Modeling the late-time merger ejecta emission in short gamma ray bursts

The short gamma ray bursts (GRBs) are the aftermath of the merger of binary compact objects (neutron star–neutron star or neutron star–black hole systems). With the simultaneous detection of gravitational wave (GW) signal from GW 170817 and GRB 170817A, the much-hypothesized connection between GWs and short GRBs has been proved beyond doubt. The resultant product of the merger could be a millisecond magnetar or a black hole depending on the binary masses and their equation of state. In the case of a magnetar central engine, fraction of the rotational energy deposited to the emerging ejecta produces late-time synchrotron radio emission from the interaction with the ambient medium. In this paper, we present an analysis of a sample of short GRBs located at a redshift of z≤0.16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z \le 0.16$$\end{document}, which were observed at the late-time to search for the emission from merger ejecta. Our sample consists of seven short GRBs, which have radio upper limits available from very large array and Australian telescope compact array observations. We generate the model light curves using the standard magnetar model incorporating the relativistic correction. Using the model light curves and upper limits we constrain the number density of the ambient medium to be 10-5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-5}$$\end{document}–10-3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-3}$$\end{document} cm-3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-3}$$\end{document} for rotational energy of the magnetar Erot∼5×1051\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\mathrm{rot} \sim 5\times 10^{51}$$\end{document} erg. Variation in ejecta mass does not play a significant role in constraining the number density.