tokens: typically multi-periodic oscillators that can show very rich pulsation frequency spectra that challenge asteroseismic analyses and the theoretical interpretation of the observed pulsation frequencies. A- and F-type stars can also show a combination of pressure ( p -), gravity ( g -), and Rossby ( r -) modes (e.g. Uytterhoeven et al. 2011 ; Saio et al. 2018 ). Hence, we investigated all available photometric data sets of β Cas for the presence of g - and r- modes in addition to the already described p -modes. g -modes would be found in the range of ∼3.3 to 0.3 d −1 in frequency (corresponding to ∼0.3 to 3.0 days in period; Kaye et al. 1999 ); r- modes appear as a group of peaks below m times the rotational frequency. BRITE-Constellation and SMEI data are known to allow the detection of g -mode pulsations when the standard procedures for data reduction are applied (e.g. Kallinger et al. 2017 ; Zwintz et al. 2017 ). The BRITE-Constellation and SMEI data for β Cas do not show any signs for g -mode pulsations. We also checked the TESS data for the potential presence of g -modes before we applied the Gaussian filter to remove the instrumental signal, and also did not find any evidence for them (see Fig. B.1 ). In all our data sets, we do not detect a frequency that can be attributed to the rotation of β Cas or a group of peaks typical for r -modes. There are two prominent physical effects that complicate the asteroseismic analysis of δ Scuti stars. One effect is moderate to fast rotation, which can cause a splitting of the pulsation modes with the same n and l values but different m values (e.g. Lignières et al. 2006 ). The second effect is the presence of magnetic fields, which is a rather recent discovery for δ Scuti stars (e.g. Neiner Lampens 2015 ; Neiner et al. 2017 ). In this context, β Cas is a special case because observationally it shows only three independent p -mode pulsation frequencies and not several dozen to hundreds of modes. The reason might be connected to the inclination angle of only 19° ( Che et al. 2011 ) and the presence of the magnetic field. Despite the rather high rotational speed of β Cas, no sign of a rotational splitting can be detected in the present observational material. We calculated the pulsation constant, Q , based on our values for the three independent frequencies, F 1 , F 2 , and F 4 , and our fundamental parameters, T eff = 6920 K and log g = 3.53 cgs. The pulsation constant Q ( Petersen 1976 ; Stellingwerf 1979 ) can be expressed as: where P is the pulsation period in days and M bol is the bolometric magnitude, which is defined as M bol = M V + BC. The absolute magnitude of 1.14 mag is calculated from the distance of 16.8 pc, and the bolometric correction, BC, can be calculated from the relation given by Reed (1998) . The pulsation constant has a value of 0.033 for fundamental mode pulsation ( n = 0), 0.025 for the first overtone ( n = 1), 0.020 for the second overtone ( n = 2), and 0.017 for the third
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