Longer Baseline Detectors in Space

7 Longer Baseline Detectors in Space

Perhaps the most interesting gravitational wave signals – those resulting from the formation and coalescence of black holes in the range 10³ to 10⁶ solar masses – will lie in the region of 10^–4 Hz to 10^–1 Hz, and a detector whose strain sensitivity is approximately 10^–23 over relevant timescales is required to search for these. The most promising way of looking for such signals is to fly a laser interferometer in space, i.e. to launch a number of drag free space craft into orbit and to compare the distances between test masses in these craft using laser interferometry. LISA – Laser Interferometer Space Antenna (see for example [83 , 58 , 57 ]) – is being proposed by an American/European team; it consists of an array of three drag free spacecraft at the vertices of an equilateral triangle of length of side 5 × 10⁶ km. This cluster is placed in an Earth-like orbit at a distance of 1 AU from the Sun, and 20 degrees behind the Earth. Proof masses inside the spacecraft (two in each spacecraft) form the end points of three separate but not independent interferometers. Each single two-arm Michelson type interferometer is formed from a vertex (actually consisting of the proof masses in a ‘central’ spacecraft), and the masses in two remote spacecraft as indicated in Figure 12 .

Figure 12: The proposed LISA detector.

The three-interferometer configuration provides redundancy against component failure, gives better detection probability, and allows the determination of polarisation of the incoming radiation. The spacecraft in which they are accommodated shields each pair of proof masses from external disturbances (e.g. solar radiation pressure). Drag free control servos enable the spacecraft to follow the proof masses to a high level of precision, the drag compensation being effected using proportional electric thrusters. Illumination of the interferometers is by highly stabilised laser light from Nd:YAG lasers at a wavelength of 1.064 microns, laser powers of $≃$ 1 W being available from monolithic, non planar ring oscillators which are diode pumped. For each interferometer – consisting of a central spacecraft and two distant spacecraft – two lasers in the central spacecraft, each pointing along one of the arms, are phase locked together so they effectively behave as a single laser. For LISA to achieve its design performance, adjacent arm lengths have to be sensed to an accuracy of better than 30 pm (Hz)^–1/2. Because of the long distances involved and the spatial extent of the laser beams (the diffraction limited laser spot size, after travelling 5 × 10⁶ km, is approximately 50 km in diameter), the low photon fluxes make it impossible to use standard mirrors for reflection; thus active mirrors with phase locked laser transponders on the spacecraft will be implemented. Telescope mirrors will be used to reduce diffraction losses on transmission of the beam and to increase the collecting area for reception of the beam. Given that the available laser power in each arm is of the order of 1 W, and that arguments similar to those already discussed for ground based detectors can be made, photoelectron shot noise considerations suggest that the diameters of the transmitting and receiving mirrors on the space craft need to be $≃$ 30 cm.

Further, just as in the case of the ground based detectors, the presence of laser frequency noise is a limiting factor. It leads to an error in the measurement of each arm length. If the arms are equal these errors cancel out but if they are unequal, the comparison of lengths used to search for gravitational waves may be dominated by frequency noise. For the 5 × 10⁹ m long arms of LISA, a difference in arm length of 10⁸ m is likely. Then for a relative arm length measurement of 2 × 10^–12 m(Hz)^–1/2 (the error budget level allowed in the LISA design for this noise source), Equation (12 ) suggests that a laser stability of $≃$ 6 × 10^–6 Hz(Hz)^–1/2 is required, a level much better than can be achieved from the laser on its own. Thus frequency stabilisation has to be provided. The primary method of stabilisation is to lock the frequency of one laser in the system on to a Fabry–Pérot cavity mounted on one of the craft – see for example [62 ] – and then to effectively transfer this stability to other lasers in the system by phase locking techniques. With the temperature fluctuations inside each craft limited in the region of 10^–3 Hz to approximately 10^–6 K(Hz)^–1/2 by three stages of thermal insulation, a cavity formed of material of low expansion coefficient such as ULE allows a stability level of approximately 30 Hz(Hz)^–1/2. This level of laser frequency noise is clearly much worse than the required 6 × 10^–6 Hz(Hz)^–1/2 and a further correction scheme is needed. Further frequency correction is provided by comparing the phase of the light returning in each arm with the phase of the transmitted light. The phase difference, measured over the time of flight in the arm, allows an estimate of laser frequency noise to be made [90 , 27 , 34 ]. For the arm of length $L$

and thus if the spectral density $δϕ$ is measured, the spectral density $δν$ can be estimated. This estimate can then be used to correct the signal obtained by subtracting the phase difference measurements in two adjacent arms, allowing the search for gravitational waves to be carried out. This correction is made easier if each arm length is known to a few km and the difference in arm length is known to a few tens of metres. These quantities should be available from radar and optical ranging measurements. If however they are not well enough known then they can be found by searching through a range of possible values to minimise the effect of frequency noise on the ‘gravitational wave’ signal.

There are many other issues associated with the laser interferometry for LISA which are not dealt with here and the interested reader should refer to [46 ] for a discussion of some of these.

LISA has been adopted by ESA as a Cornerstone project in their post Horizon 2000 programme and the possibility of it being a joint ESA/NASA collaborative mission is being enthusiastically addressed at present.