Function: inspiral_dist()

void inspiral_dist(double *deff, double *z, double *Vc, double m1_z,
                   double m2_z, double snr, double S_h[], int npoint,
                   double srate, double h100)

This function computes the effective distance to which a binary inspiral with redshifted masses m1_z and m2_z can be seen with the noise spectrum S_h[].

It uses the energy spectrum

$${dE_{\rm gw}\over df} = {\pi^{2/3} \over 3}\mu M^{2/3} f^{-1/3}$$ (6.33.157)

to describe the inspiral for frequencies $f < f_{\rm merge} = 0.02/M$, and zero above $f_{\rm merge}$ (as in reference [13]). To convert from luminosity distance to redshift, it assumes a universe flat cosmology ($\Lambda=0$, $\Omega=1$) with a Hubble constant $H_0 = 75\,{\rm km}/{{\rm Mpc}\,{\rm sec}}$, and uses an Eq. (11) from [18]. To convert from redshift to comoving volume, it uses Eq. (27) of [19] or Eq. (2.56) with $q_0=1/2$ of [20].

The arguments to the function are:

deff: Output. The effective distance in megaparsecs.

z: Output. Redshift corresponding that effective distance.

Vc: Output. Comoving volume at the redshift in cubic megaparsecs.

m1_z: Input. Redshifted mass one, $(1+z)m_1$.

m2_z: Input. Redshifted mass two, $(1+z)m_2$.

snr: Input. The signal-to-noise ratio at which the effective distance is deff.

S_h: Input. The spectral density of noise in Hz$^{-1}$.

npoint: Input. The number of data points in S_h.

srate: Input. The sampling rate used to construct the noise spectrum, Hz.

h100: Input. The Hubble constant in units of 100 km/sec/Mpc.

Author: Scott Hughes, hughes@tapir.caltech.edu