Title: Predictions of planet detections with near infrared radial velocities in the up-coming SPIRou Legacy Survey-Planet Search,
Abstract: The SPIRou near infrared spectro-polarimeter is destined to begin science
operations at the Canada-France-Hawaii Telescope in mid-2018. One of the
instrument's primary science goals is to discover the closest exoplanets to the
Solar System by conducting a 3-5 year long radial velocity survey of nearby M
dwarfs at an expected precision of $\sim 1$ m s$^{-1}$; the SPIRou Legacy
Survey-Planet Search (SLS-PS). In this study we conduct a detailed Monte-Carlo
simulation of the SLS-PS using our current understanding of the occurrence rate
of M dwarf planetary systems and physical models of stellar activity. From
simultaneous modelling of planetary signals and activity, we predict the
population of planets detected in the SLS-PS. With our fiducial survey strategy
and expected instrument performance over a nominal survey length of $\sim 3$
years, we expect SPIRou to detect $85.3^{+29.3}_{-12.4}$ planets including
$20.0^{+16.8}_{-7.2}$ habitable zone planets and $8.1^{+7.6}_{-3.2}$ Earth-like
planets from a sample of 100 M1-M8.5 dwarfs out to 11 pc. By studying
mid-to-late M dwarfs previously inaccessible to existing optical velocimeters,
SPIRou will put meaningful constraints on the occurrence rate of planets around
those stars including the value of $\eta_{\oplus}$ at an expected level of
precision of $\lesssim 45$%. We also predict a subset of $46.7^{+16.0}_{-6.0}$
planets may be accessible with dedicated high-contrast imagers on the next
generation of ELTs including $4.9^{+4.7}_{-2.0}$ potentially imagable
Earth-like planets. Lastly, we compare the results of our fiducial survey
strategy to other foreseeable survey versions to quantify which strategy is
optimized to reach the SLS-PS science goals. The results of our simulations are
made available to the community on github.