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

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: $\sim$1,400 cold exoplanets via microlensing and $\sim$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 {\em ratio} relation (PHRR) to couple directly microlensing and transit observables in demographic forward-modelling simulations. Unlike the MRR, a PHRR uses parameters that are always measured and so can potentially leverage the full Roman exoplanet sample. Using 908 confirmed exoplanets from the NASA Exoplanet Archive, we show that transit depth, $δ$, 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 $δ(q,T_\star, P)$, 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 $δ$ for all $q$. Approximately $5%$ of the sample has a transit depth that is strongly over-predicted by the PHRR; around half of these are associated with large stars ($R_\star > 2.5 , R_{\odot}$) potentially subject to Malmquist bias.

💡 Research Summary

The paper addresses a fundamental challenge that will arise with the NASA Nancy Grace Roman Space Telescope: how to combine the vastly different observables produced by its microlensing and transit surveys into a single, coherent demographic framework. Microlensing directly yields the planet‑to‑host mass ratio (q), while transits provide the transit depth (δ), the square of the planet‑to‑host radius ratio. Traditional planet mass–radius relations (MRR) require both mass and radius to be measured, which is only possible for a minority of the expected Roman sample. To exploit the full yield—∼1,400 cold planets from microlensing and ∼200,000 hot planets from transits—the authors propose a Planet‑Host Ratio Relation (PHRR) that links q and δ directly.

Using the NASA Exoplanet Archive, they assembled a clean sample of 986 confirmed planets with well‑determined masses, radii, host effective temperatures (T★), and orbital periods (P). Strict cuts removed objects with unphysical densities (e.g., exceeding a pure‑iron model), masses above the deuterium‑burning limit, or large uncertainties (>0.2 dex in log‑space). The resulting dataset spans q≈10⁻⁶–10⁻² and shows a continuous, monotonic relationship between log δ and log q, unlike the broken regimes seen in traditional MRRs.

Visual inspection revealed two key trends: (1) a clear “break” in the slope around q_br≈10⁻⁴, where the dependence of δ on q flattens, and (2) a systematic temperature gradient—planets orbiting hotter, larger stars have smaller δ at a given q. This motivated a broken power‑law model in log‑space, with separate slopes (n₁ for q ≤ q_br, n₂ for q > q_br). To capture the temperature and period dependence, n₂ was allowed to vary linearly with log T★ and log P: n₂ = α log T★ + β log P + γ. The full functional form is:

log δ = b + n₁ · (log q − log q_br) (q ≤ q_br)
log δ = b +