Interferometry & Asteroseismology of Delta Scu} Stars

. 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, Mul-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 idenﬁcaon 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

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. and theoretical We can defini- mode tation.scopic The data exceptionally to infer the spherical small rotational degreesof velocity the modes. of 44 The Tau lat- al- tivelypositions. identify Instead, the frequencies we obtain af1 goodand f consistency5 as ℓ = 0modes, for inefffi2,cientf3, lowster approach to reduce has these been problems successfully because applied the rotational in the case splitting of FG Vir is convectionf4 and f6 as (ℓα=MLT1modes.! 0.2).f7 Incan the be two identified diagrams as anin Fig.ℓ = 2mode. 5 the po- very(Daszy small.nska-Daszkiewicz´ There are several et al.techniques 2005). The that azimuthal either make order use of Thesitions observational of observed formal modes errors are compared for the remaining to the theoretical frequencies pre- photometricpulsation modes dataFig. can in two10. only filtersIncrement be determined or combine fromof them the spectroscopy. exponentialwith spectro- aredictions amplitude too large for ato model draw growth, a with conclusion. ineγ,forunstablefficient However, convection. an identification We can defini- as Fig. 8. Comparison between observed and predicted frequenciesscopic for data a to infermodes the spherical of ℓ degrees3forthepost-MSmodelshowninFig.6.Thetrapped of the modes. The lat- tively identify the frequencies f and f as ℓ = 0modes, f , f , ≤ 1 5 2 3 main sequence (upper panel)andpost-mainsequence(lowerter panel approach) hasℓ been= 1modesaremarkedwithblacktriangles. successfully applied in the case of FG Vir f4 and f6 as ℓ = 1modes.f7 can be identified as an ℓ = 2mode. (Daszynska-Daszkiewicz´ et al. 2005). The azimuthal order of The observational formal errors for the remaining frequencies case. Observed frequencies are marked by vertical lines. The numberspulsation modes can only be determined from spectroscopy. are too large to draw a conclusion. However, an identification as above the lines denote the corresponding mode degree, ℓ,asidentified from photometry and spectroscopy. of modes that are not trapped. Consequently, it may be easier to excite trapped modes to observable amplitudes. In Fig. 9 the 1.875 M were chosen. The corresponding frequency spectrum distribution of the kinetic energy density of pulsation along the for this model⊙ that fits the observed radial modes can be seen in stellar radius for two trapped ℓ = 1modesandforamodewhich Fig. 8 (lower panel). is not trapped is shown. The frequency spectrum of nonradial modes is much denser Mode trapping can also explain the tendency of detected fre- than that of main sequence models. In fact, for post-main se- quencies to build groups around radial frequencies as can be seen quence models many more frequencies are predicted than ob- in Fig. 10. This diagram shows the increment of the exponential served. An extreme example is 4 CVn, one of the most evolved amplitude growth, γ = Im(ω), where ω is the complex eigen- δ Scuti stars, for which approximately 500 modes are predicted frequency. γ is proportional− to the work integral and inversely (Breger & Pamyatnykh 2002). There exist some rules that select proportional to the kinetic energy of a given mode. Just the ki- only a few modes to be excited to observable amplitudes. Mode netic energy is responsible for its nonmonotonic behavior. The trapping in the acoustic cavity in the stellar envelope can be increment γ is significantly higher for trapped modes. one of these rules, as discussed by Dziembowski & Krolikowska We can also see that trapping of ℓ = 2modesisratherweak (1990). compared to the ℓ = 1andℓ = 3case(seeFig.10).Therea- Trapped modes can be considered as nonradial counterparts son for this becomes clear when the run of the Brunt-Väisälä of radial modes. Most of the energy of trapped modes is con- frequency, N,andtheLambfrequency,L,isexaminedinde- fined in the envelope, where the density is low. Therefore, the tail. These characteristic frequencies determine the regions with total kinetic energy of these modes is much smaller than that oscillatory behaviour in the star as shown in Fig. 11. Similar 4P.Lenzetal.:Aδ Scuti star in the post-MS contraction phase: 44 Tauri

P. Lenz et al.: A δ Scuti star in the post-MS contraction phase: 44 Tauri 5

(a) Models constructed with the GN93 element mixture. (b) Models constructed with the A04 element mixture.

Fig. 2. HR diagram with evolutionary tracks for models with a good fit of all 15 observed modes. The models were constructed with OPAL opacities and two different solar element mixtures: the GN93 element mixture (a) and the A04 element mixture (b). Fig. 1. Comparison between observed frequencies (vertical Fig. 3. Instability parameter, η,forModel3.Positivevaluesin- lines) and predicted unstable frequencies (circles) for a post-MS dicate mode driving, modes with negativeLenz, Pamyatnykhη are damped. et al. 2010 contraction model (Model 4 in Table 2). If the spherical degree of a mode was not observationally determined, a full verticalline is shown. Predicted frequencies that match observed frequencies The predicted frequency range of unstable modes agrees well are marked as filled circles. The rotational splitting is smaller with the observed frequency range as shown in Fig. 3 for one of than the size of the symbols. the models that can be considered representative of all OPAL models. Additional unstable modes are predicted between 13 and 17 cd−1.Themodeinstabilityatthesehighfrequenciesis To describe the goodness of the fit, we used a dimensionless sensitive to the efficiency of convection. If αMLT is decreased merit function similar to the one used in Brassard et al. (2001): from 0.2 to lower values, the highest frequencies become stable. In our study we relied on the standard mixing-length theory of 15 i − i 2 νobs νmodel convection and the frozen flux approximation. Time-dependent χ2 = ⎛ ⎞ (2) ! ⎜ σi ⎟ convection models, such as those used in some other recent stud- Fig. 5. HR diagram with evolutionary tracks of two models con- i=1 ⎜ ⎟ structed with enhanced and standard OP opacities. Both models ⎝ ⎠ ies about δ Scuti stars (e.g., Montalbán & Dupret 2007, Dupret provide a good 15-frequency fit. i i et al. 2005), would yield a more accurate determination of the where νobs and νmodel are the observed and corresponding theo- σi high-frequency border of instability. pare the models in Fig. 2a with Model 7 in Fig. 5). The models retical frequency, respectively. The weighting factor, ,isde- constructed with OPAL A04 are already situated at the TAMS fined as the width of the observed frequency window of 5- (Fig. 2b). To fit the avoided crossing of ℓ = 1modesandthe −1 13 cd divided by the number of theoretically predicted modes ℓ = 2modesinstandardOPA04models,αov would have to be 3.2. Results with OP opacities reduced more than possible for a model in the overall contraction within this frequency window. Contrary to Brassard et al. (2001) Fig. 4. Radial fundamental and first overtone mode as probes phase. However, the use of enhanced OP opacities in combina- we determine a weighting factor for each spherical degree sepa- Lenz et al. (2007) found that post-MS expansion modelsfor of opacities. Upper panel: kinetic energy density inside the tion with the A04 element mixture allows for a 15-frequency fit. star. Middle panel: comparison between OPAL and OP opacities The corresponding models are listed in Table 2. rately to take the different mode densities into account. For the 44 Tau constructed with OP opacities have significantly lowefor ther same model. Lower panel: absolute values of Rosseland models shown in Table 2, σi for ℓ = 0modesamountsto8/3, temperature and luminosity values than observed. This probmeanlem opacities from OPAL and OP data. for ℓ = 1modes8/7andforℓ = 2modes8/11 cd−1.There- persists for post-MS contraction models. Montalbán & Miglio 4. Mixed modes as probes of the stellar core 2 (2008) explain this by differences of 10% between OPAL and The partial mixing processes at the convective core boundaryare sults are shown in the last column of Table 2. The lowest χ OP tables are currently underestimated in the temperature region currently not fully understood. During the hydrogen core burn- value provides the best agreement between the model and the OP opacities at temperatures around log T = 6.05. This corre-around log T = 6.0. ing phase, we expect a region around the convective core that observations. If the azimuthal order of a mode was not uniquely sponds to the temperature region in which the period ratio is Fora models constructed with standard OP opacities, a fit of is partially mixed due to several mechanisms: (i) overshooting 2 all 15 frequencies is only possible with the GN93 element mix- from the convective core, (ii) rotationally induced mixing (the determined, the theoretical m = 0modewasusedtocomputeχ . sensitive probe as can be seen in the two uppermost panelsture. in Adopting OP instead of OPAL opacities shifts the mod- core rotates faster than the envelope leading to additional mix- If the m-component closest to the observed frequency is used in- Fig. 4. els that fit all 15 frequencies closer to the TAMS (e.g., com- ing). stead, the χ2 values are slightly lower but exhibit the same gen- The diagram shows the kinetic energy density of the radial eral trends. fundamental and first overtone mode inside the star. Pulsation The position of OPAL models in the HR diagram is shown in modes are sensitive to the conditions in temperature regionsin Fig. 2 for models obtained with the GN93 and the A04 element which the kinetic energy density is high. Because of the position mixture. The effective temperatures of these pulsation models of its node, the radial first overtone mode probes the temperature are somewhat cooler than the values derived from photometric region between log T = 4.5 and 7.0 with different weights than and spectroscopic measurements. the radial fundamental mode. The pulsation models obtained with the A04 mixture are The differences between OPAL and OP opacities are shown closer to the TAMS. A 15-frequency fit with w=2.0 is not pos- in the middle panel of Fig. 4. The lower panel shows the location sible, because the required overshooting distance would be less of opacity bumps inside the star. We artificially enhanced theOP than possible for models in the overall contraction phase. The opacities by up to 15% around log T = 6.0 and tested the impact main reason for the differences between pulsation models ob- on models in the contraction phase after the main sequence. tained with the GN93 and the A04 mixture is the slightly differ- The results are shown in Fig. 5. The corresponding model pa- ent opacity in the overshoot layer that affects the size of the con- rameters can be found in Table 2. Contrary to models constructed vective core. The uncertainties in the element abundances (and with standard OP opacities, models obtained with enhanced OP opacities) in 44 Tau therefore lead to an uncertainty in the deter- opacities are closer to the photometric error box in the HR dia- mination of the overshooting distance, αov. gram. This may indicate that the Rosseland mean opacities of the 29 Cygni

• Vsini <= 80 km/s • Main sequence, slightly evolved • logTeﬀ= 3.902+/- 0.009, log g=4.12+/-0.25 • Lambda Boo star (unusually weak lines of iron-peak elements, whereas C,N,O and S have solar abundance) • 14 frequencies, mul-color photometry mode ID. & seismic modeling, Casas 09 29 Cygni CHARA/PAVO R=1.886 +/- 0.156

M=1.86 Evoluon of frequencies and mode excitaon

FT of 29 Cyg

L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 L=0 L=1 L=2 p5 p5 p4 p4 p3 p3 p2 p2 p1 p1

L=0 L=1, m=0 p3 p2 p1 f p1 g1

L=0 L=2, m=0 p5 p4 p3

L=1, m=0 p3

L=1, m=0, +1, -1 p3

L=1, m=0, +1, -1 Avoided crossings Mode changing properes, as revealed from their rotaonal splings p3

L=1, m=0, +1, -1 L=2, m=0, +1,+2, -1,-2 L=0 L=1, m=0,+1,-1 L=2, m=0,+1,+2,-1,-2

L=0 L=1, m=0,+1,-1 L=3,m=(0, 1, 2, 3 , -1, -2, -3) L=2, m=0,+1,+2,-1,-2

K. Zwintz et al.: Reﬁned asteroseismic model of HD 144277

HD144277

M=1.70, Z=0.011, near ZAMS, V=80 km/s

Near degeneracy mode Coupling:

Fig. 6. Top panel:observedmodes.Middle panel:theoreticalmodeswith. ℓ 2: retrograde (L=0), (light grey),(L=2,m=0) zonal (dark grey), and prograde (black) modes. LowerZwintz panel, :stepwiseadditionofvariousrotationaleRyabchikova, Lenz, Pamyatnykhﬀects et al on the2014 mode≤ frequencies in near-degenerate mode perturbation theory (spherical symmetry, linear splitting, non-spherical distortion, and three-mode coupling). Only ℓ = 0, 1, 2areshownforclarityasﬁlledcircles,squares,and triangles.

4. Refinement of the asteroseismic model orders are equal. We therefore also considered the effects of rotational mode coupling according totheformalismpresentedin The asteroseismic model presented in Paper I was mainly de- Soufi et al. (1998)andDaszynska-Daszkiewicz´ et al. (2002). In rived based on information extracted from the observed fre- our study we considered the rotational coupling of up to three quency spectrum. With our new spectroscopic observations, we modes and conducted tests thereby adopting various values for gained additional constraints on the fundamental parameters of the rotational velocity. The adopted evolutionary and pulsational the star. Consequently, the asteroseismic model can now be codes were the same as those used in Paper I. We again used tested and possibly refined. OPAL opacities (Iglesias & Rogers, 1996)andtheAsplundetal. The new observations could confirm a lower metallicity (2009)proportionsintheheavyelementabundancestobecon- compared to solar composition, which was predicted by the as- sistent with Paper I. teroseismic models in Paper I in order to explain the pulsational instability of the observed modes. The spectroscopically We find that the best agreement between observational and theoretical frequencies is found if we assume a rotational ve- determined temperature, luminosity, and radius agree within one 1 sigma to the values derived from asteroseismology, whereas the locity at the equator between 60 and 80 km s− .Forhigherro- theoretical and spectroscopical log g values match only within tation there are no clear patterns in the theoretical frequency 2σ (see Table 2). On the other hand, spectroscopy indicates spectra that can be matched to the very regular pattern of the 1 that with v sin i = 62.0 2.0kms− the rotational velocity of observed frequencies. This finding implies a nearly equator-on HD 144277 is higher than± assumed in the asteroseismic mod- view. As can be seen in Fig. 6,theobservedgroupsoffrequen- 1 1 els in Paper I, where an equatorial rotation velocity of 15 km s− cies at 60 and 67 d− correspond to prograde and zonal dipole was adopted. Since most fundamental parameters of the original modes, while the other two groups are related to the radial and asteroseismic model are in good agreement with the new obser- quadrupole modes. vations, we used Model 2 from Paper I as a referencemodel (see Table 2 presents a comparison between the fundamental pa- Table 2)andincreaseditsrotationalvelocitytostudytheinflu- rameters of Model 2 from Paper I and the new model presented ence on the predicted frequencies and mode instability. in this paper (denoted as Model 3). The position of the model in To estimate the effects of rotation on the frequencies we used the Hertzsprung-Russell (HR) diagram is shown in Fig. 7.For asecond-orderperturbationtheory,whichissufficient only for the refined asteroseismic model a small increase in the metallic- reasonably slow rotators. Increasing the rotational velocity at the ity was adopted to improve the agreement between the instability 1 1 equator from 15 km s− to 60 km s− implies that the effects of of theoretical modes and observed unstable modes (see Fig. 8). near-degeneracies gain importance. As shown in, e.g., Goupil However, with Z = 0.011 the model remains clearly metal un- et al. (2000)modescancoupleif(i)theyarecloseinfrequency; derabundant compared to the solar value of Z = 0.0134 (Asplund (ii) their spherical degree differs by 2; and (iii) their azimuthal et al. 2009).

A4, page 5 of 7 K. Zwintz et al.: Reﬁned asteroseismic model of HD 144277

HD144277

M=1.70, Z=0.011, near ZAMS, V=80 km/s

Fig. 6. Top panel:observedmodes.Middle panel:theoreticalmodeswith. ℓ 2: retrograde (light grey), zonal (dark grey), and prograde (black) modes. LowerZwintz panel, :stepwiseadditionofvariousrotationaleRyabchikova, Lenz, Pamyatnykhﬀects et al on the2014 mode≤ frequencies in near-degenerate mode perturbation theory (spherical symmetry, linear splitting, non-spherical distortion, and three-mode coupling). Only ℓ = 0, 1, 2areshownforclarityasﬁlledcircles,squares,and triangles.

A4, page 5 of 7 K. Zwintz et al.: Reﬁned asteroseismic model of HD 144277

HD144277

M=1.70, Z=0.011, near ZAMS, V=80 km/s

my reproducon

Fig. 6. Top panel:observedmodes.Middle panel:theoreticalmodeswithℓ 2: retrograde. (light grey), zonal (dark grey), and prograde (black) modes. Lower panel:stepwiseadditionofvariousrotationaleZwintz, Ryabchikova, Lenz,ﬀects Pamyatnykh on the mode≤ frequencies et al 2014 in near-degenerate mode perturbation theory (spherical symmetry, linear splitting, non-spherical distortion, and three-mode coupling). Only ℓ = 0, 1, 2areshownforclarityasﬁlledcircles,squares,and triangles.

A4, page 5 of 7 4P.Lenzetal.:Aδ Scuti star in the post-MS contraction phase: 44 Tauri

Fig. 1. Comparison between observed frequencies (vertical Fig. 3. Instability parameter, η,forModel3.Positivevaluesin- lines) and predicted unstable frequencies (circles) for a post-MS dicate mode driving, modes with negative η are damped. contraction model (Model 4 in Table 2). If the spherical degree of a mode was not observationally determined, a full verticalline is shown. Predicted frequencies that match observed frequencies The predicted frequency range of unstable modes agrees well are marked as filled circles. The rotational splitting is smaller with the observed frequency range as shown in Fig. 3 for one of than the size of the symbols. MLE the models that can be considered representative of all OPAL • Do you really think that Chi^2 minimizaon models. Additional unstable modes are predicted between 13 and 17 cd−1.Themodeinstabilityatthesehighfrequenciesis will give youTo the describecorrect the goodnessanswer in the of the fit,seismic we used a dimensionless sensitive to the efficiency of convection. If αMLT is decreased modeling?merit function similar to the one used in Brassard et al. (2001): from 0.2 to lower values, the highest frequencies become stable. In our study we relied on the standard mixing-length theory of 15 i − i 2 νobs νmodel convection and the frozen flux approximation. Time-dependent χ2 = ⎛ ⎞ (2) ! ⎜ σi ⎟ convection models, such as those used in some other recent stud- = ⎜ ⎟ i 1 ⎝⎜ ⎠⎟ ies about δ Scuti stars (e.g., Montalbán & Dupret 2007, Dupret where νi and νi are the observed and corresponding theo- et al. 2005), would yield a more accurate determination of the We do have some priorobs knowledgemodel: retical frequency, respectively. The weighting factor, σi,isde- high-frequency border of instability.

mode seleconfined, mode as visibility the width, stellar of the evoluon observed, ... frequency window of 5- −1 13 cd divided by the number of theoretically predicted modes 3.2. Results with OP opacities within this frequency window. Contrary to Brassard et al. (2001) we determine a weighting factor for each spherical degree sepa- Lenz et al. (2007) found that post-MS expansion models of rately to take the different mode densities into account. For the 44 Tau constructed with OP opacities have significantly lower models shown in Table 2, σi for ℓ = 0modesamountsto8/3, temperature and luminosity values than observed. This problem for ℓ = 1modes8/7andforℓ = 2modes8/11 cd−1.There- persists for post-MS contraction models. Montalbán & Miglio sults are shown in the last column of Table 2. The lowest χ2 (2008) explain this by differences of 10% between OPAL and value provides the best agreement between the model and the OP opacities at temperatures around log T = 6.05. This corre- observations. If the azimuthal order of a mode was not uniquely sponds to the temperature region in which the period ratio is a determined, the theoretical m = 0modewasusedtocomputeχ2. sensitive probe as can be seen in the two uppermost panels in If the m-component closest to the observed frequency is used in- Fig. 4. stead, the χ2 values are slightly lower but exhibit the same gen- The diagram shows the kinetic energy density of the radial eral trends. fundamental and first overtone mode inside the star. Pulsation The position of OPAL models in the HR diagram is shown in modes are sensitive to the conditions in temperature regionsin Fig. 2 for models obtained with the GN93 and the A04 element which the kinetic energy density is high. Because of the position mixture. The effective temperatures of these pulsation models of its node, the radial first overtone mode probes the temperature are somewhat cooler than the values derived from photometric region between log T = 4.5 and 7.0 with different weights than and spectroscopic measurements. the radial fundamental mode. The pulsation models obtained with the A04 mixture are The differences between OPAL and OP opacities are shown closer to the TAMS. A 15-frequency fit with w=2.0 is not pos- in the middle panel of Fig. 4. The lower panel shows the location sible, because the required overshooting distance would be less of opacity bumps inside the star. We artificially enhanced theOP than possible for models in the overall contraction phase. The opacities by up to 15% around log T = 6.0 and tested the impact main reason for the differences between pulsation models ob- on models in the contraction phase after the main sequence. tained with the GN93 and the A04 mixture is the slightly differ- The results are shown in Fig. 5. The corresponding model pa- ent opacity in the overshoot layer that affects the size of the con- rameters can be found in Table 2. Contrary to models constructed vective core. The uncertainties in the element abundances (and with standard OP opacities, models obtained with enhanced OP opacities) in 44 Tau therefore lead to an uncertainty in the deter- opacities are closer to the photometric error box in the HR dia- mination of the overshooting distance, αov. gram. This may indicate that the Rosseland mean opacities of the A General Framework of Bayesian Inference • Parameter to infer: θ • Given observables (data): D

• We update our prior knowledge of θ, p(θ) given D, using Bayes’ theorem • posterior p(θ|D) =p(θ) p(D|θ) /p(D)

Θ and D

Isochrone fing: Field stars: θ=[M, d, t] D=[Teff, logg, Z] Star cluster: θ=[Mi, d, t, Z] D=[Teffi, loggi, Zi] (Jorgensen & Lindegren 2005; Serenelli 2013)

Eclipsing binaries: θ=[M, Z, t, …] D=[Mi, Ri,Teﬃ, loggi, Zi, …] (Prada Moroni 2012)

Solar-like oscillators (SEEK package): θ=[M, Z, t, X0, α …] D=[Teﬀ, logg, Z, δν, Δν, νmax, …] (Quirion2010) -> No mode ID problem -> Individual frequencies not used

Θ and D (Upper MS pulsators)

(without rotaon) • Parameters: θ=[M, Z, t, Li, ni, fov…] • Given observables: D=[R, Teﬀ, logg, Z, fi …]

Turn the Prior knowledge into appropriate prior for theta p(θ) e.g. P(M): inial mass funcon, e.g. Salpeter: m^-2.35 P(Z): usually ﬂat, but stars in cluster, halo? Pop I, II? P(t): usually ﬂat, evidence of youth? Old pop.?

Priors on the mode degree and radial order P(L): L=0,1,2 more probable; HADs, L=0;

P(n): excited modes-> higher probability be careful, problems with excitaon? Prior on n and L

M=1.86 L=2 excited n_pg: (-35 -> -10) L=1 excited n_pg: (-21 -> -4) P(L): Assign higher L=0 probability to L=0

excited n_pg: (1 -> 5) than L=1,2 ?

P(n):

Log ( Im( freq) ) Trapped L=1 modes: n_pg =-20, -14,-13, -9,-8, -6 Should assign higher Probability, similar to L=0 modes Steps: (one f)

parameters observables

Prior:

Posterior:

( Posterior mode idenﬁcaon for L ) To evaluate:

Numerical integraon:

( Posterior mode radial order n ) Steps: (two frequencies: fa, )

Extend to more frequencies:

-> 15 frequencies for 44 Tau, two radial -> 14 for 29 Cyg Θ and D (Upper MS pulsators)

(with rotaon) • Parameters: θ=[M, Z, t, Li, ni, mi, fov, V, incl …]

• Given observables: D=[R, Teﬀ, logg, Z, vsini, fi, incl …]

• P(mi): depends on incl. (Gizon & Solanki 2003) But not enrely true for heat-driven pulsators, how to revise? • P(mi): some evidence of prograde mode prefered? • P(incl): EBs? Interferometric imaging?

What is BRITE?

BRIght Target Explorer

- nanosatellites 20 x 20 x 20 cm - ca. 7 kg - 3-cm telescope for observations of bright (V < 5) stars - time-resolved two-colour (B, R) photometry

BRITE-Constellation:

BRITE-Lem (BLb) XBRITE-Montreal (BMb) UniBRITE (UBr) BRITE-Toronto (BTr) BRITE-AUSTRIA (BAb) BRITE-Heweliusz (BHr)

Courtesy: Gerald Handler Lessons from BRITE: (not in alphabetical order)

- Precision photometric studies with nanosatellites in low Earth orbits are possible ν - gravity mode pulsation among b Cep stars is rather common Eri, α Lup, PT Pup, σ Sco - interior rotation of SPB stars can be studied HD 201433 - magneto-asteroseismology is on the horizon βCen, ε Lup … - pulsation-mass loss interaction in Be stars βCen, … - massive heartbeat stars are around and can be investigated ιOri - a link between large-scale wind structures and their photospheric origin has been found

See Gerald Handler’s talk at KITP BRITE observations so far

Field from to DT [day] # stars Orion I 01.12.2013 18.03.2014 108 15 Centaurus 25.03.2014 18.08.2014 147 32 Sagittarius 29.04.2014 06.09.2014 42 19 Cygnus I 12.06.2014 25.11.2014 167 36 Perseus 02.09.2014 18.02.2015 170 37 Orion II 24.09.2014 17.03.2015 175 38 Vel/Pup 11.12.2014 28.05.2015 169 52 Scorpius 18.03.2015 31.08.2015 167 26 Cygnus II 01.06.2015 25.11.2015 178 27 Cas/Cep 23.08.2015 17.10.2015 55 23 CMa/Pup 18.10.2015 14.04.2016 ~180 33 Cru/Car 22.01.2016 22.07.2016 183 45 Cyg/Lyr 05.04.2016 02.10.2016 177 20 Sgr II 21.04.2016 23.09.2016 158 17 Cas II 07.08.2016 03.02.2017 ~174 18 Aur/Per 14.09.2016 07.03.2017 ~171 25 Cet/Eri 06.10.2016 26.12.2016 83 11 Vel/Pic 04.11.2016 29.04.2017 173 21 Total ~410 Courtesy: Gerald Handler BRITE photometry Wiki page: hp://brite.craq-astro.ca/doku.php Cross-match BRITE with JMMC catalog The Massive Heartbeat ◆ Orionis 7

0.0016

Orion I - Blue 0.0012

f1 f2

0.0008 f4 f3

0.0004

0.0000 0.00.51.01.52.02.53.0 0.0016 The Massive Heartbeat ◆ Orionis 5 Orion I - Red

0.0012 BRITE light curve Table 2. ◆ Ori Fundamental Parameters compared with those of Marchenk et al. (2000) 0.0008 f f3 2 Iota Ori f5 Marchenko et al. (2000) O9 III + 0.0004 Parameter Primary Secondary Primary Secondary B1 III/IV 0.0000 0.00.51.01.52.02.53.0 P orb(d)29.13376(fixed)29.13376(fixed) 0.0016 Orion II - Blue T0(HJDP=29 d 2450000)Flux Amplitude 1121.658 (fixed) 1121.658 0.046 0.0012 +0.17 ± e=0.75 i ()62.86 0.14 – f4 0.0008 +0.11 =122 f1 ! ()122.15 f6 130.0 2.1 0.11 f2 RV curve ± 0.0004 +0.0010 Incl. =63 e 0.7452 0.0014 0.764 0.007 ± 0.0000 +0.0077 q 0.000.5798.510.0084 .01.520.571 .020.025 .53.0 M1=22, ± 0.0016 R1=9.1 +1.01 a (R )132.32 0.96 – Orion II - Red Teff1=31000 0.0012 FT of light curve residual 1 f +0.30 v (kms )321 .02 0.32 31.3 1.220.4 2.1 f 0.0008 4 ± ± f6 M2=13.4, +531f2 f Te↵ (K)31000(fixed)183193 f –– 2 7 758 R =4.94 0.0004 Teff2=18319 +0.12 +0.16 R (R )9.10 0.10R 4.94 0.23 –– 0.0000 0.00.51.01.52.02.53.0 0.34 +2.78 1 f 14.86 0.23 28.14 2.017Frequency (d–– ) Pablo et al. 2017+0.57 +0.30 M (M )23.18 0.53M 13.44 0.30 ––

Figure 3. Discrete Fourier transforms of the BRITE data, binned on orbital phase, for Orion I blue (top) and red (second from top), and Orion II blue (third from top), and red (bottom). The dashed line in each graph denotes the 3.6 signifance level, though some peak values will change during the process of pre-whitening other signals. The grey line in each graph denotes the noise ﬂoor. MNRAS 000, 1–11 (2016)

Figure 2. Binary solution of ◆ Ori. In the top panel are the phase-folded red filter light curve (red) and blue filter light curve (cyan) overlaid with the PHOEBE fit (black). The data shown here has not been cleaned in order to show the TEOS present in both light curves in the top panel, most notably around phase=0.9. The blue filter light curve has been artificially shifted in flux to facilitatethe display both light curves. The bottom panel shows the radial velocity data from Marchenko et al. (2000) (black x) and Ritter Observatory (black dots) overlaid with the PHOEBE fit in red.

MNRAS 000, 1–11 (2016) The Massive Heartbeat ◆ Orionis 7

0.0016

Orion I - Blue 0.0012

f1 f2

0.0008 f4 f3

0.0004

0.0000 0.00.51.01.52.02.53.0

0.0016

Orion I - Red

0.0012

0.0008 f f3 2

0.0004

0.0000 0.00.51.01.52.02.53.0

0.0016

Orion II - Blue Flux Amplitude 0.0012

f4 0.0008 f1 f6 f2

0.0004

0.0000 0.00.51.01.52.02.53.0

0.0016

Orion II - Red

0.0012

f 0.0008 4 f6 f2 f3 f7 0.0004

0.0000 0.00.51.01.52.02.53.0 1 Frequency (d )

Theory works

Figure 3. Discrete Fourier transforms of the BRITE data, binned on orbital phase, for Orion I blue (top) and red (second from top), and Orion II blue (third from top), and red (bottom). The dashed line in each graph denotesAmplitudes the 3.6 signifance agree with level, though some peak values will change during the process of pre-whitening other signals. The grey line in each graph denotes the noise ﬂoor. MNRAS 000, 1–11 (2016) L=2 m=2 prograde modes

Phases: most agree with L=2,m=2

Pablo et al. 2017 Interferometric Orbit of Iota Ori CHARA/MIRC

2.5 Preliminary results:

2.0 Nov 16 2010Nov05

1.5 2008Dec02

1.0 Oct 24 2016Nov18 Scheduled observaons 2017 2011Dec09 0.5 DEC (mas)

Oct 26 Oct 30 Pablo et al. 2017 0.0

−0.5 Iota Ori −1.0 2.0 1.5 1.0 0.5 0.0 −0.5 −1.0 −1.5 RA (mas) By Gail Schaefer & Doug Gies Summary. Mode selection and amplitude limitation in pulsating 1. Angular diameter measurementsstars of 44 Tau and 29 Cyg Radosław Smolec 2. A probabiliscNicolaus Copernicus approach Astronomical of seismic Centre, modeling PAS of δ Scu stars, taking into account our prior knowledge on rotaon, stellar evoluon, and mode selecon.

3. A lot of interesng asteroseismic targets from BRITE satellite, awaing for interferometric observaons

Thanks very much for your aenon!

Zhao Guo –18–

Table 4. Model Parameters –18–

Parameter Solution

Period (days) 1.61301476a Time of primary minimum (HJD-2400000) 55432.522844 0.000007 ± Mass ratio q = M /M 0.104 0.002 2 1 ± Orbital eccentricity e 0.0a Orbital inclination Tablei (degree) 4. Model Parameters 75.203 0.007 ± Semi-major axisKIC8262223 Parameters a (R )7 .45 0.11 ± M1 (M )1Parameter Solution.94 0.06 ± M2 (M )0.20 0.01 Period (days) 1.61301476± a R1 (R )1.67 0.03 Time of primary minimum (HJD-2400000) 55432.522844± 0.000007 R2 (R )1.31 ±0.02 Mass ratio q = M2/M1 0.104 ±0.002 Filling factor f1 0.314± 0.003 Orbital eccentricity e 0.±0a Filling factor f2 0.672 0.001 Orbital inclination i (degree) 75.203± a0.007 Gravity brightening, 1 0.25± Semi-major axis a (R )7.45 0a.11 Gravity brightening, 2 0.±08 M1 (M )1.94 a0.06 Bolometric albedo 1 1±.0 M2 (M )0.20 0.01 Bolometric albedo 2 0±.22 R1 (R )1.67 0a.03 Beaming parameter 1 2.±76 R2 (R )1.31 0a.02 Beaming parameter 2 3.±48 Filling factor f1 0.314 0a.003 Te↵1 (K) 9128± Filling factor f 0.672 0.001 T (K)2 6849 15 e↵2 ± a Gravity brightening, 1 0.25± log g1 (cgs) 4.28 0.04 Gravity brightening, 0.08±a log g (cgs)2 3.51 0.06 2 a Bolometric albedo 11 1.±0 Synchronous v sin i1 (km s ) 50.6 0.9 Bolometric albedo 21 0.22± Synchronous v sin i2 (km s ) 39.6 0.6 Beaming parameter 1 2.76±a Beaming parameter 2 3.48a a Fixed. a Te↵1 (K) 9128 T (K) 6849 15 e↵2 ± log g (cgs) 4.28 0.04 1 ± log g (cgs) 3.51 0.06 2 ± Synchronous v sin i (km s 1) 50.6 0.9 1 ± Synchronous v sin i (km s 1) 39.6 0.6 2 ±

aFixed. Delta Scu instability

3.0Rsun Inial (ﬁnal) M1=1.35 (0.22) M2=1.15 (1.72)

P =2.9d (3.6d) 2.0Rsun M1 M2 Onset of mass transfer ZAMS

End of mass transfer 1.0Rsun

Guo, Gies, Matson et al. 2017 0.10 l=0 l=1 l=2 0.05 ) η

Modes excited 0.00 Modes damped Stability Parameter ( -0.05

-0.10 30 40 50 60 70 80 Frequency (d-1) Primary star:

Structure Models from single stellar evoluon have some diﬃcules explaining the driving(unstable range) frequencies of this Post-mass transfer Delta Scu star KIC8262223 7

Frequency Distribuon of Kepler Delta Scu stars

Balona, Daszynska, Pamyatnykh (2015)

Models(blue lines) cannot explain the overabundance of high-frequency Delta Scu stars.

Binary Evoluon ?

Figure 1.3 The observed (ﬁlled) and theoretical (solid blue curves) frequency distributions of Scuti stars. Only unstable modes with degrees, l 6areconsidered,andthemode  frequencies have been corrected for rotational e↵ects with perturbation theory to the third order. All models have metal abundance Z = 0.015. The lower 10 panels correspond to the labeled regions on the H-R diagram shown in the upper panel. Figure is taken from Balona et al. (2015). Scientific results: magnetic stars

(Buysschaert, Neiner & Aerts 2017, Proc. IAUS 329, in press) Scientific results: asteroseismology

g modes, g modes everywhere! Beta Cephei star driving problems

(Daszyńska-Daszkiewicz et al. 2017, MNRAS 466, 2284) Correct for the eﬀect of mode densies • Observable D: one frequency f=7.47 c/d • Prior: p(n)=1 (if excited); 0 (otherwise) p(L)= 1/3 (L=0) 1/3 (L=1) 1/3 (L=2)

Posterior: p(L|D)= 0.01 (L=0) 0.32 (L=1) 0.67 (L=2)

p4 p3 p2 p1 f g1

L=2, m=0 L=2, m=0, +1,+2, -1,-2 L=2, m=0, +1,+2, -1,-2 L=2, m=0, +1,+2, -1,-2