Showing papers by "Pawan Kumar published in 1995"

Polar solvation dynamics of polyatomic solutes: Simulation studies in acetonitrile and methanol

Abstract: This paper describes results of simulations of solvation dynamics of a variety of solutes in two reference solvents, acetonitrile and methanol. Part of these studies involve attempts to realistically model the solvation dynamics observed experimentally with the fluorescence probe coumarin 153 (C153). After showing that linear response simulations afford a reliable route to the dynamics of interest, experimental and simulation results for C153 are compared. Agreement between the observed and calculated dynamics is found to be satisfactory in the case of acetonitrile but poor in the case of methanol. The latter failure is traced to a lack of realism in the dielectric properties of the methanol model employed. A number of further simulations are then reported for solvation of a number of atomic, diatomic, and benzenelike solutes which are used to elucidate what features of the solute are important for determining the time dependence of the solvation response. As far as large polyatomic solutes like C153 are ...

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

Abstract: 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.

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

Abstract: 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.

Nonlinear Damping of Oscillations in Tidal-Capture Binaries

Abstract: 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 $\equiv\eta^{-1}\approx 4 E_{0,42}^{-1/2}$ 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, $\delta R/R_*\approx 0.002E_{0,42}^{1/2}$. Although the daughter modes are limited by their own nonlinearities, collectively they absorb most of the primary mode's energy after a time $\sim 10\eta^{-1}$ 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.

Observational Searches for Solar g-modes: Some Theoretical Considerations

Abstract: 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.

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

Abstract: 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.