Seismic analysis of the double-mode radial pulsator SX Phoenicis

Abstract

We present the results of complex seismic analysis of the prototype star SX Phoenicis. This analysis consists of a simultaneous fitting of the two radial-mode frequencies, the corresponding values of the bolometric flux amplitude (the parameter f) and of the intrinsic mode amplitude ϵ. The effects of various parameters as well as the opacity data are examined. With each opacity table it is possible to find seismic models that reproduce the two observed frequencies with masses allowed by evolutionary models appropriate for the observed values of the effective temperature and luminosity. All seismic models are in the post-main sequence phase. The OPAL and OP seismic models are in hydrogen shell-burning phase and the OPLIB seismic model has just finished an overall contraction and starts to burn hydrogen in a shell. The OP and OPLIB models are less likely due to the requirement of high initial hydrogen abundance (X0 = 0.75) and too high metallicity (Z ≈ 0.004) as for a Population II star. The fitting of the parameter f, whose empirical values are derived from multi-colour photometric observations, provides constraints on the efficiency of convective transport in the outer layers of the star and on the microturbulent velocity in the atmosphere. Our complex seismic analysis with each opacity data indicates low to moderately efficient convection in the star’s envelope, described by the mixing length parameter of αMLT ∈ (0.0, 0.7), and the microturbulent velocity in the atmosphere of about ξt ∈ (4, 8) km s−1.

KIC 5950759: a high-amplitude δ Sct star with amplitude and frequency modulation near the terminal age main sequence

“…The high frequency of the fundamental radial mode in KIC 5950759, and the relatively large observed frequency ratio of 0.77554 also support that KIC 5950759 is a metal-poor star (see e.g. Petersen & Christensen-Dalsgaard 1996;Poretti 2003;Murphy et al 2013b;Daszyńska-Daszkiewicz et al 2020).…”

“…Thus, Petersen diagrams offer a useful diagnostic in constraining these parameters of radial pulsators (see e.g. Petersen 1973;Petersen & Christensen-Dalsgaard 1996;Daszyńska-Daszkiewicz et al 2020).…”

“…5, we provide the best-fitting mass, age, effective temperature, luminosity, theoretical frequency of the first overtone radial mode, and the frequency ratio of the fundamental and first overtone radial modes in Table 3. For each best-fitting model, we also calculate the normalised instability parameters η(p 1 ) and η(p 2 ) (as defined by Stellingwerf 1978; see also Daszyńska-Daszkiewicz et al 2020), for which positive values indicate that a pulsation mode is excited (i.e. unstable) and negative values indicate it is not (i.e.…”

Mode identification and seismic study of $δ$ Scuti, the prototype of a class of pulsating stars

“…As one can see from Table 2, the models computed for MLT = 0.5 and MLT = 1.8 have nearly the same effective temperatures and luminosities but the values of for the radial fundamental mode differ enormously. This strong sensitivity is well known and can be used to derive constraints on MLT in case of Sct and SX Phe pulsators if the empirical values of are determinable from multicolour photometric variability (Daszyńska-Daszkiewicz et al 2003, 2005aDaszyńska-Daszkiewicz 2007;Daszyńska-Daszkiewicz et al 2020). The next finding is that the initial hydrogen abundance 0 and metallicity do not affect significantly the values of at roughly the same effective temperature and luminosity.…”

“…Thinking the other way, one can expect constraints on the efficiency of envelope convection from a comparison of the theoretical and empirical values of . Such constraints have been derived for several Scuti stars (Daszyńska-Daszkiewicz et al 2003, 2005aDaszyńska-Daszkiewicz 2007), and, recently, for SX Phoenicis, the prototype of Population II counterparts of Sct stars (Daszyńska-Daszkiewicz et al 2020). The general conclusion was that convective transport in the envelope of SX Phe is poor to moderately efficient.…”