td>62.46</td><td>40.67</td><td>0.0233</td><td>59.98</td><td>40.70</td><td>0.0282</td></tr><tr><td>7</td><td>66.94</td><td>40.78</td><td>71.65</td><td>41.01</td><td>0.0334</td><td>67.67</td><td>40.85</td><td>0.0283</td><td>65.49</td><td>40.69</td><td>0.0182</td></tr><tr><td>6</td><td>75.80</td><td>40.95</td><td>78.82</td><td>41.05</td><td>0.0221</td><td>76.28</td><td>40.95</td><td>0.0202</td><td>73.92</td><td>40.96</td><td>0.0291</td></tr><tr><td>5</td><td>84.37</td><td>41.36</td><td>91.18</td><td>41.39</td><td>0.0272</td><td>85.69</td><td>41.39</td><td>0.0460</td><td>81.14</td><td>41.21</td><td>0.0396</td></tr><tr><td>4</td><td>95.67</td><td>41.44</td><td>101.22</td><td>41.77</td><td>0.0337</td><td>96.26</td><td>41.47</td><td>0.0281</td><td>93.49</td><td>41.38</td><td>0.0287</td></tr><tr><td>3</td><td>113.06</td><td>42.11</td><td>121.04</td><td>42.07</td><td>0.0184</td><td>115.15</td><td>42.07</td><td>0.0644</td><td>107.36</td><td>42.02</td><td>0.0833</td></tr><tr><td>2</td><td>126.60</td><td>42.30</td><td>139.43</td><td>43.07</td><td>0.0346</td><td>128.46</td><td>42.43</td><td>0.0685</td><td>123.52</td><td>42.15</td><td>0.0412</td></tr><tr><td>1</td><td>158.54</td><td>43.68</td><td>175.69</td><td>43.16</td><td>0.0182</td><td>168.83</td><td>43.37</td><td>0.2376</td><td>153.18</td><td>43.46</td><td>0.1776</td></tr><tr><td>0</td><td>176.73</td><td>43.20</td><td>...</td><td>...</td><td>...</td><td>177.72</td><td>43.38</td><td>0.1187</td><td>174.80</td><td>43.17</td><td>0.0245</td></tr><tr><td>1</td><td>...</td><td>...</td><td>455.31</td><td>48.25</td><td>0.4134</td><td>299.44</td><td>47.38</td><td>0.0960</td><td>242.40</td><td>46.61</td><td>0.0177</td></tr><tr><td>2</td><td>...</td><td>...</td><td>665.13</td><td>47.87</td><td>0.4420</td><td>411.33</td><td>47.48</td><td>0.1148</td><td>316.34</td><td>47.06</td><td>0.0363</td></tr><tr><td>3</td><td>...</td><td>...</td><td>900.44</td><td>47.25</td><td>0.4566</td><td>538.60</td><td>47.02</td><td>0.1264</td><td>398.84</td><td>46.74</td><td>0.0462</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1147.70</td><td>46.22</td><td>0.4692</td><td>676.27</td><td>46.04</td><td>0.1381</td><td>491.51</td><td>45.78</td><td>0.0578</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1309.42</td><td>45.12</td><td>0.5116</td><td>761.47</td><td>45.05</td><td>0.1799</td><td>544.02</td><td>44.95</td><td>0.0982</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1440.90</td><td>45.65</td><td>0.4850</td><td>842.16</td><td>45.67</td><td>0.1507</td><td>606.13</td><td>45.70</td><td>0.0663</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1685.18</td><td>46.24</td><td>0.4819</td><td>982.78</td><td>46.24</td><td>0.1489</td><td>704.99</td><td>46.24</td><td>0.0659</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1945.80</td><td>46.42</td><td>0.4925</td><td>1132.27</td><td>46.42</td><td>0.1521</td><td>809.72</td><td>46.42</td><td>0.0691</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2214.81</td><td>46.38</td><td>0.4881</td><td>1286.70</td><td>46.39</td><td>0.1549</td><td>918.07</td><td>46.39</td><td>0.0718</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2487.70</td><td>46.12</td><td>0.4901</td><td>1443.53</td><td>46.13</td><td>0.1569</td><td>1028.25</td><td>46.14</td><td>0.0737</td></tr></tbody></table>
<table><caption>Modèle # 5, M = 0.4758 + 0.0002 M⊙, T<sub>eff</sub> = 31292 K, log g = 5.82, âge = 28.83 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>53.04</td><td>40.43</td><td>55.87</td><td>40.44</td><td>0.0198</td><td>53.66</td><td>40.46</td><td>0.0234</td><td>51.87</td><td>40.33</td><td>0.0175</td></tr><tr><td>9</td><td>57.74</td><td>40.42</td><td>60.15</td><td>40.60</td><td>0.0241</td><td>58.13</td><td>40.44</td><td>0.0160</td><td>56.80</td><td>40.41</td><td>0.0157</td></tr><tr><td>8</td><td>63.57</td><td>40.70</td><td>66.55</td><td>40.65</td><td>0.0174</td><td>64.29</td><td>40.68</td><td>0.0249</td><td>61.75</td><td>40.69</td><td>0.0283</td></tr><tr><td>7</td><td>69.10</td><td>40.77</td><td>73.74</td><td>41.00</td><td>0.0325</td><td>69.82</td><td>40.83</td><td>0.0282</td><td>67.60</td><td>40.69</td><td>0.0197</td></tr><tr><td>6</td><td>78.11</td><td>40.95</td><td>81.43</td><td>41.04</td><td>0.0223</td><td>78.68</td><td>40.95</td><td>0.0228</td><td>76.07</td><td>40.97</td><td>0.0319</td></tr><tr><td>5</td><td>86.88</td><td>41.33</td><td>93.89</td><td>41.39</td><td>0.0282</td><td>88.21</td><td>41.37</td><td>0.0463</td><td>83.72</td><td>41.19</td><td>0.0398</td></tr><tr><td>4</td><td>98.84</td><td>41.43</td><td>104.51</td><td>41.74</td><td>0.0313</td><td>99.53</td><td>41.47</td><td>0.0307</td><td>96.48</td><td>41.38</td><td>0.0331</td></tr><tr><td>3</td><td>116.00</td><td>42.10</td><td>125.05</td><td>42.08</td><td>0.0193</td><td>118.39</td><td>42.07</td><td>0.0711</td><td>110.41</td><td>41.98</td><td>0.0834</td></tr><tr><td>2</td><td>130.86</td><td>42.28</td><td>143.57</td><td>43.02</td><td>0.0319</td><td>132.81</td><td>42.40</td><td>0.0695</td><td>127.85</td><td>42.15</td><td>0.0450</td></tr><tr><td>1</td><td>161.44</td><td>43.67</td><td>182.08</td><td>43.16</td><td>0.0183</td><td>172.51</td><td>43.49</td><td>0.2786</td><td>156.85</td><td>43.43</td><td>0.1733</td></tr><tr><td>0</td><td>183.06</td><td>43.20</td><td>...</td><td>...</td><td>...</td><td>183.39</td><td>43.30</td><td>0.0802</td><td>181.09</td><td>43.17</td><td>0.0233</td></tr><tr><td>1</td><td>...</td><td>...</td><td>444.15</td><td>48.27</td><td>0.4218</td><td>292.46</td><td>47.30</td><td>0.1024</td><td>237.92</td><td>46.46</td><td>0.0226</td></tr><tr><td>2</td><td>...</td><td>...</td><td>655.27</td><td>47.88</td><td>0.4474</td><td>401.33</td><td>47.46</td><td>0.1193</td><td>305.57</td><td>46.98</td><td>0.0399</td></tr><tr><td>3</td><td>...</td><td>...</td><td>904.67</td><td>47.27</td><td>0.4575</td><td>538.73</td><td>47.05</td><td>0.1264</td><td>397.08</td><td>46.75</td><td>0.0450</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1164.61</td><td>46.29</td><td>0.4685</td><td>685.17</td><td>46.12</td><td>0.1367</td><td>497.34</td><td>45.88</td><td>0.0554</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1344.21</td><td>45.15</td><td>0.5058</td><td>781.86</td><td>45.07</td><td>0.1745</td><td>558.73</td><td>44.96</td><td>0.0934</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1474.80</td><td>45.57</td><td>0.4868</td><td>860.95</td><td>45.58</td><td>0.1524</td><td>618.80</td><td>45.60</td><td>0.0677</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1723.15</td><td>46.18</td><td>0.4823</td><td>1004.32</td><td>46.18</td><td>0.1492</td><td>719.96</td><td>46.18</td><td>0.0661</td></tr><tr><td>8</td><td>...</td><td>...</td><td>1991.01</td><td>46.38</td><td>0.4854</td><td>1158.08</td><td>46.38</td><td>0.1523</td><td>827.78</td><td>46.38</td><td>0.0693</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2267.29</td><td>46.35</td><td>0.4882</td><td>1316.78</td><td>46.36</td><td>0.1550</td><td>939.19</td><td>46.36</td><td>0.0719</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2547.15</td><td>46.11</td><td>0.4902</td><td>1477.69</td><td>46.11</td><td>0.1569</td><td>1052.27</td><td>46.13</td><td>0.0738</td></tr></tbody></table>

<table><caption>Modèle # 6, M = 0.4758 + 0.0002 M⊙, T<sub>eff</sub> = 31254 K, log g = 5.78, âge = 46.87 millions d'années depuis la ZAEHB</caption><thead><tr><th rowspan="2">k</th><th colspan="2">l = 0</th><th colspan="3">l = 1</th><th colspan="3">l = 2</th><th colspan="3">l = 3</th></tr><tr><th>P (s)</th><th>log E<sub>cin</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th><th>P (s)</th><th>log E<sub>cin</sub></th><th>C<sub>kl</sub></th></tr></thead><tbody><tr><td>10</td><td>56.79</td><td>40.38</td><td>59.81</td><td>40.44</td><td>0.0217</td><td>57.37</td><td>40.42</td><td>0.0231</td><td>55.59</td><td>40.28</td><td>0.0166</td></tr><tr><td>9</td><td>62.02</td><td>40.41</td><td>64.44</td><td>40.55</td><td>0.0221</td><td>62.40</td><td>40.42</td><td>0.0164</td><td>60.89</td><td>40.41</td><td>0.0181</td></tr><tr><td>8</td><td>68.02</td><td>40.69</td><td>71.46</td><td>40.64</td><td>0.0184</td><td>68.76</td><td>40.68</td><td>0.0277</td><td>65.98</td><td>40.64</td><td>0.0285</td></tr><tr><td>7</td><td>74.19</td><td>40.73</td><td>78.82</td><td>40.96</td><td>0.0315</td><td>74.82</td><td>40.78</td><td>0.0268</td><td>72.58</td><td>40.66</td><td>0.0204</td></tr><tr><td>6</td><td>83.84</td><td>40.94</td><td>87.49</td><td>41.00</td><td>0.0207</td><td>84.44</td><td>40.94</td><td>0.0258</td><td>81.36</td><td>40.96</td><td>0.0361</td></tr><tr><td>5</td><td>92.97</td><td>41.27</td><td>100.53</td><td>41.38</td><td>0.0288</td><td>94.22</td><td>41.32</td><td>0.0477</td><td>89.68</td><td>41.12</td><td>0.0386</td></tr><tr><td>4</td><td>106.32</td><td>41.40</td><td>112.02</td><td>41.66</td><td>0.0270</td><td>107.00</td><td>41.42</td><td>0.0325</td><td>103.57</td><td>41.35</td><td>0.0380</td></tr><tr><td>3</td><td>123.63</td><td>42.06</td><td>134.41</td><td>42.05</td><td>0.0193</td><td>126.26</td><td>42.05</td><td>0.0831</td><td>117.70</td><td>41.91</td><td>0.0835</td></tr><tr><td>2</td><td>140.57</td><td>42.21</td><td>153.11</td><td>42.89</td><td>0.0279</td><td>142.37</td><td>42.30</td><td>0.0687</td><td>137.52</td><td>42.10</td><td>0.0465</td></tr><tr><td>1</td><td>169.95</td><td>43.59</td><td>196.48</td><td>43.13</td><td>0.0183</td><td>180.40</td><td>43.64</td><td>0.2968</td><td>165.63</td><td>43.36</td><td>0.1599</td></tr><tr><td>0</td><td>197.40</td><td>43.16</td><td>...</td><td>...</td><td>...</td><td>196.82</td><td>43.18</td><td>0.0397</td><td>195.06</td><td>43.13</td><td>0.0191</td></tr><tr><td>1</td><td>...</td><td>...</td><td>437.08</td><td>48.22</td><td>0.4374</td><td>286.26</td><td>47.04</td><td>0.1172</td><td>232.21</td><td>45.92</td><td>0.0348</td></tr><tr><td>2</td><td>...</td><td>...</td><td>667.19</td><td>47.86</td><td>0.4514</td><td>405.43</td><td>47.36</td><td>0.1222</td><td>306.07</td><td>46.77</td><td>0.0408</td></tr><tr><td>3</td><td>...</td><td>...</td><td>939.44</td><td>47.27</td><td>0.4582</td><td>558.13</td><td>47.03</td><td>0.1264</td><td>410.49</td><td>46.72</td><td>0.0444</td></tr><tr><td>4</td><td>...</td><td>...</td><td>1217.30</td><td>46.31</td><td>0.4684</td><td>715.57</td><td>46.15</td><td>0.1362</td><td>518.98</td><td>45.91</td><td>0.0545</td></tr><tr><td>5</td><td>...</td><td>...</td><td>1416.36</td><td>45.17</td><td>0.5024</td><td>824.10</td><td>45.08</td><td>0.1713</td><td>589.18</td><td>44.96</td><td>0.0906</td></tr><tr><td>6</td><td>...</td><td>...</td><td>1550.89</td><td>45.49</td><td>0.4887</td><td>904.63</td><td>45.49</td><td>0.1542</td><td>649.50</td><td>45.50</td><td>0.0694</td></tr><tr><td>7</td><td>...</td><td>...</td><td>1808.79</td><td>46.13</td><td>0.4838</td><td>1053.86</td><td>46.12</td><td>0.1496</td><td>755.07</td><td>46.12</td><td>0.0665</td></tr><tr><td>8</td><td>...</td><td>...</td><td>2090.57</td><td>46.35</td><td>0.4858</td><td>1215.73</td><td>46.35</td><td>0.1525</td><td>868.67</td><td>46.34</td><td>0.0695</td></tr><tr><td>9</td><td>...</td><td>...</td><td>2380.70</td><td>46.34</td><td>0.4883</td><td>1382.53</td><td>46.34</td><td>0.1551</td><td>985.85</td><td>46.34</td><td>0.0720</td></tr><tr><td>10</td><td>...</td><td>...</td><td>2673.46</td><td>46.12</td><td>0.4902</td><td>1551.02</td><td>46.12</td><td>0.1570</td><td>1104.39</td><td>46.13</td><td>0.0739</td></tr></tbody></table>