Effects of Varying the Three-Body Molecular Hydrogen Formation Rate in Primordial Star Formation

The transformation of atomic hydrogen to molecular hydrogen through three-body reactions is a crucial stage in the collapse of primordial, metal-free halos, where the first generation of stars (Population III stars) in the Universe are formed. However, in the published literature, the rate coefficient for this reaction is uncertain by nearly an order of magnitude. We report on the results of both adaptive mesh refinement (AMR) and smoothed particle hydrodynamics (SPH) simulations of the collapse of metal-free halos as a function of the value of this rate coefficient. For each simulation method, we have simulated a single halo three times, using three different values of the rate coefficient. We find that while variation between halo realizations may be greater than that caused by the three-body rate coefficient being used, both the accretion physics onto Population III protostars as well as the long-term stability of the disk and any potential fragmentation may depend strongly on this rate coefficient.Comment: 29 pages, 7 figures; Accepted for publication in The Astrophysical Journa

Long-term follow-up of patients with chronic musculoskeletal pain attending interdisciplinary pain rehabilitation:outcomes and predictive factors

The long-term outcomes of interdisciplinary pain rehabilitation (IPR) in patients with chronic musculoskeletal pain (CMP) and its predictors has been studied to a limited extent. In this historical cohort study, functioning, satisfaction with life domains, and pain were assessed at baseline, discharge, and at 6-15 years follow-up. At follow-up, most patients (77%) rated the effects of the IPR as temporarily or persistently positive. The gains in functioning, satisfaction with life domains, and pain made during IPR remained for 6-15 years after the IPR. Patients who were single, retired, or not in work, and those having higher pain and lower functioning at baseline, had lower functioning at follow-up, while patients with traumatic pain disorders had higher functioning at follow-up. Gains made during IPR, particularly gains in social and mental functioning and in pain predicted functioning at follow-up. Treatments and events between discharge and follow-up also influenced the long-term outcome. In conclusion, on average, outcomes achieved during IPR persisted at long-term follow-up. Predictors of a better long-term outcome were mainly baseline characteristics

Simulations on a Moving Mesh: The Clustered Formation of Population III Protostars

The cosmic dark ages ended a few hundred million years after the Big Bang, when the first stars began to fill the universe with new light. It has generally been argued that these stars formed in isolation and were extremely massive - perhaps 100 times as massive as the Sun. In a recent study, Clark and collaborators showed that this picture requires revision. They demonstrated that the accretion disks that build up around Population III stars are strongly susceptible to fragmentation and that the first stars should therefore form in clusters rather than in isolation. We here use a series of high-resolution hydrodynamical simulations performed with the moving mesh code AREPO to follow up on this proposal and to study the influence of environmental parameters on the level of fragmentation. We model the collapse of five independent minihalos from cosmological initial conditions, through the runaway condensation of their central gas clouds, to the formation of the first protostar, and beyond for a further 1000 years. During this latter accretion phase, we represent the optically thick regions of protostars by sink particles. Gas accumulates rapidly in the circumstellar disk around the first protostar, fragmenting vigorously to produce a small group of protostars. After an initial burst, gravitational instability recurs periodically, forming additional protostars with masses ranging from ~ 0.1 to 10 M_sun. Although the shape, multiplicity, and normalization of the protostellar mass function depend on the details of the sink-particle algorithm, fragmentation into protostars with diverse masses occurs in all cases, confirming earlier reports of Population III stars forming in clusters. Depending on the efficiency of later accretion and merging, Population III stars may enter the main sequence in clusters and with much more diverse masses than are commonly assumed.Comment: 21 pages, 17 figures, accepted for publication in Ap

The First Stars: Mass Growth Under Protostellar Feedback

We perform three-dimensional cosmological simulations to examine the growth of metal-free, Population III (Pop III) stars under radiative feedback. We begin our simulation at z=100 and trace the evolution of gas and dark matter until the formation of the first minihalo. We then follow the collapse of the gas within the minihalo up to densities of n = 10^12 cm^-3, at which point we replace the high-density particles with a sink particle to represent the growing protostar. We model the effect of Lyman-Werner (LW) radiation emitted by the protostar, and employ a ray-tracing scheme to follow the growth of the surrounding H II region over the next 5000 yr. We find that a disk assembles around the first protostar, and that radiative feedback will not prevent further fragmentation of the disk to form multiple Pop III stars. Ionization of neutral hydrogen and photodissociation of H_2 by LW radiation leads to heating of the dense gas to several thousand Kelvin, and this warm region expands outward at the gas sound speed. Once the extent of this warm region becomes equivalent to the size of the disk, the disk mass declines while the accretion rate onto the protostars is reduced by an order of magnitude. This occurs when the largest sink has grown to ~ 20 M_sol while the second sink has grown to 7 M_sol, and we estimate the main sink will approach an asymptotic value of ~ 30 M_sol by the time it reaches the main sequence. Our simulation thus indicates that the most likely outcome is a massive Pop III binary. However, we simulate only one minihalo, and the statistical variation between minihaloes may be substantial. If Pop III stars were typically unable to grow to more than a few tens of solar masses, this would have important consequences for the occurence of pair-instability supernovae in the early Universe as well as the Pop III chemical signature in the oldest stars observable today.Comment: 21 pages, 11 figures, to appear in MNRA

The first stars: formation of binaries and small multiple systems

We investigate the formation of metal-free, Population III (Pop III), stars within a minihalo at z ~ 20 with a smoothed particle hydrodynamics (SPH) simulation, starting from cosmological initial conditions. Employing a hierarchical, zoom-in procedure, we achieve sufficient numerical resolution to follow the collapsing gas in the center of the minihalo up to number densities of 10^12 cm^-3. This allows us to study the protostellar accretion onto the initial hydrostatic core, which we represent as a growing sink particle, in improved physical detail. The accretion process, and in particular its termination, governs the final masses that were reached by the first stars. The primordial initial mass function (IMF), in turn, played an important role in determining to what extent the first stars drove early cosmic evolution. We continue our simulation for 5000 yr after the first sink particle has formed. During this time period, a disk-like configuration is assembled around the first protostar. The disk is gravitationally unstable, develops a pronounced spiral structure, and fragments into several other protostellar seeds. At the end of the simulation, a small multiple system has formed, dominated by a binary with masses ~ 40 M_Sun and ~ 10 M_Sun. If Pop III stars were to form typically in binaries or small multiples, the standard model of primordial star formation, where single, isolated stars are predicted to form in minihaloes, would have to be modified. This would have crucial consequences for the observational signature of the first stars, such as their nucleosynthetic pattern, and the gravitational-wave emission from possible Pop III black-hole binaries.Comment: Accepted to MNRAS. New section with new figure added. 18 pages, 13 figures. Supplementary material and high resolution version at http://www.as.utexas.edu/~minerva

Rotation Speed of the First Stars

We estimate the rotation speed of Population III (Pop III) stars within a minihalo at z ~ 20 using a smoothed particle hydrodynamics (SPH) simulation, beginning from cosmological initial conditions. We follow the evolution of the primordial gas up to densities of 10^12 cm^-3. Representing the growing hydrostatic cores with accreting sink particles, we measure the velocities and angular momenta of all particles that fall onto these protostellar regions. This allows us to record the angular momentum of the sinks and estimate the rotational velocity of the Pop III stars expected to form within them. The rotation rate has important implications for the evolution of the star, the fate encountered at the end of its life, and the potential for triggering a gamma-ray burst (GRB). We find that there is sufficient angular momentum to yield rapidly rotating stars (> 1000 km s^-1, or near break-up speeds). This indicates that Pop III stars likely experienced strong rotational mixing, impacting their structure and nucleosynthetic yields. A subset of them was also likely to result in hypernova explosions, and possibly GRBs.Comment: 14 pages, 7 figures, accepted for publication in MNRA

Rotation and Internal Structure of Population III Protostars

We analyze the cosmological simulations performed in the recent work of Greif et al. (2012), which followed the early growth and merger history of Pop III stars while resolving scales as small as 0.05 R_sol. This is the first set of cosmological simulations to self-consistently resolve the rotation and internal structure of Pop III protostars. We find that Pop III stars form under significant rotational support which is maintained for the duration of the simulations. The protostellar surfaces spin from ~50% to nearly 100% of Keplerian rotational velocity. These rotation rates persist after experiencing multiple stellar merger events. In the brief time period simulated (~ 10 yr), the protostars show little indication of convective instability, and their properties furthermore show little correlation with the properties of their host minihaloes. If Pop III protostars within this range of environments generally form with high degrees of rotational support, and if this rotational support is maintained for a sufficient amount of time, this has a number of crucial implications for Pop III evolution and nucleosynthesis, as well as the possibility for Pop III pair-instability supernovae, and the question of whether the first stars produced gamma-ray bursts.Comment: 19 pages, 12 figures, to appear in MNRA

Star Formation in the First Galaxies I: Collapse Delayed by Lyman-Werner Radiation

We investigate the process of metal-free star formation in the first galaxies with a high-resolution cosmological simulation. We consider the cosmologically motivated scenario in which a strong molecule-destroying Lyman-Werner (LW) background inhibits effective cooling in low-mass haloes, delaying star formation until the collapse or more massive haloes. Only when molecular hydrogen (H2) can self-shield from LW radiation, which requires a halo capable of cooling by atomic line emission, will star formation be possible. To follow the formation of multiple gravitationally bound objects, at high gas densities we introduce sink particles which accrete gas directly from the computational grid. We find that in a 1 Mpc^3 (comoving) box, runaway collapse first occurs in a 3x10^7 M_sun dark matter halo at z~12 assuming a background intensity of J21=100. Due to a runaway increase in the H2 abundance and cooling rate, a self-shielding, supersonically turbulent core develops abruptly with ~10^4 M_sun in cold gas available for star formation. We analyze the formation of this self-shielding core, the character of turbulence, and the prospects for star formation. Due to a lack of fragmentation on scales we resolve, we argue that LW-delayed metal-free star formation in atomic cooling haloes is very similar to star formation in primordial minihaloes, although in making this conclusion we ignore internal stellar feedback. Finally, we briefly discuss the detectability of metal-free stellar clusters with the James Webb Space Telescope.Comment: 22 pages, 1 new figure, accepted for publication in MNRA

Laurent inversion

There are well-understood methods, going back to Givental and Hori--Vafa, that to a Fano toric complete intersection X associate a Laurent polynomial f that corresponds to X under mirror symmetry. We describe a technique for inverting this process, constructing the toric complete intersection X directly from its Laurent polynomial mirror f. We use this technique to construct a new four-dimensional Fano manifold

Effect of Population III Multiplicity on Dark Star Formation

We numerically study the mutual interaction between dark matter (DM) and Population III (Pop III) stellar systems in order to explore the possibility of Pop III dark stars within this physical scenario. We perform a cosmological simulation, initialized at z ~ 100, which follows the evolution of gas and DM. We analyze the formation of the first minihalo at z ~ 20 and the subsequent collapse of the gas to densities of 10^12 cm^-3. We then use this simulation to initialize a set of smaller-scale `cut-out' simulations in which we further refine the DM to have spatial resolution similar to that of the gas. We test multiple DM density profiles, and we employ the sink particle method to represent the accreting star-forming region. We find that, for a range of DM configurations, the motion of the Pop III star-disk system serves to separate the positions of the protostars with respect to the DM density peak, such that there is insufficient DM to influence the formation and evolution of the protostars for more than ~ 5000 years. In addition, the star-disk system causes gravitational scattering of the central DM to lower densities, further decreasing the influence of DM over time. Any DM-powered phase of Pop III stars will thus be very short-lived for the typical multiple system, and DM will not serve to significantly prolong the life of Pop III stars.Comment: 16 pages, 11 figures, to appear in MNRA