Twinkle Twinkle Little Star, Roman Sees Where You Are: Predicting Exoplanet Transit Yields in the Rosette Nebula with the Nancy Grace Roman Space Telescope

Young stars host only a small fraction of the known exoplanet population because their photometric variability, magnetic activity, and frequent placement in dense, poorly-resolved regions hamper exoplanet detections. Yet, measuring planets at these ages is crucial since these phases are when dynamical processes that drive planetary migration are most active. We assess the expected yield of a hypothetical Nancy Grace Roman Space Telescope transit survey of the Rosette Nebula, a ${\sim}10$ Myr star-forming region with a dense and diverse stellar population. Using the Roman Exposure Time Calculator to quantify sensitivity to Rosette members, we establish detection thresholds for companions and evaluate yields via Monte Carlo injection-recovery simulations, accounting for nebular extinction and youth-driven stellar variability. We predict the detection of $33 \pm 9$ young transiting exoplanets orbiting stellar hosts in a month-long survey, and $29 \pm 8$ in a two-week survey. The extended baseline primarily improves sensitivity to longer-period planets orbiting FGK stars, while most M dwarf detections are well-sampled within two weeks. Irrespective of the temporal baseline, transit detections are dominated by of 1-2 $R_\oplus$ super-Earths and sub-Neptunes with $P\lesssim8$ days. Such a sample would substantially expand the census of only three detected transiting planets younger than 20 Myr around stars less massive than the Sun, probing an age regime in which planetary radii remain inflated, the stability of close-in orbits is uncertain, and planetary migration may still be ongoing. This survey offers a path to constrain early planetary evolution and establish prime follow-up targets for JWST, Rubin, and the Habitable Worlds Observatory.