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Pawan Kumar

Publications and source records attributed to Pawan Kumar.

At least 235 records · Page 13Linked to original sources
arXiv2001

Observational Prospects for Afterglows of Short Duration Gamma-ray Bursts

If the efficiency for producing $γ$-rays is the same in short duration ($\siml 2$ s) Gamma-Ray Bursts (GRBs) as in long duration GRBs, then the average kinetic energy of short GRBs must be $\sim 20$ times less than that of long GRBs. Assuming further that the relativistic shocks in short and long duration GRBs have similar parameters, we show that the afterglows of short GRBs will be on average 10--40 times dimmer than those of long GRBs. We find that the afterglow of a typical short GRB will be below the detection limit ($\siml 10 \microJy$) of searches at radio frequencies. The afterglow would be difficult to observe also in the optical, where we predict $R \simg 23$ a few hours after the burst. The radio and optical afterglow would be even fainter if short GRBs occur in a low-density medium, as expected in NS-NS and NS-BH merger models. The best prospects for detecting short-GRB afterglows are with early ($\siml 1$ day) observations in X-rays.

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arXiv2001

Accretion Models of Gamma-Ray Bursts

Many models of gamma-ray bursts (GRBs) involve accretion onto a compact object, usually a black hole, at a mass accretion rate of order a fraction of a solar mass per second. If the accretion disk is larger than a few tens or hundreds of Schwarzschild radii, the accretion will proceed via a convection-dominated accretion flow (CDAF) in which most of the matter escapes to infinity rather than falling onto the black hole. Models involving the mergers of black hole white dwarf binaries and black hole helium star binaries fall in this category. These models are unlikely to produce GRBs since very little mass reaches the black hole. If the accretion disk is smaller, then accretion will proceed via neutrino cooling in a neutrino-dominated accretion disk (NDAF) and most of the mass will reach the center. Models involving the mergers of double neutron star binaries and black hole neutron star binaries fall in this category and are capable of producing bright GRBs. If the viscosity parameter $α$ in the NDAF has a standard value $\sim0.1$, these mergers can explain short GRBs with durations under a second, but they are unlikely to produce long GRBs with durations of tens or hundred of seconds. If the accretion disk is fed by fallback of material after a supernova explosion, as in the collapsar model, then the time scale of the burst is determined by fallback, not accretion. Such a model can produce long GRBs. Fallback models again require that the accretion should proceed via an NDAF rather than a CDAF in order for a significant amount of mass to reach the black hole. This condition imposes an upper limit on the radius of injection of the gas.

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arXiv2001

BeppoSAX confirmation of beamed afterglow emission from GRB990510

We compare the prompt X-ray (2-10 keV) emission of GRB990510 measured by the BeppoSAX Wide Field Cameras (WFC) during the burst to the X-ray afterglow detected by the BeppoSAX Narrow Field Instruments. A single power-law model for the afterglow, f(t) ~ t^{-1.42}, is ruled out. Provided the initial time of the afterglow is assumed to coincide with the last short pulse in the X-ray prompt event (i.e., 72 seconds after the GRB trigger time), the X-ray emission from \~80 to 10^5 seconds after the GRB trigger is well described by an external shock expanding in a decelerating jet, in which synchrotron radiation takes place. This model, represented by a double power-law of indices alpha_1 ~ 1 and alpha_2 ~ 2 before and after a jet collimation break time of ~0.5 days after GRB, respectively, is consistent with the second and third upper limits measured by the WFC, but not with the first. This may be related to inhomogeneities in the circumburst medium. Our finding indicates that the temporal behavior of the GRB990510 X-ray afterglow is similar to that at optical wavelengths, and thus strengthens the interpretation of the multiwavelength afterglow as synchrotron emission in a jet with decreasing Lorentz factor. GRB990510 is thus the only burst in which evidence of a spreading jet has been found in X-rays.

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arXiv2000

Afterglow Emission from Naked Gamma-Ray Bursts

We calculate the {\it afterglow} emission for Gamma-Ray Bursts (GRBs) going off in an extremely low density medium, referred to as {\it naked bursts}. Our results also apply to the case where the external medium density falls off sharply at some distance from the burst. The observed afterglow flux in this case originates at high latitudes, i.e. where the angle between the fluid velocity and the observer line of sight is greater than $Γ^{-1}$. The observed peak frequency of the spectrum for naked bursts decreases with observer time as $t^{-1}$, and the flux at the peak of the spectrum falls off as $t^{-2}$. The 2--10 keV $X$-ray flux from a naked burst of average fluence should be observable by the SWIFT satellite for time duration of about $10^3$ longer than the burst variability timescale. The high latitude emission contributes to the early $X$-ray afterglow flux for any GRB, not just naked bursts, and can be separated from the shocked inter-stellar medium (ISM) emission by their different spectral and temporal properties. Measurements of the high latitude emission could be used to map the angular structure of GRB producing shells.

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arXiv2000

Source depth for solar p-modes

Theoretically calculated power spectra are compares with observed solar p-mode velocity power spectra over a range of mode degree and frequency. The depth for the sources responsible for exciting p-modes of frequency 2.0 mHz is determined from the asymmetry of their power spectra and found to be about 800 km below the photosphere for quadrupole sources and 150 km if sources are dipole. The source depth for high frequency oscillations of frequency greater than about 6 mHz is 180 (50) km for quadrupole (dipole) sources.

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arXiv2000

Some Observational Consequences of GRB Shock Models

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 $\sim 7 γ_{0c}^2 (E_2/E_1)^{1.1}$, 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 (γ_{0c} E_2/E_1)^{5/3} $; where $γ_{0c}$ 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.

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arXiv2000

Tidal spin-up of stars in dense stellar cusps around massive black holes

We show that main-sequence stars in dense stellar cusps around massive black holes are likely to rotate at a significant fraction of the centrifugal breakup velocity due to spin-up by hyperbolic tidal encounters. We use realistic stellar structure models to calculate analytically the tidal spin-up in soft encounters, and extrapolate these results to close and penetrating collisions using smoothed particle hydrodynamics simulations. We find that the spin-up falls off only slowly with distance from the black hole because the increased tidal coupling in slower collisions at larger distances compensates for the decrease in the stellar density. We apply our results to the stars near the massive black hole in the Galactic Center. Over their lifetime, ~1 Msol main sequence stars in the inner 0.3 pc of the Galactic Center are spun-up on average to ~10%--30% of the centrifugal breakup limit. Such rotation is ~20--60 times higher than is usual for such stars and may affect their subsequent evolution and their observed properties.

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arXiv2000

Steepening of Afterglow Decay for Jets Interacting with Stratified Media

We calculate light-curves for Gamma-Ray Burst afterglows when material ejected in the explosion is confined to a jet which propagates in a medium with a power-law density profile. The observed light-curve decay steepens by a factor of $Γ^2$ when an observer sees the edge of the jet. In a uniform density medium the increase in the power-law index ($β$) of the light-curve as a result of this {\it edge effect} is $\sim0.7$ and is completed over one decade in observer time. For a pre-ejected stellar wind ($ρ\propto r^{-2}$) $β$ increases by $\sim0.4$ over two decades in time due to the edge effect and the steepening of the light-curve due to the jet sideways expansion takes about four decades in time. Therefore, a break in the light-curve for a jet in a wind model is unlikely to be detected even for very narrow jets of opening angle of a few degrees or less, in which case the lateral expansion occurs at early times when the afterglow is bright. The light-curve for the afterglow of GRB 990510, for which an increase in $β$ of approximately 1.35 was observed on a time scale of 3 days, cannot be explained only by the sideways expansion and the edge effects in a jet in a uniform ISM -- the increase in $β$ is too large and too rapid. However, the passage of the cooling or synchrotron peak frequencies through the observing band at about 0.1 -- 1 day together with jet edge effect explains the observed data. The jet opening angle is found to be $\sim 5^o$ and the energy in the explosion to be less than about $10^{50}$ erg.

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arXiv1999

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

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 ($ε_e$) are each less than about one order of magnitude and the FWHM for the electron energy index is 0.6 or less.

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arXiv1999

Energetics and Luminosity Function of Gamma-ray Bursts

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 $γ$-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, $γ^{-1}$. 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 $γ$-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 $γ$-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.

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arXiv1999

Gamma-ray Burst Energetics

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.

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arXiv1999

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

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 $α$-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 $α=0.1$), 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 $α$-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 $r^{-0.35}$.

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arXiv1999

Angular momentum redistribution by waves in the Sun

We calculate the angular momentum transport by gravito-inertial-Alfvén 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 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 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.

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arXiv1999

Line asymmetry of solar p-modes: Reversal of asymmetry in intensity power spectra

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 which 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 which can provide a test of the model discussed here.

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arXiv1999

Line asymmetry of solar p-modes: Properties of acoustic sources

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 km and 1050 km below the top of the convection zone. The dipole sources give a good fit for significantly shallower source, with a source-depth of between 120 km and 350 km. The main uncertainty in the determination of depth arises due to poor knowledge of nature of power leakages from modes with adjacent degrees, and the background in the observed spectra.

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arXiv1997

Dissipation of a tide in a differentially rotating star

The orbital period of the binary pulsar PSR J0045-7319, which is located in our neighbouring galaxy the Small Magellanic Cloud (SMC), appears to be decreasing on a timescale of half a million year. This timescale is more than two orders of magnitude smaller than what is expected from the standard theory of tidal dissipation. Kumar and Quataert (1997a) proposed that this rapid evolution can be understood provided that the neutron star's companion, a main sequence B-star, has set up significant differential rotation. They showed that the spin synchronization time for the B-star is similar to the orbit circularization time, whereas the time to synchronize the surface rotation is much shorter, and thus significant differential rotation in the star is indeed expected. However, their calculation did not include the various processes that can redistribute angular momentum in the star, possibly forcing it into solid body rotation; in that case the dissipation of the tide would not be enhanced. The goal of this paper is to include the redistribution of angular momentum in the B-star due to meridional circulation and shear stresses and to calculate the resulting rotation profile as a function of time. We find that although angular momentum redistribution is important, the B-star continues to have sufficient differential rotation so that tidal waves are entirely absorbed as they arrive at the surface. The mechanism proposed by Kumar and Quataert to speed up the orbital evolution of the SMC binary pulsar should therefore work as suggested.

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arXiv1997

Gas accretion in a clumpy disk with application to AGNs

We analyze the collective gravitational interaction among gas clouds in the inner regions of galactic disks and find that it leads to accretion at a rate $\sim M_{mc}Ω(M_{mc}/M_t)^2$; where $M_{mc}$ is the molecular mass of the disk, $M_t$ is sum of the central plus any axisymmetrically distributed mass, and $Ω$ is the mean angular speed of clumps. We discuss applications of this result to the mega-maser galaxy NGC 4258, for which we have observational evidence that the maser spots are concentrated in a thin molecular disk which is clumpy, and find the accretion rate to be about $1.5\times 10^{-3}$ solar mass per year. If the gravitational energy release of this inward falling gas were to be radiated away efficiently, then the resulting luminosity would greatly exceed the observed central luminosity of NGC 4258, indicating that most of the thermal energy of the gas is advected with the flow into the blackhole as proposed by Lasota et al. (1996). The gravitational interactions among molecular clouds lying within the inner kpc of our galaxy give an accretion rate of about $10^{-5}$ solar mass per year, which is consistent with the value obtained by Narayan et al. (1995) by fitting the spectrum of Sagitarrius A$^*$. We also discuss possible application of this work to quasar evolution.

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