Abstract
The canonical theory for planet formation in circumstellar disks proposes that planets are grown from initially much smaller seeds1,2,3,4,5. The long-considered alternative theory proposes that giant protoplanets can be formed directly from collapsing fragments of vast spiral arms6,7,8,9,10,11 induced by gravitational instability12,13,14—if the disk is gravitationally unstable. For this to be possible, the disk must be massive compared with the central star: a disk-to-star mass ratio of 1:10 is widely held as the rough threshold for triggering gravitational instability, inciting substantial non-Keplerian dynamics and generating prominent spiral arms15,16,17,18. Although estimating disk masses has historically been challenging19,20,21, the motion of the gas can reveal the presence of gravitational instability through its effect on the disk-velocity structure22,23,24. Here we present kinematic evidence of gravitational instability in the disk around AB Aurigae, using deep observations of 13CO and C18O line emission with the Atacama Large Millimeter/submillimeter Array (ALMA). The observed kinematic signals strongly resemble predictions from simulations and analytic modelling. From quantitative comparisons, we infer a disk mass of up to a third of the stellar mass enclosed within 1″ to 5″ on the sky.
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Data availability
All observational data products presented in this work are available through the CANFAR Data Publication Service at https://doi.org/10.11570/24.0087. All simulated data products are available at https://doi.org/10.5281/zenodo.11668694. The raw ALMA data are publicly available at the ALMA archive (https://almascience.nrao.edu/aq/) under project ID 2021.1.00690.S. The raw VLT/SPHERE data are publicly available from the ESO Science Archive Facility (https://archive.eso.org/eso/eso_archive_main.html) under programme 0104.C-0157(B). Source data are provided with this paper.
Code availability
ALMA data-reduction and imaging scripts are available at https://jjspeedie.github.io/guide.2021.1.00690.S. The following Python packages were used in this work: bettermoments (https://github.com/richteague/bettermoments), eddy (https://github.com/richteague/eddy), giggle v0 (https://doi.org/10.5281/zenodo.10205110), PHANTOM (https://github.com/danieljprice/phantom) and MCFOST (https://github.com/cpinte/mcfost).
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Acknowledgements
We thank our referees for their careful and insightful comments that improved the manuscript. We thank K. Kratter for enlightening discussions and valuable suggestions. J.S. thanks R. Loomis, S. Wood and T. Ashton at the North American ALMA Science Center (NAASC) for providing science support and technical guidance on the ALMA data as part of a data reduction visit to the NAASC, which was financed by the NAASC. The reduction and imaging of the ALMA data were performed on NAASC computing facilities. J.S. thanks C. Pinte, D. Price and J. Calcino for support with MCFOST, L. Keyte and F. Zagaria for discussions on self-calibrating ALMA data and C. White for sharing perceptually uniform colour maps. J.S. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Canada Graduate Scholarships Doctoral (CGS D) programme. R.D. acknowledges financial support provided by the NSERC through a Discovery Grant, as well as the Alfred P. Sloan Foundation through a Sloan Research Fellowship. C.L. and G.L. acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 823823 (RISE DUSTBUSTERS project). C.L. acknowledges funding from the UK Science and Technology Facilities Council (STFC) through the consolidated grant ST/W000997/1. B.V. acknowledges funding from the ERC CoG project PODCAST no. 864965. Y.-W.T. acknowledges support through National Science and Technology Council grant nos. 111-2112-M-001-064- and 112-2112-M-001-066-. J.H. was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI grant nos. 21H00059, 22H01274 and 23K03463. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2021.1.00690.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. Based on data products created from observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 0104.C-0157(B). This work has made use of the SPHERE Data Centre, jointly operated by OSUG/IPAG (Grenoble), PYTHEAS/LAM/CESAM (Marseille), OCA/Lagrange (Nice), Observatoire de Paris/LESIA (Paris) and Observatoire de Lyon. This research used the Canadian Advanced Network for Astronomical Research (CANFAR) operated in partnership by the Canadian Astronomy Data Centre and the Digital Research Alliance of Canada, with support from the National Research Council of Canada, the Canadian Space Agency, CANARIE and the Canada Foundation for Innovation.
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R.D. led the ALMA proposal. J.S. processed the ALMA data. J.H. processed the VLT/SPHERE data. C.H. performed the SPH simulations. J.S. performed the radiative-transfer calculations. C.L. and G.L. developed the analytic model. J.S. performed all presented analyses. J.S. and R.D. wrote the manuscript. All co-authors provided input to the ALMA proposal and/or the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Moment maps: AB Aur observations and GI disk simulations.
a–c, Integrated intensity (moment 0), intensity-weighted mean velocity (moment 1) and intensity-weighted linewidth (moment 2) maps for the ALMA 13CO observations towards AB Aur. Panel b appears in the main text as Fig. 2a. d–f, Moment 0, 1 and 2 maps for the synthetic ALMA 13CO observations of the SPH GI disk simulation. Like the AB Aur observations, the simulated GI disk shows a prominent GI wiggle along the southern minor axis (indicated by white arrows).
Extended Data Fig. 2 Filtered moment maps: AB Aur observations and GI disk simulations.
Expanding kernel filter residuals of the maps shown in Extended Data Fig. 1, highlighting global spirals and velocity disturbances generated by GI. Panels a–c appear in the main text as Fig. 1b–d. The minor-axis GI wiggle indicated by arrows in Extended Data Fig. 1b,e is shown here as an isovelocity contour at vlos = vsys ± vchan in all panels.
Extended Data Fig. 3 Global GI wiggles in analytic models, SPH simulations and the AB Aur disk.
Isovelocity contours in line-of-sight velocity maps at the velocity values indicated by the colour bar. a, vlos map of the 2D analytic GI disk model (shown in Fig. 2b). b, vlos map of the 2D analytic Keplerian disk model (shown in Fig. 2b inset). c, Synthetic ALMA 13CO moment 1 map for the 3D SPH GI disk simulation (shown in Fig. 2c). d, Synthetic ALMA 13CO moment 1 map for the 3D SPH Keplerian disk simulation (shown in Fig. 2c inset). e, Observed ALMA 13CO moment 1 map for the AB Aur disk, imaged with robust 0.5 (shown in Fig. 2a). f, Like e but imaged with robust 1.5.
Extended Data Fig. 4 Obtaining velocity residuals in the AB Aur disk.
a, ALMA 13CO moment 1 map, imaged with robust 0.5, as shown in Fig. 2a. b, Background model made with a Keplerian rotation profile, assuming a geometrically thin axisymmetric disk (equation (1)). c, Velocity residuals after subtracting the model in panel b. Global spiral substructure is visible but unevenly so. The model does not capture the non-axisymmetric emission surface morphology and/or super-Keplerian rotation. d, Background model made with the expanding kernel filter (equation (15)). e, Velocity residuals after subtracting the model in panel d, as shown in Fig. 1b. f–j, Like a–e but with the ALMA C18O moment 1 map, imaged with robust 1.5.
Extended Data Fig. 5 Kinematics of GI-driven spiral arms.
a–d, 2D analytic modelling23. e–h, Synthetic ALMA 13CO observations of the 3D SPH GI disk simulation. i–l, ALMA observations of the AB Aur disk. a, Disk surface density (equations (4) and (5)). b, Line-of-sight velocity (equation (2)), as in Fig. 2b. c, Velocity residuals from Keplerian (that is, subtracting Fig. 2b inset). d, Line-of-sight component of the radial velocity (first term of equation (2)). e, Filtered moment 0. f, Moment 1. g, Moment 1 residuals from Keplerian. h, Filtered moment 1. i, ALMA 13CO filtered moment 0. j, ALMA 13CO filtered moment 2. k, ALMA 13CO filtered moment 1. l, ALMA C18O filtered moment 1 (robust 1.5). Panel l inset overlays the VLT/SPHERE H-band scattered-light spirals S1–S7 (refs. 37,38) in red and 13CO spirals S1–S9 we identify in black.
Extended Data Fig. 6 Methods for isolating the sinusoidal component of the southern minor-axis PV wiggle in the AB Aur disk.
a, Detrending the ALMA 13CO line centres from Fig. 3a with linear and quadratic trend lines found by a least-squares fit. b, Detrending with the expanding kernel high-pass filter, varying the kernel width parameter w0 and keeping the kernel radial power-law index fixed to γ = 0.25 (equation (15)). We find the background trend lines by extracting the velocity values from the high-pass-filter background map (for example, Extended Data Fig. 4d) within the same 0.5°-wide wedge-shaped mask as we do for the line centres, positioned along the southern disk minor axis. c, Like b but varying γ and keeping w0 fixed to w0 = 0.30″. The high-pass-filter detrending approach converges to the same measured PV wiggle magnitude as the quadratic fit approach.
Extended Data Fig. 7 PV wiggle morphology, magnitude and disk mass recovery in the SPH GI disk simulation.
Like Fig. 4 but for the synthetic ALMA observations of the SPH GI disk simulation. a, The synthetic ALMA 13CO line centres along the southern minor axis from Fig. 3c after quadratic detrending. Uncertainties on the line centres are shown by yellow-shaded regions. The magnitude of this PV wiggle is measured to be 39.1 ± 1.9 m s−1. The analytic model shown in the background for qualitative comparison has the same parameters as the underlying SPH simulation (Mdisk/M⋆ = 0.29 and β = 10) and its PV wiggle magnitude is 39.0 m s−1. b, As in Fig. 4c, a map of the minor-axis PV wiggle magnitude of 60 × 60 analytic models on a grid of disk-to-star mass ratios and cooling timescales. A contour is drawn at the measured magnitude of the synthetic 13CO PV wiggle in panel a and dashed lines represent the quoted uncertainties. The technique successfully recovers the disk mass set in the SPH simulation.
Extended Data Fig. 8 Comparisons with further sets of analytic models.
Like Fig. 4 but varying the azimuthal wavenumber m and surface density power-law index p in the comparison grid of analytic GI model disks. Each upper subpanel shows the quadratically detrended 13CO and C18O line centres (yellow) behind a demonstrative analytic PV wiggle (black) computed with the combination of m and p indicated by the row and column labels (keeping Mdisk/M⋆ = 0.3 and β = 10 fixed). Each lower subpanel shows the corresponding map of PV wiggle magnitude computed for a 60 × 60 grid of analytic models in Mdisk/M⋆ and β, again with the combination of m and p indicated by the row and column labels. The two yellow contours are drawn at the magnitude values measured for the observed AB Aur 13CO and C18O southern minor-axis PV wiggles. The white-shaded region between two white curves represents plausible β ranges from r = 1–5″. The combination shown in Fig. 4c is m = 3, p = 1.0.
Extended Data Fig. 9 Candidate sites of planet formation.
Coloured crosses mark the locations of candidate protoplanets reported in the literature35,45,46. A table providing the coordinates of the candidates on the sky, estimated masses and the reporting references is available as source data. a, Filtered ALMA 13CO moment 0 map, as in Fig. 1c. b, VLT/SPHERE H-band scattered-light image (ref. 35), as in Fig. 1a. The inset zooms into the central 2″ × 2″ region to show the spiral structures in different tracers at spatial scales unresolved by the present ALMA observations. The H-band scattered-light image is shown after high-pass filtering and orange contours show the two spirals identified in ALMA 12CO J = 2–1 moment 0 (ref. 45) at levels from 25 to 50 mJy per beam km s−1 in increments of 5 mJy per beam km s−1.
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Speedie, J., Dong, R., Hall, C. et al. Gravitational instability in a planet-forming disk. Nature 633, 58–62 (2024). https://doi.org/10.1038/s41586-024-07877-0
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DOI: https://doi.org/10.1038/s41586-024-07877-0
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