Showing papers by "Pawan Kumar published in 2000"

Afterglow Emission from Naked Gamma-Ray Bursts

Abstract: We calculate the afterglow emission for gamma-ray bursts (GRBs) going off in an extremely low density medium, referred to as 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 103 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 interstellar medium 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.

Analytic Light Curves of Gamma-Ray Burst Afterglows: Homogeneous versus Wind External Media

Abstract: Assuming an adiabatic evolution of a gamma-ray burst (GRB) remnant interacting with an external medium, we calculate the injection, cooling, and absorption break frequencies and the afterglow flux for plausible orderings of the break and observing frequencies. The analytical calculations are restricted to a relativistic remnant and, in the case of collimated ejecta, to the phase where there is an insignificant lateral expansion. Results are given for both a homogeneous external medium and a wind ejected by the GRB progenitor. We compare the afterglow emission at different observing frequencies, for each type of external medium. It is found that observations at submillimeter frequencies during the first day provide the best way of discriminating between the two models. By taking into account the effect of inverse Compton (IC) scatterings on the electron cooling, a new possible time dependence of the cooling break is identified. The signature of the upscattering losses could be seen in the optical synchrotron emission from a GRB remnant interacting with a preejected wind, as a temporary mild flattening of the afterglow decay. The upscattered radiation itself should be detected in the soft X-ray emission from GRB remnants running into denser external media, starting a few hours after the main event.

Some Observational Consequences of Gamma-Ray Burst Shock Models

Abstract: Gamma-ray bursts (GRBs) are believed to be produced when fast-moving ejecta from some central source collides with slower moving, but relativistic, shells that were ejected at an earlier time. In this so-called internal shock scenario 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 interstellar medium. This gives rise to a forward shock that moves into the outer shell, producing a bump in the afterglow light curve of the 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 ~7γ(E2/E1)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 ~8(γ0cE2/E1)5/3; where γ0c is the bulk Lorentz factor of the outer shell at the time of collision, and E1 and E2 are the total energy in the outer and the inner shells, respectively. The Lorentz factor is related to the observer time as ~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 E2/E1 is small. Future multiwavelength 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 a small Lorentz factor, which is expected generically in the internal shock models for the GRBs.

Steepening of Afterglow Decay for Jets Interacting with Stratified Media

Abstract: We calculate light curves for gamma-ray burst afterglows when material ejected in the explosion is confined to a jet that propagates in a medium with a power-law density profile. The observed light-curve decay steepens by a factor of Γ2 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 edge effect is ~0.7 and is completed over one decade in observer time. For a preejected stellar wind (ρ ∝ r-2), β increases by ~0.4 over two decades in time as a result of the edge effect, and the steepening of the light curve as a result of 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 a very narrow opening angle of a few degrees or less, a case where 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 timescale of 3 days, cannot be explained by only the sideways expansion and the edge effects in a jet in a uniform interstellar medium—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 ~5°, and the energy in the explosion to be about 1051 ergs.

Energetics and Luminosity Function of Gamma-Ray Bursts

Abstract: Gamma-ray bursts (GRBs) 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 sight 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. The energy budget for an average GRB in this model is, however, same as in the uniform shell model. 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 2 orders of magnitude if the number of shells ejected along different lines of sight is 10 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, for δ-function energy distribution in explosions 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.

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

Abstract: We calculate the luminosity function for gamma-ray burst afterglows in some fixed observed frequency band and at some fixed elapsed time in observer frame (tobs) in two models—one in which the explosion takes place in a uniform density medium and another in which the density falls off as inverse square (expected for stellar winds). For photon energies greater than about 500 eV and tobs 103 s, the afterglow flux is independent of interstellar medium (ISM) density and luminosity functions for wind and uniform ISM are identical. We deduce from the width of the observed X-ray afterglow distribution, 5 hr after the burst, that the FWHM of the distribution for isotropic energy in explosion and the fractional energy in electrons (e) are each less than about 1 order of magnitude and the FWHM for the electron energy index is 0.6 or less.

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

Abstract: 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.

BeppoSAX confirmation of beamed afterglow emission from GRB990510

Abstract: 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.

Analytic Light-Curves of Gamma-Ray Burst Afterglows: Homogeneous versus Wind External Media

Abstract: Assuming an adiabatic evolution of a Gamma-Ray Burst (GRB) remnant interacting with an external medium, we calculate the injection, cooling, and absorption break frequencies, and the afterglow flux for plausible orderings of the break and observing frequencies. The analytical calculations are restricted to a relativistic remnant and, in the case of collimated ejecta, to the phase where there is an insignificant lateral expansion. Results are given for both a homogeneous external medium and for a wind ejected by the GRB progenitor. We compare the afterglow emission at different observing frequencies, for each type of external medium. It is found that observations at sub-millimeter frequencies during the first day provide the best way of discriminating between the two models. By taking into account the effect of inverse Compton scatterings on the electron cooling, a new possible time-dependence of the cooling break is identified. The signature of the up-scattering losses could be seen in the optical synchrotron emission from a GRB remnant interacting with a pre-ejected wind, as a temporary mild flattening of the afterglow decay. The up-scattered radiation itself should be detected in the soft X-ray emission from GRB remnants running into denser external media, starting few hours after the main event.

Afterglow Emission from Naked Gamma-Ray Bursts

Abstract: 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 $\Gamma^{-1}$. 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.

Source Depth for Solar p-Modes

Abstract: Theoretically calculated power spectra are comparable 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 greater than ~6 mHz is 180 (50) km for quadrupole (dipole) sources.

Source depth for solar p-modes

Abstract: 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.