Gravitational Instability, Spiral Substructure, and Modest Grain Growth in a Typical Protostellar Disk: Modeling Multiwavelength Dust Continuum Observations of TMC1A

Abstract

Embedded class 0/I protostellar disks represent the initial condition for planet formation. This calls for a better understanding of their bulk properties and the dust grains within them. We model multiwavelength dust continuum observations of the disk surrounding the class I protostar TMC1A to provide insight on these properties. The observations can be well fit by a gravitationally self-regulated (i.e., marginally gravitationally unstable and internally heated) disk model with surface density Σ ∼ 1720( R /10 au) ^−1.96 g cm ^−2 and midplane temperature T _mid ∼ 185( R /10 au) ^−1.27 K. The observed disk contains an m = 1 spiral substructure; we use our model to predict the spiral’s pitch angle, and the prediction is consistent with the observations. This agreement serves as both a test of our model and strong evidence of the gravitational nature of the spiral. Our model estimates a maximum grain size ${a}_{\max }\sim 196{(R/10\,\mathrm{au})}^{-2.45}\mu {\rm{m}}$ , which is consistent with grain growth being capped by a fragmentation barrier with a threshold velocity of ∼1 m s ^−1 . We further demonstrate that the observational properties of TMC1A are typical among the observed population of class 0/I disks, which hints that traditional methods of disk data analysis based on Gaussian fitting and the assumption of optically thin dust emission could have systematically underestimated the disk size and mass and overestimated the grain size.

Keywords

• Protoplanetary disks
• Gravitational instability
• Dust continuum emission
• Astronomy data modeling
• Planet formation