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

TL;DR

This paper addresses how to synthesize microlensing and transiting exoplanet demographics from the Roman Space Telescope by introducing a planet–host ratio relation (PHRR) that directly links transit depth $δ$ and planet–host mass ratio $q$. Using a curated sample of 908 confirmed exoplanets, the authors demonstrate that the $δ$–$q$ relation is continuous and well described by an empirical, mostly power-law PHRR, particularly when host temperature $T_\star$ and orbital period $P$ are included. The favored model is a two-regime PHRR in $q$ with $q_{br}$ and the slopes depending on $T_\star$, plus a weak $P$-dependence, with $q_{br} \propto (T_\star/T_\odot)^{-1.9}$ and $δ \propto (q/q_{br})^n (T_\star/T_\odot)^{-3.7} (P/10\,\mathrm{d})^{-0.10}$. The results support using a PHRR to jointly analyze Roman’s microlensing and transit samples, enabling demographic inferences even when individual masses or radii are not measured, though the authors caution that detection biases must be carefully considered and self-calibration with Roman data is essential.

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: $\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.

Figures (10)

• Figure 1: The observed distribution of transit depth versus planet--host mass ratio for the selected sample of 986 exoplanets. The colour map depicts host effective temperature, $T_\star$, with blue to red spanning cooler to hotter hosts, respectively, on a logarithmic stretch. Stratification of the distribution with $T_\star$ is clearly evident.
• Figure 2: The distributions of transit depth (top), mass ratio (middle) and stellar effective temperature (bottom) from our dataset of 986 exoplanets overlaid against the parent distributions from the NASA Exoplanet Archive.
• Figure 3: A $q$-$\delta$ diagram for our dataset of 986 exoplanets, colour-mapped according to the effective temperature of the host star. The ODR best-fit model with a universal $n_1$ and universal $q_{br}$ is plotted for several representative values of $T_\star$, where the colour of the line also corresponds to the legend at the bottom. The bottom panel shows the residuals (measured minus predicted where the prediction for each planet is calculated using its measured value of $T_\star$) along with the RMS residual (grey dashed line). 22 planets that orbit large stars ($R_\star \gtrsim 2.5 R_\odot$) are marked in both panels by black rings.
• Figure 4: Host luminosity plotted against host radius for each of the 986 planets in our dataset.The colour scale represents the log residuals (log transit depth subtract model prediction in log-space) from the universal $n_1$ and universal $q_{br}$ model in Figure \ref{['fig:large_star_q_delta']} such that blue points are over-predictions and red points are under-predictions. Our chosen large-star threshold at $\log \left( \frac{R_\star}{R_\odot} \right) = 0.4$ is shown by the black dashed line. Hosts which have subsequently been removed by iterative sigma clipping and fall below the large star threshold are denoted by open black triangles -- this has removed more than one planet for some hosts hence there are less than 22 outliers visibly plotted here.
• Figure 5: Relative residuals in transit depth (observed minus predicted over observed) plotted against the normalised mass-ratio ($q / q_{br}$) for the PHRR model with universal $n_1$ and universal $q_{br}$. Error bars are plotted but are often smaller than the size of the data point symbols. Data is colour-mapped according to $T_\star$. The left panel uses the original dataset of $N = 986$ exoplanets selected in Section \ref{['sec:data']}, the middle panel shows the effect of removing large stars before fitting, and the right panel demonstrates the impact of iterative sigma clipping at $3\sigma$ following the removal of large stars. The RMS relative residual is plotted (grey dashed lines) and displayed on each panel along with the Bayesian Information Criterion.