# Inclined Massive Planets in a Protoplanetary Disc: Gap Opening, Disc Breaking, and Observational Signatures

## TL;DR

This study uses 3D hydrodynamical simulations and radiative transfer calculations to explore how massive inclined planets can cause disc breaking, misalignment, and observable signatures like shadows and gaps, aiding in planet detection.

## Contribution

It provides new analytical formulas and simulation results linking planet mass, gap properties, and disc breaking conditions, advancing understanding of planet-disc interactions.

## Key findings

- Massive planets induce deep gaps and disc breaking.
- Disc misalignment leads to observable shadows and kinematic signatures.
- Deep gaseous gaps are associated with disc shadowing in observed systems.

## Abstract

We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the disc's secular evolution induced by the planet. We find that, when the planet is massive enough and the induced gap is deep enough, the disc inside the planet's orbit breaks from the outer disc. The inner and outer discs precess around the system's total angular momentum vector independently at different precession rates, which causes significant disc misalignment. We derive the analytical formulae, which are also verified numerically, for: 1) the relationship between the planet mass and the depth/width of the induced gap, 2) the migration and inclination damping rates for massive inclined planets, and 3) the condition under which the inner and outer discs can break and undergo differential precession. Then, we carry out Monte-Carlo radiative transfer calculations for the simulated broken discs. Both disc shadowing in near-IR images and gas kinematics probed by molecular lines (e.g. from ALMA) can reveal the misaligned inner disc. The relationship between the rotation rate of the disc shadow and the precession rate of the inner disc is also provided. Using our disc breaking condition, we conclude that the disc shadowing due to misaligned discs should be accompanied by deep gaseous gaps (e.g. in Pre/Transitional discs). This scenario naturally explains both the disc shadowing and deep gaps in several systems (e.g. HD 100453, DoAr 44, AA Tau, HD 143006) and these systems should be the prime targets for searching young massive planets ($>M_J$) in discs.