Ellen is a sixth-year graduate student at the Center for Astrophysics | Harvard & Smithsonian. Her thesis advisor is Prof. Karin Öberg, with whom she studies the effects of combined chemistry and fluid dynamics in protoplanetary disks. Ellen plans to graduate with her PhD in May 2021 and is actively seeking job opportunities. You can contact her at ellen.price@cfa.harvard.edu with any questions or comments about this poster. Further information is available at her website and her ORCiD page.

Prof. Rogers is a professor at the University of Chicago. She studies the formation, interior structure, and evolution of exoplanets. The main goals of her research group are to deepen the current understanding of the rich physics governing sub-Neptune-size planet interiors, to discover bulk composition trends in the growing census of known exoplanets, and to connect these composition trends back to distinct planet formation pathways. You can contact Prof. Rogers at larogers@uchicago.edu or visit her ORCiD page.

Tidally Distorted, Iron-enhanced Exoplanets Closely Orbiting Their Stars

The transiting planet candidate KOI 1843.03 (0.6$R_\oplus$ radius, 4.245 hr orbital period, 0.46$M_\odot$ host star) has the shortest orbital period of any known planet. Here we show, using the first three-dimensional interior structure simulations of ultra-short-period tidally distorted rocky exoplanets, that KOI 1843.03 may be shaped like an American football, elongated along the planet-star axis with an aspect ratio of up to 1.79. Furthermore, for KOI 1843.03 to have avoided tidal disruption (wherein the planet is pulled apart by the tidal gravity of its host star) on such a close-in orbit, KOI 1843.03 must be as iron-rich as Mercury (about 66% by mass iron compared to Mercury's 70% by mass iron). Of the ultra-short-period ($P_\mathrm{orb} \leq 1$ day) planets with physically meaningful constraints on their densities characterized to date, just under half (four out of nine) are iron-enhanced. As more are discovered, we will better understand the diversity of rocky planet compositions and the variety of processes that lead to planetary iron enhancement.

Methods

We follow Hachisu (1986a,b) and use a numerical relaxation method to compute the shapes of tidally-distorted exoplanets. The simulation space and coordinate system are shown. We assume a tidally-locked exoplanet in a circular orbit around a point-source star; note that Hachisu (1986a,b) did not include any point sources, so we modified the method to account for this.

The relaxation method iterates between two phases. First, the density field of the planet (initialized with a constant guess) is converted to an enthalpy via a potential solver. Then, the resulting enthalpy is converted back to a density through the assumed equation of state. We repeat the iteration until convergence to a user-specified tolerance is reached.

One challenge of our method is that it is not numerically feasible at present to specify system properties such as the host star mass or core mass fraction of the planet; we obtain these only at the end of the relaxation method. So, we build a large “grid” of model planets and interpolate the observable properties on that grid instead of simulating our target planets directly.

Results

One exciting example of a rocky planet that may be tidally distorted is KOI-1843.03 (Rappaport et al. 2013). On a 4.2-hour orbit around its host star, it is orbiting at a remarkable speed (about six times faster than Mercury). To better understand this planet, we attempted to constrain its properties with two different equations of state. The first has a pure iron core surrounded by a silicate mantle, while the second has a “polluted” iron core — pure FeS — surrounded by a silicate mantle. These two compositions represent the end member configurations; KOI-1843.03 likely falls somewhere in between.

In the figures below, we show some constraints on the composition and shape of KOI-1843.03. We find that KOI-1843.03 is probably not consistent with the pure FeS core equation of state but that it can easily survive if its core is pure iron.

Contours of core mass fraction as a function of minimum orbital period and transit radius for planets in our model grid with a pure Fe core. We find that this composition allows KOI-1843.03 to exist at its current location; the vertical gray bar indicates the range of measured values for KOI-1843.03.

Contours of core mass fraction as a function of minimum orbital period and transit radius for planets in our model grid with a pure FeS core. We see that, now, the vertical gray bar that indicates KOI-1843.03's measured properties falls mostly outside the contours, so it can only have survived if the measured transit radius is larger than the mean value.

Aspect ratio as a function of core mass fraction for KOI-1843.03. In addition to a contour at the measured transit radius, we also show a contour for the $\pm 1\sigma$ limits. From this, we find that KOI-1843.03 could be distorted to an aspect ratio of up to about 1.8.

Conclusions

For the first time, we have undertaken consistent, three-dimensional modeling of tidally-distorted rocky exoplanets. We put constraints on a few previously-discovered exoplanets from Kepler and K2. TESS is likely to find many more of these fascinating planets, and, as that number grows, we are sure to learn more about the variety of compositions of these planets and what formation scenarios are possible.

References

  1. Hachisu, I. 1986a, ApJS, 61, 479, doi: 10.1086/191121
  2. Hachisu, I. 1986b, ApJS, 62, 461, doi: 10.1086/191148
  3. Rappaport, S., Sanchis-Ojeda, R., Rogers, L. A., Levine, A., Winn, J. N. 2013, ApJL, 773, L15, doi: 10.1088/2041-8205/773/1/L15

Acknowledgements

This material is based upon work supported by a National Science Foundation Graduate Research Fellowship under Grant Nos. DGE1144152 and DGE1745303. L.A.R. acknowledges NSF grant AST-1615315. The computations in this work were carried out with resources provided by the University of Chicago Research Computing Center.