University of Leicester
A_population_synthesis_model_for_young_stars_and_their_discs.pdf (2.26 MB)

On the time evolution of the M-d-M-* and (M)over dot-M-* correlations for protoplanetary discs: the viscous time-scale increases with stellar mass

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journal contribution
posted on 2022-10-03, 15:55 authored by Alice Somigliana, Claudia Toci, Giovanni Rosotti, Giuseppe Lodato, Marco Tazzari, Carlo F Manara, Leonardo Testi, Federico Lepri
Large surveys of star-forming regions have unveiled power-law correlations between the stellar mass and the disc parameters, such as the disc mass Md-M∗ and the accretion rate M-M∗. The observed slopes appear to be increasing with time, but the reason behind the establishment of these correlations and their subsequent evolution is still uncertain. We conduct a theoretical analysis of the impact of viscous evolution on power-law initial conditions for a population of protoplanetary discs. We find that, for evolved populations, viscous evolution enforces the two correlations to have the same slope, λm = λacc, and that this limit is uniquely determined by the initial slopes λm, 0 and λacc, 0. We recover the increasing trend claimed from the observations when the difference in the initial values, δ0 = λm, 0-λacc, 0, is larger than 1/2; moreover, we find that this increasing trend is a consequence of a positive correlation between the viscous time-scale and the stellar mass. We also present the results of disc population synthesis numerical simulations, that allow us to introduce a spread and analyse the effect of sampling, which show a good agreement with our analytical predictions. Finally, we perform a preliminary comparison of our numerical results with observational data, which allows us to constrain the parameter space of the initial conditions to λm, 0 ∈[1.2, 2.1], λacc, 0 ∈[0.7, 1.5].


Italian Ministero dell’Istruzione, Università e Ricerca through the grant Progetti Premiali 2012 – iALMA (CUP C52I13000140001)

Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Ref no. 325594231 FOR 2634/1 TE 1024/1-1

DFG cluster of excellence Origins (, and from the European Research Council (ERC) via the ERC Synergy Grant ECOGAL (grant 855130)

Connecting theories and observations of planet formation

Science and Technology Facilities Council

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Consolidated Grant Astronomy Observation and Theory 2019-2022

Science and Technology Facilities Council

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European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 823823 (RISE DUSTBUSTERS project)


Author affiliation

School of Physics and Astronomy, University of Leicester


  • AM (Accepted Manuscript)

Published in

Monthly Notices of the Royal Astronomical Society






5927 - 5940


Oxford University Press (OUP) for Royal Astronomical Society





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