The Coalescence Rate of Double Neutron Star Systems

V Kalogera,J H Taylor,D N Spergel,R Narayan

doi:10.1086/321583

Abstract

We estimate the coalescence rate of close binaries with two neutron stars (NS) and discuss the prospects for the detection of NS-NS inspiral events by ground-based gravitational-wave observatories, such as LIGO. We derive the Galactic coalescence rate using the observed sample of close NS-NS binaries (PSR B1913+16 and PSR B1534+12) and examine in detail each of the sources of uncertainty associated with the estimate. Specifically, we investigate (i) the dynamical evolution of NS-NS binaries in the Galactic potential and the vertical scale height of the population, (ii) the pulsar lifetimes, (iii) the effects of the faint end of the radio pulsar luminosity function and their dependence on the small number of observed objects, (iv) the beaming fraction, and (v) the extrapolation of the Galactic rate to extragalactic distances expected to be reachable by LIGO. We find that the dominant source of uncertainty is the correction factor (up to about 200) for faint (undetectable) pulsars. All other sources are much less important, each with uncertainty factors smaller than 2. Despite the relatively large uncertainty, the derived coalescence rate is approximately consistent with previously derived upper limits, and is more accurate than rates obtained from population studies. We obtain a most conservative lower limit for the LIGO II detection rate of 2 events per year. Our upper limit on the detection rate lies between 300 to more than 1000 events per year.

Highlights

The importance of close binaries with two neutron stars (NS–NS) for gravitational wave physics was established a few years after the discovery of the prototype NS–NS system, the binary PSR B1913+16 (Hulse & Taylor 1975), with the measurement of orbital decay at a rate consistent with gravitational wave emission as predicted by general relativity (Taylor & Weisberg 1982; 1989; 1999, unpublished)
Based on our results on the NS–NS scale height we obtained S1913+16 = 45 − 60 and S1534+12 = 145 − 200. We combine these results with the estimated lifetimes of the two systems and obtain an estimate for the NS–NS coalescence rate in the range 2 − 4 × 10−7 yr−1
9We have explored the dependence of our results on R0 and z0 by running models for R0 = 8 kpc and z0 = 3 kpc and the changes are negligible. This Galactic rate must be further corrected for the fraction of coalescing NS–NS binaries with pulsars that do not beam in our direction

Summary

Introduction

The importance of close binaries with two neutron stars (NS–NS) for gravitational wave physics was established a few years after the discovery of the prototype NS–NS system, the binary PSR B1913+16 (Hulse & Taylor 1975), with the measurement of orbital decay at a rate consistent with gravitational wave emission as predicted by general relativity (at a 3 × 10−3 accuracy level) (Taylor & Weisberg 1982; 1989; 1999, unpublished) This orbital decay is expected to end catastrophically with the merger of the two neutron stars as the binary orbital separation becomes comparable to the NS radii (for a recent review, see Rasio & Shapiro 1999). Such Galactic estimates have been obtained in two different ways so far: empirically, based on the observed NS–NS sample, and purely theoretically, based on our understanding of NS–NS formation

Results

Discussion

Conclusion