The cooling of shock-compressed primordial gas

We find that at redshifts z > 10, HD line cooling allows strongly-shocked primordial gas to cool to the temperature of the cosmic microwave background (CMB). This temperature is the minimum value attainable via radiative cooling. Provided that the abundance of HD, normalized to the total number density, exceeds a critical level of ~ 10^{-8}, the CMB temperature floor is reached in a time which is short compared to the Hubble time. We estimate the characteristic masses of stars formed out of shocked primordial gas in the wake of the first supernovae, and resulting from the mergers of dark matter haloes during hierarchical structure formation to be ~ 10 M_{solar}. In addition, we show that cooling by HD enables the primordial gas in relic H II regions to cool to temperatures considerably lower than those reached via H_2 cooling alone. We confirm that HD cooling is unimportant in cases where the primordial gas does not go through an ionized phase, as in the formation process of the very first stars in z ~ 20 minihaloes of mass ~ 10^{6} M_{solar}.Comment: 10 pages, 10 figures, accepted for publication in MNRAS with minor revisions, new table adde

Uncovering The Chemical Signature Of The First Stars In The Universe

The chemical abundance patterns observed in metal-poor Galactic halo stars contain the signature of the first supernovae, and thus allow us to probe the first stars that formed in the universe. We construct a theoretical model for the early chemical enrichment history of the Milky Way, aiming in particular at the contribution from pair-instability supernovae (PISNe). These are a natural consequence of current theoretical models for primordial star formation at the highest masses. However, no metal-poor star displaying the distinct PISN signature has yet been observed. We here argue that this apparent absence of any PISN signature is due to an observational selection effect. Whereas most surveys traditionally focus on the most metal-poor stars, we predict that early PISN enrichment tends to "overshoot,'' reaching enrichment levels of [Ca/H] similar or equal to -2.5 that would be missed by current searches. We utilize existing observational data to place constraints on the primordial initial mass function (IMF). The number fraction of PISNe in the primordial stellar population is estimated to be 90%) contribution from PISNe is merely similar to 10(-4) to 5 x 10(-4). The corresponding fraction of stars formed from gas exclusively enriched by PISNe is a factor of similar to 4 smaller. With the advent of next-generation telescopes and new, deeper surveys, we should be able to test these predictions.NSF AST 07-08795Astronom

Towards the First Galaxies

The formation of the first galaxies at redshifts z~10-15 signaled the transition from the simple initial state of the universe to one of ever increasing complexity. We here review recent progress in understanding their assembly process with numerical simulations, starting with cosmological initial conditions and modelling the detailed physics of star formation. In particular, we study the role of HD cooling in ionized primordial gas, the impact of UV radiation produced by the first stars, and the propagation of the supernova blast waves triggered at the end of their brief lives. We conclude by discussing promising observational diagnostics that will allow us to probe the properties of the first galaxies, such as their contribution to reionization and the chemical abundance pattern observed in extremely low-metallicity stars.Comment: 12 pages, 14 figures, appeared in "First Stars III", eds. B. O'Shea, A. Heger and T. Abel, a high resolution version (highly recommended) can be found at http://www.ita.uni-heidelberg.de/~tgreif/files/gjb07.pd

Two New Bounds on the Random-Edge Simplex Algorithm

We prove that the Random-Edge simplex algorithm requires an expected number of at most 13n/sqrt(d) pivot steps on any simple d-polytope with n vertices. This is the first nontrivial upper bound for general polytopes. We also describe a refined analysis that potentially yields much better bounds for specific classes of polytopes. As one application, we show that for combinatorial d-cubes, the trivial upper bound of 2^d on the performance of Random-Edge can asymptotically be improved by any desired polynomial factor in d.Comment: 10 page

Stochasticity & Predictability in Terrestrial Planet Formation

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This is a result of the chaotic evolution of trajectories which are highly sensitive to minuscule displacements. We determine that differences between systems evolved from virtually identical initial conditions can be larger than the differences between systems evolved from very different initial conditions. This implies that individual simulations lack predictive power. For example, there is not a reproducible mapping between the initial and final surface density profiles. However, some key global properties can still be extracted if the statistical spread across many simulations is considered. Based on these spreads, we explore the collisional growth and orbital properties of terrestrial planets which assemble from different initial conditions (we vary the initial planetesimal distribution, planetesimal masses, and giant planet orbits). Confirming past work, we find that the resulting planetary systems are sculpted by sweeping secular resonances. Configurations with giant planets on eccentric orbits produce fewer and more massive terrestrial planets on tighter orbits than those with giants on circular orbits. This is further enhanced if the initial mass distribution is biased to the inner regions. In all cases, the outer edge of the system is set by the final location of the $\nu_6$ resonance and we find that the mass distribution peaks at the $\nu_5$ resonance. Using existing observations, we find that extrasolar systems follow similar trends. Although differences between our numerical modelling and exoplanetary systems remain, we suggest that CoRoT-7, HD 20003, and HD 20781 may host undetected giant planets.Comment: replaced to match published version, 20 pages, 11 figures, published in MNRAS, simulation outputs available at https://cheleb.net/astro/sp15

High capacity associative memory with bipolar and binary, biased patterns

The high capacity associative memory model is interesting due to its significantly higher capacity when compared with the standard Hopfield model. These networks can use either bipolar or binary patterns, which may also be biased. This paper investigates the performance of a high capacity associative memory model trained with biased patterns, using either bipolar or binary representations. Our results indicate that the binary network performs less well under low bias, but better in other situations, compared with the bipolar network.Peer reviewe