We examine the role of opacities in stellar pulsation with reference to
Cepheids and RR Lyraes, and examine the effect of augmented opacities on the
theoretical pulsation light curves in key temperature ranges. The temperature
ranges are provided by recent experimental and theoretical work that have
suggested that the iron opacities have been considerably underestimated. For
Cepheids, we find that the augmented opacities have noticeable effects in
certain period ranges (around $\log P \approx 1$) even though there is a
degeneracy with mixing length. We also find significant effects in theoretical
models of B-star pulsators.Comment: 6 pages, 3 Figures, Proceeding for the "Workshop on Astrophysical
  Opacities

Bhardwaj, A.

Kanbur, S. M.

Kundu, R.

Marconi, M.

Singh, H. P.

English

arXiv

We examine the role of opacities in stellar pulsation with reference to Cepheids and RR Lyraes, and examine the effect of augmented opacities on the theoretical pulsation light curves in key temperature ranges. The temperature ranges are provided by recent experimental and theoretical works that have suggested that the iron opacities have been considerably underestimated. For Cepheids, we find that the augmented opacities have noticeable effects in certain period ranges (around logP ≍1) even though there is a degeneracy with mixing length. We also find significant effects in theoretical models of B-star pulsators

MARCONI, Marcella

OA@INAF - Istituto Nazionale di Astrofisica

2018Publication Year2021-01-13T15:52:29ZAcceptance in OA@INAFThe Role of Opacities in Stellar PulsationTitleKanbur, S. M.; MARCONI, Marcella; Bhardwaj, A.; Kundu, R.; Singh, H. P.Authorshttp://hdl.handle.net/20.500.12386/29759HandleASTRONOMICAL SOCIETY OF THE PACIFIC CONFERENCE SERIESSeries515NumberarXiv:1806.02996v1  [astro-ph.SR]  8 Jun 2018The Role of Opacities in Stellar PulsationS. M. Kanbur,1 M. Marconi,2 A. Bhardwaj,3 R. Kundu,3, and H. P. Singh,31 Department of Physics, SUNY Oswego, Oswego, NY 13126, USA;shashi.kanbur@oswego.edu2 Osservatorio di Capodimonte, Napoli, Italy;marcella.marconi@oacn.inaf.it3 Department of Physics & Astrophysics, University of Delhi, Delhi, India;anupam.bhardwajj@gmail.comAbstract. We examine the role of opacities in stellar pulsation with reference toCepheids and RR Lyraes, and examine the effect of augmented opacities on the the-oretical pulsation light curves in key temperature ranges. The temperature ranges areprovided by recent experimental and theoretical work that have suggested that the ironopacities have been considerably underestimated. For Cepheids, we find that the aug-mented opacities have noticeable effects in certain period ranges (around log P ≈ 1)even though there is a degeneracy with mixing length. We also find significant effectsin theoretical models of B-star pulsators.1. IntroductionOpacity is a crucial quantity in theoretical stellar pulsation and evolution. It is an atomicdataset required in the calculation of the radiative flux, and hence, determines both theequilibrium structure of the star and its subsequent pulsation properties. Moreover,through the kappa and gamma effects, the opacity is an important source of pulsationaldriving and damping. The hydrogen and helium ionization regions in the outer enve-lope are such that the opacity increases upon compression, storing up energy duringcompression and releasing it during the subsequent expansion, thus amplifying any de-partures from hydrostatic equilibrium (Cox 1980).In order to obtain consistency between stellar evolution and pulsation, it is im-portant for stellar pulsation models to reproduce observed pulsation characteristics atmasses and luminosities mandated by stellar evolution calculations. This was the orig-inal motivation that led Simon (1982) to issue a plea for the recalculation of Rosse-land mean opacities inasmuch as to reconcile observed and theoretical characteristicsof bump and beat Cepheids. Simon (1982) found that this could be accomplished byaugmenting the metal opacities to resolve a number of discrepancies between evolu-tion and pulsation. This prompted two groups, the OP consortium (Seaton et al. 1994)and the OPAL group (Iglesias & Rogers 1991) to recalculate Rosseland mean opacitiesusing two different approaches. Both groups produced somewhat similar results andmanaged to resolve the bump and beat Cepheid discrepancies using the observed dataat the time (Moskalik et al. 1992; Kanbur & Simon 1994).12 Kanbur et al.In recent years, there has been an explosion of accurate, multi-wavelength datafor Cepheids and RR Lyraes due mainly to transient and/or microlensing surveys (e.g.,Udalski et al. 1993; Soszyński et al. 2008, 2015). However, there has also been re-cent experimental evidence that the iron opacities are still underestimated (Bailey et al.2015). The OP project were not able to treat iron with the full R-matrix technique dueto computational limitations. Now Pradhan & Nahar (2009) have started to recalculateiron opacities using this method; preliminary calculations suggest an increase in ironopacities translating to an increase in Rosseland mean opacities of about 15% at hightemperatures. In the present work we investigate the effect of increasing Rosselandmean opacities by a factor of 1.15 for the temperature range 5.1 < log T < 5.5.2. Fourier AnalysisSimon & Lee (1981) introduced Fourier analysis to quantify the non-linear structureof the Cepheid and RR Lyrae light curves, and applied this method to the data thatwere available then. In this method, both observational and theoretical light curves aresubject to the following decomposition:V = A0 +N∑k=1Ak cos(kωt + φk)Rk1 = Ak/A1φk1 = φk − kφ1 ,where ω = 2π/P, the period P being in days, and N is the order of the fit. The preferredmethod of constraining theory with observations is then a comparison of the theoret-ical and observed Fourier parameters and their trend with the period. Fig. 1 presentssuch results: we use Galactic and Magellanic Cloud data and recent full amplitudepulsation model light curves at a number of wavelengths (Bhardwaj et al. 2017). Theblue and red colors represent models made with canonical (log L = 0.9 + 3.34 log M +1.36 log Y − 0.34 log Z) and non-canonical (log L is the canonical luminosity plus 0.25dex) mass–luminosity (ML) relations. We note that the superb quality and quantity ofobservational data have provided a rigorous test-bed with which to constrain theoreticalmodels. These results are discussed in detail in Bhardwaj et al. (2015, 2017).3. Augmented OpacitiesWe computed a few pulsation models with augmented opacities (increased by a factor of1.15 in the temperature range 5.1 < log T < 5.5). We also computed a sample of stellarevolutionary tracks with and without this artificial opacity enhancement using MESA.Fig. 2 displays the results for a 7 M⊙ star with a Z = 0.008; Y = 0.256 composition. Thetracks with normal and enhanced opacity are quite similar except perhaps at the blueloop. We also computed a series of full amplitude Cepheid pulsation models spanninga range of periods with and without augmented opacities, Z = 0.02; Y = 0.28, with acanonical ML relation, and a fixed mixing length. We computed the theoretical lightcurves at V/K wavelengths and carried out a Fourier analysis as described above. Fig. 3presents the Fourier parameters (Rk1, φk1) plotted against the logarithm of the period (indays) at V/K bands in the left/right panel, respectively. We see that the differences canThe Role of Opacities in Stellar Pulsation 30.6 0.8 1.0 1.2 1.4 1.6log(P)0π2πφ 31φ 310.6 0.8 1.0 1.2 1.4 1.6log(P)0π2π0.6 0.8 1.0 1.2 1.4 1.6log(P)0π2π0.6 0.8 1.0 1.2 1.4 1.6log(P)0π2πφ 210.6 0.8 1.0 1.2 1.4 1.6log(P)0π2π0.6 0.8 1.0 1.2 1.4 1.6log(P)0π2π0.6 0.8 1.0 1.2 1.4 1.6log(P)0.00.40.8R310.6 0.8 1.0 1.2 1.4 1.6log(P)0.00.40.80.6 0.8 1.0 1.2 1.4 1.6log(P)0.00.40.8Observed     Canonical    Non-canonical0.6 0.8 1.0 1.2 1.4 1.6log(P)0.20.61.0R21Galaxy0.6 0.8 1.0 1.2 1.4 1.6log(P)0.20.61.0LMC0.6 0.8 1.0 1.2 1.4 1.6log(P)0.20.61.0SMCFigure 1. Comparison of theoretical (red and blue open symbols) and observed(black dots) Fourier parameters for Cepheid variables in the Galaxy and MagellanicClouds at I band. The theoretical models use canonical (blue open diamonds) andnon-canonical (red open triangles) ML relations.be large at short wavelengths and in certain period ranges (log P ≈ 1). The differencesin the Fourier parameters between the normal and enhanced opacity models are muchlarger than the errors in these parameters, though we note from Fig. 1 and the results inBhardwaj et al. (2015, 2017) that the changes in the mixing length parameters can alsoproduce large differences in the Fourier parameters.The superb quality of current observational data coupled with the Fourier methodto study the nonlinear structure of Cepheid/RR Lyrae light curves do offer the pos-sibility of using variable star observations to test newly computed opacities in stellarpulsation/evolution models.4. B Star PulsationsOP/OPAL/OPLIB opacities cannot reproduce the observed frequencies of B-star pul-sators. Daszyńska-Daszkiewicz et al. (2002) studied the early main sequence B-typestar v Eri, and modified the mean opacity profile to reproduce the observed range of4 Kanbur et al.4.4 4.2 4.0 3.8 3.6 3.42.53.03.54.04.5Log(Teff)Log(L/L 0)Normal opacitiesEnhanced opacitiesFigure 2. Evolutionary tracks for a 7M⊙ star with a Z = 0.008; Y = 0.256 compo-sition. Solid red line: enhanced opacities. Dashed black line: normal opacities.0.5 1.0 1.5log(P)0π2πφ 31φ 310.5 1.0 1.5log(P)0π2π0.5 1.0 1.5log(P)0π2π0.5 1.0 1.5log(P)0π2π0.5 1.0 1.5log(P)π2πφ 21Z=0.02, Y=0.280.5 1.0 1.5log(P)π2πZ=0.008, Y=0.250.5 1.0 1.5log(P)π2πZ=0.02, Y=0.280.5 1.0 1.5log(P)π2πZ=0.008, Y=0.250.5 1.0 1.5log(P)0.00.2R310.5 1.0 1.5log(P)0.00.20.5 1.0 1.5log(P)0.00.20.5 1.0 1.5log(P)0.00.20.5 1.0 1.5log(P)0.00.30.6R210.5 1.0 1.5log(P)0.00.30.60.5 1.0 1.5log(P)0.00.30.60.5 1.0 1.5log(P)0.00.30.6 StandardEnhancedFigure 3. Fourier parameters as a function of period with normal (solid symbols)and enhanced (open symbol) opacities. Left panels: V band. Right panels: K band.The Role of Opacities in Stellar Pulsation 5frequencies. Their modifications were similar to the ones used in this paper. With thismodification, they were able to reproduce observations. Here we tried a similar modifi-cation using MESA and GYRE with the following parameters: 7M⊙, Y = 0.2815, andZ = 0.015 considering only the fundamental and first overtone modes. Table 1 presentsour results. In this table, we consider two mixing lengths, 1.5 and 5 and use both normaland enhanced opacity (as defined in the section on augmented opacities) models. Wecalculated the fundamental and first overtone period with GYRE whenever the track onthe HR diagra, as computed by MESA, became pulsationally unstable. Since both fun-damental (FU) and first overtone (FO) modes become unstable at a number of places,we have presented the period at all these points for this one 7M⊙ model. Our interestis primarily in the difference that enhanced opacities can make. We see that augmentedopacities can indeed make a significant change in the theoretical periods and, hence,concur with previous work (Daszyńska-Daszkiewicz et al. 2002).Table 1. LNA analysis of a 7M⊙ models appropriate for v Eri usingMESA+GYRE and normal and enhanced opacities.Mixing Length 1.5Period with normal opacitiesFU 0.256774 7.51159 14.7145 17.5200FO 4.82029 9.45686 11.2258Period with enhanced opacitiesFU 0.260017 7.61011 15.2465 17.6854FO 4.80815 9.63397 11.5206Mixing length 5Period with normal opacitiesFU 0.260284 5.94326 11.0175 12.9086FO 3.88381 8.16356 7.01949Period with enhanced opacitiesFU 0.259143 6.06253 11.3137 13.1524FO 3.81356 8.16799 7.09209Notes: Periods are in days. We use GYRE to compute the period every time the 7M⊙ becomes unstable forthe fundamental (FU) and first overtone (FO) models. Hence the period (in days) in the last four columnscorrespond to different evolutionary phases while crossing the HR diagram.Acknowledgments. SMK and HPS acknowledge support from IUSSTF providedto the Indo-US joint center on Theoretical Analysis of Variable Star Data in the Era ofLarge Surveys. RK thanks CSIR for a Junior Research Fellowship.ReferencesBailey, J. E., Nagayama, T., Loisel, G. P., et al. 2015, Nature, 517, 56Bhardwaj, A., Kanbur, S. M., Marconi, M., et al. 2017, MNRAS, 466, 2805Bhardwaj, A., Kanbur, S. M., Singh, H. P., Macri, L. M., & Ngeow, C.-C. 2015, MNRAS, 447,3342Cox, J. P. 1980, Theory of stellar pulsation (Princeton, NJ: Princeton University Press), 393Daszyńska-Daszkiewicz, J., Dziembowski, W. A., Pamyatnykh, A. A., & Goupil, M.-J. 2002,A&A, 392, 1516 Kanbur et al.Iglesias, C. A., & Rogers, F. J. 1991, ApJ, 371, 408Kanbur, S. M., & Simon, N. R. 1994, ApJ, 420, 880Moskalik, P., Buchler, J. R., & Marom, A. 1992, ApJ, 385, 685Pradhan, A. K., & Nahar, S. N. 2009, in Recent Directions in Astrophysical Quantitative Spec-troscopy and Radiation Hydrodynamics, edited by I. Hubeny, J. M. Stone, K. MacGre-gor, & K. Werner (Melville, NY: AIP Publishing), vol. 1171 of AIP Conf. Ser., 52Seaton, M. J., Yan, Y., Mihalas, D., & Pradhan, A. 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