Pulsations of blue supergiants before and after helium core ignition
aa r X i v : . [ a s t r o - ph . S R ] D ec Precision AsteroseismologyProceedings IAU Symposium No. 301, 2014J.A. Guzik, W.J. Chaplin, G. Handler & A. Pigulski, eds. c (cid:13) Pulsations of blue supergiants before andafter helium core ignition
Jakub Ostrowski and Jadwiga Daszy´nska-Daszkiewicz
Instytut Astronomiczny, Uniwersytet Wroc lawski, ul. Kopernika 11, 51-622 Wroc law, Polandemail: [email protected]
Abstract.
We present results of pulsation analyses of B-type supergiant models with massesof 14 − M ⊙ , considering evolutionary stages before and after helium core ignition. Using anon-adiabatic pulsation code, we compute instability domains for low degree modes. For selectedmodels in these two evolutionary phases, we compare properties of pulsation modes. Significantdifferences are found in oscillation spectra and the kinetic energy density of pulsation modes. Keywords. stars: early-type, stars: supergiants, stars: oscillations, stars: evolution
1. Introduction
Slowly Pulsating B-type supergiants (SPBsg) are a new class of pulsating variable stars.They have been discovered by Saio et al. (2006) who found 48 frequencies in the lightvariations of the blue supergiant HD 163899 (B2 Ib/II, Klare & Neckel 1977, Schmidt &Carruthers 1996) and attributed them to g- and p-mode pulsations. This was unexpectedbecause it was believed that g modes cannot propagate in stars beyond the main sequencedue to very strong radiative damping in the helium core.The discovery has prompted a few groups (Godart et al. 2009, Daszy´nska-Daszkiewiczet al. 2013) to reanalyse pulsation stability in models of B-type stars after the TerminalAge Main Sequence (TAMS) and to further studies of SPBsg variables. The presenceof g-mode pulsations in B-type post-main-sequence stars has been explained by a par-tial reflection of some modes at an intermediate convective zone (ICZ) related to thehydrogen-burning shell or at a chemical gradient zone surrounding the radiative core.However, all studies of these objects published so far are based on the assumption thatHD 163899 has not reached the phase of helium core ignition, i.e., it is in the phase ofhydrogen shell burning. This assumption does not have to be made, because the blueloop can reach temperatures of early B spectral types. In this paper we investigate thispossibility and compare two SPBsg models: before and after He core ignition.
2. Instability domains
Our evolutionary models were calculated with the MESA evolution code (Modules forExperiments in Stellar Astrophysics, Paxton et al. 2011, Paxton et al. 2013). We adopteda hydrogen abundance at ZAMS of X = 0 .
7, metal abundance of Z = 0 .
015 and OPALopacity tables (Iglesias & Rogers 1996) with the AGSS09 metal mixture (Asplund etal. 2009). We took into account convective overshooting from the hydrogen and heliumcore and inward overshooting from non-burning convective zones, using the exponentialformula (Herwig 2000): D OV = D conv exp( − zf λ P ) , (2.1)1 Jakub Ostrowski & Jadwiga Daszy´nska-Daszkiewicz logT eff l og L / L S Figure 1.
The H-R diagram with instability domains, marked as thick lines, for modes ofdegree ℓ = 0 , , − M ⊙ . where D conv is the mixing-length-theory-derived diffusion coefficient at a user-definedlocation near the core boundary, λ P is the pressure scale height at that location, z is thedistance in the radiative layer away from that location, and f is an adjustable parameter,which we set to 0 .
01. All effects of rotation and mass loss were neglected. We performednon-adiabatic pulsation analyses using the code of Dziembowski (1977).In Fig. 1, we present instability domains for the modes of the degree ℓ = 0 , , − M ⊙ . There is an instability strip beyond the TAMSwhich is very similar to the one from previous calculations (e.g. Daszy´nska-Daszkiewiczet al. 2013). The main difference is the presence of unstable non-radial modes on the blueloops for more massive models ( M & M ⊙ and log T eff & .
2) whereas radial modesare stable in this evolutionary stage. The existence of pulsation instability on the blueloop, as well as the blue loops themselves, depend critically on the metallicity, Z . Forexample, for Z = 0 .
02 there are no unstable modes on the blue loops in the consideredrange of masses. More details will be given by Ostrowski & Daszy´nska-Daszkiewicz (inpreparation).
3. Pulsation modes before and after He core ignition
We compare pulsation properties of two models with similar positions in the H-R dia-gram: one during the hydrogen shell burning phase (16 M ⊙ , log T eff = 4 . L/L ⊙ =4 . M ⊙ , log T eff = 4 . L/L ⊙ = 4 . ulsations of blue supergiants -1.0-0.8-0.6-0.4-0.20.00.2 0.15 0.20 0.25 0.30 0.35 η ν [d -1 ]Model 1 1.5 2.0 2.5 3.0 3.5 l=0l=1l=2-1.0-0.8-0.6-0.4-0.20.00.2 0.10 0.20 0.30 0.40 0.50 0.60 0.70 η ν [d -1 ]Model 2 Figure 2.
Instability parameter, η , for Model 1 (top panel) and Model 2 (bottom panel). In Fig. 2 we depict the instability parameter, η , as a function of frequency for Model 1(top panel) and Model 2 (bottom panel). This parameter tells us whether the pulsationmode is unstable ( η >
0) or not ( η κ mechanism operating in the Z-bumpregion to efficiently drive the mode.A similar plot for the blue-loop model is shown in the bottom panel of Fig. 3. There arealso two very close frequency quadrupole high order g modes, one unstable (left panel)and one stable (right panel). The behavior of E k is different for these modes than forthe modes from the model before core helium burning. The entire energy of the stablemode is confined to the radiative zone in-between the convective core and the ICZ (thereis strong damping in this area), whereas the unstable mode has almost all of its energytrapped in the outer radiative zone. That means that unstable modes on the blue loopshave to be almost entirely reflected at the ICZ. This could explain why we observe in ourmodels that undergo core helium burning many fewer unstable modes than in modelsbefore helium core ignition. Jakub Ostrowski & Jadwiga Daszy´nska-Daszkiewicz k logTl = 2freq = 0.301 c/deta = 0.093logT eff = 4.343logL/L S = 4.705 4.55.05.56.06.57.07.5 l = 2freq = 0.296 c/deta = -0.987logT eff = 4.343logL/L S = 4.7050.00.51.01.52.02.53.0 4.55.05.56.06.57.07.58.0E k logTl = 2freq = 0.160 c/deta = 0.067logT eff = 4.244logL/L S = 4.815 4.55.05.56.06.57.07.58.0 l = 2freq = 0.162 c/deta = -1.000logT eff = 4.244logL/L S = 4.815 Figure 3.
Top panel: the kinetic energy density of unstable (left panel) and stable (right panel) ℓ = 2 modes with close frequencies from Model 1. The values of ν and η are listed in the panels.Bottom panel: the same as in the top panel, except for Model 2.
4. Conclusions
Our work has shown that blue loops can reach temperatures of B spectral types andthere are unstable modes during this phase of evolution. It means that SPBsg starsmight undergo core helium burning but whether they actually do or not is still an openquestion. We found that there is a huge difference in the behavior of the kinetic energydensity of pulsation modes between models before and after helium core ignition. On theblue loop, the pulsation modes have to be almost entirely reflected at the ICZ in orderto be unstable whereas for the models that undergo hydrogen shell-burning beyond theTAMS, a partial reflection at the ICZ is sufficient.
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