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At present, the giant impact (GI) is the most widely accepted model for theorigin of the Moon. Most of the numerical simulations of GI have been carriedout with the smoothed particle hydrodynamics (SPH) method. Recently, however,it has been pointed out that standard formulation of SPH (SSPH) hasdifficulties in the treatment of a contact discontinuity such as a core-mantleboundary and a free surface such as a planetary surface. This difficulty comesfrom the assumption of differentiability of density in SSPH. We have developedan alternative formulation of SPH, density independent SPH (DISPH), which isbased on differentiability of pressure instead of density to solve the problemof a contact discontinuity. In this paper, we report the results of the GIsimulations with DISPH and compare them with those obtained with SSPH. We foundthat the disk properties, such as mass and angular momentum produced by DISPHis different from that of SSPH. In general, the disks formed by DISPH are morecompact: while formation of a smaller mass moon for low-oblique impacts isexpected with DISPH, inhibition of ejection would promote formation of a largermass moon for high-oblique impacts. Since only the improvement of core-mantleboundary significantly affects the properties of circumplanetary disksgenerated by GI and DISPH has not been significantly improved from SSPH for afree surface, we should be very careful when some conclusions are drawn fromthe numerical simulations for GI. And it is necessary to develop the numericalhydrodynamical scheme for GI that can properly treat the free surface as wellas the contact discontinuity.

The Giant Impact Simulations with Density Independent Smoothed Particle Hydrodynamics