Broad-band modelling of short gamma-ray bursts with energy injection from magnetar spin-down and its implications for radio detectability

B P Gompertz,G A Wynn,P T O'Brien,A J Van Der Horst,K Wiersema

doi:10.1093/mnras/stu2752

Abstract

The magnetar model has been proposed to explain the apparent energy injection in the X-ray light curves of short gamma-ray bursts (SGRBs), but its implications across the full broadband spectrum are not well explored. We investigate the broadband modelling of four SGRBs with evidence for energy injection in their X-ray light curves, applying a physically motivated model in which a newly formed magnetar injects energy into a forward shock as it loses angular momentum along open field lines. By performing an order of magnitude search for the underlying physical parameters in the blast wave, we constrain the characteristic break frequencies of the synchrotron spectrum against their manifestations in the available multi-wavelength observations for each burst. The application of the magnetar energy injection profile restricts the successful matches to a limited family of models that are self-consistent within the magnetic dipole spin-down framework.We produce synthetic light curves that describe how the radio signatures of these SGRBs ought to have looked given the restrictions imposed by the available data, and discuss the detectability of these signatures with present-day and near-future radio telescopes. Our results show that both the Atacama Large Millimetre Array and the upgraded Very Large Array are now sensitive enough to detect the radio signature within two weeks of trigger in most SGRBs, assuming our sample is representative of the population as a whole. We also find that the upcoming Square Kilometre Array will be sensitive to depths greater than those of our lower limit predictions.

Highlights

Gamma-ray bursts (GRBs) are extreme outbursts of electromagnetic radiation, releasing energies of the order of 1048–1052 erg in a relativistic outflow, when collimation of this outflow is accounted for (e.g. Cenko et al 2011)
The fit each model gave to other optical and UV observations was inspected for consistency, and those that violated upper limits or provided a poor match to the data were rejected. 16 models were found for GRB 051221A, 6 models were found for GRB 060614, 21 models were found for GRB 070714B, and 17 models were found for GRB 130603B
While it could be argued that the single detection in GRB 051221A is itself due to scintillation, the situation is even worse in GRB 130603B, where consecutive detections at 6.7 GHz and a further observation at 4.9 GHz cannot be matched by models without rising above multiple upper limits

Summary

Introduction

Gamma-ray bursts (GRBs) are extreme outbursts of electromagnetic radiation, releasing energies of the order of 1048–1052 erg in a relativistic outflow, when collimation of this outflow is accounted for (e.g. Cenko et al 2011). This extended emission (EE) was discovered in ∼1/3 of SGRBs (Norris & Bonnell 2006) It usually begins 10 s after the trigger, and while it often has a lower luminosity than the prompt emission, it can last for a few hundred seconds, implying that the total energy contained is comparable (Perley et al 2009). Those bursts that were believed to exhibit EE were catalogued by Norris, Gehrels & Scargle (2010), and that sample was updated and expanded in Gompertz et al (2013)

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