Short gamma-ray bursts and gravitational-wave observations from eccentric compact binaries

Mergers of compact binaries, such as binary neutron stars (BNSs), neutron star-black hole binaries (NSBHs) and binary black holes (BBHs), are expected to be the best candidates for sources of gravitational waves (GWs) and the leading theoretical models for short gamma-ray bursts (SGRBs). Based on observations of SGRBs, we can derive the merger rates of these compact binaries and study stochastic GW backgrounds (SGWBs) or the co-detection rates of GWs associated with SGRBs (GW-SGRBs). Before that, however, the most important thing is to derive the GW spectrum from a single GW source. Usually, a GW spectrum from a circular-orbit binary is assumed. However, observations of the large spatial offsets of SGRBs from their host galaxies imply that SGRB progenitors may be formed by dynamical processes and will merge with residual eccentricities (e_r). The orbital eccentricity has an important effect on GW spectra and therefore on the SGWB and GW-SGRB co-detection rate. Our results show that the power spectra of SGWBs from eccentric compact binaries are greatly suppressed at low frequencies (e.g. f ≲ 1 Hz). In particular, SGWBs from binaries with high residual eccentricities (e.g. e_r ≳ 0.1 for BNSs) will be hard to detect (above the detection frequency of ∼ 100 Hz). Regarding the co-detection rates of GW-SGRB events, they could be ∼1.4 times higher than the circular case within some particular ranges of e_r (e.g. 0.01 ≲ e_r ≲ 0.1 for BBHs), but greatly reduced for high residual eccentricities (e.g. e_r > 0.1 for BNSs). In general, BBH progenitors produce 200 and 10 times higher GW-SGRB events than BNS and NSBH progenitors, respectively. Therefore, binaries with low residual eccentricities (e.g. 0.001 ≲ e_r ≲ 0.1) and high total masses will be easier to detect by Advanced LIGO (aLIGO). However, only a small fraction of BBHs can be SGRB progenitors (if they can produce SGRBs), because the predicted GW-SGRB event rate (60∼100 per year) is too high compared with recent observations, unless they merge with high residual eccentricities (e.g. e_r > 0.7).