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Register a new userEnhanced mixing in giant impact simulations with a new Lagrangian method
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Giant impacts (GIs) are common in the late stage of planet formation. The Smoothed Particle Hydrodynamics (SPH) method is widely used for simulating the outcome of such violent collisions, one prominent example being the formation of the Moon. However, a decade of numerical studies in various areas of computational astrophysics has shown that the standard formulation of SPH suffers from several shortcomings such as artificial surface tension and its tendency to promptly damp turbulent motions on scales much larger than the physical dissipation scale, both resulting in the suppression of mixing. In order to quantify how severe these limitations are when modeling GIs we carried out a comparison of simulations with identical initial conditions performed with the standard SPH as well as with the novel Lagrangian Meshless Finite Mass (MFM) method in the GIZMO code. We confirm the lack of mixing between the impactor and target when SPH is employed, while MFM is capable of driving vigorous sub-sonic turbulence and leads to significant mixing between the two bodies. Modern SPH variants with artificial conductivity, a different formulation of the hydro force or reduced artificial viscosity, do not improve mixing as significantly. Angular momentum is conserved similarly well in both methods, but MFM does not suffer from spurious transport induced by artificial viscosity, resulting in a slightly higher angular momentum of the proto-lunar disk. Furthermore, SPH initial conditions exhibit an unphysical density discontinuity at the core-mantle boundary which is easily removed in MFM.
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In this paper we present solutions to three short comings of Smoothed Particles Hydrodynamics (SPH) encountered in previous work when applying it to Giant Impacts. First we introduce a novel method to obtain accurate SPH representations of a planets equilibrium initial conditions based on equal area tessellations of the sphere. This allows one to imprint an arbitrary density and internal energy profile with very low noise which substantially reduces computation because these models require no relaxation prior to use. As a consequence one can significantly increase the resolution and more flexibly change the initial bodies to explore larger parts of the impact parameter space in simulations. The second issue addressed is the proper treatment of the matter/vacuum boundary at a planets surface with a modified SPH density estimator that properly calculates the density stabilizing the models and avoiding an artificially low density atmosphere prior to impact. Further we present a novel SPH scheme that simultaneously conserves both energy and entropy for an arbitrary equation of state. This prevents loss of entropy during the simulation and further assures that the material does not evolve into unphysical states. Application of these modifications to impact simulations for different resolutions up to $6.4 cdot 10^6$ particles show a general agreement with prior result. However, we observe resolution dependent differences in the evolution and composition of post collision ejecta. This strongly suggests that the use of more sophisticated equations of state also demands a large number of particles in such simulations.
At present, the giant impact (GI) is the most widely accepted model for the origin of the Moon. Most of the numerical simulations of GI have been carried out with the smoothed particle hydrodynamics (SPH) method. Recently, however, it has been pointed out that standard formulation of SPH (SSPH) has difficulties in the treatment of a contact discontinuity such as a core-mantle boundary and a free surface such as a planetary surface. This difficulty comes from the assumption of differentiability of density in SSPH. We have developed an alternative formulation of SPH, density independent SPH (DISPH), which is based on differentiability of pressure instead of density to solve the problem of a contact discontinuity. In this paper, we report the results of the GI simulations with DISPH and compare them with those obtained with SSPH. We found that the disk properties, such as mass and angular momentum produced by DISPH is different from that of SSPH. In general, the disks formed by DISPH are more compact: while formation of a smaller mass moon for low-oblique impacts is expected with DISPH, inhibition of ejection would promote formation of a larger mass moon for high-oblique impacts. Since only the improvement of core-mantle boundary significantly affects the properties of circumplanetary disks generated by GI and DISPH has not been significantly improved from SSPH for a free surface, we should be very careful when some conclusions are drawn from the numerical simulations for GI. And it is necessary to develop the numerical hydrodynamical scheme for GI that can properly treat the free surface as well as the contact discontinuity.
Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in {Delta}17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average {Delta}17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.
We present results of 3D hydrodynamical simulations of HD209458b including a coupled, radiatively-active cloud model ({sc EddySed}). We investigate the role of the mixing by replacing the default convective treatment used in previous works with a more physically relevant mixing treatment ($K_{zz}$) based on global circulation. We find that uncertainty in the efficiency of sedimentation through the sedimentation factor $f_mathrm{sed}$ plays a larger role in shaping cloud thickness and its radiative feedback on the local gas temperatures -- e.g. hot spot shift and day-to-night side temperature gradient -- than the switch in mixing treatment. We demonstrate using our new mixing treatments that simulations with cloud scales which are a fraction of the pressure scale height improve agreement with the observed transmission spectra, the emission spectra, and the Spitzer 4.5 $mathrm{mu m}$ phase curve, although our models are still unable to reproduce the optical and UV transmission spectra. We also find that the inclusion of cloud increases the transit asymmetry in the optical between the east and west limbs, although the difference remains small ($lesssim 1%$).
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.
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