Thermal evolution of protoplanetary disks: from $\beta$-cooling to decoupled gas and dust temperatures

Abstract

Aims: We explore the long-term evolution of young protoplanetary disks with different approaches to computing the thermal structure determined by various cooling and heating processes in the disk and its surroundings. Methods: Numerical hydrodynamics simulations in the thin-disk limit were complemented with three thermal evolution schemes: a simplified $\beta$-cooling approach with and without irradiation, in which the rate of disk cooling is proportional to the local dynamical time, a fiducial model with equal dust and gas temperatures calculated taking viscous heating, irradiation, and radiative cooling into account, and also a more sophisticated approach allowing decoupled dust and gas temperatures. Results: We found that the gas temperature may significantly exceed that of dust in the outer regions of young disks thanks to additional compressional heating caused by the infalling envelope material in the early stages of disk evolution and slow collisional exchange of energy between gas and dust in low-density disk regions. The outer envelope however shows an inverse trend with the gas temperatures dropping below that of dust. The global disk evolution is only weakly sensitive to temperature decoupling. Nevertheless, separate dust and gas temperatures may affect the chemical composition, dust evolution, and disk mass estimates. Constant-$\beta$ models without stellar and background irradiation fail to reproduce the disk evolution with more sophisticated thermal schemes because of intrinsically variable nature of the $\beta$-parameter. Constant-$\beta$ models with irradiation can better match the dynamical and thermal evolution, but the agreement is still incomplete. Conclusions: Models allowing separate dust and gas temperatures are needed when emphasis is placed on the chemical or dust evolution in protoplanetary disks, particularly in sub-solar metallicity environments.

19 pages, 21 Figures, accepeted for publication in Astronomy & Astrophysics

References in corpus (20)

• Protoplanetary Disk Structures in Ophiuchus
• On the diversity and statistical properties of protostellar discs
• Uncertainties in H2 and HD Chemistry and Cooling and their Role in Early Structure Formation
• Characterising the Gravitational Instability in Cooling Accretion Discs
• Fragmentation of gravitationally unstable gaseous protoplanetary disks with radiative transfer
• Radiative transfer and the energy equation in SPH simulations of star formation
• Treating gravity in thin disk simulations
• Secular evolution of viscous and self-gravitating circumstellar discs
• Convergence of the critical cooling rate for protoplanetary disk fragmentation achieved; the key role of numerical dissipation of angular momentum
• Effects of radiation transfer on the structure of self-gravitating disks, their fragmentation and evolution of the fragments
• Dawes Review. The tidal downsizing hypothesis of planet formation
• The effects of disk self-gravity and radiative cooling on the formation of gaps and spirals by young planets
• The effect of radiative feedback on disc fragmentation
• Combining radiative transfer and diffuse interstellar medium physics to model star formation
• Temperature profiles of young disk-like structures: The case of IRAS 16293A
• The Effect of Protoplanetary Disk Cooling Times on the Formation of Gas Giant Planets by Gravitational Instability
• Upper stellar mass limit by radiative feedback at low-metallicities: metallicity and accretion rate dependence
• Gravitational stability and fragmentation condition for discs around accreting supermassive stars
• Thermal structure of a protostellar envelope
• On fragmentation of turbulent self-gravitating discs in the long cooling time regime

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• Isotopic and vibrational-level dependence of H${}_2$ dissociation by electron impact
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• Semi-analytic calculations for extended mid-Infrared emission associated with FU Ori-type objects