# Stratification of the elements in the atmospheres of blue horizontal-branch stars

F. Leblanc, A. Hui-Bon-Hoa, V. R. Khalack

► To cite this version:

F. Leblanc, A. Hui-Bon-Hoa, V. R. Khalack. Stratification of the elements in the atmospheres of blue horizontal-branch stars. Monthly Notices of the Royal Astronomical Society, 2010, 409 (4), pp.1606-1610. 10.1111/j.1365-2966.2010.17404.x. hal-04838556

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# Stratification of the elements in the atmospheres of blue horizontal-branch stars

F. LeBlanc,<fnref n="1" />* A. Hui-Bon-Hoa<fnref n="2" /> and V. R. Khalack<fnref n="1" />

Accepted 2010 July 22. Received 2010 July 21; in original form 2010 June 14

## ABSTRACT

Blue horizontal-branch (BHB) stars with $T_{\text{eff}}$ approximately larger than 11 500 K show several observational anomalies. In globular clusters, they exhibit low rotational velocities, abundance anomalies (as compared to cluster abundances), photometric jumps and gaps and spectroscopic gravities lower than predicted by canonical models. It is commonly believed that the low rotational velocities of these stars permit atomic diffusion to be efficient in their atmosphere thereby causing the observed anomalies. Recent detections of vertical stratification of iron (and some other chemical elements) in several BHB stars concur with this framework. In this paper, improved model atmospheres that include the vertical stratification of the elements are applied to BHB stars to verify if they can explain their observational anomalies. The results from theoretical model atmospheres are consistent with the photometric jumps and gaps observed for BHB stars in globular clusters. It is found that iron stratification in the theoretical models and that obtained from observations have similar tendencies. Our results also show that the spectroscopic gravities obtained while using chemically homogeneous model atmospheres to fit observations are underestimated. These results significantly strengthen the belief that atomic diffusion is responsible for these BHB-star anomalies.

**Key words:** diffusion – stars: abundances – stars: atmospheres – stars: horizontal branch.

## 1 INTRODUCTION

Horizontal-branch stars are evolved intermediate-mass stars that are burning helium in their core (e.g. Hoyle & Schwarzschild 1955). Some hot blue horizontal-branch (hereafter BHB) stars with $T_{\text{eff}}$ larger than approximately 11 500 K are very interesting objects since they exhibit several observational anomalies. This paper aims to study certain aspects of these astronomical objects in the light of recent modelling and observational results.

First, abundance anomalies are observed for such BHB stars in several globular clusters (Glaspey et al. 1989; Behr et al. 1999; Moehler et al. 1999; Behr, Cohen & McCarthy 2000a; Behr 2003a; Hubrig et al. 2009). Khalack et al. (2007, 2008, 2010) have detected vertical stratification of the abundance of several chemical elements including Fe in the atmosphere of some stars of this type. Khalack et al. (2008) found that the iron abundance increases towards the lower atmosphere in three BHB stars. Nitrogen and sulfur stratification was also detected in the hot BHB star HD 135485 (Khalack et al. 2007). The abundances of these two elements are found to increase towards the upper atmosphere. More recently, Khalack, LeBlanc & Behr (2010) determined the vertical Fe abundance gra-

dient in a sample of 14 BHB stars using the observed spectra of Behr (2003a). They detected vertical Fe stratification in five (and possibly seven) of these BHB stars. Isotopic anomalies have also been recently detected in BHB stars (Hubrig et al. 2009).

Photometric jumps are observed on the hot side of $T_{\text{eff}} \simeq 11\,500\,\text{K}$ for the horizontal-branch sequence of several globular clusters (Grundahl et al. 1999) as compared to what is predicted by canonical models. Photometric gaps are also observed for this sequence (Ferraro et al. 1998) at the same $T_{\text{eff}}$ where the photometric jump mentioned above occurs.

Another anomaly detected is that the rotational velocities of BHB stars are observed to drop abruptly for $T_{\text{eff}}$ approximately larger than 11 500 K (Peterson, Rood & Crocker 1995; Behr et al. 2000a,b; Behr 2003b).

Finally, spectroscopic gravities of BHB stars in globular clusters, at least for the metal-poor ones (e.g. Crocker, Rood & O'Connell 1988; Moehler, Heber & de Boer 1995), are also lower than those predicted by classical BHB models.

Atomic diffusion (Michaud 1970) is effective only if the medium is hydrodynamically stable enough to prevent mixing, because of the order of magnitude of the diffusion velocities which are much smaller than those of macroscopic motions. In the case of BHB stars, their relatively low rotational velocities should render their superficial layer stable enough for diffusion to take place. For instance,

<footnote n="1">¹Département de Physique et d'Astronomie, Université de Moncton, Moncton, N.-B. E1A 3E9, Canada</footnote>

<footnote n="2">²Laboratoire d'Astrophysique de Toulouse-Tarbes, Université de Toulouse, CNRS, 14 avenue Edouard Belin 31400, Toulouse, France</footnote>

<footnote>*E-mail: francis.leblanc@umoncton.ca</footnote>
recently, Quievy et al. (2009) showed that for values of rotational velocities found for BHB stars with $T_{\text{eff}}$ above 11 500 K, meridional circulation is not efficient enough to prevent He from gravitationally settling. This leads to the disappearance of the superficial He convection zone and renders the atmosphere more stable. Once the medium is stable enough, atomic diffusion can dominate there, leading to abundance anomalies and vertical abundance stratification of the chemical elements through the migration of the particles caused by the disbalance of gravity and radiative forces, and yielding superficial abundance anomalies. Stratification of the elements has an effect on the physical structure of the atmosphere through the change in the opacities, thus leading to photometric anomalies, and to a change of the shape of the Balmer lines, explaining the low values of surface gravity obtained by fitting of these lines, if one uses canonical models. The scenario outlined above, where atomic diffusion takes place in the atmospheres of hot BHB stars, may therefore explain the various observational anomalies observed for these stars.

Hui-Bon-Hoa, LeBlanc & Hauschildt (2000) constructed stellar atmosphere models of BHB stars with vertical stratification of the elements, and self-consistent atmospheric structure. These models were successful in qualitatively reproducing the above-mentioned anomalies when assuming that atomic diffusion becomes efficient in BHB stars with $T_{\text{eff}} > 11$ 500 K (i.e. the temperature above which the vast majority of the BHB stars rotate slowly). These models have been improved recently (LeBlanc et al. 2009), and the aim of this paper is to apply these new models to BHB stars and to compare the results to observational data. Among the improvements, the convergence scheme to obtain self-consistent abundance stratification was ameliorated in these models. Also, the diffusion coefficients now used take into account the interaction between the ions and neutral hydrogen. Moreover, in these new models, upper and lower abundance limits were imposed to avoid that certain elements attain extremely large (for the test-particle approximation of the diffusion theory to still be valid) or small (to avoid numerical problems) abundances at certain depths (see section 3 of LeBlanc et al. 2009 for more details).

First, the new model atmospheres with elemental stratification will be briefly described. Theoretical vertical stratification of Fe in models of various $T_{\text{eff}}$ will be compared to the observational results of Khalack et al. (2007, 2008, 2010). The synthetic photometry obtained with these models will then be presented, checking if they are able to reproduce observed photometric jumps and gaps for globular cluster BHB sequences. Synthetic Balmer lines are also compared between models with different prescriptions to show how the diffusion model can account for the low values of gravity derived when using canonical models.

## 2 MODEL ATMOSPHERES WITH STRATIFIED ABUNDANCES

The process of elemental stratification relies on the diffusion velocity, which causes the migration of the different chemical elements within stars. The leading terms that cause this velocity are gravity and the radiative acceleration resulting from the momentum transfer between the radiation field and each chemical species (e.g. Gonzalez et al. 1995). This transfer depends on the opacity of the species under consideration and the local monochromatic radiation field, which, in turn, via the monochromatic opacities, depends on the local abundances of the different species. The stratification of the abundances is thus a time-dependent process and it is therefore complex to treat it thoroughly. As the radiative transfer equation has to

be solved explicitly in stellar atmospheres, which are optically thin media, time-dependent calculations are not feasible at the present time. Studies of abundance stratification can, however, be performed assuming that an equilibrium state can be reached, when the diffusion velocity of each element is nil at each layer of the atmosphere. This is the framework within which our calculations are performed. Even though the elemental stratification profiles can possibly differ from those computed time-dependently, this approximation can be used to gauge the impact of vertical stratification of the abundances on the atmospheric structure and on certain observed quantities. For a more detailed discussion surrounding time-dependent diffusion and equilibrium solution, the reader is referred to Alecian-Stift (2007) in which Ap stars are studied.

The model atmospheres presented here are calculated with a modified version of the PHOENIX code (Hauschildt, Allard & Baron 1999) as described by LeBlanc et al. (2009). The models computed here are in local thermodynamic equilibrium (LTE) and include 39 elements (H-Ga, Kr-Nb, Ba and La). To build the stratification profile for each element, the code seeks iteratively a solution where the atmospheric structure and the vertical abundance stratifications yield a nil diffusion velocity for each chemical species (i.e. the equilibrium solution). Indeed, as the abundance of each species changes locally, so do the opacities, and thus the atmospheric structure. The resulting model atmospheres are thus self-consistent from this point of view.

For the evaluation of the radiative accelerations, both bound-bound and bound-free transitions are considered for each species while assuming LTE (Hui-Bon-Hoa et al. 2002). As the radiative transfer is solved with the opacity sampling method, the radiative accelerations, along with the radiative flux, are calculated using a sufficiently fine frequency grid to ensure adequate precision (e.g. LeBlanc, Michaud & Richer 2000). Several improvements were brought to the models presented here as compared to the models used in Hui-Bon-Hoa et al. (2000). For example, the convergence scheme used to compute the stratification of the abundances has been modified. Also, more precise diffusion coefficients are used. More details concerning the improvements brought to the atmospheric code are found in LeBlanc et al. (2009).

A series of BHB model atmospheres from $T_{\text{eff}} = 11$ 000 to 18 000 K (see Table 1) were constructed while including abundance stratifications. The surface gravities and masses used here are those of the zero-age horizontal-branch (ZAHB) models of VandenBerg et al. (2000).

The stratification of the elements predicted at equilibrium strongly modifies the physical structure of the stellar atmospheres of hot BHB stars. Fig. 1 shows the ratio of the temperature as a function of optical depth in several of these models as compared to the temperature of corresponding models (with the same fundamental parameters) with homogeneous models with a metallicity of $-1.5$ dex solar. The abundances used for these homogeneous models

<table><caption>**Table 1.** Physical parameters of models.</caption><thead><tr><td>$T_{\text{eff}}$ (K)</td><td>log g</td><td>$M(M_{\odot})$</td></tr></thead><tbody><tr><td>11 000</td><td>3.78</td><td>0.663</td></tr><tr><td>12 000</td><td>3.95</td><td>0.643</td></tr><tr><td>13 000</td><td>4.11</td><td>0.625</td></tr><tr><td>14 000</td><td>4.26</td><td>0.609</td></tr><tr><td>16 000</td><td>4.52</td><td>0.581</td></tr><tr><td>18 000</td><td>4.74</td><td>0.561</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** The ratio of the temperature as a function of optical depth in various models including stratification to that of a chemically homogeneous model with metallicity of −1.5 dex solar of the same effective temperature and surface gravity. The dot-dashed line shows the position of a ratio of one.</figcaption></figure>

are chosen to be −1.5 dex compared to solar abundances which are typical of well-studied globular cluster metallicity (e.g. M13, M3, etc.). The large modifications in the structure of the self-consistent model atmospheres in the line-formation region as compared to homogeneous ones can give rise to detectable observational effects. As will be discussed below, the diffusion process not only causes abundance stratification of the elements but can also lead to visible effects related to the photometric colours and spectroscopic gravities of hot BHB stars. The results of these theoretical models are compared below to well-established anomalies of hot BHB stars.

## 3 STRATIFICATION OF IRON IN BHB STARS

The vertical stratification of Fe in our stratified model atmospheres is shown in Fig. 2. The results presented in this figure clearly show that the gradient of the Fe abundance (as a function of optical depth in the atmosphere) in the range −4 ≤ log τ<sub>5000</sub> ≤ −2 decreases with the increase of T<sub>eff</sub>. Since this range of optical depth is where a lot of the iron lines are formed, such a tendency can be verified with spectroscopic studies.

Fig. 3 compares the slopes of the detected Fe abundance gradients or lack thereof for a large number of BHB stars (Khalack 2007, 2008, 2010) to those predicted by the theoretical model atmospheres of LeBlanc et al. (2009). In these observational studies, the vertical stratification of iron was gauged by determining the abundance of individual lines formed at various optical depths. The dots in this figure represent individual hot BHB stars while the solid line is a quadratic fit of the observed abundance slopes. The filled diamonds connected by a dashed line give the linear slopes of Fe

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Abundance of Fe relative to optical depth for self-consistent model atmospheres of BHB stars with T<sub>eff</sub> from 11 000 to 18 000 K.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Slope of the vertical Fe abundance obtained from the analysis of observed spectra (filled dots with their corresponding error bars) taken from Khalack et al. (2007, 2008, 2010). Also shown in this figure is a quadratic fit of these observed slopes (solid line) and the linear slopes (filled diamonds joined by dashed line) obtained in the theoretical models in the range −5 < log τ<sub>5000</sub> < −2 which corresponds to the depth from where most of the Fe lines emanate. The dotted line shows the position of a nil slope.</figcaption></figure>

abundance in the theoretical models. These slopes are those of the linear fit of the abundance stratification of iron for the atmospheric layers in the range −5 < log τ<sub>5000</sub> < −2 for each T<sub>eff</sub>. These layers correspond to the atmospheric depths where most of the Fe lines are formed and where iron stratification is detected (see fig. 1 of Khalack et al. 2010). Fig. 3 shows that the observed slopes of the Fe abundance decreases with T<sub>eff</sub> for hot BHB stars and eventually becomes undetectable at T<sub>eff</sub> ≃ 14 000 K, in agreement with the theoretical results of the models of LeBlanc et al. (2009) shown in Fig. 2. These results may serve as additional proof that elemental stratification due to atomic diffusion occurs in the atmospheres of hot BHB stars.

## 4 PHOTOMETRIC JUMPS AND GAPS

BHB stars in globular clusters exhibit several photometric anomalies, namely photometric jumps and gaps. This section aims to interpret them in the light of self-consistent stratified model atmospheres.

Grundahl et al. (1999) observed a photometric jump in the (u, u − y) colour–magnitude diagram for the horizontal-branch sequence in several globular clusters. This jump consists of a shift towards brighter stars of the horizontal-branch sequence with respect to canonical models, and occurs for stars with T<sub>eff</sub> higher than approximately 11 500 K. Therefore, there exists a difference (for T<sub>eff</sub> ≥ 11 500 K) between the observed and predicted colours. The PHOENIX model atmospheres including elemental stratification of Hui-Bon-Hoa et al. (2000) were able to qualitatively explain this jump, when stars with T<sub>eff</sub> larger than 11 500 K become stable enough to allow atomic diffusion to have visible effects. This section aims to verify if the new models of LeBlanc et al. (2009) also reproduce this jump.

Fig. 4 shows the (u, u − y) colour–magnitude diagram for stars with and without elemental stratification. These results are consistent with the observational results of Grundahl et al. (1999) when compared to canonical models. Our results show that if diffusion becomes efficient at T<sub>eff</sub> ≃ 11 500 K, a jump occurs in the (u, u − y) diagram. The difference in the u-bandpass magnitude between the homogeneous models (at −1.5 dex solar abundance for the metals) and those with stratification is 0.5 mag or more.

Two other curves are also shown in this figure. The results while assuming that there is general enrichment of the metals (as compared
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Colour–magnitude diagram (u, u − y) for the several sets of BHB-star models. The filled dots represent models from T<sub>eff</sub> = 11 000 to 18 000 K described in Table 1 (T<sub>eff</sub> increases from right- to left-hand side in this figure) that include vertical elemental stratification while the empty dots represent models with homogeneous abundances (with metals at −1.5 dex their solar values). An arrow shows the photometric jump predicted if diffusion becomes efficient at T<sub>eff</sub> = 11 500 K. The dotted curve represents atmosphere with homogeneous abundances equal to solar values. The dashed curve are the results when assuming stratification but without changing the structure of the atmosphere.</figcaption></figure>

to average cluster abundances) equal to a solar value is shown
(dotted curve). This curve clearly shows that a general enrichment
of the metals throughout the atmosphere cannot account for the
photometric jump observed. The other curve shown in Fig. 4 (dashed
curve) represents the colours when one calculates the stratification
profiles in the stars but without modifying the atmospheric structure
(i.e. keeping the structure equal to that of the homogeneous model
with −1.5 dex solar abundances). This shows that opacity changes
cannot by themselves explain the photometric jump for BHB stars
and that the structural changes are essential for this anomaly to
occur. In summary, the photometric changes of the stratified models
as compared to the homogeneous models are brought about by the
change of the atmospheric structure due to the vertical stratification
of the elements. For instance, the temperature in the line-forming
regions of hot BHB stars (see Fig. 1) found in the models with
stratification is significantly larger (by up to approximately 20 per
cent) as compared to the models with an homogeneous composition
with −1.5 dex metal solar abundances.

Photometric gaps are also observed on the horizontal-branch se-
quence of globular clusters. These gaps in colour–magnitude dia-
grams are characterized by an underpopulation of stars for specific
values of colours. For example, a photometric gap is observed in the
(V, U − V) colour–magnitude diagram (Ferraro et al. 1998). This
gap corresponds to T<sub>eff</sub> ≃ 11 500 K where rotation plumets for BHB
stars (Peterson et al. 1995; Behr et al. 2000a,b; Behr et al. 2003b)
and where diffusion could begin to be efficient. Hui-Bon-Hoa et al.
(2000) had shown that this gap may be explained if diffusion be-
comes efficient at T<sub>eff</sub> ≃ 11 500 K. The new models presented here
also show the same feature (see Fig. 5). The width of the gap is
more than 0.1 mag which is consistent with the observations (see
gap named G1 in fig. 3 of Ferraro et al. 1998). As in Fig. 4, two
other curves are plotted as well to show that the photometric gap
cannot be explained by a homogeneous enrichment of the metals
nor elemental stratification without structural changes.

5 SPECTROSCOPIC GRAVITIES

Several spectroscopic studies of BHB stars in metal-poor globular
clusters give surface gravities lower than those predicted by canon-

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Colour–magnitude diagram (V, U − V) that shows the presence of a gap assuming that diffusion becomes efficient at T<sub>eff</sub> = 11 500 K. The curves are defined in the caption of Fig. 4.</figcaption></figure>

ical ZAHB models for stars with temperatures between 11 000 and
20 000 K (see Crocker et al. 1988; Moehler et al. 1995). The values
of the surface gravities are determined through the study of Balmer
lines profiles.

To see the effect of stratified model atmospheres on the value
of surface gravities obtained this way, we synthesized Balmer lines
for the self-consistent model atmospheres with the different effec-
tive temperatures used in the previous sections. Fig. 6 summarizes
our results. Computed with values of surface gravity of canoni-
cal horizontal-branch models (see Table 1), the stratified models
show Balmer line profiles closer to those of homogenous mod-
els of the same effective temperature but with lower gravity (by
approximately 0.4–0.5 dex, see dashed line of Fig. 6). For exam-
ple, for the 14 000 K model, the homogeneous model with log g =
3.8 (dashed line) better fits the wings of the Hβ line predicted by
the self-consistent stratified model than the homogeneous model
with the canonical value of log g = 4.26 (dotted line). Thus, try-
ing to determine spectroscopic gravities using homogenous models
is misleading when the star has its structure altered by abundance
stratification. This effect mimics lower spectroscopic gravities when
using homogeneous models as a workbench. The use of model at-
mospheres taking into account abundance stratifications is therefore
critical for spectroscopic gravity determinations.

As a test (not shown in Fig. 6), we also computed Balmer line
profiles using the atmospheric structure of the self-consistent strati-
fied models, but with homogenous (cluster) abundances. The result
is very close to that obtained with both the stratified model struc-
ture and abundances, showing that most of the effect arises from the
change in the atmospheric structure induced by the stratification of
the abundances.

6 DISCUSSION AND CONCLUSION

The results presented in this paper show that model atmospheres
calculated self-consistently with abundance stratifications (at equi-
librium) of LeBlanc et al. (2009) successfully reproduce several
observational anomalies of hot BHB stars. For instance, our theoret-
ical models predict that the iron abundance stratification decreases
as a function of T<sub>eff</sub> and becomes negligible for BHB stars hotter
than T<sub>eff</sub> ≃ 14 000 K. This result is consistent with the detected
iron abundance slopes found by spectral line analysis of BHB stars
undertaken by Khalack et al. (2007, 2008, 2010).

The model atmospheres with vertical stratifications also repro-
duce the photometric jumps and gaps that occur for BHB stars at
T<sub>eff</sub> ≃ 11 500 K. These anomalies were the precursors for the belief
that abundance stratification due to diffusion is present in the slowly
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Hβ line profiles for the 11 000 and 14 000 K models. The stratified model profiles are denoted 'stratified' and assume, repectively, log g = 3.78 and 4.26 (see Table 1), whereas homogenous cluster abundance models (−1.5 dex solar) are named following their value of log g used. The first value (dotted line) is that of the canonical sequence, and the second (dashed line) that of the homogenous model that fits best the stratified model.</figcaption></figure>

rotating hot BHB stars. The theoretical models presented here also predict, as previously observed, that the spectroscopic gravities obtained for these stars while using homogeneous model atmospheres to fit observations systematically underestimate their true surface gravity. The photometric and surface gravity anomalies are due to the large modification in the atmospheric structure brought about by the stratification of the elements in the atmosphere.

In summary, the results presented here re-affirm those found by Hui-Bon-Hoa et al. (2000) regarding the photometric jumps and gaps as well as for the lower spectroscopic gravities found in hot BHB stars. In addition, we have found that the general trend for the observed Fe stratification slopes in hot BHB stars is similar to the one predicted by the theoretical models (i.e. the slope of Fe abundance decreases as T<sub>eff</sub> increases).

The theoretical models used here assume that the elements attain an equilibrium where their respective diffusion velocities tend towards zero. The approach used to calculate the model atmospheres is not a time-dependent treatment of the diffusion phenomena. Such time-dependent modelling of the atmosphere is essential to obtain more precise elemental stratification profiles. Since Michaud, Richer & Richard (2008) have calculated evolutionary models for BHB stars while including atomic diffusion, their results could be

useful to constrain the amount of each element exchanged with the stellar interior, when building up time-dependent elemental stratifications in the atmospheres.

Even with the uncertainties inherent in the treatment of the diffusion phenomenon in the theoretical models used here, the results presented in this paper significantly strengthens the belief that atomic diffusion is responsible for the aforementioned anomalies observed for hot BHB stars. In the near future, we plan to investigate the error engendered by the use of homogeneous models for the photometric determination of fundamental parameters of BHB stars. Such a study is critical for ensuring the use of proper fundamental parameters for this type of star.

## ACKNOWLEDGMENTS

We thank Luc LeBlanc who has modified some computer codes used here. We also thank the Réseau Québécois de Calcul de Haute Performance (RQCHP) for computational resources. This research was partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC) and Faculté des Études Supérieures et de la Recherche de l'Université de Moncton.

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