the formation of the collisional family around the dwarf ... · the formation of the haumea system...

In preparation for Astrophysical Journal, November 4, 2009.Preprint typeset using LATEX style emulateapj v. 08/13/06

THE FORMATION OF THE COLLISIONAL FAMILY AROUND THE DWARF PLANET HAUMEAZoe M. Leinhardt

Department of Applied Mathematics and Theoretical Physics,University of Cambridge, CB3 0WA, U.K.

Robert A. MarcusAstronomy Department, Harvard University,

60 Garden St., Cambridge, MA 02138, U.S.A.

Sarah T. StewartDepartment of Earth and Planetary Sciences, Harvard University,

20 Oxford St., Cambridge, MA 02138, U.S.A.

In preparation for Astrophysical Journal, November 4, 2009.

ABSTRACTHaumea, a rapidly rotating non-spherical dwarf planet, has two satellites and is associated with a

“family” of several smaller Kuiper Belt objects (KBOs) in similar orbits. All members of the Haumeasystem share a water ice spectral feature that is distinct from all other KBOs. The relative velocitiesbetween the Haumea family members are too small to have formed by catastrophic disruption of alarge precursor body, which is the process that formed families around much smaller asteroids in theMain Belt. Here we show that all of the unusual characteristics of the Haumea system are explainedby a novel type of giant collision: a graze-and-merge impact between two comparably sized bodies.The grazing encounter imparted the high angular momentum that spun off fragments from the icycrust of the elongated merged body. The fragments became satellites and family members. Giantcollision outcomes are extremely sensitive to the impact parameters. Compared to the Main Belt, thelargest bodies in the Kuiper Belt are more massive and experience slower velocity collisions; hence,outcomes of giant collisions are dramatically different between the inner and outer solar system. Thedwarf planets in the Kuiper Belt record an unexpected number of giant collisions, requiring a specialdynamical event at the end of solar system formation.Subject headings: solar system: Kuiper Belt — dwarf planets (Haumea), methods: numerical — SPH

simulations — N -body simulations

1. INTRODUCTION

The four largest dwarf planets in the Kuiper Belt forma distinct population of bodies with high albedos andvolatile-rich surfaces (Schaller & Brown 2007; Stansberryet al. 2008). A significant history of collisions is sug-gested by the abundance of satellites in this group, whichis much higher than expected for the Kuiper Belt as awhole (Brown et al. 2006). Three of the four have knownsatellites: Pluto has three, Haumea (formerly 2003 EL61)has two, Eris (2003 UB313) has one, and Makemake(2005 FY9) has no substantial satellite (Brown 2008).The size and orbits of these satellites are different fromthose found around smaller (100-km size) Kuiper BeltObjects (KBOs), which are actually wide separation bi-naries thought to have been captured (Noll et al. 2008).Hence, a different satellite formation process is needed forthe dwarf planets, and the most promising mechanism iscollisions. Recently, numerical simulations support a gi-ant collision origin for Pluto’s massive satellite, Charon(Canup 2005). However, the formation of the smallersatellites on the other dwarf planets has not been stud-ied in detail.

Haumea is a particularly puzzling case as it is also

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associated with several smaller KBOs that share simi-lar orbits and surface properties. The Haumea systemof bodies has been likened to collisionally-produced dy-namically and compositionally associated “families” thatare observed in the asteroid belt (Brown et al. 2007).Haumea has the only known family in the Kuiper Belt.Haumea, its two satellites, and the eight confirmed familymembers all share a deep water spectral feature and neu-tral color (Brown et al. 2007; Ragozzine & Brown 2007;Schaller & Brown 2008). The water feature is uniquein the Kuiper Belt (Brown et al. 2007) and indicativeof unusually carbon-free water ice (Pinilla-Alonso et al.2009).

Haumea also has the distinction of being the only non-spherical planet. It has a spin period of only 3.9 hours(Rabinowitz et al. 2006), the fastest of all the major anddwarf planets. The surface of Haumea is nearly homoge-nous with the exception of a red spot or faint red hemi-sphere (Lacerda 2009); hence, the light curve is primarilya reflection of the non-spherical shape. Using the ob-served light curve and rotation period, Rabinowitz et al.(2006) fit a density of 2.6 g cm−3 assuming an equilib-rium fluid body (a Jacobi ellipsoid). Although the di-mensions of Haumea are not yet uniquely constrained(Lockwood & Brown 2009), the observations require atri-axial shape (see Table 2) (Rabinowitz et al. 2006).The derived density is greater than the average of ∼ 2

2 Leinhardt, Marcus, and Stewart

g cm−3 for the largest KBOs (Brown 2008), althoughthe density may be smaller with some internal friction(Holsapple 2007).

Based on the relatively clean water ice surface andhigher than average bulk density, Brown et al. (2007) ar-gue that Haumea is differentiated with a rocky core andicy mantle. They propose that the family members andsatellites are collisionally-derived fragments that origi-nated primarily from the icy mantle. The satellites andfamily members are orders of magnitude less massivethan Haumea, and the family members have a minimumvelocity at infinity (V∞) of about 150 m s−1 (Ragozzine &Brown 2007, 2009). The velocity dispersion is much lessthan expected if the Haumea family formed as the resultof a catastrophic impact, as in the formation of asteroidbelt families (e.g., Nesvorny et al. 2006; Michel et al.2004). In a catastrophic disruption event, a parent bodyis disrupted and dispersed such that the largest remnantis less than or equal to half the original mass. The smallerfragments have initial velocities relative to the largestremnant comparable to the escape speed (Vesc) of thedisrupted parent body (Benz & Asphaug 1999). Thus,the observed magnitude of the velocity dispersion (V∞)of asteroid belt families is significant with respect to Vesc

of the largest remnant; in other words, Vesc of the par-ent body was much greater than Vesc of the largest rem-nant. Unlike asteroid belt families, the velocity disper-sion among Haumea family members is a small fractionof the escape velocity from Haumea (Vesc ∼ 900 m s−1).Therefore, the Haumea family could not have formed bycatastrophic disruption of a much larger parent body.

Two impact scenarios have been proposed for the for-mation of the Haumea system. Brown et al. (2007)proposed an impact event that falls in the catstrophicdisruption category, which does not agree with the ob-served velocity dispersion among family members. Toexplain the small velocity dispersion, Schlichting & Sari(2009) suggest the breakup of a single large moon in or-bit around Haumea. However, they do not provide anexplanation for the initial state: a large moon in closeorbit around a fast-spinning, elongated planet. To date,no known impact scenario explains all of the unusualcharacteristics of the Haumea system.

In this work, we quantitatively model the formationof the Haumea system. We propose that the Haumeafamily formed via a novel type of giant collision: a grazeand merge impact between two comparably sized bodiesresulting in high angular momentum, which spun off icyfragments that became satellites and family members.The analytic and numerical methods are described in §2.The results are presented in §3, and the implications forgiant impacts in the Kuiper Belt are discussed in §4.

2. METHODS

To reduce the parameter space of possible collisionsthat produce a Haumea-like system, we used a threestep process: 1) derive an analytic prediction of plausi-ble impact parameters (§2.1); 2) conduct low-resolutionsimulations over a broad parameter space based on theresults of the analytic prediction (§2.2); and 3) simulatethe most promising impact scenarios in high resolution(§2.3). The next three sections outline the method usedin each step.

Fig. 1.— Analytic prediction of impact scenarios leading to theangular momentum of Haumea for various bulk densities and Vi.Solutions are lines as a function of impact parameter, b, and massof the projectile normalized by the total mass, MP/MTot. For Vi =Vesc (Eq. 1) the short dashed, solid, and long dashed lines showsolutions for bulk densities of 1.5, 2.0, and 2.5 g cm−3, respectively.For Vi = 1.25Vesc (Eq. 2) the dotted line shows solutions for abulk density of 2.0 g cm−3. Haumea parameters are taken fromRabinowitz et al. (2006).

2.1. Analytic Prediction of Impact ParametersFollowing Canup et al. (2001), using the conservation

of energy and momentum, we derived an expression forthe impact parameter and projectile-to-target mass ra-tio needed to obtain the observed angular momentum ofHaumea via a giant impact. Because Haumea is rotat-ing near its spin stability limit and the observed velocitydispersion among family members is small, we considerthe case where all of the angular momentum from thecollision is retained in the remaining body. Assumingthat the relative velocity between the projectile and tar-get was zero at infinity, the impact parameter, b, is givenby

b =L

Lcrit

k√2f(γ)

, (1)

where b is in units of the sum of the radii of the projec-tile and target, L is the angular momentum, and Lcrit

is the critical spin angular momentum that a sphericalbody with constant density can sustain, k is the inertialconstant (2/5 for a sphere), and f(γ) = γ(1− γ)(γ1/3 +(1 − γ1/3))1/2 sin θ where γ = MP

MT +MP, the ratio of the

projectile mass to the total mass. However, if we as-sume that the impact velocity is greater than Vesc, thetotal energy equation will no longer equal zero (Eq. B3of Canup et al. 2001). In this case, the impact parameteris constrained by

b =L

Lcrit

k√2f(γ)

Vesc

Vi, (2)

where Vi is the impact velocity and Vesc is the mutualescape velocity (Eq. 1 of Canup 2005).

For Haumea we assume a mass of 4.2× 1021 kg and aspin period 3.92 hr from Rabinowitz et al. (2006). Using

The Formation of the Haumea System 3

these values, LLcrit

ranges between 1.1 and 0.8 for a plau-sible range of bulk densities of the colliding bodies (1.5to 2.5 g cm−3). The results from Eq. 1 and 2 are shownin Fig. 1.

If the impact velocity equals the mutual escape veloc-ity of the projectile and target, Eq. 1 requires an impactparameter close to one (> 0.8) and a projectile closeto the mass of the target in order to attain the angularmomentum in Haumea (Fig. 1). Increasing the bulk den-sity of the bodies broadens the range of impact parame-ters that could transfer the observed angular momentum.Similarly, when Vi > Vesc, there is a larger range of pos-sible projectile-to-target mass ratios that could producethe angular momentum of Haumea (Eq. 2, dotted line inFig. 1 assumes the mean bulk density for large KBOs of2 g cm−3). This work assumes no initial spin in the tar-get and projectile. Initial spin in the same sense as thespin angular momentum would potentially increase therange of mass ratio that could produce a Haumea-likeremnant.

As the impact velocity increases, the remaining bodydoes not retain most of the angular momentum of theencounter, as is assumed in the equations above. Whenthe impact velocity is large enough to begin to disruptthe target (3 – 3.5 km s−1, Stewart & Leinhardt 2009),a significant amount of angular momentum will be car-ried away by the smallest fragments (see Fig. 2 in Lein-hardt et al. 2000). Compensating for the partial lossof angular momentum by further increasing the impactvelocity will lead to the catastrophic disruption regime.Recall that the catastrophic disruption regime is ruledout based on the velocity dispersion among the familymembers. Although the angular momentum distribu-tion in the catastrophic regime has not been extensivelystudied, we expect that angular momentum transfer tothe largest remnant is inefficient. The largest remnantis a gravitationally reaccumulated body from a cloud offragments; hence, the angular momentum of the reac-cumulated mass does not approach the spin instabilitylimit. Note that numerical simulations of catastrophicdisruption that resolve the shape of the largest remnantproduce spherical remnants (Leinhardt et al. 2000; Lein-hardt & Stewart 2009).

Thus, the analytic argument suggests that the moststraightforward way to create a body with high angu-lar momentum via a collision is in a grazing impact be-tween two objects of similar size at a velocity close to themutual escape speed. Note, however, that the analyticsolution makes several assumptions. For example, massthat is lost from the system as a result of the collision isnot taken into account. The escaping mass carries awaysome energy and momentum. In addition, the energyand momentum conservation are approximated and donot include terms for energy lost in heat and fracturingof the target and projectile.

2.2. Low Resolution SimulationsTo examine the predictions of the idealized analytic

solutions, we conducted a series of low-resolution simu-lations of impacts between gravitational aggregates (Ta-ble 1). Because the encounter velocities are modest(≤ 1.2 km s−1), the energy lost to shock deformationduring the collision is minimal, and gravitational forcesdominate. Thus, for efficiency, the low-resolution simu-

lations utilized the N -body gravity code pkdgrav, whichresolves inelastic particle–particle collisions (Richardsonet al. 2000; Leinhardt et al. 2000; Leinhardt & Richard-son 2002). Particle collisions were modeled using a hardsphere model, where the unbreakable spherical particlesare non-penetrating. The outcome of each inelastic col-lision were governed by conservation of momentum andtypical coefficients of restitution of 0.5 and 1.0 in the nor-mal and tangential directions, respectively, for particlesrepresenting ice or rock (see discussion in Leinhardt &Stewart 2009).

Each projectile and target was modeled as a rubblepile, a gravitationally bound aggregate of 955 particleswith no tensile strength (Leinhardt et al. 2000; Leinhardt& Richardson 2002). Previous simulations (Leinhardtet al. 2000) show that a thousand particles is enoughto resolve general shape features in a rubble pile. Weassumed two internal configurations: homogeneous anddifferentiated bodies. In the differentiated cases, the col-liding bodies had two layers: a 1.0 g cm−3 mantle rep-resenting ice and a 3.0 g cm−3 core representing rock.The mass ratio of the icy mantle to rocky core was alsovaried to reach the desired bulk density, which resultedin a range of initial radii from about 500 to 800 km.

Based on the analytic solutions, the projectile-to-target mass ratio was assumed to be one in most caseswith a subset of simulations considering MP/MT = 0.5.The parameter space included initial bulk densities from1.0 to 3.0 g cm−3, impact velocities between 0.7 to 1.2km s−1, impact parameters from 0.55 to 0.71, and totalsystem masses of 4.5 to 8.2× 1021 kg.

Due to the low resolution, each individual particle hadrelatively large mass, and it was difficult to strip materialfrom the surface of the largest remnant. As a result, weuse these simulations only to refine the impact param-eters that reproduce the observed rotation period andapproximate mass of Haumea. The calculated mass ofthe largest remnant will be biased slightly upward, andthe family members will be completely unresolved.

2.3. High Resolution SimulationsBased on the low-resolution simulation results, impact

parameters were chosen for high-resolution calculationsof the formation of Haumea and its family members (Ta-ble 2). We used a hybrid hydrocode to N -body codetechnique similar to the method used in studies of catas-trophic collisions in the asteroid belt and the outer solarsystem (Michel et al. 2003; Leinhardt & Stewart 2009).The hybrid technique captures the shock deformationduring the early stage of the collision and follows thegravity-controlled evolution of the material to very latetimes. We used GADGET (Springel 2005), a smoothedparticle hydrodynamics code (SPH) modified to use tab-ular equations of state (Marcus et al. 2009), for the hy-drocode phase and pkdgrav for the gravity phase of thecalculation.

SPH is a Lagrangian technique for solving the hydro-dynamic equations in which the mass distribution is rep-resented by spherically symmetric overlapping particlesthat are evolved with time (Gingold & Monaghan 1977;Lucy 1977). SPH has been used extensively to modelimpacts in the solar system from asteroid collisions andfamily forming events to the formation of the Pluto-Charon system (e.g. Asphaug et al. 1998; Michel et al.


2003; Canup 2005).The targets and impactors were differentiated bodies

composed of an ice mantle over a rock core with a bulkdensity of ∼ 2 g cm−3. The largest KBOs have bulk den-sities of about 2 g cm−3, which is similar to the densitypredicted from cosmochemical estimates of the rock toice ratio in the outer solar system (McKinnon et al. 1997,2008). Although the internal structures of large KBOsare unknown (Leinhardt et al. 2008), strong water fea-tures on the surfaces of the largest bodies suggest thatthey have differentiated (McKinnon et al. 2008). Hence,in this work, we consider collisions between differentiatedbodies only in the high resolution simulations.

The material in the rocky cores were modeled using atabulated version of the molecular ANEOS equation ofstate for SiO2 (Melosh 2007), and the ice mantles weremodeled with the tabular 5-Phase equation of state forH2O (Senft & Stewart 2008). The internal temperatureprofile is dependent on the ice to rock ratio and the vis-cosity of ice; models indicate that temperatures for aCharon size body are generally low (e.g., < 300 K after4 Ga McKinnon et al. 2008). As a result, a constant ini-tial temperature of 150 K was chosen. The bodies wereinitialized with hydrostatic pressure profiles. They werethen allowed to settle in isolation to negligible particlevelocities at the specified temperature. The number ofparticles ranged from ∼ 1.2× 105 to ∼ 4× 105 (∼ 24-36particles per target radius) a sufficient resolution to re-solve shock heating and the formation of family members,and the results were checked for sensitivity to resolution.As in all previous studies of giant impacts, the materialsare hydrodynamic (see discussion in §3.3).

The GADGET simulations were run as long as waspractically feasible, normally about 60 simulation hours.At this time, the collision and mass loss process wascomplete; however, more time was needed to determinethe long-term orbital stability of material bound to thelargest object.

2.3.1. Orbital Evolution of Collision FragmentsThe N-body code pkdgrav was used to integrate the

orbiting fragments for thousands of spin periods of thelargest remnant. The GADGET output was translatedand handed off to pkdgrav. In previous work on asteroidfamily formation, pairs of pkdgrav particles were mergedinto a single particle after each particle-particle collisionto reduce computation time (resulting in spherical colli-sion remnants). In this work, because of the significantelongation in the largest remnant, the shape and rotationrate needed to be preserved for the orbital evolution cal-culation, and particle merging could not be used. Hence,the pkdgrav calculation utilized inelastic collisions (§2.2)to preserve the shape and gravitational potential of thelargest remnant.

However, the number of particles in the largest rem-nant in the GADGET simulation (∼ 105 particles) istoo large to integrate in pkdgrav because of the compu-tational expense of calculating the collisions within thelargest remnant. Therefore, the largest remnant was de-resolved to contain ∼ 103 particles by placing a grid overthe body and placing all particles within a grid cell intoa single particle. Each merged particle had a mass equalto the combined mass, a position equal to the center ofmass position, and velocity vector equal to the center of

mass velocity. The spin and shape of the largest remnantwas preserved. The mass of the largest remnant usinginelastic collisions was compared with a perfect merg-ing collision outcome to test the stability of the handoff.The mass of the largest remnant was very similar in bothcases.

The shape and ice-to-rock ratio of individual smallerremnants (the satellites and family members) were notresolved in the SPH simulation. Hence, the self-gravitating remnants outside of the largest remnant weremerged into single particles. In this mannner, the de-resolved pkdgrav calculation allowed the stability sim-ulation to run for thousands of orbits in a reasonableamount of time.

3. RESULTS

3.1. A Collision Scenario for the Haumea SystemThe impact conditions and outcomes of the low-

resolution numerical simulations of possible Haumea-forming impact events are summarized in Table 1. Thelast column of the table, collision type, describes the gen-eral class of the collision. We found three different colli-sion outcomes in our restricted parameter space (see §4for further discussion): 1) merge – the projectile and tar-get merge after initial impact with little or no mass loss;2) graze & merge – the projectile initially hits the tar-get with a large impact parameter and then separates,the projectile is decelerated and subsequently recollidesat a much slower velocity resulting in a merger and afast-spinning body; 3) graze & run – the projectile andtarget hit but do not lose enough energy to remain boundto each other.

The impact parameters that produced elongated bod-ies with a total mass and spin period similar to Haumeatend to be of the graze and merge category. Thus, colli-sions that form a Haumea-like body are found in a dis-tinctly different parameter space than catastrophic dis-ruption events.

High-resolution hybrid simulations of the most success-ful collision scenarios for forming a Haumea-like planetwere conducted to investigate the properties of the satel-lites and family members (Table 2). A time series froman example collision simulation (sim. 3) is presented inFig. 2, which displays the materials in cross-section look-ing down on the collision plane. The last frame, whichhas been rotated by ninety degrees to show the collisionoutcome edge-on, shows the surfaces of the largest rem-nant and the debris field. During the collision, the rockycores of the progenitor bodies merge, and the resultingprimary body spins so quickly that it sheds icy mantlematerial from the ends in many small clumps. Some ofthis material is gravitationally bound and some escapesfrom the primary. In this scenario, the satellites andfamily members do not originate from the initial contact;instead, they are spun off after the subsequent merger.As a result, the V∞ of the family members are small; inother words, the ejection velocities of the fragments arenot much greater than the escape velocity of the mergedprimary.

The analytic and numerical results show that the op-timum parameter space to form a Haumea-like planetis in an encounter slightly more energetic than mergingbetween comparably sized bodies. Some of the merg-ing cases that are close to the transition to graze and


TABLE 1Summary of parameters and results from selected pkdgrav simulations.

R MP ρb ρc b V Mlr semi-axes of lr ρlr Plr Collision Type

km MT g/cm3 ρm – km/s MTot km×km×km g/cm3 hr

770 0.5 2.0 1.0 0.80 0.7 0.98 1270×750×690a 1.6 4.4 merge770 0.5 2.0 1.0 0.80 0.8 0.88 1000×708×670 2.0 5.0 graze & merge770 0.5 2.0 1.0 0.80 0.9 graze & run650 1.0 2.0 1.0 0.65 0.8 0.99 1396×711×632 1.7 4.9 merge650 1.0 2.0 1.0 0.65 0.9 0.99 1398×750×670 1.5 5.0 graze & merge650 1.0 2.0 1.0 0.65 1.0 graze & run800 1.0 1.0 1.0 0.6 1.0 graze & run650 1.0 2.0 3.0 0.6 1.0 graze & run630 1.0 2.6 3.0 0.6 1.0 0.99 1270×657×607 2.1 3.8 graze & merge580 1.0 3.3 3.0 0.6 1.0 0.99 1164×606×526 2.8 3.7 graze & merge650 1.0 2.0 3.0 0.55 0.7 0.99 1219×717×699 1.8 4.1 merge650 1.0 2.0 3.0 0.55 0.8 0.99 1293×692×666 1.8 4.3 merge650 1.0 2.0 3.0 0.55 0.9 0.99 1385×680×634 1.8 4.2 merge650 1.0 2.0 3.0 0.55 1.0 0.99 1362×708×647 1.7 4.5 graze & merge650 1.0 2.0 3.0 0.55 1.1 graze & run650 1.0 2.0 3.0 0.55 1.2 graze & run650 1.0 2.0 3.0 0.60 0.8 0.99 1303×702×688 1.7 4.1 merge650 1.0 2.0 3.0 0.60 0.9 0.99 1322×446×636 1.7 3.9 graze & merge650 1.0 2.0 3.0 0.60 1.0 graze & run650 1.0 2.0 3.0 0.65 0.7 0.99 1252×740×672 1.7 4.1 merge650 1.0 2.0 3.0 0.65 0.8 0.99 1273×698×697 1.7 4.2 graze & merge650 1.0 2.0 3.0 0.65 0.9 0.99 1445×699×648 1.6 4.9 graze & graze & merge

R – radius of target; MPMT

– mass of projectile normalized by mass of target; ρb, ρc/ρm – bulk density,

density ratio of core to mantle; for ρc/ρm > 1.0, ρc = 3.0 and ρm = 1.0 g cm−3; b – impact parameter; V –first impact velocity; Mlr/MTot – mass of largest remnant normalized by total mass; ρlr – bulk density of lr;Plr – spin period of lr. In all cases, each body contained 955 particles and MTot = 4.5×1021 kg. Bulk density,calculated by circumscribing all particles within an axisymmetric ellipsoid, is always a minimum value.alr is significantly non-axisymmetric.

merge also produce an elongated, fast-spinning largestremnant; however, from high-resolution simulations, wefind that such merging simulations eject less mass and,thus, do not tend to form families. Although the long-term relaxation of the bodies is not considered here, wenote that impacts with a mass ratio less than one pro-duced initially nonsymmetric largest remnants that arenot consistent with observations.

The collision parameters that achieve the best agree-ment with observations fall in a narrow parameter space:an impact speed of 800-900 m s−1 and an impact param-eter between 0.6 and 0.65 for equal mass progenitors withbulk densities of 2 g cm−3. At higher impact velocitiesor higher impact parameters, the two bodies escape fromeach other after the impact. At lower impact velocitiesor lower impact parameters, the two bodies merge andless material is ejected as potential family members. Ini-tial spin would increase or decrease the impact parameterneeded to achieve the same total angular momentum, asshown in idealized cases in Leinhardt et al. (2000).

3.2. Properties of the Satellites and FamilyThe impact conditions defined above reproduce the

mass, spin period and elongation of Haumea, as well asthe mass and velocity distributions of the observed satel-lites and family members. In Fig. 3A, the observed fam-ily (triangles and dotted line from Ragozzine & Brown2007) are normalized to the number of resolved fragmentsin sim. 3 after 2000 spin orbits to facilitate comparison.Haumea and the two known satellites are indicated byfilled triangles. The diameter of Haumea family mem-bers was derived from the absolute magnitude assumingsimilar albedo to Haumea of ∼ 0.7, and the diameter wasconverted into mass assuming a bulk density of 1 g cm−3

for a primarily ice composition. In Fig. 3B, the opentriangles below zero indicate the minimum relative ve-locities of the known family members with respect to thecenter of the family using the reconstructed position forHaumea (Ragozzine & Brown 2007).

As shown in Fig. 3B, the total mass of potential satel-lites and family members is small: < 0.07Mlr for sim. 1-3from Table 2. Although the modeled mass is larger thanthe known satellites and family members (∼ 0.01Mlr),one does not expect that all of these bodies have beenobserved or that all should survive to the present day.Hence, the modeled mass of smaller bodies is consis-tent with the observed Haumea system. In addition, themasses of individual satellite and family members aresmall, with most < 10−3Mlr, which is also in agreementwith the observed family (Fig. 3A).

Almost all of the family members have a relative ve-locity that is < 0.5Vesc with respect to the primary, with80-90% of the mass having a speed < 300 m s−1 and35-60% of the mass having a speed less than 150 m s−1.Note that 150 m s−1 is the minimum velocity dispersionof the observed family; the true values could be about twotimes larger when accounting for the unknown orbital ori-entation (Ragozzine & Brown 2007). The model predictsthat negligible mass reaches the typical velocity disper-sion among 100-km size KBOs of about 1000 m s−1.

The modeled satellite and family members are com-prised almost entirely of icy mantle material (73-86% bymass). The bulk density of the largest remnant increasesby ∼ 10% over the initial density of the progenitor bod-ies as a result of the preferential stripping of the lower-density ice mantle (Fig. 2). The modeled bulk density ofthe largest remnant is within the range of uncertainty for


Fig. 2.— Time series of a graze and merge event: 650-km diameter bodies colliding at 900 m s−1 with an impact parameter of 0.6(sim. 3 in Table 2). Cross section view through the collision plane which is in the page. Field of view is initially 5000×5000 km, increasingto 10000×10000 km at 11.1 hours. The last frame (58.9 hrs) shows the system edge on. Color denotes the provenance of the materials:icy mantles (cyan and blue) and rocky cores (light and dark grey). For visual clarity in the last frame, the radius of each dot equals onefifth of the smoothing length of the corresponding SPH particle, for all other frames the dots are point particles. Although some materialis exchanged during the first impact, each body remains largely intact after separation. The rocky cores merge after the second impact,forming a differentiated primary. The surface of the merged body has distinct patches of ice that originate from each of the precursorbodies. The fragments thrown from the merged body are primarily material from the icy mantles. An animation is available in the onlineversion of the Journal.


Fig. 3.— Mass and velocity distributions for simulations 1-3 in Table 2. (A) Cumulative number of resolved fragments larger than massM versus fragment mass (short dash, long dash, and filled circles are results from sim. 1-3 after ∼ 100 orbits, the open circles are resultsfrom sim. 3 after ∼ 2000 orbits). Triangles and dotted line are the observed family normalized to simulation 3. (B) Cumulative velocitydistribution of fragments (short dashed line, long dashed line, and thin solid line, sim. 1-3, respectively, after 100 orbits, thick black lineis from sim. 3 after 2000 orbits). The lower absicca is normalized by the escape speed from the largest remnant (model Haumea). Theleft ordinate is the mass of fragments with relative velocities greater than V normalized by the mass of the largest remnant, and the rightordinate is normalized by the total mass in smaller fragments in long running sim. 3. Open triangles below zero are minimum relativevelocities of family members.

TABLE 2Summary of Haumea family forming simulation results and observations.

Sim. MT RT µ b Vimp1 Vimp2 Mlr ρlr semi-axes of lr Plr fH2O

No. 1021 kg km m s−1 m s−1 1021 kg g cm−3 km × km × km hr

1 2.25 650 1 0.6 800 260 4.3 2.2 960× 870× 640 3.6 0.862 2.25 650 1 0.65 800 280 4.3 2.2 1100× 940× 640 3.7 0.733 2.25 650 1 0.6 900 260 4.2 2.1 1100× 810× 620 3.9 0.804a 4.80 830 0.22 0.71 3000 - 4.64 2.3 1700× 1500× 1500 28 -

Obs.b - - - - - - 4.006 2.6 1000× 750× 500 3.9 -

MT – mass of target body; RT – radius of target body; µ – mass ratio of projectile to target; b – impactparameter; Vimp1 – first impact velocity; Vimp2 – second impact velocity in graze and merge event; Mlr – mass oflargest remnant; ρlr – bulk density of lr; Plr – spin period of lr; fH2O – ice mass fraction of all smaller fragments.ρlr and fH2O from end of hydrocode phase (50–60 hrs); all other simulation results from end of gravity phase(∼ 100 orbits).aProposed impact scenario from Brown et al. (2007).bObserved characteristics of Haumea (Ragozzine & Brown 2009; Rabinowitz et al. 2006). Note: simulations

presented here attempted to match the mass of 4.21± 0.1× 1021 kg quoted in Rabinowitz et al. (2006).


the density of Haumea. These results explain the sharedwater ice spectral feature of the bodies in the Haumeasystem and the complete lack of bodies with a similarwater ice spectrum in the general (not dynamically as-sociated) KBO population around Haumea. Negligblemass was dispersed into the background KBO popula-tion in the graze and merge family-forming event.

In one simulation (no. 3), the orbits of the satellitesand family members were integrated for 2000 spin orbitsto assess the stability of the newly formed system aroundthe elongated primary. At this time, there are ∼ 35 ob-jects gravitationally bound and in orbit about the pri-mary (the mass in orbit is about 0.01Mlr and the massin family members is about 0.06Mlr). These bodies haveeccentricities below 0.9 and instantaneous orbits that donot intersect the primary. The bound objects and instan-taneous orbital parameters were determined using thecompanion code (Leinhardt & Richardson 2005). Here,we do not assess the longer term dynamical evolution ofthe collisional system. However, we demonstrate thatsome bodies remain in stable orbits around the elon-gated, fast-spinning primary well after the collision event.Unlike previously thought (Brown et al. 2006), the for-mation of multiple small satellites around Haumea doesnot require accretion in a massive disk.

3.3. The Effect of Material StrengthSimulations of giant impact events usually utilize a

SPH code (e.g., this work, Benz et al. 1986, 1988; Canup2004, 2005; Benz et al. 2007; Marinova et al. 2008). ALagrangian SPH calculation has the advantages of anarbitrarily large spatial domain and efficiency in track-ing small fragments. In an Eulerian (grid-based) code,the spatial domain must be decided upon in advanceand tracking small fragments through the mesh is com-putationally very expensive. In previous studies, giantimpact calculations have neglected material strength onthe grounds that self-gravitational forces and shock pres-sure gradients dominate the problem. Most giant impactstudies have focused on the end stages of planet for-mation and considered hypervelocity impact events thatgenerate strong shock waves. Hence, it has been reason-able to neglect material strength. For collisions betweendwarf planets at subsonic velocities, however, it is notobvious that strength can be neglected.

We conducted a few comparison three-dimensionalsimulations using the Eulerian shock physics code CTH(McGlaun et al. 1990) with adaptive mesh refinement(Crawford 1999). CTH has the option to include self-gravitational forces using the parallel tree method of(Barnes & Hut 1986). The simulations had a resolutionof 31 to 42 km (30 to 40 cells across each initial body).In the nominal simulations, each CTH cell is comparablein physical size to a single GADGET particle within theinitial bodies, although the effective resolution in CTHis slightly higher because of the differences in smoothinglengths between the two codes. Tests at twice the res-olution (in each dimension) yielded similar results. TheCTH calculations utilize the same tabulated equation ofstate models as used in the GADGET SPH simulations.Each body was initialized in gravitational equilibrium ata constant temperature of 150 K. The radii were 650 km,with an ice mantle over a rock core such that the bulkdensity was 2 g cm−3. To allow for reasonable calcula-

tion times, material in cells with a bulk density less than0.01 g cm−3 was discarded from the calculation. Hence,fragments that become the moons and family membersof Haumea are not modeled in CTH. Only the formationof the primary (Haumea) is considered.

Some simulations were hydrodynamic (no shearstrength) for direct comparison to GADGET. Other sim-ulations utilized a simple friction law (the geologicalyield model in CTH) that represents friction in fractured(damaged) ice (Senft & Stewart 2008): Y0 + µP , whereY0 = 0.1 MPa is the cohesion, µ = 0.55 is the frictioncoefficient, and P is pressure. The shear strength is lim-ited to a maximum of 0.1 GPa. Shear strength is ther-mally degraded as the temperature approaches 273 K.The tensile strength was 1.7 MPa. For simplicity, thesame strength model was used in both the ice and rockcomponents. The strength parameters are similar tomodels of sedimentary rocks (e.g., Collins et al. 2008),which are signficantly weaker than crystalline rocks.

Because the CTH calculations require significantlymore computational time than the GADGET calcula-tions, comparisons between the two codes were made atearly stages in the impact event. Hydrodynamic CTHcalculations are similar to the GADGET results (Fig. 4).The minor differences at late times are due to small dif-ferences in the initial conditions: the initial separationof the bodies and the better resolution of the ice-rockinterface in CTH.

In cases with strength, a number of differences are ob-served. The radial oscillations in each body after the ini-tial contact are not observed with strength. These oscil-lations arise from momentum transfer between the rockcore and ice mantle; the difference in particle velocitiesfrom the momentum transfer is damped with strength.The number of ‘strings of fragments’ between the twobodies after the initial contact is decreased with strength(2.8 hours in Fig. 4). Because of dissipation of energyin mechanical work during the first contact, the secondcontact occurs sooner with strength. The temperatureincrease from the impact is higher with strength becauseof dissipation of mechanical work as heat. Note thatwith and without strength, the cores of the two bodiesmerge quickly after the second contact. The purpose ofthe CTH calculation is not to try to develop a realisticstrength model for large KBOs, but simply to demon-strate that the addition of a reasonable amount of inter-nal friction yields essentially the same result as in thedetailed hydrodynamic simulations.

3.4. Impact-induced Heating and the Icy SurfaceDuring the impact event, the temperature in the por-

tions of the ice mantle in the regions of contact are raisedto the phase boundary (melting or vaporization, depend-ing on the local pressure, Fig. 4). However, negligiblemass of ice is melted or vaporized. For the ∼ 1 km s−1

impact velocities considered here and a wide range ofinitial temperatures, ice that experiences the peak shockpressures will be raised to the melting or vaporizationcurve (Stewart et al. 2008). However, no ice is expectedto completely melt or vaporize. Thus, the outcome of thecollision event is not sensitive to the initial temperatureas neither the rock nor ice components experience sign-ficant shock-induced phase changes during the collisionevent. As a confirmation, a test SPH simulation with


0.56 hr

1.9 hr

2.8 hr

4.2 hr

5.9 hr

8.9 hr

10.3 hr

1000 km

GADGET CTH Hydrodynamic

Temp. (K)

260240220200180160

CTH Strength CTH Strength

Fig. 4.— Time series of sim. 1 in Table 2 using GADGET and CTH with and without strength. View of the cross section through theimpact plane. Each panel is 4000× 4000 km. Columns 1-3: Colors represent material (blues – ice mantles; browns – rock cores). Column4: Color represents temperature.


a high temperature rock interior yielded essentially thesame result.

In a graze and merge impact, the ice mantles expe-rience severe deformation that is expected to fragmentthe ice. Upon merging, solid state differentiation occursquickly, even with some strength. The surface of the re-sulting primary (Haumea) is covered with ice fragmentsthat have been heated over a wide range: from negligiblyto the phase boundaries. The fragmented ice mantle hasnegligible cohesion and may be likened to a slurry. Icehas exceedingly low friction when warm and at modestslip velocities which are exceeded in the scenario consid-ered here (Maeno et al. 2003). Thus, we conclude thatthe ice mantle will have negligible resistance to mass lossdue to the high angular momentum of the merged body.

Because the graze and merge portions of the impactevent are similar in the GADGET and CTH calculations(with and without strength), we argue that the spin off ofice fragments at the end stages of the event is faithfullymodeled in the hydrodynamic GADGET calculations.

One of the remarkable characteristics of Haumea, itslarger satellite, and its family members is the strong wa-ter ice spectral feature. The graze and merge familyforming event explains the ice-dominated surfaces of theHaumea system. Although the simulations cannot ad-dress the details of ice separation from other phases, theresults suggest that the formation event produced an icysurface that is cleaner compared to other KBOs, as isobserved (Pinilla-Alonso et al. 2009). A relatively cleanicy mantle is necessary to prevent reddening from cosmicirradiation (Rabinowitz et al. 2008) over the time sincethe impact event (> 1 Ga, Ragozzine & Brown 2007).Because the surface of Haumea appears so homogeneousand unlike other KBOs, we argue that it is unlikelythat the surfaces of the precursor bodies were so simi-lar. Hence, the strong ice feature on the Haumea familymust be related to the family-forming impact event.

3.5. Previously Proposed Formation ScenariosBrown et al. (2007) suggested a possible impact sce-

nario to produce the Haumea collisional family basedon numerical studies of asteroidal family forming events(Benz & Asphaug 1999): impact of a projectile with 0.22the mass of the target at 3 km s−1 at an impact param-eter of 0.71. The authors suggested that such an im-pact would both strip off a portion of the target’s mantleand impart a high spin period. We conducted a high-resolution simulation of the proposed impact scenario.Our results demonstrate that there is not enough energyand momentum coupling between the projectile and thetarget to produce a fast-spinning primary (sim. 4 in Ta-ble 2). The projectile shaves off some of the target ma-terial and escapes from the system, but the remainingangular momentum is insufficient to elongate the targetbody. Based on our analytic calculations and numeri-cal results, it is not favorable for a small, fast projectileto impart enough angular momentum to create a fast-spinning elongated body.

Using an order of magnitude analysis, Schlichting &Sari (2009) suggest a different Haumea family formingscenario involving a two stage formation process. First, agiant impact creates an elongated fast-spinning primaryand a large, tightly-bound satellite. Second, a subse-quent impact onto the satellite, disrupts it and creates

the family members and small satellites. Based on nu-merical simulations, an elongated and fast spinning pri-mary is only produced in a slow collision with a largeimpact parameter and a mass ratio close to unity (Ta-ble 1, Leinhardt et al. 2000; Leinhardt & Richardson2002); furthermore, these scenarios do not create a largetightly-bound satellite. Impact events that produce alarge tightly-bound satellite (e.g., Canup 2005) do notform elongated primaries.

4. DISCUSSION

Giant impacts are common in the late stages of planetformation, and several outcomes are possible. With ap-proximately decreasing impact energy, a giant impactleads to: (i) catastrophic disruption (half or more ofthe target mass is lost, Benz & Asphaug 1999; Stew-art & Leinhardt 2009; Marcus et al. 2009). The largestremnants are aggregates of gravitationally reaccumulatedmaterial; it is the formation mechanism for asteroid beltfamilies. (ii) graze and run (a.k.a. hit and run, Asphauget al. 2006). In some oblique impacts, the projectilehits and then escapes the target with both bodies re-maining largely intact. Note that we prefer the term“graze” rather than “hit” to indicate the need for anoblique impact. (iii) graze and capture. The projectileobliquely hits the target and separates, but does not haveenough energy to escape and is captured in orbit. It isthe favored formation mechanism for the Pluto-Charonbinary (Canup 2005). (iv) graze and merge. The pro-jectile obliquely hits, separates, and then recollides andmerges with the target. The high angular momentum ofthe merged body spins off some material. Such a sce-nario explains the unusual characteristics of the Haumeacollisional family. In an alternate scenario, a graze andmerge impact to form Pluto may also produce a diskof bound material of the mass of Charon (Canup 2005).(v) merge. The projectile and target merge during thefirst contact; in some cases, a small fraction of materialmay be thrown into orbit or escape (as in the Earth’smoon forming impact Canup 2004). Each impact sce-nario (except for graze and run) has left a distinct typeof observable satellite or family system in the solar sys-tem.

The modeled impact scenarios that reproduce thePluto and Haumea systems are strikingly similar. Theimpact velocities, impact parameters, and masses of theprojectile are almost exactly the same, with the primarydifference being the mass ratio between the projectile andtarget: 0.3 for Pluto (Canup 2005) and 1.0 for Haumea.What is the liklihood of such impact events? The KuiperBelt is presently composed of multiple dynamically dis-tinct sub-populations (e.g., classical, scattered and res-onant, Morbidelli et al. 2008). There is strong evidencefor an excitation event after an initial period of colli-sional growth. The Haumea family must have formedafter the excitation event, which would have scatteredaway all the family members. Although collision proba-bilities between two 1000-km scale bodies in the classicalpopulation are negligible, Levison et al. (2008) calculatedup to a ∼ 50% probability of the impact scenario pro-posed by Brown et al. (2007) if the two bodies originatedfrom the scattered population and then entered the clas-sical population as a result of the impact. However, theestimated mean impact velocity between scattered ob-


jects is substantially higher (about 2.7 km s−1) than wefind for the Haumea-forming event. The probabilities ofslower speed collisions need to be investigated.

5. CONCLUSIONS

In this work, we show that a graze and merge collisionevent between nearly equal mass bodies is able to pro-duce a symmetrically-elongated, fast-spinning primary,a family of collisional fragments, and multiple boundsatellites. The satellites and family members are derivedfrom the icy mantle of the merged, differentiated pri-mary. The family members have a small relative velocitywith respect to the primary. This scenario matches all ofthe observed characteristics of the Haumea system. Ourresults predict that observations of future family mem-bers should all have relative velocities less than ∼ 0.5Vesc

of Haumea and that the family members should not beisotropically distributed because they formed in a plane.

We now have the tools to read the record of giant col-lisions throughout the solar system. At present, thereare several 10’s of Pluto-sized bodies known in the outersolar system (Brown 2008). The new Pan-STARRS ob-servatory will detect up to an order of magnitude morebodies in the Kuiper Belt (Trujillo 2008), which will com-plete the Haumea system and test the predictions of the

graze and merge scenario. Models of the dynamical evo-lution of the Kuiper Belt indicate that the populationmust have been much larger in the past (by a factor of∼ 1000) (Morbidelli et al. 2008). Satellite formation wasa common outcome of giant impacts, and the abundanceof satellites around dwarf planets indicates that giant im-pacts were frequent. We find that the types of collisionevents that formed the observed satellites and familiesin the outer solar system are distinctly different from theEarth’s moon formation and families in the asteroid belt.The narrow range of impact parameters that formed thePluto and Haumea systems place strong constraints onthe dynamical history of the largest bodies in the KuiperBelt.

Acknowledgements. We thank D. Ragozzine and M.Cuk for helpful discussions. The hydrocode calculationswere run on the Odyssey cluster supported by the Har-vard FAS Research Computing Group. The N-body cal-culations were run using the University of Cambridge,Astrophysical Fluids Research Group computational fa-cilities. ZML is supported by a STFC fellowship; STSby NASA grant # NNX09AP27G.

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