tokens: 1843.03. Contours are spaced in 5% intervals in core mass fraction, with darker colors corresponding to high core mass fraction and lighter colors corresponding to low core mass fraction. As expected, denser planets with higher core mass fractions survive to shorter orbital periods. The limiting orbital period of a pure iron planet is approximately 3.8 hr at , 3.6 hr for , and 3.5 hr for . We note that this figure marginalizes over stellar mass because stellar mass only weakly affects the Roche-limiting minimum orbital period (Rappaport et al. 2013 ). The stellar density does, however, affect whether the planet can reach its Roche limit before colliding with the star (i.e., a = R ⋆ ) and thereby the minimum survivable orbital period for the planet. Figure 4. Composition and mass constraints on planets with KOI 1843.03's measured transit radius and host star mass. Colored contours show the values of the planet mass, which increases with decreasing orbital period and increasing core mass fraction. The boundary of the colored contours in the lower left corner corresponds to the Roche limit. The dashed gray line indicates the measured orbital period of KOI 1843.03. Figure 4 displays interpolated planet masses for a range of orbital periods and core mass fractions in systems consistent with KOI 1843.03's host star mass and transit radius. The boundary of the colored contours in the lower left corner corresponds to the Roche limit; as orbital period decreases, the core mass fraction is more tightly constrained. As anticipated, considering a fixed orbital period in Figure 4 , increasing the planet’s iron mass fraction increases the planet’s mass. Less intuitively, at fixed core mass fraction, decreasing the planet’s orbital period also leads to an increase in the inferred planet mass. This is due to the tidal distortion of the planet; at shorter orbital periods, the volume of the planet exceeds by larger and larger factors. As it orbits less than one stellar radius from the host star’s photosphere ( a / R ⋆ = 1.9), KOI 1843.03 will be significantly elongated in the direction of the star due to tidal distortion. Based on the parameters of KOI 1843.03, our models predict that it must be at least 31% longer along the star–planet line than along the perpendicular axes (aspect ratio of about 1.3), and our models support a value up to nearly twice as long along the star–planet line (aspect ratio of almost 1.8); various possibilities are illustrated in Figure 5 . For comparison, Saturn has an aspect ratio of about 1.1. Figure 5. Aspect ratio constraints on KOI 1843.03, as a function of core mass fraction. To the left of the plot, we indicate the maximum and minimum values of aspect ratio supported by the model grid and show three representative planet cross-sections (assuming ellipsoidal shapes); peach and navy represent the iron-dominated core and silicate mantle, respectively. Results are shown both at the measured transit radius 0.61 and the 1 σ limits
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