Afterglow of binary neutron star merger

arXiv:1105.3302v1 [astro-ph.HE] 17 May 2011 Draft version November 13, 2018 Preprint typeset using LATEX style emulateapj v. 11/10/09 AFTERGLOW OF BINARY NEUTRON STAR MERGER Masaru Shibata1, Yudai Suwa1, Kenta Kiuchi1, and Kunihito Ioka2 Draft version November 13, 2018 ABSTRACT The merger of two neutron stars results often in a rapidly and differentially rotating hypermas- sive neutron star (HMNS). We show by numerical-relativity simulation that the magnetic-field profile around such HMNS is dynamically varied during its subsequent evolution, and as a result, electromag- netic radiation with a large luminosity ∼0.1B2R3Ωis emitted with baryon (B, R, and Ωare poloidal magnetic-field strength at stellar surface, stellar radius, and angular velocity of a HMNS). The pre- dicted luminosity of electromagnetic radiation, which is primarily emitted along the magnetic-dipole direction, is ∼1047(B/1013 G)2(R/10 km)3(Ω/104 rad/s) ergs/s, that is comparable to the luminosity of quasars. Subject headings: gamma-ray burst: general — magnetohydrodynamics (MHD) — methods: numerical — stars: neutron 1. INTRODUCTION Coalescence of binary neutron stars (BNS) is one of the most promising sources for next-generation kilo-meter size gravitational-wave detectors such as advanced LIGO, advanced VIRGO, and LCGT. Statistical studies have suggested that the detection rate of gravitational waves emitted by BNS will be ∼1–100 per year (Kalogera et al. 2007). Typical signal-to-noise ratio for such detection will be ∼10 or less. Thus, it will be crucial for the detec- tion of gravitational waves to find electromagnetic coun- terparts to the gravitational-wave signals. Short-hard gamma-ray bursts (SGRB) have been inferred to accom- pany with the BNS merger (Narayan et al. 1992; Piran 2004). However, this hypothesis relies on many uncertain assumptions; e.g., high magnetic-field strength or effi- cient pair annihilation of neutrino-antineutrino. In this article, we give a conservative estimate for the strength of electromagnetic signals based on a numerical-relativity simulation and show that a strong electromagnetic signal will indeed accompany with the BNS merger. BNS evolves due to gravitational radiation reaction and eventually merges. After the merger sets in, there are two possible fates (e.g., Shibata et al. (2005); Kiuchi et al. (2009)): If the total mass M is larger than a critical mass Mc, a black hole will be formed, while a hypermassive neutron star (HMNS) will be formed for M < Mc. The value of Mc depends strongly on the equation of state (EOS) of neutron stars, but the latest discovery of a high-mass neutron star with mass 1.97 ± 0.04M⊙(Demorest et al. 2010) indicates that the EOS is stiffand Mc may be larger than the typical total mass of the BNS ∼2.7M⊙(Stairs 2004). This indicates that HMNS is the likely outcome for many BNS mergers, at least temporarily (Hotokezaka et al. 2011). Neutron stars in nature have a strong magnetic field with typical field strength at the stellar surface 1011– 1013 G. One of the neutron stars in BNS often has field strength smaller than this typical value as ∼1010–1011 G 1 Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan 2 KEK Theory Center and the Graduate University for Ad- vanced Studies, Oho, Tsukuba 305-0801, Japan (Lorimer 2008), probably because of the accretion history of the first-formed neutron star during the formation of the second one. However, at least the second one is likely to have the typical magnetic-field strength. It is reasonable to believe that each neutron star in the inspiral phase (before the merger sets in) has an approx- imately dipole magnetic field as in the isolated one. Dur- ing the late inspiral phase and formation of a HMNS in the merger phase, its magnetic-field profile will be mod- ified due to magnetohydrodynamics (MHD) processes. However, in zeroth approximation, it would be safe to suppose that the dipole field is dominant. Due to this reason, we consider the evolution of a HMNS with dipole magnetic fields in the following. One of the most important properties of HMNS is that it is rapidly and differentially rotating (Shibata et al. 2005). The numerical simulations have shown that the typical angular velocity at its center is Ω>∼104 rad/s, much larger than that of ordinary pulsars, while at equa- torial surface it is ∼103 rad/s3. Because of the pres- ence of the differential rotation, the winding of magnetic fields is enhanced: Toroidal magnetic-field strength BT in HMNS increases linearly with time (t) in the pres- ence of seed poloidal (cylindrically radial) magnetic fields BP (BT increases as ∼BP Ωt). The increase of the magnetic-field strength results in the increase of mag- netic pressure. Because only dilute matter is present in the surface of HMNS, Alfv´en waves are likely to propa- gate near the rotational axis with ̟ <∼10 km, where ̟ = p x2 + y2, transporting electromagnetic energy generated in HMNS along

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