International Journal of Modern Physics D

Laser interferometer gravitational-wave (GW) detectors are observing signals from merging black hole and neutron star binaries with a frequency window from 10Hz to several kHz. Future space-based laser interferometers will open a new window of 0.1mHz to 0.1Hz. In this paper, we discuss the possibility of constructing a terrestrial GW detector named Superconducting Omni-directional Gravitational Radiation Observatory (SOGRO), which can fill the missing frequency window, 0.1 to 10Hz, with astronomically interesting sensitivity. SOGRO measures all five tensor components of the spacetime metric, which results in uniform sensitivity for all-sky directions and enables identification of the source direction and wave polarization with a single detector. Seismic and Newtonian gravity noise pose the greatest challenges for constructing ground-based detectors below 10Hz. SOGRO utilizes enhanced mechanical and electrical stabilities of materials at cryogenic temperatures to reject common-mode seismic noise to a very high degree. Further, its full-tensor characteristic gives an advantage in the rejection of the Newtonian noise over conventional detectors.

The new technique of measuring frequency by optical lattice clocks now approaches to the relative precision of $(\mathrm{\Delta }f/f)=O(10^{-18})$. We propose to place such precise clocks in space and to use Doppler tracking method for detecting low-frequency gravitational wave below 1Hz. Our idea is to locate three spacecrafts at one A.U. distance (say at L1, L4 and L5 of the Sun–Earth orbit), and apply the Doppler tracking method by communicating “the time” each other. Applying the current available technologies, we obtain the sensitivity for gravitational wave with third- or fourth-order improvement ($h_n\sim 10^{-17}$ or $10^{-18}$ level in $10^{-5}$–$1$Hz) than that of Cassini spacecraft in 2001. This sensitivity enables us to observe black hole (BH) mergers of their mass greater than $10^5{M}_{\odot }$ in the cosmological scale. Based on the hierarchical growth model of BHs in galaxies, we estimate the event rate of detection will be 20–50 a year. We nickname “INO” (Interplanetary Network of Optical Lattice Clocks) for this system, named after Tadataka Ino (1745–1818), a Japanese astronomer, cartographer, and geodesist.

Expanding the observational frequency of gravitational waves is important for the future of astronomy. Torsion-Bar Antenna (TOBA) is a mid-frequency and low-frequency gravitational wave detector using a torsion pendulum. The low resonant frequency of the rotational mode of the torsion pendulum enables ground-based observations. The overview of TOBA, including the past and present status of the prototype development, is summarized in this paper.

Atom-interferometric gravitational-wave (GW) space observatory (AIGSO) is a mission concept mainly aimed at the middle-frequency (0.1-10 Hz) GW detection. AIGSO proposes to have three spacecrafts in linear formation with extension of 10km. The three spacecrafts need to maintain $5\mathrm{\text{km}}+5\mathrm{\text{km}}$ constant arm-length formation. In this study, we address the issue of orbit design and thruster requirement. The acceleration to maintain the formation can be designed to be less than 30pm/s² and the thruster requirement is in the 30nN range. Application to other arm-length-maintaining missions is also discussed.

The Zhaoshan long-baseline Atom Interferometer Gravitation Antenna (ZAIGA) is a new type of underground laser-linked interferometer facility, and is currently under construction. It is in the 200-m-on-average underground of a mountain named Zhaoshan which is about 80km southeast to Wuhan. ZAIGA will be equipped with long-baseline atom interferometers, high-precision atom clocks, and large-scale gyros. ZAIGA facility will take an equilateral triangle configuration with two 1-km-apart atom interferometers in each arm, a 300-m vertical tunnel with atom fountain and atom clocks mounted, and a tracking-and-ranging 1-km-arm-length prototype with lattice optical clocks linked by locked lasers. The ZAIGA facility will be used for experimental research on gravitation and related problems including gravitational wave detection, high-precision test of the equivalence principle of micro-particles, clock-based gravitational red-shift measurement, rotation measurement and gravitomagnetic effect.

In previous papers, we have addressed the issues of orbit design and thruster requirement for the constant arm versions of Astrodynamical Middle-frequency Interferometric Gravitational-wave Observatory (AMIGO) mission concept and for the constant arm gravitational wave (GW) mission concept of Atom Interferometric Gravitational-wave Space Observatory (AIGSO). In this paper, we apply similar methods to the orbit design and thruster requirement for the constant arm GW missions B-DECIGO and DECIGO, and estimate the yearly propellant requirements at the specific impulse $I_{\mathrm{\text{sp}}}=300$s and $I_{\mathrm{\text{sp}}}=1000$s. For the geocentric orbit options of B-DECIGO which we have explored, the fuel mass requirement is a concern. For the heliocentric orbit options of B-DECIGO and DECIGO, the fuel requirement to keep the arm equal and constant should be easily satisfied. Furthermore, we explore the thruster and propellant requirements for constant arm versions of LISA and TAIJI missions and find the fuel mass requirement is not a show stopper either. The proof mass actuation noise is a concern. To have enough dynamical range, an alternate proof mass is required. Detailed laboratory study is warranted.

AMIGO is a first-generation Astrodynamical Middle-frequency Interferometric Gravitational Wave (GW) Observatory. The scientific goals of AMIGO are to bridge the spectra gap between first-generation high-frequency and low-frequency GW sensitivities: to detect intermediate mass BH coalescence; to detect inspiral phase and predict time of binary black hole coalescences together with binary neutron star & black hole-neutron star coalescences for ground interferometers; to detect compact binary inspirals for studying stellar evolution and galactic population. The mission concept is to use time delay interferometry (TDI) for a nearly triangular formation of three drag-free spacecraft with nominal arm length 10,000 km, emitting laser power 2–10 W and telescope diameter 300–500 mm. The design GW sensitivity in the middle frequency band is $3\times 10^{-21}$ Hz${}^{-1}$. Both geocentric and heliocentric orbit formations are considered. All options have LISA-like formations, that is, the triangular formation is $60^{\circ }$ inclined to the orbit plane. For all solar orbit options of AMIGO, the first-generation TDI satisfies the laser frequency-noise suppression requirement. We also investigate for each option of orbits under study, whether constant equal-arm implementation is feasible. For the solar-orbit options, the acceleration to maintain the formation can be designed to be less than 15 nm/s² with the thruster requirement in the 15 $\mu$N range. AMIGO would be a good place to test the feasibility of the constant equal-arm option. Fuel requirement, thruster noise requirement and test mass acceleration actuation requirement are briefly considered. From the orbit study, the solar orbit option is the mission orbit preference. We study the deployment for this orbit option. After a last-stage launch from 300 km Low Earth Orbit (LEO), each S/C’s maneuver to an appropriate 2-degree-behind-the-Earth AMIGO formation in 95 days requires only a $\mathrm{\Delta }$v of about 80 m/s.