ELECTROMAGNETIC EMISSION FROM LONG-LIVED BINARY NEUTRON STAR MERGER REMNANTS. I. FORMULATION OF THE PROBLEM

Binary neutron star (BNS) mergers are the leading model to explain the phenomenology of short gamma-ray bursts (SGRBs). Recent observations of long-lasting X-ray afterglows of SGRBs challenge standard paradigms and indicate that in a large fraction of events a long-lived neutron star (NS) may be formed rather than a black hole. Understanding the mechanisms underlying these afterglows is necessary in order to address the open questions concerning the nature of SGRB central engines. However, recent theoretical progress has been hampered by the fact that the timescales of interest for the afterglow emission are inaccessible to numerical relativity simulations. Here we present a detailed model to bridge the gap between numerical simulations of the merger process and the relevant timescales for the afterglows, assuming that the merger results in a long-lived NS. This model is formulated in terms of a set of coupled differential equations that follow the evolution of the post-merger system and predict its electromagnetic (EM) emission in a self-consistent way, starting from initial data that can be extracted from BNS merger simulations. The model presented here also allows us to search for suitable EM counterparts for multimessenger astronomy, which is expected to become reality within the next few years thanks to ground-based GW detectors such as advanced LIGO and Virgo. This paper discusses the formulation and implementation of the model. In a companion paper, we employ this model to predict the EM emission from similar to 10(-2) to similar to 10(7) s after a BNS merger and discuss the implications in the context of SGRBs and multimessenger astronomy.