Slide 17
Slide 17 text
ratio of 9:1 and a total mass of 1.05 ME
(Canup, 2004). Both the impactor and the
target are assumed to be differentiated bodies with a 30 wt% iron core and a
70 wt% silicate mantle. In these low-velocity collisions, the impactor loses kinetic
energy during its grazing collision with the target, before it is dispersed into a disk
around the target. The resulting proto-lunar disk is therefore mainly composed of
impactor material. We will call this the ‘‘canonical scenario’’.
When the assumption that no mass is lost is dropped however, the collisional
angular momentum is no longer tightly constrained, as lost mass also carries away
angular momentum. The total collisional angular momentum can therefore be con-
siderably higher than the final angular momentum in the Earth–Moon system. With
this additional degree of freedom, new regions in the collision parameter space be-
come feasible.
Apart from the disk mass, another interesting quantity is the origin of the mate-
rial which ends up in the proto-lunar disk, especially for the silicate part.
We call the fraction of target silicate to total silicate material in the disk
fT ¼ ðMsilc
targ
=Msilc
tot
Þdisk
ð1Þ
where Msilc
targ
and Msilc
tot
denote the mass of the silicate fraction of the disk derived from
the target, and the total disk mass, respectively. If we define a similar target-derived
silicate fraction for the post-impact Earth, we can deduce a deviation factor
dfT ¼ Msilc
targ
.
Msilc
tot
disk
.
Msilc
targ
.
Msilc
tot
post-impact Earth
À 1 ð2Þ
which directly reflects the compositional similarity between the silicate part of the
proto-lunar disk and the silicate part of the post-impact Earth.
Isotopic measurements show (Wiechert et al., 2001; Zhang et al., 2012) a strong
isotopic similarity between the silicate fractions of today’s Moon and Earth. Assum-
ing isotopic heterogeneity of the pre-impact bodies, this suggests that either the
material of the bodies mixed during the collision or re-equilibrated their isotopic
signatures after the collision. Either scenario is represented by a dfT $ 0 between to-
day’s Earth and the Moon. The value of dfT
right after the impact thus serves as a
starting point, from which a re-equilibration mechanism leads to todays value of
dfT $ 0.
In a typical simulation of the canonical scenario, only about 30% of the disk
material and 90% of the material of the post-impact Earth is derived from the target
(the proto-Earth) respectively (Canup, 2004), yielding a dfT
of À67%.
4. Results
The new class of collisions presented here falls into the broad regime of slow
hit-and-run collisions (Asphaug et al., 2006) with impact velocities between 1.20
and 1.40 vesc
. Hit-and-run occurs up to half the time for collisions with impact
colors. In the canonical scenario, the impactor grazes around the target’s mantle
and is deformed. Due to the low impact velocity, material supposed to end up in or
bit around the Earth must not be decelerated too strongly in order to retain enough
velocity to stay in orbit. This is only achieved for the parts of the impactor mantle
most distant to the point of impact, and some minor part of the target’s mantle. Bu
if impact velocity is increased from 1.00 (cA08) to 1.30 vesc
(cC01), parts from dee-
per within the target mantle receive the right amount of energy for orbit insertion
while the outer regions of the target mantle, retain too much velocity and leave the
system, thereby removing mass and angular momentum. Both processes work to
wards increasing the target material fraction in the proto-lunar disk. While in run
Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc
impact velocity case
(cC06) showing cuts through the impact plane. Color coded is the type and origin o
the material. Dark and light blue indicate target and impactor iron; Red and orange
show corresponding silicate material. The far right shows the situation at the time
of impact. At 0.52 h, it can be seen how the impactor ploughs deep through the
targets mantle and pushes considerable amount of target material into orbit. A
spiral arm of material forms and gravitationally collapses into fragments. The oute
portions of the arm mainly consist of impactor silicates and escapes due to having
retained a velocity well above escape velocity. The silicate fragments further inward
are stronger decelerated and enter eccentric orbits around the target. The
impactor’s iron core also looses much of its angular momentum to the outer parts
of the spiral arm and re-impacts the proto-Earth. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version o
this article.)
A. Reufer et al. / Icarus 221 (2012) 296–299 297
༷ʑͳ݄ܗγφϦΦ
[Reufer et al., Icarus, 2012]
with less angular momentum.
angular momentum by add-
pactors generated successful
wer-spinning planets. Because
m is carried away with debris
giant impacts, the spin period
ases. Thus, the spin state of
d to be near fission before or
ming impact in our scenario
entry in Table 1). However,
is near the stability limit.
Our candidate Moon-forming events have
more than double the kinetic energy of previous
scenarios, and the impact velocities were suf-
ficient to substantially vaporize silicates (33). As
a result, the silicate atmosphere and vapor-rich
disk are more massive and hotter than found
in previous work (34). At the resolution of the
simulations, the projectile-to-target mass ratio is
uniform from the atmosphere to the Roche radius.
f the
rth’s
mpact
or at
−0.3
spin-
f 2.3
Gray
oche
w of
ower
down
spin
enote
and
Earth
e disk
terial
arth’s
mpact
e S1).
view
de-
lue),
and
ensity
ne of
which
38 SCIENCE www.sciencemag.org
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Ć
uk & Stewart, Science, 2012]
into a single moon at an orbital distance of about
3.8R⊕
, where R⊕
is Earth’s radius (19, 20),
MM
MD
≈ 1:9
LD
MD
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2:9GM⊕R⊕
p
−
1:1 − 1:9
Mesc
MD
ð1Þ
where Mesc
is the mass that escapes from the
disk as the Moon accretes. To estimate MM
, we
used Eq. 1 and made the favorable assumption
that Mesc
= 0.
We tracked the origin (impactor versus tar-
get) of the particles in the final planet and the
disk. To quantify the compositional difference be-
tween the silicate portions of the disk and planet,
we define a deviation percentage
dfT
≡ [FD,tar
/FP,tar
− 1] × 100 (2)
where FD,tar
and FP,tar
are the mass fractions of
the silicate portions of the disk and of the planet
derived from the target’s mantle, respectively (21).
Identical disk-planet compositions have dfT
= 0,
whereas a disk that contains fractionally more
impactor-derived silicate than the final planet has
dfT
< 0, and a disk that contains fractionally less
impactor-derived silicate than the final planet has
dfT
> 0.
Prior impact simulations (1–3, 14, 15) that
consider g ≡ Mimp
/MT
≈ 0.1 to 0.2 produce disks
with −90% ≤ dfT
≤ −35% for cases with MM
>
ML
, where ML
is the Moon’s mass. Results with
larger impactors having g = 0.3, 0.4, and 0.45
are shown in Figs. 1 and 2 and Table 1. As the
relative size of the impactor (g) is increased, there
is generally a closer compositional match be-
tween the final disk and the planet. For g ≥ 0.4,
some disks have both sufficient mass and an-
gular momentum to yield the Moon and nearly
identical silicate compositions to that of the final
Fig. 1. An SPH simulation
of a moderately oblique,
low-velocity (v∞
= 4 km
s–1) collision between an
impactor and target with
similar masses (Table 1,
run 31). Color scales with
particle temperature in
kelvin, per color bar, with
red indicating tempera-
tures >6440 K. All particles
in the three-dimensional
simulation are overplotted.
Time is shown in hours,
and distances are shown
in units of 103 km. After
the initial impact, the plan-
ets recollided, merged,
and spun rapidly. Their
iron cores migrated to the
center, while the merged
structure developed a bar-
type mode and spiral arms
(24). The arms wrapped
up and finally dispersed
to form a disk containing
~3 lunar masses, whose
silicate composition dif-
fered from that of the
final planet by less than
1%. Because of the near
symmetry of the colli-
sion, impactor and target
material are distributed
approximately proportion-
ately throughout the final
disk, so that the disk’s dfT
value does not vary ap-
preciably with distance
from the planet.
Fig. 2. Compositional differ-
ence between the disk and final
planet (dfT
) (Eq. 2) produced by
simulations with (A) g = 0.3
and (B) g = 0.4 (triangles) and
0.45 (squares) versus the pre-
dicted mass of the moon that
would accrete from each disk
(MM
) (Eq. 1) scaled to the final
planet’s mass (MP
). There is a
change in y axis scales between
the two plots. Gray, purple, dark
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