Characteristics of small protoplanetary disc warps in kinematic observations

TL;DR

This paper investigates how small warps in protoplanetary discs can be identified through kinematic CO emission observations, highlighting the signatures, detection challenges, and implications for understanding disc misalignments.

Contribution

It introduces a method to detect small disc warps using synthetic CO emission maps and analyzes the kinematic signatures that distinguish warps from other features.

Findings

Warp signatures are detectable at moderate inclinations with accurate inclination measurements.

Asymmetries in channel maps are characteristic of warps and distinct from planetary or gravitational features.

Kinematic evidence of small warps may have been overlooked in previous observations.

Abstract

Many circumstellar discs appear to have misaligned central regions that give rise to shadows seen in scattered light observations. Small warps ($<20^\circ$ misalignment) are probably more common but are also more difficult to detect than the large misalignments studied previously. We present the characteristics of CO emission that may be used to identify a small disc warp, found from synthetic $^{13}$CO maps of a model misaligned circumbinary disc. The spectra are not symmetrical, so fitting a Keplerian model is not appropriate and can hide a warp or lead to spurious features such as spirals appearing in the residuals. We quantify the observed warp structure by fitting sinusoids to concentric annuli of the disc. From this we can trace the radial variation of the peak velocity and of the azimuth of the peak velocity, i.e., the twist. At near face-on inclinations, these radial profiles reveal the warp structure. The twist remains detectable at moderate inclinations (${i_{\rm outer~disc}\lesssim 35^{\circ}}$) in the absence of radial flows but the measured inclination must be accurate to $\lesssim 5^{\circ}$ to allow detection of the radial variation. The observed twist does not provide a direct measure of the warp structure because of its dependence on optical depth. The warp causes broad asymmetries in the channel maps that span several channels and that are distinct from localised features caused by embedded planets and gravitational instability. We suspect that kinematic evidence of warps may have been missed and we suggest a few examples where the data may be revisited.