arXiv subjects

Miki Nakajima

Publications and source records attributed to Miki Nakajima.

At least 19 recordsLinked to original sources

arXiv2025

Wind erosion and transport on planetesimals

We consider the possibility that aeolian (wind blown) processes occur on small, 1 to 100~km diameter, planetesimals when they were embedded in the protosolar nebula. Drag from a headwind within a protostellar disk is sufficiently large to loft cm and smaller sized particles off the surface of a 10 km diameter asteroid in the inner solar system (at a few AU), and micron sized particles off the surface of a 10 km diameter object in the Transneptunian region. The headwind is sufficiently strong to overcome surface cohesion in the inner solar system, but not in the outer solar system. However, in the outer solar system, surface particles can be redistributed or escape due to impacts from particles that are in the protosolar disk's wind. Based on scaling crater ejecta, we estimate that impacts from particles in the headwind will lead to erosion of mass rather than accretion for planetesimals below about 6 km in diameter. The erosion limit is independent of material strength but proportional to the wind velocity. We explore the sensitivity of splash particle trajectories to particle size, headwind velocity and Reynolds number. Winds from a protostellar disk could account for Kuiper Belt Object (486958) Arrokoth's smooth undulating terrain but only during an epoch of high particle flux and low wind velocity. These conditions could have been present during and just after coalescence of Arrokoth's building blocks.

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arXiv2024

Thermal and magnetic evolution of an Earth-like planet with a basal magma ocean

Earth's geodynamo has operated for over 3.5 billion years. The magnetic field is currently powered by thermocompositional convection in the outer core, which involves the release of light elements and latent heat as the inner core solidifies. However, since the inner core nucleated no more than 1.5 billion years ago, the early dynamo could not rely on these buoyancy sources. Given recent estimates of the thermal conductivity of the outer core, an alternative mechanism may be required to sustain the geodynamo prior to nucleation of the inner core. One possibility is a silicate dynamo operating in a long-lived basal magma ocean. Here, we investigate the structural, thermal, buoyancy, and magnetic evolution of an Earth-like terrestrial planet. Using modern equations of state and melting curves, we include a time-dependent parameterization of the compositional evolution of an iron-rich basal magma ocean. We combine an internal structure integration of the planet with energy budgets in a coupled core, basal magma ocean, and mantle system. We determine the thermocompositional convective stability of the core and the basal magma ocean, and assess their respective dynamo activity using entropy budgets and magnetic Reynolds numbers. Our conservative nominal model predicts a transient basal magma ocean dynamo followed by a core dynamo after 1 billion years. The model is sensitive to several parameters, including the initial temperature of the core-mantle boundary, the parameterization of mantle convection, the composition of the basal magma ocean, the radiogenic content of the planet, as well as convective velocity and magnetic scaling laws. We use the nominal model to constrain the range of basal magma ocean electrical conductivity and core thermal conductivity that sustain a dynamo.

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arXiv2024

Composition, Structure and Origin of the Moon

Here we critically examine the geophysical and geochemical properties of the Moon in order to identify the extent to which dynamical scenarios satisfy these observations. New joint inversions of existing lunar geophysical data (mean mass, moment of inertia, and tidal response) assuming a laterally- and vertically homogeneous lunar mantle show that, in all cases, a core with a radius of 300$\pm$20 km ($\sim$0.8 to 1.5 % the mass of the Moon) is required. However, an Earth-like Mg# (0.89) in the lunar mantle results in core densities (7800$\pm$100 kg/m$^3$) consistent with that of Fe-Ni alloy, whereas FeO-rich compositions (Mg# = 0.80--0.84) require lower densities (6100$\pm$800 kg/m$^3$). Geochemically, we use new data on mare basalts to reassess the bulk composition of the Moon for 70 elements, and show that the lunar core likely formed near 5 GPa, 2100 K and $\sim$1 log unit below the iron-wüstite buffer. Moreover, the Moon is depleted relative to the Earth's mantle in elements with volatilities higher than that of Li, with this volatile loss likely having occurred at low temperatures (1400$\pm$100 K), consistent with mass-dependent stable isotope fractionation of moderately volatile elements (e.g., Zn, K, Rb). The identical nucleosynthetic (O, Cr, Ti) and radiogenic (W) isotope compositions of the lunar and terrestrial mantles, strongly suggest the two bodies were made from the same material, rather than from an Earth-like impactor. Rb-Sr in FANs and Lu-Hf and Pb-Pb zircon ages point Moon formation close to $\sim$4500 Ma. Taken together, there is no unambiguous geochemical or isotopic evidence for the role of an impactor in the formation of the Moon, implying perfect equilibration between the proto-Earth and Moon-forming material or alternative scenarios for its genesis.

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arXiv2024

The Limited Role of the Streaming Instability During Moon and Exomoon Formation

It is generally accepted that the Moon accreted from the disk formed by an impact between the proto-Earth and impactor, but its details are highly debated. Some models suggest that a Mars-sized impactor formed a silicate melt-rich (vapor-poor) disk around Earth, whereas other models suggest that a highly energetic impact produced a silicate vapor-rich disk. Such a vapor-rich disk, however, may not be suitable for the Moon formation, because moonlets, building blocks of the Moon, of 100 m-100 km may experience strong gas drag and fall onto Earth on a short timescale, failing to grow further. This problem may be avoided if large moonlets ($\gg 100$ km) form very quickly by streaming instability, which is a process to concentrate particles enough to cause gravitational collapse and rapid formation of planetesimals or moonlets. Here, we investigate the effect of the streaming instability in the Moon-forming disk for the first time and find that this instability can quickly form $\sim 100$ km-sized moonlets. However, these moonlets are not large enough to avoid strong drag and they still fall onto Earth quickly. This suggests that the vapor-rich disks may not form the large Moon, and therefore the models that produce vapor-poor disks are supported. This result is applicable to general impact-induced moon-forming disks, supporting the previous suggestion that small planets ($<1.6 R_\oplus$) are good candidates to host large moons because their impact-induced disks would be likely vapor-poor. We find a limited role of streaming instability in a satellite formation in an impact-induced disk, whereas it plays a key role during planet formation.

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arXiv2024

Ncorpi$\mathcal{O}$N : A $\mathcal{O}(N)$ software for N-body integration in collisional and fragmenting systems

Ncorpi$\mathcal{O}$N is a $N$-body software developed for the time-efficient integration of collisional and fragmenting systems of planetesimals or moonlets orbiting a central mass. It features a fragmentation model, based on crater scaling and ejecta models, able to realistically simulate a violent impact. The user of Ncorpi$\mathcal{O}$N can choose between four different built-in modules to compute self-gravity and detect collisions. One of these makes use of a mesh-based algorithm to treat mutual interactions in $\mathcal{O}(N)$ time. Another module, much more efficient than the standard Barnes-Hut tree code, is a $\mathcal{O}(N)$ tree-based algorithm called FalcON. It relies on fast multipole expansion for gravity computation and we adapted it to collision detection as well. Computation time is reduced by building the tree structure using a three-dimensional Hilbert curve. For the same precision in mutual gravity computation, Ncorpi$\mathcal{O}$N is found to be up to 25 times faster than the famous software REBOUND. Ncorpi$\mathcal{O}$N is written entirely in the C language and only needs a C compiler to run. A python add-on, that requires only basic python libraries, produces animations of the simulations from the output files. The name Ncorpi$\mathcal{O}$N, reminding of a scorpion, comes from the French $N$-corps, meaning $N$-body, and from the mathematical notation $\mathcal{O}(N)$, due to the running time of the software being almost linear in the total number $N$ of moonlets. Ncorpi$\mathcal{O}$N is designed for the study of accreting or fragmenting disks of planetesimal or moonlets. It detects collisions and computes mutual gravity faster than REBOUND, and unlike other $N$-body integrators, it can resolve a collision by fragmentation. The fast multipole expansions are implemented up to order six to allow for a high precision in mutual gravity computation.

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arXiv2023

Large planets may not form fractionally large moons

One of the unique aspects of Earth is that it has a fractionally large Moon, which is thought to have formed from a Moon-forming disk generated by a giant impact. The Moon stabilizes the Earth's spin axis at least by several degrees and contributes to Earth's stable climate. Given that impacts are common during planet formation, exomoons, which are moons around planets in extrasolar systems, should be common as well, but no exomoon has been confirmed. Here we propose that an initially vapor-rich moon-forming disk is not capable of forming a large moon because growing moonlets, which are building blocks of a moon, experience strong gas drag and quickly fall toward the planet. Our impact simulations show that terrestrial and icy planets that are larger than $\sim 1.3-1.6 R_\oplus$ produce entirely vapor disks, which fail to form a large moon. This indicates that (1) our model supports the Moon-formation models that produce vapor-poor disks and (2) rocky and icy exoplanets whose radii are smaller than $\sim 1.6 R_\oplus$ are ideal candidates for hosting fractionally large exomoons.

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arXiv2023

Effect of Equation of State and Cutoff Density in Smoothed Particle Hydrodynamics Simulations of the Moon-Forming Giant Impact

The amount of vapor in the impact-generated protolunar disk carries implications for the dynamics, devolatilization, and moderately volatile element (MVE) isotope fractionation during lunar formation. The equation of state (EoS) used in simulations of the giant impact is required to calculate the vapor mass fraction (VMF) of the modeled protolunar disk. Recently, a new version of M-ANEOS ("Stewart M-ANEOS") was released with an improved treatment of heat capacity and expanded experimental Hugoniot. Here, we compare this new M-ANEOS version with a previous version ("N-SPH M-ANEOS") and assess the resulting differences in smoothed particle hydrodynamics (SPH) simulations. We find that Stewart M-ANEOS results in cooler disks with smaller values of VMF and results in differences in disk mass that are dependent on the initial impact angle. We also assess the implications of the minimum "cutoff" density ($ρ_{c}$), similar to a maximum smoothing length, that is set as a fast-computing alternative to an iteratively calculated smoothing length. We find that the low particle resolution of the disk typically results in $>40\%$ of disk particles falling to $ρ_c$, influencing the dynamical evolution and VMF of the disk. Our results show that choice of EoS, $ρ_{c}$, and particle resolution can cause the VMF and disk mass to vary by tens of percent. Moreover, small values of $ρ_{c}$ produce disks that are prone to numerical instability and artificial shocks. We recommend that future giant impact SPH studies review smoothing methods and ensure the thermodynamic stability of the disk over simulated time.

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arXiv2022

Geophysical Evolution During Rocky Planet Formation

Progressive astronomical characterization of planet-forming disks and rocky exoplanets highlight the need for increasing interdisciplinary efforts to understand the birth and life cycle of terrestrial worlds in a unified picture. Here, we review major geophysical and geochemical processes that shape the evolution of rocky planets and their precursor planetesimals during planetary formation and early evolution, and how these map onto the astrophysical timeline and varying accretion environments of planetary growth. The evolution of the coupled core-mantle-atmosphere system of growing protoplanets diverges in thermal, compositional, and structural states to first order, and ultimately shapes key planetary characteristics that can discern planets harboring clement surface conditions from those that do not. Astronomical campaigns seeking to investigate rocky exoplanets will require significant advances in laboratory characterization of planetary materials and time- and spatially-resolved theoretical models of planetary evolution, to extend planetary science beyond the Solar System and constrain the origins and frequency of habitable worlds like our own.

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arXiv2022

Ricochets on Asteroids II: Sensitivity of laboratory experiments of low velocity grazing impacts on substrate grain size

We compare low velocity impacts that ricochet with the same impact velocity and impact angle into granular media with similar bulk density, porosity and friction coefficient but different mean grain size. The ratio of projectile diameter to mean grain length ranges from 4 in our coarsest medium to 50 in our finest sand. Using high speed video and fluorescent markers, we measure the ratio of pre- to post-impact horizontal and vertical velocity components, which we refer to as coefficients of restitution, and the angle of deflection caused by the impact in the horizontal plane. Coefficients of restitution are sensitive to mean grain size with the ratio associated with the horizontal velocity component about twice as large for our coarsest gravel as that for our finest sand. This implies that coefficients for hydro-static-like, drag-like and lift-like forces, used in empirical force laws, are sensitive to mean grain size. The coefficient that is most strongly sensitive to grain size is the lift coefficient which decreases by a factor of 3 between our coarsest and finest media. The deflection angles are largest in the coarser media and their size approximately depends on grain size to the 3/2 power. This scaling is matched with a model where momentum transfer takes place via collisions with individual grains. The dependence of impact mechanics on substrate size distribution should be considered in future models for populations of objects that impact granular asteroid surfaces.

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arXiv2021

Scaling laws for the geometry of an impact-induced magma ocean

Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to describe these scaling laws and determine their coefficients by linear regression, minimizing the error between our model and SPH simulations. The input parameters are the impact angle $θ$ ($0^{\circ}, 30^{\circ}, 60^{\circ}$, and $90^{\circ}$), total mass $M_T$ ($1M_{\rm Mars}-53M_{\rm Mars}$, where $M_{\rm Mars}$ is the mass of Mars), impact velocity $v_{\rm imp}$ ($v_{\rm esc} - 2v_{\rm esc}$, where $v_{\rm esc}$ is the mutual escape velocity), and impactor-to-total mass ratio $γ$ ($0.03-0.5$). We find that the equilibrium pressure at the base of a melt pool can be higher (up to $\approx 80 \%$) than those of radially-uniform global magma ocean models. This could have a significant impact on element partitioning. These melt scaling laws are publicly available on GitHub ($\href{https://github.com/mikinakajima/MeltScalingLaw}{https://github.com/mikinakajima/MeltScalingLaw}$).

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arXiv2021

Origin of the Moon

The Earth-Moon system is unusual in several respects. The Moon is roughly 1/4 the radius of the Earth - a larger satellite-to-planet size ratio than all known satellites other than Pluto's Charon. The Moon has a tiny core, perhaps with only ~1% of its mass, in contrast to Earth whose core contains nearly 30% of its mass. The Earth-Moon system has a high total angular momentum, implying a rapidly spinning Earth when the Moon formed. In addition, the early Moon was hot and at least partially molten with a deep magma ocean. Identification of a model for lunar origin that can satisfactorily explain all of these features has been the focus of decades of research.

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arXiv2021

Accretion of Ornamental Equatorial Ridges on Pan, Atlas and Daphnis

We explore scenarios for the accretion of ornamental ridges on Saturn's moons Pan, Atlas, and Daphnis from material in Saturn's rings. Accretion of complex shaped ridges from ring material should be possible when the torque from accreted material does not exceed the tidal torque from Saturn that ordinarily maintains tidal lock. This gives a limit on the maximum accretion rate and the minimum duration for equatorial ridge growth. We explore the longitude distribution of ridges accreted from ring material, initially in circular orbits, onto a moon that is on a circular, inclined or eccentric orbit. Sloped and lobed ridges can be accreted if the moon tidally realigns during accretion due to its change in shape or because the disk edge surface density profile allows ring material originating at different initial semi-major axes to impact the moon at different locations on its equatorial ridge. We find that accretion from an asymmetric gap might account for a depression on Atlas's equatorial ridge. Accretion from an asymmetric gap at orbital eccentricity similar to the Hill eccentricity, might allow accretion of multiple lobes, as seen on Pan. Two possibly connected scenarios are promising for growth of ornamental equatorial ridges. The moon migrates through the ring, narrowing its gap and facilitating accretion. The moon's orbital eccentricity could increase due to orbital resonance with another moon, pushing it into its gap edges and facilitating accretion.

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arXiv2020

Ricochets on Asteroids: Experimental study of low velocity grazing impacts into granular media

Spin off events and impacts can eject boulders from an asteroid surface and rubble pile asteroids can accumulate from debris following a collision between large asteroids. These processes produce a population of gravitational bound objects in orbit that can impact an asteroid surface at low velocity and with a distribution of impact angles. We present laboratory experiments of low velocity spherical projectiles into a fine granular medium, sand. We delineate velocity and impact angles giving ricochets, those giving projectiles that roll-out from the impact crater and those that stop within their impact crater. With high speed camera images and fluorescent markers on the projectiles we track spin and projectile trajectories during impact. We find that the projectile only reaches a rolling without slipping condition well after the marble has reached peak penetration depth. The required friction coefficient during the penetration phase of impact is 4-5 times lower than that of the sand suggesting that the sand is fluidized near the projectile surface during penetration. We find that the critical grazing impact critical angle dividing ricochets from roll-outs, increases with increasing impact velocity. The critical angles for ricochet and for roll-out as a function of velocity can be matched by an empirical model during the rebound phase that balances a lift force against gravity. We estimate constraints on projectile radius, velocity and impact angle that would allow projectiles on asteroids to ricochet or roll away from impact, finally coming to rest distant from their initial impact sites.

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arXiv2020

Excitation of Tumbling in Phobos and Deimos

Mass-spring model simulations are used to investigate past spin states of a viscoelastic Phobos and Deimos. From an initially tidally locked state, we find crossing of a spin-orbit resonance with Mars or a mean motion resonance with each other does not excite tumbling in Phobos or Deimos. However, once tumbling our simulations show that these moons can remain so for an extended period and during this time their orbital eccentricity can be substantially reduced. We attribute the tendency for simulations of an initially tumbling viscoelastic body to drop into spin-synchronous state at very low eccentricity to the insensitivity of the tumbling chaotic zone volume to eccentricity. After a tumbling body enters the spin synchronous resonance, it can exhibit long lived non-principal axis rotation and this too can prolong the period of time with enhanced tidally generated energy dissipation. The low orbital eccentricities of Phobos and Deimos could in part be due to spin excitation by nearly catastrophic impacts rather than tidal evolution following orbital resonance excitation.

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arXiv2019

Boulder Stranding in Ejecta Launched by an Impact Generated Seismic Pulse

We consider how an impact generated seismic pulse affects the surface of an asteroid distant from the impact site. With laboratory experiments on dry polydisperse gravel mixtures, we track the trajectories of particles ejected from the surface by a single strong upward propagating pressure pulse. High speed video images show that ejecta trajectories are independent of particle size, and collisions primarily take place upon landing. When they land particles are ballistically sorted, as proposed by Shinbrot et al. (2017), leaving larger particles on the surface and smaller particles more widely dispersed. A single strong pulse can leave previously buried boulders stranded on the surface. Boulder stranding due to an impact excited seismic pulse is an additional mechanism that could leave large boulders present on the surface of rubble asteroids such as 162173 Ryugu, 101955 Bennu and 25143 Itokawa.

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arXiv2019

Near/Far Side Asymmetry in the Tidally Heated Moon

Using viscoelastic mass spring model simulations to track heat distribution inside a tidally perturbed body, we measure the asymmetry of heating in the crust of a spin synchronous Moon in eccentric orbit about the Earth. With the Moon within a few Earth radii of the Earth, we find that tidal heating per unit area in a lunar crustal shell is asymmetric due to the octupole order moment in the Earth's tidal field and is 10 to 20\% higher on its near side than on its far side. Tidal heating reduces the crustal basal heat flux and the rate of magma ocean crystallization. Assuming that the local crustal growth rate depends on the local basal heat flux and the distribution of tidal heating in latitude and longitude, a heat conductivity model illustrates that a moderately asymmetric and growing lunar crust could maintain its asymmetry. Near/far side asymmetric tidal heating could serve as a trigger for uneven lunar crustal growth.

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arXiv2018

Inefficient volatile loss from the Moon-forming disk: reconciling the giant impact hypothesis and a wet Moon

The Earth's Moon is thought to have formed from a circumterrestrial disk generated by a giant impact between the proto-Earth and an impactor approximately 4.5 billion years ago. Since the impact was energetic, the disk would have been hot and partially vaporized. This formation process is thought to be responsible for the geochemical observation that the Moon is depleted in volatiles. This model predicts that the Moon should be significantly depleted in water as well, but this appears to contradict some of the recently measured lunar water abundances and D/H ratios that suggest that the Moon is more water-rich than previously thought. Alternatively, the Moon could have retained its water if the upper of the disk were dominated by heavier species because hydrogen would have had to diffuse out from the heavy-element rich disk, and therefore the escape rate would have been limited by this slow diffusion process (diffusion-limited escape). To identify which escape the disk would have experienced and to quantify volatiles loss from the disk, we compute the thermal structure of the Moon-forming disk considering various bulk water abundances and mid-plane disk temperatures. Our calculations show that the upper parts of the Moon-forming disk are dominated by heavy atoms or molecules and hydrogen is a minor species. This indicates that hydrogen escape would have been diffusion-limited, and therefore the amount of lost water and hydrogen would have been small compared to the initial abundance assumed. This result indicates that the giant impact hypothesis can be consistent with the water-rich Moon. Furthermore, since the hydrogen wind would have been weak, the other volatiles would not have escaped either. Thus, the observed volatile depletion of the Moon requires another mechanism.

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arXiv2017

Formation, stratification, and mixing of the cores of Earth and Venus

Earth possesses a persistent, internally-generated magnetic field, whereas no trace of a dynamo has been detected on Venus, at present or in the past, although a high surface temperature and recent resurfacing events may have removed paleomagnetic evidence. Whether or not a terrestrial body can sustain an internally generated magnetic field by convection inside its metallic fluid core is determined in part by its initial thermodynamic state and its compositional structure, both of which are in turn set by the processes of accretion and differentiation. Here we show that the cores of Earth- and Venus-like planets should grow with stable compositional stratification unless disturbed by late energetic impacts. They do so because higher abundances of light elements are incorporated into the liquid metal that sinks to form the core as the temperatures and pressures of metal-silicate equilibration increase during accretion. We model this process and determine that this establishes a stable stratification that resists convection and inhibits the onset of a geodynamo. However, if a late energetic impact occurs, it could mechanically stir the core creating a single homogenous region within which a long-lasting geodynamo would operate. While Earth's accretion has been punctuated by a late giant impact with likely enough energy to mix the core (e.g. the impact that formed the Moon), we hypothesize that the accretion of Venus is characterized by the absence of such energetic giant impacts and the preservation of its primordial stratifications.

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