46 research outputs found
Driven waves in a two-fluid plasma
We study the physics of wave propagation in a weakly ionised plasma, as it
applies to the formation of multifluid, MHD shock waves. We model the plasma as
separate charged and neutral fluids which are coupled by ion-neutral friction.
At times much less than the ion-neutral drag time, the fluids are decoupled and
so evolve independently. At later times, the evolution is determined by the
large inertial mismatch between the charged and neutral particles. The neutral
flow continues to evolve independently; the charged flow is driven by and
slaved to the neutral flow by friction. We calculate this driven flow
analytically by considering the special but realistic case where the charged
fluid obeys linearized equations of motion. We carry out an extensive analysis
of linear, driven, MHD waves. The physics of driven MHD waves is embodied in
certain Green functions which describe wave propagation on short time scales,
ambipolar diffusion on long time scales, and transitional behavior at
intermediate times. By way of illustration, we give an approximate solution for
the formation of a multifluid shock during the collision of two identical
interstellar clouds. The collision produces forward- and reverse J shocks in
the neutral fluid and a transient in the charged fluid. The latter rapidly
evolves into a pair of magnetic precursors on the J shocks, wherein the ions
undergo force free motion and the magnetic field grows monotonically with time.
The flow appears to be self similar at the time when linear analysis ceases to
be valid.Comment: 18 pages including 24 figures, accepted by MNRA
Multifluid, Magnetohydrodynamic Shock Waves with Grain Dynamics II. Dust and the Critical Speed for C Shocks
This is the second in a series of papers on the effects of dust on
multifluid, MHD shock waves in weakly ionized molecular gas. We investigate the
influence of dust on the critical shock speed, v_crit, above which C shocks
cease to exist. Chernoff showed that v_crit cannot exceed the grain
magnetosound speed, v_gms, if dust grains are dynamically well coupled to the
magnetic field. We present numerical simulations of steady shocks where the
grains may be well- or poorly coupled to the field. We use a time-dependent,
multifluid MHD code that models the plasma as a system of interacting fluids:
neutral particles, ions, electrons, and various ``dust fluids'' comprised of
grains with different sizes and charges. Our simulations include grain inertia
and grain charge fluctuations but to highlight the essential physics we assume
adiabatic flow, single-size grains, and neglect the effects of chemistry. We
show that the existence of a phase speed v_phi does not necessarily mean that C
shocks will form for all shock speeds v_s less than v_phi. When the grains are
weakly coupled to the field, steady, adiabatic shocks resemble shocks with no
dust: the transition to J type flow occurs at v_crit = 2.76 v_nA, where v_nA is
the neutral Alfven speed, and steady shocks with v_s > 2.76 v_nA are J shocks
with magnetic precursors in the ion-electron fluid. When the grains are
strongly coupled to the field, v_crit = min(2.76 v_nA, v_gms). Shocks with
v_crit < v_s < v_gms have magnetic precursors in the ion-electron-dust fluid.
Shocks with v_s > v_gms have no magnetic precursor in any fluid. We present
time-dependent calculations to study the formation of steady multifluid shocks.
The dynamics differ qualitatively depending on whether or not the grains and
field are well coupled.Comment: 43 pages with 17 figures, aastex, accepted by The Astrophysical
Journa
Transient evolution of C-type shocks in dusty regions of varying density
Outflows of young stars drive shocks into dusty, molecular regions. Most
models of such shocks assume that they are steady and propagating perpendicular
to the magnetic field. Real shocks often violate both of these assumptions and
the media through which they propagate are inhomogeneous. We use the code
employed previously to produce the first time-dependent simulations of
fast-mode, oblique C-type shocks interacting with density perturbations. We
include a self-consistent calculation of the thermal and ionisation balances
and a fluid treatment of grains. We identify features that develop when a
multifluid shock encounters a density inhomogeneity to investigate whether any
part of the precursor region ever behaves in a quasi-steady fashion. If it does
the shock may be modelled approximately without solving the time-dependent
hydromagnetic equations. Simulations were made for initially steady oblique
C-type shocks encountering density inhomogeneities. For a semi-finite
inhomogeneity with a density larger than the surrounding medium, a transmitted
shock evolves from being J-type to a steady C-type shock on a timescale
comparable to the ion-flow time through it. A sufficiently upstream part of the
precursor of an evolving J-type shock is quasi-steady. The ion-flow timescale
is also relevant for the evolution of a shock moving into a region of
decreasing density. The models for shocks propagating into regions in which the
density increases and then decreases to its initial value cannot be entirely
described in terms of the results obtained for monotonically increasing and
decreasing densities. For the latter model, the long-term evolution to a C-type
shock cannot be approximated by quasi-steady models.Comment: 11 pages, 9 figure
Turbulent Control of the Star Formation Efficiency
Supersonic turbulence plays a dual role in molecular clouds: On one hand, it
contributes to the global support of the clouds, while on the other it promotes
the formation of small-scale density fluctuations, identifiable with clumps and
cores. Within these, the local Jeans length \Ljc is reduced, and collapse
ensues if \Ljc becomes smaller than the clump size and the magnetic support
is insufficient (i.e., the core is ``magnetically supercritical''); otherwise,
the clumps do not collapse and are expected to re-expand and disperse on a few
free-fall times. This case may correspond to a fraction of the observed
starless cores. The star formation efficiency (SFE, the fraction of the cloud's
mass that ends up in collapsed objects) is smaller than unity because the mass
contained in collapsing clumps is smaller than the total cloud mass. However,
in non-magnetic numerical simulations with realistic Mach numbers and
turbulence driving scales, the SFE is still larger than observational
estimates. The presence of a magnetic field, even if magnetically
supercritical, appears to further reduce the SFE, but by reducing the
probability of core formation rather than by delaying the collapse of
individual cores, as was formerly thought. Precise quantification of these
effects as a function of global cloud parameters is still needed.Comment: Invited review for the conference "IMF@50: the Initial Mass Function
50 Years Later", to be published by Kluwer Academic Publishers, eds. E.
Corbelli, F. Palla, and H. Zinnecke
Star Formation in Cold, Spherical, Magnetized Molecular Clouds
We present an idealized, spherical model of the evolution of a magnetized
molecular cloud due to ambipolar diffusion. This model allows us to follow the
quasi-static evolution of the cloud's core prior to collapse and the subsequent
evolution of the remaining envelope. By neglecting the thermal pressure
gradients in comparison with magnetic stresses and by assuming that the ion
velocity is small compared with the neutral velocity, we are able to find exact
analytic solutions to the MHD equations. We show that, in the case of a
centrally condensed cloud, a core of finite mass collapses into the origin
leaving behind a quasi-static envelope, whereas initially homogeneous clouds
never develop any structure in the absence of thermal stresses, and collapse as
a whole. Prior to the collapse of the core, the cloud's evolution is
characterized by two phases: a long, quasi-static phase where the relevant
timescale is the ambipolar diffusion time (treated in this paper), and a short,
dynamical phase where the characteristic timescale is the free-fall time. The
collapse of the core is an "outside-in" collapse. The quasi-static evolution
terminates when the cloud becomes magnetically supercritical; thereafter its
evolution is dynamical, and a singularity develops at the origin-a protostar.
After the initial formation of the protostar, the outer envelope continues to
evolve quasi-statically, while the region of dynamical infall grows with
time-an "inside-out" collapse. We use our solution to estimate the magnetic
flux trapped in the collapsing core and the mass accretion rate onto the newly
formed protostar. Our results agree, within factors of order unity, with the
numerical results of Fiedler & Mouschovias (1992) for the physical quantities
in the midplane ofComment: 18 postscript figures Accepted by The Astrophysical Journa
Control of star formation by supersonic turbulence
Understanding the formation of stars in galaxies is central to much of modern
astrophysics. For several decades it has been thought that stellar birth is
primarily controlled by the interplay between gravity and magnetostatic
support, modulated by ambipolar diffusion. Recently, however, both
observational and numerical work has begun to suggest that support by
supersonic turbulence rather than magnetic fields controls star formation. In
this review we outline a new theory of star formation relying on the control by
turbulence. We demonstrate that although supersonic turbulence can provide
global support, it nevertheless produces density enhancements that allow local
collapse. Inefficient, isolated star formation is a hallmark of turbulent
support, while efficient, clustered star formation occurs in its absence. The
consequences of this theory are then explored for both local star formation and
galactic scale star formation. (ABSTRACT ABBREVIATED)Comment: Invited review for "Reviews of Modern Physics", 87 pages including 28
figures, in pres
Self-Similar Collapse of Nonrotating Magnetic Molecular Cloud Cores
We obtain self-similar solutions that describe the gravitational collapse of
nonrotating, isothermal, magnetic molecular cloud cores. We use simplifying
assumptions but explicitly include the induction equation, and the semianalytic
solutions we derive are the first to account for the effects of ambipolar
diffusion following the formation of a central point mass. Our results
demonstrate that, after the protostar first forms, ambipolar diffusion causes
the magnetic flux to decouple in a growing region around the center. The
decoupled field lines remain approximately stationary and drive a hydromagnetic
C-shock that moves outward at a fraction of the speed of sound (typically a few
tenths of a kilometer per second), reaching a distance of a few thousand AU at
the end of the main accretion phase for a solar-mass star. We also show that,
in the absence of field diffusivity, a contracting core will not give rise to a
shock if, as is likely to be the case, the inflow speed near the origin is
nonzero at the time of point-mass formation. Although the evolution of
realistic molecular cloud cores will not be exactly self-similar, our results
reproduce the main qualitative features found in detailed core-collapse
simulations (Ciolek & Konigl 1998)Comment: 25 pages, 3 figures, AASTeXv4.0 Accepted for publication in The
Astrophysical Journa