What are hot Earths?

At one extreme of planet formation are the so-called ultra-short-period planets (USP) loosely defined as small planets with orbital period shorter than 1 day. They occur around 0.5% Sun-like stars and their radii almost never exceed 2 R⊕. Often bathed in stellar irradiation thousand times stronger than that of the Earth, the surface equilibrium temperature of these planets may exceed 2000K, melting most of the rock-forming minerals and earning these planets the nickname “Lava worlds” or “Hot Earths”.

The composition of hot Earths

Hot Earths may represent our best chance of constraining the composition of Earth-sized planet in the near future. For a true Earth analogue on 1 year orbit around a sun-like star. The induced radial velocity semi-amplitude is only ~10 cm/s. This is beyond the capability of current state-of-art spectrographs which can consistently achieve 1m/s precision. With a much closer orbit, a hot Earth can induce radial velocity signal that is almost one order of magnitude stronger, putting it within the reach of current technologies. Moreover, the photoevaporation theory predicts that many hot Earths should be devoid of H/He envelope. This helps to remove some of the degeneracy in the core composition when only the mass and radius of planet are measured.

Over the past few years, we have discovered and measured the masses of 5 hot Earth systems with the NASA K2 mission and a suite of ground-based facilities including HARPS, HARPSN, Magellan/PFS etc. One of the great challenges in measuring the masses of these planets was to disentangle the planetary signal from the spurious radial velocity variation due to stellar activity. We used a method called Gaussian Process regression which models the correlated stellar noise with a covariance matrix. It turns out that stellar activity not only affects the measured radial velocities, but also the measured light curve in a similar fashion. One can use the light curve which is measured with better precision and higher cadence to train the Gaussian Process model before applying it to radial velocity dataset.

With this technique, we performed a homogeneous analysis of all hot Earths that reside in the so-called photoevaporation desert (photoevaporation desert > 650 F⊕, read more here). Planets in the photoevaporation desert should be devoid of H/He envelope that complicates the inference of planet's core composition. We used Gaia DR2 parallax to refine the stellar parameters. The resultant mean stellar density was imposed as prior in transit analysis to better constrain planet radius.

As a group, hot Earths are mostly consistent with an Earth-like composition of iron and rock mixture. WASP-47e and 55 Cnc e the two largest planets in this sample have the lowest density. They either have a very low Fe content or some amount of volatiles on top of a earth-like core. Curiously, WASP-47 and 55 Cnc e are the most metal-rich in this sample with [Fe/H] = 0.38 and 0.31. Moreover, both system have short-period giant planet companions on 4 and 15 day orbits which unlikely formed in-situ. Both systems may be the products of disk migration from outside snowline where the giant planets underwent run-away accretion and the small planets obtained substantial amount of volatile materials.

Orbital Configuration of hot Earths

At such close-in orbit (often just a few stellar radii away from their host star), the hot Earths presented quite a puzzle to planet formation theories. Many are within the dust sublimation radius or even the radius of the host star during the pre-main sequence. It seems very unlikely that hot Earths could have formed where we see them today.

Several formation scenarios have been proposed to reconcile the existence of these hot Earths with more conventional planet formation theories. For example, Lee and Chiang 2017 proposed that the inner edge of planet formation is set by magnetosphere truncation. Planets on shorter period are increasingly rare because they have to be brought in by asynchronous equilibrium tides after disk dissipation.

An alternative theory proposed by Petrovich et al 2018 claims that hot Earths were initially the innermost planet of a multi-planet system. The innermost planets can be excited to a high eccentricity through secular interaction with outer planets. When the eccentricity is high enough (~0.8), tidal interaction with the host star takes over and start to shrink the orbits of these planets. A key prediction of this scenario is that the shortest-period planets should have high inclinations (10-50 degrees) relative to their outer planets since secular interaction often excites eccentricity and inclination together. In contrast, in Lee and Chiang’s dynamically colder scenario, the inclination of the shortest-period planets should be low.

We put these ideas to test by directly measuring the mutual inclination of about 100 transiting multi-planet systems discovered by Kepler . We inferred the orbital inclinations of the planets using their transit profiles. To remove some of the degeneracies between orbital inclination and mean stellar density, we used Gaia DR2 to pin down the stellar parameters before using it as a prior in transit analysis.

Our results (Dai et al 2018) show that at larger orbital distance (a/Rs>5), the mutual inclination is generally low: less than 5 degree or so. This is consistent with previous works such as Tremaine and Dong 2012 (less than 5 deg), Fang and Margot 2012 (less than 3 deg) and Fabrycky et al 2014 (1-2 deg). However for the shortest-period planets (a/Rs less than 5), the mutual inclination fills up to the detectable range of 10-15 deg. Moreover, the higher mutual inclinations are also associated with larger period ratio between neighbouring planets. We argue that this favors a dynamically hot origin for the hot Earths that generated orbital shrinkage and larger mutual inclination simultaneously e.g. the "secular chaos" scenario by Petrovich et al 2018.