The Variation of Integrated Star IMFs among Galaxies

The integrated galaxial initial mass function (IGIMF) is the relevant distribution function containing the information on the distribution of stellar remnants, the number of supernovae and the chemical enrichment history of a galaxy. Since most stars form in embedded star clusters with different masses the IGIMF becomes an integral of the assumed (universal or invariant) stellar IMF over the embedded star-cluster mass function (ECMF). For a range of reasonable assumptions about the IMF and the ECMF we find the IGIMF to be steeper (containing fewer massive stars per star) than the stellar IMF, but below a few Msol it is invariant and identical to the stellar IMF for all galaxies. However, the steepening sensitively depends on the form of the ECMF in the low-mass regime. Furthermore, observations indicate a relation between the star formation rate of a galaxy and the most massive young stellar cluster in it. The assumption that this cluster mass marks the upper end of a young-cluster mass function leads to a connection of the star formation rate and the slope of the IGIMF above a few Msol. The IGIMF varies with the star formation history of a galaxy. Notably, large variations of the IGIMF are evident for dE, dIrr and LSB galaxies with a small to modest stellar mass. We find that for any galaxy the number of supernovae per star (NSNS) is suppressed relative to that expected for a Salpeter IMF. Dwarf galaxies have a smaller NSNS compared to massive galaxies. For dwarf galaxies the NSNS varies substantially depending on the galaxy assembly history and the assumptions made about the low-mass end of the ECMF. The findings presented here may be of some consequence for the cosmological evolution of the number of supernovae per low-mass star and the chemical enrichment of galaxies of different mass.Comment: 27 pages, accepted for publication by Ap

CCD photometric and mass function study of 9 young Large Magellanic Cloud star clusters

We present CCD photometric and mass function study of 9 young Large Magellanic Cloud star clusters namely NGC 1767, NGC 1994, NGC 2002, NGC 2003, NGC 2006, SL 538, NGC 2011, NGC 2098 and NGC 2136. The BVRI data reaching down to V ~ 21 mag, are collected from 3.5-meter NTT/EFOSC2 in sub-arcsec seeing conditions. For NGC 1767, NGC 1994, NGC 2002, NGC 2003, NGC 2011 and NGC 2136, broad band photometric CCD data are presented for the first time. Seven of the 9 clusters have ages between 16 to 25 Myr while remaining two clusters have ages $32\pm4$ Myr (NGC 2098) and $90\pm10$ Myr (NGC 2136). For 7 younger clusters, the age estimates based on a recent model and the integrated spectra are found to be systematically lower ($\sim$ 10 Myr) from the present estimate. In the mass range of $\sim 2 - 12$ $M_{\odot}$, the MF slopes for 8 out of nine clusters were found to be similar with the value of $\gamma$ ranging from $-1.90\pm0.16$ to $-2.28\pm0.21$. For NGC 1767 it is flatter with $\gamma = -1.23\pm0.27$. Mass segregation effects are observed for NGC 2002, NGC 2006, NGC 2136 and NGC 2098. This is consistent with the findings of Kontizas et al. for NGC 2098. Presence of mass segregation in these clusters could be an imprint of star formation process as their ages are significantly smaller than their dynamical evolution time. Mean MF slope of $\gamma = -2.22\pm0.16$ derived for a sample of 25 young ($\le 100$ Myr) dynamically unevolved LMC stellar systems provide support for the universality of IMF in the intermediate mass range $\sim 2-12 M_{\odot}$.Comment: To appear in MNRA

Optical Observations and Multiband Modelling of the Afterglow of GRB 041006: Evidence of A Hard Electron Energy Spectrum

We present the CCD Cousins R band photometric observations of the afterglow of GRB 041006. The multiband afterglow evolution is modelled using an underlying `hard' electron energy spectrum with a $p_1 \sim 1.3$. The burst appears to be of very low energy ($E \sim 10^{48}$ ergs) confined to a narrow cone of opening angle $\theta \sim 2.3^{\circ}$. The associated supernova is compared with SN1998bw and is found to be brighter.Comment: Accepted for publication in Bull. Astr. Soc. India (BASI

Effect of shape anisotropy on transport in a 2-dimensional computational model: Numerical simulations showing experimental features observed in biomembranes

We propose a 2-d computational model-system comprising a mixture of spheres and the objects of some other shapes, interacting via the Lennard-Jones potential. We propose a reliable and efficient numerical algorithm to obtain void statistics. The void distribution, in turn, determines the selective permeability across the system and bears a remarkable similarity with features reported in certain biological experiments.Comment: 1 tex file, 2 sty files and 5 figures. To appear in Proc. of StatPhys conference held in Calcutta, Physica A 199

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 Late-Time Flattening of Afterglow Light Curves

We present a sample of radio afterglow light curves with measured decay slopes which show evidence for a flattening at late times compared to optical and X-ray decay indices. The simplest origin for this behavior is that the change in slope is due to a jet-like outflow making a transition to sub-relativistic expansion. This can explain the late-time radio light curves for many but not all of the bursts in the sample. We investigate several possible modifications to the standard fireball model which can flatten late-time light curves. Changes to the shock microphysics which govern particle acceleration, or energy injection to the shock (either radially or azimuthally) can reproduce the observed behavior. Distinguishing between these different possibilities will require simultaneous optical/radio monitoring of afterglows at late times.Comment: ApJ, submitte

Continued Radio Monitoring of the Gamma Ray Burst 991208

We present radio observations of the afterglow of the bright gamma-ray burst GRB 991208 at frequencies of 1.4, 4.9 and 8.5 GHz, taken between two weeks and 300 days after the burst. The well-sampled radio light curve at 8.5 GHz shows that the peak flux density peaked about 10 days after the burst and decayed thereafter as a power-law t^-1.07. This decay rate is more shallow than the optical afterglow with t^-2.2, which was measured during the first week. These late-time data are combined with extensive optical, millimeter and centimeter measurements and fitted to the standard relativistic blast wave model. In agreement with previous findings, we find that an isotropic explosion in a constant density or wind-blown medium cannot explain these broadband data without modifying the assumption of a single power-law slope for the electron energy distribution. A jet-like expansion provides a reasonable fit to the data. In this case, the flatter radio light curve compared to the optical may be due to emission from an underlying host galaxy, or due to the blastwave making a transition to non-relativistic expansion. The model that best represents the data is a free-form model in which it is assumed that the broadband emission originates from a synchrotron spectrum, while the time-evolution of the break frequencies and peak flux density are solved for explicitly. Although the decay indices for most of the synchrotron parameters are similar to the jet model, the evolution of the cooling break is unusually rapid, and therefore requires some non-standard evolution in the shock. (abridged)Comment: ApJ, in pres

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