Constraints on PDS 70 b and c from the dust continuum emission of the circumplanetary discs considering in situ dust evolution

Context. The young T Tauri star PDS 70 has two gas accreting planets sharing one large gap in a pre-transitional disc. Dust continuum emission from PDS 70 c has been detected by Atacama Large Millimeter/submillimeter Array (ALMA) Band 7, considered as the evidence of a circumplanetary disc. However, there has been no detection of the dust emission from the CPD of PDS 70 b. Aims. We constrain the planet mass and the gas accretion rate of the planets by introducing a model of dust evolution in the CPDs and reproducing the detection and non-detection of the dust emission. Methods. We first develop a 1D steady gas disc model of the CPDs reflecting the planet properties. We then calculate the radial distribution of the dust profiles considering the dust evolution in the gas disc and calculate the total flux density of dust thermal emission from the CPDs. Results. We find positive correlations between the flux density of dust emission and three planet properties, the planet mass, gas accretion rate, and their product called 'MMdot'. We then find that the MMdot of PDS 70 c is >= 4 x 10(-7)M(J)(2) yr(-1), corresponding to the planet mass of >= 5 M-J and the gas accretion rate of >= 2 x 10(-8)M(J) yr(-1). This is the first case to succeed in obtaining constraints on planet properties from the flux density of dust continuum emission from a CPD. We also find some loose constraints on the properties of PDS 70 b from the non-detection of its dust emission. Conclusions. We propose possible scenarios for PDS 70 b and c explaining the non-detection respectively detection of the dust emission from their CPDs. The first explanation is that planet c has larger planet mass, larger gas accretion rate, or both than planet b. The other possibility is that the CPD of planet c has a larger amount of dust supply, weaker turbulence, or both than that of planet b. If the dust supply to planet c is larger than b due to its closeness to the outer dust ring, it is also quantitatively consistent with that planet c has weaker H alpha line emission than planet b considering the dust extinction effect.