Abstract
The discovery of wide-orbit giant exoplanets has posed a challenge to our conventional understanding of planet formation through the coagulation of dust grains and planetesimals and the subsequent accretion of protoplanetary disk gas. As an alternative mechanism, the direct in situ formation of planets or planetary cores by gravitational instability (GI) in protoplanetary disks has been proposed. However, observational evidence for GI in regions where wide-orbit planets form is still lacking. Theoretical studies predict that GI induces spiral arms moving at the local Keplerian speed in a disk. Based on several high-angular-resolution observations over a 7-year time baseline using the Atacama Large Millimeter/submillimeter Array, here we report the evidence for spiral arms following the Keplerian rotation in the dust continuum disk around the young star IM Lup. This demonstrates that GI can operate in wide-orbit planet-forming regions, establishing it as a plausible formation mechanism for such planets.
The work presents evidence of gravitational instability (GI) in the protoplanetary disk around IM Lup and posits it as a plausible formation mechanism of wide-orbit giant planets (planets at around 20 AU to 70 AU from their star) in situ.
The work is solely concerned with the in situ formation of giant planets and thus its scope must be considered limited to explaining how could some planets, that we see today from our telescopes, have formed at the locations where they are right now, without the involvement of migration or planet-planet/star scattering.
When it comes to in situ formation of giant planets that far out, there are a few problems. The most accepted formation pathway for giant planets is through core accretion. We can estimate this as follows:
Safronov (1972) gives the expression of solid core growth
where
Rice & Armitage (2003) provide reference values for a giant planet at the current location of Jupiter to estimate the growth time scale. A similar treatment can be found in Armitage (2020)2 which derives a very slow growth rate at the location of Jupiter. In any case, we can do some algebra and derive how does this rate vary with radius:
if we assume
which implies the timescale of growth will be even larger at larger radii (for a body of size
One of most evident signatures of GI is spiral arms, however because these substructures can also be produced through alternate pathways (planet-disk interactions, stellar fly-bys and even shadows cast by the inner disk), it is essential to categorically devise a way to distinguish between these possibilities. Additionally, spiral arms induced by GI or planet-disk interaction present two different scenarios of planet formation. If the spirals are being induced by a planet, this implies the planet already exists and must have formed at a much earlier stage of the disk lifetime. On the other hand, GI-induced spirals point to several other key things. If our goal is assert that GI is present, then one of the most useful metric is the Toomre’s Q parameter, which requires following condition for instability in a Keplerian disk:
In simpler terms, a disk becomes unstable when the gravity is strong enough to overcome the stabilizing internal forces of rotation and thermal pressure. Under our metric,
According to this work, IM Lup has gravitational self-regulation, which is to say that the disk maintains a marginally unstable state, which prevents the system going too further in either direction (runaway expansion or collapse). In terms of Toomre’s Q, marginally unstable refers to
Now coming back to the differences between GI-induced spirals and planet-induced spirals, the former spirals follow the local Keplerian motion, whereas in the case of latter, the spirals move as if they were single rigid body and follow the Keplerian motion at the radius of the companion. Building on this idea, this work attempts to measure the speed of the spirals observed in IM Lup across seven years of observation from ALMA, to find the evidence for GI.
The next step is decide what kind of ALMA observations might help us. For instance, we cannot use kinematic structures in CO emissions as those emission do not originate form the region we are interested in (where wide-orbit exoplanets are detected). The high resolution observations of IM Lup reveal that grand-design, two-armed symmetric spiral arms are present, and the absence of any shadow in the infrared eliminates the possibility of the shadow scenario. There is evidence of strong turbulence in IM Lup, but only in the elevated disk layers. However, the claims of kinematic detection of embedded Jupiter-mass planets also exist which could have caused these spirals we have observed. The idea is to use the data across seven years and categorize the driver behind the motion of these spirals.
Before moving on to analysis of the observations, we need to decide what observations to use. This paper uses both continuum and gas emission images to aid in the different steps of the process. First, CO rotation curves provide the Toomre’s Q parameter, establishing the disk has GI (or at least is marginally unstable). But because they only trace outer and upper layers, we need to use something else. Dust rotation curves reveal spirals throughout the range of our interest (20-70 AU), so authors used them to characterize the motion of the spirals.
Continuum emissions from IM Lup
The work uses 4 separate observational epochs, and thus the first step is to convolve them to a set beamsize and position angle.
Images Analysis method
Log-likelihood of wrt to each epoch: