Comparative study of low-temperature opacities with GARSTEC models

We present a comparative study of the effect of low-temperature opacities on stellar models up to the Red Giant branch (RGB), computed with the GARching STellar Evolution Code. We have used two sets of low-temperature opacities; {\AE}SOPUS ({\AE}) from the University of Padova and those from the Wichita State University group (F05). In the relevant range of temperatures for this study, log \k{appa}{\AE}<log \k{appa}F 05. Therefore, to compare stellar evolutionary tracks, we performed a solar calibration of the {\alpha}mlt, for each set of low-temperature opacities. After carrying such a calibration, we find that stellar evolutionary tracks are almost unaffected by the choice of low-temperature opacities, with largest variations of 25-30 K at the latest evolutionary stages of the RGB phase.


INTRODUCTION
Several sets of Rosseland mean opacities for stellar interiors, with different physical inputs and conditions have been developed, such as The Opacity Project OP [Badnell et al. (2005)] and OPAL [Iglesias & Rogers (1996)] among many others.In this research note we compared two sets of low-temperature opacities in the range 3.50 ≤ log T ≤ 4.50, which include molecules and dust as opacity sources in addition to atoms, and the impact they have in stellar evolutionary tracks for different masses, from the MS and up to the RGB phase.The scope of the comparison, encompasses the AESOPUS 1 web interface (Accurate Equation of State and OPacity Unit Software) [Marigo & Aringer (2009)] and [Marigo et al. (2022)] and the database set up by the Wichita State University group [Ferguson et al. (2005)], hereafter F05.A recent study of AESOPUS opacities on the AGB phase has been presented in [Cinquegrana & Joyce (2022)].Results presented here use the MB22 [Magg et al. (2022)] solar mixture, but we tested that other chemical compositions such as GS98 [Grevesse & Sauval (1998)] and AGSS09 [Asplund et al. (2009)] show similar results [Diaz Reeve & Serenelli (2023)].Stellar models were computed using GARSTEC [Weiss & Schlattl (2008)] version 20.1.

Preliminary Overview of the Opacity Data Sets
Left panel in Figure 1 shows the differences in the Rosseland mean opacity between AESOPUS and F05, ∆ log κ = log κ AE − log κ F 05 , for MB22 chemical composition and for the cases X = 0.70 and Z = 0.004, 0.02 and 0.04, for temperatures between 3.50 ≤ log T ≤ 4.50, throughout the range -8.00 ≤ log R ≤ 1.00, where log R = log ρ−3 log T +18.Such differences, in the range 3.50 ≤ log T ≤ 4.00 lie between +0.05/−0.08dex, except for a peak at log T = 3.60 where differences reach up to −0.10 dex.For 4.00 ≤ log T ≤ 4.50 differences seem to be in a wider range between ± 0.10 dex and reaching at most −0.14 dex at log T = 4.25 for the case Z = 0.04.Differences appear to be larger with the increasing metallicity.Gray shaded regions show the differences for the whole log R range, while maroon, yellow and purple lines show differences for the cases log R = 0.00, -1.00 and -2.00 respectively, which span the log R values that better reproduce the approximate conditions in 0.70 -1.50 M ⊙ stellar envelopes, up to the RGB phase.

Solar Calibration
We carried out solar calibrations using the AESOPUS and F05 opacities.The chemical composition is almost independent of the choice of low-temperature opacities.Initial abundances are X ⊙ = 0.70988 (0.70982), Y ⊙ = 0.27190 (0.27196) and Z ⊙ = 0.01822 (0.01822) for the AESOPUS (respectively F05) solar model.A more relevant difference appeared on the value of the α mlt parameter, as its calibration in a solar model is sensitive to the choice of lowtemperature opacities.We found α AE mlt = 2.0530 for AESOPUS while for F05 the value was α F 05 mlt = 2.1487, i.e. α AE mlt < α F 05 mlt .
Near the solar surface at log T ≃ 3.76, AESOPUS shows smaller opacities than F05 (see left panel in Figure 1), making the star more luminous (less opaque) and as a consequence, increasing its effective temperature.To compensate this change in temperature the mixing length parameter α mlt decreases for less opaque models decreasing the effective temperature of the model star so that the solar effective temperature and luminosity are matched.

Comparative Study with GARSTEC models
We computed stellar evolution models for masses M/M ⊙ = 0.70, 1.00 and 1.50 and Z = 0.01998, close to the solar calibrated Z ⊙ .The α mlt was used consistently with the low-temperature opacities as described above.Models extend up to the RGB phase.Right panel in Figure 1 shows the computed evolutionary tracks.
Both sets of models were computed using low-temperature opacities for 3.20 ≤ log T ≤ 4.00, so the effect of molecules and dust, besides the atomic effects, are included in stellar evolutionary models, and OP opacities for log T ≥ 4.10.
Differences between models along the MS and the SGB phases are almost negligible for stellar evolutionary tracks for all masses, with differences of 10-15 K in the effective temperature of the model stars.Differences increase slightly at the latest stages of the RGB, reaching maximum values of 25-30 K at the RGB-tip.Such differences are originated mainly due to the fact that near log T ≃ 3.50, log κ AE > log κ F 05 , i.e. there is a sign reversal in the opacity difference, so the effect of the solar calibration on α mlt is no longer able to compensate for the opacity differences and effective temperature differences appear.

DISCUSSION
From the preliminary overview of the opacity data sets we found that differences between AESOPUS and F05 increase with metallicity and that the range of variation was wider for temperatures above log T = 4.00.However, mean differences between data sets were in the range ± 0.10 dex for temperatures 3.50 ≤ log ≤ 4.50 and for -8.00 ≤ log R ≤ 1.00.Near the solar surface AESOPUS shows lower opacities than F05, which in a solar calibration was compensated by reducing the efficiency of the energy transport in near-surface convection, decreasing the value of the α mlt in less opaque models.Results are presented for MB22 chemical composition, however GS98 and AGSS09 solar compositions show similar results.
Stellar models for masses M/M ⊙ = 0.70, 1.00 and 1.50 and Z = 0.01998, showed differences around 10-15 K along the MS and SGB phases, while differences around 25-30 K appeared on the latest evolutionary phases of the RGB.We conclude that stellar models computed with low-temperature opacities either from AESOPUS or F05, are in agreement

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Figure 1.Left: Comparison of the Rosseland mean opacity for AESOPUS and F05 for X = 0.70, Z = 0.004, 0.02 and 0.04.Gray vertical line shows the solar effective temperature log T ≃ 3.76, and gray shaded profile shows the range of variation for all log R values.Right: Evolutionary tracks for stellar models computed with GARSTEC with Z = 0.01998, and for M/M⊙ = 0.70 (red track), 1.00 (blue track) and 1.50 (black track).