Instabilities and pulsations in models of the B-type supergiant $kappa$ Cassiopeiae (HD 2905). (arXiv:2011.08164v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Yadav_A/0/1/0/all/0/1">Abhay Pratap Yadav</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Joshi_S/0/1/0/all/0/1">Santosh Joshi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Glatzel_W/0/1/0/all/0/1">Wolfgang Glatzel</a>

For the B-type supergiant $kappa$ Cassiopeiae (HD 2905) variabilities with
periods between several hours and a few days have been observed both
photometrically and spectroscopically. A recent study of this star by
Sim’on-D'{i}az et al. (2018) has revealed variability with a dominant period
of 2.7 days. To understand this variability, we present a linear non-adiabatic
stability analysis with respect to radial perturbations for models of $kappa$
Cassiopeiae. Instabilities associated with the fundamental mode and the first
overtone are identified for models with masses between 27 M$_{odot}$ and 44
M$_{odot}$. For selected models, the instabilities are followed into the
non-linear regime by numerical simulations. As a result, finite amplitude
pulsations with periods between 3 and 1.8 days are found. The model with a mass
of 34.5 M$_{odot}$ exhibits a pulsation period of 2.7 days consistent with the
observations. In the non-linear regime, the instabilities may cause a
substantial inflation of the envelope.

For the B-type supergiant $kappa$ Cassiopeiae (HD 2905) variabilities with
periods between several hours and a few days have been observed both
photometrically and spectroscopically. A recent study of this star by
Sim’on-D'{i}az et al. (2018) has revealed variability with a dominant period
of 2.7 days. To understand this variability, we present a linear non-adiabatic
stability analysis with respect to radial perturbations for models of $kappa$
Cassiopeiae. Instabilities associated with the fundamental mode and the first
overtone are identified for models with masses between 27 M$_{odot}$ and 44
M$_{odot}$. For selected models, the instabilities are followed into the
non-linear regime by numerical simulations. As a result, finite amplitude
pulsations with periods between 3 and 1.8 days are found. The model with a mass
of 34.5 M$_{odot}$ exhibits a pulsation period of 2.7 days consistent with the
observations. In the non-linear regime, the instabilities may cause a
substantial inflation of the envelope.

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