3 years ago

# Imprints of the redshift evolution of double neutron star merger rate on the signal to noise ratio distribution.

K G Arun, Shilpa Kastha

Proposed third generation gravitational wave (GW) interferometers such as Einstein Telescope will have the sensitivity to observe double neutron star (DNS) mergers up to a redshift of $\sim 2$ with good signal to noise ratios. We argue that the measurement of {\it redshifted signal to noise ratio} defined by $\sigma=\rho (1+z)^{1/6}$, where $\rho$ is the signal to noise ratio (SNR) of a detected GW event and $z$ is its redshift can be used to study the distribution of DNS mergers. We show that if the DNS binaries are distributed uniformly within the co-moving volume, the distribution of redshifted SNR, $\sigma$, will be inversely proportional to the fourth power of $\sigma$, $p(\sigma)\propto \frac{1}{\sigma^4}$. We argue that the redshift evolution of DNS mergers will leave imprints on the distribution of $\sigma$ and hence this may provide a method to probe their redshift evolution. Using various parametric models for evolution of co-moving merger rate density as a function of redshift and assuming the sensitivity of Einstein Telescope, we discuss the distinguishability of the $\sigma$ distributions of these models with that of constant co-moving number density of the mergers.

Publisher URL: http://arxiv.org/abs/1801.05942

DOI: arXiv:1801.05942v1

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