THE EIGHTH MOSCOW SOLAR SYSTEM SYMPOSIUM 2017 8MS3-PA-01 HETEROGENEOUS ACCRETION: SOME RESULTS OF THE COMPUTER MODELING (Dedicated to the memory of Tobias Owen) M.Ya. Marov, S.I. Ipatov Vernadsky Institute of Geochemistry and Analytical Chemistry, Kosygin st., 19, Moscow 119991, Russia, [email protected] KEYWORDS: heterogeneous accretion, migration, planetesimals, matter delivery, water, vol- atiles, terrestrial planets INTRODUCTION: Toby Owen contributed in many important fields of planetary sciences involv- ing both theoretical research and experimental results returned by space mis- sions. It was a great privilege to discuss with him the most challenging ideas concerning the structure and composition of atmospheres of inner and outer planets, specifically isotopic ratios of noble gases on Mars and Venus aiming to reveal origin and evolution of these planets. Here we address one of these pioneering ideas discussed by Toby Owen in the paper co-authored by F. Anders and published in Science magazine as early as in 1977 [1]. Authors attempted to explain lacking of water and other vola- tiles on Earth after its accum ulation invoking a postulated migration process of volatile-rich bodies from periphery of the solar system at the later phase of its evolution, mainly in the course of Late Heavy Bombardment (LHB) dated around 4 billion years ago. Delivery such a matter and its layered sedimentation (late veneer) on the inner planets’ surface the authors called the mechanism of heterogeneous accretion. The idea drew attention and took further development including computer modeling to ensure its more rigorous support. Results of the study can be found in the numerous publications showing the great advancement in the field (see, e.g., [2, 3] and references therein). The study was mostly focused on the numerical models of comets, asteroids and dust transport from Kuiper belt and outer giant planets region inward through the migration mechanism involving different orbital perturbations. Based on this scenario quantitative estimates of water/volatiles that could be potentially delivered to Earth, Venus and Mars were made. Concurrently, it was attempted to evaluate bulk of water stored in the planet interior in due course of its accumulation from primordial matter in the framework of chondrite model and released later on the surface. The idea was most recently supported by the lab analysis of olivine in the archaean komatiites-basaltic associations (ultramafic lavas) resulted from melting under extreme conditions of the Earth’s mantle, which argue for deep-mantle water reservoir [4]. Anyway, nowadays it is difficult to find a rationale and distinguish between exogenic or endogenic sources of water abundance that inner plan- ets could acquire and the problem remains not unambiguous. Our interest to the problem goes back to the time of Anders/Owen paper appearance while computer modeling aimed to volatiles amount delivery assessment began since the 1990s. Results of the original study can be found elsewhere (see, e. g., [2, 5-9]). In this paper we present a summary of how this research is in progress addressing several scenarios of migration in the course of planetary system evolution. COMPUTER SIMULATIONS OF INWARD MIGRATION OF PLANETESIMALS FROM THE FEEDING ZONE OF JUPITER AND SATURN: Recently we [5] made computer simulations of migration of 104 planetesimals from the feeding zone of Jupiter and Saturn to forming terrestrial planets expe- rienced gravitational influence of the planets. In series JN, all planets were assumed as having their present orbits and masses. In series JS, Uranus and Neptune were excluded. Initial eccentricities and inclinations of planetesimals were assumed to be 0.3 and 0.15 rad, respectively, while the initial semi-ma- jor axes of planetesimals were taken between 4.5 and 12 AU. We further 1-abstract 8MS3-PA-01 THE EIGHTH MOSCOW SOLAR SYSTEM SYMPOSIUM 2017 assumed masses of planets moving in orbits of the currently existed terrestrial planets to be equal their present masses in JS and JN series, while they were assumed to be smaller by a factor of 10 in the JS01 and JN01 series. These runs allowed us to model accumulation of embryos of the terrestrial planets. Based on an accepted set of orbital elements during evolution, the probabilities of collisions of migrating bodies with planets during their dynamical lifetimes were estimated. Also, calculations were carried out for a case when giant planets of present mass were initially located closer to each other compared to their present position. In such a scenario at least one of giant planets (not Jupiter) was ejected into a hyperbolic orbit in the process of evolution. For these runs probability pE of planetesimal collision with Earth turned out not smaller than the values of pE for series JS, JN, JS01 and JN01. COMPUTER SIMULATIONS OF INWARD MIGRATION OF JUPITER-CROSSING OBJECTS: The orbital evolution of more than 30,000 bodies having initial orbits close to those of Jupiter-family comets (JFCs), Halley-type comets, long-period comets, and asteroids in the resonances 3/1 and 5/2 with Jupiter was inte- grated until these bodies either reached radial distance 2000 AU or collided with the Sun [2, 6-9]. In such runs all planets moved in the present orbits and had their present masses. The symplectic or Bulirsh-Stoer codes were utilized. The probability pE of collision with Earth of JFCs under consideration exceeded 4×10-6. DELIVERY OF WATER AND VOLATILES TO THE TERRESTRIAL PLANETS: Water and volatiles caused by exogenic source could be delivered to the ter- restrial planets from different radial distances from the Sun. The main goal was to reconcile the D/H ratio in the cometary and Earth’s oceans water. Alter- natively to comets, bodies from the asteroid belt [3] were suggested as such a source. However arguments were brought [10] against this idea because oxygen isotopic composition in the primitive upper mantle better matches that of anhydrous ordinary chondrites rather than hydrous carbonaceous chon- drites. Because the deep mantle water has a low D/H ratio there was assumed that it could be acquired due to water adsorption on fractal grains during the Earth’s accretion [11]. As a compromise one may admit the ocean water (and respectively its D/H ratio) resulted from mixing of several sources. The results of our computer modeling showed that ratio of the fraction of plan- etesimals collided with the Earth’s embryo was about 2×10-6 and 4×10-7 for the Earth’s mass embryos mE and to 0.1mE, respectively. We derived that during the growth of Earth’s embryo up to 0.5mE the amount of water delivered from the feeding zone of Jupiter and Saturn could be about 30% of the overall mass of water that Earth obtained from this feeding zone. In turn, mass of water delivered to Earth from the feeding zone of the giant planets and beyond turned -4 out comparable with the total mass of the Earth’s oceans (about 2.25×10 mE). Assuming the total mass of planetesimals (composed half of water) in the feed- ing zone of Jupiter and Saturn equal to 100mE and their collision probability -6 with Earth pE=2×10 this source gives rise a half of the Earth’s ocean water, another a half coming from more distant regions. It should be emphasize that bulk of water delivered from these regions to the Earth’s embryo came when its mass exceeded ~ 0.5mE. The mass of water delivered to other terrestrial planets turned out proportional to the ration of their masses to that of Earth. In the series JS it was smaller by a factor of 2, 1.25, and 1.3 for Mars, Venus and Mercury, respectively while for the series JN of 3.4, 0.7 и 0.8, respectively. For the Earth’s embryo of mass m growing due to accretion of planetesimals coming from the feeding zone of Jupiter and Saturn, the increase of its mass turned out proportional to m0.74. In our calculations of the migration of objects which initially moved in come- tary-type Jupiter-crossing orbits, the fraction pE of the objects collided with the Earth exceeded 4×10-6 [7-9]. This value was greater than the above mentioned values of pE for planetesimals because initial eccentricities of the planetes- imals were smaller than those of cometary objects. Besides, not all plane- tesimals reached Jupiter’s orbit during their lifetimes. Taking into account the mutual gravitational influence of planetesimals would increase their eccen- tricities during the evolution resulting in greater values of pE as compared the model where such effect is neglected. Study of migration of the Jupiter-cross- ing objects and planetesimals showed that the ratio of mass of water delivered 2-abstact THE EIGHTH MOSCOW SOLAR SYSTEM SYMPOSIUM 2017 8MS3-PA-01 by such bodies to the bulk mass of a planet was not smaller for Mars, Venus, and Mercury, than that for Earth. Interestingly, this larger mass fraction would result in relatively large ancient oceans on Mars and Venus. Let us note that orbits of Earth-crossing objects migrating from outside Jupi- ter’s orbit are typically highly eccentric. For such eccentric orbits, an amount of the material, including water, delivered from outside Jupiter’s orbit is approxi- mately proportional to effective radii of Earth and the Moon and therefore could be only by an order of magnitude smaller for the Moon than for Earth. CONCLUSIONS: Anders/Owen publication in the middle of 1970s on heterogeneous accretion stimulated our advanced study of the problem through the modern computer modeling. We studied migration of bodies and dust to the terrestrial planets from the regions beyond the snow line, specifically inward migration of plane- tesimals from the feeding zone of Jupiter and Saturn, and estimated delivery of water and volatiles to these planets.