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Register a new userSeismic analysis of the double-mode radial pulsator SX Phoenicis
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Added by
Jadwiga Daszy\\'nska-Daszkiewicz
Publication date
2020
fields
Physics
and research's language is
English
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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 $varepsilon$. 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 ($X_0=0.75)$ and too high metallicity ($Zapprox 0.004$) 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 stars envelope, described by the mixing length parameter of $alpha_{rm MLT}in (0.0,~0.7)$, and the microturbulent velocity in the atmosphere of about $xi_{rm t}in(4,~8)~kms$.
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New time-series VI CCD photometry of the globular cluster NGC 6362 is studied with the aim of estimating the reddening, mean metallicity and distance of the cluster from its population of RR Lyrae stars. The Fourier decomposition of carefully selected single-mode RR Lyrae light curves, and the use of well-established semi-empirical calibrations and revised zero points, lead to the values of [Fe/H]UVES =1:066 +// 0:126 and -1:08 +/- 0:16 and the distance 7:93 +/- 0:32 and 8:02 +/- 0:15 kpc from the RRab and RRc stars respectively. The distribution of RR Lyrae stars in the horizontal branch shows a neat segregation of pulsating modes about the red edge of the first overtone instability strip, which is not necessarily expected in an OoI type cluster like NGC 6362. Four RRab stars are found likely advanced in their evolution towards the AGB. One new foreground SX Phe star, some 4 kpc in front of the cluster and projected onto the field of our images is reported. We comment on the heavy light contamination, by a very close neighbouring star, of the peculiar double-mode V37 variable, recently postulated as a non-typical RRc variable.
In this work, the photometric data from the American Association of Variable Star Observers are collected and analyzed on the SX Phoenicis star DY Pegasi (DY Peg). From the frequency analysis, we get three independent frequencies: $f_0 = 13.71249 rm{c days^{-1}}$, $f_1 = 17.7000 rm{c days^{-1}}$, and $f_2 =18.138 rm{c days^{-1}}$, in which $f_0$ and $f_1$ are the radial fundamental and first overtone mode, respectively, while $f_2$ is detected for the first time and should belong to a nonradial mode. The $O-C$ diagram of the times of maximum light shows that DY Peg has a period change rate $(1/P_0)(mathrm{d} P_0/mathrm{d} t) = -(5.87 pm 0.03) times 10^{-8} mathrm{yr^{-1}}$ for its fundamental pulsation mode, and should belong to a binary system that has an orbital period $P_{mathrm{orb}} = 15425.0 pm 205.7 mathrm{days}$. Based on the spectroscopic information, single star evolutionary models are constructed to fit the observed frequencies. However, some important parameters of the fitted models are not consistent with that from observations. Combing with the information from observation and theoretical calculation, we conclude that DY Peg should be an SX Phoenicis star in a binary system and accreting mass from a dust disk, which was the residue of its evolved companion (most probably a hot white dwarf at the present stage) produced in the asymptotic giant branch phase. Further observations are needed to confirm this inference, and it might be potentially a universal formation mechanism and evolutionary history for SX Phoenicis stars.
Non-radial modes are excited in classical pulsators, both in Cepheids and in RR Lyrae stars. Firm evidence come from the first overtone pulsators, in which additional shorter period mode is detected with characteristic period ratio falling in between 0.60 and 0.65. In the case of first overtone Cepheids three separate sequences populated by nearly 200 stars are formed in the Petersen diagram, i.e. the diagram of period ratio versus longer period. In the case of first overtone RR Lyrae stars (RRc stars) situation is less clear. A dozen or so such stars are known which form a clump in the Petersen diagram without any obvious structure. Interestingly, all first overtone RR Lyrae stars for which precise space-borne photometry is available show the additional mode, which suggests that its excitation is common. Motivated by these results we searched for non-radial modes in the OGLE-III photometry of RRc stars from the Galactic bulge. We report the discovery of 147 stars, members of a new group of double-mode, radial-non-radial mode pulsators. They form a clear and tight sequence in the Petersen diagram, with period ratios clustering around 0.613 with a signature of possible second sequence with higher period ratio (0.631). The scatter in period ratios of the already known stars is explained as due to population effects. Judging from the results of space observations this still mysterious form of pulsation must be common among RRc stars and with our analysis of the OGLE data we just touch the tip of the iceberg.
The candidate SX Phe star KIC 11754974 shows a remarkably high number of combination frequencies in the Fourier amplitude spectrum: 123 of the 166 frequencies in our multi-frequency fit are linear combinations of independent modes. Predictable patterns in frequency spacings are seen in the Fourier transform of the light curve. We present an analysis of 180 d of short-cadence Kepler photometry and of new spectroscopic data for this evolved, late A-type star. We infer from the 1150-d, long-cadence light curve, and in two different ways, that our target is the primary of a 343-d, non-eclipsing binary system. According to both methods, the mass function is similar, f(M)=0.0207 +/- 0.0003 Msun. The observed pulsations are modelled extensively, using separate, state-of-the-art, time-dependent convection (TDC) and rotating models. The models match the observed temperature and low metallicity, finding a mass of 1.50-1.56 Msun. The models suggest the whole star is metal-poor, and that the low metallicity is not just a surface abundance peculiarity. This is the best frequency analysis of an SX Phe star, and the only Kepler delta Sct star to be modelled with both TDC and rotating models.
We analyse the OGLE-IV photometry of the first overtone and double-mode RR Lyrae stars (RRc/RRd) in the two fields towards the Galactic bulge observed with high cadence. In 27 per cent of RRc stars we find additional non-radial mode, with characteristic period ratio, P x /P 1O in (0.6, 0.64). It strongly corroborates the conclusion arising from the analysis of space photometry of RRc stars, that this form of pulsation must be common. In the Petersen diagram the stars form three sequences. In 20 stars we find two or three close secondary modes simultaneously. The additional modes are clearly non-stationary. Their amplitude and/or phase vary in time. As a result, the patterns observed in the frequency spectra of these stars may be very complex. In some stars the additional modes split into doublets, triplets or appear as a more complex bands of increased power. Subharmonics of additional modes are detected in 20 per cent of stars. They also display a complex structure. Including our previous study of the OGLE-III Galactic bulge data, we have discovered 260 RRc and 2 RRd stars with the additional non-radial mode, which is the largest sample of these stars so far. The additional mode is also detected in two Blazhko RRc stars, which shows that the modulation and additional non-radial mode are not exclusive.
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