Figure 1. Renderings of two simulated circumbinary discs. The binary at the centre of the discs on the left and right have mass ratios đť‘š2/(đť‘š1+đť‘š2)
of 0.1 and 0.3 respectively. An inner ring has torn off the disc on the right but the disc on the left has only a gentle warp. This indicates that a planetary companion, or any companion with a tenth of the stellar mass or less cannot tear a protoplanetary disc.
The star- and planet-forming environment is highly dynamic. Stars commonly form in binary or multiple systems, and the angular momentum vector of a disc may be shifted by stellar flybys or through the accretion of remnants of the molecular cloud. In the last decade it has been possible to resolve structures in protoplanetary discs with telescope facilities including ALMA and the VLT. Many images of discs reveal complex structures such as misaligned inner and outer discs. One way of generating a misaligned inner disc is if the protoplanetary disc surrounds a binary star system and orbits in a different plane to the binary. This misalignment results in a gravitational torque that drives precession in the disc. Because precession is a steep function of radius, concentric rings within the disc precess more slowly at larger radii. This causes the disc to become warped and this warp perturbation travels through the disc as a bending wave (i.e. protoplanetary discs are in the “wavelike” regime of warp propagation). If the warp cannot be communicated effectively through the disc then the disc may tear into two components.
We have run a number of high-resolution simulations to determine the circumstances in which a protoplanetary disc is susceptible to tearing. Previous work has considered thin and viscous discs in which the warp propagation is viscous rather than wavelike, or has used insufficient resolution to accurately recover the effects. For this reason, we focussed on simulating discs that more closely resemble the low viscosity, relatively thick, wavelike protoplanetary discs.
No single parameter can predict whether or not a protoplanetary disc will break. It is rather the combination of factors, such as misalignment angle between the binary and disc planes and the radial temperature profile of the disc. We can however rule out disc tearing caused by an unseen planetary companion since we don’t observe disc breaking for a mass ratio of 0.1 (Fig.1). In other words, if an object is massive enough to tear the disc, then it will be bright enough to detect.
At the moment, we do not have an accurate analytical prediction of where a disc breaks (the breaking radius) in the wavelike regime. We show that the expression derived by Nixon, King & Price (2013) significantly underestimates the breaking radius. The reason for this, it turns out, is that the precession torque acting locally in a disc is not solely due to the central stars. The bending wave launched near the inner edge of the disc efficiently transports the torque outwards. Consequently, the precession torque at radius R is greater than the analytical expression predicts which means that the conditions where a disc is susceptible to breaking occur further out in the disc than expected.
This work made use of DIaL2 at Leicester, dp269 “Fragmenting protoplanetary discs in the cluster environment”. It is published in Young et al. (2023) https://academic.oup.com/mnras/article/525/2/2616/7246072
