Interferometry & Asteroseismology of Delta Scu} Stars
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Mode selection and amplitude limitation in pulsating stars Radosław Smolec InterferometryNicolaus Copernicus & Astronomical Asteroseismology Centre, PAS of Delta Scu Stars: 44 Tau and 29 Cyg Zhao Guo Copernicus Astronomical Center (CAMK) & Georgia State University (GSU) Jeremy Jones (GSU) Alosza Pamyatnykh (CAMK) Doug Gies (GSU) Wojtek Dziembowski (CAMK) Gail Schaefer (CHARA) Asteroseismology of Eclipsing Binaries • Gamma Dor stars Guo, Gies, & Matson 2017, ApJ, in press. • Post-mass transfer Delta Scu stars Guo,Gies, Matson, et al. 2017, ApJ, 834, 59 • Normal Delta Scu stars Guo,Gies, Matson, Garcia Hernandez. 2016, ApJ, 826, 69 • Heartbeat stars with dally excited oscillaons Guo,Gies, & Fuller 2017, ApJ, 837, 114 44 Tau Spectroscopy, Mul6-site photometry: mode ID: Zima 07 Rodler 03, Antoci 07 Seismic modeling: Lenz 08,10 Interferometry -> evolved -> Intrinsic slow rotator: Veq <= 5km/s -> Non-rotang models OK -> Solar metallicity Teff= 6900+/- 100K, log g=3.6 +/- 0.1 -> 15 frequencies, most with mode iden6ficaon 6.90 c/d 8.96 c/d CHARA: R=3.25+/-0.08 M=2.0 M=1.9 M=1.8 Z=0.02, MLT=1.8 M=1.7 Fundamental radial mode= 6.90 +/- 0.10 (c/d) 1st overtone radial = 8.96 +/- 0.10 (c/d) CHARA: R=3.25+/-0.08 M=2.0 M=1.9 M=1.8 Z=0.02, MLT=1.8 M=1.7 Fundamental radial mode= 6.90 +/- 0.10 (c/d) 1st overtone radial = 8.96 +/- 0.10 (c/d) 860 P. Lenz et al.: An asteroseismic study of the δ Scuti star 44 Tauri P. Lenz et al.: An asteroseismic study of the δ Scuti star 44 Tauri 857 P. Lenz et al.: An asteroseismic study of the δ Scuti star 44 Tauri 857 Fig. 2. The Hertzsprung-Russell diagram showing the location of mod- Fig. 3. Petersen diagrams for a main sequence (upper panel)andapost- els that fit radial fundamental and first overtone modes to the observed main sequence model (lower panel). The asterisk corresponds to the 5 1 frequencies for the main sequence (upper panel)andpost-mainse- observed values of 44 Tau. The uncertainties in period ( 1.4 10− cd− ) 6 ∼ × quence case (lower panel). The asterisk indicates the center of the pho- and period ratio ( 2 10− )aresmallerthanthesymbolsize. Fig. 2. The Hertzsprung-Russell diagram showing the location of mod- Fig. 3. Petersen diagrams for a main sequence (upper panel)andapost- tometric error box. Grey points represent models with Z values between ∼ × els that fit radial fundamental and first overtone modes to the observed main sequence model (lower panel). The asterisk corresponds to the 0.019–0.04 (MS) or 0.015–0.025 (post-MS) and an overshooting pa- 5 1 frequencies for the main sequence (upper panel)andpost-mainse- observed values of 44 Tau. The uncertainties in period ( 1.4 10− cd− ) rameter αov ranging from 0 to 0.4. Representative evolutionary tracks 6 ∼ × quence case (lower panel). The asterisk indicates the center of the pho- and period ratio ( 2 10− )aresmallerthanthesymbolsize. for the models listedFig. in 9. TableKinetic 2 are plotted. energy density of pulsationTo obtain along reliable∼ × the photometric stellar radiusmode identification for we com- Fig. 7. Comparison of the observed and theoreticalLenz, frequency Pamyatnykhtometric ranges error et box. al. Grey 2008 points represent models with Z values between 1 0.019–0.04 (MS)three or 0.015–0.025ℓ = 1modes.Themodesat9.21and11.65cd (post-MS) and an overshooting pa- puted average amplitude ratios− are and trapped, phase differences in the for main sequence (upper panel)andpost-mainsequence(lower panel) 1 Strömgren filters v and y using weights for each observing sea- rameter αov rangingwhereas from 0 to the 0.4. Representative mode at 10.25 evolutionary cd− tracksis not. The energy contribution from models. The normalized growth-rate, η,ispositiveforunstablemodes.forthe the eff modelsect of listed different in Table opacity 2 are tables plotted. and the new solar element sonTo to account obtain reliable for the photometric different amount mode and identification quality of the we data com- mixture on thethe period outer ratio. envelope is significant for the(seeputed two formulae average trapped in amplitude the Appendix modes. ratios of and Breger phase et al. di 1999).fferences The in ob- the The vertical lines represent the observed frequencies (with longer linesWe have computed stellar models for a large set of different servationalStrömgren uncertainties filters v and y wereusing derived weights by error for each propagation observing from sea- for ℓ = 0modes). theinput effect parameters of different such opacity as chemi tablescal composition, and the new mixing-length solar element theson uncertainties to account for of the the annual different solutions. amount These and quality results of are the given data in Table 1. mixtureparameter, on theαMLT period,andtheparameterforovershootingfromthe ratio. (see formulae in the Appendix of Breger et al. 1999). The ob- convectiveWe have core, computedαov.Ourresultsshowthatmainsequenceand stellar models for a large set of different servationalFor δ Scuti uncertainties stars theoretical were derived mode by positions error propagation in the ampli- from post-main sequence models that fit the radial fundamental and input parameters such as chemical composition, mixing-length tudethe uncertainties ratio vs. phase of the diff annualerence solutions.diagram are These sensitive results to are the given ef- first overtone modes are clearly separated in the HR diagram ficiency of convection in the stellar envelope. Montalbán & parameter, α ,andtheparameterforovershootingfromthe in Table 1. (see Fig. 2).MLT For each case an evolutionary track of a selected Dupret (2007) showed that different treatments of convection af- convective core, α .Ourresultsshowthatmainsequenceand δ model is delineated.ov Post-main sequence models are located in- fectFor the phaseScuti diff starserences theoretical and amplitude mode positions ratios as well.in the In ampli- our post-main sequence models that fit the radial fundamental and side the photometric error box, whereas main sequence models computations,tude ratio vs. phasewe use di thefference mixing-length diagram are theory sensitive of convection to the ef- firstare overtonepredicted modesat significantly are clearly lower separated effective in temperatures the HR diagram in the andficiency assume of convectionthe frozen convective in the stellar flux envelope. approximation Montalbán for the & (seeHR Fig. diagram. 2). For The each given case family an evolutionary of models was track computed of a selected using pulsation-convectionDupret (2007) showed interaction. that different This treatments assumption of convection may not be af- modelawiderangeofparameters,suchas is delineated. Post-main sequenceZ between models 0.015 are located and 0.04 in- adequatefect the phase for cold diδfferencesScuti stars and and amplitude result in large ratios uncertainties as well. In in our side the photometric error box, whereas main sequence models computations, we use the mixing-length theory of convection and with an overshooting parameter αov of up to 0.4 pressure the mode identification. However, Montalbán & Dupret (2007) arescale predicted heights. at As significantly a representativ lowereexample,thePetersendiagram effective temperatures in the findand that assume for frequencies the frozen close convective to that flux of the approximation radial fundamental for the HRfor diagram. two selected The models given family is shown of modelsin Fig. 3. was The computed corresponding using modepulsation-convection the convection-pulsation interaction. treatment This assumption does not influence may not the be awiderangeofparameters,suchasmodel parameters are listed in Table 2.Z between 0.015 and 0.04 determinationadequate for cold of modeδ Scuti degree, starsℓ and. result in large uncertainties in and with an overshooting parameter αov of up to 0.4 pressure theWe mode tested identification. different values However, of the Montalbán mixing-length & Dupret parameter (2007) scale heights. As a representativeexample,thePetersendiagram αfind thatfor for a stellar frequencies model close with standardto that of chemical the radial composition fundamental 3.4. Identification of nonradial modes MLT for two selected models is shown in Fig. 3. The corresponding andmode a mass the convection-pulsation of 1.85 M .Theresultsofthesecomputationsare treatment does not influence the modelIn the parameters previous section are listed we have in Table noted 2. that the observation of two showndetermination in Fig. 4 of and mode 5.⊙ The degree, theoreticalℓ. mode positions were cal- radial modes puts strong constraints on the models. For complete culatedWe according tested diff toerent Daszy valuesnska-Daszkiewicz´ of the mixing-length et al. (2003) parameter using α for a stellar model with standard chemical composition 3.4.seismic Identification modelling of it nonradialis necessary modes to obtain an identification for a photometricMLT data in two passbands. sufficient number of observed nonradial pulsation modes. andAs a mass can be of seen 1.85 inM Fig..Theresultsofthesecomputationsare 4, for α = 0.5(orhigher)there ⊙ MLT In theMode previous identification section we is have often noted complicated that the by observation the effects of of two ro- isshown no reliable in Fig. agreement 4 and 5. The between theoretical observed mode and positions theoretical were mode cal- radialtation. modes The exceptionally puts strong constraints small rotational on the velocitymodels.For of 44 complete Tau al- positions.culated according Instead, towe Daszy obtainnska-Daszkiewicz´ a good consistency et al. for (2003) inefficient using seismiclows to modelling reduce these it is problems necessary because to obtain the an rotational identification splitting for is a convectionphotometric (α dataMLT in! two0.2). passbands. In the two diagrams in Fig. 5 the po- suveryfficient small. number There of are observed several techniquesnonradial pulsation that either modes. make use of sitionsAs of can observed be seen modes in Fig. are 4, compared for αMLT = to0 the.5(orhigher)there theoretical pre- photometricMode identification data in two is oftfiltersen complicated or combine by them the with effects spectro- of ro- dictionsis no reliable for a agreementmodel with between inefficient observed convection.