An analytical solution to measure the gas size in protoplanetary discs in the viscous self-similar scenario. Issue 1 (29th October 2022)

• Record Type: Journal Article
• Authors: Toci, Claudia; Lodato, Giuseppe; Livio, Francesco Gerardo; Rosotti, Giovanni; Trapman, Leon
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 518:Issue 1(2022)
• Page Start: L69
• Page End: L74
• Publication Date: 2022-10-29
• Subjects: accretion, accretion discs -- planets and satellites: formation -- protoplanetary discs; Astronomy -- Research -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnrasl/slac137
• Languages: English
• ISSNs: 1745-3933

Abstract

ABSTRACT: In order to understand which mechanism is responsible for accretion in protoplanetary discs, a robust knowledge of the observed disc radius using gas tracers such as 12 CO and other CO isotopologues is pivotal. Indeed, the two main theories proposed, viscous accretion and wind-driven accretion, predict different time evolution for the disc radii. In this letter, we present an analytical solution for the evolution of the disc radii in viscously evolving protoplanetary discs using 12 CO as a tracer, under the assumption that the 12 CO radius is the radius where the surface density of the disc is equal to the threshold for CO photodissociation. We discuss the properties of the solution and the limits of its applicability as a simple numerical prescription to evaluate the observed disc radii of populations of discs. Our results suggest that, in addition to photodissociation, also freeze out plays an important role in setting the disc size. We find an effective reduction of the CO abundance by about two orders of magnitude at the location of CO photodissociation, which, however, should not be interpreted as the bulk abundance of CO in the disc. The use of our analytical solution will allow to compute disc sizes for large quantities of models without using expensive computational resources such as radiative transfer calculations.