High-eccentricity migration of hot and warm Jupiters

I worked on my thesis trying to understand how the hundreds of Jupiter-like planets discovered in short-period orbits (<10 days, the so-called hot Jupiters) could have attained their extreme orbits.

One formation channel that I studied is known as high-eccentricity migration. This channel postulates that Jovian planets are generally formed in wide orbits (like Jupiter), but after its birth gas disk dissipates a fraction (less than ~10%) of them can somehow reach extreme eccentricities and approach their host star very closely. During these close approaches the tidal forces acting on the planet become very strong and can drive efficient energy dissipation so the planet's orbit shrinks and circularizes to give rise to a hot Jupiter (see cartoon below).

It turns out that the way the planet attains its high eccentricity really matters and can have a different imprint in the final orbital distributions of the hot Jupiters that can be compared to the observed distributions of:

- orbital periods (or semi-major axes);

- orbital eccentricities;

- spin-orbit angles (or stellar obliquity, angle between the star's equator and the orbital plane).

This comparison of orbital configurations along with observations of companions of hot Jupiters (stars or planets in wider orbits) has allowed me (and others) to test the high-eccentricity theory.

I describe some of the high-lights from each paper below.

Coplanar High-eccentricity Migration (CHEM) from Petrovich 2015a

I proposed that high-e migration by secular gravitational interactions with an eccentric outer planet in a nearly coplanar orbit, which I termed Coplanar High-e Migration, is a promising mechanism to explain the population of low-obliquity hot Jupiters. I based this conclusion on the matching to the orbital period distribution, the formation rates, and the prevalence of long-period planets companions of hot Jupiters with are usually observed to be eccentric.

Low-obliquity hot Jupiters, which constitutes most of the observed sample, are hard to form by other high-e channels and are generally attributed to disk-migration. My work proposes an alternative and sound mechanism.

The figure below shows a typical evolution. The end-state: a hot Jupiter at ~3-4 day circular orbit with low spin-orbit angle with a nearly coplanar planet-mass companion at >~5 AU.

Example of a planet undergoing Coplanar High-Eccentricity Migration ("in"=inner or migrating planet)

Lidov-Kozai migration in stellar binaries from Petrovich 2015b

One popular high-e channel is through the Lidov-Kozai mechanism in stellar binaries. As first proposed by Wu & Murray 2003, this channel could explain the current orbit of HD80606b, a Jovian planet at ~0.4 AU with a remarkable eccentricity of e~0.93 and spin-orbit angle of >45 degrees, since the primary is orbited by a wide binary companion.

This channel has become appealing because in the last ~10 years many hot Jupiters have been found with large of spin-orbit angles, including retrograde orbits (>90 degs). Moreover, a significant fraction of planetary systems are part of a binary.

In the longest paper I ever wrote, I studied the steady-state orbital distributions of planets migrating through this channel. There are various results that came out of this work, but probably the main one is simple: proto-hot Jupiters tend to be tidally disrupted before they circularize. As a result, the many planets are tidally disrupted and the period distribution is skewed towards smaller semi-major axes than those observed (see figure).

(in construction)

Warm Jupiters from secular planet-planet interactions from Petrovich & Tremaine 2017

Planet-planet scattering at small separations: constraining planet migration from Petrovich, Tremaine & Rafikov 2014