Surface trapping and leakage of low-frequency g modes in rotating early-type stars--I. Qualitative analysis

Abstract

A qualitative study of the surface trapping of low‐frequency non‐radial g modes in rotating early‐type stars is undertaken within the Cowling, adiabatic and traditional approximations. A dispersion relation describing the local character of waves in a rotating star is derived; this dispersion relation is then used to construct propagation diagrams for a 7‐M⊙ stellar model, which show the location and extent of wave trapping zones inside the star. It is demonstrated that, at frequencies below a cut‐off, waves cannot be fully trapped within the star, and will leak through the surface. Expressions for the cut‐off frequency are derived in both the non‐rotating and rotating cases; it is found from these expressions that the cut‐off frequency increases with the rotation rate for all but prograde sectoral modes. While waves below the cut‐off cannot be reflected at the stellar surface, the presence of a sub‐surface convective region in the stellar model, owing to He ii ionization, means that they can become partially trapped within the star. The energy leakage associated with such waves, which are assigned the moniker virtual modes owing to their discrete eigenfrequencies, means that stability analyses which disregard their existence (by assuming perfect reflection at the stellar surface) may be in error. The results are of possible relevance to the 53 Per and SPB classes of variable star, which exhibit pulsation frequencies of the same order of magnitude as the cut‐off frequencies found for the stellar model. It is suggested that observations either of an upper limit on variability periods (corresponding to the cut‐off), or of line‐profile variations owing to virtual modes, may permit asteroseismological studies of the outer layers of these systems.

Asteroseismic Fingerprints of Rotation and Mixing in the Slowly Pulsating B8 v Star Kic 7760680

“…Here, we detect a clear series of 36 frequencies (listed in Table 1) which follow a characteristic period spacing pattern (see Figure 4). There is a distinct cutoff in power toward longer periods at the frequency − 0.63051(2) day 1  ( μ 7.2976(2) Hz), which we interpret as a good proxy of the buoyancy cutoff frequency (e.g., Hansen et al 1985;Townsend 2000). This cutoff value is higher than the one of KIC 10526294 by − 0.16 day 1  ( μ 1.85 Hz), which must reflect a difference in mode energy leakage from the stellar atmosphere due to the difference in evolutionary state and/or rotation.…”

“…This cutoff value is higher than the one of KIC 10526294 by − 0.16 day 1  ( μ 1.85 Hz), which must reflect a difference in mode energy leakage from the stellar atmosphere due to the difference in evolutionary state and/or rotation. Townsend (2000) indeed concluded that the Coriolis force increases the cutoff frequency, although not so much for prograde sectoral modes. This is only the fourth main sequence B-type star where we find such a series of period spacings (after HD 50230, HD 43317, and KIC 10526294 by Degroote et al 2010;Pápics et al 2012Pápics et al , 2014.…”

r-mode oscillations in accreting white dwarfs in cataclysmic variables

“…with c s being sound speed at the surface (Townsend 2000). Among the cases of k = −1, −2, −3 the frequency gap to m f rot (i.e., ν crit ) is smallest for k = −3 because the limiting value of λ is smallest (eq.…”

“…MT Com was discovered as a bright Extreme Ultraviolet (EUV) transient in 1994 with ROSAT (Dahlem et al 1995), which is regarded as a normal dwarf nova outburst (Wheatley et al 2000). From optical time-series photometry in 2000-2004, Patterson et al (2005a detected many short period signals mainly around 1344, 1236, and 668 s (0.744, 0.809, and 1.497 mHz, respectively). These periodicities as well as those obtained by Szkody et al (2010) are shown in the lower panel of Fig.…”