adsabs/WIESP2022-NER huggingface dataset:
Paper: 2020MNRAS.498..194G (fulltext)
we apply the formalism of Brogi Line ( 2019 ). We compute the log-likelihood function of each tested model by combining the data and model variances, and the cross-covariance of data and model according to their equation (9). We assume the same total observing time as for the data set presented in Benneke et al. ( 2019 ), which is 8.4 h. Since HRS does not necessarily need out-of-transit data, this integration time would allow us to observe four full transits of the exoplanet. Our results are shown in Fig. 5 . We can successfully and confidently (>5σ) recover the H 2 O signal for all instruments at the expected values of K p and V sys , as shown by the fact that the injection values (white crosses) are within or just outside the 1σ confidence interval. Given the relatively strong detection achieved, we conclude that the best-fitting atmospheric scenario for GJ 3470b would be easily detectable with current HRS with a relatively modest investment of telescope time. The size of the confidence intervals also suggests that GIANO and SPIRou are, respectively, the least and the most sensitive instruments based on our simulations. Note that CARMENES does not cover the K band unlike the other two spectrographs but does still show a strong H 2 O detection because of its high throughput. Figure 5. Detectability of the best-fitting atmospheric scenario for exoplanet GJ 3470b as derived by Benneke et al. ( 2019 ), based on 8 h (4 transits) of simulated observations with three near-infrared high-resolution spectrographs. Shown in the plot are confidence intervals on the rest-frame velocity and radial-velocity amplitude of the planet after the likelihood of Brogi Line ( 2019 ) has been applied to the simulated data. The white cross indicated the simulated values. 3.2 Constraining H<sub>2</sub>O and cloud decks – GJ 436b We now discuss how HRS may be able to constrain abundances and cloud decks on GJ 436b using the grid of model spectra discussed in Section 2.1.2 . We chose this planet as observations of the primary transit have revealed a largely featureless spectrum (Knutson et al. 2014a ). The only constraints on H 2 O thus far have been derived from low-resolution secondary eclipse observations (Stevenson et al. 2010 ). In Fig. 6 , we show three representative high-resolution transmission models with varying H 2 O and cloud top pressures but which resulted in similar muted HST WFC3 features. We studied their detectability with CARMENES, GIANO, and SPIRou, and the ability to discriminate cloudy scenarios from high-metallicity scenarios as shown in Fig. 2 . Figure 6. Model transmission spectra and binned HST WFC3 spectral points for GJ 436b. These are shown for three cases with varying cloud pressures and H 2 O abundances. The high-resolution spectra have been binned to the Knutson et al. ( 2014a ) observations, which are also shown with their associated error bars. We offset the models in the figure to highlight the spectral features. Fig. 6 shows the three
Paper: 2019MNRAS.484.2786S (fulltext)
transpose. We use factorization with the matrix (see Silant’ev et al. 2017a ): Here , . The matrices and have the forms It is useful to introduce the vector K ( τ ): The matrix product of matrices and is denoted as . It is easy to verify that equation ( 7 ) gives rise to the conservation law of radiative flux. 3 THE INTEGRAL EQUATION FOR <bold><italic>K</italic></bold>(<italic>τ</italic>) The formal solution of equation ( 7 ) gives the integral dependence of I 0 ( μ, τ ) on K ( τ ). Substitution of this solution in equation ( 10 ) gives a homogeneous integral equation for K ( τ ): We are interested in the non-zero solution of this equation. The kernel has the form The matrices and have the forms Note that , and . The general theory to calculate the vector K ( τ ) was presented in Silant’ev, Alekseeva Novikov ( 2015 ). Recall that, according to this theory, the vector K ( τ ) has a solution through the resolvent matrix : Here and in what follows we omit the subscription ‘hom’ . The resolvent matrix obeys the equation The kernel of the equation for is symmetric: . This gives rise to the relation . The double Laplace transform of R ( τ, τ ′) over parameters a and b is equal to This property demonstrates that the matrix can be calculated, if we know the matrices and (see Silant’ev et al. 2015 ). For this reason, it is useful to study the equation for , which follows from equation ( 15 ): Using the particular form of and equation ( 16 ), we obtain the following relation: Here is the unit matrix. Hereafter in our theory, we use a = μ and a = μ /(1 + h ). Introducing the new values we obtain the following equations: Note that the H-functions E ( μ ) and K ( μ ) can be obtained from the algebraic system of equations, if we know the other functions – A ( μ ), C ( μ ), D ( μ ), G ( μ ), M ( μ ) and N ( μ ). These functions do not occur in the Milne problem. 4 FORMULAE FOR THE MILNE PROBLEM The specific feature of the Milne problem is that we need to solve an integral equation (see equation 11 ) for K ( τ ), which does not have a free term. Using the vector K ( τ ), one can obtain the solution of transfer equation ( 7 ). The vector I 0 (0, μ ) describes the emerging radiation. This vector has the form i.e. this expression depends on the Laplace transforms of K ( τ ) over variable τ . From equation ( 22 ), we obtain the particular formulae Further, we follow the simple approach of Sobolev ( 1969 ), generalizing his method for the vector case and magnetized atmosphere. The final formulae depend on K (0). Taking τ = 0 in equation ( 11 ), we obtain Now we find the relations and with the matrices and . Let us obtain the equation for derivative d K ( τ )/d τ , taking into account the fact that the kernel depends on the difference ( τ − τ ′): Equation ( 26 ) is a non-homogeneous integral equation. According to the general theory of integral equations (see Tricomi 1957 ; Smirnov 1964 ), the general solution of equation ( 26 ) consists of the sum of two terms –
Paper: 2017MNRAS.469.4726N (fulltext)
compensate for attenuation; a narrower attenuation region would imply a less steep radial dependence of the CO(3–2) effective emissivity. (vi) Values of the intensities integrated over the source size but not corrected for the loss of short spacing have been given for both CO(3–2) emission, 7.1 ± 0.4 Jy km s −1 , and continuum emission, 11.4 ± 0.5 mJy. Crude estimates of the short-spacing correction have been given at the respective levels of 1.6 Jy km s −1 and 5 mJy. The gas value is in good agreement with the value measured earlier by Dent et al. ( 2005 ) but the dust value is larger than that measured by Song et al. ( 2004 ) and close to the predictions of the disc models proposed by Hughes et al. ( 2008 ) and Roberge et al. ( 2013 ), according to which the CO mass of the disc is between ∼2 × 10 −4 and ∼10 −3 Earth masses and the 0.86 mm SED value is ∼19 mJy. The crudeness of our estimated short-spacing correction prevents a reliable resolution of this apparent disagreement, which will require new lower resolution observations. The use in this work of an effective emissivity to model the detected emission mixes the effects of temperature and density and the new results do not justify repeating the detailed analysis that Hughes et al. ( 2008 ) and Roberge et al. ( 2013 ) have made of the disc structure and chemistry for both gas and dust. (vii) Kinematics has been found to be Keplerian over a very broad range of distances from the star, typically 20–200 au, with a power index of and a rotation velocity of 5.1 ± 0.1 km s −1 at a distance of 60 au (1 arcsec) from the star, corresponding to a mass of 1.73 ± 0.10 solar masses for the central star. The observed line width was observed to be dominated by Keplerian shear over most of the disc volume and upper limits to the intrinsic line width (FWHM) have been evaluated, decreasing from 1.4 ± 0.3 km s −1 for | x | 1 arcsec to 0.8 ± 0.1 km s −1 for 2 | x | 3 arcsec. 6.2 Implications on the disc structure and chemistry (Hughes et al. <xref ref-type="bibr" rid="bib9">2008</xref>) The very detailed analysis of the chemistry that governs the morphology and temperature of the disc that was made by Hughes et al. ( 2008 ) remains essentially valid. However, some of the assumptions made by these authors need now to be modified; the inclination angle with respect to the line of sight is definitely non-zero; the dust extends to significantly larger distances from the star than the gas does, both radially and axially; the inner radius of the gas disc is nearly equal to the gravitational radius, ∼20 au, rather than twice this value; the lumpiness of the dust disc contrasts with the smoothness of the gas disc; the apparent warping of the gas disc suggested by the SMA data is not confirmed by the ALMA data; the central attenuation, for which the ALMA data gives strong evidence, can no longer be ignored. Yet, the analysis made by Hughes et al. ( 2008 ) of the factors governing the physics and chemistry of the gas
Paper: 2017MNRAS.470.1404H (fulltext)
and φ is longitude. This is an important property for the analysis to follow. Because the eigenfunctions are a complete set (with zero Lagrangian-pressure perturbation on the outer boundary, e.g. Christensen–Dalsgaard 2003 ), a general wavefield may be written as where ω is temporal frequency, a q are coefficients representing the phase and amplitude of the q th mode and we write for the sake of notational convenience. The governing equation for driven, undamped oscillations is given by where is the unperturbed source, the zeroth-order wavefield and is the unperturbed operator (whose properties are derived from a basic solar model such as model S; Christensen-Dalsgaard et al. 1996 ) as defined in equation ( 2 ). Note that the MDI and HMI missions provide time series of spherical-harmonic coefficients of oscillations, i.e. a k (ω), measured at the solar photosphere. In practice, because we only observe the side of the Sun that faces us, it is not possible to precisely spatially decompose the measured oscillation signals into individual spherical harmonics. This partial visibility leads to leakage between modes across l, introducing systematical errors in eventual inferences (e.g. Larson Schou 2015 ; Woodard 2016 ). Further, at a given frequency (between ridges for instance), many different radial orders contribute, leading to diminished ability in distinguishing between them. Temporal gaps in observations, due to instrumental or other issues, lead to mixing across temporal frequencies (and hence radial orders), thereby exacerbating this issue. To mitigate the problem of radial-order leakage, we use measurements at frequencies within a linewidth of resonance, ensuring that the associated radial order contributes a dominant fraction of observed mode power. Nevertheless, leakage across radial orders and spherical-harmonic degrees will systematically influence the results of mode-coupling analyses and needs to be carefully considered. 2.1 Perturbation theory The effects of rotation, flows, magnetic fields or thermal asphericities are modelled by adding a perturbation to the operator to in equation ( 5 ), in turn leading to a perturbation to the wavefield, . Ignoring perturbations to the source , we obtain for the wavefield in a perturbed Sun. For time-varying perturbations, behaves as a convolution operator. To the first order, we have therefore where the convolution over frequency captures the time variability of the perturbation operator (equation D4 of Appendix D ). Perturbing equation ( 4 ) while assuming that the eigenfunctions are unmodified by the perturbation, we may express the change to the wavefield as a linear combination of the original set of eigenfunctions, Using equation ( 2 ), the left hand side of equation ( 6 ) may be simplified thus Solar modes are subject to a small amount of attenuation γ k ≪ ω k that perturb the eigenfunctions and eigenfrequencies (obtained from equation 1 ) by introducing small imaginary components. However,
Paper: 2019MNRAS.488.4207S (fulltext)
determined by the resonant conditions ( 52 ) and ( 53 ) are of order unity (see ( 42 ). In the opposite short-length limit | k | ≫ 1, the eigenvalue relation ( 30 ) yields: , k, n ≠ 0, n = 1, 2, ..., i.e. the linear growthrates are also small in the radially short-length limit, , e.g. | k | ≫ 1 for n ∼ 1 and | q | ∼ 1. In the latter case the eigenfrequency is diminished together with the growthrate. Now, let us discuss the three-wave resonant interaction in the presence of the short-length modes. First, note that a resonant triad cannot be formed by three short-length modes because of the frequency resonant condition ( 53 ) that is degenerated with all three small frequencies which can be included in the mismatch value, δω. Second, the resonant condition ( 53 ) is also degenerated for two short-length modes with | k | ≫ 1 interacting with the single long-length mode with | k | ≪ 1, since all they have zero frequencies. Finally, evidently that the radial wavenumber resonant condition ( 52 ) cannot be satisfied by the single short-length term with | k | ≪ 1 and two long-length terms with | k | ≫ 1 (at axial wavenumber n ∼ 1). Thus, resonant triads cannot be formed by interacting short- and long-length modes. In particular, this means that energy transfer from very short- to very long-length modes and vice versa cannot be realized with three-wave resonant interaction. Rigorous analytical solutions of the reduced weakly non-linear VSI problem discovered in the present study can serve as a test for numerical modelling of the full non-linear hydrodynamic problem, since the intermediate non-linear stage of VSI should be inevitably crossed before saturation. Predictions of the reduced VSI model allow to identify and discover physical mechanisms that are driving the VSI and its transition to turbulence, as well as identify tuning parameters of the physical and numerical models of the full problem. Figure 1. Amplitudes α ( j ) , j = 1, 2, 3 versus slow time θ for the triad of class I. The two-mode regime of the resonant triad evolution. n (1) = 1, n (2) = 1, n (3) = 2 (see Table 1 ); R = +1; S = +1; , φ 0 = π/4, δω = +1. The scaled resonant frequencies and radial wavenumbers are in Table 1 with and , , ( j = 1, 2). Dashed and solid lines are solutions of the linear and non-linear systems ( 71 )–( 74 ), respectively, for triad amplitudes. Figure 2. Amplitudes α ( j ) , j = 1, 2, 3 versus slow time θ for the triad of class II. The two-mode regime of the resonant triad evolution as in Fig. 1 , but for S = −1. Figure 3. Triad amplitudes α ( j ) , j = 1, 2, 3 versus slow time θ for the triad of class III. The three-mode regime of bounded oscillations of all interacting modes as in Fig. 1 , but for R = −1. Figure 4. Amplitudes α ( j ) versus slow time θ for the triad of class I as in Fig. 1 ( S = +1, R = +1), but at small initial amplitudes . Figure 5. Amplitudes α ( j ) versus slow time θ for the triad of class II as in Fig. 2 ( S = −1, R = +1), but
Paper: 2017ApJ...836..225S (fulltext)
X-ray peak and a separation from continuum X-ray dominant region (DeLaney et al. 2004 ; Helder Vink 2008 ). On the other hand, we defined “south west,” “inner”, and “forward shock” regions as the “non-thermal dominant” region (light blue regions in Figure 2 ). Helder Vink ( 2008 ) and DeLaney et al. ( 2004 ) show the area dominated by a harder spectrum. As a matter of fact, these regions manifest themselves in hard X-rays. Our image also shows the inner region is bright with hard X-rays. In addition, the forward shock has a featureless non-thermal emission (e.g., Hughes et al. 2000 ; Bamba et al. 2005 ). In the forward shock, it was found that the average proper motion of Cassiopeia A is 030 yr −1 (Patnaude Fesen 2009 ), so we corrected the forward shock region of each year with this value (see the Appendix ). 3.2. Spectra With the regions defined in the Section 3.1 , we extracted spectra using a custom pipeline based on specextract in CIAO script. Here, the background spectra were extracted from outside of the whole SNR region defined in Figure 2 . Since X-ray emission from Cassiopeia A is very strong, the background contribution is almost negligible for a time variation estimation. The background fraction of the whole SNR is only ∼3% in the 4.2–7.3 keV band and this is almost constant value from 2002 to 2013. In 2000, this fraction shows a larger value (∼7%) presumably because of an increase in the charged particle flux experienced during this observation. After background subtraction, we fitted the 4.2–7.3 keV band spectra at each epoch with a power-law model and a Gaussian line with XSPEC version 12.8.2. The best-fit parameters are summarized in Table 2 . Table 2 Best-fit Parameters of the ACIS Spectra a Note. a The errors are at 1 σ confidence level. Figure 3 shows the spectra in the 4.2–7.3 keV band taken from the six regions. As described in Section 3.1 , the two bright non-thermal dominant regions south west and inner are remarkable in the hard X-ray continuum flux (Figures 1 and 3 ). Accordingly, the photon indexes of these regions are ∼2.6–3.0 while those of the thermal regions are 3.0–3.4. In the forward shock and whole SNR, photon indexes and evolutions are slightly different from the results in Patnaude et al. ( 2011 ). This is probably due to a difference in the energy band used in the spectral fitting. The fit residuals are larger for the thermal dominant regions than for the non-thermal regions. This is because weak thermal lines such as Cr–K (5.6 keV) appeared in the band. Figure 3. Time variation of the equivalent width of the Fe–K line (plot in the middle) and observed spectra in the 4.2–7.3 keV band (on both sides) at each region (whole SNR: WS, east: E, inner: I, north west: NW, south west: SW, forward shock: FS). In the central plot, the solid lines show best-fit linear models. Individual spectra were fitted with a model composed of a power law and a Gaussian. The error bars of all figures are 1 σ . As shown in Figure 3
Paper: 2021MNRAS.504.2832S (fulltext)
by myriads of DM particles. This is the reason why two convergence criteria are applied to the CDM numerical simulations to declare their results reliable (e.g. Power et al. 2003 ). First, the finite mass of the DM particles used in the simulation artificially shortens the two-body relaxation time-scale; and this artificially-set time-scale is asked to be longer than the age of the Universe, t U . This requirement prevents the thermalization of the resulting DM haloes. Secondly, the artificial thermalization starts in the centre of the DM haloes so the simulated centres are discarded within the so-called convergence radius. However, when these two restrictions are relaxed then cores with polytropic shape appear in the DM haloes produced in the numerical simulation. In this paper, we analyse two types of numerical simulations showing such cores. If the DM is assumed to be self-interacting (SIDM) then the effective relaxation time-scale t SIDM is shortened by an amount that depends on the SIDM cross-section. As soon as , t SIDM ≲ t U and the simulations produce cores. We show in Section 4 how different SIDM from several authors produce cores which after normalization are very similar and equal to the core of a polytrope within error bars. The simulations comprise haloes that go all the way from dwarf galaxies to galaxy clusters. This agreement between simulated haloes and polytropes holds even when baryons are included in the simulation (Section 4.1 ). If standard CDM numerical simulations are analysed within the convergence radius, they also show cores (e.g. Wang et al. 2020 ). These cores are also indistinguishable from polytropes, a result which holds even with halo masses differing by as much as 10 orders of magnitude (Section 5 ). Outside the convergence radius, the profiles follow the canonical NFW or Einasto shape. Thus, because the profiles within the convergence radii are excluded from the standard analysis, it is easy to understand why the profiles resulting from these numerical simulations seem to be set by the initial conditions during the big bang (Cen 2014 ; Nipoti 2015 ; Brown et al. 2020 ). As a by-product of this work, we have shown how unresolved DM clump–clump collisions cannot thermalize the DM haloes within a time-scale comparable to the age of the Universe (Appendix A ). We conclude that the presence of cores in simulated or observed density profiles can used as evidence for systems in thermodynamic equilibrium. Cores are theoretically predicted and also generated in self-gravitating system known to be in thermodynamic equilibrium. APPENDIX A: TWO-BODY COLLISION CROSS-SECTION FOR A CONTINUOUS DISTRIBUTION OF UNRESOLVED DM CLUMPS Starting from the primordial density fluctuations, the gravitational collapse produces a full distribution of DM haloes with masses going from galaxy clusters to Earth-mass clumps and even smaller (e.g. Diemand, Moore Stadel 2005 ; Wang et al. 2020 ). However, numerical simulations cannot treat all
Paper: 2020A&A...635A...8C (fulltext)
regression with an objective datapoint rejection, which models the outlier distribution. The method infers the parameters of the linear fit together with the mean and variance of the distribution of outliers as well as the number of outliers at the same time. The model is run through 50 000 MCMC realizations, taking the maximum of the posterior distribution and the standard deviation as the best values of the slope, intercept, and their uncertainties. We did not attempt to perform the fits when the number of stars with abundances is smaller than 15 or when the uncertainties in the abundances are greater than 0.05 dex. In Fig. 10 we plotted some examples of the differential element abundance pairs δ X 1 vs. δ X 2 . The full matrix of differential abundances for the three clusters are found in Figs. B.3 – B.5 . We also overplotted the obtained fits. For the Hyades, we obtain statistically significant correlations (larger than 3 σ ) of all pairs of abundances that we analyze. Some elements with larger intrinsic uncertainties (e.g., Ba, Nd, Cu) tend to present less significant correlations. For the other two clusters, we have a smaller sample of stars selected as most probable members and larger uncertainties in the abundance measures. The less significant fit is the one of Na I vs. Mn I in NGC 2632, which has a posterior with two peaks. For Ruprecht 147, two fits involving Si I have lower significances than 3 σ . In Fig. 10 we see no dependence of the differential abundance pairs with respect to T eff , showing that all types of stars correlate in the same way. Fig. 10. Left : δ Ti vs. δ Si. Right : δ Mg vs. δ Fe, rows correspond to the three clusters. Color represents effective temperature. Translucid lines are the resulting linear fit according to the obtained posterior distribution in the intercept and the slope. The slope and its uncertainty is indicated in each panel. For the Hyades, a large number of slopes were retrieved, so we computed the compatibility among all of them within the quoted uncertainties: (i) The fits involving Cu I and Ba II that have non-Gaussian posterior distributions tend to not be incompatible with the others. However, in these cases, uncertainties are not well represented by the standard deviation. (ii) In the case of Nd II , all the slopes are larger than 3 σ when compared to most of the other cases. We attribute this to the larger uncertainties of this element in comparison with the others, which makes the dispersion in its dimension increase, and thus increase the value of the slope. (iii) We find compatible slopes for all other pairs of elements. This indicates that the differences in star-by-star abundance are due to a zero-point difference in the overall metallicity among the stars in the cluster, with no variation depending on the chemical element. 6.3.2. Comparison with synthetic data To better interpret our results, we generated a set of simulated spectra of stars in two cases: a chemically homogeneous