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This Technical Note (LISA reference LISA-LCST-SGS-TN-001) describes the computation of the noise power spectral density, the sensitivity curve and the signal-to-noise ratio for LISA (Laser Interferometer Antenna). It is an applicable document for ESA (European Space Agency) and the reference for the LISA Science Requirement Document.
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The Laser Interferometer Space Antenna (LISA) will open the mHz band of the gravitational wave spectrum for exploration. Sensitivity curves are a useful tool for surveying the types of sources that can be detected by the LISA mission. Here we describe how the sensitivity curve is constructed, and how it can be used to compute the signal-to-noise ratio for a wide range of binary systems. We adopt the 2018 LISA Phase-0 reference design parameters. We consider both sky-averaged sensitivities, and the sensitivity to sources at particular sky locations. The calculations are included in a publicly available {em Python} notebook.
The success of LISA Pathfinder in demonstrating the LISA drag-free requirement paved the road of using space missions for detecting low-frequency and middle-frequency GWs. The new LISA GW mission proposes to use arm length of 2.5 Gm (1 Gm = 106 km). The TAIJI GW mission proposes to use arm length of 3 Gm. In order to attain the requisite sensitivity, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for original LISA, ASTROD-GW and eLISA together with a LISA-type mission with a nominal arm length of 2 Gm using the CGC 2.7/CGC2.7.1 ephemeris framework. In this paper, we follow the same procedure to simulate the time delay interferometry numerically for the new LISA mission and the TAIJI mission together with LISA-like missions of arm length 1, 2, 4, 5 and 6 Gm. The resulting optical path differences of the second-generation TDI calculated for new LISA, TAIJI, and LISA-like missions or arm length 1, 2, 4, 5 & 6 Gm are well below their respective limits which the laser frequency noise is required to be suppressed. However, for of the first generation X, Y, and Z TDI configurations, the original requirements need to be relaxed by 3 to 30 fold to be satisfied. For the new LISA and TAIJI, about one order of magnitude relaxation would be good and recommended; this could be borne on the laser stability requirement in view of recent progress in laser stability. Compared with X, Y and Z, the X+Y+Z configuration does have a good cancellation of path length differences and could serve as a null string detection check. We compile and compare the resulting differences of various TDI configurations due to the different arm lengths for various LISA-like mission proposals and for the ASTROD-GW mission proposal.
Space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) design operate by synthesizing one or more interferometers from fringe velocity measurements generated by changes in the light travel time between three spacecraft in a special set of drag-free heliocentric orbits. These orbits determine the inclination of the synthesized interferometer with respect to the ecliptic plane. Once these spacecraft are placed in their orbits, the orientation of the interferometers at any future time is fixed by Keplers Laws based on the initial orientation of the spacecraft constellation, which may be freely chosen. Over the course of a full solar orbit, the initial orientation determines a set of locations on the sky were the detector has greatest sensitivity to gravitational waves as well as a set of locations where nulls in the detector response fall. By artful choice of the initial orientation, we can choose to optimize or suppress the antennas sensitivity to sources whose location may be known in advance (e.g., the Galactic Center or globular clusters).
In a space based gravitational wave antenna like LISA, involving long light paths linking distant emitter/receiver spacecrafts, signal detection amounts to measuring the light-distance variationsthrough a phase change at the receiver. This is why spurious phase fluctuations due to various mechanical/thermal effects must be carefully studied. We consider here a possible pointing jitter in the light beam sent from the emitter. We show how the resulting phase noise depends on the quality of the wavefront due to the incident beam impinging on the telescope and due to the imperfections of the telescope itself. Namely, we numerically assess the crossed influence of various defects (aberrations and astigmatisms), inherent to a real telescope with pointing fluctuations.
Compact Galactic binary systems with orbital periods of a few hours are expected to be detected in gravitational waves (GW) by LISA or a similar mission. At present, these so-called verification binaries provide predictions for GW frequency and amplitude. A full polarisation prediction would provide a new method to calibrate LISA and other GW observatories, but requires resolving the orientation of the binary on the sky, which is not currently possible. We suggest a method to determine the elusive binary orientation and hence predict the GW polarisation, using km-scale optical intensity interferometry. The most promising candidate is CD-30$^{circ}$ 11223, consisting of a hot helium subdwarf with $m_B = 12$ and a much fainter white dwarf companion, in a nearly edge-on orbit with period 70.5 min. We estimate that the brighter star is tidally stretched by 6%. Resolving the tidal stretching would provide the binary orientation. The resolution needed is far beyond any current instrument, but not beyond current technology. We consider scenarios where an array of telescopes with km-scale baselines and/or the Very Large Telescope (VLT) and Extremely Large Telescope (ELT) are equipped with recently-developed kilo-pixel sub-ns single-photon counters and used for intensity interferometry. We estimate that a team-up of the VLT and ELT could measure the orientation to $pm 1^{circ}$ at 2$sigma$ confidence in 24 hours of observation.
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