Now consider the contribution of old NS population from other galaxies. For distances described by Euclidean geometry ( 100 Mpc) we may do a crude estimate as follows. For specific events, the rate within the volume V (Mpc-3) relates to the galactic event rate (e.g., Phinney 1991) as , where km s-1 Mpc-1 is the Hubble constant. Therefore, for a population of old NS within Mpc we obtain
ten times smaller than from galactic NS.
Going further away, however, cosmological effects become significant. Old NS population from other galaxies may fairly well be considered isotropic and of probably not strongly varying comoving density. Then we should use the mean photometric distance in (15) which is in the standard flat Friedman Universe is (if ). For limiting redshifts we find Gpc. The supernova rate even with strong evolutionary effets is per year (for baryonic content in stars ; see Jorgensen et al. (1997) for more detail), so we obtain .
We have shown that if the NS form ellipticity is present, the stochastic GR background produced by old NS population is naturally formed due to NS rotation braking. In the limiting case when only GR angular momentum loss causes NS spin-down, this background is independent on both exact value of the NS form ellipticity and frequency and can be detected by advanced LIGO/VIRGO interferometers. In reality, the magnetic field of NS causes more effective electromagnetic energy loss: to be insignificant, the magnetic field of a NS should be less than (see Eq. (17))
According to Urpin & Muslimov (1992), the magnetic field can decay very fastly provided that the field was initially concentrated in the outer crust layers with the density g cm-3, and such very low magnetic field for old NS may be possible. In the limiting case that the NS magnetic field does not decay at all (for example, if only accretion-induced field decay is possible in binary systems (Bisnovatyi-Kogan & Komberg 1974)), old NS should lose their energy through electromagnetic losses and be very slow rotators with periods of about a few seconds. Then the initial magnetic field distribution becomes crucial. If it is centered at G (as implied by radipulsar P - measurements), we have little chances to detect the old NS population at 10-100 Hz frequency band unless close mean distances ( 10 kpc) are assumed (Giazotto et al. 1997). However, if nature prefers a scale-free law (like ), the fraction of low-field NS could amount to a few and they can contribute to the frequency-independent GR background. Then Eq. (15) implies that such a background can be detected by the advanced LIGO/VIRGO interferometer in the frequency band 10-1000 Hz in one-year integration even if the formation rate of such NS is as small as 1 per 300 years and the characteristic distance to them is 100 kpc.
© European Southern Observatory (ESO) 1997
Online publication: April 8, 1998