Stellar Radius Research Articles

Asteroseismic modelling strategies in the PLATO era

Context. In the framework of the PLATO mission, to be launched in late 2026, seismic inversion techniques will play a key role in determining the mission precision requirements in terms of stellar mass, radius, and age. It is therefore relevant to discuss the challenges of the automation of seismic inversions, which were originally developed for individual modelling. Aims. We tested the performance of our newly developed quality assessment procedure of seismic inversions, which was designed for pipeline implementation. Methods. We applied our assessment procedure to a testing set composed of 26 reference models. We divided our testing set into two categories: calibrator targets whose inversion behaviour is well known from the literature and targets for which we assessed the quality of the inversion manually. We then compared the results of our assessment procedure with our expectations as a human modeller for three types of inversions: the mean density inversion, the acoustic radius inversion, and the central entropy inversion. Results. We find that our quality assessment procedure performs as well as a human modeller. The mean density inversion and the acoustic radius inversion are suited to large-scale applications, but not the central entropy inversion, at least in its current form. Conclusions. Our assessment procedure shows promising results for a pipeline implementation. It is based on the by-products of the inversion and therefore requires few numerical resources to quickly assess the quality of an inversion result.

Shape Asymmetries and the Relation between Lopsidedness and Radial Alignment in Simulated Galaxies

Galaxies are observed to be lopsided, meaning that they are more massive and more extended along one side than the opposite side. In this work, we provide a statistical analysis of the lopsided morphology of 1780 isolated satellite galaxies generated by the TNG50-1 simulation, incorporating the effect of tidal fields from halo centers. The isolated satellites are galaxies without nearby substructures whose mass is over 1% of the satellites within their virial radii. We study the radial alignment (RA) between the major axes of satellites and the radial direction of their halo centers in radial ranges of 0–2, 2–5, and 5–10 R h , with R h being the stellar half-mass radius. According to our results, the RA is virtually undetectable in inner and intermediate regions, yet it is significantly evident in outer regions. We also calculate the far-to-near-side semiaxial ratios of the major axes, denoted by a −/a +, which measure the semiaxial ratios of the major axes in the hemispheres between those facing away from (far side) and facing toward (nearside) halo centers. In all the radial bins of the satellites, the numbers of satellites with longer semiaxes on the far side are found to be almost equal to those with longer semiaxes on the near side. Therefore, the tidal fields from halo centers play a minor role in the generation of lopsided satellites. The long semimajor-axes radial alignment (LRA), i.e., an alignment between the long semimajor axes of satellite galaxies and the radial directions to their halo centers, is further studied. No clear evidence of LRA is found in our sample within the framework of ΛCDM Newtonian dynamics. Finally, we briefly discuss the possible origins of the asymmetry of galaxies in TNG50-1.

Locked differential rotation in core-helium burning red giants

Context. Oscillation modes of a mixed character are able to probe the inner region of evolved low-mass stars and offer access to a range of information, in particular, the mean core rotation. Ensemble asteroseismology observations are then able to provide clear views on the transfer of angular momentum when stars evolve as red giants. Aims. Previous catalogs of core rotation rates in evolved low-mass stars have focussed on hydrogen-shell burning stars. Our aim is to complete the compilation of rotation measurements toward more evolved stages, with a detailed analysis of the mean core rotation in core-helium burning giants. Methods. The asymptotic expansion for dipole mixed modes allows us to fit oscillation spectra of red clump stars and derive their core rotation rates. We used a range of prior seismic analyses, complete with new data, to get statistically significant results. Results. We measured the mean core rotation rates for more than 1500 red clump stars. We find that the evolution of the core rotation rate in core-helium-burning stars scales with the inverse square of the stellar radius, with a small dependence on mass. Conclusions. Assuming the conservation of the global angular momentum, a simple model allows us to infer that the mean core rotation and envelope rotation are necessarily coupled. The coupling mechanism ensures that the differential rotation in core-helium-burning red giants is locked.

Measuring the stellar and planetary parameters of the 51 Eridani system

Abstract In order to study exoplanets, a comprehensive characterisation of the fundamental properties of the host stars – such as angular diameter, temperature, luminosity, and age, is essential, as the formation and evolution of exoplanets are directly influenced by the host stars at various points in time. In this paper, we present interferometric observations taken of directly imaged planet host 51 Eridani at the CHARA Array. We measure the limb-darkened angular diameter of 51 Eridani to be $\theta_\mathrm{LD} = 0.450\pm 0.006$ mas and combining with the Gaia zero-point corrected parallax, we get a stellar radius of $1.45 \pm 0.02$ R $_{\odot}$ . We use the PARSEC isochrones to estimate an age of $23.2^{+1.7}_{-2.0}$ Myr and a mass of $1.550^{+0.006}_{-0.005}$ M $_{\odot}$ . The age and mass agree well with values in the literature, determined through a variety of methods ranging from dynamical age trace-backs to lithium depletion boundary methods. We derive a mass of $4.1\pm0.4$ M $_\mathrm{Jup}$ for 51 Eri b using the Sonora Bobcat models, which further supports the possibility of 51 Eri b forming under either the hot-start formation model or the warm-start formation model.

Planet-driven scatterings of planetesimals into a star: probability, time-scale, and applications

ABSTRACT A planetary system can undergo multiple episodes of intense dynamical activities throughout its life, resulting in the production of star-grazing planetesimals (or exocomets) and pollution of the host star. Such activity is especially pronounced when giant planets interact with other small bodies during the system’s evolution. However, due to the chaotic nature of the dynamics, it is difficult to determine the properties of the perturbing planet(s) from the observed planetesimal-disruption activities. In this study, we examine the outcomes of planetesimal-planet scatterings in a general setting. We focus on one-planet systems, and determine the likelihood and time-scale of planetesimal disruption by the host star as a function of the planet properties. We obtain a new analytical expression for the minimum distance a scattering body can reach, extending previous results by considering finite planet eccentricity and non-zero planetesimal mass. Through N-body simulations, we derive the distribution of minimum distances and the likelihood and time-scales of three possible outcomes of planetesimal-planet scatterings: collision with the planet, ejection, and disruption by the star. For planetesimals with negligible mass, we identify four defining dimensionless parameters (the planet eccentricity, planet-to-star mass ratio, planet radius to semimajor axis ratio, and the stellar disruption radius to planet semimajor axis ratio) that enable us to scale the problem and generalize our findings to a wide range of orbital configurations. Using these results, we explore three applications: falling evaporating bodies in the β Pictoris system, white dwarf pollution due to planetesimal disruption and planet engulfment by main-sequence stars.

Bottom-up dust nucleation theory in oxygen-rich evolved stars

Context. Spinel (MgAl2O4) and krotite (CaAl2O4) are alternative candidates to alumina (Al2O3) as primary dust condensates in the atmospheres of oxygen-rich evolved stars. Moreover, spinel was proposed as a potential carrier of the circumstellar 13 μm feature. However, the formation of nucleating spinel clusters is challenging; in particular, the inclusion of Mg constitutes a kinetic bottleneck. Aims. We aim to understand the initial steps of cosmic dust formation (i.e. nucleation) in oxygen-rich environments using a quantum-chemical bottom-up approach. Methods. Starting with an elemental gas-phase composition, we constructed a detailed chemical-kinetic network that describes the formation and destruction of magnesium-, calcium-, and aluminium-bearing molecules as well as the smallest dust-forming (MgAl2O4)1 and (CaAl2O4)1 monomer clusters. Different formation scenarios with exothermic pathways were explored, including the alumina (Al2O3) cluster chemistry studied in Paper I of this series. The resulting extensive network was applied to two model stars, a semi-regular variable and a Mira-type star, and to different circumstellar gas trajectories, including a non-pulsating outflow and a pulsating model. We employed global optimisation techniques to find the most favourable (MgAl2O4)n, (CaAl2O4)n, and mixed (MgxCa(1−x)Al2O4)n isomers, with n = 1–7 and x∈[0..1], and we used high level quantum-chemical methods to determine their potential energies. The growth of larger clusters with n = 2–7 is described by the temperature-dependent Gibbs free energies. Results. In the considered stellar outflow models, spinel clusters do not form in significant amounts. However, we find that in the Mira-type non-pulsating model CaAl2O3(OH)2, a hydroxylated form of the calcium aluminate krotite monomer forms at abundances as large as 2 × 10−8 at 3 stellar radii, corresponding to a dust-to-gas mass ratio of 1.5 × 10−6. Moreover, we present global minimum (GM) candidates for (MgAl2O4)n and (CaAl2O4)n, where n = 1–7. For cluster sizes n = 3–7, we find new, hitherto unreported GM candidates. All spinel GM candidates found are energetically more favourable than their corresponding magnesium-rich silicate clusters with an olivine stoichiometry, namely (Mg2SiO4)n. Moreover, calcium aluminate clusters, (CaAl2O4)n, are more favourable than their Mg-rich counterparts; the latter show a gradual enhancement in stability when Mg atoms are substituted step by step with Ca. Conclusions. Alumina clusters with a dust-to-gas mass ratio of the order of 10−4 remain the favoured seed particle candidate in our physico-chemical models. However, CaAl2O4 could contribute to stellar dust formation and the mass-loss process. In contrast, the formation of MgAl2O4 is negligible due to the low reactivity of the Mg atom.

The isolated dark matter-poor galaxy that ran away

Since the discovery of dark matter-deficient galaxies, numerous studies have shown that these exotic galaxies naturally occur in the ΛCDM model due to stronger tidal interactions. They are typically satellites, with stellar masses in the 108 − 109 M⊙ range, of more massive galaxies. The recent discovery of a massive galaxy lacking dark matter and also lacking a more massive neighbor is puzzling. Two possible scenarios have been suggested in the literature: either the galaxy lost its dark matter early or it had been lacking ab initio. As a proof of concept for the former assumption, we present an example from IllustrisTNG300. At present, the galaxy has a stellar mass of M⋆ ≃ 6.8 × 109 M⊙, with no gas, MDM/MB ≃ 1.31, and a stellar half-mass radius of R0.5, ⋆ = 2.45 kpc. It lost the majority of its dark matter early, between z = 2.32 and z = 1.53. Since then, it has continued to dwell in the cluster environment, interacting with the cluster members without merging, while accelerating on its orbit. Eventually, it left the cluster and it has spent the last ∼2 Gyr in isolation, residing just outside the most massive cluster in the simulation. Thus, the galaxy represents the first example found in simulations of both an isolated dark matter-poor galaxy that lost its extended envelope early and a fairly compact stellar system that has managed to escape.

Deducing neutron star equation of state from telescope spectra with machine-learning-derived likelihoods

The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra.

Pulsational Velocity Variations of the Radial Mode sdBV Star BPM 36430

Hot subdwarf B stars are core-helium burning objects that were once red giants stripped of their outer H envelopes due to binary interactions. Many exhibit pulsations that can be used to determine fundamental stellar parameters like mass and radius. High-cadence TESS photometry of the sdB star BPM 36430 revealed it to be a hybrid-mode pulsator showing several g-mode pulsations and a single strong p-mode oscillation. The latter is likely a radial mode oscillation, given its period (342 s) and high photometric amplitude (2%). Using time-series spectroscopy from the Goodman spectrograph on the 4.1 m SOAR telescope, we detect a sinusoidal radial velocity variation with a semi-amplitude of 4.4 ± 0.4 km s−1 and period consistent with photometry of the p-mode oscillation. This detection provides further evidence the 342 s mode is radial in nature, and that the Baade–Wesselink method can be used with additional observations to constrain the stellar mass and radius.

On the orbital decay of the gas giant Kepler-1658b

ABSTRACT The gas giant Kepler-1658b has been inferred to be spiralling into its sub-giant F-type host star Kepler-1658a (KOI-4). The measured rate of change of its orbital period is $\stackrel{\bf \centerdot }{\textstyle {P}}_{\rm orb}\, =\, -\, 131^{+20}_{-22}\,\rm {ms\,yr^{ -1}}$, which can be explained by tidal dissipation in the star if its modified tidal quality factor is as low as $Q^{\, \prime }\approx 2.50\times {10}^{4}$. We explore whether this could plausibly be consistent with theoretical predictions based on applying up-to-date tidal theory in stellar models (varying stellar mass, age, and metallicity) consistent with our newly derived observational constraints. In most of our models matching the combined constraints on the stellar effective temperature and radius, the dissipation in the star is far too weak, capable of providing $Q^{\, \prime }\gtrsim 10^9$, hence contributing negligibly to orbital evolution. Using only constraints on the stellar radius, efficient tidal dissipation sufficient to explain observations is possible due to inertial waves in the convective envelope during the sub-giant phase, providing $Q^{\, \prime }\sim 10^4$, but this period in the evolution is very short-lived (shorter than 102 yr in our models). We show that dissipation in the planet is capable of explaining the observed $\dot{P}_\mathrm{orb}$ only if the planet rotates non-synchronously. Tidally induced pericentre precession is a viable explanation if the periastron argument is near 3π/2 and the planet's quadrupolar Love number is above 0.26. Further observations constraining the stellar and planetary properties in this system have the exciting potential to test tidal theories in stars and planets.

TESS giants transiting giants V – two hot Jupiters orbiting red giant hosts

ABSTRACT In this work, we present the discovery and confirmation of two hot Jupiters orbiting red giant stars, TOI-4377 b and TOI-4551 b, observed by Transiting Exoplanet Survey Satellite in the Southern ecliptic hemisphere and later followed-up with radial-velocity (RV) observations. For TOI-4377 b, we report a mass of $0.957^{+0.089}_{-0.087} \ M_\mathrm{J}$ and a inflated radius of 1.348 ± 0.081 RJ orbiting an evolved intermediate-mass star (1.36 M⊙ and 3.52 R⊙; TIC 394918211) on a period of of 4.378 d. For TOI-4551 b, we report a mass of 1.49 ± 0.13 MJ and a radius that is not obviously inflated of $1.058^{+0.110}_{-0.062} \ R_\mathrm{J}$, also orbiting an evolved intermediate-mass star (1.31 M⊙ and 3.55 R⊙; TIC 204650483) on a period of 9.956 d. We place both planets in context of known systems with hot Jupiters orbiting evolved hosts, and note that both planets follow the observed trend of the known stellar incident flux-planetary radius relation observed for these short-period giants. Additionally, we produce planetary interior models to estimate the heating efficiency with which stellar incident flux is deposited in the planet’s interior, estimating values of $1.91 \pm 0.48~{{\ \rm per\ cent}}$ and $2.19 \pm 0.45~{{\ \rm per\ cent}}$ for TOI-4377 b and TOI-4551 b, respectively. These values are in line with the known population of hot Jupiters, including hot Jupiters orbiting main-sequence hosts, which suggests that the radii of our planets have re-inflated in step with their parent star’s brightening as they evolved into the post-main sequence. Finally, we evaluate the potential to observe orbital decay in both systems.

The impact of bar origin and morphology on stellar migration

ABSTRACT Different mechanisms driving bar structure formation indicate that bar origins should be distinguishable in the stellar populations of galaxies. To study how these origins affect different bar morphologies and impact stellar orbits and migration, we analyse three simulated discs which are representative of bar formation under isolated evolution motivated by disc instability, and interaction-driven tidal development. The first isolated disc and the tidally driven disc produce similar bar structure, while the second isolated disc, generated by the tidal initial condition without the companion, is visibly dissimilar. Changes to radial and vertical positions, angular momentum in the disc-plane, orbital eccentricity, and the subsequent disc metallicities are assessed, as is the dependence on stellar age and formation radii. Bar origin is distinguishable, with the tidal disc displaying larger migration overall, higher metallicity difference between the inner and outer disc, and a population of inner disc stars displaced to large radii and below the disc-plane. The effect of closest approach on populations of stars formed before, after, and during this period is evident. However, bar morphology is also found to be a significant factor in the evolution of disc stellar properties, with similar bars producing similar traits in migration tendency with radius, particularly in vertical stellar motion and in the evolution of central metallicity features.

Anisotropic strange stars and its maximum mass in Finch-Skea geometry in dimensions D ≥ 4

In this article, we have demonstrated a stellar model for compact stars in the presence of strange matter embedded in D ≥ 4 dimensional space-time defined by the Finch-Skea metric. To study the relevant physical properties of the interior matter, we consider the equation of state (henceforth EOS) as proposed in the MIT bag model, where B is termed the bag constant. The mass-radius relationship in four and higher dimensions is determined using the range of values of surface density through the relation ρ s = 4B, for which bulk strange matter may be a viable issue for compact objects. Here, we choose the range of B so that stable strange matter may exist relative to a neutron at zero external pressure. We note that a maximum value of the stellar radius exists when B is fixed at a given allowed value for which metric functions considered to be real here. This is the maximum allowed radius in this model, which depends on the surface density of a strange star. In four dimensions, the compactness of a star is found to be greater than 0.33. In the case of higher dimensions (D > 4), we observed different values of compactness. Causality conditions are satisfied interior to the star up to the maximum allowed radius , for which the metric function is real. The validity of the energy conditions, surface redshift and other parameters of the stellar configuration are studied, and new results are found. The stability of the model is also studied.

Planetary perturbers: flaring star–planet interactions in Kepler and TESS

ABSTRACT In many star–planet systems discovered so far, the innermost planet orbits within only a few stellar radii. In these systems, planets could become in situ probes of the extended stellar magnetic field. Because they disturb the field as they move, they are expected to trigger flares in the corona. Potential differences to the energies and morphologies of intrinsic flares are poorly constrained. However, as we expect planet-induced flares to correlate with the planet’s orbital period, we can identify them from a clustering of flares in phase with the planet’s orbit. We used the excellent phase coverage from Kepler and the Transiting Exoplanet Survey Satellite to find flaring star–planet systems, compile a catalogue of all their flares, and measure how much they cluster in orbital phase. In the 1811 searched systems, we found 25 single stars with three or more flares each. We quantified the significance of the clustering in each system, and compared it against the theoretically expected power of magnetic interaction that leads to planet-induced flaring. Most systems do not show any clustering, consistent with low expected power. Those we expect to show clustering fall on two branches. An inactive one, without any signs of clustering, and a tentative active one, where the clustering becomes more pronounced as the expected power of interaction increases. The flares in HIP 67522 are prominently clustered (p < 0.006). This young hot Jupiter system is the most promising candidate for magnetic star–planet interaction in our sample.

Can Charged Stars be Singularity‐Free?

AbstractWhile the configuration of a static spherically symmetric distribution of perfect fluid in an electric field has received extensive attention in the literature, only a few works have investigated the conformally flat case. The model exhibits a remarkable property being regular or singularity free is proposed. This is unexpected given that Coulombic repulsion opposes the collapse of a star to the center generally making the center unreachable. The conformally flat geometry thus enables the approach to the center of a charged star as shown in our model. Presently there is no known reported exact model that satisfies all the elementary requirements for physical acceptability. Some reported models that have claimed to be physically reliable have been shown to be deficient. The conditions for the existence of physically relevant models and show that exact solutions satisfying the conditions exist is investigated. Then a model satisfying all the requirements with isotropic particle pressure graphically for a carefully chosen parameter space is exhibited. The model admits a barotropic equation of state. The interior spacetime is successfully matched to the exterior Reissner‐Nordstrom metric. The causality criterion as well as the adiabatic stability lower bound of Chandrasekar are shown to hold. The energy conditions are also valid within the stellar radius. Other interesting models are considered.

The spectroscopic orbit of Polaris and its pulsation properties

ABSTRACT Polaris is the nearest and brightest classical Cepheid, and pulsates with a period of about 4 d. It has long been known as a single-lined spectroscopic binary with an orbital period of 30 yr. Historical photometric and spectroscopic records indicate that, until recently, the pulsation period has been increasing at a rate of about 4.5 s yr−1, and that the amplitude of the pulsation declined for most of the 20th century, but more recently halted its decline and began to increase. Here, we report an analysis of the more than 3600 individual radial velocity measurements of Polaris available from the literature over the past 126 yr. We find that the pulsation period is now becoming shorter, and that the amplitude of the velocity variations has stopped increasing, and may be getting smaller again. We also find tantalizing evidence that these changes in pulsation behaviour over the last century may be related to the binary nature of the system, as they seem to occur near each periastron passage, when the secondary comes within 29 stellar radii of the Cepheid in its eccentric orbit. This suggests the companion may be perturbing the atmosphere of the Cepheid and altering its pulsation properties at each encounter. After removal of the pulsation component of the velocities, we derive a much improved spectroscopic orbit for the binary that should serve as the basis for a more accurate determination of the dynamical masses, which are still rather uncertain.

The effect of the adiabatic assumption on asteroseismic scaling relations for luminous red giants

ABSTRACT Although stellar radii from asteroseismic scaling relations agree at the per cent level with independent estimates for main sequence and most first-ascent red giant branch (RGB) stars, the scaling relations over-predict radii at the tens of per cent level for the most luminous stars ($R \gtrsim 30 \, \mathrm{R}_{\odot }$). These evolved stars have significantly superadiabatic envelopes, and the extent of these regions increase with increasing radius. However, adiabaticity is assumed in the theoretical derivation of the scaling relations as well as in corrections to the large frequency separation. Here, we show that a part of the scaling relation radius inflation may arise from this assumption of adiabaticity. With a new reduction of Kepler asteroseismic data, we find that scaling relation radii and Gaia radii agree to within at least 2 per cent for stars with $R \lesssim 30\, \mathrm{R}_{\odot }$, when treated under the adiabatic assumption. The accuracy of scaling relation radii for stars with $50\, \mathrm{R}_{\odot }\lesssim R \lesssim 100\, \mathrm{R}_{\odot }$, however, is not better than $10~{{\ \rm per \, cent}}-15~{{\ \rm per \, cent}}$ using adiabatic large frequency separation corrections. We find that up to one third of this disagreement for stars with $R \approx 100\, \mathrm{R}_{\odot }$ could be caused by the adiabatic assumption, and that this adiabatic error increases with radius to reach 10 per cent at the tip of the RGB. We demonstrate that, unlike the solar case, the superadiabatic gradient remains large very deep in luminous stars. A large fraction of the acoustic cavity is also in the optically thin atmosphere. The observed discrepancies may therefore reflect the simplified treatment of convection and atmospheres.

Two super-Earths at the edge of the habitable zone of the nearby M dwarf TOI-2095

The main scientific goal of TESS is to find planets smaller than Neptune around stars that are bright enough to allow for further characterization studies. Given our current instrumentation and detection biases, M dwarfs are prime targets in the search for small planets that are in (or near) the habitable zone of their host star. In this work, we use photometric observations and CARMENES radial velocity (RV) measurements to validate a pair of transiting planet candidates found by TESS. The data were fitted simultaneously, using a Bayesian Markov chain Monte Carlo (MCMC) procedure and taking into account the stellar variability present in the photometric and spectroscopic time series. We confirm the planetary origin of the two transiting candidates orbiting around TOI-2095 (LSPM J1902+7525). The star is a nearby M dwarf (d = 41.90 ± 0.03 pc, Teff = 3759 ± 87 K, V = 12.6 mag), with a stellar mass and radius of M* = 0.44 ± 0.02 M⊙ and R* = 0.44 ± 0.02 R⊙, respectively. The planetary system is composed of two transiting planets: TOI-2095b, with an orbital period of Pb = 17.66484 ± (7 × 10−5) days, and TOI-2095c, with Pc = 28.17232 ± (14 × 10−5) days. Both planets have similar sizes with Rb = 1.25 ± 0.07 R⊕ and Rc = 1.33 ± 0.08 R⊕ for planet b and planet c, respectively. Although we did not detect the induced RV variations of any planet with significance, our CARMENES data allow us to set stringent upper limits on the masses of these objects. We find Mb < 4.1 M⊕ for the inner and Mc < 7.4 M⊕ for the outer planet (95% confidence level). These two planets present equilibrium temperatures in the range of 300–350 K and are close to the inner edge of the habitable zone of their star.

Three-dimensional Simulations of Massive Stars. II. Age Dependence

We present 3D full star simulations, reaching up to 90% of the total stellar radius, for three 7 M ⊙ stars of different ages: zero-age main sequence (ZAMS), mid–main sequence (midMS), and terminal-age main sequence (TAMS). A comparison with several theoretical prescriptions shows that the generation spectra for all three ages are dominated by convective plumes. Two distinct overshooting layers are observed, with most plumes stopped within the layer situated directly above the convective boundary; overshooting to the second, deeper layer becomes progressively more infrequent with increasing stellar age. Internal gravity wave (IGW) propagation is significantly impacted in the midMS and TAMS models as a result of some IGWs getting trapped within their Brunt–Väisälä frequency spikes. A fundamental change in the wave structure across radius is also observed, driven by the effect of density stratification on IGW propagation causing waves to become evanescent within the radiative zone, with older stars being affected more strongly. We find that the steepness of the frequency spectrum at the surface increases from ZAMS to the older models, with older stars also showing more modes in their spectra.

The white dwarf mass–orbital period relation under wind mass-loss

ABSTRACT Helium white dwarfs (HeWDs) are thought to form from low-mass red giant stars experiencing binary interaction. Because the helium core mass of a red giant star is closely related to the stellar radius, there exists well-known relation between the orbital period (Porb) and the mass (MWD) of the HeWDs, which is almost independent of the type of the companion star. Traditional derivation of the MWD–Porb relation generally neglected the effect of wind mass-loss from the red giants, while observations show that wind mass-loss from red giants in binary systems is systematically higher than that from isolated stars. In this work, we calculate binary evolution with tidally enhanced stellar wind (TEW) and find that it causes significantly scatter of the traditional MWD–Porb relation. The TEW can prevent the red giants from overflowing their Roche lobes and slow down the growth of the helium core, leaving a lower mass HeWD for given orbital period. This scenario may account for some of the HeWD binaries that deviate from the traditional MWD–Porb relation. However, we point out that observations of more HeWD binaries in wide orbits are needed to test the TEW model and to constrain the enhanced wind factor.