Signatures of protoplanetary disc warps

Exoplanets form in cold discs of gas and dust around young stars. Our long-standing picture of these so-called protoplanetary discs is that all the planet-forming material orbits in a single plane (as with the planets in the Solar System). However, recent observations with the Hubble Space Telescope, the ESO VLT, and ALMA, have shown that many planet-forming discs are not coherently aligned, but are instead warped or twisted. A few discs show very large misalignments (which can even be greater than 90 degrees!), but smaller tilts and warps – of a few degrees – are more common. Such warps may be caused by the gravity of newly-formed planets, but because we can only observe a 2-D projection of these 3-D structures, our observations often struggle to distinguish between warps and other disc structures (such as spiral waves).

Fig.1: Simulated molecular line emission from a protoplanetary disc with a small warp. The background colour-scale shows the so-called “moment 1 map” of the ¹³CO 3-2 line, which traces the line-of-sight velocity of the gas (due to the Doppler shift): blue regions are moving towards us, while red regions are moving away from us. When viewed face-on the disc rotates in the plane of the sky, so any velocity along our line-of-sight traces out-of-plane motion (i.e., a warp). The smaller panels show the velocity profile of the emission line at each point in the disc. The line profiles are asymmetric, and these asymmetries provide a clear means of distinguishing a warp from other disc structures.

One way to break this degeneracy is to study the disc kinematics, as a warped disc moves quite differently to similar-looking co-planar structures. We used DiRAC’s Data Intensive at Leicester (DIaL) cluster to run sophisticated numerical simulations of warped discs, and study their observational appearance in detail. We used 3-D smoothed particle hydrodynamics to simulate the dynamics of disc with small warps, and these simulations were then taken as inputs to radiative transfer calculations. This allowed us to build up a detailed picture of how these discs appear to our telescopes, and understand which observable diagnostics probe the warp structure reliably. The most useful tracer is emission from cold gas molecules (such as CO), observed by ALMA, as Doppler shifts of these emission lines allow us to measure the disc kinematics directly. We showed that if discs are seen close to face-on then the CO kinematics can identify small warps clearly, but at higher inclinations these signatures become impossible to disentangle from the disc’s rotation. However, the amplitude of the inferred warp is strongly affected by the optical depth of the observed lines, so care is needed if we are to measure warp angles this way. We applied our models to several well-known discs, and found that in some cases disc warps may have been misinterpreted as other effects. Future observations are likely to discover many more such systems, and provide much-needed insight into the processes that shape young planetary systems.

These results were published in Characteristics of small protoplanetary disc warps in kinematic observations, A.K.Young et al., Monthly Notices of the Royal Astronomical Society, 513, 487 (2022).