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 the sources of gravitational waves (GWs) and the
leading theoretical models for short gamma-ray bursts (SGRBs). Based on the
observations of SGRBs, we could derive the merger rates of these compact
binaries, and study the stochastic GW backgrounds (SGWBs) or the co-detection
rates of GWs associate with SGRBs (GW-SGRBs). But before that, the most
important thing is to derive the GW spectrum from a single GW source. Usually,
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 the dynamical processes, and will merge with
residual eccentricities. The orbital eccentricity has important effect on GW
spectra, and therefore on the SGWB and GW-SGRB co-detection rate. Our results
show that the power spectra of the SGWBs from eccentric compact binaries are
greatly suppressed at low frequencies. Especially, SGWBs from binaries with
high residual eccentricities will hard to be detected (above the detection
frequency of $\sim100~\rm Hz$). For the co-detection rates of GW-SGRB events,
they could be $\sim1.4$ times higher than the circular case within some
particular ranges of $e_{\rm r}$ , but greatly reduced for high residual
eccentricities (e.g., $e_{\rm r}>0.1$ for BNSs). In general, the BBH
progenitors produce 200 and 10 times higher GW-SGRB events than the BNS and
NSBH progenitors, respectively. Therefore, binaries with low residual
eccentricities and high total masses will easier to be detected by aLIGO.
