ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O B-Software I-Software I-Software I-Software I-Software O O O O B-CelestialObject I-CelestialObject O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O
tokens: with gravity modes or motions caused by subsurface convection, the cause of these variabilities is not properly understood. Thus, with the motivation to understand the dominant variability of 2.7 d in κ Cassiopeiae, we shall present here a linear non-adiabatic stability analysis of models for κ Cassiopeiae. The result of instabilities will then be determined by following them into the nonlinear regime for selected unstable models using a fully conservative numerical scheme. This paper falls into five sections where a description of the models used is given in Section 2 , and the linear stability analysis together with its results are discussed in Section 3 . The nonlinear simulations and their results are presented in Section 4 . A discussion and conclusions follow in Section 5 . 2 MODELS FOR κ CASSIOPEIAE Although the star κ Cassiopeiae has been the subject of several studies (see e.g. Underhill 1979 ; Percy 1981 ; Hayes 1984 ; Katushkina et al. 2018 ), its fundamental parameters (in particular its mass) are not precisely known. For the present investigation, we adopt the effective temperature ( T eff = 24 600 K) and luminosity (log L /L ⊙ = 5.69) estimated by Simón-Díaz et al. ( 2018 ) using high-resolution spectra of κ Cassiopeiae. These values are close to those determined by Kudritzki et al. ( 1999 ), Smartt et al. ( 2002 ), and Evans et al. ( 2004 ). Due to the uncertainty of the mass, we consider a range of models with masses between 27 and 44 M ⊙ . This mass range covers the mass of 33 M ⊙ suggested for κ Cassiopeiae by Searle et al. ( 2008 ) on the basis of stellar evolution calculations. Evolutionary tracks for models having solar chemical composition and masses of 30, 35, 40, and 45 M ⊙ respectively are shown in Fig. 1 where a thick dot corresponds to the observed position of κ Cassiopeiae in the Hertzsprung–Russell (HR) diagram. These tracks have been generated by the ‘mad star’ stellar evolution code. 1 The position of κ Cassiopeiae in the HR diagram suggests that models representing this star have masses below and close to 40 M ⊙ (see Fig. 1 ). Figure 1. Evolutionary tracks of stars with solar chemical composition and having masses in the range between 30 and 45 M ⊙ . The observed location of κ Cassiopeiae in the Hertzsprung–Russell diagram is marked by a thick dot. The amplitudes of radial eigenmodes decay exponentially from the stellar surface to the core. Thus, the latter may be disregarded when studying stellar stability (see e.g. Glatzel Kiriakidis 1993 ; Glatzel, Kiriakidis Fricke 1993 ; Saio 2011 ; Yadav Glatzel 2016 , 2017a ). Accordingly, our present study is restricted to envelope models of κ Cassiopeiae thus disregarding any influence of nuclear energy generation and nucleosynthesis. The envelope models with solar chemical composition ( X = 0.70, Y = 0.28, and Z = 0.02; where X , Y , and Z represent the mass fraction of hydrogen, helium, and heavy elements, respectively) are constructed by integrating the stellar