Stochastic Background of Gravitational Waves Generated by Compact Binary Systems

The Gravitational Wave Background from Coalescing Compact Binaries: A New Method

“…where δz << 1, and z p is the value of redshift corresponding to each observed frequency by means of (13). Now, in order to calculate (14), dR can be written in the following form…”

“…Since we are considering that black holes have masses in the interval 5M ⊙ − 20M ⊙ , the emitted frequencies will have minimum and maximum values given by ν min = 114Hz and ν max = 997Hz, respectively. Moreover, considering (13) and (19), one notes that for each value of ν obs , one has continuous ranges of values for z and m bh . However, in the case of BHNS systems, (1) must be integrated over z but not over m bh , since these variables are not independent.…”

“…We present here the main steps for the calculation of dR/dV (we refer the reader to Refs. [12,13] for details).…”

“…When z min < 0 or z max > 20, we set z min = 0 and z max = 20, respectively. Once the interval of integration is set, the variables m bh and ν in the integral can be written as functions of z by solving (19) and (13).…”

“…At this point, one could ask in what the present study differs from the previous ones. We will see that the main difference has to do with the application of a new method to calculate dR developed in our previous papers [12,13].…”