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Star-disk alignment in the protoplanetary disks: SPH simulation of the collapse of turbulent molecular cloud cores

We perform a series of three-dimensional smoothed particle hydrodynamics (SPH) simulations to study the evolution of the angle between the protostellar spin and the protoplanetary disk rotation axes (the star-disk angle $ψ_{\rm sd}$) in turbulent molecular cloud cores. While $ψ_{\rm sd}$ at the protostar formation epoch exhibits broad distribution up to $\sim 130^{\circ}$, $ψ_{\rm sd}$ decreases ($\lesssim 20^{\circ}$) in a timescale of $\sim 10^{4}$ yr. This timescale of the star-disk alignment, $t_{\rm alignment}$, corresponds basically to the mass doubling time of the central protostar, in which the protostar forgets its initial spin direction due to the mass accretion from the disk. Values of $ψ_{\rm sd}$ both at $t=10^2$ yr and $t=10^5$ yr after the protostar formation are independent of the ratios of thermal and turbulent energies to gravitational energy of the initial cloud cores: $α=E_{\rm thermal}/|E_{\rm gravity}|$ and $γ_{\rm turb}=E_{\rm turbulence}/|E_{\rm gravity}|$. We also find that a warped disk is possibly formed by the turbulent accretion flow from the circumstellar envelope.