Baryon Loaded Relativistic Blast Waves in Supernovae

Abstract

We provide a new analytic blast wave solution which generalizes the Blandford-McKee solution to arbitrary ejecta masses and Lorentz factors. Until recently relativistic supernovae have been discovered only through their association with long-duration gamma-ray bursts (GRBs). The blast waves of such explosions are well described by the Blandford-McKee (in the ultra-relativistic regime) and Sedov-Taylor (in the non-relativistic regime) solutions during their afterglows, as the ejecta mass is negligible in comparison to the swept-up mass. The recent discovery of the relativistic supernova SN 2009bb, without a detected GRB, opens up the possibility of highly baryon loaded, mildly relativistic outflows which remains in nearly free-expansion phase during the radio afterglow. In this work, we consider a massive, relativistic shell, launched by a Central Engine Driven EXplosion (CEDEX), decelerating adiabatically due to its collision with the pre-explosion circumstellar wind profile of the progenitor. We compute the synchrotron emission from relativistic electrons in the shock amplified magnetic field. This models the radio emission from the circumstellar interaction of a CEDEX. We show that this model explains the observed radio evolution of the prototypical SN 2009bb and demonstrate that SN 2009bb had a highly baryon loaded, mildly relativistic outflow. We discuss the effect of baryon loading on the dynamics and observational manifestations of a CEDEX. In particular, our predicted angular size of SN 2009bb is consistent with very long baseline interferometric (VLBI) upper limits on day 85, but is presently resolvable on VLBI angular scales, since the relativistic ejecta is still in the nearly free-expansion phase.

Radio Emission from the Cocoon of a GRB Jet: Implications for Relativistic Supernovae and Off-axis GRB Emission

“…Their spectral evolution is in fact consistent with that of a decelerating, mildly relativistic shock with R ∝ t m (with m = 0.8 − 0.9) and v sh ≈ 0.6 − 0.8 c, and an associated energy of ≈ 10 49 erg Chakraborti & Ray 2011;Margutti et al 2014;Chakraborti et al 2015;Milisavljevic et al 2015; see how- the dynamical evolution of a long gamma-ray burst jet. The color bar corresponds to the following density range (top to bottom panels, with larger densities in red and low densities in blue): (10 22 , 10 30 ) cm −3 ; (10 11 , 10 30 ) cm −3 ; (10 3 , 10 22 ) cm −3 ; (1,10 15 ) cm −3 .…”

X-RAY EMISSION FROM SN 2004dj: A TALE OF TWO SHOCKS

“…which has the same temporal evolution as derived in Chakraborti & Ray (2011). For the epochs at which it was observed in the radio This is much higher than the frequencies accessible with the EVLA, therefore synchrotron cooling will be unimportant for studying the radio light curves of SN 2004dj.…”

Jets in Hydrogen-poor Superluminous Supernovae: Constraints from a Comprehensive Analysis of Radio Observations

“…Relativistic SNe are characterized by mildly-relativistic ejecta, bright radio emission-but faint X-ray emission that clearly sets relativistic SNe apart from sub-energetic GRBs-and a kinetic energy profile E k (Γβ) (Fig. 6) that is suggestive of the presence of a central engine driving the explosion (Soderberg et al 2010b;Bietenholz et al 2010;Chakraborti & Ray 2011;Margutti et al 2014;Chakraborti et al 2015). These observed properties are attributed to a scenario where a jet is present but fails to successfully break through the stellar envelope, possibly due to a shorter-lived engine, or a larger envelope mass (Lazzati et al 2012;Margutti et al 2014, see also Mazzali et al 2008).…”