Stellar Interior Models Research Articles

Anisotropic interior models with Kohler–Chao–Tikekar-like complexity factor

This work explores the construction of spherically symmetric models of stellar interiors by incorporating the null complexity factor (CF) as an additional constraint. This supplementary condition helps us to close an array of stellar structure equations resulting from the process of gravitational decoupling. By making use of MGD-type gravitational decoupling we analyze the role of gravitational decoupling and its impact on the complexity of static, self-gravitational systems. We begin by considering an anisotropic seed solution described by the Kohler–Chao–Tikekar metric ansatz. We then apply the minimal geometric deformation technique to this seed solution, imposing the constraint that the effective anisotropic factor vanishes. This constraint leads to the generation of an isotropic stellar solution. Furthermore, we construct a second family of solutions in which the CF, remains the same for both the seed solution and its minimally deformed counterpart. Our analysis further investigated the influence of both the deformation parameter and the CF on the structural properties of the static and spherically symmetric stellar objects.

The Araucaria project: High-precision orbital parallaxes and masses of binary stars

Aims. We aim to measure very precise and accurate model-independent masses and distances of detached binary stars. Precise masses at the < 1% level are necessary to test and calibrate stellar interior and evolution models, while precise and independent orbital parallaxes are essential to check for the next Gaia data releases. Methods. We combined RV measurements with interferometric observations to determine orbital and physical parameters of ten double-lined spectroscopic systems. We report new relative astrometry from VLTI/GRAVITY and, for some systems, new VLT/UVES spectra to determine the radial velocities of each component. Results. We measured the distance of ten binary systems and the mass of their components with a precision as high as 0.03% (average level 0.2%). They are combined with other stellar parameters (effective temperatures, radii, flux ratios, etc.) to fit stellar isochrones and determine their evolution stage and age. We also compared our orbital parallaxes with Gaia and showed that half of the stars are beyond 1σ with our orbital parallaxes; although, their RUWE is below the frequently used cutoff of 1.4 for reliable Gaia astrometry. By fitting the telluric features in the GRAVITY spectra, we also estimated the accuracy of the wavelength calibration to be ∼0.02% in high and medium spectral resolution modes. Conclusions. We demonstrate that combining spectroscopic and interferometric observations of binary stars provides extremely precise and accurate dynamical masses and orbital parallaxes. As they are detached binaries, they can be used as benchmark stars to calibrate stellar evolution models and test the Gaia parallaxes.

Planet-star interactions with precise transit timing

Context. Hot Jupiters on extremely short-period orbits are expected to be unstable due to tidal dissipation and spiral toward their host stars. That is because they transfer the angular momentum of the orbital motion through tidal dissipation into the stellar interior. Although the magnitude of this phenomenon is related to the physical properties of a specific star-planet system, statistical studies show that tidal dissipation might shape the architecture of hot Jupiter systems during the stellar lifetime on the main sequence. Aims. The efficiency of tidal dissipation remains poorly constrained in star-planet systems. Stellar interior models show that the dissipation of dynamical tides in radiation zones could be the dominant mechanism driving planetary orbital decay. These theoretical predictions can be verified with the transit timing method. Methods. We acquired new precise transit mid-times for five planets. They were previously identified as the best candidates for which orbital decay might be detected. Analysis of the timing data allowed us to place tighter constraints on the orbital decay rate. Results. No statistically significant changes in their orbital periods were detected for all five hot Jupiters in systems HAT-P-23, KELT-1, KELT-16, WASP-18, and WASP-103. For planets HAT-P-23 b, WASP-18 b, and WASP-103 b, observations show that the mechanism of the dynamical tidal dissipation probably does not operate in their host stars, preventing their orbits from rapidly decaying. This finding aligns with the models of stellar interiors of F-type stars, in which dynamical tides are not fully damped due to convective cores. For KELT-16 b, the span of transit timing data was not long enough to verify the theoretical predictions. KELT-1 b was identified as a potential laboratory for studying the dissipative tidal interactions of inertial waves in a convective layer. Continued observations of those two planets may provide further empirical verification of the tidal dissipation theory.

Yıldız İç Yapı Modellerinin Asterosismik Olarak İncelenmesi

The stellar interior models are generally used to understand the structure and evolution of stars. The models that best represent the stars are decided by the observation parameters. For this purpose, the output data of the models obtained are compared with the observation data. A star can be represented from its core to the surface with the help of models. While the surface observation parameters and model surface parameters can be compared thanks to the photons taken from the stars, it is very difficult to compare the central conditions. Today, thanks to the developing technology and space telescopes, stellar seismology (asteroseismology) can now have observational data about the core and central regions of the stars. Thus, the internal structure models can be examined in more detail and the basic direct observation parameters of the stars can be determined more easily and precisely. In this study, models in solar composition were examined for the mass range of 1.00-1.60 M⊙ with the MESA evolution code. Thanks to these models, the asteroseismic and non-asteroseismic parameters of the star were compared with each other. In this way, information about the age, which is difficult to detect, was obtained with the internal structure models of the stars. Here,the fist time, a linear relationship was found between 2/R3 obtained from the models and age.

Asteroseismic analysis of eight solar-like oscillating evolved stars in the open cluster NGC 6811

ABSTRACT The Kepler space telescope has provided exquisite data with which to perform asteroseismic analysis on evolved star ensembles. Studying star clusters offers significant insight into stellar evolution and structure, due to having a large number of stars with essentially the same age, distance, and chemical composition. This study analysed eight solar-like oscillating evolved stars that are members of the open cluster NGC 6811 and modelled them for the first time. The fundamental stellar parameters are obtained from the interior model using observational asteroseismic and non-asteroseismic constraints. The stellar interior models are constructed using the mesa evolution code. The mass-loss method is included in the interior models of the stars. The stellar masses and radius ranges of the stars are 2.23–2.40 M⊙ and 8.47–12.38 R⊙, respectively. Typical uncertainties for the mass and radius are ∼0.11 M⊙ and ∼0.09 R⊙, respectively. The model masses and radii are compared with masses and radii obtained from asteroseismic and non-asteroseismic methods (scaling relations and classic methods). The stellar ages fell in the range between 0.71 and 0.82 Gyr, with a typical uncertainty of ${\sim}18$ per cent. The model ages of the stars calculated in this study are compatible with those reported in the literature for NGC 6811.

Detecting axisymmetric magnetic fields using gravity modes in intermediate-mass stars

Context.Angular momentum (AM) transport models of stellar interiors require improvements to explain the strong extraction of AM from stellar cores that is observed with asteroseismology. One of the frequently invoked mediators of AM transport are internal magnetic fields, even though their properties, observational signatures, and influence on stellar evolution are largely unknown.Aims.We study how a fossil, axisymmetric internal magnetic field affects period spacing patterns of dipolar gravity mode oscillations in main sequence stars with masses of 1.3, 2.0, and 3.0 M⊙. We assess the influence of fundamental stellar parameters on the magnitude of pulsation mode frequency shifts.Methods.We computed dipolar gravity mode frequency shifts due to a fossil, axisymmetric poloidal–toroidal internal magnetic field for a grid of stellar evolution models, varying stellar fundamental parameters. Rigid rotation was taken into account using the traditional approximation of rotation, and the influence of the magnetic field was computed using a perturbative approach.Results.We find magnetic signatures for dipolar gravity mode oscillations in terminal-age main sequence stars that are measurable for a near-core field strength larger than 105G. The predicted signatures differ appreciably from those due to rotation.Conclusions.Our formalism demonstrates the potential for the future detection and characterization of strong fossil, axisymmetric internal magnetic fields in gravity-mode pulsators near the end of core-hydrogen burning fromKeplerphotometry, if such fields exist.

A realistic two-dimensional model of Altair

Context. Fast rotation is responsible for important changes in the structure and evolution of stars and the way we see them. Optical long baseline interferometry now allows for the study of its effects on the stellar surface, mainly gravity darkening and flattening. Aims. We aim to determine the fundamental parameters of the fast-rotating star Altair, in particular its evolutionary stage (represented here by the core hydrogen mass fraction Xc), mass, and differential rotation, using state-of-the-art stellar interior and atmosphere models together with interferometric (ESO-VLTI), spectroscopic, and asteroseismic observations. Methods. We use ESTER two-dimensional stellar models to produce the relevant surface parameters needed to create intensity maps from atmosphere models. Interferometric and spectroscopic observables are computed from these intensity maps and several stellar parameters are then adjusted using the publicly available MCMC algorithm Emcee. Results. We determined Altair’s equatorial radius to be Req = 2.008 ± 0.006 R⊙, the position angle PA = 301.1 ± 0.3°, the inclination i = 50.7 ± 1.2°, and the equatorial angular velocity Ω = 0.74 ± 0.01 times the Keplerian angular velocity at equator. This angular velocity leads to a flattening of ε = 0.220 ± 0.003. We also deduce from the spectroscopically derived v sin i ≃ 243 km s−1, a true equatorial velocity of ∼314 km s−1 corresponding to a rotation period of 7h46m (∼3 cycles/day). The data also impose a strong correlation between mass, metallicity, hydrogen abundance, and core evolution. Thanks to asteroseismic data, and provided our frequencies identification is correct, we constrain the mass of Altair to 1.86 ± 0.03 M⊙ and further deduce its metallicity Z = 0.019 and its core hydrogen mass fraction Xc = 0.71, assuming an initial solar hydrogen mass fraction X = 0.739. These values suggest that Altair is a young star ∼100 Myr old. Finally, the 2D ESTER model also gives the internal differential rotation of Altair, showing that its core rotates approximately 50% faster than the envelope, while the surface differential rotation does not exceed 6%.

Asteroseismic investigation of 20 planet and planet-candidate host stars

ABSTRACT Planets and planet candidates are subjected to great investigation in recent years. In this study, we analyse 20 planet and planet-candidate host stars at different evolutionary phases. We construct stellar interior models of the host stars with the mesa e.volution code and obtain their fundamental parameters under influence of observational asteroseismic and non-asteroseismic constraints. Model mass range of the host stars is 0.74–1.55 $\rm M_{\odot }$. The mean value of the so-called large separation between oscillation frequencies and its variation about the minima shows the diagnostic potential of asteroseismic properties. Comparison of variations of model and observed large separations versus the oscillation frequencies leads to inference of fundamental parameters of the host stars. Using these parameters, we revise orbital and fundamental parameters of 34 planets and four planet candidates. According to our findings, radius range of the planets is 0.35–16.50 $\rm R_{{\oplus }}$. The maximum difference between the transit and revised radii occurs for Kepler-444b-f is about 25 per cent.

Period spacings of gravity modes in rapidly rotating magnetic stars

Context.Stellar magnetic fields are often invoked to explain the missing transport of angular momentum observed in models of stellar interiors. However, the properties of an internal magnetic field and the consequences of its presence on stellar evolution are largely unknown.Aims.We study the effect of an axisymmetric internal magnetic field on the frequency of gravity modes in rapidly rotating stars to check whether gravity modes can be used to detect and probe such a field.Methods.Rotation is taken into account using the traditional approximation of rotation and the effect of the magnetic field is computed using a perturbative approach. As a proof of concept, we compute frequency shifts due to a mixed (i.e. with both poloidal and toroidal components) fossil magnetic field for a representative model of a known magnetic, rapidly rotating, slowly pulsating B-type star: HD 43317.Results.We find that frequency shifts induced by the magnetic field scale with the square of its amplitude. A magnetic field with a near-core strength of the order of 150 kG (which is consistent with the observed surface field strength of the order of 1 kG) leads to signatures that are detectable in period spacings for high-radial-order gravity modes.Conclusions.The predicted frequency shifts can be used to constrain internal magnetic fields and offer the potential for a significant step forward in our interpretation of the observed structure of gravity-mode period spacing patterns in rapidly rotating stars.

Carbon Abundance Inhomogeneities and Deep Mixing Rates in Galactic Globular Clusters

Abstract Among stars in Galactic globular clusters the carbon abundance tends to decrease with increasing luminosity on the upper red giant branch, particularly within the lowest metallicity clusters. While such a phenomena is not predicted by canonical models of stellar interiors and evolution, it is widely held to be the result of some extra mixing operating during red giant branch ascent which transports material exposed to the CN(O)-cycle across the radiative zone in the stellar interior and into the base of the convective envelope, whereupon it is brought rapidly to the stellar surface. Here we present measurements of [C/Fe] abundances among 67 red giants in 19 globular clusters within the Milky Way. Building on the work of Martell et al., we have concentrated on giants with absolute magnitudes of M V ∼ −1.5 within clusters encompassing a range of metallicity (−2.4 < [Fe/H] < −0.3). The Kitt Peak National Observatory (KPNO) 4 m and Southern Astrophysical Research (SOAR) 4.1 m telescopes were used to obtain spectra covering the λ4300 CH and λ3883 CN bands. The CH absorption features in these spectra have been analyzed via synthetic spectra in order to obtain [C/Fe] abundances. These abundances and the luminosities of the observed stars were used to infer the rate at which C abundances change with time during upper red giant branch evolution (i.e., the mixing efficiency). By establishing rates over a range of metallicity, the dependence of deep mixing on metallicity is explored. We find that the inferred carbon depletion rate decreases as a function of metallicity, although our results are dependent on the initial [C/Fe] composition assumed for each star.

Clumping in stellar winds and interiors

AbstractThe uncertain clumping properties pose a major problem for the quantitative analysis and the modelling of hot star winds. New results suggest that also the outer envelopes of massive stars may be affected by clumping, with important consequences for their observable radii and ionising properties. In this talk I will discuss how clumping is incorporated in stellar interior and wind/atmosphere models, how current theoretical results compare with observations, and what we can learn from a combination of stellar interior models and winds.

Fundamental properties ofKeplerandCoRoTtargets – III. Tuning scaling relations using the first adiabatic exponent

So called scaling relations have the potential to reveal the mass and radius of solar-like oscillating stars, based on oscillation frequencies. In derivation of these relations, it is assumed that the first adiabatic exponent at the surface (Gamma_1s) of such stars is constant. However, by constructing interior models for the mass range 0.8-1.6 Msun, we show that Gamma_1s is not constant at stellar surfaces for the effective temperature range with which we deal. Furthermore, the well-known relation between large separation and mean density also depends on Gamma_1s. Such knowledge is the basis for our aim of modifying scaling relations. There are significant differences between masses and radii found from modified and conventional scaling relations. However, comparison of predictions of these relations with the non-asteroseismic observations of Procyon A reveals that new scaling relations are effective in determining the mass and radius of stars. In the present study, solar-like oscillation frequencies of 89 target stars (mostly Kepler and CoRoT) were analysed. As well as two new reference frequencies (nu_min1 and nu_min2) found in the spacing of solar-like oscillation frequencies of stellar interior models, we also take into account nu_min0. In addition to the frequency of maximum amplitude, these frequencies have very strong diagnostic potential for determination of fundamental properties. The present study involves the application of derived relations from the models to the solar-like oscillating stars, and computes their effective temperatures using purely asteroseismic methods. There are in general very close agreements between effective temperatures from asteroseismic and non-asteroseismic (spectral and photometric) methods. For the Sun and Procyon A, for example, the agreement is almost total.

Solution of the Einstein–Maxwell equations with anisotropic negative pressure as a potential model of a dark energy star

We have obtained a new class of solutions for the Einstein–Maxwell field equations for static spherically symmetric space–times by considering the negative anisotropic pressures, which represents a potential model of a dark energy star. We take the equation of state pr = −ρ, where pr is the radial pressure and ρ is the density. We have also checked that for these solutions metric coefficients, mass density, radial pressure, transverse pressure, electric field, and current density are well defined for suitable values of the parameters involved in the solution. These exact solutions can be used to develop models of dark energy stellar interiors satisfying all physical constraints except for the causality condition, which cannot be satisfied for the equation of state considered here, and which is arguably not an applicable physical constraint for dark matter–energy.

Single stars in the Hyades open cluster

Age and mass determinations for isolated stellar objects remain model-dependent. While stellar interior and atmospheric theoretical models are rapidly evolving, we need a powerful tool to test them. Open clusters are good candidates for this role. We complement previous studies on the Hyades multiplicity by Lucky Imaging observations with the AstraLux Norte camera. This allows us to exclude possible binary and multiple systems with companions outside 2--7 AU separation and to create a "single-star sequence" for the Hyades. The sequence encompasses 250 main-sequence stars ranging from A5V to M6V. Using the "Tool for Astrophysical Data Analysis" (TA-DA), we create various theoretical isochrones applying different combinations of interior and atmospheric models. We compare the isochrones with the observed Hyades single-star sequence on J vs. J - K_s, J vs. J - H and K_s vs. H - K_s color-magnitude diagrams. As a reference we also compute absolute fluxes and magnitudes for all stars from X-ray to mid-infrared based on photometric measurements available in the literature(ROSAT X-ray, GALEX UV, APASS gri, 2MASS JHK_s, and WISE W1 to W).We find that combinations of both PISA and DARTMOUTH stellar interior models with BT-Settl 2010 atmospheric models describe the observed sequence well. The full sequence covers the mass range 0.13 to 2.3 Msun, and effective temperatures between 3060 K and 8200 K. Within the measurement uncertainties, the current generation of models agree well with the single-star sequence. The primary limitations are the uncertainties in the measurement of the distance to individual Hyades members, and uncertainties in the photometry. Additionally, a small (~0.05 mag) systematic offset can be noted on J vs. J - K and K vs. H - K diagrams - the observed sequence is shifted to redder colors from the theoretical predictions.

Red giant branch bump star counts in data and stellar models

We compare model predictions to observations of star counts in the red giant branch bump (RGBB) relative to the number density of first-ascent red giant branch at the magnitude of the RGBB, $EW_{RGBB}$. The predictions are shown to exceed the data by $(5.2 \pm 4.3)$% for the BaSTI models and by $(17.1 \pm 4.3)$% for the Dartmouth models, where the listed errors are purely statistical. These two offsets are brought to zero if the Galactic globular cluster metallicity scale is assumed to be overestimated by a linear shift of $\sim 0.11$ dex and $\sim 0.36$ dex respectively. This inference based on RGBB star counts goes in the opposite direction to the increase in metallicities of ${\Delta}$[M/H]$\approx$0.20 dex that would be required to fix the offset between predicted and observed RGBB luminosities. This comparison is a constraint on "deep mixing" models of stellar interiors, which predict decreased rather than increased RGBB star counts. We tabulate the predictions for RGBB star counts as a function of [Fe/H], [$\alpha$/Fe], CNONa, initial helium abundance, and age. Though our study suggests a small zero-point calibration issue, RGBB star counts should nonetheless be an actionable parameter with which to constrain stellar populations in the differential sense. The most significant outliers are toward the clusters NGC 5025 (M53), NGC 6723, and NGC 7089 (M2), each of which shows a $\sim 2 \sigma$ deficit in their RGBB star counts.

Pre-main-sequence isochrones – III. The Cluster Collaboration isochrone server

We present an isochrone server for semi-empirical pre-main-sequence model isochrones in the following systems: Johnson-Cousins, Sloan Digital Sky Survey, Two-Micron All-Sky Survey, Isaac Newton Telescope (INT) Wide-Field Camera, and INT Photometric H$\alpha$ Survey (IPHAS)/UV-Excess Survey (UVEX). The server can be accessed via the Cluster Collaboration webpage {http://www.astro.ex.ac.uk/people/timn/isochrones/}. To achieve this we have used the observed colours of member stars in young clusters with well-established age, distance and reddening to create fiducial loci in the colour-magnitude diagram. These empirical sequences have been used to quantify the discrepancy between the models and data arising from uncertainties in both the interior and atmospheric models, resulting in tables of semi-empirical bolometric corrections (BCs) in the various photometric systems. The model isochrones made available through the server are based on existing stellar interior models coupled with our newly derived semi-empirical BCs. As part of this analysis we also present new cluster parameters for both the Pleiades and Praesepe, yielding ages of $135^{+20}_{-11}$ and $665^{+14}_{-7}\,\rm{Myr}$ as well as distances of $132 \pm 2$ and $184 \pm 2\,\rm{pc}$ respectively (statistical uncertainty only).

Chemical abundances of fast-rotating OB stars

AbstractFast rotation in massive stars is predicted to induce mixing in their interior, but a population of fast-rotating stars with normal nitrogen abundances at their surface has recently been revealed (Hunter et al.2009; Brott et al.2011, but see Maeder et al.2014). However, as the binary fraction of these stars is unknown, no definitive statements about the ability of single-star evolutionary models including rotation to reproduce these observations can be made. Our work combines for the first time a detailed surface abundance analysis with a radial-velocity monitoring for a sample of bright, fast-rotating Galactic OB stars to put strong constraints on stellar evolutionary and interior models.

Revised physical elements of the astrophysically important O9.5+O9.5V eclipsing binary system Y Cygni

Thanks to its long and rich observational history and rapid apsidal motion, the massive eclipsing binary Y Cyg represents one of the cornestones to critical tests of stellar evolution theory for massive stars. Yet, the determination of the basic physical properties is less accurate than it could be given the existing number of spectral and photometric observations. Our goal is to analyze all these data simultaneously with the new dedicated series of our own spectral and photometric observations from observatories widely separated in longitude. We obtained new series of UBV observations at three observatories separated in local time to obtain complete light curves of Y Cyg for its orbital period close to 3 days. This new photometry was reduced and carefully transformed to the standard UBV system using the HEC22 program. We also obtained new series of red spectra secured at two observatories and re-analyzed earlier obtained blue electronic spectra. Our analyses provide the most accurate so far published value of the apsidal period of 47.805 +/- 0.030 yrs and the following physical elements: M1=17.72+/-0.35$ Msun, M2=17.73+/-0.30 Msun, R1=5.785+/-0.091 Rsun, and R2=5.816+/-0.063 Rsun. The disentangling thus resulted in the masses, which are somewhat higher than all previous determinations and virtually the same for both stars, while the light curve implies a slighly higher radius and luminosity for star 2. The above empirical values imply the logarithm of the internal structure constant log k2 = -1.937. A comparison with Claret's stellar interior models implies an age close to 2 millions yrs for both stars. The claimed accuracy of modern element determination of 1-2 per cent seems still a bit too optimistic and obtaining new high-dispersion and high-resolution spectra is desirable.

THE BERLIN EXOPLANET SEARCH TELESCOPE II CATALOG OF VARIABLE STARS. I. CHARACTERIZATION OF THREE SOUTHERN TARGET FIELDS

A photometric survey of three Southern target fields with BEST II yielded the detection of 2,406 previously unknown variable stars and an additional 617 stars with suspected variability. This study presents a catalog including their coordinates, magnitudes, light curves, ephemerides, amplitudes, and type of variability. In addition, the variability of 17 known objects is confirmed, thus validating the results. The catalog contains a number of known and new variables that are of interest for further astrophysical investigations, in order to, e.g., search for additional bodies in eclipsing binary systems, or to test stellar interior models. Altogether, 209,070 stars were monitored with BEST II during a total of 128 nights in 2009/2010. The overall variability fraction of 1.2-1.5% in these target fields is well comparable to similar ground-based photometric surveys. Within the main magnitude range of $R\in\left[11,17\right]$, we identify 0.67(3)% of all stars to be eclipsing binaries, which indicates a completeness of about one third for this particular type in comparison to space surveys.

CHARACTERIZATION OF THE RED GIANT HR 2582 USING THE CHARA ARRAY

We present the fundamental parameters of HR 2582, a high-mass red giant star whose evolutionary state is a mystery. We used the CHARA Array interferometer to directly measure the star's limb-darkened angular diameter (1.006+/-0.020 mas) and combined our measurement with parallax and photometry from the literature to calculate its physical radius (35.76+/-5.31 R_Sun), luminosity (517.8+/-17.5 L_Sun), bolometric flux (14.8+/-0.5 e-8 erg s-1 cm-2) and effective temperature (4577+/-60 K). We then determined the star's mass (5.6+/-1.7 M_Sun) using our new values with stellar oscillation results from Baudin et al. Finally, using the Yonsei-Yale evolutionary models, we estimated HR 2582's age to be 165 +20/-15 Myr. While our measurements do not provide the precision required to definitively state where the star is in its evolution, it remains an excellent test case for evaluating stellar interior models.