The Stochastic Gravitational Wave Background: Some Astrophysical Sources Jonah Kanner, University of Maryland, College Park, MD 20740 March 15, 2007 ABSTRACT This work is a review of some of the literature on expected astrophysical sources of stochastic gravitational waves. A brief introduction is provided on the nature and characteristics of a stochastic background. Results presented include the expected energy density parameter, ΩGW ,for several sources. Particularly, we present backgrounds from eccentric, rotating neutron stars, supernovae, and double neutron star coalescence. Some of these predictions place ΩGW at 100 Hz at 10^-9 or stronger. Such a signal could be detected by planned second generation interferometers such as Advanced LIGO. I. Introduction In recent years, the construction of long-baseline interferometric gravity wave detectors has made broadband, sensitive searches for gravitational waves a reality. Projects such as LIGO, TAMA, GEO, and VIRGO, as well as a network of resonant-mass detectors, are currently searching our local space-time for the illusive ghosts of Einstein’s theory. A gravitational wave (GW) signal may be classified into one of three categories: burst, periodic, or stochastic. Bursts are well localized in the time domain, periodic signals are well localized in the frequency domain, and stochastic signals are spread over many frequencies and long times (Allen 1996). Sources in the “burst group” may include coalescing binary systems of black holes and/or neutron stars, gravity waves from gamma ray bursts, and supernovae. The second group, periodic signals, most notably includes signals from rotating neutron stars. A detected signal falling under either of these classifications most likely originates from a single event or object in the sky. The third type of signal can be more difficult to grasp conceptually. It is also, potentially, the most exciting. The stochastic GW background is the gravitational analog of the Cosmic Microwave Background (CMB) in the electromagnetic spectrum (Allen 1996). Like the CMB, the stochastic background would come from all (or, at least, many) points on the sky. Also like the CMB, a component of the stochastic background may carry information about the early universe (Maggiore 2000). However, unlike CMB photons, which had their last scattering about 105 years after the big bang, early universe gravitational signals in the LIGO frequency range may have decoupled 10-22 seconds after the dawn of time (Allen 1996). The information they contain could prove a valuable tool to cosmologists. In addition, there is expected to be a second component to the GW stochastic background that has no obvious analog in the electromagnetic spectrum. This signal originates from the so-called “astrophysical” sources of stochastic GW’s. Optical telescopes can be resolved to see only a small piece of the sky. GW detectors have no such resolving power – at any time a detector is sensitive to most of the sky! As a consequence, the GW stochastic background, in say, a given second, likely includes the sum of dozens or hundreds of signals coming from point sources all over the sky. The same types of objects that lead to resolvable signals when close enough - for example, coalescing binaries, rotating neutron stars, and supernovas – will contribute to the stochastic background in the form of many irresolvable signals coming from large distances. An analogy to how we hear sound might make this more obvious. Imagine sitting down to dinner in a large ballroom, with the tables spread far apart. If a friend speaks in conversational volume while sitting on the other side of the room, you could never hear her, 1even were all the other dinner guests to hold their breath. On the other hand, consider the sound of all the guests freely conversing. They are each far away – at least, most of them are not at your table. So, any one person is too quiet to hear. However, the collective noise of all those conversations would certainly be noticeable! In this way, far away point sources of gravity waves may combine incoherently to produce a stochastic signal in GW detectors. This contribution to the stochastic signal is said to come from astrophysical sources, as opposed to a signal from the very early universe, which is known as cosmological (Abbott et al. 2006). One of the basic differences between astrophysical signals and cosmological signals is the time that they are emitted. Cosmological sources come from a time well before last scattering. In terms of redshift, this means cosmological GW’s originate at z > 1000. Astrophysical GW’s typically come from some time after star formation has begun. In the papers considered below, the astrophysical sources all originate at z < 5. II. Characterization In the literature, bounds on the stochastic background are usually stated in terms of a dimensionless quantity, Ω (Abbott et al. 2006). Ω(f) = (f/ρc)(dρGW/df) Here, f is the GW frequency being considered, ρc is the critical energy density necessary for a flat universe, and ρGW is the energy density of the stochastic gravitational wave signal. So, Ω(f) is a measure of the differential energy density of the stochastic signal in a unit logarithmic frequency interval (Allen 1996). If the stochastic signal meets the criteria of being isotropic, stationary, and Gaussian, this function Ω(f) is enough to completely characterize the background (Allen 1996). This is analogous to saying that the CMB is completely characterized as blackbody radiation at 2.7 K. As a practical point, setting bounds on Ω(f) in a given frequency range with a GW detector demands some kind of model for the frequency dependence of Ω. This leads to a quantity Ω0 often quoted in the literature. This quantity is the value (or bound) of Ω(f), assuming that Ω(f) has no frequency dependence. For detectors probing Ω in a narrow bandwidth, Ω0 ≈ Ω(f). GW detectors measure the dimensionless strain, h. In terms of detectability, we might wish to think of Ω in terms of the strain associated with it. If we ask for the strain that would be produced in a bandwidth equal to the observational frequency (Allen 1996), we find: h(f) ≈ (100Hz/f) (2x10-20) √Ω(f) III. Measurement Known bounds, excluding GW detectors, on the GW spectrum from indirect measurements are