Short gamma-ray bursts at the dawn of the gravitational wave era

¹ INAF–Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy
e-mail: giancarlo.ghirlanda@brera.inaf.it
² Dipartimento di Fisica G. Occhialini, Università di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
³ Istituto Nazionale di Fisica Nucleare (INFN) – sede di Milano Bicocca, piazza della Scienza 3, 20123 Milano, Italy
⁴ Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy
⁵ INAF–IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁶ Astroparticule et Cosmologie APC, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cité, 75205 Paris, France
⁷ Laboratoire Univers et Particules de Montpellier, Université Montpellier 2, 34095 Montpellier, France
⁸ Universitá degli studi di Urbino “Carlo Bo”, via Saffi 2, 61029 Urbino, Italy
⁹ INFN, Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
¹⁰ Physics Department, University of Trento, via Sommarive 14, 38123 Trento, Italy
¹¹ INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, via Sommarive 14, 38123 Trento, Italy
¹² AIM, UMR 7158 CEA/DSM-CNRS-Université Paris Diderot, Irfu/Service d’Astrophysique, Saclay, France
¹³ GEPI, Observatoire de Paris, CNRS, Univ. Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France
¹⁴ Università degli Studi di Milano, Physics Department, via Giovanni Celoria 16, 20133 Milano, Italy

Received: 24 May 2016
Accepted: 24 July 2016

Abstract

We derive the luminosity function φ(L) and redshift distribution Ψ(z) of short gamma-ray bursts (SGRBs) using all the available observer-frame constraints (i.e. peak flux, fluence, peak energy and duration distributions) of the large population of Fermi SGRBs and the rest-frame properties of a complete sample of SGRBs detected by Swift. We show that a steep φ(L) ∝ L^{− α} with α ≥ 2.0 is excluded if the full set of constraints is considered. We implement a Markov chain Monte Carlo method to derive the φ(L) and Ψ(z) functions assuming intrinsic E_p−L_iso and E_p−E_iso correlations to hold or, alternatively, that the distributions of intrinsic peak energy, luminosity, and duration are independent. To make our results independent from assumptions on the progenitor (NS−NS binary mergers or other channels) and from uncertainties on the star formation history, we assume a parametric form for the redshift distribution of the population of SGRBs. We find that a relatively flat luminosity function with slope ~0.5 below a characteristic break luminosity ~3 × 10⁵² erg s^-1 and a redshift distribution of SGRBs peaking at z ~ 1.5−2 satisfy all our constraints. These results also hold if no E_p−L_iso and E_p−E_iso correlations are assumed and they do not depend on the choice of the minimum luminosity of the SGRB population. We estimate, within ~200 Mpc (i.e. the design aLIGO range for the detection of gravitational waves produced by NS−NS merger events), that there should be 0.007−0.03 SGRBs yr^-1 detectable as γ-ray events. Assuming current estimates of NS−NS merger rates and that all NS−NS mergers lead to a SGRB event, we derive a conservative estimate of the average opening angle of SGRBs ⟨ θ_jet ⟩ ~ 3°−6°. The luminosity function implies a prompt emission average luminosity ⟨L⟩ ~ 1.5 × 10⁵² erg s^-1, higher by nearly two orders of magnitude than previous findings in the literature, which greatly enhances the chance of observing SGRB “orphan” afterglows. Effort should go in the direction of finding and identifying such orphan afterglows as counterparts of GW events.