A Complete Reference of the Analytical Synchrotron External Shock Models of Gamma-Ray Bursts

Gamma-ray bursts are most luminous explosions in the universe. Their ejecta are believed to move towards Earth with a relativistic speed. The interaction between this "relativistic jet" and a circum burst medium drives a pair of (forward and reverse) shocks. The electrons accelerated in these shocks radiate synchrotron emission to power the broad-band afterglow of GRBs. The external shock theory is an elegant theory, since it invokes a limit number of model parameters, and has well predicted spectral and temporal properties. On the other hand, depending on many factors (e.g. the energy content, ambient density profile, collimation of the ejecta, forward vs. reverse shock dynamics, and synchrotron spectral regimes), there is a wide variety of the models. These models have distinct predictions on the afterglow decaying indices, the spectral indices, and the relations between them (the so-called "closure relations"), which have been widely used to interpret the rich multi-wavelength afterglow observations. This review article provides a complete reference of all the analytical synchrotron external shock afterglow models by deriving the temporal and spectral indices of all the models in all spectral regimes, including some regimes that have not been published before. The review article is designated to serve as a useful tool for afterglow observers to quickly identify relevant models to interpret their data. The limitations of the analytical models are reviewed, with a list of situations summarized when numerical treatments are needed.Comment: 119 pages, 45 figures, invited review accepted for publication in New Astronomy Review

The extension of variability properties in gamma-ray bursts to blazars

Both gamma-ray bursts (GRBs) and blazars have relativistic jets pointing at a small angle from our line of sight. Several recent studies suggested that these two kinds of sources may share similar jet physics. In this work, we explore the variability properties for GRBs and blazars as a whole. We find that the correlation between minimum variability timescale (MTS) and Lorentz factor, $\Gamma$, as found only in GRBs by Sonbas et al. can be extended to blazars with a joint correlation of $\rm MTS\propto\Gamma^{-4.7\pm0.3}$. The same applies to the $\rm MTS\propto \it L_{\gamma}^{\rm -1.0\pm0.1}$ correlation as found in GRBs, which can be well extended into blazars as well. These results provide further evidence that the jets in these two kinds of sources are similar despite of the very different mass scale of their central engines. Further investigations of the physical origin of these correlations are needed, which can shed light on the nature of the jet physics.Comment: 6 pages, 2 figures, accepted for publication in MNRA

A feedback-driven bubble G24.136+00.436: a possible site of triggered star formation

We present a multi-wavelength study of the IR bubble G24.136+00.436. The J=1-0 observations of $^{12}$CO, $^{13}$CO and C$^{18}$O were carried out with the Purple Mountain Observatory 13.7 m telescope. Molecular gas with a velocity of 94.8 km s$^{-1}$ is found prominently in the southeast of the bubble, shaping as a shell with a total mass of $\sim2\times10^{4}$ $M_{\odot}$. It is likely assembled during the expansion of the bubble. The expanding shell consists of six dense cores. Their dense (a few of $10^{3}$ cm$^{-3}$) and massive (a few of $10^{3}$ $M_{\odot}$) characteristics coupled with the broad linewidths ($>$ 2.5 km s$^{-1}$) suggest they are promising sites of forming high-mass stars or clusters. This could be further consolidated by the detection of compact HII regions in Cores A and E. We tentatively identified and classified 63 candidate YSOs based on the \emph{Spitzer} and UKIDSS data. They are found to be dominantly distributed in regions with strong emission of molecular gas, indicative of active star formation especially in the shell. The HII region inside the bubble is mainly ionized by a $\sim$O8V star(s), of the dynamical age $\sim$1.6 Myr. The enhanced number of candidate YSOs and secondary star formation in the shell as well as time scales involved, indicate a possible scenario of triggering star formation, signified by the "collect and collapse" process.Comment: 13 pages, 10 figures, 4 tables, accepted by Ap