First Generation Interferometers

The status and plans for the first generation long baseline suspended mass interferometers TAMA, GEO, LIGO and Virgo are presented, as well as the expected performances. INTRODUCTION The effect of the propagating gravitational wave is to deform space in a quadrupolar form. The characteristics of the deformation are indicated in Fig. 1. 0 ~ o T <\ \ 9 ^ * ^ © Gravitational Waves z FIGURE 1. The effect of gravitational waves for one polarization is shown at the top on a ring of free particles. The circle alternately elongates vertically while squashing horizontally and vice versa with the frequency of the gravitational wave. The detection technique of interferometry being employed in the new generation of detectors is indicated in the lower figure. The interferometer measures the difference in distance in two perpendicular directions, which if sensitive enough could detect the passage of a gravitational wave For an astrophysical source, one can estimate the frequency of the emitted gravitational wave. An upper limit on the gravitational wave source frequency can be estimated from the Schwarzshild radius 2GM/C of the radiated object. We do not CP575, Astrophysical Sources for Ground-Based Gravitational Wave Detectors, edited by J. M. Centrella © 2001 American Institute of Physics 0-7354-0014-8/01/$18.00 Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp expect strong emission for periods shorter than the light travel time 4rcGM/c3 around its circumference. From this we can estimate the maximum frequency as about 10 Hz for a solar mass object. Of course, the frequency can be much lower as illustrated by the 8 hour period of PSR1916+13, which is emitting gravitational radiation. Frequencies in the higher frequency range IHz <f< 10 Hz are potentially reachable using detectors on the earth's surface, while the lower frequencies require putting an instrument into space. The physics goals of the terrestrial detectors and the LISA space mission are complementary, much like different frequency bands are used in observational astronomy for electromagnetic radiation The strength of a gravitational wave signal depends crucially on the quadrupole moment of the source. We can roughly estimate how large the effect could be from astrophysical sources. If we denote the quadrupole moment of the mass distribution of a source by Q, a dimensional argument, along with the assumption that gravitational radiation couples to the quadrupole moment yields: c r c r where G is the gravitational constant and £TM*-*" is the non-symmetrical part of the kinetic energy. For the purpose of estimation, let us consider the case where one solar mass is in the form of non-symmetric kinetic energy. Then, at a distance of the Virgo cluster we estimate a strain of h ~ 10~. This is a good guide to the largest signals that might be observed. At larger distances or for sources with a smaller quadrupole component the signal will be weaker LONG BASELINE INTERFEROMETRY A Michelson interferometer operating between freely suspended masses is ideally suited to detect the antisymmetric (compression along one dimension and expansion along an orthogonal one) distortions of space induced by the gravitational waves as was illustrated in figure 1. Other optical configurations or interferometer schemes, like a Sagnac, might also be used and could have advantages, but the present generation of interferometers discussed here are of the Michelson type. The simplest configuration, a white light (equal arm) Michelson interferometer is instructive in visualizing many of the concepts. In such a system the two interferometer arms are identical in length and in the light storage time. Light brought to the beam splitter is divided evenly between the two arms of the interferometer. The light is transmitted through the splitter to reach one arm and reflected by the splitter to reach the other arm. The light traverses the arms and is returned to the splitter by the distant arm mirrors. The roles of reflection and transmission are interchanged on this return and, furthermore, due to the Fresnel laws of E & M the return reflection is accompanied by a sign reversal of the optical electric field. When the optical electric fields that have come from the two arms are recombined at the beam splitter, the beams that were treated to a reflection (transmission) followed by a transmission Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp (reflection) emerge at the antisymmetric port of the beam splitter while those that have been treated to successive reflections (transmissions) will emerge at the symmetric port. In a simple Michelson configuration the detector is placed at the antisymmetric port and the light source at the symmetric port. If the beam geometry is such as to have a single phase over the propagating wavefront (an idealized uniphase plane wave has this property as does the Gaussian wavefront in the lowest order spatial mode of a laser), then, providing the arms are equal in length (or their difference in length is a multiple of 1/2 the light wavelength), the entire field at the antisymmetric port will be dark. The destructive interference over the entire beam wavefront is complete and all the light will constructively recombine at the symmetric port. The interferometer acts like a light valve sending light to the antisymmetric or symmetric port depending on the path length difference in the arms. If the system is balanced so that no light appears at the antisymmetric port, the gravitational wave passing though the interferometer will disturb the balance and cause light to fall on the photodetector at the dark port. This is the basis of the detection of gravitational waves in a suspended mass interferometer. In order to obtain the required sensitivity, the arms of the interferometer must be long.