# On the 9:7 Mean Motion Resonance Capture in a System of Two Equal-mass Super-Earths

## TL;DR

This study investigates how two equal-mass super-Earths can be captured into the 9:7 mean motion resonance during their migration in a protoplanetary disk, highlighting the disk conditions and initial parameters that facilitate this process.

## Contribution

The paper provides the first detailed hydrodynamic simulations identifying the specific disk properties and initial conditions that enable 9:7 resonance capture of super-Earths.

## Key findings

- Capture occurs during convergent migration within a specific resonance angle window.
- The width of the capture window depends on the relative migration and circularization rates.
- High migration rates can prevent resonance capture altogether.

## Abstract

We study the formation of the 9:7 mean motion resonance in a system of two low-mass planets ($m_{1}=m_{2}=3M_{\oplus}$) embedded in a gaseous protoplanetary disk employing a full 2D hydrodynamic treatment of the disk-planet interactions. Our aim is to determine the disk properties that favor a capture of two equal-mass super-Earths into this second-order resonance. For this purpose, we have performed a series of numerical hydrodynamic simulations of the system of two super-Earths migrating in disks with a variety of different initial parameters and found conditions for the permanent or temporary locking in the 9:7 resonance. We observe that capture occurs during the convergent migration of planets if their resonance angle at the moment of arrival at the resonance assumes values in a certain range (inside a window of capture). The width of such a window depends on the relative migration and circularization rates that are determined by the disk parameters. The window is wide if the relative migration rate is slow, and it becomes narrower as the relative migration rate increases. The window will be closed if the migration rate is sufficiently high, and the capture will not take place. We illustrate also how the 9:7 resonance window of capture is affected by the initial eccentricities and the initial orbits of the planets.