arXiv subjects

Pawan Kumar

Publications and source records attributed to Pawan Kumar.

246 records · Page 14Linked to original sources

arXiv1996

On the orbital decay of the PSR J0045-7319 Binary

Recent observations of PSR J0045-7319, a radio pulsar in a close eccentric orbit with a massive main sequence B-star companion, indicate that the system's orbital period is decreasing on a timescale $\sim 5 x 10^{5}$ years (Kaspi et al. 1996). Timing observations of PSR J0045-7319 also indicate that the B-star is rotating rapidly, perhaps close to its breakup rotation rate. For rapid (super-synchronous) prograde rotation of the B-star, tidal dissipation leads to an increasing orbital period for the binary system, while for retrograde rotation of any magnitude, the orbital period decreases with time. We show that if tidal effects are to account for the observed orbital decay of the PSR J0045-7319 binary, the B-star must have retrograde rotation. This implies that the supernova that produced the pulsar in this binary system likely had a dipole anisotropy. For a reasonably wide range of retrograde rotation rates, the energy in the dynamical tide of the B-star needs to be dissipated in about one orbital period in order to account for the observed orbital evolution time for the PSR J0045-7319 binary. We show, however, that the radiative dissipation of the dynamical tide in a rigidly rotating B-star is too inefficient by a factor of $\approx$ 10$^3$, regardless of the magnitude of the rotation rate. We describe how, when the surface of the B-star is rotating nearly synchronously (which is expected from the work of Goldreich and Nicholson, 1989), the energy in the dynamical tide is dissipated in less than an orbital period, thus reconciling the theoretical and observed rates of orbital evolution.

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arXiv1996

Excitation of Solar Acoustic Oscillations

The stochastic excitation of solar oscillations due to turbulent convection is reviewed. A number of different observational results that provide test for solar p-mode excitation theories are described. I discuss how well the stochastic excitation theory does in explaining these observations. The location and properties of sources that excite solar p-modes are also described. Finally, I discuss why solar g-modes should be linearly stable, and estimate the surface velocity amplitudes of low degree g-modes assuming that they are stochastically excited by the turbulent convection in the sun.

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arXiv1996

HI Observations of two Molecular Clouds with Extremely Large Velocity Dispersions

We have mapped two molecular clouds at (l, b) = (3.2 degrees, + 0.3 degrees) and (l, b) = (5.4 degrees, -0.5 degrees) in 21-cm line and continuum emission. These clouds show unusually large velocity dispersions of more than 100 km/s (FWHM) which has also been seen in $^{12}$CO, $^{13}$CO, and CS emissions. This dispersion is roughly an order of magnitude larger compared to giant molecular clouds. From our HI observation we estimate that the atomic mass of the cloud at l = 3.2 degrees is about $1.5\times 10^5 M_\odot$ and the mass of the cloud at l = 5.4 degrees is $7\times 10^4 M_\odot$. The ratio of total molecular mass to atomic mass for these clouds appears to be normal for clouds near the galactic center. The main peculiar feature of these clouds is their abnormally large velocity dispersion; the extent in velocity is from about 0 km/s (LSR) to 200 km/s. These clouds are connected, in the l-v plane, to high velocity ridges that extend over several degrees of the longitude. These properties, we believe, provide important clues to the physical process responsible for their large velocity dispersion.

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arXiv1996

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.

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arXiv1996

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.

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arXiv1996

Asymmetries of Solar p-mode Line Profiles

Recent observations indicate that solar p-mode line profiles are not exactly Lorentzian, but rather exhibit varying amounts of asymmetry about their respective peaks. We analyze p-mode line asymmetry using both a simplified one-dimensional model and a more realistic solar model. We find that the amount of asymmetry exhibited by a given mode depends on the location of the sources exciting the mode, the mode frequency, and weakly on the mode spherical harmonic degree, but not on the particular mechanism or location of the damping. We calculate the dependence of line asymmetry on source location for solar p-modes, and provide physical explanations of our results in terms of the simplified model. A comparison of our results to the observations of line asymmetry in velocity spectra reported by Duvall et al. (1993) for modes of frequency $\sim$ 2.3 mHz suggests that the sources for these modes are located more than 325 km beneath the photosphere. This source depth is greater than that found by Kumar (1994) for acoustic waves of frequency $\sim$ 6 mHz. The difference may indicate that waves of different frequencies are excited at different depths in the convection zone. We find that line asymmetry causes the frequency obtained from a Lorentzian fit to a peak in the power spectrum to differ from the corresponding eigenfrequency by an amount proportional to a dimensionless asymmetry parameter and to the mode linewidth.

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arXiv1995

Observational Searches for Solar g-modes: Some Theoretical Considerations

We argue that the solar g-modes are unlikely to have caused the discrete peaks in the power spectrum of the solar wind flux observed by Thomson et al. (1995). The lower limit to the energy of individual g-modes, using the amplitudes given by Thomson et al., is estimated to be at least 10$^{36}$ erg for low order g-modes; the resulting surface velocity amplitude is at least 50 cm s$^{-1}$, larger than the observational upper limit (5 cm s$^{-1}$). We suggest that the most likely source for the excitation of solar g-modes is turbulent stresses in the convection zone. The surface velocity amplitude of low degree and low order g-modes resulting from this process is estimated to be of order 10$^{-2}$ cm s$^{-1}$. This amplitude is interestingly close to the detection threshold of the SOHO satellite. The long lifetime of g-modes ($\sim 10^6$ years for low order modes) should be helpful in detecting these small amplitude pulsations.

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arXiv1995

On the Validity of the Classical Apsidal Motion Formula for Tidal Distortion

We check the validity of the widely used classical apsidal motion formula as a function of orbital parameters, stellar structure, and stellar rotation rate by comparing dynamical calculations of the periastron advance with the static tidal formula. We find that the classical formula gives very accurate results when the periods of the low order quadrupole g, f and p modes are smaller than the periastron passage time by a factor of about 7 or more. However, when this condition is not satisfied, the difference between the classical formula and the exact result can be quite large, and even periastron recession can result. The largest difference arises when one of the low order modes of the star is nearly resonant with an integer multiple of the orbital frequency minus twice the rotation rate of the star. The resonance of higher order g-modes (number of radial nodes $\gta 4$) with the orbit is very unlikely to cause significant deviation from the classical result because of their weak coupling to the tidal force and thus their small contribution to the apsidal motion. Resonances involving rotational modes of the star are also unlikely to make much contribution to the apsidal motion because of their small overlap with the tidal force, even though they have periods comparable to the periastron passage time. We apply our work to two famous binary systems (AS Cam and DI Her) which show abnormally small apsidal motion, and conclude that dynamical effects are unimportant for these systems, i.e. the static tide assumption is an excellent approximation.

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arXiv1995

Nonlinear Damping of Oscillations in Tidal-Capture Binaries

We calculate the damping of quadrupole f and low order g modes (primary modes) by nonlinear coupling to other modes of the star. This damping is orders of magnitude more rapid than direct radiative damping when the primary amplitude is large, as in tidal capture. Primary modes destabilize high degree g-modes of half their frequency (daughter modes) by 3-mode coupling in radiative zones. In sunlike stars, the growth time $\equivη^{-1}\approx 4 E_{0,42}^{-1/2}$ days, where $E_{0,42}$ is the initial energy of the primary mode in units of $10^{42}~$erg, and of order $10^{10}E_{0,42}^{5/4}$ daughters are unstable. The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, $δR/R_*\approx 0.002E_{0,42}^{1/2}$. Although the daughter modes are limited by their own nonlinearities, collectively they absorb most of the primary mode's energy after a time $\sim 10η^{-1}$ provided $E_{0}> 10^{40}~\mbox{erg}$. In fact nonlinear mode interaction may be the dominant damping process if $E_0\gtrsim 10^{37}~\mbox{erg}$. Our results have application to tidally captured main sequence globular cluster stars of mass $\ge 0.5 M_{\sun}$; the tidal energy is dissipated in the radiative core of the star in about a month, which is less than the initial orbital period.

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arXiv1995

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.

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arXiv1994

Causality in Strong Shear Flows

It is well known that the standard transport equations violate causality when gradients are large or when temporal variations are rapid. We derive a modified set of transport equations that satisfy causality. These equations are obtained from the underlying Boltzmann equation. We use a simple model for particle collisions which enables us to derive moment equations non-perturbatively, i.e. without making the usual assumption that the distribution function deviates only slightly from its equilibrium value. We apply the model to two problems: particle diffusion and viscous transport. In both cases we show that signals propagate at a finite speed and therefore that the formalism obeys causality. When the velocity gradient is large on the scale of a mean free path, the viscous shear stress is suppressed relative to the prediction of the standard diffusion approximation. The shear stress reaches a maximum at a finite value of the shear amplitude and then decreases as the velocity gradient increases. In the case of a steady Keplerian accretion disk with hydrodynamic turbulent viscosity, the stress-limit translates to an upper bound on the Shakura-Sunyaev $α$-parameter, namely $α<0.07$. The limit on $α$ is much stronger in narrow boundary layers where the velocity shear is larger than Keplerian.

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arXiv1993

g-modes and the Solar Neutrino Problem

We show that low-order g-modes with large enough amplitudes to affect significantly the solar neutrino fluxes would produce surface velocities that are $10^4$ times larger than the observed upper limits and hence are ruled out by existing data. We also demonstrate that any large-amplitude, short-period oscillations that grow on a Kelvin-Helmholtz time scale will require, to affect solar neutrino fluxes, a large amount of energy (for g-modes, $10^9$ times the energy in the observed $p-$ mode oscillations) and a tiny amount of dissipation (for g-modes, $10^{-8}$ the dissipation rate of the $p$-modes).

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