A planet-host ratio relation to synthesize microlensing and transiting exoplanet demography from Roman

Abstract: The NASA Nancy Grace Roman Space Telescope (Roman) will be the first survey able to detect large numbers of both cold and hot exoplanets across Galactic distances: ~1,400 cold exoplanets via microlensing and ~200,000 hot, transiting planets. Differing sensitivities to planet bulk properties between the microlensing and transit methods require relations like a planet mass-radius relation (MRR) to mediate. We propose using instead a planet-host ratio relation (PHRR) to couple directly microlensing and transit observables. Unlike the MRR, a PHRR uses parameters that are always measured and so can leverage the full Roman exoplanet sample. Using 908 confirmed exoplanets from the NASA Exoplanet Archive, we show that transit depth, $\delta$, and planet-host mass ratio, $q$, obey a PHRR that is continuous over all planet scales. The PHRR is improved by including orbital period, $P$, and host effective temperature, $T_{\star}$. We compare several candidate PHRRs of the form $\delta (q,T_\star, P)$, with the Bayesian Information Criterion favouring power-law dependence on $T_\star$ and $P$, and broken power-law dependence on $q$. The break in $q$ itself depends on $T_\star$, as do the power-law slopes in $q$ either side of the break. The favoured PHRR achieves a fairly uniform $50\%$ relative precision in $\delta$ for all $q$. Approximately $5\%$ of the sample has a transit depth that is strongly under-predicted by the PHRR; around half of these are associated with large stars ($R_\star > 2.5 \, R_{\odot}$) potentially subject to Malmquist bias.