Earth and Terrestrial Planet Formation

The growth and composition of Earth is a direct consequence of planet formation throughout the Solar System. We discuss the known history of the Solar System, the proposed stages of growth and how the early stages of planet formation may be dominated by pebble growth processes. Pebbles are small bodies whose strong interactions with the nebula gas lead to remarkable new accretion mechanisms for the formation of planetesimals and the growth of planetary embryos. Many of the popular models for the later stages of planet formation are presented. The classical models with the giant planets on fixed orbits are not consistent with the known history of the Solar System, fail to create a high Earth/Mars mass ratio, and, in many cases, are also internally inconsistent. The successful Grand Tack model creates a small Mars, a wet Earth, a realistic asteroid belt and the mass-orbit structure of the terrestrial planets. In the Grand Tack scenario, growth curves for Earth most closely match a Weibull model. The feeding zones, which determine the compositions of Earth and Venus follow a particular pattern determined by Jupiter, while the feeding zones of Mars and Theia, the last giant impactor on Earth, appear to randomly sample the terrestrial disk. The late accreted mass samples the disk nearly evenly.Comment: Accepted for publication in Early Earth an AGU Monograph edited by James Badro and Michael J. Walte

Planet formation models: the interplay with the planetesimal disc

According to the sequential accretion model, giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. In order to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. We compute the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. We compute the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate mass planets that have not started yet their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have either masses below 10 ME or above several Jupiter masses. To form giant planets before the dissipation of the disc, small planetesimals (~ 0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate mass planets. Other processes must therefore be at work in order to explain the population of extrasolar planets presently known.Comment: Accepted for publication in Astronomy and Astrophysic

Accretion among preplanetary bodies: the many faces of runaway growth

(abridged) When preplanetary bodies reach proportions of ~1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R_0. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion.Comment: Accepted for publication in Icaru

A Massively Parallel Dynamic Programming for Approximate Rectangle Escape Problem

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For $n$ axis-aligned rectangles inside an axis-aligned bounding box $B$, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches $B$ and the density $k$ is minimized, where $k$ is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box $B$. REP is NP-hard for $k>1$. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a $2$-approximation algorithm for SEP with $k\geq2$ with time complexity $O(n^{3/2}k^2)$. This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for $k\geq 3$ is $3/2$ which is tight. We also give a $8$-approximation algorithm for REP with time complexity $O(n\log n+nk)$ and give a MPC version of this algorithm for $k=O(1)$ which is the first parallel algorithm for this problem

Classical Helium Atom with Radiation Reaction

We study a classical model of Helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero--dipole manifold, that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time--evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular with respect to that of Lebesgue.Comment: 16 pages, 3 figure

Investigating the retention of intermediate-mass black holes in star clusters using N-body simulations

Contrary to supermassive and stellar-mass black holes (SBHs), the existence of intermediate-mass black holes (IMBHs) with masses ranging between 10^{2-5} Msun has not yet been confirmed. The main problem in the detection is that the innermost stellar kinematics of globular clusters (GCs) or small galaxies, the possible natural loci to IMBHs, are very difficult to resolve. However, if IMBHs reside in the centre of GCs, a possibility is that they interact dynamically with their environment. A binary formed with the IMBH and a compact object of the GC would naturally lead to a prominent source of gravitational radiation, detectable with future observatories. We use N-body simulations to study the evolution of GCs containing an IMBH and calculate the gravitational radiation emitted from dynamically formed IMBH-SBH binaries and the possibility that the IMBH escapes the GC after an IMBH-SBH merger. We run for the first time direct-summation integrations of GCs with an IMBH including the dynamical evolution of the IMBH with the stellar system and relativistic effects, such as energy loss in gravitational waves (GWs) and periapsis shift, and gravitational recoil. We find in one of our models an intermediate mass-ratio inspiral (IMRI), which leads to a merger with a recoiling velocity higher than the escape velocity of the GC. The GWs emitted fall in the range of frequencies that a LISA-like observatory could detect, like the European eLISA or in mission options considered in the recent preliminary mission study conducted in China. The merger has an impact on the global dynamics of the cluster, as an important heating source is removed when the merged system leaves the GC. The detection of one IMRI would constitute a test of GR, as well as an irrefutable proof of the existence of IMBHs.Comment: Accepted for publication by A&A, minor modification

Heat Transfer in Reactor Scale-Up

Minor temperature rises in lab scale reactions are sometimes not relayed to engineers in charge of scale-up, potentially causing runaway reactions. This project investigated differences in heat transfer between round bottom flasks and industrial sized equipment through research, laboratory experiments, and computer modeling. A non-linear relationship between reactor size and cooling capability was established, and the feasibility of accurate computer modeling was determined

Unraveling the Origins of Nearby Young Stars

A systematic search for close conjunctions and clusterings in the past of nearby stars younger than the Pleiades is undertaken, which may reveal the time, location, and mechanism of formation of these often isolated, disconnected from clusters and star-forming regions, objects. The sample under investigation includes 101 T Tauri, post-TT, and main-sequence stars and stellar systems with signs of youth, culled from the literature. Their Galactic orbits are traced back in time and near approaches are evaluated in time, distance, and relative velocity. Numerous clustering events are detected, providing clues to the origin of very young, isolated stars. Each star's orbit is also matched with those of nearby young open clusters, OB and TT associations and star-forming molecular clouds, including the Ophiuchus, Lupus, Corona Australis, and Chamaeleon regions. Ejection of young stars from open clusters is ruled out for nearly all investigated objects, but the nearest OB associations in Scorpius-Centaurus, and especially, the dense clouds in Ophiuchus and Corona Australis have likely played a major role in the generation of the local streams (TWA, Beta Pic, and Tucana-Horologium) that happen to be close to the Sun today. The core of the Tucana-Horologium association probably originated from the vicinity of the Upper Scorpius association 28 Myr ago. A few proposed members of the AB Dor moving group were in conjunction with the coeval Cepheus OB6 association 38 Myr ago

Rectangular core-collapse supernova remnants: application to Puppis A

Core-collapse supernova remnants are the gaseous nebulae of galactic interstellar media (ISM) formed after the explosive death of massive stars. Their morphology and emission properties depend both on the surrounding circumstellar structure shaped by the stellar wind-ISM interaction of the progenitor star and on the local conditions of the ambient medium. In the warm phase of the Galactic plane (n = 1/cm3, T = 8000 K), an organised magnetic field of strength 7 microG has profound consequences on the morphology of the wind bubble of massive stars at rest. In this paper we show through 2.5D magneto-hydrodynamical simulations, in the context of a Wolf-Rayet-evolving 35 Mo star, that it affects the development of its supernova remnant. When the supernova remnant reaches its middle age (15 to 20 kyr), it adopts a tubular shape that results from the interaction between the isotropic supernova ejecta and the anisotropic, magnetised, shocked stellar progenitor bubble into which the supernova blast wave expands. Our calculations for non-thermal emission, i.e. radio synchrotron and inverse Compton radiation, reveal that such supernova remnants can, due to projection effects, appear as rectangular objects in certain cases. This mechanism for shaping a supernova remnant is similar to the bipolar and elliptical planetary nebula production by wind-wind interaction in the low-mass regime of stellar evolution. If such a rectangular core-collapse supernova remnant is created, the progenitor star must not have been a runaway star. We propose that such a mechanism is at work in the shaping of the asymmetric core-collapse supernova remnant Puppis A.Comment: Accepted at MNRA