Science with LIGO

Maria Alessandra Papa, Albert Einstein Institute papa-at-aei.mpg.de

The sensitivity band of LIGO extends between 50 Hz and 1500 Hz. In this band we expect gravitational wave signals from compact binary systems during their inspiral, coalescence and merger phases and from the oscillations of the object that forms after the merger. We expect gravitational waves to be emitted during supernova collapse events; we also expect emission of continuous gravitational waves and a stochastic gravitational wave background. LIGO data is searched for all these types of signals.

Binary systems of compact objects evolve in orbits that gradually shrink in time, due to the emission of gravitational radiation . The exact time-frequency evolution of the signal depends on a number of parameters, but the large timescales are set by the total mass of the system and systems with masses up to 200 solar masses are expected to emit signals with significant energy content in LIGO's band. The sensitivity of a search for binary inspiral signals may be characterized by its horizon distance $d_H$. This is the distance at which an optimally located and oriented equal mass binary system is expected to produce a signal with matched-filter SNR = 8. Fig.1 shows estimates of the horizon distance during the S5 run (the most sensitive and longest science run of LIGO [1,2]), which

Figure 1: Typical horizon distance during the S5 run as a function of the total mass of the binary system. H1 and H2 are the two Hanford 4 and 2 km baseline detectors. L1 is the 4 km detector in Louisiana. Courtesy of the LSC.

comprise hundreds of Galaxies even for relatively low mass systems [3]. Still, the detection of a gravitational wave signal from a binary inspiral signal is not at all ensured in S5 data: the S5 expected detection rates are 1 event per 400 to 25 years for 1.4-1.4 solar mass systems; 1 event every 2700 to 20 years for 5-5 solar mass systems and 1 event every 450 to 3 years for 10-10 solar mass systems. Enhanced detectors are expected to achieve an improvement in strain sensitivity of a factor of $\approx$ 2. With a horizon distance of 60 Mpc to neutron star systems the expected rates grow to 1 event every 60 to 4 years of actual observing time. Advanced detectors operating at a horizon distance of 450 Mpc to neutron star systems, bring the expected detection rates between several to order hundred events per year of observing time.

More sensitive than blind searches are triggered searches that take place when an independent observation is available. In February 2007 a short hard GRB, GRB 070201, was detected and localized within an area which includes one of the spiral arms of the M31 Galaxy. Since GRBs may be produced in the merger phase of binary neutron star systems (BNS) or neutron star-black hole binaries (NSBH) this particular GRB could well have been associated with a detectable gravitational wave signal if coming from M31, at 800 kpc. An inspiral search was carried out on the available gravitational wave data for systems with component masses in the range 1-3 and 1-40 solar masses respectively but no signal was found [5]. This null result excluded the possibility that the GRB be due to a binary neutron star or NSBH inspiral signal in M31 with very high confidence (greater than 99%). It also excluded various companion mass - distance ranges significantly further than M31, as shown in Fig. 3 of [5].

A search for a burst signal associated with GRB070201 was also carried out and resulted in an upper limit on the isotropic gravitational wave energy emission at the distance of M31 around $150$ Hz of $\approx 8\times 10^{50}$ erg. This result is significantly less informative than the one from the inspiral searches because the upper limit is orders of magnitude larger that the estimated energy release in gamma rays at the same distance. A soft gamma ray repeater (SGR) flare event in M31 is consistent with the gamma-ray energy release and is not ruled out by the gravitational wave analysis [6].

A systematic search of gravitational wave signals associated with 191 SGR bursts was carried out using S5 data and prior data in coincidence with the 27 Dec 2004 giant flare from SGR 1806-20 [7]. No signals were found and upper limits on the isotropic gravitational wave energy were placed. At a nominal distance of 10 kpc these upper limits overlap with the range of electro-magnetic isotropic energy emission in SGR giant flares ($10^{44}$ - $10^{46}$ erg) and some of the upper limits on the ratio of the gravitational wave and electromagnetic energies are within the range of theoretically possible values.

In general there are many circumstances in which short bursts of gravitational waves are expected, lasting from a few ms to a few seconds involving the merger phase of a binary system or the collapse of a stellar core. Blind searches for these types of events are routinely carried out. Preliminary estimates of the reach of S5 burst searches show that, at best, 50% detection efficiency can be achieved for signals generated by converting of order 5% of a solar mass at the distance of the Virgo cluster, or $\sim 2\times 10^{-8}$ of a solar mass at the Galactic center. Estimates of the expected amplitude of burst signals vary quite widely and scenarios exist which predict emission that is detectable in S5. For example [4] predicts for black hole mergers the emission of up to 3% of solar masses in gravitational waves. A system of this type formed by two 50 solar mass black holes at $\approx$ 100 Mpc would produce gravitational waves which could be detected with 50% efficiency in S5.

An isotropic stochastic background of gravitational radiation is expected due to the superposition of many unresolved signals, both of cosmological and astrophysical origin. The background is described by a function $\Omega_{GW}(f)$, which is proportional to the energy density in gravitational waves per logarithmic frequency interval. The most recent results from searches for isotropic backgrounds come from the analysis of the S4 LIGO data and for a flat gravitational wave spectrum put a 90% Bayesian upper limit at $\Omega_{GW} \times \left[ {H_0\over {72 {\rm {km s^{-1} Mpc^{-1}}}}}\right] < 6.5\times 10^{-5}$, in the frequency range 50-150 Hz [8]. This limit is still above the one that may be inferred from measurements of light-element abundances, WMAP data and the big bang nucleosynthesis model, but it is expected that the data from the S5 run will probe values of $\Omega_{GW}$ below this.

Fast rotating neutron stars are expected to emit a continuous gravitational wave signal if they present a deviation from a perfectly axisymmetric shape, if their r-modes are excited, or if their rotation axis is not aligned with their symmetry axis ([14]). In all cases the expected signal at any given time is orders of magnitude smaller than any of the short-lived signals that have been described above. However, since the signal is present for a very long time (to all practical purposes, in most cases, one may consider it there all the time), one can increase the SNR by integrating for a suitably long time.

No gravitational wave signal has been detected while searching for continuous gravitational waves from known radio pulsars. This is not unexpected because for most systems the indirect upper limit on the amplitude of gravitational waves that one may infer from the measured spin-down rate of the systems is more constraining that the limit determined by the gravitational wave observations. However in one case gravitational wave observations are actually beating the electromagnetic spin-down limit and starting to probe new ground. This is the case of the Crab pulsar. With 9 months of S5 data LIGO observations beat the spin-down upper limit by a factor of about 4 [10]. More importantly, assuming phase coherence between the gravitational wave and radio signals, the gravitational wave luminosity is constrained to less than 6% of the observed spin-down luminosity. On other pulsars, albeit not beating the spin-down upper limits, the LIGO results are expected to reach values as low as a few $10^{-26}$ in the intrinsic gravitational wave amplitude $h_0$ [13] and several $10^{-8}$ in ellipticity $\epsilon$. These results show that at the current sensitivity, it is possible that LIGO could detect a continuous gravitational wave signal, coming from an unusually nearby object, unknown electromagnetically and rotating close to $\sim 75$ Hz.

The most promising searches look for previously unknown objects, and are often refered to as blind searches ([14,15,16,17]). Deep blind searches require an enormous amount of computational power and in fact are carried out by Einstein@Home, a public distributed computing project that uses compute cycles donated by the general public. Einstein@Home is the second largest public compute project in the world and delivers an average 100Tflops of compute power continuously [18]. In the absence of a detection, upper limits are placed on the intrinsic amplitude of the gravitational wave signal at the detector, $h_0$, and may be recast as frequency-first frequency derivative curves which represent an excluded gravitational wave signal at a fixed distance. On the same plane one can overlay constant ellipticity $\epsilon$ curves and understand what ellipticity values the distance parametrized curves refer to. Fig.2 shows this type of curve, deduced from the Hanford 4km interferometer S4 data stack-slide search upper limits of [16]. In S5, the most sensitive Einstein@Home searches are expected to yield a sensitivity improvement in $h_0$ close to a factor of 10, resulting in a detectability range of $\sim$ 1 kpc at $150$ Hz with $\epsilon \sim 10^{-5}$.

Figure 2: Solid curves: Frequency and frequency-derivative values of a signal that would be detectable by the S4 stack-slide search described in [16]. Dashed lines: lines of constant ellipticity.