Young stars are born surrounded by cold discs or dust and gas. These discs act as a conduit for accretion of mass on to the central star, and also provide the raw material for planet formation. At early times these discs are thought to be sufficiently massive that they can be unstable to their own gravity. This gravitational instability initially leads to the formation of spiral density waves in the disc, and these spirals transport angular momentum very efficiently, increasing the disc accretion rate dramatically. In some cases the instability can also lead to fragmentation of the disc, leading directly to the formation of giant planets or brown dwarfs. Understanding gravitational instabilities is therefore crucial to understanding both star and planet formation. However, in the early stages of star formation discs are typically still enshrouded in their parent molecular clouds, making them difficult to observe, and measurements of the disc mass are plagued by systematic uncertainties (because the molecular hydrogen that comprises the bulk of the disc mass is largely invisible to our telescopes). Moreover, there are numerous other processes (such as disc-planet interactions) which can give rise to spiral structures in discs, and distinguishing these from the spirals caused by gravitational instabilities is challenging. It is therefore still not clear when, where, or even if, real discs become gravitationally unstable.

In recent years new observational facilities, especially the Atacama Large Millimetre/sub-millimetre Array (ALMA), have provided us with astonishing new high-resolution observations of discs around young stars. These discs have uncovered an unexpected wealth of structure in discs – gaps, rings, spirals, shadows – and have given us a huge array of new insights into the processes of star and planet formation. However, in the case of gravitational instabilities we have not been able to exploit these observations fully, because it was not clear what our telescopes should be looking for. By exploiting the power of DiRAC’s Data Intensive at Leicester (DIaL) cluster, we were able to perform a suite of 3-D Smoothed Particle Hydrodynamics simulations of gravitationally unstable discs, and then couple those simulations to radiative transfer calculations to generate synthetic observations of unstable discs. We found that the critical, unambiguous signature of gravitational instability lies not just in the existence of spirals, but rather in their kinematics, and that this signature is readily detectable in ALMA observations. Emission lines from carbon monoxide molecules provide the best probe of disc kinematics. In a “normal” (non-self-gravitating) disc the disc’s rotation results in a well-known “butterfly” pattern in the velocity structure, which is readily seen in ALMA’s so-called channel maps (essentially a series images of the CO emission at a particular velocities). Our DiRAC simulations showed that this is radically altered in self-gravitating discs, with the spiral density waves resulting in a characteristic “wiggle” in the channel maps (see Fig.1). This wiggle is a unique signature of the spirals generated by self-gravity, and represents the smoking gun of gravitational instability in discs around young stars. The race is now on to detect this signal in real observations, and these results will provide crucial new insight into the formation of stars and planets.

These results were published as Predicting the Kinematic Evidence of Gravitational Instability, C.Hall et al., The Astrophysical Journal, vol. 904, article 148 (2020).

Fig.1: Synthetic ALMA channel maps – “images” of the emission at a particular velocity – for the CO J=3-2 line from our simulated discs. The lower panels show the results for a disc without self-gravity, which shows the “butterfly” pattern resulting from Keplerian rotation. The upper panels show the corresponding channel maps for a gravitationally unstable disc: the spiral density waves manifest as very clear “GI-wiggles” in the channel maps. If detected in real discs, these wiggles would represent unambiguous evidence for gravitational instability.