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Register a new userImpact Erosion Model for Gravity-Dominated Planetesimals
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Disruptive collisions have been regarded as an important process for planet formation, while non-disruptive, small-scale collisions (hereafter called erosive collisions) have been underestimated or neglected by many studies. However, recent studies have suggested that erosive collisions are also important to the growth of planets, because they are much more frequent than disruptive collisions. Although the thresholds of the specific impact energy for disruptive collisions (Q_RD^*) have been investigated well, there is no reliable model for erosive collisions. In this study, we systematically carried out impact simulations of gravity-dominated planetesimals for a wide range of specific impact energy (Q_R) from disruptive collisions (Q_R ~ Q_RD^*) to erosive ones (Q_R << Q_RD^*) using the smoothed particle hydrodynamics method. We found that the ejected mass normalized by the total mass (M_ej/M_tot) depends on the numerical resolution, the target radius (R_tar) and the impact velocity (v_imp), as well as on Q_R, but that it can be nicely scaled by Q_RD^* for the parameter ranges investigated (R_tar = 30-300 km, v_imp = 2-5 km/s). This means that M_ej/M_tot depends only on Q_R/Q_RD^* in these parameter ranges. We confirmed that the collision outcomes for much less erosive collisions (Q_R < 0.01 Q_RD^*) converge to the results of an impact onto a planar target for various impact angles and that M_ej/M_tot = C * QR/QRD* holds. For disruptive collisions (Q_R ~ Q_RD^*), the curvature of the target has a significant effect on Mej/Mtot. We also examined the angle-averaged value of M_ej/M_tot and found that the numerically obtained relation between angle-averaged M_ej/M_tot and Q_R/Q_RD^* is very similar to the cases for 45-degree impacts. We proposed a new erosion model based on our numerical simulations for future research on planet formation with collisional erosion.
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Impacts between planetesimals have largely been ruled out as a heat source in the early Solar System, by calculations that show them to be an inefficient heat source and unlikely to cause global heating. However, the long-term, localized thermal effects of impacts on planetesimals have never been fully quantified. Here, we simulate a range of impact scenarios between planetesimals to determine the post-impact thermal histories of the parent bodies, and hence the importance of impact heating in the thermal evolution of planetesimals. We find on a local scale that heating material to petrologic type 6 is achievable for a range of impact velocities and initial porosities, and impact melting is possible in porous material at a velocity of > 4 km/s. Burial of heated impactor material beneath the impact crater is common, insulating that material and allowing the parent body to retain the heat for extended periods (~ millions of years). Cooling rates at 773 K are typically 1 - 1000 K/Ma, matching a wide range of measurements of metallographic cooling rates from chondritic materials. While the heating presented here is localized to the impact site, multiple impacts over the lifetime of a parent body are likely to have occurred. Moreover, as most meteorite samples are on the centimeter to meter scale, the localized effects of impact heating cannot be ignored.
We investigate the influence of impacts of large planetesimals and small planetary embryos on the early Martian surface on the hydrodynamic escape of an early steam atmosphere that is exposed to the high soft X-ray and EUV flux of the young Sun. Impact statistics in terms of number, masses, velocities, and angles of asteroid impacts onto the early Mars are determined via n-body integrations. Based on these statistics, smoothed particle hydrodynamics (SPH) simulations result in estimates of energy transfer into the planetary surface material and according surface heating. For the estimation of the atmospheric escape rates we applied a soft X-ray and EUV absorption model and a 1-D upper atmosphere hydrodynamic model to a magma ocean-related catastrophically outgassed steam atmosphere with surface pressure values of 52 bar H2O and 11 bar CO2. The estimated impact rates and energy deposition onto an early Martian surface can account for substantial heating. The energy influx and conversion rate into internal energy is most likely sufficient to keep a shallow magma ocean liquid for an extended period of time. Higher surface temperatures keep the outgassed steam atmosphere longer in vapor form and therefore enhance its escape to space within about 0.6 Myr after its formation.
Numerical simulations of the stochastic end stage of planet formation typically begin with a population of embryos and planetesimals that grow into planets by merging. We analyzed the impact parameters of collisions leading to the growth of terrestrial planets from recent $N$-body simulations that assumed perfect merging and calculated more realistic outcomes using a new analytic collision physics model. We find that collision outcomes are diverse and span all possible regimes: hit-and-run, merging, partial accretion, partial erosion, and catastrophic disruption. The primary outcomes of giant impacts between planetary embryos are approximately evenly split between partial accretion, graze-and-merge, and hit-and-run events. To explore the cumulative effects of more realistic collision outcomes, we modeled the growth of individual planets with a Monte Carlo technique using the distribution of impact parameters from $N$-body simulations. We find that fewer planets reached masses $>0.7 M_{rm Earth}$ using the collision physics model compared to simulations that assumed every collision results in perfect merging. For final planets with masses $>0.7 M_{rm Earth}$, 60% are enriched in their core-to-mantle mass fraction by >10% compared to the initial embryo composition. Fragmentation during planet formation produces significant debris ($sim15$% of the final mass) and occurs primarily by erosion of the smaller body in partial accretion and hit-and-run events. In partial accretion events, the target body grows by preferentially accreting the iron core of the projectile and the escaping fragments are derived primarily from the silicate mantles of both bodies. Thus, the bulk composition of a planet can evolve via stochastic giant impacts.
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Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals {rev with radii ranging from 1 to $10^3$,km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter $alpha=10^{-2}$), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent ($alpha=10^{-4}$) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency $x_{filter,MMSN}$ scales with $r^{-7/4}$ (where $r$ is the orbital distance) in the geometric regime, but with $r^{-1/4}$ to $r^{1/4}$ in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesimals by other mechanisms (e.g., orderly growth, capture into vortexes). Further refinement of our work concerns, among other things: a quantitative description of the transition region between the hydro and settling regimes; an assessment of the role of disk turbulence for collisions, in particular in the hydro regime; and the coupling of our model to a planetesimal formation model.
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