The impact of dynamic pressure bumps on the observational properties of protoplanetary disks

¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: jochen.stadler@oca.eu
² Université Côte-d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 06304 Nice, France
³ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁴ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
⁵ Zentrum für Astronomie, Heidelberg University, Albert-Ueberle-Straße 2, 69117 Heidelberg, Germany
⁶ University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 Munich, Germany
⁷ Exzellenscluster ORIGINS, Boltzmannstr. 2, 85748 Garching, Germany

Received: 16 February 2022
Accepted: 22 August 2022

Abstract

Context. Over the last years, large (sub-)millimetre surveys of protoplanetary disks in different star forming regions have well constrained the demographics of disks, such as their millimetre luminosities, spectral indices, and disk radii. Additionally, several high-resolution observations have revealed an abundance of substructures in the disk’s dust continuum. The most prominent are ring like structures, which are likely caused by pressure bumps trapping dust particles. The origins and characteristics of these pressure bumps, nevertheless, need to be further investigated.

Aims. The purpose of this work is to study how dynamic pressure bumps affect observational properties of protoplanetary disks. We further aim to differentiate between the planetary- versus zonal flow-origin of pressure bumps.

Methods. We perform one-dimensional gas and dust evolution simulations, setting up models with varying pressure bump features, including their amplitude and location, growth time, and number of bumps. We subsequently run radiative transfer calculations to obtain synthetic images, from which we obtain the different quantities of observations.

Results. We find that the outermost pressure bump determines the disk’s dust size across different millimetre wavelengths and confirm that the observed dust masses of disks with optically thick inner bumps (<40 au) are underestimated by up to an order of magnitude. Our modelled dust traps need to form early (<0.1 Myr), fast (on viscous timescales), and must be long lived (>Myr) to obtain the observed high millimetre luminosities and low spectral indices of disks. While the planetary bump models can reproduce these observables irrespectively of the opacity prescription, the highest opacities are needed for the dynamic bump model, which mimics zonal flows in disks, to be in line with observations.

Conclusions. Our findings favour the planetary- over the zonal flow-origin of pressure bumps and support the idea that planet formation already occurs in early class 0–1 stages of circumstellar disks. The determination of the disk’s effective size through its outermost pressure bump also delivers a possible answer to why disks in recent low-resolution surveys appear to have the same sizes across different millimetre wavelengths.