The   Cep/SPB star 12 Lacertae: extended mode identification and complex seismic modelling

Abstract

Results of mode identification and seismic modelling of the β Cep/SBP star 12 Lacertae are presented. Using data on the multi-colour photometry and radial velocity variations, we determine or constrain the mode degree, ℓ, for all pulsational frequencies. Including the effects of rotation, we show that the dominant frequency, ν 1 , is most likely a pure ℓ = 1 mode and the low frequency, ν A , is a dipole retrograde mode. We construct a set of seismic models which fit two pulsational frequencies corresponding to the modes ℓ = 0, p 1 and ℓ = 1, g 1 and reproduce also the complex amplitude of the bolometric flux variations, f , for both frequencies simultaneously. Some of these seismic models reproduce also the frequency ν A , as a mode ℓ = 1, g 13 or g 14 , and its empirical values of f . Moreover, it was possible to find a model fitting the six 12 Lac frequencies (the first five and ν A ), only if the rotational splitting was calculated for a velocity of V rot ≈ 75 km/s. In the next step, we check the effects of model atmospheres, opacity data, chemical mixture and opacity enhancement. Our results show that the OP tables are preferred and an increase of opacities in the Z−bump spoils the concordance of the empirical and theoretical values of f .

Wider pulsation instability regions forβCephei and SPB stars calculated using new Los Alamos opacities

“…The commonly used data, such as OP tables from the international Opacity Project (Seaton 2005) and OPAL tables from Lawrence Livermore National Laboratory (Iglesias & Rogers 1996), may be underestimated near the Z-bump. A postulated increase in the opacities can solve some problems in asteroseismic analysis (Pamyatnykh et al 2004;Zdravkov & Pamyatnykh 2008;Salmon et al 2012;Walczak et al 2013;Daszyńska-Daszkiewicz et al 2013b). Therefore, we tested the new OPLIB opacity tables, which were generated with the ATOMIC code at Los Alamos National Laboratory (Colgan et al 2013(Colgan et al , 2015.…”

Revising the Evolutionary Stage of HD 163899: The Effects of Convective Overshooting and Rotation

“…They obtained the best fit for the models with overshooting of f = 0.017 − 0.018, however the mass of the star was in the range of [3.15, 3.25] M ⊙ , which is significantly lower than the stars we study. More interesting insight about the value of overshooting can be found in the seismic modelling of two hybrid β Cephei/SPB pulsators: 12 Lacertae (Daszyńska-Daszkiewicz et al 2013b) and γ Pegasi (Walczak et al 2013). In both cases the models that fit the observed frequencies can be found within a quite wide range of overshooting parameter (α ov ∼ 0.2 − 0.45) because obviously other factors such as metallicity or opacities affect seismic models.…”

Testing microphysics data

“…2 were adopted from Walczak et al (2013). We chose two well identified β Cep modes: the radial p 1 (ν 1 = 6.58974 d −1 ) and dipole g 1 (ν 5 = 6.01616 d −1 ), and constructed models fitting them.…”

“…It is important to add that the empirical f -parameter depends slightly on the input from model atmospheres. The discussion of these effects can be found in Daszyńska-Daszkiewicz & Szewczuk (2012) and Daszyńska-Daszkiewicz et al (2013). Here, in all computations we adopt the LTE models of stellar atmospheres by Kurucz (2004) with microturbulence velocity of ξ t = 2 km s −1 .…”