# Physical properties of asteroid Dimorphos as derived from the DART impact

S.D<EMAIL_ADDRESS>Space Research and Planetary Sciences,
Physics Institute, University of Bern, Switzerland  M. Jutzi  Space Research
and Planetary Sciences, Physics Institute, University of Bern, Switzerland
A.F. Cheng  Johns Hopkins University Applied Physics Laboratory, Laurel, MD,
USA  Y. Zhang  Department of Aerospace Engineering, University of Maryland,
College Park, MD, USA  O. Barnouin  Johns Hopkins University Applied Physics
Laboratory, Laurel, MD, USA  G. S. Collins  Department of Earth Science and
Engineering, Imperial College London, UK  R. T. Daly  Johns Hopkins University
Applied Physics Laboratory, Laurel, MD, USA  T. M. Davison  Department of
Earth Science and Engineering, Imperial College London, UK  C.M. Ernst  Johns
Hopkins University Applied Physics Laboratory, Laurel, MD, USA  T. L. Farnham
Department of Aerospace Engineering, University of Maryland, College Park, MD,
USA  F. Ferrari  Department of Aerospace Science and Technology, Politecnico
di Milano, Italy  M. Hirabayashi  Guggenheim School of Aerospace Engineering,
Georgia Institute of Technology, Atlanta, GA, USA  Department of Aerospace
Engineering, Auburn University, Auburn, AL, USA  K. M. Kumamoto  Lawrence
Livermore National Laboratory, Livermore, CA, USA  P. Michel  Université Côte
dAzur, Observatoire de la Côte dAzur, CNRS, Laboratoire Lagrange, Nice, France
University of Tokyo, Department of Systems Innovation, School of Engineering,
Tokyo, Japan  N. Murdoch  Institut Supérieur de l’Aéronautique et de l’Espace
(ISAE-SUPAERO), Université de Toulouse, Toulouse, France  R. Nakano
Guggenheim School of Aerospace Engineering, Georgia Institute of Technology,
Atlanta, GA, USA  Department of Aerospace Engineering, Auburn University,
Auburn, AL, USA  M. Pajola  INAF-OAPD Astronomical Observatory of Padova,
Italy  A. Rossi  IFAC-CNR, Sesto Fiorentino (FI), Italy  H. F. Agrusa
Université Côte dAzur, Observatoire de la Côte dAzur, CNRS, Laboratoire
Lagrange, Nice, France  Department of Aerospace Engineering, University of
Maryland, College Park, MD, USA  B. W. Barbee  NASA/Goddard Space Flight
Center, Greenbelt, MD, USA  M. Bruck Syal  Lawrence Livermore National
Laboratory, Livermore, CA, USA  N. L. Chabot  Johns Hopkins University Applied
Physics Laboratory, Laurel, MD, USA  E. Dotto  INAF-Osservatorio Astronomico
di Roma, Italy  E. G. Fahnestock  Jet Propulsion Laboratory, California
Institute of Technology, Pasadena, CA, USA  P. H. Hasselmann  INAF-
Osservatorio Astronomico di Roma, Italy  I. Herreros  Centro de Astrobiología
(CAB), CSIC-INTA, Carretera de Ajalvir km4, 28850 Torrejón de Ardoz, Spain  S.
Ivanovski  INAF-Osservatorio Astronomico di Trieste, Trieste, Italy  J.-Y. Li
Planetary Science Institute, Tucson, AZ, USA  A. Lucchetti  INAF-OAPD
Astronomical Observatory of Padova, Italy  R. Luther  Museum für Naturkunde,
Leibniz Institute for Evolution and Biodiversity Science, Berlin, Germany  J.
Ormö  Centro de Astrobiología (CAB), CSIC-INTA, Carretera de Ajalvir km4,
28850 Torrejón de Ardoz, Spain  M. Owen  Lawrence Livermore National
Laboratory, Livermore, CA, USA  P. Pravec  Astronomical Institute of the Czech
Academy of Sciences, Czech Republic  A. S. Rivkin  Johns Hopkins University
Applied Physics Laboratory, Laurel, MD, USA  C. Q. Robin  Institut Supérieur
de l’Aéronautique et de l’Espace (ISAE-SUPAERO), Université de Toulouse,
Toulouse, France  P. Sánchez  Colorado Center for Astrodynamics Research,
University of Colorado Boulder, Boulder, CO, USA  F. Tusberti  INAF-OAPD
Astronomical Observatory of Padova, Italy  K. Wünnemann  Museum für
Naturkunde, Leibniz Institute for Evolution and Biodiversity Science, Berlin,
Germany  A. Zinzi  Agenzia Spaziale Italiana; ASI Space Science Data Center,
Italy  E. Mazzotta Epifani  INAF-Osservatorio Astronomico di Roma, Italy  C.
Manzoni  London Stereoscopic Company, London, UK  B. H. May  London
Stereoscopic Company, London, UK

On September 26, 2022, NASA’s Double Asteroid Redirection Test (DART) mission
successfully impacted Dimorphos, the natural satellite of the binary near-
Earth asteroid (65803) Didymos. Numerical simulations of the impact provide a
means to explore target surface material properties and structures, consistent
with the observed momentum deflection efficiency, ejecta cone geometry, and
ejected mass. Our simulation, which best matches observations, indicates that
Dimorphos is weak, with a cohesive strength of less than a few pascals (Pa),
similar to asteroids (162173) Ryugu and (101955) Bennu. We find that a bulk
density of Dimorphos, $\rho_{B}$, lower than $\approx$ 2400 kg/m3, and a low
volume fraction of boulders ($\lesssim$ 40 vol%) on the surface and in the
shallow subsurface, are consistent with measured data from the DART
experiment. These findings suggest Dimorphos is a rubble pile that might have
formed through rotational mass shedding and re-accumulation from Didymos. Our
simulations indicate that the DART impact caused global deformation and
resurfacing of Dimorphos. ESA’s upcoming Hera mission may find a re-shaped
asteroid, rather than a well-defined crater.

## Introduction

DART was a planetary defense mission to demonstrate the feasibility of using a
kinetic impactor to change the trajectory of an asteroid [1]. The impact was
successful and highly effective, resulting in a reduction in Dimorphos’
orbital period around Didymos, which was initially 11 hours and 55 minutes, by
33 $\pm$ 1 minutes [2]. The LICIACube Unit Key Explorer (LUKE) instrument
onboard the cubesat [3] captured images of the system between 29 and 320
seconds after impact, revealing filamentary streams of ejecta and other
complex patterns that expanded for several kilometres from the impact site
[4]. Moreover, the dramatic brightening of the Didymos system by solar
illumination of released impact ejecta was observed from ground- and space-
based telescopes [2, 5, 6] for many weeks after the impact.

The obtained 33-minute reduction in the binary orbital period [2] implies a
momentum transfer to Dimorphos that exceeded the incident momentum of the DART
spacecraft by a factor $\beta$, ranging from 2.2 to 4.9, depending on the mass
of Dimorphos [7] – which is not currently known but will be measured by the
ESA Hera spacecraft in early 2027 [8]. The $\beta$ parameter is defined as the
ratio of the target momentum increment after the impact to the impactor
momentum, in the direction of the net ejecta momentum, and is related to the
additional thrust from the production of impact ejecta [7, 9]. $\beta$
strongly depends on impact conditions (i.e., impact velocity and impact angle
[1]) and target material properties, such as strength, porosity, bulk density
and target surface structure [10, 11, 12].

The spacecraft information, location and impact angle for the DART impact are
well understood [1]. However, the mass and surface properties of Dimorphos are
still ambiguous. It was not possible to directly measure the mass and bulk
density of Dimorphos with DART or LICIACube. Instead, these parameters were
estimated from the total mass of the binary system, derived from Dimorphos’
orbit [13], and updated volume estimates of Didymos and Dimorphos provided by
DART [1]. The estimated bulk density of Dimorphos ranges from $\rho_{B}$ =
1500 to 3300 kg/m3 [1, 7].

The surface material properties and sub-surface structure of Dimorphos were
also not directly measured. However, these target parameters are vital for
understanding the impact process and transforming the kinetic impactor method
from a full-scale experiment by DART into a well-understood and reliable
mitigation technique for planetary defence. Moreover, knowledge of the
material properties of Dimorphos relates to the origin and evolution of the
Didymos-Dimorphos system, as well as the overall characteristics of rubble-
pile asteroids and binary asteroid systems.

In this work, we simulate the DART impact numerically and compare the results
with observations to infer the properties of Dimorphos. We performed numerical
simulations of the DART impact using the shock physics code Bern SPH [14, 15]
over a range of assumed sets of material properties and interior structures
for Dimorphos. We represented the DART spacecraft as a low-density spherical
projectile of equivalent mass (see Projectile section in Methods), and the
impact velocity and angle were also kept fixed. We simulated the asteroid’s
response to the DART impact for up to one hour after the time of impact, using
the numerical approach developed in [16, 17] to model late-stage, low-speed
deformation (see Modelling approach for the late stage evolution in Methods).
Bern SPH’s fast-integration scheme was validated against laboratory
experiments [18] and recently applied successfully to the Hayabusa2 SCI impact
modelling [17]. Due to the relatively short timescales modelled, the rotation
of Dimorphos around Didymos and Didymos’s gravity were not accounted for.

We obtain realistic configurations of boulders for our rubble-pile targets
from simulations of gravitational collapse of a cloud of spherical particles
with a predefined size-frequency distribution (SFD) [1, 19]. To closely
replicate the topography described by [1], we then selectively removed
particles positioned near the surface.

To explore a large possible range of boulder volume fractions (0 vol% to 50
vol%), we replaced some of these boulders with matrix material when we built
our target asteroid. We only explicitly modelled boulders larger than 2.5 m in
diameter, and the space between boulders was filled with matrix material.
Boulders smaller than 2.5 m were removed from the SFD because they were too
small to be resolved individually. Thus, components smaller than 2.5 m were
considered part of the matrix, which was modelled as a granular material with
low, but limited cohesion. This approach created an asteroid whose interior
structure is similar to its surface and whose structure overall is consistent
with a gravitational collapse. For the purpose of this study, other deep
interior structures are not considered.

The bulk porosity of Dimorphos results from macroporosity between individual
rocks and boulders as well as microporosity within rocks. Analysis of
reflectance spectra of Didymos indicates that the best meteorite analogues for
boulders on Dimorphos are L/LL ordinary chondrites [20, 21, 22], which have
grain densities of $\approx$ 3200–3600 kg/m3, and low microporosities of
$\approx$ 8–10% [23]. Using the method described by [24] (See Dimorphos
macroporosity calculations in Methods), we calculated macroporosities of 38
$\pm$ 3% from the boulder SFD in the last complete image taken by DART [1] and
34 $\pm$ 4% from the global SFDs measured on Dimorphos [19]. The derived
macroporosity is primarily determined by the boulder SFD and the
sphericity/roundness of the boulders. It is important to note that the
macroporosity estimation is largely independent of the assumed minimum boulder
size. In our simulations, the initial micropososity within boulders was fixed
at 10% and the initial porosity of the matrix (macroporosity + microporosity)
was varied between 35% and 65%. Both the porosity in the boulders and in the
matrix were modelled using the $P-\alpha$ porosity compaction model [14].

Based on laboratory measurements of meteorite falls, the average tensile
strength of ordinary chondrites is 24 $\pm$ 11 MPa, with no statistical
difference between L and LL types [23]. In all our simulations, the initial
material properties of the boulders were kept the same and we employed the
tensile strength and fracture model as described in [14, 15], with parameters
corresponding to a tensile strength $Y_{T}\approx$ 20 MPa for a $\approx$ 2 cm
specimen. For the boulders on Dimorphos, the average $Y_{T}\approx$ 10 MPa
(Table 1). However, based on previous impact studies [[, e.g.,]]ormo2022, we
do not expect the impact outcome to be very sensitive to the boulder tensile
strength.

The target matrix material response to shear deformation is described by a
simple pressure-dependent strength model [25, 26]. The ability of a material
to resist different types of stresses is an indicator of its strength.
Granular materials, for instance, may exhibit considerable shear strength due
to the presence of van der Waals forces and the particles’ inability to
separate or slide over each other due to interlocking mechanisms [27, 28, 29].
Here we focus on the influence of the shear strength at zero pressure,
commonly known as cohesion (or cohesive strength). Another important term in
the strength model is the coefficient of internal friction. Though this
parameter cannot be directly determined, it is possible to relate it to the
angle of repose (See Methods) and bound the range of plausible values by
making reasonable assumptions. The angle of repose of low cohesion materials
has been measured to be $\theta$ = 22∘ ($f$ = 0.4) for glass beads [30],
$\theta$ = 30∘ ($f$ = 0.55) for quartz sand [31] and $\theta$ = 35–-45∘ ($f$ =
0.7–0.9) for lunar regolith [32].

On Dimorphos, for values of cohesion lower than $Y_{0}$ $\approx$ 4 Pa, the
impact occurs in the gravity-dominated regime where crater growth is halted by
the asteroid’s small gravity, rather than its cohesion [33]. Therefore, we
first model impacts into cohesionless rubble-piles (i.e., $Y_{0}$ = 0 Pa, but
with a coefficient of internal friction of $f$ = 0.55 [31], which is
equivalent to $\theta$ $\approx$ 30∘). Given our other assumptions regarding
material properties, we consider that these models of impacts into targets
with no cohesion provide an upper limit on the possible momentum enhancement
that can be achieved from the DART impact for a given asteroid mass.

The momentum enhancement, $\beta$, was calculated using two distinct methods.
For the first method, $\beta$ was calculated by summing the momentum over all
the SPH particles with ejection velocities larger than $v_{esc}$. For a given
impact, the magnitude of ejecta momentum in the direction of the net ejecta
momentum is given by

${p_{ej}}=|\sum m_{e}\vec{v_{ej}}|,$ (1)

where $m_{e}$ and $\vec{v_{ej}}$ are the mass and velocity vector of
individual SPH particles, respectively. The ${p_{ej}}$ calculation takes the
gravitational influence of Dimorphos into account, however, it does not
account for the gravitational influence of Didymos. The second method,
described in [34], tracks the velocity magnitude of the asteroid centre of
mass post-impact by summing the momentum of all material that remains below
the escape velocity after the reaccumulation of the ejecta. The absolute
difference in $\beta$ resulting from the two calculation methods is used in
the error calculation of our reported $\beta$ values.

## Results

First, we vary the boulder volume fraction (i.e., the volume fraction of
objects $>$2.5 m in size) within the target between 0 and 50 vol%, while
keeping the asteroid volume constant (Table 1). As a result, the mass and the
bulk density of the asteroid vary with boulder packing. Our simulations show
that $\beta$ is relatively insensitive to the boulder volume fractions up to
$\approx$ 30 vol% (Fig. 1a). For boulder volume fractions larger than about 30
vol%, the number of boulders much larger than the projectile close to the
impact point is high enough that the crater efficiency and, subsequently,
$\beta$ is drastically reduced by boulder interlocking [35] and possibly
armouring [36], which hinders the crater growth. These results indicate that
at least the surface and shallow subsurface of Dimorphos have a low volume
fraction of boulders larger than 2.5 m (less than $\approx$ 40 vol%), which is
consistent with the last few images sent by DART before impact [1].

Our simulation results for the DART impact on a cohesionless surface of
Dimorphos also provide a means to constrain the bulk density of the asteroid
using the measured $\beta$ (Fig. 1b), assuming a grain density in the range of
3200–3500 kg/m3. For a body with a fixed volume and grain density (Table 1),
the bulk density is influenced by its porosity. The dominant effect of
additional target porosity is a reduction in bulk density of the target,
rather than a reduction in ejecta from compaction of pore space. For example,
decreasing the bulk density of Dimorphos will increase the overall crater size
and decrease the asteroid’s mass (for a fixed volume) and escape velocity.
This allows for a greater total volume of ejecta to escape, but the ejecta
mass is similar. Increasing the bulk density has the opposite effect. The
consequence is that the total momentum of escaping ejecta measured constrains
the target bulk density and porosity: for a cohesionless surface of Dimorphos,
the upper bound on $\beta$ ($\approx$ 3.6) implies that the bulk density of
Dimorphos is less than the current best estimate of the asteroid’s bulk
density of 2400 kg/m3 [1]. Thus, Dimorphos is likely more porous and therefore
may have a rubble-pile structure throughout the whole body.

Since the surface strength of Dimorphos is poorly constrained, for a fixed
boulder distribution (30 vol%), matrix porosity ($\phi_{0}$ = 45%) and grain
density ($\rho_{g}$ = 3200 and 3500 kg/m3) we vary the matrix material
cohesion ($Y_{0}$ = 0–50 Pa) and coefficient of internal friction ($f$ =
0.4–0.7) (See Table 1; Methods). Multiple possible combinations of cohesion,
coefficient of internal friction, and bulk density could result in the
observed deflection and account for the observed momentum enhancement (Fig.
1c, d). Despite this non-uniqueness, it is possible to bound the range of
plausible values by making reasonable assumptions since $f$ = 0.4 is a lower
limit for geological materials. For a target with $f$ = 0.4 and $\phi_{0}$ =
45% the cohesion on the surface of Dimorphos is likely lower than $\approx$ 50
Pa (Fig. 1c, d). However, lower bulk densities ($\rho_{B}<2000$ kg/m3) or
higher matrix porosities ($\phi_{0}>55\%$) would require higher cohesion to
match the observations (Fig. 1).

## Ejecta curtain opening angle and morphology

In our simulations of the DART impact into Dimorphos-like rubble pile targets,
we observe the temporal changes of the ejecta cone opening angle and study
dependences on target properties. We find no significant dependences of ejecta
cone opening angle on the friction coefficient of the targets. This finding
contrasts with the strong dependence of the cone opening angle on the
coefficient of internal friction that is found in simulations [37] of the DART
impact into homogeneous planar targets. Our present simulations of impacts
into Dimorphos-like rubble piles find that the ejecta cone opening angle and
ejecta mass depend on target cohesion. In Figures 2 and 3 results for
cohesionless targets ($Y_{0}$ = 0 Pa) are compared with those for cohesive
targets ($Y_{0}$ = 500 Pa).

The ejecta plume for the cohesionless target (Fig. 2c, g) is more massive than
for the cohesive target (Fig. 2d, h). For both cases, the fastest ejecta,
released shortly after the impact with velocities higher than a few tens of
m/s, form a cone opening angle $\omega\approx$ 90∘ (Fig. 3a, b). Such fast
ejecta are influenced by the spacecraft geometry (e.g., [38, 39]), which is
highly simplified in this study. On the other hand, slower ejecta, released at
late times after the impact (hundreds to thousands of seconds) with velocities
$v_{esc}<v<$ 5 m/s, form a wider ejecta cone angle of $\approx$ 140∘ (at 1
m/s, Fig. 3a) for the cohesionless target. For the cohesive target ($Y_{0}$ =
500 Pa), crater growth ceases about 100 seconds after the impact, before the
crater grows large enough for the ejection angle to be influenced by target
curvature. In this case, the maximum ejecta opening angle is $\approx$ 120∘
(at 1 m/s, Fig. 3b). On the other hand, for the low cohesion target cases, the
mass ejected at low velocities ($v_{esc}<v<$ 10 m/s) greatly exceeds the low
velocity ejecta mass from the cohesive target case ($Y_{0}$ = 500 Pa),
implying a larger cratering efficiency and crater growth continuing to later
times, and resulting in a wider cone opening angle influenced by target
curvature.

The characteristics of the ejecta plume observed by LICIACube provide
constraints regarding the target cohesion. At time after impact $T$ = 160 s,
LICIACube’s LUKE acquired images that showed ejecta concentrated into rays
which cast shadows along the ejecta cone (Fig. 2a, b). At $T$ = 178 s, the
bottom of the ejecta cone and the surface of Dimorphos are obscured by the
shadow cast by the ejecta (Fig. 2e,f). The shadow observed at $T$ = 178 s
implies that crater growth and release of low speed ejecta continued to that
time, consistent only with low cohesion target cases [[, e.g.,]]Holsapple2007.

Images obtained from LICIACube [4] and Hubble Space Telescope observations [5]
revealed a wide ejecta cone angle, estimated to be $\omega\approx$ 115–139∘.
These observations determined the ejecta opening angle at specific times, up
to 3 minutes after the impact for LICIACube [4] and up to 8 hr after the
impact for Hubble [5]. To compare simulations results with observations of the
ejecta opening angle at a specific time after impact, we determine the implied
ejecta velocity at the base of the visible cone in the LICIACube images ([4];
Fig. 2e, f) using its distance above the surface and time after impact (Fig.
3).

Overall, we find that to qualitatively reproduce the amount of material
observed in the ejecta cone (Fig. 2c, g), as well as the observed cone opening
angle of up to $\omega\approx$ 139∘, Dimorphos’ surface cohesion must not
exceed $\approx$ 500 Pa. From our suite of numerical simulations with the
assumed boulder packing, matrix porosity, and grain density summarised in
Table 1, we find the target case with $f$ = 0.55, $\rho_{B}$ = 2200 kg/m3, and
$Y_{0}$ less than a few Pa is consistent with target mechanical properties
inferred from surface geology [41] and produces a $\beta$-value (Fig. 1),
excavation timescale (Fig. 2) and ejecta opening angle (Fig. 3) most
consistent with observations.

## Deformation

Observations from the first few hours after impact imply that more than
1.3–2.2 $\times$ 107 kg of ejecta were released from the DART impact
(equivalent to 0.3–0.5% of Dimorphos’s mass, assuming a bulk density of 2400
kg/m3) [6]. Our simulation results for weak ($Y_{0}<$ 50 Pa), Dimorphos-like
targets ($f=0.55$ in Fig. 1c) show that the amount of ejected material could
be as high as 1% of Dimorphos’ mass (Fig. 4a). At the same time, up to 8% of
Dimorphos’ mass may have been displaced or ejected below the escape velocity
of Dimorphos. In all impact scenarios simulated here, the DART impact does not
produce a conventional impact crater and instead causes global deformation of
the target (Fig.4b).

The outcome of the impact in terms of the post-impact target morphology is
highly sensitive to the target cohesion. For a cohesionless target, the ratio
of the major to intermediate axes, $a/b$, could have changed from the reported
pre-impact value of 1.02 $\pm$ 0.02 [1] to as much as 1.2. Such a large change
in the $a/b$ ratio is detectable with the highest-quality post-impact
lightcurve data [42, 13].

Global deformation of Dimorphos modifies the gravitational field between
Didymos and Dimorphos and leads to significant implications for its orbit. The
shape change would cause an additional perturbation to Dimorphos’s orbit, on
top of those caused by the spacecraft momentum and ejecta recoil, and this
effect can account for a few seconds to several minutes of the observed orbit
period change (i.e., $\sim$ 33 minutes), depending on the magnitude of the
deformation [43]. Any deformation would alter Dimorphos’s mass distribution
and affect its post-impact rotation state (e.g., [44, 45]).

## Implications for binary asteroid system formation

Our numerical simulations suggest that Dimorphos is likely a rubble-pile
asteroid with a bulk density comparable to or lower than that of Didymos. Our
calculations based on the observed boulder SFD indicate that the macroporosity
estimate for the surface of Dimorphos ($\approx$ 35%) is approximately twice
the value obtained for the surface of Ryugu, as determined through the same
method [24, 46], but comparable with the macroporosity on Itokawa [47, 24].
However, it is worth noting that this estimate is only a rough approximation
due to the limited data currently available and the upcoming Hera mission will
be able to provide better constrains.

Our findings serve as crucial evidence regarding the origin of Dimorphos as a
secondary in a double asteroid system. To maintain its structural stability
given its rapid rotation period of 2.26 hours, the primary, Didymos, likely
requires a higher cohesive strength, estimated to be on the order of 10s Pa
[48]. This level of cohesion can be attributed to van der Waals forces acting
between the fine regolith grains [49], or to a coherent inner core [50].
However, our best-fit scenarios indicate that Dimorphos, the satellite of
Didymos, exhibits a cohesive strength of less than a few Pa. This observed
disparity in cohesive strength between Didymos and Dimorphos suggests a
potential scarcity of fine grains within Dimorphos’ structure as well as a
weak and fragmented internal structure.

The material properties estimated in our study support the hypothesis that
Dimorphos formed through rotationally or impact-induced mass shedding and
subsequent re-accumulation from Didymos. The accretion of orbiting mass shed
from Didymos occurs over a period of several days to years [51], during which
fine grains tend to escape from the system due to solar radiation pressure
[52]. As a result, the accreted satellite, Dimorphos, has limited fines and
cohesion.

While the mechanical properties of Dimorphos resemble those of Ryugu and Bennu
(e.g., [53, 17, 54, 55]), these findings may not be applicable to single small
S-type asteroids, specifically to their moons. The implications of our study
may extend beyond Dimorphos and provide valuable insights into the formation
processes of similar small S-type binary asteroid systems.

Moreover, since the DART spacecraft likely caused global deformation of
Dimorphos, we can infer that similarly formed asteroid moons are easily
reshaped and their surfaces are relatively young [16]. Overall, the findings
of this study provide valuable information for understanding the formation and
characteristics of binary asteroids, and will inform future exploration and
asteroid deflection efforts.

## Data Availability

Additional supporting information and input data for the model simulations
used in this work is archived on GitHub (doi:10.5281/zenodo.10246671).

## Code availability

A compiled version of the Bern SPH code, as well as the necessary input files
are available from the corresponding author upon request. SPH data
visualisation was produced using the NCAR Visualization and Analysis Platform
for Ocean, Atmosphere, and Solar Researchers (VAPOR version 3.8.0) [Software]
(doi:10.5281/zenodo.7779648).

## Acknowledgments

We thank Jessica Sunshine, Mallory DeCoster, Dawn Graninger, Jason Pearl,
Angela Stickle and the rest of the DART Impact Working Group for the
constructive discussions.

SDR and MJ acknowledge support by the Swiss National Science Foundation
(project number 200021_207359). This work was supported by the DART mission,
NASA Contract No. 80MSFC20D0004. GSC and TMD acknowledge support from UK
Science and Technology Facilities Council Grant ST/S000615/1. FF acknowledges
funding from the Swiss National Science Foundation (SNSF) Ambizione grant No.
193346. KMK, MBS, JMO Portions of this work were performed by Lawrence
Livermore National Laboratory under DOE Contract DE-AC52-07NA27344. LLNL-
JRNL-846795, PM acknowledges financial support from the CNRS through the MITI
interdisciplinary programs through its exploratory research program an, from
ESA and from the University of Tokyo. PM, RL, KW, NM and CQR acknowledge the
support from the European Union’s Horizon 2020 research and innovation
program, grant agreement No. 870377 (project NEO-MAPP). NM, CQR and PM
acknowledge funding support from the Centre National d’Etudes Spatiales
(CNES). RN acknowledges support from NASA/FINESST
(NNH20ZDA001N/80NSSC21K1527). ED, EME, PHH, SI, AL, MP, AR and FT acknowledge
financial support from Agenzia Spaziale Italiana (ASI, contract No.
2019-31-HH.0). MP, AL and FT also acknowledge support from ASI, contract No.
2022-8-HH.0. Work by EGF was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration ($\\#$80NM0018D0004). JO acknowledge
support by grant PID2021-125883NB-C22 by the Spanish Ministry of Science and
Innovation/State Agency of Research MCIN/AEI/ 10.13039/501100011033 and by
‘ERDF A way of making Europe’. JO, IH, SR, MJ, RL, KW acknowledge support by
Consejo Superior de Investigaciones Científicas (CSIC) (project ILINK22061).
The work by PP was supported by the Grant Agency of the Czech Republic, grant
20-04431S.

## Author contributions

SDR, MJ, AFC conceptualised the study. SDR ran the simulations and analysed
the data. SDR, MJ, AFC, OB, GSC wrote the initial draft. YZ provided rubble-
pile models. RTD, CME, OB provided the shape model of Dimorphos. TLF provided
the viewing geometry for comparison to LICIACube data. MH, JYL, PHH provided
measurements of the ejecta. YZ, FF, HFA helped with the interpretation of
results. RN helped with the deformation affects on dynamics. MP, AL, FT
provided boulder SFDs. CQR, NM provided the boulder shapes. AFC, HFA, BWB
provided momentum enhancement measurements. AR, ED, PHH provided LICIACube
measurements. PP provided observational inputs. PS helped with the
interpretation of cohesion. TMD, KMK, PM, MBS, NLC, ED, EGF, IH, SI, RL, JO,
MO, ASR, KW, AZ, EME provided comments that substantively revised the
manuscript. CM, BHM provided the stereographs of the Didymos system.

## Competing interests

The authors declare no competing interests

## Tables

Table 1: Table of fixed and varied target parameters. Fixed parameters |
---|---
Target dimensions [1] | 177 $\times$ 174 $\times$ 116 m
Target volume [1] | 0.00181 km3
Boulders SFD [19] | see Methods
Boulders at impact location [1] | see Methods
Boulder tensile strength | 10 MPa
Boulder porosity | 10%
Varied parameters |
Boulder packing | 0 – 50 vol%
Grain density, $\rho_{g}$ | 3200/3500 kg/m3
Matrix porosity, $\phi_{0}$ | 35 – 65%
Matrix cohesion, $Y_{0}$ | 0 – 500 Pa
Matrix internal friction coeff., $f$ | 0.4 – 0.7

## Figure Legends/Captions

Figure 1: Momentum enhancement, $\beta$, as derived from SPH simulations. The
continuous black lines show the $\beta$ dependence on Dimorphos’ bulk density,
$\rho_{B}$, derived from dynamical simulations [7] (1-$\sigma$ uncertainty is
shown by the dashed lines). Data points that cross the solid black line are
consistent with the measured $\beta$ from the DART impact. The uncertainty on
each simulation data (vertical bars) is calculated from the absolute
difference in $\beta$ calculated from two different methods (see Momentum
enhancement calculations; Methods). (a) $\beta$ as a function of $\rho_{B}$,
for cohesionless targets with the same dimensions as Dimorphos [1] and with
boulder volume fractions ranging from 0 vol% (no boulders larger than 2.5 m)
to 50 vol%. For fixed target volume (0.00181 km3) and fixed matrix porosity
($\phi_{0}=45\%$), the mass and bulk density of Dimorphos vary with boulder
packing. (b) $\beta$ as a function of $\rho_{B}$ for cohesionless targets with
varying matrix porosity, between 35 and 65% and two boulder packings: 21 and
30 vol%. $\rho_{B}$ is calculated for a fixed asteroid volume and it varies
with matrix porosity and boulder packing. (c) $\beta$ as a function of matrix
cohesion ($Y_{0}$) for the DART impact into targets with varying coefficient
of internal friction ($f$ = 0.4–0.55), an assumed grain density, $\rho_{g}$ =
3200 kg/m3 and a 30 vol% boulder packing. The horizontal line shows the
$\beta$ derived from dynamical simulations for a target with $\rho_{B}$ = 2160
kg/m3 (minimum density consistent with 1a and 1b results). (d) $\beta$ as a
function of $Y_{0}$ for the DART impact into targets with $f$ = 0.4–0.70,
$\rho_{g}$ = 3500 kg/m3 and 30 vol% boulder packing. The horizontal line shows
the $\beta$ derived from dynamical simulations for a target with $\rho_{B}$ =
2360 kg/m3 (maximum density consistent with 1a and 1b results). Figure 2:
LICIACube images of the expanding ejecta cone adapted from [4] compared with
SPH simulation results. (a) Image acquired by the LUKE instrument onboard
LICIACube at a distance of $\approx$ 76 km, 160 seconds after the impact. (b)
Zoomed-in image of Dimorphos and impact ejecta. The approximate outline of the
asteroid is shown in yellow. The ejecta curtain exhibits undulations,
filamentary patterns, and shadows. (c) Bern SPH simulation of the DART impact
into a cohesionless, rubble-pile Dimorphos-sized target (with $f$ = 0.55 and
$\phi_{0}$ = 45%), at $T$ = 160 s. Due to the limited visualisation domain,
only a portion of the ejecta are shown. (d) Simulation of the impact into a
rubble-pile Dimorphos-sized target with $Y_{0}$ = 500 Pa ($\beta$ =
2.26$\pm$0.28). (e) Image acquired by LUKE at a distance of $\approx$ 71 km,
178 seconds after the impact. (f) Zoomed-in image of Dimorphos and impact
ejecta. (g) Same as (c) but at $T$ = 178 s. (h) Same as (d) but at $T$ = 178
s. The optical depth of the ejecta cone is not computed for this comparison
between the observations and simulations output. Figure 3: Ejecta cone opening
angle. (a) Cone opening angle derived from cohesionless ($Y_{0}$ = 0 Pa) SPH
simulations (shown in Fig. 2c and g) in the N-S direction ($x=0$ plane) and in
the E-W direction ($z$ = 0 plane). (b) Cone opening angle derived from SPH
simulations with $Y_{0}$ = 500 Pa in the N-S direction ($x=0$ plane) and in
the E-W direction ($z$ = 0 plane). In both (a) and (b) the cone opening angle
derived from observations is plotted for comparison: $\omega$ = 135 $\pm$ 4∘
is measured from LICIACube data based on the opening angle at the base of the
cone at $T$ $\approx$ 170 s, resulting in ejecta velocities in the range of a
few cm/s – a few tens cm/s [4] and $\omega$ = 125 $\pm$ 10∘ is measured in the
Hubble Space Telescope (HST) data for ejecta in the range of 1–10 m/s [5].
Temporal evolution measurements of the observed ejecta cone is not possible
due to the limited observation window. Figure 4: Global deformation of
Dimorphos. (a) Total target mass ejected with speeds above $v_{esc}$ and total
target mass displaced or ejected below $v_{esc}$, normalised by the initial
target mass, $M_{T}$, for a Dimorphos-like target with $f$ = 0.55, $\phi_{0}$
= 45% and cohesion levels between $Y_{0}$ 0 and 50 Pa. (b) Two-dimensional
slices (taken at $x$ = 0 in the $y-z$ plane and at $z$ = 0 in the $x-y$
plane), at $T\approx$ 1 hour after the impact. The boulder material is shown
in yellow and the matrix material is shown in blue. The red contour shows the
initial target profile, before the impact. The black arrows show the impact
direction.

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