We report the detection with the Proportional Counter Array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) of millisecond variability in the X-ray emission from the low-mass X-ray binary 4U 1728Ϫ34. Pulsations at 363 Hz with amplitudes (rms) of 2.5%-10% are present in six of the eight bursts analyzed to date. The strongest were seen in two successive bursts recorded on 1996 February 16 when the quiescent count rate was near the highest seen by PCA. The pulsations during these bursts show frequency changes of 1.5 Hz during the first few seconds but become effectively coherent as the burst decays. We interpret the 363 Hz pulsations as rotationally induced modulations of inhomogeneous burst emission. This represents the first compelling evidence for a millisecond spin period in a low-mass X-ray binary. Complex, intensity-dependent, millisecond X-ray variability is also present in all the quiescent flux intervals we examined. Most interesting was the behavior as the count rate approached its highest observed level. Two quasi-periodic oscillations (QPOs) were simultaneously observed in the 650 -1100 Hz range. Both QPOs increased in frequency together, maintaining a nearly constant frequency separation of about 363 Hz, the spin period inferred from the burst oscillations. This phenomenology is strongly suggestive of the magnetospheric beat frequency model proposed for the horizontal-branch oscillations (HBOs) seen in Z sources. We discuss this and several other possible physical interpretations for the observed X-ray variability.
Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung-Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order m appear as groups at slightly lower frequency than m times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A and F stars, we find that r modes are present in many γ Dor stars (as first discovered by Van Reeth et al. 2016), spotted stars, and so-called Heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating γ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many Heartbeat stars, a group of frequencies can be fitted with symmetric m = 1 r modes, which can be used to obtain rotation frequencies of these stars.
We investigate the modal properties of the r-modes of rotating neutron stars with the core filled with neutron and proton superfluids, taking account of entrainment effects between the superfluids. The stability of the r-modes against gravitational radiation reaction is also examined considering viscous dissipation due to shear and a damping mechanism called '' mutual friction '' between the superfluids in the core. We find that the r-modes in the superfluid core are split into ordinary r-modes and superfluid r-modes, which we call, respectively, r o -and r s -modes. The two superfluids in the core flow together for the r o -modes, while they countermove for the r s -modes. For the r o -modes, the coefficient 0 lim !0 != is equal to 2m=½l 0 ðl 0 þ 1Þ, almost independent of the parameter that parameterizes the entrainment effects between the superfluids, where is the angular frequency of rotation, ! is the oscillation frequency observed in the corotating frame of the star, and l 0 and m are the indices of the spherical harmonic function representing the angular dependence of the r-modes. For the r s -modes, on the other hand, 0 is equal to 2m=½l 0 ðl 0 þ 1Þ at ¼ 0 (no entrainment), and it almost linearly increases as is increased from ¼ 0. The r o -modes, for which w 0 v 0 p À v 0 n / 3 , correspond to the r-modes discussed by L. Lindblom & G. Mendell, where v 0 n and v 0 p are the Eulerian velocity perturbations of the neutron and proton superfluids, respectively. The mutual friction in the superfluid core is found ineffective to stabilize the r-mode instability caused by the r o -mode except in a few narrow regions of . The r-mode instability caused by the r s -modes, on the other hand, is extremely weak and easily damped by dissipative processes in the star.
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