arXiv subjects

Christian Reinhardt

Publications and source records attributed to Christian Reinhardt.

24 records · Page 2Linked to original sources

arXiv2019

Primordial Earth mantle heterogeneity caused by the Moon-forming giant impact

The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally similar to the disk, out of which the Moon evolves, whereas the lower layer preserves proto-Earth characteristics. As long as this predicted compositional stratification can at least partially be preserved over the subsequent billions of years of Earth mantle convection, the compositional similarity between the Moon and the accessible Earth's mantle is a natural outcome of realistic and high-probability Moon-forming impact scenarios. The preservation of primordial heterogeneity in the modern Earth not only reconciles geochemical constraints but is also consistent with recent geophysical observations. Furthermore, for significant preservation of a proto-Earth reservoir, the bulk composition of the Earth-Moon system may be systematically shifted towards chondritic values.

astro-ph.EP↗

arXiv2019

A special giant impact model: implications on core-mantle chemical differentiation

The Earths core formation process has decisive effect in the chemical differentiation between the Earths core and its mantle. Here, we propose a new core formation model which is caused by a special giant impact. This model suggests that the impactors core can be kept intact by its own sticky mantle under appropriate impacting conditions and let it merge into the targets core without contact with the targets mantle. We call this special giant impact that caused the new core formation mode as glue ball impact model (GBI). By simulating hundreds of giant impacts with the sizes from planetesimals to planets, the conditions that can lead to GBI have been found out. If with small impact angle (i.e., less than 20 degree), small impact velocity and small impactors mass but larger than 0.07 Mearth, there is a good chance to produce a GBI at the final stage of the Earths accretion. We find that it will be much easier to have GBIs at the late stage of the Earths accretion rather than at the early stage of it. The GBI model will pose a great challenge to many problems between the equilibrium of Earths core and mantle. It provides an additional source for the excess of highly siderophile elements in the Earths mantle and also brings excessive lithophile elements to the Earths core. The GBI model may shed light on the study of Moon-formation and chemical differentiations of the pro-Earth.

astro-ph.EP↗

arXiv2018

Enhanced mixing in giant impact simulations with a new Lagrangian method

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.

astro-ph.EP↗

arXiv2018

Forming Mercury by Giant Impacts

The origin of Mercury's high iron-to-rock ratio is still unknown. In this work we investigate Mercury's formation via giant impacts and consider the possibilities of a single giant impact, a hit-and-run, and multiple collisions in one theoretical framework. We study the standard collision parameters (impact velocity, mass ratio, impact parameter), along with the impactor's composition and the cooling of the target. It is found that the impactor's composition affects the iron distribution within the planet and the final mass of the target by up to 15\%, although the resulting mean iron fraction is similar. We suggest that an efficient giant impact requires to be head-on with high velocities, while in the hit-and-run case the impact can occur closer to the most probable collision angle (45$^{\circ}$). It is also shown that Mercury's current iron-to-rock ratio can be a result of multiple-collisions, with their exact number depending on the collision parameters. Mass loss is found to be more significant when the collisions are tight in time.

astro-ph.EP↗

arXiv2017

Numerical aspects of Giant Impact simulations

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 planet's 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 planet's 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.

astro-ph.EP↗

arXiv2016

Fourier-Taylor Parameterization of Unstable Manifolds for Parabolic Partial Differential Equations: Formalization, Implementation, and Rigorous Validation

In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an infinitesimal invariance equation for the chart map that recovers the dynamics on the manifold in terms of a simple conjugacy. We develop formal series solutions for the invariance equation and efficient numerical methods for computing the series coefficients to any desired finite order. We show, under mild non-resonance conditions, that the formal series expansion converges in a small enough neighborhood of the equilibrium. An a-posteriori computer assisted argument proves convergence in larger neighborhoods. We implement the method for a spatially inhomogeneous Fisher's equation and numerically compute and validate high order expansions of some local unstable manifolds for morse index one and two. We also provide a computer assisted existence proof of a saddle-to-sink heteroclinic connecting orbit.

math.DS↗