Space-borne Gravitational Wave Detector LISA/eLISA
[Yan Wang is the recipient of the 2014 Stefano Braccini Thesis Prize administered by the Gravitational Wave International Committee (GWIC) for his PhD thesis “On inter-satellite laser ranging, clock synchronization and gravitational wave data analysis” (PDF). His thesis work was carried out at Leibniz University of Hannover, Germany.
The Stefano Braccini Thesis Prize was established to honor the memory of a talented gravitational wave physicist whose promising career was cut short. Stefano worked with the French-Italian Virgo project, and contributed to the superattentuator design, to the integration and commissioning of Virgo and to its data analysis efforts. -- 2Physics.com]
Author: Yan Wang
Affiliation: School of physics, University of Western Australia, Perth, Australia.
Observations of electromagnetic radiation have revolutionized our understanding of the Universe and fundamental physics during the last century. With the advent of the expected first detection of gravitational waves (GWs) in near future, a completely new window onto the Universe will soon be opened by GW astronomy. GWs are spacetime ripples, predicted by Einstein’s theory of General Relativity. Their existence has been indirectly proven by measurements of the orbital decay due to gravitational radiation of the binary pulsar PSR 1913+16 , for which Hulse and Taylor won the 1993 Nobel Prize, but, due to their weak coupling with matter (i.e. GWs pass through stars, galaxies, Earth, Sun, and everything), direct detection of GWs has been beyond our technological capabilities until now. This weak coupling does mean, however, that GWs carry uncorrupted physical, astrophysical and cosmological information, enabling us to probe deep into the very early Universe, to test general relativity (GR) with unprecedented precision, and to measure the masses and spins of black holes (BHs) with exquisite accuracy.
Currently, large laser interferometers are the most sensitive GW detectors. There are several existing ground-based interferometric GW detectors: LIGO (Hanford and Livingston) , VIRGO , GEO600 , either operating or being upgraded; and KAGRA  under construction. During the past few decades, scientists took all efforts to isolate or mitigate various kinds of disturbances on the Earth, in order to increase the sensitivity of the detectors. These detectors are expected to detect GWs in near future.
Figure 1: Classic LISA configuration.
There are also space-borne interferometric GW detector (planned) missions. Among them, the most mature one is the Laser Interferometer Space Antenna (LISA) [6-7] ‘family’ (e.g. classic LISA, eLISA, and variations). LISA/eLISA consists of three spacecrafts (Fig. 1), each individually following a slightly elliptical orbit around the Sun, trailing the Earth by about 20 degree. These orbits are chosen such that the three spacecrafts retain an equilateral triangular configuration with an arm length of a few million kilometers as much as possible. This is accomplished by tilting the plane of the triangle by about 60 degree out of the ecliptic. Graphically, the triangular configuration does a cartwheel motion around the Sun.
The benefits of sending an interferometric GW detector to space are mainly: (i) Less noise disturbances, (ii) More GW sources. Roughly speaking, laser interferometric GW detectors are most sensitive to celestial systems of a size comparable to the interferometers’ arm length. LISA/eLISA is sitting in a frequency band, where there are most abundant GW sources (Fig. 2). There are several known white dwarf binaries in our galaxy directly visible to LISA/eLISA. In addition, LISA/eLISA can resolve thousands of other white dwarf binaries in our galaxy. LISA/eLISA can also observe massive black hole mergers throughout the entire universe . Extreme mass ratio inspirals (i.e. stellar mass compact object orbiting a massive black hole) and primordial GWs from the birth of the universe add great scientific values to the mission as well .
Figure 2: (Click on the image to view with higher resolution) The GW spectrum from extremely low frequency to high frequency [Image courtesy: Chris Henze]
For many years, scientists have been spending great effort -- both theoretically and experimentally -- in preparation of LISA/eLISA. Some of the key techniques required by LISA/eLISA cannot be tested on the ground. LISA pathfinder satellite is going to be launched in this November (2015) to test the drag-free altitude control system in space, laser interferometry with picometer resolution at mHz band, the reliability of the instruments in the space environment, etc.
Unlike the ground-based interferometric GW detectors, the arm lengths of LISA/eLISA are varying significantly with time due to celestial mechanics in the solar system. As a result, the arm lengths differ by about one percent (i.e. tens of kilometers), and the dominating laser-frequency noise will not cancel out. The remaining laser-frequency noise would be stronger than other noises by about 8 orders of magnitude. Fortunately, the coupling between distance variations and the laser-frequency noise is very well known and understood. Therefore, we can use time-delay interferometry (TDI) techniques , which combine the measurement data series with appropriate time delays, in order to cancel the laser-frequency noise to the desired level.
However, the performance of TDI depends largely on the knowledge of arm lengths and relative longitudinal velocities between the spacecrafts, which are required to determine the correct delays to be adopted in the TDI combinations. In addition, the raw data are referred to the individual spacecraft clocks, which are not physically synchronized but independently drifting and jittering. This timing mismatch would degrade the performance of TDI variables. Therefore, they need to be referred to a virtual common constellation clock which needs to be synthesized from the inter-spacecraft measurements. Simultaneously, one also needs to extract the inter-spacecraft separations and synchronize the time-stamps properly to ensure the TDI performance. This has been a long existing gap.
Recently [10-11], we have tried to bridge this gap by designing sophisticated first stage data analysis algorithms for LISA/eLISA. The following are the main steps involved in the algorithms: (i) different types of inter-spacecraft measurements (e.g. the pseudo ranging measurements, the beat-notes of the carrier frequencies of the lasers emitted from one spacecraft and a remote spacecraft, the beat-notes of the laser sidebands) are precisely formulated as functions of the system state variables; (ii) several precise and effective dynamic models are designed for the system state variables (these models basically describe how the state variables evolve with time); (iii) the measurement data are pre-processed so that they can be used by a optimal filtering algorithm; (iv) the information of the measurements and the information from the dynamic models of the system state variables are optimally combined via a Kalman-like optimal filter, in order to reduce the noise in the measurements and the clock recording time stamps.
Simulation shows that our algorithms can successfully calibrate and synchronize the phasemeter raw data, estimate the inter-spacecraft distances and the clock errors, hence making the raw measurements usable for TDI techniques and astrophysical data analysis algorithms. This result can significantly increase the robustness of the LISA/eLISA project. The flexible design structure of our algorithms also provides a general framework of first stage LISA/eLISA data preparation, which can be easily extended to deal with various emergent scenarios in the future.
 Joel M. Weisberg, Joseph H. Taylor, "The Relativistic Binary Pulsar B1913+16: Thirty Years of Observations and Analysis", ASP Conference Series on 'Binary Radio Pulsars', vol. 328, p25 (2005). Article.
 LISA International Science Team 2011 (European Space Agency), "LISA Unveiling a hidden universe", LISA Assessment Study Report (Yellow Book), ESA/SRE(2011) 3. Link.
 The eLISA Constortium, "The Gravitational Universe", Whitepaper submitted to ESA for the L2/L3 Cosmic Vision call. arXiv:1305.5720 [astro-ph.CO] (2013).
 Massimo Tinto, Sanjeev V. Dhurandhar, "Time-Delay Interferometry", Living Review Relativity 17 (2014), 6. Article.
 Y. Wang, Thesis: ‘On inter-satellite laser ranging, clock synchronization and gravitational wave data analysis’ (2014). Link.
 Yan Wang, Gerhard Heinzel, Karsten Danzmann, "First stage of LISA data processing: Clock synchronization and arm-length determination via a hybrid-extended Kalman filter", Physical Review D, 90, 064016 (2014). Abstract.