Showing papers by "Pawan Kumar published in 1999"

Some Observational Consequences of GRB Shock Models

Abstract: In the internal shock scenario for GRBs we expect some fraction of the energy of the burst to be carried by slow moving shells that were ejected at late times. These slow shells collide with faster moving outer shells when the outer shells have slowed down as a result of sweeping up material from the ISM. This gives rise to a forward shock that moves into the outer shell producing a bump in the afterglow light curve of amplitude roughly proportional to the ratio of the energy in the inner and the outer shells. In addition, a reverse shock propagates in the inner shell and produces emission at a characteristic frequency that is typically much smaller than the peak of the emission from the outer shell by a factor of $\sim 7 \gamma_{0c}^2 (E_2/E_1)^{1.1}$, and the observed flux at this frequency from the reverse shock is larger compared to the flux from the outer shell by a factor of $\sim 8 (\gamma_{0c} E_2/E_1)^{5/3} $; where $\gamma_{0c}$ is the bulk Lorentz factor of the outer shell at the time of collision, and $E_1 & E_2$ are the total energy in the outer and the inner shells respectively. The Lorentz factor is related to the observer time as $\sim 5 (t/day)^{3/8}$. The shell collision could produce initial temporal variability in the early afterglow signal. The lack of significant deviation from a power-law decline of the optical afterglow from half a dozen bursts suggests that $E_2/E_1$ is small. Future multi-wavelength observations should be able to either detect bumps in the light curve corresponding to both the forward and the reverse shocks or further constrain the late time release of energy in ejecta with small Lorentz factor, which is expected generically in the internal shock models for the gamma-ray bursts.

Gamma-Ray Burst Energetics

Abstract: We estimate the fraction of the total energy in a gamma-ray burst (GRB) that is radiated in photons during the main burst. Random internal collisions among different shells limit the efficiency for converting bulk kinetic energy to photons. About 1% of the energy of explosion is converted to radiation, in the 10-103 keV energy band in the observer frame, for long-duration bursts (lasting 10 s or more); the efficiency is significantly smaller for shorter duration bursts. Moreover, about 50% of the energy of the initial explosion could be lost to neutrinos during the early phase of the burst if the initial fireball temperature is ~10 MeV. If isotropic, the total energy budget of the brightest GRBs is 1055 ergs, a factor of 20 larger than previously estimated. Anisotropy of explosion, as evidenced in two GRBs, could reduce the energy requirement by a factor of 10-100. Putting these two effects together, we find that the energy release in the most energetic bursts is about 1054 ergs.

Angular Momentum Redistribution by Waves in the Sun

Abstract: We calculate the angular momentum transport by gravito-inertial-Alfven waves and show that, so long as prograde and retrograde gravity waves are excited to roughly the same amplitude, the sign of angular momentum deposit in the radiative interior of the Sun is such as to lead to an exponential growth of any existing small radial gradient of rotation velocity just below the convection zone. This leads to formation of a strong thin shear layer (of thickness about 0.3% R☉) near the top of the radiative zone of the Sun on a timescale of order 20 yr. When the magnitude of differential rotation across this layer reaches about 0.1 μHz, the layer becomes unstable to shear instability and undergoes mixing, and the excess angular momentum deposited in the layer is returned to the convection zone. The strong shear in this layer generates a toroidal magnetic field which is also deposited in the convection zone when the layer becomes unstable. This could possibly start a new magnetic activity cycle seen at the surface.

Angular momentum redistribution by waves in the Sun

Abstract: We calculate the angular momentum transport by gravito-inertial-Alfv\'en waves and show that, so long as prograde and retrograde gravity waves are excited to roughly the same amplitude, the sign of angular momentum deposit in the radiative interior of the Sun is such as to lead to an exponential growth of any existing small radial gradient of rotation velocity just below the convection zone. This leads to formation of a strong thin shear layer (of thickness about 0.3% R_\odot) near the top of the radiative zone of the Sun on a time-scale of order 20 years. When the magnitude of differential rotation across this layer reaches about 0.1 \mu Hz, the layer becomes unstable to shear instability and undergoes mixing, and the excess angular momentum deposited in the layer is returned to the convection zone. The strong shear in this layer generates toroidal magnetic field which is also deposited in the convection zone when the layer becomes unstable. This could possibly start a new magnetic activity cycle seen at the surface.

Energetics and Luminosity Function of Gamma-ray Bursts

Abstract: Gamma-ray bursts are believed to be some catastrophic event in which material is ejected at a relativistic velocity, and internal collisions within this ejecta produce the observed $\gamma$-ray flash. The angular size of a causally connected region within a relativistic flow is of the order the angular width of the relativistic beaming, $\gamma^{-1}$. Thus, different observers along different lines of sights could see drastically different fluxes from the same burst. Specifically, we propose that the most energetic bursts correspond to exceptionally bright spots along the line of sight on colliding shells, and do not represent much larger energy release in the explosion. We calculate the distribution function of the observed fluence for random angular-fluctuation of ejecta. We find that the width of the distribution function for the observed fluence is about two orders of magnitude if the number of shells ejected along different lines of sight is ten or less. The distribution function becomes narrower if number of shells along typical lines of sight increases. The analysis of the $\gamma$-ray fluence and afterglow emissions for GRBs with known redshifts provides support for our model i.e. the large width of GRB luminosity function is not due to a large spread in the energy release but instead is due to large angular fluctuations in ejected material. We outline several observational tests of this model. In particular, we predict little correlation between the $\gamma$-ray fluence and the afterglow emission as in fact is observed. We predict that the early (minutes to hours) afterglow would depict large temporal fluctuations whose amplitude decreases with time. Finally we predict that there should be many weak bursts with about average afterglow luminosity in this scenario.

Gamma-ray Burst Energetics

Abstract: We estimate the fraction of the total energy in a Gamma-Ray Burst (GRB) that is radiated in photons during the main burst. Random internal collisions among different shells limit the efficiency for converting bulk kinetic energy to photons. About 1% of the energy of explosion is converted to radiation, in 10-1000 kev energy band in the observer frame, for long duration bursts (lasting 10s or more); the efficiency is significantly smaller for shorter duration bursts. Moreover, about 50% of the energy of the initial explosion could be lost to neutrinos during the early phase of the burst if the initial fireball temperature is about 10 Mev or greater. If isotropic, the total energy budget of the brightest GRBs is about $10^{55}$erg, a factor of more than 20 larger than previously estimated. Anisotropy of explosion, as evidenced in two GRBs, could reduce the energy requirement by a factor of 10-100. Putting these two effects together we find that the energy release in the most energetic bursts is about 10$^{54}$ erg.

The Distribution of Burst Energy and Shock Parameters for Gamma-ray Bursts

Abstract: We calculate the statistical distribution of observed afterglow flux, in some fixed observed frequency band, and at some fixed observer time after the explosion ($t_{obs}$) in two models - one where the explosion takes place in a uniform density medium and the other where the surrounding medium has a power-law stratification such as is expected for a stellar wind. For photon energies greater than about 500 electron-volt and $t_{obs}\gta 10^3$ sec the afterglow flux distribution functions for the uniform ISM and the wind models are nearly identical. We compare the width of the theoretical distribution with the observed x-ray afterglow flux and find that the FWHM of the distribution for energy in explosion and the fractional energy in electrons ($\epsilon_e$) are each less than about one order of magnitude and the FWHM for the electron energy index is 0.6 or less.

The Structure of the Central Disk of NGC 1068: A Clumpy Disk Model

Abstract: NGC 1068 is one of the best-studied Seyfert II galaxies, for which the black hole mass has been determined from the Doppler velocities of water maser. We show that the standard α-disk model of NGC 1068 gives disk mass between the radii of 0.65 and 1.1 pc (the region from which water maser emission is detected) to be about 7 × 107 M☉ (for α = 0.1), more than 4 times the black hole mass, and a Toomre Q-parameter for the disk is ~0.001. This disk is therefore highly self-gravitating and is subject to large-amplitude density fluctuations. We conclude that the standard α-viscosity description for the structure of the accretion disk is invalid for NGC 1068. In this paper, we develop a new model for the accretion disk. The disk is considered to be composed of gravitationally bound clumps; accretion in this clumped disk model arises because of gravitational interaction of clumps with each other and the dynamical frictional drag exerted on clumps from the stars in the central region of the galaxy. The clumped disk model provides a self-consistent description of the observations of NGC 1068. The computed temperature and density are within the allowed parameter range for water maser emission, and the rotational velocity in the disk falls off as r-0.35.

Line Asymmetry of Solar p-Modes: Reversal of Asymmetry in Intensity Power Spectra

Abstract: The sense of line asymmetry of solar p-modes in the intensity power spectra is observed to be opposite of that seen in the velocity power spectra. Theoretical calculations provide a good understanding and fit to the observed velocity power spectra, whereas the reverse sense of asymmetry in the intensity power spectrum has been poorly understood. We show that when turbulent eddies arrive at the top of the convection zone they give rise to an observable intensity fluctuation that is correlated with the oscillation they generate, thereby affecting the shape of the line in the p-mode power spectra and reversing the sense of asymmetry (this point was recognized by Nigam et al. and Roxburgh & Vorontsov). The addition of the correlated noise displaces the frequencies of peaks in the power spectrum. Depending on the amplitude of the noise source, the shift in the position of the peak can be substantially larger than the frequency shift in the velocity power spectra. In neither case are the peak frequencies precisely equal to the eigenfrequencies of p-modes. We suggest two observations that can provide a test of the model discussed here.

Line Asymmetry of Solar p-Modes: Properties of Acoustic Sources

Abstract: The observed solar p-mode velocity power spectra are compared with theoretically calculated power spectra over a range of mode degree and frequency. The shape of the theoretical power spectra depends on the depth of acoustic sources responsible for the excitation of p-modes and also on the multipole nature of the source. We vary the source depth to obtain the best fit to the observed spectra. We find that quadrupole acoustic sources provide a good fit to the observed spectra provided that the sources are located between 700 and 1050 km below the top of the convection zone. The dipole sources give a good fit for a significantly shallower source, with a source depth of between 120 and 350 km. The main uncertainty in the determination of depth arises because of poor knowledge of the nature of power leakages from modes with adjacent degrees and the background in the observed spectra.

The structure of the central disk of NGC 1068: a clumpy disk model

Abstract: NGC 1068 is one of the best studied Seyfert II galaxies, for which the blackhole mass has been determined from the Doppler velocities of water maser. We show that the standard $\alpha$-disk model of NGC 1068 gives disk mass between the radii of 0.65 pc and 1.1 pc (the region from which water maser emission is detected) to be about 7x10$^7$ M$_\odot$ (for $\alpha=0.1$), more than four times the blackhole mass, and a Toomre Q-parameter for the disk is $\sim$0.001. This disk is therefore highly self-gravitating and is subject to large-amplitude density fluctuations. We conclude that the standard $\alpha$-viscosity description for the structure of the accretion disk is invalid for NGC 1068. In this paper we develop a new model for the accretion disk. The disk is considered to be composed of gravitationally bound clumps; accretion in this clumped disk model arises because of gravitational interaction of clumps with each other and the dynamical frictional drag exerted on clumps from the stars in the central region of the galaxy. The clumped disk model provides a self-consistent description of the observations of NGC 1068. The computed temperature and density are within the allowed parameter range for water maser emission, and the rotational velocity in the disk falls off as $r^{-0.35}$.