Time evolution of a viscous protoplanetary disk with a free geometry: toward a more self-consistent picture

Abstract

Observations of protoplanetary disks show that some characteristics seem recurrent, even in star formation regions that are physically distant such as surface mass density profiles varying as $r^{-1}$, or aspect ratios about 0.03 to 0.23. Accretion rates are also recurrently found around $10^{-8}-10^{-6}{\mathrm{M}}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}$ for disks already evolved (Isella et al., 2009, Andrews et al., 2009, 2010). Several models have been developed in order to recover these properties. However, most of them usually simplify the disk geometry if not its mid-plane temperature. This has major consequences for modeling the disk evolution over million years and consequently planet migration. In the present paper, we develop a viscous evolution hydrodynamical numerical code that determines simultaneously the disk photosphere geometry and the mid-plane temperature. We then compare our results of long-term simulations with similar simulations of disks with a constrained geometry along the Chiang & Goldreich (1997) prescription (dlnH/dlnr = 9/7). We find that the constrained geometry models provide a good approximation of the disk surface density evolution. However, they differ significantly regarding the temperature time evolution. In addition, we find that shadowed regions naturally appear at the transition between viscously dominated and radiation dominated regions that falls in the region of planetary formation. We show that $\chi$ (photosphere height to pressure scale height ratio) cannot be considered as a constant, consistently with Watanabe et al. (2008). Comparisons with observations show that all disk naturally evolve toward a shallow surface density disk ($\Sigma \propto r^{-1}$). The mass flux across the disk stabilizes in about 1 million year typically.

arXiv comment43 pages, 16 figures Accepted in Astrophysical Journal

References in corpus (29)

• Spectral Energy Distributions of T Tauri Stars With Passive Circumstellar Disks
• Passive irradiated circumstellar disks with an inner hole
• Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks
• Protoplanetary Disk Structures in Ophiuchus
• Gas- and dust evolution in protoplanetary disks
• Accretion Disks around Young Objects. I. The Detailed Vertical Structure
• Accretion Disks Around Young Objects. III. Grain Growth
• Protoplanetary Disk Structures in Ophiuchus II: Extension to Fainter Sources
• Radiation-Hydrodynamic Models of X-Ray & EUV Photoevaporating Protoplanetary Discs
• Evolution of protoplanetary disks: Constraints from DM Tauri and GM Aurigae
• Structure and evolution of pre-main sequence circumstellar disks
• Analytical protostellar disk models 1: the effect of internal dissipation and surface irradiation on the structure of disks and the location of the snow line around Sun-like stars
• Photoevaporation of Circumstellar Disks around Young Stars
• Dust dynamics during protoplanetary disc clearing
• Dust settling in local simulations of turbulent protoplanetary disks
• Giant planet migration, disk evolution, and the origin of transitional disks
• Stellar irradiated discs and implications on migration of embedded planets I: equilibrium discs
• Long-term Evolution of Protostellar and Protoplanetary Disks. I. Outbursts
• Two-Dimensional Transport of Solids in Viscous Protoplanetary Disks
• The Origin of Planetary System Architectures. I. Multiple Planet Traps in Gaseous Discs
• Self-regulated gravitational accretion in protostellar discs
• Particle transport in evolving protoplanetary disks: Implications for results from Stardust
• Long-wavelength excesses of FU Orionis objects: flared outer disks or infalling envelopes?
• A method for coupling dynamical and collisional evolution of dust in circumstellar disks: the effect of a dead zone
• Thermal Waves in Irradiated Protoplanetary Disks
• Planet Shadows in Protoplanetary Disks. I: Temperature Perturbations
• Surface convection and red giants radii measurements
• Shadows, gaps, and ring-like structures in protoplanetary disks
• Disk Temperature Variations and Effects on the Snow Line in the Presence of Small Protoplanets

Cited by in corpus (10)

• Composition of Early Planetary Atmospheres I: Connecting Disk Astrochemistry to the Formation of Planetary Atmospheres
• Time evolution of snow regions and planet traps in an evolving protoplanetary disk
• Eccentricity excitation and merging of planetary embryos heated by pebble accretion
• Thermal Wave Instability as an Origin of Gap and Ring Structures in Protoplanetary Disks
• Trapping planets in an evolving protoplanetary disk: preferred time, locations and planet mass
• Growth of calcium-aluminum-rich inclusions by coagulation and fragmentation in a turbulent protoplanetary disk: observations and modelisation
• Early Planet Formation in Embedded Disks (eDisk) V: Possible Annular Substructure in a Circumstellar Disk in the Ced110 IRS4 System
• Building protoplanetary disks from the molecular cloud: redefining the disk timeline
• Binary planet formation by gas-assisted encounters of planetary embryos
• Molecules with ALMA at Planet-forming Scales (MAPS) XII: Inferring the C/O and S/H ratios in Protoplanetary Disks with Sulfur Molecules