60 research outputs found

### Modeling the Pollution of Pristine Gas in the Early Universe

We conduct a comprehensive theoretical and numerical investigation of the
pollution of pristine gas in turbulent flows, designed to provide new tools for
modeling the evolution of the first generation of stars. The properties of such
Population III (Pop III) stars are thought to be very different than later
generations, because cooling is dramatically different in gas with a
metallicity below a critical value Z_c, which lies between ~10^-6 and 10^-3
solar value. Z_c is much smaller than the typical average metallicity, , and
thus the mixing efficiency of the pristine gas in the interstellar medium plays
a crucial role in the transition from Pop III to normal star formation. The
small critical value, Z_c, corresponds to the far left tail of the probability
distribution function (PDF) of the metallicity. Based on closure models for the
PDF formulation of turbulent mixing, we derive equations for the fraction of
gas, P, lying below Z_c, in compressible turbulence. Our simulation data shows
that the evolution of the fraction P can be well approximated by a generalized
self-convolution model, which predicts dP/dt = -n/tau_con P (1-P^(1/n)), where
n is a measure of the locality of the PDF convolution and the timescale tau_con
is determined by the rate at which turbulence stretches the pollutants. Using a
suite of simulations with Mach numbers ranging from M = 0.9 to 6.2, we provide
accurate fits to n and tau_con as a function of M, Z_c/, and the scale, L_p,
at which pollutants are added to the flow. For P>0.9, mixing occurs only in the
regions surrounding the pollutants, such that n=1. For smaller P, n is larger
as mixing becomes more global. We show how the results can be used to construct
one-zone models for the evolution of Pop III stars in a single high-redshift
galaxy, as well as subgrid models for tracking the evolution of the first stars
in large cosmological simulations.Comment: 37 pages, accepted by Ap

### Turbulence-Induced Relative Velocity of Dust Particles II: The Bidisperse Case

We extend our earlier work on turbulence-induced relative velocity between
equal-size particles (Pan and Padoan, Paper I) to particles of arbitrarily
different sizes. The Pan and Padoan (PP10) model shows that the relative
velocity between different particles has two contributions, named the
generalized shear and acceleration terms, respectively. The generalized shear
term represents the particles' memory of the spatial flow velocity difference
across the particle distance in the past, while the acceleration term is
associated with the temporal flow velocity difference on individual particle
trajectories. Using the simulation of Paper I, we compute the root-mean-square
relative velocity, ^1/2, as a function of the friction times, tau_p1 and
tau_p2, of the two particles, and show that the PP10 prediction is in
satisfactory agreement with the data, confirming its physical picture. For a
given tau_p1 below the Lagrangian correlation time of the flow, T_L, ^1/2
as a function of tau_p2 shows a dip at tau_p2~tau_p1, indicating tighter
velocity correlation between similar particles. Defining a ratio
f=tau_pl/tau_ph, with tau_pl and tau_ph the friction times of the smaller and
larger particles, we find that ^1/2 increases with decreasing f due to the
generalized acceleration contribution, which dominates at f<1/4. At a fixed f,
our model predicts that ^1/2 scales as tau_ph^1/2 for tau_p,h in the
inertial range of the flow, stays roughly constant for T_L <tau_ph < T_L/f, and
finally decreases as tau_ph^-1/2 for tau_ph>>T_L/f. The acceleration term is
independent of the particle distance, r, and thus reduces the r-dependence of
^1/2 in the bidisperse case.Comment: 23 pages, 12 figures, Accepted to Ap

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