Upper limits on exosatellites around β Pictoris b

$\beta$ Pictoris b is one of the closest known directly-imaged gas giant exoplanets with an orbit that is almost edge-on to our line of sight, making it an ideal target for radial velocity monitoring to search for massive exomoons. We measure the radial velocity of $\beta$ Pictoris b over several epochs between October 2024 and March 2025 by using the cross-correlation of a template spectrum with absorption lines in the planet's atmosphere, giving a mean precision of 160 m s$^{-1}$. The resultant set of radial velocities is analysed with a periodogram to search for candidate RV signals indicating a massive exomoon. Although we do not detect an exomoon signal in our data, our detection limits for a single moon are 80 Earth masses at P=1 day and 1 Jupiter at P=200 days, comparable to RV exomoon searches around other substellar companions. The RV limit is comparable with the astrometric exomoon limit at a period of 7 days and a mass of 150 Earth masses, where for longer periods the astrometric searches have lower mass limits. With an additional observing season, CRIRES+ can detect a planet/moon mass ratio of $10^{-3}$ (4 Earth masses) with a period of up to one day, and can detect a Neptune-mass moon at hundreds of Jupiter radii.