Lunar-forming impacts: High-resolution SPH and AMR-CTH simulations

doi:10.1016/j.icarus.2012.10.011

Icarus

Volume 222, Issue 1, January 2013, Pages 200-219

https://doi.org/10.1016/j.icarus.2012.10.011 Get rights and content

Abstract

We present results of the highest-resolution simulations to date of potential Moon-forming impacts using a Lagrangian, particle-based method (smooth particle hydrodynamics, or SPH) and an Eulerian, grid-based method with adaptive mesh refinement (AMR-CTH). We consider a few candidate impacts advocated by recent works, directly comparing simulations performed at varying resolutions and with both numerical methods and their predictions for the properties of resulting protolunar disks. For a fixed set of impact conditions, simulations with either method and with different resolutions yield very similar results for the initial impact and the first few hours of the post-impact period. The subsequent disk properties in the ∼5–20 h time period can vary substantially from case-to-case, depending on the orbits of and mutual interactions between large bound clumps of ejecta that often form after the initial impact. After such clumps have completed at least one orbit (which typically requires ∼25–50 h), the predicted protolunar disk mass and its angular momentum converge to within about 10% for simulations of very similar impact conditions using different resolutions or methods. The disks produced by the CTH simulations are consistently about 10% less massive than those produced by SPH simulations, due presumably to inherent differences between the codes. The two methods predict broadly similar values for the fraction of the protolunar disk that originates from the target vs. the impactor, and for the initial disk radial surface density and temperature profiles.

Highlights

► We model lunar-forming impacts with high-resolution SPH and AMR-CTH simulations. ► We compare impacts simulated with two hydrodynamical methods and varied resolutions. ► We focus on the predicted properties of the protolunar disk. ► Resulting disk masses and angular momenta are similar to within ∼10%. ► The fraction of the disk originating from the target is also not strongly affected.

Section snippets

Background

The giant impact theory proposes that the Moon formed from material ejected when a roughly Mars-sized protoplanet obliquely impacted the Earth (e.g., Cameron and Ward, 1976, Benz et al., 1989, Canup and Asphaug, 2001). Forming Earth-sized planets is thought to require collisions between large protoplanetary embryos (e.g., Chambers and Wetherill, 1998), so that giant impacts should have been common during the final stage of terrestrial planet accretion (e.g., Agnor et al., 1999). The impact

Constraints and trends in impact outcome

The lunar forming impact was probably the last major event in Earth’s accretion. In the simplest case, the impact leaves an approximately Earth-mass planet, together with a planet-disk pair whose total angular momentum is comparable to that in the current Earth–Moon system, L_EM ≡ 3.5 × 10⁴¹ g cm² s⁻¹. A successful candidate impact must also produce a protolunar disk with sufficient mass and angular momentum to eventually accumulate into a Moon of mass M_L = 0.012M_⊕ = 7.35 × 10²⁵ g exterior to the Earth’s

Methods

Hydrodynamical models of giant impacts have primarily used smooth particle hydrodynamics, or SPH (e.g., Benz et al., 1986, Benz et al., 1987, Benz et al., 1989; Canup and Asphaug, 2001, Canup, 2004a, Canup, 2008). SPH represents matter as particles whose individual evolutions due to gravity, pressure forces, and shock dissipation are calculated as a function of time. The Lagrangian formulation of SPH is well suited to tracking different materials and particle histories (e.g., whether the mass

Oblique, low-velocity collision with CTH

We begin by comparing results obtained by using AMR-CTH to simulate a giant impact at four resolutions with an impactor-to-total mass ratio γ = 0.11, a total colliding mass M_T ∼ 1.02M_⊕, a scaled impact parameter b′ = 0.82, and an impact velocity v_imp = v_esc, where $v_{esc} = \sqrt{2 {GM}_{T} / (R_{i} + R_{t})}$ , and R_i and R_T are the radii of the impactor and target. This is similar to run #24 from Canup and Asphaug (2001). That work considered a basalt mantle and the Tillotson equation of state, which leads to a more massive disk

Discussion

To assess whether changes in resolution or numerical method affect the mass, angular momentum, and provenance of material in the protolunar disk, we have performed the first direct comparison between lunar-forming impact simulations performed with both an Eulerian (AMR-CTH) and a Lagrangian (SPH) code. We have also tested the effect of varying resolutions with both methods on impact outcome. We focus primarily on successful candidate impacts involving low-velocity, oblique impacts by an

Acknowledgments

The authors thank H.J. Melosh and E. Asphaug for detailed and helpful reviews. R.M.C. was supported by NASA’s LASER program and the NASA Lunar Science Institute (NLSI); A.C.B. acknowledges support from NLSI. D.A.C. is an employee of Sandia, a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.

References (54)

C.B. Agnor et al.
On the character and consequences of large impacts in the late stage of terrestrial planet formation
Icarus
(1999)
E. Asphaug
Similar-sized collisions and the diversity of planets
Chem. Erde – Geochem.
(2010)
D. Balsara
Von Neumann stability analysis of smooth particle hydrodynamics–suggestions for optimal algorithms
J. Comput. Phys.
(1995)
W. Benz et al.
The origin of the Moon and the single impact hypothesis I
Icarus
(1986)
W. Benz et al.
The origin of the Moon and the single impact hypothesis II
Icarus
(1987)
W. Benz et al.
The origin of the Moon and the single impact hypothesis III
Icarus
(1989)
R.M. Canup
Simulations of a late lunar forming impact
Icarus
(2004)
R.M. Canup
Lunar-forming collisions with pre-impact rotation
Icarus
(2008)
R.M. Canup et al.
A scaling relationship for satellite-forming impacts
Icarus
(2001)
J.E. Chambers et al.
Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions
Icarus
(1998)

E. Kokubo et al.

Evolution of a circumterrestrial disk and formation of a single Moon

Icarus

(2000)

J.M. McGlaun et al.

CTH: A 3-dimensional shock-wave physics code

Int. J. Imp. Eng.

(1990)

K. Pahlevan et al.

Equilibration in the aftermath of the lunar-forming giant impact

Earth Planet. Sci. Lett.

(2007)

K. Pahlevan et al.

Chemical fractionation in the silicate vapor atmosphere of the Earth

Earth Planet. Sci. Lett.

(2011)

E. Pierazzo et al.

A reevaluation of impact melt production

Icarus

(1997)

A. Reufer et al.

A hit-and-run giant impact scenario

Icarus

(2012)

C.B. Agnor et al.

Accretion efficiency during planetary collisions

Astrophys. J.

(2004)

J. Barnes et al.

A hierarchical O(N log N) force-calculation algorithm

Nature

(1986)

E. Belbruno et al.

Where did the Moon come from?

Astron. J.

(2005)

Cameron, A.G.W., Ward, W.R., 1976. The origin of the Moon. Lunar Planet. Sci. VII,...

R.M. Canup

Dynamics of lunar formation

Ann. Rev. Astron. Astrophys.

(2004)

R.M. Canup et al.

Origin of the Moon in a giant impact near the end of the Earth’s formation

Nature

(2001)

Canup, R.M., Barr, A.C., 2010. Modeling Moon-forming impacts: High-resolution SPH and CTH simulations. Lunar Planet....

Canup, R.M., Asphaug, E., Pierazzo, E., Melosh, H.J., 2002. Simulations of Moon-forming impacts. Lunar Planet. Sci....

Crawford, D.A., 2011a. CTH simulations of candidate Moon forming impacts. Lunar Planet. Sci....

Crawford, D.A., 2011b. Parallel N-body gravitational interaction in CTH for planetary defense and large impact...

Crawford, D.A., Kipp, M.E., 2010. Giant impact theory for origin of the Moon: High resolution CTH simulations. Lunar...

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Lunar-forming impacts: High-resolution SPH and AMR-CTH simulations

Abstract

Highlights

Section snippets

Background

Constraints and trends in impact outcome

Methods

Oblique, low-velocity collision with CTH

Discussion

Acknowledgments

Icarus

Chem. Erde – Geochem.

J. Comput. Phys.

Icarus

Icarus

Icarus

Icarus

Icarus

Icarus

Icarus

Icarus

Int. J. Imp. Eng.

Earth Planet. Sci. Lett.

Earth Planet. Sci. Lett.

Icarus

Icarus

Accretion efficiency during planetary collisions

Astrophys. J.

A hierarchical O(N log N) force-calculation algorithm

Nature

Where did the Moon come from?

Astron. J.

Dynamics of lunar formation

Ann. Rev. Astron. Astrophys.

Origin of the Moon in a giant impact near the end of the Earth’s formation

Nature