Excitation of a nonradial mode in a millisecond X-ray pulsar XTE J1751-305

We discuss candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. The spin frequency of the pulsar is $\nu_{\rm spin}\cong435$Hz and the identified coherent frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}$. Assuming the frequency identified is that observed in the corotating frame of the neutron star, we find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $\epsilon$-mechanism due to helium burning in the thin shell can give the frequency ratio $\kappa=\nu_{\rm osc}/\nu_{\rm spin}\simeq0.57$ at $\nu_{\rm spin}=435$Hz. As another candidate for the observed ratio $\kappa$, we also suggest a toroidal crustal mode that has penetrating amplitudes in the fluid core and is destabilized by gravitational wave emission. Since the surface fluid layer is separated from the fluid core by a solid crust, the amplitudes of an $r$-mode in the core, which is destabilized by emitting gravitational waves, can be by a large factor different from those in the fluid ocean. We find that the amplification factor defined as $f_{\rm amp}=\alpha_{\rm surface}/\alpha_{\rm core}$ is as large as $f_{\rm amp}\sim 10^2$ for the $l^\prime=m=2$ $r$-mode at $\nu_{\rm spin}=435$Hz for a $M=1.4M_\odot$ neutron star model. Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star.Comment: 7 pages, 5 figure

R modes of slowly pulsating B stars

We examine pulsational stability of low $m$ $r$ modes in SPB stars by calculating fully nonadiabatic oscillations of uniformly rotating stars, where $m$ is an integer representing the azimuthal wave number around the rotation axis. $R$ modes are rotationally induced, non-axisymmetric, oscillation modes, whose oscillation frequency strongly depends on the rotation frequency $\Omega$ of the star. They are conveniently classified by using two integer indices $m$ and $l^\prime\ge |m|$ that define the asymptotic oscillation frequency $2m\Omega/[l^\prime(l^\prime+1)]$ in the limit of $\Omega\to 0$. We find low $m$, high radial order, odd $r$ modes with $l^\prime=m$ in SPB stars are excited by the same iron opacity bump mechanism that excites low frequency $g$ modes of the variables, when the rotation frequency $\Omega$ is sufficiently high. No even $r$ modes with low $m$ are found to be pulsationally unstable. Since the surface pattern of the temperature perturbation of odd modes is antisymmetric about the equator of the star, observed photometric amplitudes caused by the unstable odd $r$ modes with $l^\prime=m$ are strongly dependent on the inclination angle between the axis of rotation and the line of sight. Applying the wave-meanflow interaction formalism to nonadiabatic $r$ modes in rapidly rotating SPB models, we find that because of the $r\phi$ component of the Reynolds stress and the radial transport of the eddy fluctuation of density in the rotating star, the surface rotation is accelerated by the forcing due to the low $l^\prime=m$ unstable $r$ modes.Comment: submitted to m