7.1 Laser Interferometer Space Antenna (LISA)

Until early 2011, the Laser Interferometer Space Antenna (LISA) – see, for example, [125, 272, 217, 216] – was under consideration as a joint ESA/NASA mission as one L-class candidate within the ESA Cosmic Visions program [118Jump To The Next Citation Point]. Funding constraints within the US now mean that ESA must examine the possibility of flying an L-class mission with European-only funding [240Jump To The Next Citation Point]. Accordingly all three L-class candidates are undergoing a rapid redesign phase with the goal of meeting the new European-only cost cap. Financial, programmatic and scientific issues will be reassessed following the redesigns and it is currently expected that the selection of the first L-class mission will take place in 2014.

However, for the rest of this article we will discuss the plans for LISA prior to these developments. More concrete information is expected to emerge very soon.

LISA would consist of an array of three drag-free spacecraft at the vertices of an equilateral triangle of length of side 5 × 106 km, with the cluster placed in an Earth-like orbit at a distance of 1 AU from the Sun, 20° behind the Earth and inclined at 60° to the ecliptic. A current review of LISA technologies, with expanded discussion of, and references for, topics touched upon below, can be found in [192Jump To The Next Citation Point]. Here we will focus upon a couple of topics regarding the interferometry needed to give the required sensitivity.

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Figure 20: A design sensitivity amplitude spectral density curve for LISA created using the standard parameters in the online generator at [208]. The curve assumes equal length arms, sensitivity averaged over the whole sky and all polarisations, and an SNR of 1. Also included is a curve showing the expected background noise from galactic white-dwarf–binary systems, which will dominate over the instrumental noise in the range from ≈ 0.1 – 1 mHz.

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 21View Image. The three-interferometer configuration provides redundancy against component failure, gives better detection probability, and allows the determination of the polarisation of the incoming radiation. The spacecraft, which house the optical benches, are essentially there as a way to shield 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 ≃ 2 W being available from monolithic, non-planar ring oscillators, which are diode pumped. For LISA to achieve its design performance strain sensitivity of around 10–20 Hz–1/2, adjacent arm lengths have to be sensed to an accuracy of about 10 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. With the given laser power, and using arguments similar to those already discussed for ground-based detectors with regard to photoelectron shot noise considerations, means that for the required sensitivity the transmitting and receiving telescope mirrors on the spacecraft will have diameters of 40 cm.

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Figure 21: The proposed LISA detector.

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 (14View Equation) 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 first method of stabilisation is to lock the frequency of one laser in the system on to a local frequency reference, e.g., a Fabry–Pérot cavity mounted on one of the craft (see, for example, [229]), 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 3 mHz 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 (again at 3 mHz). This level of laser frequency noise is clearly much worse than the required 1.2 × 10–6 Hz Hz–1/2 (at 3 mHz) and a further correction scheme is needed. A second possible stage of frequency stabilisation is arm-locking [285], which relies on the fact that, by design, the fractional stability of the LISA arms is of order −21 −1∕2 δl∕L ∼ 10 Hz to derive an error signal from the phase difference between the local laser and the received light. As the received light is phase locked with the local laser from the craft that sent it, it caries a replica of the frequency noise of the local laser noise delayed by one round trip time τ = 33 s. Using this fact, this noise can be suppressed at frequencies smaller than the round trip frequency f = 1∕τ = 30 mHz. This scheme requires no additional hardware and can be completely implemented in software, but it will still leave frequency noise that is several orders of magnitude above required levels. A third stage frequency stabilisation scheme, which is a post-processing step, is time-delay interferometry (TDI). This makes use of the fact that, because the beams coming down each arm are not combined, the phase of each beam can be measured and recorded. Therefore, correlations in the frequency noise can be calculated and subtracted by algebraically combining phase measurements from different craft delayed by the multiples of the time delay between the spacecraft. The accuracy of this is set by the phase measurement accuracy, which allows frequency noise subtraction to below the required level. A simple TDI scheme, for a much simplified constellation, was first based in the frequency domain [152], but due to complexities in taking into account changing arm lengths and a more complex interferometric scheme, subsequent implementations have been in the time domain. A mathematical overview of the TDI scheme, along with moving spacecraft and unequal arm lengths, can be found in [297].

One of the major components of LISA is the disturbance reduction system (DRS), which is responsible for making sure the test masses follow, as far as possible, purely gravitational orbits. This consists of the gravitational reference sensor (GRS) and the control and propulsion systems used to keep the spacecraft centred on the test mass. The test masses for LISA are 1.96 kg cubes, with sides of 46 mm and made of an alloy of 75% gold and 25% platinum, chosen because of its very small magnetic susceptibility. The masses are housed in a cube of electrodes designed to capacitively sense their position and to have measurement noise levels of 1.8 nm Hz–1/2. The masses need to be tightly held in place during launch and then released, so a caging mechanism has been designed consisting of 8 hydraulic fingers (one for each corner of the mass) pushing with 1200 N of force. There will be adhesion between the fingers and the masses, which will require about 10 N of force per finger to break. To provide this force two plungers will push on the the top and bottom surfaces of the masses releasing them from the fingers, followed by pushing smaller release tips in each plunger, and quickly retracting them, to overcome their adhesion to the masses. Charged particles produced by cosmic radiation interacting with the surrounding spacecraft can cause the test masses to become charged at a rate of about 50 electrons per second. Current plans are to use UV light from mercury lamps (or potentially UV LEDs) to discharge the masses. Another key technology for the DRS are the micro-Newton thrusters, which provide the fine control needed for drag-free flight. These will mainly be used to counteract solar radiation pressure on the spacecraft, which requires about 10 µN per relevant thruster. Thrust noise as a function of frequency is required to be smaller than

∘ ----(---------)-- − 1∕2 10-mHz-- 4 0.1μN Hz × 1 + f .

Two types of system, both of which meet the requirements, will be tested on LISA Pathfinder: the US colloid micro-Newton thruster (CMNT); and the European field emission electric propulsion system (FEEP). The CMNT uses small drops of a colloid, which it ionises through field emission, accelerates and ejects from the thruster. Two designs of FEEP currently exist, one using Indium and the other Caesium and with different geometries, which, instead of ionising a droplet of colloid, just use single ions. This means FEEPs have a better charge to mass ratio. The current baseline is to use caesium FEEPs. Many of the systems above are being tested in the LISA Pathfinder mission (see below) and use the nominal LISA designs.

There are many other issues associated with laser interferometry, and other aspects of the mission mentioned above, for LISA, which are not dealt with here and the interested reader should refer to [183, 192, 193Jump To The Next Citation Point] for a discussion of some of these.

For LISA the baseline mission design was finalised in 2005. An industrial contract was awarded to Astrium GmbH for the LISA Mission Formulation study [193]. Within the current ESA Science Programme LISA is in the Cosmic Vision 2015 – 2025 Programme [118], and launch after 2020 seems likely. In 2007 the National Research Council report on the NASA Beyond Einstein Program (soon to become the Physics of the Cosmos Program) gave LISA the highest scientific ranking, and it has been rated very highly in the Astro2010 decadal survey [87]. However, as stated above, as of earlier this year (2011) ESA is considering the feasibility of LISA as a single agency mission [240]. Recent technical reports for LISA can be found at [218].

Several of the key technologies for LISA are being testing on the LISA Pathfinder mission (formerly SMART-2). Details of the current status of this mission can be found in [84]. LISA Pathfinder will fly the LISA Technology Package (LTP), which essentially consists of a downscaled version of one LISA arm compressed from 5 million km to 38 cm. The LTP arm contains two test masses (an emitter and a receiver) with a Doppler link between them. The three main things it will measure are: the acceleration phase noise caused by the relative motion of the emitter and receiver from non-gravitational forces; the readout noise; and noise caused by the departure of the Doppler link from the ideal scheme, due to the fact that we are not truly measuring the relative accelerations of two point particles, but instead a more complex system of multiple Doppler links and extended masses. It is designed to test the accuracy of these to within an order of magnitude of that required by the full LISA. Other aspects of the mission that will be tested are the discharging of the test masses, the caging and release of the masses following launch and the micro-Newton thrusters. As much as possible the nominal LISA systems and hardware are being used. LISA Pathfinder is currently scheduled for launch in mid 2013, after which it will orbit the L1 point, with a 180-day mission plan.

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