Dust mass in protoplanetary disks with porous dust opacities

¹ School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
² Purple Mountain Observatory, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, China
³ Institut d’Astrophysique de Paris, Sorbonne Université, CNRS (UMR7095), 75014 Paris, France
⁴ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁵ Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstr. 15, 24118 Kiel, Germany
⁶ Sterrenkundig Observatorium, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium
⁷ Institute for Astronomy, School of Physics, Zhejiang University, 866 Yu Hang Tang Road, Hangzhou, Zhejiang 310027, China

^★ Corresponding author; yliu@swjtu.edu.cn

Received: 25 August 2024
Accepted: 30 October 2024

Abstract

Atacama Large Millimeter/submillimeter Array surveys have suggested that protoplanetary disks are not massive enough to form the known exoplanet population, based on the assumption that the millimeter continuum emission is optically thin. In this work, we investigate how the mass determination is influenced when the porosity of dust grains is considered in radiative transfer models. The results show that disks with porous dust opacities yield similar dust temperatures, but systematically lower millimeter fluxes, as compared to disks that incorporate compact dust grains. Moreover, we have recalibrated the relation between dust temperature and stellar luminosity for a wide range of stellar parameters. We also calculated the dust masses of a large sample of disks using the traditionally analytic approach. The median dust mass from our calculation is about six times higher than the literature result, and this is mostly driven by the different opacities of porous and compact grains. A comparison of the cumulative distribution function between disk dust masses and exoplanet masses shows that the median exoplanet mass is about two times lower than the median dust mass when grains are assumed to be porous and there are no exoplanetary systems with masses higher than the most massive disks. Our analysis suggests that adopting porous dust opacities may alleviate the mass budget problem for planet formation. As an example illustrating the combined effects of optical depth and porous dust opacities on the mass estimation, we conducted new IRAM/NIKA-2 observations toward the IRAS 04370+2559 disk and performed a detailed radiative transfer modeling of the spectral energy distribution (SED). The best-fit dust mass is roughly 100 times higher than the value given by a traditionally analytic calculation. Future spatially resolved observations at various wavelengths are required to better constrain the dust mass.