Possible sources of gravitational wave bursts detectable today

We discuss the possibility that galactic gravitational wave sources might give burst signals at a rate of several events per year, detectable by state-of-the-art detectors. We are stimulated by the results of the data collected by the EXPLORER and NAUTILUS bar detectors in the 2001 run, which suggest an excess of coincidences between the two detectors, when the resonant bars are orthogonal to the galactic plane. Signals due to the coalescence of galactic compact binaries fulfill the energy requirements but are problematic for lack of known candidates with the necessary merging rate. We examine the limits imposed by galactic dynamics on the mass loss of the Galaxy due to gravitational wave (GW) emission, and we use them to put constraints also on the GW radiation from exotic objects, like binaries made of primordial black holes. We discuss the possibility that the events are due to GW bursts coming repeatedly from a single or a few compact sources. We examine different possible realizations of this idea, such as accreting neutron stars, strange quark stars, and the highly magnetized neutron stars (“magnetars”) introduced to explain soft gamma repeaters. Various possibilities are excluded or appear very unlikely, while others at present cannot be excluded.

Figure 1

The number of coincidences found in the 2001 run (solid line) and the estimated background (dashed line), against sidereal time $\overline{t}=(t_{\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{l}}+t_{\mathrm{N}\mathrm{a}\mathrm{u}})/2$ (adapted from Fig. 5 of Ref. 1).

Figure 2

The location of the galactic plane in the equatorial coordinate system. The position of the galactic center is marked by a circle.

Figure 3

${sin}^4\theta$ against sidereal time $\overline{t}$ (in hr) for the galactic center.

Figure 4

${sin}^4\theta$ against sidereal time $\overline{t}$ (in hr) for a source with coordinates $\alpha ={135}^o$ and $\delta =-{40}^o$.

Figure 5

${sin}^4\theta$ against sidereal time $\overline{t}$ (in hr) for a source with $\alpha ={266.405}^o,\delta ={80}^o$.

Figure 6

${sin}^2\theta$ as a function of sidereal time $t$ and of the declination $\delta$, for $\alpha ={135}^o$.

Figure 7

The energy of the events in the various sidereal time bins, compared to two possible thresholds of the detectors (the dotted lines marked as A and B).

Figure 8

A simulation of the number of events per bin, for a distribution of sources in the galactic plane (chosen to be uniform in galactic longitude) when the detector threshold is such that $E/E_0=0.9$.

Figure 9

The response function in energy for unpolarized GWs (the envelope), for the $+$ polarization (thick line), and for the $\times$ polarization (dotted line), for a source at the galactic center.

Figure 10

The square of the quantities shown in Fig. 9 (which is the appropriate response function for a two-detector correlation).

Figure 11

The same as Fig. 9, for a source with coordinates $\alpha ={135}^o,\delta =-{40}^o$, and with a shift $\psi \to \psi -{\psi }_0$ with ${\psi }_0=0.25\mathrm{r}\mathrm{a}\mathrm{d}$.

Figure 12

The distribution of distances $r$ against mass $M$ for the eight 2001 events at the peak at sidereal hours 3 and 4.

Figure 13

The distribution of distances $r$ against $\cos \iota$ for the eight 2001 events at the peak at sidereal hours 3 and 4, setting $M=1.35M_{\odot }$.

Figure 14

A schematic drawing of the evolution of $R$ against time for an accreting NS. The dashed line is the evolution of an idealized fluid NS while the solid line is the evolution of a real NS with a solid crust.

Figure 15

The sensitivity curve of the bar for the acoustic detection of massive particle, as a function of the incoming angle $\theta$ (solid line). To appreciate the fact that the response function is quite narrowly peaked, we also plot for comparison the function ${cos}^2\theta$ (dashed line). The cusp at $\theta =2R/L\simeq 0.2$ reflects the fact that this is the maximum angle for which the particles traverse the bar longitudinally. We averaged over all possible impact points on the surface of the bar.

Figure 16

The response function of the bar for the acoustic detection of massive particle, for a source located at the center of the Virgo cluster (dashed line), and for a source in the galactic center (solid line), as a function of sidereal time $\overline{t}$.

Figure 17

The geometric setting discussed in Appendix .

Figure 18

The rotation between the coordinates systems $(\widehat{E},{\widehat{N}}_L,\widehat{Z})$ and $(\widehat{E},\widehat{N},{\widehat{E}}_{\perp })$. The unit vector $\widehat{E}$ is perpendicular to the plane of the figure, pointing downward.

Figure 19

The vector $\widehat{v}=\widehat{N}\times \widehat{z}$, where $\widehat{z}$ point in the direction of the Galactic North Pole. The vector $\widehat{v}$ is in the $(\gamma ,{\gamma }_{\perp })$ plane.

Figure 20

The geometry for microlensing discussed in the text. S, L, O denote the source, lens and observer, respectively.