Dust mass in protoplanetary disks with porous dust opacities

ALMA surveys have suggested that protoplanetary disks are not massive enough to form the known exoplanet population, under 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 temperature, but systematically lower millimeter fluxes compared to disks incorporating compact dust grains. Moreover, we recalibrate the relation between dust temperature and stellar luminosity for a wide range of stellar parameters, and calculate the dust masses of a large sample of disks using the traditionally analytic approach. The median dust mass from our calculation is about 6 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 show that the median exoplanet mass is about 2 times lower than the median dust mass, if grains are 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 conduct new IRAM/NIKA-2 observations toward the IRAS 04370+2559 disk and perform a detailed radiative transfer modeling of the spectral energy distribution. The best-fit dust mass is roughly 100 times higher than the value from the traditionally analytic calculation. Future spatially resolved observations at various wavelengths are required to better constrain the dust mass.