Waltzing binaries: Probing line-of-sight acceleration of merging compact objects with gravitational waves

Line-of-sight acceleration of a compact binary coalescence (CBC) event would modulate the shape of the gravitational waves (GWs) it produces with respect to the corresponding non-accelerated CBC. Such modulations could be indicative of its astrophysical environment. We investigate the prospects of detecting this acceleration in future observing runs of the LIGO-Virgo-KAGRA network, as well as in next-generation (XG) detectors and the proposed DECIGO. We place the first observational constraints on this acceleration, for putative binary neutron star mergers GW170817 and GW190425. We find no evidence of line-of-sight acceleration in these events at $90\mathrm{\%}$ confidence. Prospective constraints for the fifth observing run of the LIGO at A+ sensitivity suggest that accelerations for typical BNSs could be constrained with a precision of $a\mathrm{/}c\sim {10}^{-7}[{\mathrm{s}}^{-1}]$, assuming a signal-to-noise ratio of $10$. These improve to $a\mathrm{/}c\sim {10}^{-9}[{\mathrm{s}}^{-1}]$ in XG detectors, and $a\mathrm{/}c\sim {10}^{-16}[{\mathrm{s}}^{-1}]$ in DECIGO. We also interpret these constraints in the context of mergers around supermassive black holes.