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Register a new userFull analytical formulas for frequency response of space-based gravitational wave detectors
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The discovery of gravitational waves, which are ripples of space-time itself, opened a new window to test general relativity, because it predicts that there are only plus and cross polarizations for gravitational waves. For alternative theories of gravity, there may be up to six polarizations. The measurement of the polarization is one of the major scientific goals for future gravitational wave detectors. To evaluate the capability of the detector, we need to use the frequency dependent response functions averaged over the source direction and polarization angle. We derive the full analytical formulas of the averaged response functions for all six possible polarizations and present their asymptotic behaviors based on these analytical formulas. Compared with the numerical simulation, the full analytical formulas are more efficient and valid for any equal-arm interferometric gravitational wave detector without optical cavities in the arms and for a time-delay-interferometry Michelson combination.
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Gravitational waves are perturbations of the metric of space-time. Six polarizations are possible, although general relativity predicts that only two such polarizations, tensor plus and tensor cross are present for gravitational waves. We give the analytical formulas for the antenna response functions for the six polarizations which are valid for any equal-arm interferometric gravitational-wave detectors without optical cavities in the arms.The response function averaged over the source direction and polarization angle decreases at high frequencies which deteriorates the signal-to-noise ratio registered in the detector. At high frequencies, the averaged response functions for the tensor and breathing modes fall of as $1/f^2$, the averaged response function for the longitudinal mode falls off as $1/f$ and the averaged response function for the vector mode falls off as $ln(f)/f^2$.
Space-based gravitational wave detectors cannot keep rigid structures and precise arm length equality, so the precise equality of detector arms which is required in a ground-based interferometer to cancel the overwhelming laser noise is impossible. The time-delay interferometry method is applied to unequal arm lengths to cancel the laser frequency noise. We give analytical formulas of the averaged response functions for tensor, vector, breathing and longitudinal polarizations in different TDI combinations, and obtain their asymptotic behaviors. At low frequencies, $fll f_*$, the averaged response functions of all TDI combinations increase as $f^2$ for all six polarizations. The one exception is the averaged response functions of $zeta$ for all six polarizations increase as $f^4$ in the equilateral-triangle case. At high frequencies, $fgg f_*$, the averaged response functions of all TDI combinations for the tensor and breathing modes fall off as $1/f^2$, the averaged response functions of all TDI combinations for the vector mode fall off as $ln(f)/f^2$ , and the averaged response functions of all TDI combinations for the longitudinal mode fall as $1/f$. We also give LISA and TianQin sensitivity curves in different TDI combinations for tensor, vector, breathing and longitudinal polarizations.
Direct detection of gravitational radiation in the audio band is being pursued with a network of kilometer-scale interferometers (LIGO, Virgo, KAGRA). Several space missions (LISA, DECIGO, BBO) have been proposed to search for sub-Hz radiation from massive astrophysical sources. Here we examine the potential sensitivity of three ground-based detector concepts aimed at radiation in the 0.1 -- 10,Hz band. We describe the plethora of potential astrophysical sources in this band and make estimates for their event rates and thereby, the sensitivity requirements for these detectors. The scientific payoff from measuring astrophysical gravitational waves in this frequency band is great. Although we find no fundamental limits to the detector sensitivity in this band, the remaining technical limits will be extremely challenging to overcome.
Unlike ground-based gravitational wave detectors, space-based gravitational wave detectors can detect the ringdown signals from massive black hole binary mergers with large signal-to-noise ratio, and help to extract the source parameters and localize the source. To reduce the computation time in Fisher information matrix, we derive the analytical formulas of frequency-domain ringdown signals for heliocentric detectors and geocentric detectors by considering the effect of the harmonic phases, the rotation period of the geocentric detector, and the detector arm length. We explore the median errors of parameter estimation and source localization with ringdown singals from binaries with different masses and different redshifts. Using a binary source with the total mass $M=10^7 M_odot$ at the redshift $z=1$, we analyze the dependence of these errors on the sky position. We find that the network of space-based gravitational wave detectors can significantly improve the source localization at the ringdown stage.
In order to detect high frequency gravitational waves, we need a new detection method. In this paper, we develop a formalism for a gravitational wave detector using magnons in a cavity. Using Fermi normal coordinates and taking the non-relativistic limit, we obtain a Hamiltonian for magnons in gravitational wave backgrounds. Given the Hamiltonian, we show how to use the magnons for detecting high frequency gravitational waves. Furthermore, as a demonstration of the magnon gravitational wave detector, we give upper limits on GHz gravitational waves by utilizing known results of magnon experiments for an axion dark matter search.
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