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Register a new userOrbital effects on time delay interferometry for TianQin
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The proposed space-borne laser interferometric gravitational wave (GW) observatory TianQin adopts a geocentric orbit for its nearly equilateral triangular constellation formed by three identical drag-free satellites. The geocentric distance of each satellite is $approx 1.0 times 10^{5} ~mathrm{km}$, which makes the armlengths of the interferometer be $approx 1.73 times 10^{5} ~mathrm{km}$. It is aimed to detect the GWs in $0.1 ~mathrm{mHz}-1 ~mathrm{Hz}$. For space-borne detectors, the armlengths are unequal and change continuously which results in that the laser frequency noise is nearly $7-8$ orders of magnitude higher than the secondary noises (such as acceleration noise, optical path noise, etc.). The time delay interferometry (TDI) that synthesizes virtual interferometers from time-delayed one-way frequency measurements has been proposed to suppress the laser frequency noise to the level that is comparable or below the secondary noises. In this work, we evaluate the performance of various data combinations for both first- and second-generation TDI based on the five-year numerically optimized orbits of the TianQins satellites which exhibit the actual rotating and flexing of the constellation. We find that the time differences of symmetric interference paths of the data combinations are $sim 10^{-8}$ s for the first-generation TDI and $sim 10^{-12}$ s for the second-generation TDI, respectively. While the second-generation TDI is guaranteed to be valid for TianQin, the first-generation TDI is possible to be competent for GW signal detection with improved stabilization of the laser frequency noise in the concerned GW frequencies.
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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.
TianQin is a proposed space-based gravitational wave observatory. It is designed to detect the gravitational wave signals in the frequency range of 0.1 mHz -- 1 Hz. At a geocentric distance of $10^5$ km, the plasma in the earth magnetosphere will contribute as the main source of environmental noises. Here, we analyze the acceleration noises that are caused by the magnetic field of space plasma for the test mass of TianQin. The real solar wind data observed by the Advanced Composition Explorer are taken as the input of the magnetohydrodynamic simulation. The Space Weather Modeling Framework is used to simulate the global magnetosphere of the earth, from which we obtain the plasma and magnetic field parameters on the detectors orbits. We calculate the time series of the residual accelerations and the corresponding amplitude spectral densities on these orbit configurations. We find that the residual acceleration produced by the interaction between the TMs magnetic moment induced by the space magnetic field and the spacecraft magnetic field ($bm{a}_{rm M1}$) is the dominant term, which can approach $10^{-15}$ m/s$^2$/Hz$^{1/2}$ at $f approx$ 0.2 mHz for the nominal values of the magnetic susceptibility ($chi_{rm m} = 10^{-5}$) and the magnetic shielding factor ($xi_{rm m} = 10$) of the test mass. The ratios between the amplitude spectral density of the acceleration noise caused by the space magnetic field and the preliminary goal of the inertial sensor are 0.38 and 0.08 at 1 mHz and 10 mHz, respectively. We discuss the further reduction of this acceleration noise by decreasing $chi_{rm m}$ and/or increasing $xi_{rm m}$ in the future instrumentation development for TianQin.
We use the Fisher information matrix method to calculate the parameter estimation accuracy of inspiraling supermassive black holes binaries for TianQin, a space-borne laser interferometric detector aimed at detecting gravitational waves in the millihertz frequency band. The `restricted post-Newtonian waveform in which third order post-Newtonian (3PN) phase including spin effects (spin-orbit $beta$ and spin-spin $sigma$) and first-order eccentricity contribution is employed. Monte Carlo simulations using $10^3$ binaries for mass pairs with component masses in the range of $({10^5},{10^7}){M_ odot }$ and cosmological redshift $z=0.5$ show that the medians of the root-mean-square error distributions for the chirp mass $M_c$ and symmetric mass ratio $eta$ are in the range of $sim 0.02% - 0.7% $ and $sim 4% - 8% $, respectively. The luminosity distance $D_L$ can be determined to be $sim 1% - 3% $, and the angular resolution of source $Delta Omega $ is better than 12 deg$^2$. The corresponding results for $z=1.0$ and $2.0$, which are deteriorated with the decreasing of the signal-to-noise ratio, have also been given. We show that adding spin parameters degrades measurement accuracy of the mass parameters (${M_c}$, $eta$), and the time and the orbital phase of coalescence ($t_c$, $phi _c$); the inclusion of the first-order eccentricity correction to the phase worsens the estimation accuracy comparing with the circular cases. We also show the effects of post-Newtonian order on parameter estimation accuracy by comparing the results based on second order and third order post-Newtonian phases. Moreover, we calculate the horizon distance of supermassive black hole binaries for TianQin.
The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. Laser frequency noise enters the interferometric measurements and dominates the expected gravitational signals by many orders of magnitude. Time-delay interferometry (TDI) is a technique that reduces this laser noise by synthesizing virtual equal-arm interferometric measurements. Laboratory experiments and numerical simulations have confirmed that this reduction is sufficient to meet the scientific goals of the mission in proof-of-concept setups. In this paper, we show that the on-board antialiasing filters play an important role in TDIs performance when the flexing of the constellation is accounted for. This coupling was neglected in previous studies. To reach an optimal reduction level, filters with vanishing group delays must be used on board or synthesized off-line. We propose a theoretical model of the residual laser noise including this flexing-filtering coupling. We also use two independent simulators to produce realistic measurement signals and compute the corresponding TDI Michelson variables. We show that our theoretical model agrees with the simulated data with exquisite precision. Using these two complementary approaches, we confirm TDIs ability to reduce laser frequency noise in a more realistic mission setup. The theoretical model provides insight on filter design and implementation.
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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