The Kepler mission observed thousands of transiting exoplanet candidates around hundreds of thousands of FGK dwarf stars. He, Ford, & Ragozzine (2019) applied forward modelling to infer the distribution of intrinsic architectures of planetary systems, developed a clustered Poisson point process model for exoplanetary systems (SysSim) to reproduce the marginal distributions of the observed Kepler population, and showed that orbital periods and planet radii are clustered within a given planetary system. Here, we extend the clustered model to explore correlations between planetary systems and their host star properties. We split the sample of Kepler FGK dwarfs into two halves and model the fraction of stars with planets (between 0.5−10$R_{Earth}$ and 3–300 d), $f_{swpa}$, as a linear function of the Gaia DR2 $b_p−r_p$ color. We find that the occurrence of these planets rises significantly towards later type (redder or higher $b_p−r_p$) stars, with a slope of $df_{swpa}/d(b_p−r_p)=0.53^{+0.19}_{−0.19}$. The fraction of stars with planets increases from $f_{swpa}=0.34^{+0.08}_{−0.11}$ for F2V dwarfs to $f_{swpa}=0.91^{+0.09}_{−0.18}$ for mid K-dwarfs. About half ($f_{swpa}=0.54^{+0.08}_{−0.13}$) of all solar-type (G2V) dwarfs harbour a planetary system between 3 and 300 d. While this linear $f_{swpa}(b_p−r_p)$ model is simple, it can closely match the observed multiplicity distributions of both bluer and redder halves in our sample, suggesting that the architectures of planetary systems around stars of different spectral types may be similar aside from a shift in the overall fraction of planet hosting stars.

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Figure caption: The best-fitting relation for the fraction of stars with planets $f_{swpa}$ as a function of the Gaia $b_p-r_p$ colour, from our linear model. Light blue and green lines show 100 best models each passing our KS and AD distance thresholds, respectively. The bolded blue line shows a single model with $df_{swpa}/d(b_p-r_p) = 0.6$ and $f_{swpa,med} = 0.6$, while the shaded blue region represents the 68.3% credible interval from our KS analysis. The dashed vertical line denotes the median colour of our sample ($(b_p - r_p)_{med} \simeq 0.95$). A few other exemplary values (magenta) are labeled with arrows, including red for the solar value ($T_{eff} = 5770$ K), where we have used a table relating $T_{eff}$ and $b_p - r_p$ from Pecaut & Mamajeck (2013). The fraction of Sun-like stars with planets (with orbital periods in the range 3–300 d and radii in the range $0.5-10 R_\oplus$) is very close to half. The fraction increases by over a factor of two from the bluest (early F) to the reddest (late K) dwarfs in our sample, and reaches 100% at $b_p - r_p \simeq 1.6$, which may suggest that a more complicated model than a linear relation is necessary. The top panel shows a histogram for the distribution of $b_p - r_p$ colours for our stellar sample, where arrows indicate the 10% and 90% quantiles. ia