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Abstract:
Redshifts of an astronomical body measured atmultiple epochs (e.g., separated by 10 yr)
are different due to the cosmic expansion. This so-called Sandage–Loeb test offers a
direct measurement of the expansion rate of the Universe. However, acceleration in
the motion of the Solar System with respect to the cosmic microwave background also
changes redshifts measured at multiple epochs. If not accounted for, it yields a biased
cosmological inference. To address this,we calculate the acceleration of the Solar System
with respect to the Local Group of galaxies to quantify the change in themeasured redshift
due to local motion. Our study is motivated by the recent determination of the mass of
the Large Magellanic Cloud (LMC), which indicates a significant fraction of the MilkyWay
mass. We find that the acceleration towards the Galactic Center dominates, which gives
a redshift change of 7 cms−1 in 10 yr, while the accelerations due to the LMC and M31
cannot be ignored, depending on lines of sight. We create all-sky maps of the expected
change in redshift and the corresponding uncertainty, which can be used to correct for
this effect.
