Neutron Star Collapse Times, Gamma-Ray Bursts and Fast Radio Bursts
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MNRAS 441, 2433–2439 (2014) doi:10.1093/mnras/stu720 The birth of black holes: neutron star collapse times, gamma-ray bursts and fast radio bursts ‹ Vikram Ravi1,2 and Paul D. Lasky1 Downloaded from https://academic.oup.com/mnras/article-abstract/441/3/2433/1126394 by California Institute of Technology user on 24 June 2019 1School of Physics, University of Melbourne, Parkville, VIC 3010, Australia 2CSIRO Astronomy and Space Science, Australia Telescope National Facility, PO Box 76, Epping, NSW 1710, Australia Accepted 2014 April 8. Received 2014 April 7; in original form 2013 November 29 ABSTRACT Recent observations of short gamma-ray bursts (SGRBs) suggest that binary neutron star (NS) mergers can create highly magnetized, millisecond NSs. Sharp cut-offs in X-ray afterglow plateaus of some SGRBs hint at the gravitational collapse of these remnant NSs to black holes. The collapse of such ‘supramassive’ NSs also describes the blitzar model, a leading candidate for the progenitors of fast radio bursts (FRBs). The observation of an FRB associated with an SGRB would provide compelling evidence for the blitzar model and the binary NS merger scenario of SGRBs, and lead to interesting constraints on the NS equation of state. We predict the collapse times of supramassive NSs created in binary NS mergers, finding that such stars collapse ∼10–4.4 × 104 s (95 per cent confidence) after the merger. This directly impacts observations targeting NS remnants of binary NS mergers, providing the optimal window for high time resolution radio and X-ray follow-up of SGRBs and gravitational wave bursts. Key words: black hole physics – equation of state – gamma-ray burst: general – stars: magne- tars – radio continuum: general. the resulting outwardly propagating magnetic shock dissipates as 1 INTRODUCTION a short, intense radio burst (Dionysopoulou et al. 2013; Falcke & Fast radio bursts (FRBs; Lorimer et al. 2007; Keane et al. 2012; Rezzolla 2014). Thornton et al. 2013) are among the most exciting astronomical dis- The merger of two NSs is one possible formation channel for coveries of the last decade. They are intense, millisecond-duration supramassive NSs. In general, there are three possible outcomes broad-band bursts of radio waves so far detected in the 1.2–1.6 GHz of such a merger, which, for a given NS equation of state (EOS), −3 band, with dispersion measures between 300 and 1200 cm pc. depend on the nascent NS mass, Mp, and angular momentum dis- FRBs are not associated with any known astrophysical object. Their tribution. These outcomes are as follows. anomalously large dispersion measures, given their high Galactic (i) If M ≤ M ,whereM is the maximum non-rotating latitudes, combined with the observed effects of scattering consis- p TOV TOV mass, the NS will settle to an equilibrium state that is uniformly tent with propagation through a large ionized volume (Lorimer et al. rotating and eternally stable (e.g. Giacomazzo & Perna 2013). 2007; Thornton et al. 2013), suggest a cosmological origin for FRBs (ii) If M > M , and if magnetic braking has caused the star (although see Burke-Spolaor et al. 2011; Bannister & Madsen 2014; p TOV to rotate uniformly (see below), it will survive for 1 s as a supra- Loeb, Shvartzvald & Maoz 2014). massive star until centrifugal support is reduced to the point where Numerous physical mechanisms have been suggested to produce the star collapses to a black hole (e.g. Duez et al. 2006). FRBs at cosmological distances, including magnetar hyperflares (iii) If M is greater than the maximum mass that may be sup- (e.g. Popov & Postnov 2013), binary white dwarf (Kashiyama, Ioka p ported by uniform rotation, the NS may either instantly collapse to &Mesz´ aros´ 2013)orneutronstar(NS;Totani2013) mergers, and a black hole or survive for 10−100 ms as a hypermassive star sup- the collapse of supramassive NSs to form black holes (Falcke & ported by differential rotation and thermal pressures (e.g. Baiotti, Rezzolla 2014). Here, we focus on the latter mechanism, termed Giacomazzo & Rezzolla 2008;Kiuchietal.2009; Rezzolla et al. the ‘blitzar’ model. A supramassive NS is one that has a mass 2011; Hotokezaka et al. 2013). greater than the non-rotating maximum mass, but is supported from collapse by rotation. As these stars spin down, they lose centrifugal Gamma-ray bursts (GRBs) with short durations (2 s) and hard support and eventually collapse to black holes. When magnetic spectra are associated with the coalescences of compact object bina- field lines cross the newly formed horizon, they snap violently, and ries, i.e. either NS–NS or NS–black hole mergers (Lee & Ramirez- Ruiz 2007; Nakar 2007;Berger2013). However, the emission mech- anisms of short GRBs (SGRBs) are not well understood. From E-mail: [email protected] a theoretical standpoint, a short-lived, collimated, relativistic jet C 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 2434 V. Ravi and P. D. Lasky can be launched from both black hole (e.g. Rezzolla et al. 2011) decline in the plateau phase of an SGRB X-ray light curve would and NS (e.g. Metzger, Quataert & Thompson 2008) remnants of provide powerful evidence for the protomagnetar model for SGRBs, compact binary coalescences, as necessitated by the ‘relativistic as well as the blitzar model of FRBs. FRB/SGRB associations may fireball’ model of prompt GRB emission (e.g. Piran 1999;Lee& also be used to characterize the intergalactic baryon content of the Ramirez-Ruiz 2007; Nakar 2007). Jet launching through magnetic Universe (Deng & Zhang 2014) through measurements of FRB dis- acceleration requires a short-lived (∼0.1–1 s) accretion disc, and persion measures and SGRB redshifts. Our results also provide a toroidal and small-opening-angle poloidal magnetic fields that are quantitative guide to interpreting observations of declines in SGRB Downloaded from https://academic.oup.com/mnras/article-abstract/441/3/2433/1126394 by California Institute of Technology user on 24 June 2019 both ∼1015 G (e.g. Komissarov et al. 2009). Numerical simulations X-ray light curves (Rowlinson et al. 2013) in the context of supra- of the merger of two 1.5 M NSs with 1012 G poloidal magnetic massive protomagnetar collapse. In particular, secure measurements fields (Rezzolla et al. 2011) result in a black hole remnant with the of the lifetimes of supramassive NSs produced in binary NS merg- necessary conditions, where the magnetic field is amplified through ers allow for interesting new constraints to be placed on the EOS of magnetohydrodynamic instabilities, to launch a jet with an energy nuclear matter (Lasky et al. 2014). output of ∼1.2 × 1051 erg. This is consistent with SGRB observa- Mergers of binary NSs are prime candidate sources for ground- tions (Lee & Ramirez-Ruiz 2007; Nakar 2007). Simulations of a based gravitational wave (GW) interferometers (Abadie et al. 2010). lower mass NS binary coalescence by Giacomazzo & Perna (2013) However, the collimated nature of SGRBs (e.g. Burrows et al. 2006) resulted in a stable millisecond ‘protomagnetar’, although the small- implies not all GW events will be associated with SGRBs. Some scale instabilities required to amplify the magnetic field to ∼1015 G alternative EM signals of GW bursts (Gao et al. 2013; Zhang 2013) were unresolved. On the other hand, high-resolution simulations rely on the births of stable or supramassive NSs acting as central of isolated NSs (e.g. Duez et al. 2006) show that magnetic field engines, implying that the time-scales for these signals are sensi- amplification to ∼1015 G and accretion disc formation is possi- tively related to the lifetimes of the nascent NSs and therefore the ble for nascent protomagnetars, suggesting that protomagnetars can calculations performed herein. power prompt SGRB emission through magnetically accelerated We show that, if a binary NS merger remnant does not collapse jets. Baryon-free energy deposition through neutrino–antineutrino in the first ∼4.4 × 104 s after formation, it is unlikely to collapse annihilation, driven by accretion on to protomagnetars, is another at all (97.5 per cent confidence). That is, almost all supramassive mechanism to power prompt SGRBs (Metzger et al. 2008). In this NSs born from binary NS mergers will collapse to form black holes paper, we assume that nascent protomagnetars formed through bi- within ∼4.4 × 104 s. In Section 2, we summarize our method for nary NS coalescences can power prompt SGRB emission, although calculating the range of collapse times of merger remnants. We we note that a deeper understanding is still required. check the consistency of this method against a sample of SGRBs The most attractive characteristic of the protomagnetar model for with X-ray plateaus from Rowlinson et al. (2013) in Section 3. SGRBs is its ability to explain features of the X-ray afterglows (Gao In Section 4, we generalize our calculations to the full population &Fan2006; Metzger et al. 2008). Lasting a few hundred seconds of binary NS merger remnants, and we present our conclusions in following the initial burst, these features are either extremely bright Section 5. (up to 30 times the fluence of the prompt emission; Perley et al. 2009) and variable on time-scales comparable to prompt emission 2 PREDICTING SUPRAMASSIVE NEUTRON variability, or smoothly decaying plateaus (Rowlinson et al. 2013). STAR COLLAPSE TIMES Both features are difficult to explain through, for example, fall-back accretion on to black hole central engines (Metzger et al. 2008;Buc- The problem of identifying the spin-down torques on nascent NSs ciantini et al. 2012, and references therein), although see Siegel, has been extensively studied over the last 50 years, with the pri- Ciolfi & Rezzolla (2014).