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Register a new userAnalyses of residual accelerations for TianQin based on the global MHD simulation
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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.
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TianQin is a proposed space-borne gravitational wave (GW) observatory composed of three identical satellites orbiting around the geocenter with a radius of $10^5$ km. It aims at detecting GWs in the frequency range of 0.1 mHz -- 1 Hz. The detection of GW relies on the high precision measurement of optical path length at $10^{-12}$~m level. The dispersion of space plasma can lead to the optical path difference (OPD, $Delta l$) along the propagation of laser beams between any pair of satellites. Here, we study the OPD noises for TianQin. The Space Weather Modeling Framework is used to simulate the interaction between the Earth magnetosphere and solar wind. From the simulations, we extract the magnetic field and plasma parameters on the orbits of TianQin at four relative positions of the satellite constellation in the Earth magnetosphere. We calculate the OPD noise for single link, Michelson combination, and Time-Delay Interferometry (TDI) combinations ($alpha$ and $X$). For single link and Michelson interferometer, the maxima of $|Delta l|$ are on the order of 1 pm. For the TDI combinations, these can be suppressed to about 0.004 and 0.008 pm for $alpha$ and $X$. The OPD noise of the Michelson combination is colored in the concerned frequency range; while the ones for the TDI combinations are approximately white. Furthermore, we calculate the ratio of the equivalent strain of the OPD noise to that of TQ, and find that the OPD noises for the TDI combinations can be neglected in the most sensitive frequency range of TQ.
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.
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.
In this work, we study the prospect of detecting the stochastic gravitational-wave background with the TianQin observatory. We consider both astrophysical-origin and cosmological-origin sources, including stellar-mass binary black holes, binary neutron stars, Galactic white dwarves, inflation, first order phase transition, and cosmic defects. For the detector configurations, we considered TianQin, TianQin I+II and TianQin + LISA. We studied the detectability of stochastic gravitational-wave backgrounds with the assumed methods of both cross-correlation and null channel, and present the corresponding power-law integrated sensitivity curves. We introduce the definition of the joint foreground with a network of detectors. With the joint foreground, the number of resolved double white dwarves in the Galaxy will be increased by 5% $sim$ 22% compared with simple combination of individual detectors. The astrophysical background from the binary black holes and the binary neutron stars under the theoretical models are predicted to be detectable with signal-to-noise ratio of around 10 after five years operation. As for the cosmological sources, their models are highly uncertain, and we only roughly estimate the detection capability under certain cases.
We study the prospect of using TianQin to detect stellar-mass binary black holes (SBBHs). We estimate the expected detection number as well as the precision of parameter estimation on SBBH inspirals, using five different population models. We note TianQin can possibly detect a few SBBH inspirals with signal to noise ratios greater than 12; lowering the threshold and combining multiple detectors can both boost the detection number. The source parameters can be recovered with good precision for most events above the detection threshold. For example, the precision of the merger time most likely occurs near 1s, making it possible to guide the detection of the ground-based detectors, the precision of the eccentricity $e_0$ most likely occurs near $10^{-4}$, making it possible to distinguish the formation channels, and the precision of the mass parameter is better than $10^{-6}$ in general and most likely occurs near $10^{-7}$. We note, in particular, that for a typical merger event, the error volume is likely to be small enough to contain only the host galaxy, which could greatly help in the study of gravitational wave cosmology and relevant studies through the multimessenger observation.
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