Shock Heating Due to Accretion of a Clumpy Cloud onto a Protoplanetary Disk

Abstract

As a candidate of mechanism of chondrule formation we have investigated the accretion of a compact clumpy cloud onto the protoplanetary disk near the asteroid orbit by means of numerical simulations in a framework of local one-dimensional gas dynamics. In our simulation, we have taken into account precisely the process of radiative transfer which governs the temperature of the disk. On the other hand, we neglected the detailed structure of the shocks because heating of dust particles in the shock regions is not effective. The accreting clump is characterized by two parameters, i.e., the sizezcland the surface density Σcl, where we assume that the velocity of the clump is equal to the free fall velocity. For the various clumpy parameters,zcland Σcl, we have made numerical simulations and found the qualitative features of the generation and the propagation of the shock formed by a clumpy cloud infalling onto the disk. Furthermore, we have found the quantitative behavior of the highest temperature attained in the clumpy accretion. The highest temperature depends in a complicated manner on the parameters (zcland Σcl) and typical size of dust particles in the diskrd.By the present numerical simulations, we have found suitable sets of the parameters with which the clumpy accretion leads to the high temperature stage (≳1500 K). Furthermore, based on the numerical simulations we have theoretically derived a simple formula which gives approximately the highest temperature as a function of the clumpy parameters. In comparison with the observed representative clumpy clouds, more than about 102to 103times surface densities for the same size of the representative clump are needed to produce chondrules. To confirm the possibility that chondrule formation is due to the clumpy accretion, more extensive observational and detailed theoretical works on the clumpy clouds are necessary.