Orbit optimization and time delay interferometry for inclined ASTROD-GW formation with half-year precession-period

TL;DR

This paper optimizes the orbits and analyzes time delay interferometry for the inclined ASTROD-GW mission with a half-year precession period, aiming to enhance gravitational wave detection sensitivity and resolve source position ambiguities.

Contribution

It introduces a numerical orbit optimization and TDI simulation for inclined ASTROD-GW formations with various inclinations, improving detection sensitivity and source localization.

Findings

Inclined formations improve source position determination.

Optimized orbits achieve required sensitivity by suppressing laser noise.

Inclination angles up to 3 degrees are feasible for mission design.

Abstract

ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave detection) is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirals (EMRIs) and galactic compact binaries, together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecrafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD-GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry (TDI) for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precession-period. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle is 0{\deg} (no inclination), 0.5{\deg}, 1.0{\deg}, 1.5{\deg}, 2.0{\deg}, 2.5{\deg} and 3.0{\deg}. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0{\deg} as example to show the orbit optimization and TDI simulation.