Tidal Excitation of Modes in Binary Systems with Applications to Binary Pulsars

We consider the tidal excitation of modes in a binary system of arbitrary eccentricity. For a circular orbit, the modes generally undergo forced oscillation with a period equal to the orbital period ($T$). For an eccentric orbit, the amplitude of each tidally excited mode can be written approximately as the sum of an oscillatory term that varies sinusoidally with the mode frequency and a `static' term that follows the time dependence of the tidal forcing function. The oscillatory term falls off exponentially with increasing \b (defined as the ratio of the periastron passage time to the mode period), whereas the `static' term is independent of \b. For small \b modes (\b \approx 1), the two terms are comparable, and the magnitude of the mode amplitude is nearly constant over the orbit. For large \b modes (\b \gta a few), the oscillatory term is very small compared to the `static' term, in which case the mode amplitude, like the tidal force, varies as the distance cubed. For main sequence stars, $p$, $f$, and low order $g$-modes generally have large \b and hence small amplitudes of oscillation. High overtone $g$-modes, however, have small overlap with the tidal forcing function. Thus, we expect an intermediate overtone $g$-mode with \b \sim 1 to have the largest oscillation amplitude. The dependence on mode damping and the stellar rotation rate is considered, as well as the effects of orbital evolution. We apply our work to the two binary pulsar system: PSR J0045-7319 and PSR B1259-63.Comment: 28 pages of uuencoded compressed postscript. 9 postscript figures available by anonymous ftp from ftp://brmha.mit.edu/ To be published in ApJ

Angular momentum transport by gravity waves and its effect on the rotation of the solar interior

We calculate the excitation of low frequency gravity waves by turbulent convection in the sun and the effect of the angular momentum carried by these waves on the rotation profile of the sun's radiative interior. We find that the gravity waves generated by convection in the sun provide a very efficient means of coupling the rotation in the radiative interior to that of the convection zone. In a differentially rotating star, waves of different azimuthal number have their frequencies in the local rest frame of the star Doppler shifted by different amounts. This leads to a difference in their local dissipation rate and hence a redistribution of angular momentum in the star. We find that the time scale for establishing uniform rotation throughout much of the radiative interior of the sun is $\sim 10^7$ years, which provides a possible explanation for the helioseismic observations that the solar interior is rotating as a solid body.Comment: 10 pages, tex, 3 figures. To appear in ApJ lette

Differential rotation enhanced dissipation of tides in the PSR J0045-7319 Binary

Recent observations of PSR J0045-7319, a radio pulsar in a close eccentric orbit with a massive B-star companion, indicate that the system's orbital period is decreasing on a timescale of $\approx 5 \times10^{5}$ years, which is much shorter than the timescale of $\approx$ 10^9 years given by the standard theory of tidal dissipation in radiative stars. Observations also provide strong evidence that the B-star is rotating rapidly, perhaps at nearly its break up speed. We show that the dissipation of the dynamical tide in a star rotating in the same direction as the orbital motion of its companion (prograde rotation) with a speed greater than the orbital angular speed of the star at periastron results in an increase in the orbital period of the binary system with time. Thus, since the observed time derivative of the orbital period is large and negative, the B-star in the PSR J0045-7319 binary must have retrograde rotation if tidal effects are to account for the orbital decay. We also show that the time scale for the synchronization of the B-star's spin with the orbital angular speed of the star at periastron is comparable to the orbital evolution time. From the work of Goldreich and Nicholson (1989) we therefore expect that the B-star should be rotating differentially, with the outer layers rotating more slowly than the interior. We show that the dissipation of the dynamical tide in such a differentially rotating B-star is enhanced by almost three orders of magnitude leading to an orbital evolution time for the PSR J0045-7319 Binary that is consistent with the observations.Comment: 8 pages, tex. Submitted to Ap

Wind-Fed GRMHD Simulations of Sagittarius A*: Tilt and Alignment of Jets and Accretion Discs, Electron Thermodynamics, and Multi-Scale Modeling of the Rotation Measure

Wind-fed models offer a unique way to form predictive models of the accretion flow surrounding Sagittarius A*. We present 3D, wind-fed MHD and GRMHD simulations spanning the entire dynamic range of accretion from parsec scales to the event horizon. We expand on previous work by including nonzero black hole spin and dynamically evolved electron thermodynamics. Initial conditions for these simulations are generated from simulations of the observed Wolf-Rayet stellar winds in the Galactic Centre. The resulting flow tends to be highly magnetized ($\beta \approx 2$) with an $\sim$ $r^{-1}$ density profile independent of the strength of magnetic fields in the winds. Our simulations reach the MAD state for some, but not all cases. In tilted flows, SANE jets tend to align with the angular momentum of the gas at large scales, even if that direction is perpendicular to the black hole spin axis. Conversely, MAD jets tend to align with the black hole spin axis. The gas angular momentum shows similar behavior: SANE flows tend to only partially align while MAD flows tend to fully align. With a limited number of dynamical free parameters, our models can produce accretion rates, 230 GHz flux, and unresolved linear polarization fractions roughly consistent with observations for several choices of electron heating fraction. Absent another source of large-scale magnetic field, winds with a higher degree of magnetization (e.g., where the magnetic pressure is 1/100 of the ram pressure in the winds) may be required to get a sufficiently large RM with consistent sign.Comment: Accepted by MNRAS. Animations for several figures in the paper are available at https://www.youtube.com/playlist?list=PL3pLmTeUPcqSd4jVBnRubYQpa-Dma25i