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Delivery of Water and Volatiles to the Terrestrial Planets and the Moon

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  • Vernadsky Institute of Chemistry and Analytical Chemistry of Russian Academy of Sciences

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From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter’s orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth’s embryo, when its mass was smaller than the current mass of the Earth. While the Earth’s embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiter’s orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two−three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter’s orbit could be less than that for the Earth by a factor not more than 20.
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ISSN 0038-0946, Solar System Research, 2018, Vol. 52, No. 5, pp. 392–400. © Pleiades Publishing, Inc., 2018.
Original Russian Text © M.Ya. Marov, S.I. Ipatov, 2018, published in Astronomicheskii Vestnik, 2018, Vol. 52, No. 5, pp. 402–410.
Delivery of Water and Volatiles to the Terrestrial Planets
and the Moon1
M. Ya. Marova, * and S. I. Ipatova, **
aVernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow, 119991 Russia
*e-mail: marovmail@yandex.ru
**e-mail: siipatov@hotmail.com
Received April 1, 2018
AbstractFrom modeling the evolution of disks of planetesimals under the influence of planets, it has been
shown that the mass of water delivered to the Earth from beyond Jupiter’s orbit could be comparable to the
mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth’s
embryo, when its mass was smaller than the current mass of the Earth. While the Earth’s embryo mass was
growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30%
of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the
terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios.
The mass of water delivered to Venus from beyond Jupiter’s orbit was almost the same as that for the Earth,
if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was
two−three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter’s
orbit could be less than that for the Earth by a factor not more than 20.
Keywords: planetesimals, delivery of water and volatiles, terrestrial planets, Earth, Moon
DOI: 10.1134/S0038094618050052
INTRODUCTION
The problem of the delivery of water and volatiles
to the terrestrial planets is important for studying the
origin and evolution of life in the Solar System and
extrasolar systems (Marov et al., 2008; Marov, 2017).
Liquid water is required for life to appear on planets.
This problem is fundamental, since the Earth and ter-
restrial planets were formed in a high-temperature
(~1000 K) zone of the protoplanetary disk, where
water and volatiles are not retained, but accumulated
beyond “the snow line” at a distance of R > 3.5 AU.
Endogenous and exogenous sources of water, as
the main potential mechanisms forming terrestrial
oceans, are considered in laboratory examinations of
the materials and in computer simulations. In the lab-
oratory, the terrestrial rocks are analyzed, while com-
puter modeling is focused on the studies of a complex
of the dynamical processes that occurred over the
whole history of the Solar System. Both mechanisms
have corresponding limitations, and we cannot
exclude their mutual contribution to the solution of
this problem.
The endogenous sources of water could include
direct absorption of hydrogen from the nebula gas into
the magmatic melts and a subsequent reaction of H2
with FeO, which could increase the D/H ratio in the
terrestrial oceans by a factor of 2−9 (Genda and
Icoma, 2008), and accumulation of water by particles
of the protoplanetary disk before gas began to dissipate
in the inner part of the early Solar System (Drake and
Campins, 2006; Muralidharan et al., 2008). The idea
of a large amount of water in the mantle is confirmed
by several studies; among them are the laboratory
analysis of olivine in Archaean komatiite−basalt asso-
ciations (ultramafic lavas in green belts of the Earth)
produced in melting under extremal conditions at the
boundary of the upper mantle of the Earth (Sobolev et
al., 2016). The results of the study suggest that the
mantle melts under a temperature of 1630 K and a
fractional water content of ~0.5%, which corresponds
to several terrestrial oceans, if extrapolated to the
whole volume. The volume of water in minerals of the
silicate Earth is estimated at 5−6 (to 50) volumes of
the terrestrial oceans (Drake and Campins, 2006). A
considerable amount of endogenous water may be
contained in Mars and Venus. A limitation of the
model is the formation of the Earth with temperatures
higher than 500 K, which means that water and vola-
tiles are not retained on the surface. Hallis et al. (2015)
noted that the deep-mantle water has a small D/H
ratio and could be acquired due to the water absorp-
tion by fractal particles during the accretion of the
1Reported at the Sixth International Bredikhin Conference (Sep-
tember 4–8, 2017, Zavolzhsk, Russia).
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
DELIVERY OF WATER AND VOLATILES TO THE TERRESTRIAL PLANETS 393
Earth. The water in oceans and its D/H ratio could
have resulted from mixing the water from several
sources with higher and lower D/H ratios.
The exogenous sources could originate from the
migration of bodies from the outer part of the Main
asteroid belt (OBrien et al., 2014; Morbidelli et al.,
2000, 2012; Petit et al., 2001; Raymond et al., 2004;
Lunine et al., 2003, 2007) and migration of planetesi-
mals from beyond Jupiter’s orbit (Morbidelli et al.,
2000; Levison et al., 2001; Marov and Ipatov, 2001;
2005; Ipatov and Mather, 2004, 2006, 2007; Ipatov,
2010). For the Grand Tack model, Rubie et al. (2015)
considered the migration of planetesimals from a zone
of 6−9.5 AU. In these scenarios, the authors estimated
the probability of collisions of bodies with the Earth
and other terrestrial planets and the mass of delivered
water/volatiles. According to Drake and Campins
(2006), a contribution of the bodies from beyond Jupi-
ter’s orbit to the water delivered to the Earth did not
exceed ~50%.
Some authors believe that a substantial fraction of
the water that came to the Earth from the outer aster-
oid belt. For example, Petit et al. (2001) thought that
several embryos, which arrived from the outer asteroid
belt at the end of Earth’s formation, could deliver such
amount of water to the Earth that is 10 times larger
than the current amount of water on the Earth.
O’Brien et al. (2014) supposed that water from the
outer asteroid belt was mainly delivered by embryos as
large as Mars. Drake and Campins (2006) noted that a
key argument against the asteroid source of water, as
the main source of water for the Earth, is that the iso-
topic composition of osmium (Os) of Earths primitive
upper mantle matches that of anhydrous ordinary
chondrites, not hydrous carbonaceous chondrites.
The model for the abundance of water and volatiles
on the Earth (including the oceans and the atmo-
sphere), which is based on migration of bodies from
the outer Solar System, makes it possible to avoid the
difficulties connected with the formation of terrestrial
planets in a high-temperature zone of the protosolar
disk. The model is limited by the difference between
the D/H ratio for comets (excluding several comets,
e.g., comet 103P/Hartley 2) and the standard value
D/H = 1.5576 × 10−4 for the terrestrial oceans (the
Vienna Standard Mean Ocean Water (SMOW)). This
limitation can be removed by the assumption that the
main water source on the Earth was CI- and CM-
chondrites rather than comets. Since, according to the
investigations of lavas (Hallis et al., 2015), the deep-
mantle water is likely to have a lower D/H ratio, it can
be supposed that the present SMOW ratio is a result of
some contribution of endogenous sources.
Pavlov et al. (1999) explained the deuterium-to-tri-
tium paradox of the terrestrial oceans by the fact that
the solar-wind-implanted hydrogen on dust particles
provided the terrestrial oceans with a required fraction
of water with a low D/H ratio. Delsemme (1999)
believed that a large portion of ocean water was deli-
vered by comets originated from Jupiter’s zone, where
vapor from the inner Solar System had condensed on
interstellar ice grains before they accreted into large
bodies. Drake and Campins (2006) suppose that the
D/H and Ar/O ratios measured in cometary comas
and tails do not adequately represent cometary interi-
ors. Yang et al. (2013) showed that the D/H ratio for
water is different for the bodies formed at different dis-
tances from the Sun. It was low for a hot inner disk,
and then it increased with distance from the Sun and
decreased again. Raymond and Izidoro (2017) think
that C-type asteroids were formed at a distance of
5−20 AU from the Sun and passed to the current orbits
when gas was still present in this zone. The character-
istic time for the gas presence is estimated at 3−5 Myr
(Zheng et al., 2017). As previously mentioned, some
scientists believe that the supposition of the outer
asteroid belt as the main source of water on the Earth
explains the D/H ratio in the terrestrial oceans. How-
ever, if C-type asteroids came from the feeding zones
of giants, as Raymond and Izidoro (2017) think, the
water in the bodies, which arrived directly to the Earth
from these zones, could also have the same D/H ratio
as that in C-type asteroids and terrestrial oceans.
Our earlier studies of the delivery of water and vol-
atiles to the terrestrial planets (e.g., Marov and Ipatov,
2001, 2005; Ipatov, 2010; Ipatov and Mather, 2004,
2006, 2007) were based on the results of numerical
simulations of the migration of many thousands of
small bodies and dust grains originating from such bod-
ies; we considered the gravity effect of all of the planets
for the case where the initial orbits of the bodies are close
to the orbits of known comets and the masses and orbits
of the planets take the current values.
The present analysis of the delivery of water and
volatiles to the terrestrial planets from a zone beyond
Jupiter’s orbit is based on the results of our new calcu-
lations of the migration of planetesimals in the devel-
oping Solar System, and these simulations take into
account the delivery of water to the growing terrestrial
planets. They were also made for the embryos of the
terrestrial planets rather than only for the planets
themselves.
INITIAL DATA AND ALGORITHMS
TO MODEL THE MIGRATION
OF SMALL BODIES
In our calculations, we modeled the migration of
planetesimals under the gravity of planets. The current
orbits and masses of the terrestrial planets, Jupiter, and
Saturn were considered in the JS series of calculations.
In the JS01 series, the masses of terrestrial planets were
10 times smaller than their current values (in some
cosmogonic models, it is assumed that Jupiter and
Saturn were almost completely formed when the
masses of terrestrial planets were far from their current
394
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
MAROV, IPATOV
values). In the JN and JN01 series, Uranus and Nep-
tune on their current orbits were additionally consid-
ered.
In four calculation series, JS, JS01, JN, and JN01,
the semimajor axes a of initial orbits of planetesimals
were varied from amin = 4.5 to amax = 12 AU; and the
number of planetesimals with a semimajor axis close
to a was proportional to a1/2. The eccentricities and
inclinations of initial orbits of planetesimals were 0.3
and 0.15 rad, respectively. As Ipatov (1993, 2000)
noted, such eccentricities and inclinations could be
reached due to the gravitational influence of planetes-
imals and planets. Two hundred and fifty planetesi-
mals were usually considered in one calculation run,
and the total number N of planetesimals in a calcula-
tion series was 2000–2500.
We also considered the evolution of disks of plane-
tesimals in the case where the giant planets (with their
current masses) were located more closely to each
other than at present (the maximum values of the
semimajor axes of planetary orbits were varied from 15
to 20 AU) and amax did not exceed 23 AU. Specifically,
in the JN15 calculation series, the semimajor axes of
initial orbits of the giants (with their current masses)
were 5.45, 8.5, 12, and 15 AU, respectively, while the
semimajor axes of the initial orbits of planetesimals
were between 4.5 and 20 AU. Some runs (with 250
planetesimals) of these series of calculations (with
closer orbits of giants, particularly, in the JN15 calcula-
tion series) resulted in ejection of at least one of the
giant planets (but not Jupiter) to a hyperbolic orbit in
th e co urs e of evolution . Note that from ob ser vation s of
the microlensing events (Clanton and Gaudi, 2017), it
is supposed that, on average, at least one free-floating
exoplanet corresponds to one star.
To integrate the equations of motion, we used the
symplectic method from the Swift package (Levison
and Duncan, 1994). The gravitational influence of
planets was taken into account. In different runs of
calculations, the integration step was varied from 10 to
30 days and was constant in each of the runs. Earlier,
we considered the evolution of orbits of more than
30000 bodies with initial orbits close to those of Jupi-
ter-family comets (JFC), comet Halley, long-period
comets and asteroids under the 3/1 and 5/2 reso-
nances with Jupiter, and more than 20000 dust grains
produced by these small bodies (Marov and Ipatov,
2005; Ipatov and Mather, 2004, 2006, 2007; Ipatov,
2010). In our previous calculations, we used the
Bulirsch–Stoer algorithm (BULSTO) and the sym-
plectic method of integration, which yielded almost
the same results. In all of the considered series of cal-
culations, when the initial orbits of bodies were close
to those of several Jupiter-family comets, the proba-
bility pE of their collisions with the Earth during the
dynamical evolution exceeded 4 × 10–6, even if several
bodies with the highest collision probability are
excluded from the analysis. If the number of consid-
ered bodies is rather large, pE > 10–5. For the calcula-
tion series with the initial orbits that are close to the
orbit of one of the comets, the values of pE for different
comets could differ by a factor of almost 100. Among
almost 30000 objects, whose initial orbits crossed
Jupiter’s orbit (the so-called Jupiter-crossing objects
(JCOs)), several objects during the evolution acquired
orbits lying completely within Jupiter’s orbit and were
moving along such orbits for millions or even hun-
dreds of millions of years. The probability of collision
of such an object with a terrestrial planet could be
larger than the summed probability of thousands of
other objects with almost the same initial orbits. The
real objects that arrived from beyond Jupiter’s orbit
most likely break down to minicomets and dust grains
during millions of years. However, the probability of
falls of remnants of these objects on the planets is
apparently not smaller than such a probability for the
objects themselves. The probability that objects fall
into the Sun did not exceed 0.02.
In the calculation runs for 250 planetesimals, the
largest dynamical lifetime of planetesimals (till the
moment when the distance of the last planetesimal to
the Sun reaches 2000 AU or when it collides with the
Sun) was varied from 0.9 to 3.9 Myr and from 5.9 to
47.2 Myr for the JS and JN series, respectively. The
orbital elements of planetesimals obtained in our cal-
culations for their dynamical lifetime were saved in the
computer’s memory and used to calculate the proba-
bility of planetesimal–planet collisions. For the JS,
JS01, JN, JN01, and JN15 calculation series, the proba-
bility of planetesimal–planet collisions during the
dynamical lifetime of planetesimals are presented in
Table 1. In the first line of Table 1, the data on 2250
planetesimals for the JS series are given. In the second
line of this table, the probabilities are specified for
2550 planetesimals, including the previous 2250 pre-
planetesimals. The main differences between these
two lines were obtained for the probability of collisions
with Mercury, since the additional calculation runs
included the planetesimal with an orbit that crossed
Mercury’s orbit for a longer time than that in the other
simulations.
On the basis of the obtained data arrays of the
orbital elements for the dynamical lifetime of plane-
tesimals, the probabilities of planetesimal–planet col-
lisions were calculated. These probabilities were cal-
culated not only for that mass of a planet on the
Earth’s orbit, which was used to model the evolution
of disks of planetesimals, but also for a different mass
of this planet. In simulations of the migration of plan-
etesimals, the elements of their orbits were saved with
a step of dt = 500 yr. For each set of the orbital ele-
ments of planetesimals and planets, the probabilities
of collisions of planetesimals with a planet were calcu-
lated for an interval of 500 yr; and these probabilities
were summed up over all sets of orbital elements.
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
DELIVERY OF WATER AND VOLATILES TO THE TERRESTRIAL PLANETS 395
In calculations of the probability pdts of approaches
of a planetesimal and a planet to the distance equal to
the radius of the considered sphere rs (the sphere of
action of a planet) for the time interval dt, the follow-
ing formulas were used in the 3D model (Ipatov,
2000): pdts = dt/T3, where T3 = 2π2kp
TsR2Δi/(kfi) is
the characteristic time before the encounter, Δi is the
angle (expressed in radians) between the orbital planes
of the encountering celestial bodies, R is the distance
from the encounter location to the Sun, kfi is the sum
of angles (expressed in radians) with vertices in the
Sun, within which the distance between the projec-
tions of orbits onto the plane of the ecliptic is smaller
than rs, Ts is the synodic period, kp = P2/P1, P2> P1, Pi
is the rotation period of the ith object (a planetesimal or
a planet) about the Sun, = (2a/R – 1)1/2, and a is the
semimajor axis of the planetesimal’s orbit (the coeffi-
cient was introduced by Ipatov and Mather (2004)
to take into account the dependence of the encounter
velocity versus the planetesimal’s position on the
eccentric orbit). The collision probability for the
objects, which entered the sphere of action, was
assumed to be pdtc = (rΣ/rs)2(1 + ( / )2), where
= (2GmΣ/rΣ)1/2 is the parabolic velocity, is the
relative velocity of the objects coming to the distance
rs of each other, rΣ is the sum of the radii of encounter-
ing objects with a total mass mΣ, and G is the gravita-
k
v
2
s
r
k
v
k
v
v
rel
v
v
rel
v
tional constant. When the values Δi are small, the for-
mulas used in the algorithm were different. The algo-
rithms (and their basis) to calculate kfi and the
characteristic time between collisions of objects were
described by S.I. Ipatov in Appendix 3 of Report О-
1211 of the Keldysh Institute of Applied Mathematics
of the Academy of Sciences of the Soviet Union for
1985 (p. 86−130). The probability of the planetesimal–
planet collision pdt for the time dt is pdts × pdtc. The values
of pdt were summed up through the whole dynamical
lifetime of a planetesimal.
Table 2 lists the values of ppl/pE and pmE =
(ppl/mpl)/(pE/mE), where mpl is the mass of a planet, ppl
is the probability of the planetesimal–planet collision,
pE and mE are the quantities ppl and mpl for the Earth,
respectively. The values of ppl/pE characterize the
ratios of the probability of collisions between planetes-
imals and terrestrial planets to the probability of colli-
sions between planetesimals and the Earth. The values
of the probability of collisions between planetesimals
and a planet on the Earth’s orbit pE and pE01 (see Table 3)
were calculated for the planetary mass equal to that of
the Earth mE and 0.1mE, respectively.
Table 4 presents the probabilities of collisions of
planetesimals from the feeding zone of Jupiter and
Saturn with a planet on the Earth’s orbit pM and pM01
for the planetary mass equal to that of the Moon mM
and 0.1mM, respectively (in the JN15 series, amax = 20
Table 1. Probabilities ppl of collisions of planetesimals from the feeding zone of Jupiter and Saturn with different planets
NMercury Venus Earth Mars Jupiter Saturn
JS 2250 1.5 8 × 10–7 2.05 × 10–6 2.07 × 10–6 4.35 × 10–7 0.048 0.0077
JS 2550 7.3 9 × 10–7 2.54 × 10–6 2.62 × 10–6 4.51 × 10–7 0.047 0.0076
JN 2000 0.92 × 10–7 1.15 × 10–6 1. 9 2 × 10–6 7.2 × 10 –7 0.041 0.006
JS01 2250 1.0 9 × 10 –7 2.35 × 10–6 2.02 × 10–6 4.49 × 10–7 0.060 0.019
JN01 2000 1.3 2 × 10–7 7.07 × 10–7 1.11 × 10–6 3.09 × 10–7 0.041 0.0043
JN15 2550 6.11 × 10–7 3.10 × 10–6 4.52 × 10–6 7.29 × 10–7 0.186 0.031
Table 2. Relative probabilities of collisions of planetesimals with terrestrial planets. The quantities ppl/pE and pmE
=(ppl/mpl)/(pE/mE), where mpl is the mass of a planet, ppl is the collision probability for a planetesimal and a planet, and pE
and mE are the values of ppl and mpl for the Earth
NMercury Venus Earth Mars
ppl/pEpmE ppl/pEpmE ppl/pEpmE ppl/pEpmE
JS 2250 0.076 1.38 0.99 1.21 1 1 0.210 1.91
JS 2550 0.282 5.10 0.97 1.19 1 1 0.172 1.56
JN 2000 0.048 0.87 0.60 0.73 1 1 0.375 3.41
JS01 2250 0.0054 0.98 1.16 1.427 1 1 0.222 2.02
JN01 2000 0.0119 2.15 0.637 0.782 1 1 0.278 2.53
JN15 2550 0.0135 2.44 0.686 0.842 110.1611.47
396
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
MAROV, IPATOV
rather than 12 AU, as in the other calculation series).
Since the orbits of the planetesimals crossing the
Earth’s orbit are strongly eccentric, the planetesimals
moved in the sphere of action of the Earth to the lunar
orbit (the semimajor axis of the lunar orbit is 2.4 times
smaller than the radius of the sphere of action of the
Earth and 3.8 times smaller than the Hill’s radius of
the Earth) along the trajectories slightly deviating
from a rectilinear segment. Due to this, the calculated
values of pM and pM01 do not differ much from the real
probabilities.
CALCULATION RESULTS
FOR THE PLANETESIMALS’ MIGRATION
In our previous calculations (Ipatov and Mather,
2004, 2006, 2007), we considered the migration of
bodies, whose initial orbits were close to those of com-
ets crossing Jupiter’s orbit. For the current orbits and
masses of the planets, those calculations yielded the
values of pE higher than 4 × 10–6. In new JS and JN
series of calculations, the probability pE of a planetesi-
mal–Earth collision is approximately 2 × 10–6. This
value was obtained in the consideration of thousands
of planetesimals. In different runs with 250 initial
planetesimals, the values of pE may differ by an order
of magnitude for the same series of calculations. For
planetesimals that initially were in the inner part of the
disk, pE > 2 × 10–6. In the calculations made by Mor-
bidelli et al. (2000) for planetesimals that initially were
on circular orbits with zero inclinations, the values of
pE were around (1–3) × 10–6 for the semimajor axes of
orbits ranging from 5 to 8 AU. In our JS, JN, and JS01
calculation series, the collision probability pE01 for a
planetesimal and the Earth’s embryo 0.1mE in mass
was estimated at approximately 4 × 10–7.
In the Grand Tack model, the region between 3
and 6 AU was considered to be cleared of planetesi-
mals due to the migration of Jupiter toward the Sun
and back (Rubie et al., 2015). In the paper by Ray-
mond and Izidoro (2017), it is affirmed that, after the
formation of Jupiter, most planetesimals left a zone
between 4 and 7 AU during approximately 1 Myr,
when gas was still present there. If a lower boundary of
the disk is assumed at 6 AU instead of 4.5 AU used in
our calculations, the obtained value of pE can be some-
what smaller than that in our simulations.
In the JS, JS01, JN, and JN01 calculation series, a
portion of planetesimals reaching the Earth’s orbit was
12–14%. If pE is calculated only for such planetesi-
mals, pE will be almost an order of magnitude higher
than 2 × 10–6. In the calculation series with initially
close mutual positions of the giant planets, the values
of pE and pE01 were mostly not smaller than those for
the JS, JS01, JN, and JN01 series. Specifically, pE
4.5 × 10–6 in the JN15 series, where 2/3 of the initial
planetesimals had the semimajor axes larger than 12 AU.
The larger values of pE are caused by the more intense
migration of planetesimals toward the Earth’s orbit.
The stronger migration of planetesimals inward the
Solar System could be obtained from the consider-
ation of the mutual gravitation influence of planetesi-
Table 3. Probabilities pE and pE01 of collisions of planetesimals from the feeding zone of Jupiter and Saturn with the planets mE
and 0.1mE in mass, respectively, on the Earth’s orbit
JS JS JS01 JN JN01 JN15
N2250 2550 2250 2000 2000 2550
pE2.07 × 10–6 2.62 × 10–6 2.02 × 10–6 1.92 × 10–6 1.11 × 10–6 4.52 × 10–6
pE01 3.66 × 10–7 4.70 × 10–7 3.66 × 10–7 3.32 × 10–7 1.99 × 10–7 8.24 × 10–7
pE/pE01 5.65 5.57 5.52 5.78 5.58 5.49
log(pE/pE01) 0.752 0.746 0.742 0.762 0.746 0.740
Table 4. Probabilities pM and pM01 of collisions of planetesimals from the feeding zone of Jupiter and Saturn with the plan-
ets mM and 0.1mM in mass, respectively, on the Earth’s orbit
JS JS JS01 JN JN01 JN15
N2250 2550 2250 2000 2000 2550
pM1.2 4 × 10–7 1.5 9 × 10–7 1.21 × 10–7 1.16 × 10–7 6.74 × 10–8 2.71 × 10–7
pM01 2.64 × 10–8 3.39 × 10–8 2.58 × 10–8 2.49 × 10–8 1.4 4 × 10–8 5.75 × 10–8
pE/pM16.70 16.50 16.72 16.58 16.47 16.68
pM/pM01 4.70 4.68 4.69 4.66 4.68 4.71
lg(pM/pM01) 0.672 0.670 0.670 0.670 0.670 0.673
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
DELIVERY OF WATER AND VOLATILES TO THE TERRESTRIAL PLANETS 397
mals, which was ignored in our simulations. Because
of this, in the real Solar System, the probability of col-
lisions of planetesimals, which came from the feeding
zone of the giants, with the Earth could be of the order
of 4 × 10–6.
DELIVERY OF WATER
TO TERRESTRIAL PLANETS
From the assumption that pE = 2 × 10–6 and the
total mass of planetesimals in the feeding zone of Jupi-
ter and Saturn was roughly 100 Earth masses (Ipatov,
1993, 2000), while the fraction of water kw in planetes-
imals was 0.5, we find that the total mass of water
delivered from this zone to the Earth could be approx-
imately 10–4mE (about 6 × 1020 kg), i.e., roughly half
the water mass in the terrestrial oceans (the latter is
1.4 × 1021 kg). Moreover, almost the same amount of
water could be delivered to the Earth from a zone that
is beyond 12 AU from the Sun. Planetesimals could
mostly migrate from this zone later than from the
feeding zone of Jupiter and Saturn; and a substantial
portion of water, which came from beyond Saturns
orbit, could fall on the Earth’s embryo when its mass
was not small. Accounting for the mutual gravitational
influence of planetesimals leads to the increase in the
orbital eccentricities of many planetesimals, the por-
tion of planetesimals reaching the Earth’s orbit, and
the probability of collisions of planetesimals with the
Earth and other terrestrial planets. The total mass of
water delivered to the Earth from beyond Jupiter’s
orbit could be comparable to that in the terrestrial
oceans.
In the above estimates of the amount of water
delivered to the Earth, the total mass of bodies beyond
Jupiter’s orbit was approximately determined as
200 Earth masses. The disk of planetesimals with a
mass up to 200mE was also considered by Hahn and
Malhotra (1999). Morbidelli et al. (2012) assumed this
mass to be equal to 35–50 Earth masses, while the
contribution of such bodies to the terrestrial oceans
was estimated at 10%. In support of the hypothesis of
a probable large total mass of planetesimals beyond
Jupiter’s orbit, we note that, in our calculations, the
fraction of planetesimals that experienced collisions
with Saturn was essentially less than 1%, while it was
even smaller for Uranus and Neptune. Because of this,
for each body that encountered these three planets,
there were dozens of bodies ejected to hyperbolic
orbits, while the total mass of only Uranus and Nep-
tune exceeds 30mE.
If the estimates of the water fraction in planetesi-
mals are lower, the estimates of water delivered to the
Earth from beyond Jupiter’s orbit are smaller. Mor-
bidelli et al. (2012) and Marty et al. (2016) noted that
the fraction of water in planetesimals did not exceed
50%. Rubie et al. (2015) believed that the fraction of
water ice in the bodies formed at a distance larger than
6 AU was 20%. According to Greenberg (1998), in a
cometary nucleus, the water fraction is about 30%.
Davidsson et al. (2016) came to conclusion that the
fraction of ice in comet 67Р is within the limits from 14
to 33%. Some authors believe that primary planetesi-
mals could contain more ice than comets in our day.
Fulle et al. (2017) suppose that, though the volume
fraction of water in comet 67Р and trans-Neptunian
objects is approximately 20%, the bodies born close to
the snow line contained more water than trans-Neptu-
nian objects.
If the loss of water in collisions of planetesimals
with the Earth is taken into account, the estimate of a
water portion delivered to the Earth from beyond Jupi-
ter’s orbit decreases. Canup and Pierazzo (2006)
found that, if a planetesimal collides with the Earth
with a velocity which is higher than the parabolic
velocity by more than 1.4 times and the collision angle
is larger than 30°, more than 50% of impactor’s water
is lost.
In the runs presented in Table 2, the ratio ppl/mpl of
the probability of planetesimal–planet collisions to
the planetary mass calculated for Mars, Venus, and
Mercury is higher than that for the Earth by 1.5–3.4,
0.7–1.4, and 0.9–5.1 times, respectively. These esti-
mates suggest that the mass of planetesimals or water
delivered to Venus from beyond Jupiter’s orbit was
approximately the same as that for the Earth, if taken
per unit mass of the planet; at the same time, the anal-
ogous mass of planetesimals or water delivered to Mars
was 2−3 times larger than that for the Earth, if taken
per unit mass of the planet. In absolute value, the
water mass delivered to Mars from beyond Jupiter’s
orbit was 3−5 times smaller than that delivered to the
Earth. For Mercury, the ratio pmE = (ppl/mpl)/(pE/mE)
was not smaller than that for the Earth. These values of
the probability of planetesimal–planet collisions are
consistent with our earlier estimates made for the
objects, the initial orbits of which crossed Jupiter’s
orbit (Ipatov and Mather, 2004, 2006, 2007). The esti-
mates are indicative of the presence of ancient oceans
on Mars and Venus, which could partially survive deep
under the surface (as on Mars (Usui, 2017; Wade,
2017)) or were lost in the course of evolution (as on
Venus (Kasting, 1988; Marov, Grinspoon, 1998,
chapter 9; Chassefière et al., 2012; Marov, 2017,
p. 145–147)).
FALL OF PLANETESIMALS
ONTO A GROWING EMBRYO OF THE EARTH
From the arrays of the orbital elements of planetes-
imals and planets calculated for different times, the
probabilities of collisions of planetesimals or comets
with a planet on the Earth’s orbit were determined for
the mass of the planet equal to mE and 0.1mE; and the
ratio of probabilities pE/pE01 was found in the range
from 5.5 ≈ 100.74 to 5.8 ≈ 100.76. Thus, the ratio of the
398
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
MAROV, IPATOV
mass of planetesimals falling onto the planet to the
mass of the planet is approximately two times higher
for the planetary mass 0.1mE than for mE. Here, we
consider the planetesimals that came from the feeding
zone of giant planets (let us call them j-planetesimals).
For the planetesimals that came from the feeding zone
of terrestrial planets, the index of power is larger than 1;
i.e., the larger planets grew faster.
If we take into account that the effective radius of
the planet of radius r is approximately reffr(1 +
(/)2)1/2 and the parabolic velocity on the plane-
tary surface is proportional to r−1/2, we can find the
relative velocity of a planetesimal entering the sphere of
action of the planet ≈ 11.2(1 – 10–5/3(pE/pE01))1/2/
(10–2/3(pE/pE01) – 1)1/2 km/s from the ratio pE/pE01 =
(reffE/reffE01)2 (where reffE and reffE01 are the effective
radii of the Earth and its embryo of mass 0.1mE,
respectively). In particular, vrel is 21.0, 23.1, and
24.4 km/s, if pE/pE01 is 5.8, 5.6, and 5.5 respectively.
For comparison, according to several models by Nes-
vorný et al. (2017), asteroids, which initially were on
the orbits with semimajor axes ranging from 1.6 to
3.3 AU, have mean velocities of collisions with the
Earth varying from 21 to 23.5 km/s.
If the effective radius of the body is close to its
radius, the effective cross-section of the body of mass
m is roughly proportional to m2/3. For such a model,
the power index is 2/3 ≈ 0.667, which is slightly smaller
than the power indices obtained in the analysis of col-
lisions of j-planetesimals with the Earth. The ratio of
the effective cross-section (proportional to m2/3) to the
mass m is proportional to m–1/3; i.e., in this case, the
relative growth of the planetary mass is more rapid for
less massive planets. For weakly eccentric orbits, on
the contrary, the larger bodies grow quicker.
If the relative mass increase of an embryo at the
expense of j-planetesimals is proportional to m0.74, the
ratio of the embryo’s mass increase from 0 to kmE to
that from 0 to mE is k1.74 . And, 0.51.74 ≈ 0.3 and 0.81.74
0.68. The fraction of j-planetesimals, which fell onto
the embryo during its increase in mass to kmE, may be
smaller than k1.74 if the ratio of the inflow of j-plane-
tesimals to that of “local” planetesimals at terminal
stages of the planet formation was larger than such a
ratio at early stages of the embryo growth. With the
above estimates of the material migration from beyond
Jupiter’s orbit to the Earth, we may find that, when the
Earth’s embryo was growing to 0.5mE, the mass of
water delivered to the embryo could be around 30% of
all the water delivered from the feeding zones of Jupi-
ter and Saturn. The above estimates show that a sub-
stantial mass of water could be delivered to the Earth’s
embryo when its mass was smaller than the present mass
of the Earth. In the Grand Tack model, most bodies
which originated from the zone beyond 6–7 AU fell onto
v
rel
v
par
v
rel
v
the Earth after the latter possessed 60–80% of its final
mass (Rubie et al., 2015).
DELIVERY OF WATER AND VOLATILES
TO THE MOON
In the calculation series presented in Table 4, the
probability of collisions of planetesimals with the
Moon varied from 7 × 10–8 to 2.7 × 10–7; and, in three
calculation series, they were approximately 1.2 × 10–7.
In the considered calculation series, the ratio of the
probability of collisions of planetesimals with the
Earth to that with the Moon pE/pM was within the lim-
its from 16.5 to 16.7. In the JS and JN calculation runs
with N = 250 planetesimals, the ratio pE/pM varied
from 16.53 to 16.9 and from 16.08 to 16.74, respec-
tively. In the calculation runs, where the initial posi-
tions of the giant planets were assumed to be closer (in
particular, JN15), the ratio pE/pM varied from 16.0 to
17.0. By comparison, the squared ratio of the radii of
the Earth and the Moon is 13.48. In different runs with
N = 250 in the same calculation series, the probabili-
ties of collisions with the Moon (or any planet) could
differ by more than 10 times. The mass of planetesi-
mals and water delivered to the Moon from beyond
Jupiter’s orbit could be smaller than that for the Earth
by the factor not more than 20.
For migrating objects, the initial orbits of which
crossed Jupiter’s orbit and were close to those of Jupi-
ter-family comets, the ratios pE/pM were also calcu-
lated in different runs (with 250 objects) (Ipatov and
Mather, 2004, 2006, 2007). These values varied from
15.2 to 17.6. For asteroids from the 3 : 1 resonance with
Jupiter and comets with eccentricity е = 0.975, pE/pM
reached 18.6 and 15.2, respectively. In these simula-
tions, the scattering in the pE/pM values was from 5.1 to
6.0. The ratio of the probability of collisions with the
Moon with its present density to that with its density
equal to that of the Earth was close to 1.39 in all calcu-
lation runs.
For comets from the trans-Neptunian belt (with
initial distances in a range of 20–30 AU), Nesvorný
et al. (2017) found that the probabilities of collisions
with Venus, the Earth, Mars, and the Moon are 3.7 ×
10–7, 5.0 × 10–7, 9.1 × 10–8, and 2.6 × 10–8, respec-
tively. For asteroids with initially large semimajor axes,
from 1.6 to 3.3 AU, these probabilities were (1.2–1.5) ×
10–2, (1.0–1.1) × 10–2, (3.6–3.9) × 10–3, (4.4–5.3) × 10–4,
respectively. From the data reported in the abovemen-
tioned paper, the ratio pE/pM can be estimated as 19
and 21–23 for comets and asteroids, respectively.
CONCLUSIONS
The evolution of disks of planetesimals under the
influence of planets was simulated. The results of cal-
culations showed that, in the course of the formation
of the Solar System, the mass of water delivered to the
SOLAR SYSTEM RESEARCH Vol. 52 No. 5 2018
DELIVERY OF WATER AND VOLATILES TO THE TERRESTRIAL PLANETS 399
Earth from beyond Jupiter’s orbit could be compara-
ble to the mass of terrestrial oceans. While the Earth’s
embryo was growing to half the present mass of the
Earth, the mass of water delivered to the embryo could
be approximately 30% of all the water delivered to the
Earth from the feeding zone of Jupiter and Saturn.
The water in terrestrial oceans and its D/H ratio could
result from the mixing of water from several sources
with high and low D/H ratios. The mass of water
delivered to Venus from beyond Jupiter’s orbit was
approximately the same as that for the Earth, if taken
per unit mass of the planet; at the same time, the anal-
ogous per-unit mass of water delivered to Mars was
2−3 times larger than that for the Earth. In absolute
value, the water mass delivered to Mars from beyond
Jupiter’s orbit was 3−5 times smaller than that deliv-
ered to the Earth. The mass of water delivered to Mer-
cury was not smaller than that for the Earth, if taken
per unit mass of the planet. The mass of water deliv-
ered to the Moon from beyond Jupiter’s orbit could be
smaller than that for the Earth by the factor not more
than 20.
ACKNOWLEDGMENTS
The studies of the material migration to the Moon
were supported by the Russian Scientific Foundation
(project no. 17-17-01279), and the studies of the deliv-
ery of water and volatiles to the terrestrial planets were
supported by the Program 17 of the Presidium of the
Russian Academy of Sciences (government contract
no. 00137-2018-0030 of the Vernadsky Institute of
Geochemistry and Analytical Chemistry of the Rus-
sian Academy of Sciences).
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Translated by E. Petrova
... The orbital elements of migrated planetesimals were saved in the computer memory with a step of 500 yr. Based on the arrays of the orbital elements, similar to simulations by Ipatov and Mather (2003, 2004a, 2004b and Marov and Ipatov (2018), the probabilities of collisions of planetesimals with the planets, the Moon, and their embryos were calculated for time interval T. In this procedure, based on these arrays of the orbital elements of migrated planetesimals, the probabilities were calculated not only for collisions between the planetesimals and the planetary embryos and the Moon, which were considered in numerical integration of the equations of motion in the analysis of planetesimals' migration, but also for collisions between the planetesimals and the embryos of the other masses (though the embryos of the other masses were ignored in the integration). This kind of approach to the analysis of the growth of planetary embryos at the expense of planetesimals which initially were at different distances from the Sun has never been used before. ...
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... for e 0 = 0.05 and 0.3, respectively). When studying the migration of planetesimals from the feeding zone of Jupiter and Saturn, Marov and Ipatov (2018) obtained that the ratio of the probabilities p E /p E01 was in a range from 5.5 ≈ 10 0.74 to 5.8 ≈ 10 0.76 ...
Preprint
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Migration of planetesimals from the feeding zone of the terrestrial planets, which was divided into seven regions depending on the distance to the Sun, was simulated. The influence of gravity of all planets was taken into account. In some cases, the embryos of the terrestrial planets rather than the planets themselves were considered; their masses were assumed to be 0.1 or 0.3 of the current masses of the planets. The arrays of orbital elements of migrated planetesimals were used to calculate the probabilities of their collisions with the planets, the Moon, or their embryos. Based on our calculations, we drew conclusions on the process of accumulation of the terrestrial planets. The embryos of the terrestrial planets, the masses of which did not exceed a tenth of the current planetary masses, accumulated planetesimals mainly from the vicinity of their orbits. When planetesimals fell onto the embryos of the terrestrial planets from the feeding zone of Jupiter and Saturn, these embryos had not yet acquired the current masses of the planets, and the material of this zone (including water and volatiles) could be accumulated in the inner layers of the terrestrial planets. The inner layers of each of the terrestrial planets were mainly formed from the material located in the vicinity of the orbit of a certain planet. The outer layers of the Earth and Venus could accumulate the same material for these two planets from different parts of the feeding zone of the terrestrial planets. The Earth and Venus could acquire more than half of their masses in 5 Myr. A relatively rapid growth of the bulk of the Martian mass can be explained by the formation of Mars' embryo (the mass of which is several times less than that of Mars) due to contraction of a rarefied condensation.
... Water is a virus-friendly environment and water is the most common molecule in the cosmos. Therefore, it is possible that water-infestedviruses may have been initially deposited on Earth via watery comets, asteroids and meteors during the heavy bombardment era (Joseph 2000) which gave rise to the oceans (Albertsson et al. 2014;O'Brien et al. 2018, Marov et al. 2018 which are infiltrated with billions of trillions of viruses. ...
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Astrovirology is the study of beneficial vs harmful viruses that originated from comets, meteors, solar winds, and ejecta from other planets, or which mutated when lofted by winds into the upper atmosphere. That these upper atmospheric and putative extraterrestrial viruses have contributed to the evolution of the biosphere and life on Earth, and caused disease and plague, is discussed, and the role of astro-viruses and endogenous retroviruses in the evolution of life and biosphere is reviewed. Evolution leading to the Cambrian Explosion and continuing to humans is characterized by repeated viral invasions and insertion of retroviral genes into host species' genomes. "Evolution" parallels the genetic-biological engineering of the environment (e.g. oxygen production), which activates inherited retroviral genes. Viral plagues are associated with comets, and have caused extinctions that served to promote evolution and eradicate those not "fit." Given evidence of life on Mars and association of plague with comets, extraterrestrial viruses may be commonplace. Extraterrestrial viruses may have acquired genes via interplanetary horizontal gene transfer which in turn have been transferred to the genomes of eukaryotes on Earth. "Evolution" may be the metamorphosis and replication of life and biospheres that evolved on other planets.
... For the bodies coming from beyond Jupiter's orbit and falling onto the Earth, the typical velocities of collisions with the Earth are somewhat larger than those for the NEOs originating in the asteroid belt. According to estimates by Marov and Ipatov (2018), the typical velocities of these bodies, which entered the Earth's activity sphere, are in a range of 21−24 km/s. Ipatov (2000) noted that, among the bodies that came from zones of the giant planets, the portion of bodies with Earth-crossing orbits is an order of magnitude higher than that of bodies with Mars-crossing orbits and their eccentricities usually exceed 0.6. ...
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We compare the number of lunar craters larger than 15 km across and younger than 1.1 Ga to the estimates of the number of craters that could have been formed for 1.1 Ga if the number of near-Earth objects and their orbital elements during that time were close to the corresponding current values. The comparison was performed for craters over the entire lunar surface and in the region of the Oceanus Procellarum and maria on the near side of the Moon. In these estimates, we used the values of collision probabilities of near-Earth objects with the Moon and the dependences of the crater diameters on the impactor sizes. According to the estimates made by different authors, the number density of known Copernican craters with diameters D ≥ 15 km in mare regions is at least double the corresponding number for the remaining lunar surface. Our estimates do not contradict the growth in the number of near-Earth objects after probable catastrophic frag-mentations of large main-belt asteroids, which may have occurred over the recent 300 Ma; however, they do not prove this increase. Particularly, they do not conflict with the inference made by Mazrouei et al. (2019) that 290 Ma ago the frequency of collisions of near-Earth asteroids with the Moon increased by 2.6 times. The number of Copernican lunar craters with diameters not smaller than 15 km is probably higher than that reported by Mazrouei et al. (2019). For a probability of a collision of an Earth-crossing object (ECO) with the Earth in a year equaled to 10-8 , our estimates of the number of craters agree with the model, according to which the number densities of the 15-km Copernican craters for the whole lunar surface would have been the same as that for mare regions if the data by Losiak et al. (2015) for D < 30 km were as complete as those for D > 30 km. With this collision probability of ECOs with the Earth and for this model, the cratering rate may have been constant over the recent 1.1 Ga.
... For the bodies coming from beyond Jupiter's orbit and falling onto the Earth, the typical velocities of collisions with the Earth are somewhat larger than those for the NEOs originating in the asteroid belt. According to estimates by Marov and Ipatov (2018), the typical velocities of these bodies, which entered the Earth's activity sphere, are in a range of 21−24 km/s. Ipatov (2000) noted that, among the bodies that came from zones of the giant planets, the portion of bodies with Earth-crossing orbits is an order of magnitude higher than that of bodies with Mars-crossing orbits and their eccentricities usually exceed 0.6. ...
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We compare the number of lunar craters larger than 15 km across and younger than 1.1 Ga to the estimates of the number of craters that could have been formed for 1.1 Ga if the number of near-Earth objects and their orbital elements during that time were close to the corresponding current values. The comparison was performed for craters over the entire lunar surface and in the region of the Oceanus Procellarum and maria on the near side of the Moon. In these estimates, we used the values of collision probabilities of near-Earth objects with the Moon and the dependences of the crater diameters on the impactor sizes. According to the estimates made by different authors, the number density of known Copernican craters with diameters D>15 km in mare regions is at least double the corresponding number for the remaining lunar surface. Our estimates do not contradict the growth in the number of near-Earth objects after probable catastrophic fragmentations of large main-belt asteroids, which may have occurred over the recent 300 Ma; however, they do not prove this increase. Particularly, they do not conflict with the inference made by Mazrouei et al. (2019) that 290 Ma ago the frequency of collisions of near-Earth asteroids with the Moon increased by 2.6 times. For a probability of a collision of an Earth-crossing object (ECO) with the Earth in a year equaled to 10^-8, our estimates of the number of craters agree with the model, according to which the number densities of the 15-km Copernican craters for the whole lunar surface would have been the same as that for mare regions if the data by Losiak et al. (2015) for D<30 km were as complete as those for D>30 km. With this collision probability of ECOs with the Earth and for this model, the cratering rate may have been constant over the recent 1.1 Ga.
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There is a long-standing debate regarding the origin of the terrestrial planets’ water as well as the hydrated C-type asteroids. Here we show that the inner Solar System’s water is a simple byproduct of the giant planets’ formation. Giant planet cores accrete gas slowly until the conditions are met for a rapid phase of runaway growth. As a gas giant’s mass rapidly increases, the orbits of nearby planetesimals are destabilized and gravitationally scattered in all directions. Under the action of aerodynamic gas drag, a fraction of scattered planetesimals are deposited onto stable orbits interior to Jupiter’s. This process is effective in populating the outer main belt with C-type asteroids that originated from a broad (5-20 AU-wide) region of the disk. As the disk starts to dissipate, scattered planetesimals reach sufficiently eccentric orbits to cross the terrestrial planet region and deliver water to the growing Earth. This mechanism does not depend strongly on the giant planets’ orbital migration history and is generic: whenever a giant planet forms it invariably pollutes its inner planetary system with water-rich bodies.
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The impact cratering record of the Moon and the terrestrial planets provides important clues about the formation and evolution of the Solar System. Especially intriguing is the epoch 3.8-3.9 Gyr ago (Ga), known as the Late Heavy Bombardment (LHB), when the youngest lunar basins such as Imbrium and Orientale formed. The LHB was suggested to originate from a slowly declining impactor flux or from a late dynamical instability. Here we develop a model for the historical flux of large asteroid impacts and discuss how it depends on various parameters, including the time and nature of the planetary migration/instability. We find that the asteroid impact flux dropped by 1 to 2 orders of magnitude during the first 1 Gyr and remained relatively unchanged over the last 3 Gyr. The early impacts were produced by asteroids whose orbits became excited during the planetary migration/instability, and by those originating from the inner extension of the main belt (E-belt; semimajor axis 1.6<a<2.1 au). The profiles obtained for the early and late versions of the planetary instability initially differ, but end up being similar after ~3 Ga. Thus, the time of the instability can only be determined by considering the cratering and other constraints during the first ~1.5 Gyr of the Solar System history. Our absolute calibration of the impact flux indicates that asteroids were probably not responsible for the LHB, independently of whether the instability happened early or late, because the calibrated flux is not large enough to explain Imbrium/Orientale and a significant share of large lunar craters. Comets and leftovers of the terrestrial planet formation provided additional, and probably dominant source of impacts during early epochs.
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The distribution of heavy elements is anomalously low in the asteroid main belt region compared with elsewhere in the solar system. Observational surveys also indicate a deficit in the number of small ($ \le 50$~km size) asteroids that is two orders of magnitude lower than what is expected from the single power-law distribution that results from a collisional coagulation and fragmentation equilibrium. Here, we consider the possibility that a major fraction of the original asteroid population may have been cleared out by Jupiter's secular resonance, as it swept through the main asteroid belt during the depletion of the solar nebula. This effect leads to the excitation of the asteroids' orbital eccentricities. Concurrently, hydrodynamic drag and planet-disk tidal interaction effectively damp the eccentricities of sub-100 km-size and of super-lunar-size planetesimals, respectively. These combined effects lead to the asteroids' orbital decay and clearing from the present-day main belt region ($\sim 2.1-3.3$~AU). The intermediate-size (50 to several hundreds of kilometers) planetesimals therefore preferentially remain as main belt asteroids near their birthplaces, with modest asymptotic eccentricities. The smaller asteroids are the fragments of subsequent disruptive collisions at later times as suggested by the present-day asteroid families. This scenario provides a natural explanation for both the observed low surface density and the size distribution of asteroids in the main belt. It also offers an explanation for the confined spatial extent of the terrestrial planet building blocks without the requirement of extensive migration of Jupiter.
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A microlensing survey by Sumi et al. (2011) exhibits an overabundance of short-timescale events (STEs; t_E<2 days) relative to what is expected from known stellar populations and a smooth power-law extrapolation down to the brown dwarf regime. This excess has been interpreted as a population of ~Jupiter-mass objects that outnumber main-sequence stars by nearly twofold; however the microlensing data alone cannot distinguish between events due to wide-separation (a>~10 AU) and free-floating planets. Assuming these STEs are indeed due to planetary-mass objects, we aim to constrain the fraction of these events that can be explained by bound but wide-separation planets. We fit the observed timescale distribution with a lens mass function comprised of brown dwarfs, main-sequence stars, and stellar remnants, finding and thus corroborating the initial identification of an excess of STEs. We then include a population of bound planets that are expected not to show signatures of the primary lens (host) in their microlensing light curves and that are also consistent with results from representative microlensing, radial velocity, and direct imaging surveys. We find that bound planets alone cannot explain the entire STE excess without violating the constraints from the surveys we consider and thus some fraction of these events must be due to free-floating planets, if our model for bound planets holds. We estimate a median fraction of STEs due to free-floating planets to be f=0.67 (0.23-0.85 at 95% confidence) when assuming "hot-start" planet evolutionary models and f=0.58 (0.14-0.83 at 95% confidence) for "cold-start" models. Assuming a delta-function distribution of free-floating planets of mass m_p=2 M_Jup yields a number of free-floating planets per main-sequence star of N=1.4 (0.48-1.8 at 95% confidence) in the "hot-start" case and N=1.2 (0.29-1.8 at 95% confidence) in the "cold-start" case.
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Context. We investigate the formation and evolution of comet nuclei and other trans-Neptunian objects (TNOs) in the solar nebula and primordial disk prior to the giant planet orbit instability foreseen by the Nice model. Aims. Our goal is to determine whether most observed comet nuclei are primordial rubble-pile survivors that formed in the solar nebula and young primordial disk or collisional rubble piles formed later in the aftermath of catastrophic disruptions of larger parent bodies. We also propose a concurrent comet and TNO formation scenario that is consistent with observations. Methods. We used observations of comet 67P/Churyumov-Gerasimenko by the ESA Rosetta spacecraft, particularly by the OSIRIS camera system, combined with data from the NASA Stardust sample-return mission to comet 81P/Wild 2 and from meteoritics; we also used existing observations from ground or from spacecraft of irregular satellites of the giant planets, Centaurs, and TNOs. We performed modeling of thermophysics, hydrostatics, orbit evolution, and collision physics. Results. We find that thermal processing due to short-lived radionuclides, combined with collisional processing during accretion in the primordial disk, creates a population of medium-sized bodies that are comparably dense, compacted, strong, heavily depleted in supervolatiles like CO and CO2; they contain little to no amorphous water ice, and have experienced extensive metasomatism and aqueous alteration due to liquid water. Irregular satellites Phoebe and Himalia are potential representatives of this population. Collisional rubble piles inherit these properties from their parents. Contrarily, comet nuclei have low density, high porosity, weak strength, are rich in supervolatiles, may contain amorphous water ice, and do not display convincing evidence of in situ metasomatism or aqueous alteration. We outline a comet formation scenario that starts in the solar nebula and ends in the primordial disk, that reproduces these observed properties, and additionally explains the presence of extensive layering on 67P/Churyumov-Gerasimenko (and on 9P/Tempel 1 observed by Deep Impact), its bi-lobed shape, the extremely slow growth of comet nuclei as evidenced by recent radiometric dating, and the low collision probability that allows primordial nuclei to survive the age of the solar system. Conclusions. We conclude that observed comet nuclei are primordial rubble piles, and not collisional rubble piles. We argue that TNOs formed as a result of streaming instabilities at sizes below ~400 km and that ~350 of these grew slowly in a low-mass primordial disk to the size of Triton, Pluto, and Eris, causing little viscous stirring during growth. We thus propose a dynamically cold primordial disk, which prevented medium-sized TNOs from breaking into collisional rubble piles and allowed the survival of primordial rubble-pile comets. We argue that comets formed by hierarchical agglomeration out of material that remained after TNO formation, and that this slow growth was a necessity to avoid thermal processing by short-lived radionuclides that would lead to loss of supervolatiles, and that allowed comet nuclei to incorporate ~3 Myr old material from the inner solar system.