The first large wide-band gravitational interferometric antennas, the French-Italian VIRGO and the American LIGO, should be fully operational at the beginning of the next century. The expected sensitivity of these detectors in terms of the gravitational strain is of the order of h for short-lived, impulsive bursts, and h for periodic "long-lived" sources for which integration times of about 107 s are possible. Clearly, a major concern of these detectors is to understand and minimize the sources of noise which define the sensitivity of the antenna, but the identification of a possible "standard" source (or sources), having a well defined waveform, is also a relevant problem in the context of the signal detection.
Among the possible candidates, it is expected that neutron stars, which are known to be quite abundant in the Galaxy, could rank among conspicuous emitters of gravitational waves (GW). Rotating neutron stars may have a time-varying quadrupole moment and hence radiate GW, by either having a triaxial shape or a misalignment between the symmetry and the spin axes, which produces a wobble in the stellar motion (Ferrari & Ruffini 1969; Zimmerman & Szedenits 1979; Shapiro & Teukolsky 1983; de Araújo et al. 1994). Moreover, fast rotating proto-neutron stars may develop different instabilities such as the so-called Chandrasekhar-Friedman - Schutz (CFS) instability (Chandrasekhar 1970; Friedman & Schutz 1978), responsible for the excitation of density waves traveling around the star in the sense opposite to its rotation, or to undergo a transition from axi-symmetric to triaxial shapes through the dynamical "bar"-mode instability (Lai & Shapiro 1995). All these mechanisms are potentially able to emit large amounts of energy in the form of GW.
Continuous GW emission by the entire population of rotating neutron stars, assumed to have small deviations from axisymmetry, raises the possibility of detecting their combined signals. The contribution of individual observed sources, like galactic pulsars, has been considered by Barone et al. (1988), Velloso et al. (1996), among others. However, detected radio pulsars constitute only a small fraction of the actual galactic population. Attempts to estimate the gravitational strain of the total pulsar population have been made by Schutz (1991), Giazotto et al. (1997, hereafter GBG97), de Freitas Pacheco & Horvath (1997), Giamperi (1998). Excepting Schutz (1991), all these authors proposed to detect the square of the gravitational strain, and the sidereal modulation of the integrated signal was examined by GBG97 as well by Giamperi (1998). In order to perform such an estimation, the actual distribution of the rotation periods must be known. The rotation period is a critical parameter, because the gravitational strain depends on the square of the angular velocity. Unfortunately, the observed distribution does not necessarily reflect the real period distribution due to different selection effects present in all pulsar searches. GBG97 assumed for their estimate an (optimistic) average rotation period of 5 ms, which now seems a rather short value. If we exclude binary millisecond pulsars, which have probably been spun-up by accretion mechanisms, several observational facts indicate that population I pulsars are born with smaller rotation velocities (Bhattacharya 1990). Moreover, several population synthesis calculations also suggest higher initial periods (Narayan 1987; Bhattacharya et al. 1992). Magnetic coupling between the proto-neutron star and the outer envelope could be an efficient mechanism for transferring angular momentum, so reducing the initial angular velocity. Proto-neutron stars are expected to be hot, with temperatures around 109 K. In this situation, depending on the viscosity, a rapidly rotating proto-neutron star may excite r-modes, emitting GW which decelerates considerably the star. According to computations by Andersson et al. (1999), this mechanism sets a limit around P 20 ms for the fastest newly born neutron stars. However, it should be emphasized that this value is a function of the adopted (uncertain) viscosity law.
In the present work we revisit the problem of the contribution to the continuous GW emission from the pulsar population inside the galactic disk. We estimate the actual period distribution by using population synthesis based on Monte Carlo methods, looking for the best pulsar population parameters by comparing our simulation results with data. Using the model population, we compute the gravitational strain for each pulsar emitting GW in the frequency band of VIRGO, the total square of the signal as well the amplitude modulation due to the sidereal motion. We show, in agreement with the expectations made by de Freitas Pacheco & Horvath (1997), that the signal is strongly dominated by a few fast pulsars and/or by the nearest ones. The plan of this paper is the following: in Sect. 2 we describe our population synthesis method; in Sect. 3 we present the properties of the simulated population; in Sect. 4 we estimate the contribution to the continuous gravitational strain of such a population and finally, in Sect. 5 we present our main conclusions.
© European Southern Observatory (ESO) 2000
Online publication: June 30, 2000