Red Giant Model Research Articles

Realising efficient computation of individual frequencies for red-giant models. The truncated scanning method

Realising efficient computation of individual frequencies for red-giant models. The truncated scanning method

Benchmarking the effective temperature scale of red giant branch stellar models: The case of the metal-poor halo giant HD 122563

Context. There is plenty of evidence in the literature of significant discrepancies between the observations and models of metal-poor red giant branch stars, in particular regarding the effective temperature Teff scale. Aims. We revisit the benchmark star HD 122563 using the most recent observations from Gaia Data Release 3, to investigate if these new constraints may help in resolving this discrepancy. Methods. We review the most recent spectroscopic determinations of the metallicity [Fe/H] of HD 122563, and provide a new assessment of its fundamental parameters, specifically, bolometric luminosity, Teff, surface gravity, plus a photometric determination of its metal content. Using these constraints, we compare the position of the star in the Hertzsprung-Russell (H–R) diagram with various recent sets of stellar evolution tracks. Results. The H-R diagram analysis reveals a significant disagreement between observed and theoretical Teff values, when adopting the most recent spectroscopic estimate of [Fe/H]. On the other hand, by using the photometric determination of [Fe/H], some of the selected sets of stellar tracks appear in fair agreement with observations. The sets with discrepant Teff can be made to agree with observations either by modifying the prescription adopted to calculate the models’ outer boundary conditions, and/or by reducing the adopted value of the mixing length parameter with respect to the solar-calibration. Conclusions. A definitive assessment of whether the Teff scale of metal-poor stellar red giant branch models is consistent with observations requires a more robust determination of the fundamental parameters of HD 122563 and also a larger sample of calibrators. From the theoretical side, it is crucial to minimise the current uncertainties in the treatment (boundary conditions, temperature gradient) of the outer layers of stellar models with convective envelopes.

Evolutionary and Observational Properties of Red Giant Acoustic Glitch Signatures

While solar-like oscillations in red giants have been observed at massive scales by the Kepler mission, few features of these oscillation mode frequencies, other than their global properties, have been exploited for stellar characterization. The signatures of acoustic glitches in mode frequencies have been used for studying main-sequence stars, but the validity of applying such techniques to evolved red giants, particularly pertaining to the inclusion of nonradial modes, has been less well examined. Making use of new theoretical developments, we characterize glitches using the π modes associated with red giant stellar models, and use our procedure to examine for the first time how the properties of the He ii acoustic glitch—specifically its amplitude and associated acoustic depth—vary over the course of evolution up the red giant branch, and with respect to other fundamental stellar properties. We find that the acoustic depths of these glitches, in conjunction with other spectroscopic information, discriminate between red giants in the first-ascent and core-helium-burning phases. We critically reexamine previous attempts to constrain acoustic glitches from nonradial (in particular dipole) modes in red giants. Finally, we apply our fitting procedure to Kepler data, to evaluate its robustness to noise and other observational systematics.

Mixed-mode Asteroseismology of Red Giant Stars Through the Luminosity Bump

Most current models of low-mass red giant stars do not reproduce the observed position of the red giant branch luminosity bump, a diagnostic of the maximum extent of the convective envelope during the first dredge up. Global asteroseismic parameters, the large frequency separation and frequency of maximum oscillation power, measured for large samples of red giants, show that modeling convective overshoot below the convective envelope helps match the modeled luminosity bump positions to observations; however, these global parameters cannot be used to probe envelope overshoot in a star-by-star manner. Red giant mixed modes, which behave like acoustic modes at the surface and like gravity modes in the core, contain important information about the interior structure of the star, especially near the convective boundary. Therefore, these modes may be used to probe interior processes, such as overshoot. Using a grid of red giant models with varying mass, metallicity, surface gravity, overshoot treatment, and amount of envelope overshoot, we find that changing the overshoot amplitude (and prescription) of overshoot below the convection zone in red giant stellar models results in significant differences in the evolution of the models’ dipole mixed-mode oscillation frequencies, the average mixed-mode period spacing (〈ΔP〉), and gravity-mode phase offset term (ϵ g ).

Seismic signature of electron degeneracy in the core of red giants: Hints for mass transfer between close red-giant companions

The detection of mixed modes in red giants with space missions COROT and Kepler has revealed their deep internal structure. These modes allow us to characterize the pattern of pressure modes (through the measurement of their asymptotic frequency separation Δν) and the pattern of gravity modes (through the determination of their asymptotic period spacing ΔΠ1). It has been shown that red giant branch (RGB) stars regroup on a well-defined sequence in the Δν − ΔΠ1 plane. Our first goal is to theoretically explain the features of this sequence and understand how it can be used to probe the interiors of red giants. Using a grid of red giant models computed with MESA, we demonstrate that red giants join the Δν − ΔΠ1 sequence whenever electron degeneracy becomes strong in the core. We argue that this can be used to estimate the central densities of these stars, and potentially to measure the amount of core overshooting during the main sequence part of the evolution. We also investigate a puzzling subsample of red giants that are located below the RGB sequence, in contradiction with stellar evolution models. After checking the measurements of the asymptotic period spacing for these stars, we show that they are mainly intermediate-mass red giants. This is doubly peculiar because these stars should have nondegenerate cores and they are expected to be located well above the RGB sequence. We show that these peculiarities are well accounted for if these stars result from the interaction between two low-mass (M ≲ 2 M⊙) close companions during the red giant branch phase. If the secondary component has already developed a degenerate core before mass transfer begins, it becomes an intermediate-mass giant with a degenerate core. The secondary star is then located below the degenerate sequence, which is in agreement with the observations.

On using dipolar modes to constrain the helium glitch in red giant stars

ABSTRACT The space-borne missions CoRoT and Kepler have revealed numerous mixed modes in red giant stars. These modes carry a wealth of information about red giant cores, but are of limited use when constraining rapid structural variations in their envelopes. This limitation can be circumvented if we have access to the frequencies of the pure acoustic dipolar modes in red giants, i.e. the dipole modes that would exist in the absence of coupling between gravity and acoustic waves. We present a pilot study aimed at evaluating the implications of using these pure acoustic mode frequencies in seismic studies of the helium structural variation in red giants. The study is based on artificial seismic data for a red giant branch stellar model, bracketing seven acoustic dipole radial orders around νmax. The pure acoustic dipole-mode frequencies are derived from a fit to the mixed-mode period spacings and then used to compute the pure acoustic dipole-mode second differences. The pure acoustic dipole-mode second differences inferred through this procedure follow the same oscillatory function as the radial-mode second differences. The additional constraints brought by the dipolar modes allow us to adopt a more complete description of the glitch signature when performing the fit to the second differences. The amplitude of the glitch retrieved from this fit is 15${{\ \rm per\ cent}}$ smaller than that from the fit based on the radial modes alone. Also, we find that thanks to the additional constraints, a bias in the inferred glitch location, found when adopting the simpler description of the glitch, is avoided.

Asteroseismic sensitivity to internal rotation along the red-giant branch

Context. Transport of angular momentum in stellar interiors is currently not well understood. Asteroseismology can provide us with estimates of internal rotation of stars and thereby advances our understanding of angular momentum transport. Aims. We can measure core-rotation rates in red-giant stars and we can place upper bounds on surface-rotation rates using measurements of dipole (l = 1) modes. Here, we aim to determine the theoretical sensitivity of modes of different spherical degree towards the surface rotation. Additionally, we aim to identify modes that can potentially add sensitivity at intermediate radii. Methods. We used asteroseismic rotational inversions to probe the internal stellar rotation profiles in red-giant models from the base of the red-giant branch up to the luminosity bump. We used the inversion method of multiplicative optimally localised averages to assess how well internal and surface rotation rates can be recovered from different mode sets and different synthetic rotation profiles. Results. We confirm that dipole mixed modes are sufficient to set constraints on the average core-rotation rates in red giants. However, surface-rotation rates estimated with only dipole mixed modes are contaminated by the core rotation. We show that the sensitivity to surface rotation decreases from the base of the red-giant branch until it reaches a minimum at 60–80% of the bump luminosity due to a glitch in the buoyancy frequency. Thereafter, a narrow range of increased surface sensitivity just below the bump luminosity exists. Quadrupole and octopole modes have more sensitivity in the outer parts of the star. To obtain accurate estimates of rotation rates at intermediate radii (i.e. a fractional radius of ∼0.4), acoustic oscillation modes with a spherical degree of l ≈ 10 are needed. Conclusions. We find a minimum and subsequent maximum in the sensitivity to the surface rotation rate in red giants below the luminosity bump. Furthermore, we show that, if observed, quadrupole and octopole modes enable us to distinguish between differential and solid body rotation in the convection zone. This will be important when investigating the transport of angular momentum between the core and the envelope.

Core magnetic field imprint in the non-radial oscillations of red giant stars

ABSTRACT Magnetic fields in red giant stars remain a poorly understood topic, particularly in what concerns their intensity in regions far below the surface. In this work, we propose that gravity-dominated mixed modes of high absolute radial order and low angular degree can be used to probe the magnetic field in their radiative cores. Using two poloidal, axisymmetric configurations for the field in the core and the classical perturbative approach, we derive an analytical expression for the magnetic frequency splitting of these oscillation modes. Considering three distinct red giant models, with masses of 1.3, 1.6, and 2.0 M⊙, we find that a field strength of 105 G is necessary in the core of these stars to induce a frequency splitting of the order of a μHz in dipole and quadrupole oscillation modes. Moreover, taking into account observational limits, we estimate that magnetic fields in the cores of red giants that do not present observable magnetic splittings cannot exceed 104 G. Given the general absence of observable splittings in the oscillation spectra of these stars, and assuming that present mode suppression mechanisms are not biased towards certain azimuthal orders and retain all peaks in each multiplet, our results lead us to conclude that internal fields with the considered configurations and strengths above 104 G are not prevalent in red giants.

Variations of the mixing character of dipolar mixed modes in red giant stars

ABSTRACT Because of the high-quality data of space missions, the detection of mixed modes has become possible in numerous stars. In this work, we investigate how the mixing character of dipolar mixed modes changes with stellar evolution, as well as with frequency within each stellar model. This is achieved by monitoring the variations in the coupling strength and the period spacing of dipolar mixed modes in red-giant models. These parameters are measured by fitting the asymptotic expansion of mixed modes to the model frequencies of a grid of red-giant models with masses between 1.0 and 2.0 M⊙ and three different chemical abundances. The coupling strength and the period spacing decrease with stellar evolution. We find that the slopes of their decreasing trends depend on the radial order of the pressure mode component. A non-negligible increase of the coupling strength with frequency by up to around 40 per cent is found in the observable frequency range for a set of red-giant models. On the contrary, no significant changes of the period spacing with frequency are found. The changes in the mixing character of the modes are in most cases affected by the model mass and metallicity. Buoyancy glitches also have an impact on the mixing character. Significant fluctuations in the estimated coupling strength and period spacing are found for models approaching the luminosity bump, if the glitch impact of the frequencies is not considered in the applied asymptotic expansion.

Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars

Although observational data unequivocally point out to the presence of chromospheres in red giant stars, no attempts have been made so far to model them using 3D hydrodynamical model atmospheres. We therefore compute an exploratory 3D hydrodynamical model atmosphere for a cool red giant in order to study the dynamical and thermodynamic properties of its chromosphere, as well as the influence of the chromosphere on its observable properties. 3D radiation hydrodynamics simulations are carried out with the CO5BOLD model atmosphere code for a star with the atmospheric parameters (Teff=4010 K, log g=1.5, [M/H]=0.0), which are similar to those of the K-type giant star Aldebaran (alpha Tau). ... we compute the emergent continuum intensity maps at different wavelengths, spectral line profiles of Ca II K, the Ca II infrared triplet line at 854.2nm, and H alpha, as well as the spectral energy distribution (SED) of the emergent radiative flux. The initial model quickly develops a dynamical chromosphere characterised by propagating and interacting shock waves. The peak temperatures in the chromospheric shock fronts reach values on the order of up to 5000 K although the shock fronts remain quite narrow. Like for the Sun, the gas temperature distribution in the upper layers is composed of a cool component due to adiabatic cooling in the expanding post-shock regions and a hot component due to shock waves. For this red giant model, the hot component is a rather flat high-temperature tail, which nevertheless affects the resulting average temperatures significantly. The simulations show that the atmospheres of red giant stars are dynamic and intermittent. Consequently, many observable properties cannot be reproduced with one-dimensional static models but demand for advanced 3D HD modelling. Furthermore, including a chromosphere in the models might produce significant contributions to the emergent UV flux.

ChromaStarDB: SQL Database-driven Spectrum Synthesis and More

We present an alternate deployment of the GrayStarServer (now ChromaStarServer (CSS)) pedagogical stellar atmosphere and spectrum synthesis WWW application, namely ChromaStarDB (CSDB), in which the atomic line list used for spectrum synthesis is implemented as an SQL database table rather than as a more conventional byte-data file. This allows for very flexible selection criteria to determine which transitions are extracted from the line list for inclusion in the synthesis, and enables novel pedagogical and research experiments in spectrum synthesis. This line selection flexibility is reflected in the CSDB UI. The database extraction is very fast and would be appropriate for the larger line lists of research-grade modeling codes. We also take the opportunity to present major additions to the ChromaStar and CSS codes that are also reflected in CSDB: (1) TiO band opacity in the JOLA approximation, (2) Metal b − f and Rayleigh scattering opacity, (3) 2D implementation of the flux integral, (4) Improvement of the convergence, (5) Expansion of the exo-planet modeling parameters, (6) A red giant template model for the initial guess at the structure, and (7) General improvements to the UI. The applications may be found at the home page of the OpenStar project: http://www.ap.smu.ca/OpenStars/.

Asteroseismic Diagram for Subgiants and Red Giants

Abstract Asteroseismology is a powerful tool for constraining stellar parameters. NASA’s Kepler mission is providing individual eigenfrequencies for a huge number of stars, including thousands of red giants. Besides the frequencies of acoustic modes, an important breakthrough of the Kepler mission is the detection of nonradial gravity-dominated mixed-mode oscillations in red giants. Unlike pure acoustic modes, mixed modes probe deeply into the interior of stars, allowing the stellar core properties and evolution of stars to be derived. In this work, using the gravity-mode period spacing and the large frequency separation, we construct the ΔΠ1–Δν asteroseismic diagram from models of subgiants and red giants with various masses and metallicities. The relationship ΔΠ1–Δν is able to constrain the ages and masses of the subgiants. Meanwhile, for red giants with masses above 1.5 M ⊙, the ΔΠ1–Δν asteroseismic diagram can also work well to constrain the stellar age and mass. Additionally, we calculate the relative “isochrones” τ, which indicate similar evolution states especially for similar mass stars, on the ΔΠ1–Δν diagram.

Oscillations in g-mode period spacings in red giants as a way to determine their state of evolution

In this work we consider the sensitivity of gravity-mode period spacings to sharp changes in the inner structure of red giant stars, more specifically in the buoyancy frequency inside the g-mode propagation cavity. Based on a comparison between the solutions to the linear pulsation equations in the Cowling approximation for pure g-modes with results obtained with a full oscillation code we identify and correctly interpret the signature of the above-mentioned sharp variations in the period spacings. Two examples, of red giant models in different evolutionary phases, are discussed. Detection of these signatures in CoRoT, Kepler or future PLATO red-giant stars would pin down their evolutionary state in an unprecedented way.

Fingering convection in red giants revisited

Fingering (thermohaline) convection has been invoked for several years as a possible extra-mixing which could occur in Red Giant stars due to the modification of the chemical composition induced by nuclear reactions in the hydrogen burning zone. Recent studies show however that this mixing is not sufficient to account for the needed surface abundances. A new prescription for fingering convection, based on 3D numerical simulations has recently been proposed (BGS). The resulting mixing coefficient is larger than the ones previously given in the literature. We compute models using this new coefficient and compare them to previous studies. We use the LPCODE stellar evolution code with the GNA generalized version of the mixing length theory to compute Red Giant models and we introduce fingering convection using the BGS prescription. The results show that, although the fingering zone now reaches the outer dynamical convective zone, the efficiency of the mixing is not enough to account for the observations. The fingering mixing coefficient should be increased by two orders of magnitude for the needed surface abundances to be reached. We confirm that fingering convection cannot be the mixing process needed to account for surface abundances in RGB stars.

Verification of asymptotic relation for mixed modes in red giant stars

High-precision space observations, such as made by the \kepler\ and \corot\ missions, allow us to detect mixed modes for $l = 1$ modes in their high signal-to-noise photometry data. By means of asteroseismology, the inner structure of red giant (RG) stars is revealed the first time with the help of mixed modes. We analyse these mixed modes of a 1.3 M$_{\sun}$ RG model theoretically from the approximate asymptotic descriptions of oscillations. While fitting observed frequencies with the eigenvalue condition for mixed modes, a good estimate of period spacing and coupling strength is also acquired for more evolved models. We show that the behaviour of the mode inertia in a given mode varies dramatically when the coupling is strong. An approximation of period spacings is also obtained from the asymptotic dispersion relation, which provides a good estimate of the coupling strength as well as period spacing when g-mode-like mixed modes are sufficiently dense. By comparing the theoretical coupling strength from the integral expression with the ones from fitting methods, we confirmed that the theoretical asymptotic equation is problematic in the evanescent region due to the potential singularities as well as the use of the Cowling approximation.

IPHAS and the symbiotic stars

Context. The IPHAS Hα survey provides a rich database to search for emission-line sources in the northern Galactic plane.Aims. We are systematically searching for symbiotic stars in the Milky Way using IPHAS. Our final goal, a complete census of this class of objects in the Galaxy, is a fundamental figure for discussing their overall properties and relevance to other classes of stars.Methods. Candidate symbiotic stars were selected using a refined combination of IPHAS and 2MASS photometric colours. Optical spectroscopy, together with the analysis of their spectral energy distribution in the IR, were obtained to confirm their nature and determine their main properties.Results. Five new symbiotic stars have been confirmed from spectroscopy at the 10.4 m GTC telescope. In one case, confirming the presence of a red giant star required near infrared spectroscopy. In another case, its symbiotic nature was adopted based on the strong similarity of its optical spectrum and spectral energy distribution to those of other genuinely symbiotic stars. The spectral energy distribution of the two S-types found is well fitted by red-giant model atmospheres up to 22 μ m without evidence of IR excesses due to dust. In contrast, the three D-types mostly show emission from hot dust with a temperature around 1000 K. We also present the spectroscopic and photometric monitoring of the symbiotic star IPHASJ190832.31+051226.6 that was originally discovered in outburst, and it has now returned to a lower luminosity status. The spectra of thirteen other sources, all classified as young stellar objects except for a new compact planetary nebula, are also presented.Conclusions. The refinement of our discovery method, the completion of the IPHAS survey and photometric calibration, and the start of the twin survey in the south, VPHAS+, provide excellent perspectives for completing a reliable census of symbiotic stars in the Galaxy in the next few years.

TURBULENT CONVECTION IN STELLAR INTERIORS. III. MEAN-FIELD ANALYSIS AND STRATIFICATION EFFECTS

We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M☉ red giant star and in the oxygen-burning shell of a 23 M☉ supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier–Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.

Seismic diagnostics for transport of angular momentum in stars

Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles. Our aim is to obtain seismic constraints on the internal transport and surface loss of angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes. We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of $1.3 M_{\odot}$ models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch. Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars.

Inference from adiabatic analysis of solar‐like oscilations in red giants

AbstractThe clear detection with CoRoT and Kepler of radial and non‐radial solar‐like oscillations in many red giants paves the way to seismic inferences on the structure of such stars. We present an overview of the properties of the adiabatic frequencies and frequency separations of radial and non‐radial oscillation modes, highlighting how their detection allows a deeper insight into the properties of the internal structure of red giants. In our study we consider models of red giants in different evolutionary stages, as well as of different masses and chemical composition. We describe how the large and small separations computed with radial modes and with non‐radial modes mostly trapped in the envelope depend on the stellar global parameters and evolutionary state, and we compare our theoretical predictions and first Kepler data.Finally, we find that the properties of dipole modes constitute a promising seismic diagnostic of the evolutionary state of red‐giant stars (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical amplitudes and lifetimes of non-radial solar-like oscillations in red giants

Solar-like oscillations have been observed in numerous red giants from ground and from space. An important question arises: could we expect to detect non-radial modes probing the internal structure of these stars? We investigate under what physical circumstances non-radial modes could be observable in red giants; what would be their amplitudes, lifetimes and heights in the power spectrum (PS)? Using a non-radial non-adiabatic pulsation code including a non-local time-dependent treatment of convection, we compute the theoretical lifetimes of radial and non-radial modes in several red giant models. Next, using a stochastic excitation model, we compute the amplitudes of these modes and their heights in the PS. Very distinct results are found depending on the evolutionary status of the star.