Using Mass Loss to Probe Super-Earth Populations

Title: How Thermal Evolution and Mass Loss Sculpt Populations of Super-Earths and Sub-Neptune: Application to the Kepler-11 System and Beyond
Authors: Eric Lopez, Jonathan Fortney, Neil Miller
Author’s institution: UC Santa Cruz


Planet Densities: Tricky to Determine

The Kepler telescope is discovering thousands of small planets with radii between the radii of Earth and Neptune. While it is great to detect all of these planets, we also want to know their compositions. Are they rocky, icy, or gassy, and what kind of atmospheres do they have? Few of Kepler’s planet candidates have a measured mass, which, combined with the radius from the transit, would allow us to calculate the density. The density would give us clues about the planet’s composition. If it’s very dense, it must be rocky; if it has a very low density, it must have a fluffy hydrogen-helium envelope. Intermediate densities get tricky: see for example this astrobite about GJ 1214b.

We would very much like to understand planet densities for the entire population of planets. To probe this question, this team from UC Santa Cruz investigated how planets lose mass over their lifetimes, and determined how this loss will affect planet populations.

Mass Loss: a Key to Understanding the Super-Earth Population

For a planet of a given mass, if it is dense (for example, a rocky or water-based planet) it will have a small radius, and its atmosphere will be held on by a strong gravitational force. In contrast, if it has a low density (a fluffy hydrogen-helium envelope) the radius is larger and the gravitational force at the top of the atmosphere is smaller. The low-density planet then loses mass much more quickly, driven by high-energy UV radiation from the host star. By understanding this mass loss, we could constrain the density of many super-Earths: low-density planets close to their stars will not be able to hold an atmosphere during their evolution.

Modeling Mass Loss for Small Planets

In this study, the mass loss is assumed to be ‘energy-limited.’ This assumption means that a constant fraction (dubbed the ‘efficiency’) of the energy deposited into the planet by UV irradiation from the host star goes into driving mass away from the planet. The energy of UV photons is thus balanced by the gravitational energy it takes to eject mass away. The mass loss model accounts for the changing irradiation from the host star over time; this is critical,  as the amount of UV flux shrinks by a factor of almost 100 from the planet’s childhood to Earth’s current age (4.5 billion years).

To model mass loss properly at these early times, the mass loss model must be coupled to a planetary evolution model. This is very important because the planet is born with a large internal temperature and radius, and shrinks over time as it ages and cools. Recall that a larger radius makes the planet more susceptible to mass loss, since the gravitational force at the top of the atmosphere will be smaller.

These models are applied to the system of 6 planets discovered last year, Kepler-11. The models show that these planets are probably dense and rich in water, rather than rocky with extended hydrogen/helium atmospheres.

A Cutoff in Density for Super-Earths

So far, Kepler has not found any small, low-density planets that are highly irradiated (see figure 1), suggesting that such planets are rare if they exist at all.  The evolutionary models from Lopez et al. that assume an efficiency of 20% (see figure 2, upper left and bottom center panels) reproduce this observed planet population.  They demonstrate that small, low-density planets that are highly irradiated lose their fluffy atmospheres, becoming denser over time.

The incident flux from the host star is plotted against the planet density. Low-mass planets less than 15 earth masses are plotted as the colored points, color coded by composition. Red points are high-density rocky planets, orange are low-density H/He planets, and blue are intermediate density planets. (Larger exoplanets are plotted as grey crosses). Dashed lines show lines of constant mass loss at a given age. Note that there are no small, low-density planets above the dashed line of constant mass loss of 1 Earth mass per Gyr at 100 Myr.


The results of population models for planets are shown. The axes are the same as in Figure 1, with density plotted against incident flux. The color of the dot shows the H/He fraction and the size of the dot shows the size of the planet. Note that for the 20% efficiency of mass loss, the population models seem to match the population of super-Earths observed so far, which a cutoff above a threshold incident flux.


In the Future

This paper suggests that we can understand the population of small planets using mass loss models, and we make predictions using these models for the masses of irradiated super-Earths. However, currently there are only a dozen super-Earths with measured densities. To confirm that the flux-density threshold predicted here is real and widely applicable, we will need to measure the masses of more of these low-mass, low-density planets, for which mass loss seems to be an important part of their evolution.

About Caroline Morley

I am a third-year graduate student at UC Santa Cruz, working with Jonathan Fortney to model and characterize exoplanet and brown dwarf atmospheres.

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