GRB Afterglows from Anisotropic Jets

Some progenitor models of gamma-ray bursts (GRBs) (e.g., collapsars) may produce anisotropic jets in which the energy per unit solid angle is a power-law function of the angle ($\propto\theta^{-k}$). We calculate light curves and spectra for GRB afterglows when such jets expand either in the interstellar medium or in the wind medium. In particular, we take into account two kinds of wind: one ($n\propto r^{-3/2}$) possibly from a typical red supergiant star and another ($n\propto r^{-2}$) possibly from a Wolf-Rayet star. We find that in each type of medium, one break appears in the late-time afterglow light curve for small $k$ but becomes weaker and smoother as $k$ increases. When $k\ge 2$, the break seems to disappear but the afterglow decays rapidly. Thus, one expects that the emission from expanding, highly anisotropic jets provides a plausible explanation for some rapidly fading afteglows whose light curves have no break. We also present good fits to the optical afterglow light curve of GRB 991208. Finally, we argue that this burst might arise from a highly anisotropic jet expanding in the wind ($n\propto r^{-3/2}$) from a red supergiant to interpret the observed radio-to-optical-band afterglow data (spectrum and light curve).Comment: 12 pages + 10 figures, accepted by Ap

The Near Infrared and Multiwavelength Afterglow of GRB 000301c

We present near-infrared observations of the counterpart of GRB 000301c. The K' filter (2.1 micron) light curve shows a well-sampled break in the decay slope at t=3.5 days post-burst. The early time slope is very shallow (~ -0.1), while the late time slope is steep (-2.2). Comparison with the optical (R band) light curve shows marginally significant differences, especially in the early time decay slope (which is steeper in the optical) and the break time (which occurs later in the optical). This is contrary to the general expectation that light curve breaks should either be achromatic (e.g., for breaks due to collimation effects) or should occur later at longer wavelengths (for most other breaks). The observed color variations might be intrinsic to the afterglow, or might indicate systematic errors of > 0.08 magnitude in all fluxes. Even if the break is achromatic, we argue that its sharpness poses difficulties for explanations that depend on collimated ejecta. The R light curve shows further signs of fairly rapid variability (a bump, steep drop, and plateau) that are not apparent in the K' light curve. In addition, by combining the IR-optical-UV data with millimeter and radio fluxes, we are able to constrain the locations of the self-absorption break and cooling break and to infer the location of the spectral peak at t=3 days: f_nu = 3.4 mJy at nu=1e12 Hz. Using the multiwavelength spectral energy distribution, we are able to constrain the blast wave energy, which was E > 3e53 erg if the explosion was isotropic. This implies a maximum gamma ray production efficiency of ~ 0.15 for GRB 000301C.Comment: Accepted to The Astrophysical Journal. 24 pages, 4 figures, 3 tables; uses AASTeX 5 macros. This version includes a new figure (R-K' color vs. time), a better sampled R band light curve, and more extensive discussion of the optical data and error analysi

On the determination of age and mass functions of stars in young open star clusters from the analysis of their luminosity functions

Based on the CCD observations of remote young open clusters NGC 2383, NGC 2384, NGC 4103, NGC 4755, NGC 7510 and Hogg 15, we constructed their observed luminosity functions (LFs). The observed LFs are corrected for field star contamination determined with the help of galactic star count model. In the case of Hogg 15 and NGC 2383 we also considered the additional contamination from neighbouring clusters NGC 4609 and NGC 2384 respectively. These corrections provided the realistic pattern of cluster LF in the vicinity of the MS turn on point and at fainter magnitudes, revealed the so called H-feature arising due to transition of the Pre-MS phase to MS, which is dependent on the cluster age. The theoretical LFs were constructed representing a cluster population model with continuous star formation for a short time scale and a power law Initial Mass Function (IMF) and these were fitted to the observed LF. As a result we are able to determine for each cluster a set of parameters, describing cluster population (the age, duration of star formation, IMF slope and percentage of field star contamination). It was found that in spite of the non-monotonic behaviour of observed LFs, cluster IMFs can be described as the power law functions with slopes similar to Salpeter's value. The present MS turn on cluster ages are several times lower than those derived from the fitting of theoretical isochrones to the turn off region of the upper Main Sequences.Comment: 17 pages, 5 figures, To appear in MNRA

Energy Injection in GRB Afterglow Models

We extend the standard fireball model, widely used to interpret gamma-ray burst (GRB) afterglow light curves, to include energy injections, and apply the model to the afterglow light curves of GRB 990510, GRB 000301C and GRB 010222. We show that discrete energy injections can cause temporal variations in the optical light curves and present fits to the light curves of GRB 000301C as an example. A continuous injection may be required to interpret other bursts such as GRB 010222. The extended model accounts reasonably well for the observations in all bands ranging from X-rays to radio wavelengths. In some cases, the radio light curves indicate that additional model ingredients may be needed.Comment: Accepted for publication in the Astrophysical Journa

A Jet Model With a Hard Electron Distribution for the Afterglow of GRB 000301c

The parameters of the GRB 000301c afterglow are determined within the usual framework of synchrotron emission from relativistic ejecta, through fits to the available radio-to-optical data. It is found that 1) the jet energy after the GRB phase is ~3x10^{50} erg, 2) the initial opening angle of the jet is ~13 deg, 3) the medium that decelerates the afterglow has a density ~25/cm^3, 4) the power-law distribution of the shock-energized electrons is hard, with an index around 1.5, and 5) the cooling frequency was located below the optical domain. Furthermore we find that the collimation of ejecta alone cannot explain the sharp, large magnitude break observed in the R-band emission of this afterglow at few days, and that a high energy break in the electron distribution, corresponding to an electron energy close to equipartition, together with the lateral spreading of the jet accommodate better this break. Microlensing by a star in an intervening galaxy produces only a flattening of the afterglow emission and cannot explain the mild brightening exhibited by the optical emission of 000301c at ~4 days.Comment: to be published in the ApJ, v.556. Figures changed, one added. Other alterations are mino

Emission from Bow Shocks of Beamed Gamma-Ray Bursts

Beamed gamma-ray burst (GRB) sources produce a bow shock in their gaseous environment. The emitted flux from this bow shock may dominate over the direct emission from the jet for lines of sight which are outside the angular radius of the jet emission, theta. The event rate for these lines of sight is increased by a factor of 260*(theta/5_degrees)^{-2}. For typical GRB parameters, we find that the bow shock emission from a jet with half-angle of about 5 degrees is visible out to tens of Mpc in the radio and hundreds of Mpc in the X-rays. If GRBs are linked to supernovae, studies of peculiar supernovae in the local universe should reveal this non-thermal bow shock emission for weeks to months following the explosion.Comment: ApJ, submitted, 15 pages, 3 figure

Afterglow Emission from Highly Collimated Jets with Flat Electron Spectra: Application to the GRB 010222 Case?

We derive light curves of the afterglow emission from highly collimated jets if the power-law index ($p$) of the electron energy distribution is above 1 but below 2. We find (1) below the characteristic synchrotron frequency, the light curve index depends generally on $p$. (2) As long as the jet expansion is spherical, the light curve index above the characteristic frequency increases slowly as the spectral index of the emission increases. (3) Once the jet enters the spreading phase, the high-frequency emission flux decays as $\propto t^{-(p+6)/4}$ rather than $\propto t^{-p}$. All these results differ from those in the case of $p>2$. We compare our analytical results with the observations on the GRB 010222 afterglow, and conclude that the jet model may be unable to explain the observed data. Thus, a more promising explanation for this afterglow seems to be the expansion of a relativistic fireball or a mildly collimated jet in a dense medium.Comment: shortened version accepted for publication in ApJ Letter

GRB Energetics and the GRB Hubble Diagram: Promises and Limitations

We present a complete sample of 29 GRBs for which it has been possible to determine temporal breaks (or limits) from their afterglow light curves. We interpret these breaks within the framework of the uniform conical jet model, incorporating realistic estimates of the ambient density and propagating error estimates on the measured quantities. In agreement with our previous analysis of a smaller sample, the derived jet opening angles of those 16 bursts with redshifts result in a narrow clustering of geometrically-corrected gamma-ray energies about E_gamma = 1.33e51 erg; the burst-to-burst variance about this value is a factor of 2.2. Despite this rather small scatter, we demonstrate in a series of GRB Hubble diagrams, that the current sample cannot place meaningful constraints upon the fundamental parameters of the Universe. Indeed for GRBs to ever be useful in cosmographic measurements we argue the necessity of two directions. First, GRB Hubble diagrams should be based upon fundamental physical quantities such as energy, rather than empirically-derived and physically ill-understood distance indicators. Second, a more homogeneous set should be constructed by culling sub-classes from the larger sample. These sub-classes, though now first recognizable by deviant energies, ultimately must be identifiable by properties other than those directly related to energy. We identify a new sub-class of GRBs (``f-GRBs'') which appear both underluminous by factors of at least 10 and exhibit a rapid fading at early times. About 10-20% of observed long-duration bursts appear to be f-GRBs.Comment: Accepted to the Astrophysical Journal (20 May 2003). 19 pages, 3 Postscript figure

Floral resources of Karnataka: a geographic perspective

We compiled the data on the floral resources of Karnataka from diverse published sources and analysed the geographic patterns of distribution of floral diversity. Our database shows that Karnataka harbours 4758 species from 1408 genera and 178 families and accounts for about 27 per cent of the country's floral diversity. We computed the 'endemicity value' of different districts based on the number of endemic species (those restricted to a maximum of five districts) harboured by them and found that the most species-rich districts (viz. Uttara Kannada, Dakshina Kannada, Mysore, Hassan, Udupi and Kodagu) were also characterized by high values of endemicity while the species-poor districts had low values of endemicity. However, the relation between the species richness and endemicity of the districts was not linear; the species richness increases abruptly at lower levels of endemicity but plateaus off later at high levels of endemicity. Based on the number of species packed into the families, all the 27 districts segregated distinctly into three clusters that geographically correspond with the three major agro-climatic zones of the state. Our analysis showed that though the districts along the Western Ghats are florally rich, those along the dry tracts also harbour certain unique elements of the flora; thus these dry zone districts appear to be as important as those along the Western Ghats in conserving the floral resources

Wind Interaction Models for the Afterglows of GRB 991208 and GRB 000301C

The simplest model of the afterglows of the gamma-ray bursts (GRBs) envisions a spherical blast wave with a power-law distribution of electron energy above some cutoff running into a constant density medium. A refinement involves a narrow jet, often invoked to explain the steep decline and/or steepening of light curves observed in some afterglows. The constant (ambient) density jet model has been applied to GRBs 991208 and 000301C, based to a large extent on radio observations. We show that, for these two sources, a spherical wind model (with an $r^{-2}$ density ambient medium) can fit the radio data as well as the jet model. %%We demonstrate that the The relatively steep decline and the fairly abrupt steepening of the R-band light curves of, respectively, GRB 991208 and GRB 000301C can be accounted for with a non-standard, broken power-law distribution of electron energy. Our model predicts a slower late decline for the radio flux than does the jet model.Comment: 17 pages, submitted to Ap