arXiv subjects

Kjell Eriksson

Publications and source records attributed to Kjell Eriksson.

At least 19 recordsLinked to original sources

arXiv2026

An extensive grid of DARWIN models for M-type AGB stars II. Effects of pulsation periods on wind properties

Mass loss from asymptotic giant branch (AGB) stars is the result of a complex interplay between pulsation, atmospheric dynamics, dust formation, and radiative acceleration. Pulsation periods are a key input in dynamical atmosphere and wind models, and different prescriptions for assigning periods based on stellar parameters may lead to systematic differences in the predicted wind properties. To better constrain this critical parameter, we investigated how the choice of pulsation period affects the wind properties of dynamical atmosphere and wind models of M-type AGB stars by comparing models based on an empirical period-luminosity (P-L) relation with corresponding ones that adopt a period-mean density relation derived from 3D pulsation models. We analysed two grids of DARWIN models that cover a range of current stellar masses, luminosities, and effective temperatures. For each grid, pulsation periods were assigned using either the P-L relation or the period-mean density relation, allowing for a direct comparison of the resulting dynamical structures and wind properties for pairs of models differing by period only. Independent of the adopted period prescription, the time-averaged wind properties correlate strongly with $L_\star/M_\star$. The pulsation period affects the atmospheric dynamics through changes in the relative timing of shock propagation and dust formation, which affect both wind formation and the resulting wind properties. Shorter periods favour the onset of a wind, and models differing only in pulsation period can exhibit significantly different wind properties. The period-mean density relation provides a physically motivated alternative to the empirical P-L relation by accounting for stellar parameters beyond luminosity, and enables a more direct comparison between DARWIN models and observed Mira variables.

astro-ph.SR↗

arXiv2025

Dynamic atmosphere and wind models of C-type asymptotic giant branch stars. Influences of dust optical data on mass loss and observables

Mass loss through stellar winds governs the evolution of stars on the asymptotic giant branch (AGB). In the case of carbon-rich AGB stars, the wind is believed to be driven by radiation pressure on amorphous carbon (amC) dust forming in the atmosphere. The choice of dust optical data will have a significant impact on atmosphere and wind models of AGB stars. We compare two commonly used optical data sets of amC and investigate how the wind characteristics and photometric properties resulting from dynamical models of carbon-rich AGB stars are influenced by the micro-physical properties of dust grains. We computed two extensive grids of carbon star atmosphere and wind models with the DARWIN 1D radiation-hydrodynamical code. Each of the two grids uses a different amC optical data set. The stellar parameters of the models were varied to cover a wide range of possible combinations. A posteriori radiative transfer calculations were performed for a sub-set of the models, resulting in photometric fluxes and colours. We find small, but systematic differences in the predicted mass-loss rates for the two grids. The grain sizes and photometric properties are affected by the different dust optical data sets. Higher absorption efficiency leads to the formation of a greater number of grains, which are smaller. Models that are obscured by dust exhibit differences in terms of the covered colour range compared to observations, depending on the dust optical data used. An important motivation for this study was to investigate how strongly the predicted mass-loss rates depend on the choice of dust optical data, as these mass-loss values are more frequently used in stellar evolution models. Based on the current results, we conclude that mass-loss rates may typically differ by about a factor of two for DARWIN models of C-type AGB stars for commonly used dust optical data sets.

astro-ph.SR↗

arXiv2023

Synthetic photometry for carbon-rich giants. V. Effects of grain-size-dependent dust opacities

The properties and the evolution of asymptotic giant branch (AGB) stars are strongly influenced by their mass loss through a stellar wind. This is believed to be caused by radiation pressure due to the absorption and scattering of the stellar radiation by the dust grains formed in the atmosphere. The optical properties of dust are often estimated using the small particle limit (SPL) approximation, and it has been used frequently in modelling AGB stellar winds when performing radiation-hydrodynamics (RHD) simulations. We aim to investigate the effects of replacing the SPL approximation by detailed Mie calculations of the size-dependent opacities for grains of amorphous carbon forming in C-rich AGB star atmospheres. We performed RHD simulations for a large grid of carbon star atmosphere+wind models with different effective temperatures, luminosities, stellar masses, carbon excesses, and pulsation properties. Also, a posteriori radiative transfer calculations for many radial structures (snapshots) of these models were done, resulting in spectra and filter magnitudes. We find, when giving up the SPL approximation, the wind models become more strongly variable and more dominated by gusts, although the average mass-loss rates and outflow speeds do not change significantly; the increased radiative pressure on the dust throughout its formation zone does, however, result in smaller grains and lower condensation fractions (and thus higher gas-to-dust ratios). The photometric K magnitudes are generally brighter, but at V the effects of using size-dependent dust opacities are more complex: brighter for low mass-loss rates and dimmer for massive stellar winds. Given the large effects on spectra and photometric properties, it is necessary to use the detailed dust optical data instead of the simple SPL approximation in stellar atmosphere+wind modelling where dust is formed.

astro-ph.SR↗

arXiv2021

Dynamic atmospheres and winds of cool luminous giants, II. Gradual Fe enrichment of wind-driving silicate grains

The winds observed around AGB stars are generally attributed to radiation pressure on dust formed in the dynamical atmospheres of these long-period variables. The composition of wind-driving grains is affected by a feedback between their optical properties and the resulting heating due to stellar radiation. We explore the gradual Fe enrichment of wind-driving silicate grains in M-type AGB stars to derive typical values for Fe/Mg and test the effects on wind properties and synthetic spectra. We present new DARWIN models that allow for the growth of silicate grains with a variable Fe/Mg ratio and predict mass-loss rates, wind velocities, and grain properties. Synthetic spectra and other observables are computed with the COMA code. The self-regulating feedback between grain composition and radiative heating, in combination with quickly falling densities in the stellar wind, leads to low values of Fe/Mg, typically a few percent. Nevertheless, the models show distinct silicate features around 10 and 18 microns. Fe enrichment affects visual and near-IR photometry moderately, and the new DARWIN models agree well with observations in (J-K) vs. (V-K) and Spitzer color-color diagrams. The enrichment of the silicate dust with Fe is a secondary process, taking place in the stellar wind on the surface of large Fe-free grains that have initiated the outflow. Therefore, the mass-loss rates are basically unaffected, while the wind velocities tend to be slightly higher than in corresponding models with Fe-free silicate dust. The gradual Fe enrichment of silicate grains in the inner wind region should produce signatures observable in mid-IR spectro-interferometrical measurements. Mass-loss rates derived from existing DARWIN models, based on Fe-free silicates, can be applied to stellar evolution models since the mass-loss rates are not significantly affected by the inclusion of Fe in the silicate grains.

astro-ph.SR↗

arXiv2019

Constraining the thermally-pulsing asymptotic giant branch phase with resolved stellar populations in the Small Magellanic Cloud

The thermally-pulsing asymptotic giant branch (TP-AGB) experienced by low- and intermediate-mass stars is one of the most uncertain phases of stellar evolution and the models need to be calibrated with the aid of observations. To this purpose, we couple high-quality observations of resolved stars in the Small Magellanic Cloud (SMC) with detailed stellar population synthesis simulations computed with the TRILEGAL code. The strength of our approach relies on the detailed spatially-resolved star formation history of the SMC, derived from the deep near-infrared photometry of the VISTA survey of the Magellanic Clouds, as well as on the capability to quickly and accurately explore a wide variety of parameters and effects with the COLIBRI code for the TP-AGB evolution. Adopting a well-characterized set of observations -- star counts and luminosity functions -- we set up a calibration cycle along which we iteratively change a few key parameters of the TP-AGB models until we eventually reach a good fit to the observations. Our work leads to identify two best-fitting models that mainly differ in the efficiencies of the third dredge-up and mass loss in TP-AGB stars with initial masses larger than about 3 M$_{\odot}$. On the basis of these calibrated models we provide a full characterization of the TP-AGB stellar population in the SMC in terms of stellar parameters (initial masses, C/O ratios, carbon excess, mass-loss rates). Extensive tables of isochrones including these improved models are publicly available.

astro-ph.SR↗

arXiv2018

On the Interplay between Robustness and Dynamic Planning for Adaptive Radiation Therapy

Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during treatment, the authors propose a dynamic framework for robust adaptive radiation therapy in which a variety of robust adaptive treatment strategies are introduced and evaluated. This variety is a result of optimization variables with various degrees of freedom within robust optimization models that vary in their grade of conservativeness. We formulate an adaptive framework with dependence on time and/or uncertainty or neither. The framework is evaluated with either expected-value-, worst-case-, or conditional-value-at-risk-(CVaR)-optimization. The goal of this study is to identify the mathematical properties of the proposed robust adaptive strategies in order to restore the planned dose distribution. We apply a result from convex analysis to show that in our framework, the time-dependent problem has a time-independent optimal solution. This implies that the time-dependent problem can be solved by dynamically solving the corresponding time-independent problem. This is especially relevant in a clinical context, since it implies that adaptive radiation therapy can be implemented in clinical practice using commercially available treatment planning systems. We demonstrate that time-and-scenario-dependent variables are most compatible with worst-case-optimization and that including dose prediction potentially improves treatment compared to non-adaptive planning. Contrarily, time-and-scenario-independent variables appear most compatible with expected-value-optimization. Non-adaptive robust strategies may provide sufficient target coverage, comparable to robust adaptive strategies, if the occurring uncertainties follow the same distribution as those included in the robust model.

physics.med-ph↗

arXiv2018

Increased accuracy of planning tools for optimization of dynamic multileaf collimator delivery of radiotherapy through reformulated objective functions

The purpose of this study is to examine in a clinical setting a novel formulation of objective functions for intensity-modulated radiotherapy treatment plan multicriteria optimization (MCO) that we suggested in a recent study. The proposed objective functions are extended with dynamic multileaf collimator (DMLC) delivery constraints from the literature, and a tailored interior point method is described to efficiently solve the resulting optimization formulation. In a numerical planning study involving three patient cases, DMLC plans Pareto optimal to the MCO formulation with the proposed objective functions are generated. Evaluated based on pre-defined plan quality indices, these DMLC plans are compared to conventionally generated DMLC plans. Comparable or superior plan quality is observed. Supported by these results, the proposed objective functions are argued to have a potential to streamline the planning process, since they are designed to overcome the methodological shortcomings associated with the conventional penalty-based objective functions assumed to cause the current need for time-consuming trial-and-error parameter tuning. In particular, the increased accuracy of the planning tools imposed by the proposed objective functions has the potential to make the planning process less complicated. These conclusions position the proposed formulation as an alternative to existing methods for automated planning.

math.OC↗

arXiv2017

Explicit optimization of plan quality measures in intensity-modulated radiation therapy treatment planning

Conventional planning objectives in optimization of intensity-modulated radiotherapy treatment (IMRT) plans are designed to minimize the violation of dose-volume histogram (DVH) thresholds using penalty functions. Although successful in guiding the DVH curve towards these thresholds, conventional planning objectives offer limited control of the individual points on the DVH curve (doses-at-volume) used to evaluate plan quality. In this study, we abandon the usual penalty-function framework and propose planning objectives that more explicitly relate to DVH statistics. The proposed planning objectives are based on mean-tail-dose, resulting in convex optimization. We also demonstrate how to adapt a standard optimization method to the proposed formulation in order to obtain a substantial reduction in computational cost. We investigate the potential of the proposed planning objectives as tools for optimizing DVH statistics through juxtaposition with the conventional planning objectives on two patient cases. Sets of treatment plans with differently balanced planning objectives are generated using either the proposed or the conventional approach. Dominance in the sense of better distributed doses-at-volume is observed in plans optimized within the proposed framework, indicating that the DVH statistics are better optimized and more efficiently balanced using the proposed planning objectives.

physics.med-ph↗

arXiv2017

The adventure of carbon stars - Observations and modelling of a set of C-rich AGB stars

Modeling stellar atmospheres is a complex, intriguing task in modern astronomy. A systematic comparison of models with multi-technique observations is the only efficient way to constrain them. Aims: We performed a self-consistent modeling of the atmospheres of six C-rich AGB stars: R Lep, R Vol, Y Pav, AQ Sgr, U Hya and X TrA, with the aim of enlarging the knowledge of the dynamic processes occurring in their atmospheres. Methods. We used VLTI/MIDI interferometric observations, in combination with spectro-photometric data, and compared them with self-consistent dynamic models atmospheres. Results: The models can reproduce SED data well at wavelengths longwards of 1μm, and the interferometric observations between 8μm and 10μm. Discrepancies could be due to a combination of data- and model-related effects. The models best fitting the Miras are significantly extended, with a prominent shell-like structure, while the models best fitting the non-Miras are more compact, showing lower average mass-loss. The mass loss is of episodic or multi-periodic nature, but causes the visual amplitudes to be notably larger than the observed ones. Stellar parameters were derived from the model fitting: T_eff, L_bol, M, C/O, $\dot{\text{M}}$. Our findings agree well with literature values within the uncertainties. T_eff and L_bol are also in good agreement with the T derived from the angular diameter θ_{(V-K)} and L_bol from the SED fitting, except for AQ Sgr. Finally, θ_Ross and θ_(V-K) agree with each other better for the Miras than for the non-Miras,which is probably connected to the episodic nature of the latter models. We also located the stars in the H-R diagram, comparing them with evolutionary tracks. We found that the main derived properties from the model fitting are in good agreement with TP-AGB evolutionary calculations for carbon stars (COLIBRI code).

astro-ph.SR↗

arXiv2016

Towards Robust Adaptive Radiation Therapy Strategies

The authors propose robust adaptive strategies based on stochastic minimax optimization for a series of simulated treatments on a one-dimensional patient phantom. The plan applied during the first fractions should be able to handle anticipated systematic and random errors. At scheduled fractions, the impact of the measured errors on the delivered dose distribution is evaluated. For a patient receiving a dose that does not satisfy clinical goals, the plan is reoptimized based on these individually measured errors. The adapted plan is then applied during subsequent fractions until a new scheduled adaptation becomes necessary. In the first adaptive strategy, the measured systematic and random error scenarios and their assigned probabilities are updated to guide the robust reoptimization. In the second strategy, the grade of conservativeness is adapted in response to the measured dose delivery errors. In the third strategy, the uncertainty margins around the target are recalculated based on the measured errors. The simulated systematic and random errors are either similar to the anticipated errors or unpredictably larger, in order to critically evaluate the performance of the adaptive strategies. The simulations show that robustly optimized treatment plans provide sufficient treatment quality for those treatment error scenarios similar to the anticipated error scenarios. Combining robust planning with adaptation leads to improved OAR protection. In case of unpredictably larger treatment errors, the first strategy performs best at improving treatment quality in terms of target coverage and OAR protection. According to the simulations, these robust adaptive treatment strategies are able to identify candidates for an adaptive treatment, thus giving the opportunity to provide individualized plans, and improve their treatment quality through adaptation.

math.OC↗

arXiv2014

Synthetic photometry for carbon-rich giants. IV. An extensive grid of dynamic atmosphere and wind models

The evolution and spectral properties of stars on the AGB are significantly affected by mass loss through dusty stellar winds. Dynamic atmosphere and wind models are an essential tool for studying these evolved stars, both individually and as members of stellar populations, to understand their contribution to the integrated light and chemical evolution of galaxies. This paper is part of a series testing state-of-the-art atmosphere and wind models of carbon stars against observations, and making them available for use in various theoretical and observational studies. We have computed low-resolution spectra and photometry (in the wavelength range 0.35-25 mu) for a grid of 540 dynamic models with stellar parameters typical of solar-metallicity C-rich AGB stars and with a range of pulsation amplitudes. The models cover the dynamic atmosphere and dusty outflow (if present), assuming spherical symmetry, and taking opacities of gas-phase species and dust grains consistently into account. To characterize the time-dependent dynamic and photometric behaviour of the models in a concise way we defined a number of classes for models with and without winds. Comparisons with observed data in general show a quite good agreement for example regarding mass-loss rates vs. (J-K) colours or K magnitudes vs. (J-K) colours. Some exceptions from the good overall agreement, however, are found and attributed to the range of input parameters (e.g. relatively high carbon excesses) or intrinsic model assumptions (e.g. small particle limit for grain opacities). While current results indicate that some changes in model assumptions and parameter ranges should be made in the future to bring certain synthetic observables into better agreement with observations, it seems unlikely that these pending improvements will significantly affect the mass-loss rates of the models.

astro-ph.SR↗

arXiv2013

The wind of the M-type AGB star RT Virginis probed by VLTI/MIDI

We study the circumstellar environment of the M-type AGB star RT Vir using mid-infrared high spatial resolution observations from the ESO-VLTI focal instrument MIDI. The aim of this study is to provide observational constraints on theoretical prediction that the winds of M-type AGB objects can be driven by photon scattering on iron-free silicate grains located in the close environment (about 2 to 3 stellar radii) of the star. We interpreted spectro-interferometric data, first using wavelength-dependent geometric models. We then used a self-consistent dynamic model atmosphere containing a time-dependent description of grain growth for pure forsterite dust particles to reproduce the photometric, spectrometric, and interferometric measurements of RT Vir. Since the hydrodynamic computation needs stellar parameters as input, a considerable effort was first made to determine these parameters. MIDI differential phases reveal the presence of an asymmetry in the stellar vicinity. Results from the geometrical modeling give us clues to the presence of aluminum and silicate dust in the close circumstellar environment (< ~5 stellar radii). Comparison between spectro-interferometric data and a self-consistent dust-driven wind model reveals that silicate dust has to be present in the region between 2 to 3 stellar radii to reproduce the 59 and 63 m baseline visibility measurements around 9.8 micron. This gives additional observational evidence in favor of winds driven by photon scattering on iron-free silicate grains located in the close vicinity of an M-type star. However, other sources of opacity are clearly missing to reproduce the 10-13 micron visibility measurements for all baselines. This study is a first attempt to understand the wind mechanism of M-type AGB stars by comparing photometric, spectrometric, and interferometric measurements with state-of-the-art, self-consistent dust-driven wind models. The agreement of the dynamic model atmosphere with interferometric measurements in the 8-10 micron spectral region gives additional observational evidence that the winds of M-type stars can be driven by photon scattering on iron-free silicate grains. Finally, a larger statistical study and progress in advanced self-consistent 3D modeling are still required to solve the remaining problems.

astro-ph.SR↗

arXiv2010

A grid of MARCS model atmospheres for S stars

S-type stars are late-type giants whose atmosphere is enriched in carbon and s-process elements because of either extrinsic pollution by a binary companion or intrinsic nucleosynthesis and dredge-up on the thermally-pulsing AGB. A large grid of S-star model atmospheres has been computed covering the range 2700 < Teff < 4000 K with 0.5 < C/O < 0.99. ZrO and TiO band strength indices as well as VJHKL photometry are needed to disentangle Teff, C/O and [s/Fe]. A "best-model finding tool" was developed using a set of well-chosen indices and checked against photometry as well as low- and high-resolution spectroscopy. It is found that applying M-star model atmospheres (i.e., with a solar C/O ratio) to S stars can lead to errors on Teff up to 400K. We constrain the parameter space occupied by S stars of the vast sample of Henize stars in terms of Teff, [C/O] and [s/Fe].

astro-ph.SR↗

arXiv2010

Oxygen isotopic ratios in cool R Coronae Borealis stars

We investigate the relationship between R Coronae Borealis (RCB) stars and hydrogen-deficient carbon (HdC) stars by measuring precise 16O/18O ratios for five cool RCB stars. The 16O/18O ratios are derived by spectrum synthesis from high-resolution (R=50,000) K-band spectra. Lower limits to the 16O/17O and 14N/15}N ratios as well as Na and S abundances (when possible) are also given. RCB stars in our sample generally display less 18O than HdC stars - the derived 16O/18O ratios range from 3 to 20. The only exception is the RCB star WX CrA, which seems to be a HdC-like star with 16O/18O=0.3. Our result of a higher 16O/18O ratio for the RCB stars must be accounted for by a theory of the formation and evolution of HdC and RCB stars. We speculate that a late dredge-up of products of He-burning, principally 12C and 16O, may convert a 18O-rich HdC star into a 18O-poor RCB star as the H-deficient star begins its final evolution from a cool supergiant to the top of the white dwarf cooling track.

astro-ph.SR↗

arXiv2009

Abundances in bulge stars from high-resolution, near-IR spectra I. The CNO elements observed during the science verification of CRIRES at VLT

The formation and evolution of the Milky Way bulge is not yet well understood and its classification is ambiguous. Constraints can, however, be obtained by studying the abundances of key elements in bulge stars. The aim of this study is to determine the chemical evolution of CNO, and a few other elements in stars in the Galactic bulge, and to discuss the sensitivities of the derived abundances from molecular lines. High-resolution, near-IR spectra in the H band were recorded using VLT/CRIRES. Due to the high and variable visual extinction in the line-of-sight towards the bulge, an analysis in the near-IR is preferred. The CNO abundances can all be determined simultaneously from the numerous molecular lines in the wavelength range observed. The three giant stars in Baade's window presented here are the first bulge stars observed with CRIRES. We have especially determined the CNO abundances, with uncertainties of less than 0.20 dex, from CO, CN, and OH lines. Since the systematic uncertainties in the derived CNO abundances due to uncertainties in the stellar fundamental parameters, notably Teff, are significant, a detailed discussion of the sensitivities of the derived abundances is included. We find good agreement between near-IR and optically determined O, Ti, Fe, and Si abundances. Two of our stars show a solar [C+N/Fe], suggesting that these giants have experienced the first dredge-up and that the oxygen abundance should reflect the original abundance of the giants. The two giants fit into the picture, in which there is no significant difference between the O abundance in bulge and thick-disk stars. Our determination of the S abundances is the first for bulge stars. The high [S/Fe] values for all the stars indicate a high star-formation rate in an early phase of the bulge evolution.

astro-ph.SR↗

arXiv2008

HE 1327-2326, an unevolved star with [Fe/H]<-5.0. II. New 3D-1D corrected abundances from a VLT/UVES spectrum

We present a new abundance analysis of HE 1327-2326, the currently most iron-poor star, based on observational data obtained with VLT/UVES. We correct the 1D LTE abundances for 3D effects to provide an abundance pattern that supersedes previous works, and should be used to observationally test current models of the chemical yields of the first-generation SNe. Apart from confirming the 1D LTE abundances found in previous studies before accounting for 3D effects, we make use of a novel technique to apply the 3D-1D corrections for CNO which are a function of excitation potential and line strength for the molecular lines that comprise the observable CH, NH, and OH features. We find that the fit to the NH band at 3360 A is greatly improved due to the application of the 3D-1D corrections. This may indicate that 3D effects are actually observable in this star. We also report the first detection of several weak Ni lines. The cosmologically important element Li is still not detected; the new Li upper limit is extremely low, A(Li)<0.62, and in stark contrast with results not only from WMAP but also from other metal-poor stars. We also discuss how the new corrected abundance pattern of HE 1327-2326 is being reproduced by individual and integrated yields of SNe.

astro-ph↗

arXiv2008

A grid of MARCS model atmospheres for late-type stars I. Methods and general properties

We have constructed a grid of about 10,000 spherically symmetric and plane-parallel models with the MARCS program, and make it available for public use. Parameter ranges are: Teff=2500 to 8000 K, log g =log(GM/R2)= -1 to 5 (cgs) with various masses and radii, [Me/H]=-5 to +1, with [Alpha/Fe] = 0.0 and 0.4 and different choices of C and N abundances to also represent stars of types R, S and N, and with microturbulence parameters from 1 to 5 km/s. We also list fluxes in approximately 108,000 wavelength points. Underlying assumptions in addition to 1D stratification include hydrostatic equilibrium, MLT convection and LTE. A number of general properties of the models are discussed, in relation to the effects of changing blanketing and sphericity. Models are compared with other available grids and excellent agreement is found with plane-parallel models of Castelli and Kurucz within the overlapping parameter range. Although there are departures from the spherically symmetric NextGen models, the agreement with more recent PHOENIX models is gratifying. The models of the grid show regularities, but some interesting departures from general patterns occur for the coolest models due to the molecular opacities. We have tested rules of thumb concerning effects of blanketing and sphericity and found them to often be astonishingly accurate. Some interesting new phenomena have been discovered, such as the intricate coupling between blanketing and sphericity, and the strong effects of carbon enhancement on metal-poor models. We give further details of models and comparisons with observations in subsequent papers.

astro-ph↗

arXiv2007

On the Use of Blanketed Atmospheres as Boundary Conditions for Stellar Evolutionary Models

Stellar models have been computed for stars having [Fe/H] = 0.0 and -2.0 to determine the effects of using boundary conditions derived from the latest MARCS model atmospheres. The latter were fitted to the interior models at both the photosphere and at tau = 100, and at least for the 0.8-1.0 solar mass stars considered here, the resultant evolutionary tracks were found to be nearly independent of the chosen fitting point. Particular care was taken to treat the entire star as consistently as possible; i.e., both the interior and atmosphere codes assumed the same abundances and the same treatment of convection. Tracks were also computed using either the classical gray T(tau,T_eff) relation or that derived by Krishna Swamy (1966) to derive the boundary pressure. The latter predict warmer giant branches (by ~150 K) at solar abundances than those based on gray or MARCS atmospheres, which happens to be in good agreement with the inferred temperatures of giants in the open cluster M67 from the latest (V-K)-T_eff relations. Most of the calculations assumed Z=0.0125 (Asplund et al.), though a few models were computed for Z=0.0165 (Grevesse & Sauval) to determine the dependence of the tracks on Z_\odot. Grids of "scaled solar, differentially corrected" (SDC) atmospheres were also computed to try to improve upon theoretical MARCS models. When they were used as boundary conditions, the resultant tracks agreed very well with those based on a standard scaled-solar (e.g., Krishna Swamy) T(tau,T_eff) relation, independently of the assumed metal abundance. Fits of isochrones to the C-M diagram of the [Fe/H] = -2 globular cluster M68 were examined, as was the possibility that the mixing-length parameter varies with stellar parameters.

astro-ph↗