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Abstract

We investigate the ability of the Laser Interferometer Space Antenna (LISA)
to measure the center of mass acceleration of stellar-origin black hole
binaries emitting gravitational waves. Our analysis is based on the idea that
the acceleration of the center of mass induces a time variation in the redshift
of the gravitational wave, which in turn modifies its waveform. We confirm that
while the cosmological acceleration is too small to leave a detectable imprint
on the gravitational waveforms observable by LISA, larger peculiar
accelerations may be measurable for sufficiently long lived sources. We focus
on stellar mass black hole binaries, which will be detectable at low
frequencies by LISA and near coalescence by ground based detectors. These
sources may have large peculiar accelerations, for instance, if they form in
nuclear star clusters or in AGN accretion disks. If that is the case, we find
that in an astrophysical population calibrated to the LIGO-Virgo observed
merger rate, LISA will be able to measure the peculiar acceleration of a small
but significant fraction of the events if the mission lifetime is extended
beyond the nominal duration of 4 years. In this scenario LISA will be able to
assess whether black hole binaries form close to galactic centers, particularly
in AGN disks, and will thus help discriminate between different formation
mechanisms. Although for a nominal 4 years LISA mission the peculiar
acceleration effect cannot be measured, a consistent fraction of events may be
biased by strong peculiar accelerations which, if present, may imprint large
systematic errors on some waveform parameters. In particular, estimates of the
luminosity distance could be strongly biased and consequently induce large
systematic errors on LISA measurements of the Hubble constant with stellar mass
black hole binaries.