(ed.). Gravitational waves (IOP, 2001)(422s).

238 Sources of SGWBof interferometers). The radiation from a single source is not a problem, sinceit is easily distinguished from a stochastic background. The problem arises ifthere are many unresolved sources. (Of course this is a problem from the pointof view of the cosmological background, but the observation of the astrophysicalbackground would be very interesting in itself; techniques for the detection of thisbackground with a single interferometer using the fact that it is not isotropic andexploiting the sideral modulation of the signal have been discussed in [66].)The stochastic background from rotating neutron stars has been discussedin [67] and references therein. The main uncertainty comes from the estimateof the typical ellipticity ɛ of the neutron star, which measures its deviation fromsphericity. An upper bound on ɛ can be obtained assuming that the observedslowing down of the period of known pulsars is entirely due to the emission ofgravitational radiation. This is almost certainly a gross overestimate, since mostof the spin down is probably due to electromagnetic losses, at least for Crab-likepulsars. With realistic estimates for ɛ, [67] gives a value of h 2 0 gw(100 Hz) ∼10 −15 . This is very far from the sensitivity of even the advanced experiments. Anabsolute upper bound can be obtained assuming that the spin down is due only togravitational losses, and this gives h 2 0 gw(100 Hz) ∼ 10 −7 , but again this valueis probably a gross overestimate. Very recently the gravitational background hasalso been estimated [68] produced by a cosmological population of hot, youngand rapidly rotating neutron stars. Within a reasonable range of values of themain parameters which characterize the energy spectrum of a single source, theauthors of [68] find that h 2 0 gw( f ) show a long plateau extending from ≈300 Hzup to ≈1.7 kHz, with an amplitude of ≈(2.2–3.3) × 10 −8 .In [69] the stochastic background has been considered emitted by acosmological population of core-collapse supernovae for a range of progenitormasses leading to a black hole. The expected frequencies in this case are ofthe order of kHz or lower, depending on the redshift when these objects areproduced. Using the observational data on the star formation rate, it turnsout that the duty cycle, i.e. the ratio between the duration of a typical burstand the typical time interval between successive bursts is low, of order 0.01.Therefore, this background is not stochastic, but rather like a ‘pop noise’, andcan be distinguished from a really stochastic background. The value of h 2 0 gwfor the background from supernovae have been computed in [69] assumingaxially symmetric collapse, and assuming that all sources have the same valueof a = J/(GM 2 ), where J is the angular momentum. The results depend onthe value of a, and on h 0 . Assuming h 0 = 0.5 and typical values of a, onefinds that gw ( f ) has a maximum amplitude ranging between 10 −11 –10 −10 inthe frequency interval (1.5–2.5) kHz.These results suggest that astrophysical backgrounds might not be a problemfor the detection of a relic background at VIRGO/LIGO frequencies. Thesituation is different in the LISA frequency band [63, 65, 67, 70, 71]. LISA canreach a sensitivity of order h 2 0 gw ∼ afew×10 −13 at f ∼ 10 −3 Hz (see figure 1.3