Overview:
Protostellar Outflows and Feedback Effects in Stellar Cluster Formation
[My talk transparencies]
[McKee's
ITP talk]
[Technical overview]
Background
The formation of stars is a basic unsolved problem of astrophysics,
especially since our understanding of the evolution of galaxies is
limited by our ignorance of star formation. Models for star formation
are continually being challenenged by new observations and numerical
simulations. It is clear that stars form from dense regions inside
self-gravitating molecular clouds in the disk of the
Galaxy. These clouds appear to be supported in part by magnetic
forces, and in part by internal turbulence. This turbulence decays
rapidly, so it must be continually regenerated -- unless the clouds
are entirely transient, a topic of much recent debate.
Young stars have been implicated as sources of energy for the
turbulence. As they form, stars emit collimated, jet-like winds that
impact the gas around them and cast it into motion. The more massive
stars have more violent effects: faster winds, ionizing radiation, and
after a few million years, supernova explosions.
Theories for star formation have traditionally concentrated on the
formation of a single, isolated, low-mass star: its origin as an
overdense region within a molecular cloud; its gradual condensation as
magnetic flux leaks out of it (in the process of ambipolar diffusion),
and its eventual collapse into a star-disk system. Other investigators
have modeled the launching and collimation of a wind from the surface
or inner edge of a magnetized accretion disk.
Observations have increasingly demonstrated that stars are born in
crowded clusters, in the densest regions -- clumps
-- within molecular clouds. Star formation is therefore part of a
complex ecology, one that involves the formation of molecular clouds,
the generation and decay of turbulent motions in the magnetized gas,
the creation, condensation and collapse of the cores that
precede individual stars or binaries. All of these processes are
affected by the influence that forming stars have on the surrounding
gas, especially considering that stars form in such proximity. Which
elements of this interaction are necessary for a successful theory for
the structures and sizes of molecular clouds, for the types of stellar
clusters that emerge from them, and for the efficiency and rapidity of
star formation?
Chris McKee, my PhD
advisor, has advanced a
model for low-mass star formation in normal molecular clouds. In
this theory, the seepage of gas through the magnetic field is
regulated by the level of ionization. Stars cannot form until magnetic
flux is lost, and this only happens quickly in regions that are
shielded from ionizing light: so, star formation is regulated by the
column density of cloud gas. As stars accrete matter, winds carry away
excess angular momentum; these winds stir up the turbulent motions in
the cloud, which otherwise would die away. Since these turbulent
motions play a significant role in supporting the cloud against
gravity, the cloud as a whole achieves an equilibrium like a
star's, with the energy input from star formation balancing the
dissipation of turbulent support. This energy feedback, first proposed
in a model by
Norman and Silk, is tied in McKee's theory directly to the
cloud radius by the retarding effect of ionization on star
formation. This theory successfully explains the fact that molecular
clouds
exhibit a very narrow range of column densities, and make stars
quite
slowly compared to the maximum rate allowed by gravity.
McKee and Frank Bertoldi have
since been elaborating on this model. In order to investigate the
clustering of stars, for instance, it was necessary to apply the model
to dense clumps within a molecular cloud as well as the clouds as a
whole. However, they have realized that deviations from equilibrium
may be important, especially if a dense stellar cluster is to be
formed. To address this problem they suggested a plan of attack for
the analysis of dynamical effects in star cluster formation; here my
involvement began.
Our Project
In order to follow this plan, I found that it would be necessary to
make a detailed model for the bipolar
molecular outflows driven by protostellar winds. This led me into
an investigation of the collimation
of hydromagnetic winds from accretion disks, and the motions of the
shells of gas they sweep up. We were able to show that outflow driven
by an asymptotically force-free, magnetized wind has many of the characteristics
observed in protostellar outflows, in a broad class of ambient gas
distributions, regardless of the detailed history of the driving wind.
(Our analysis of disk winds was motivated by comments in a
1997 paper by Eve Ostriker, who informs us that she has arrived at
some of the same conclusions independently, in unpublished work.) See
our
ApJ Letter for more details on this work. For a more general explanation
why magnetized winds naturally lead to the mass-velocity relationship
commonly observed
in molecular outflows, see my proceedings for the
2000 Cargese conference on stellar clusters.
This model for protostellar outflows makes specific
predictions for the rate at which gas will be ejected
from, and energy will be injected into, the star-forming
clump. These predictions are compatible with
observations of star-forming regions, and with previous
theoretical constraints on what values the star formation
efficiency might take. See Matzner & McKee
(2000 ApJ v.545) for the theory of the rate of gas disruption by
outflows, and for a comparison to existing observations (and previous
theories).
A forming star's wind affects not only its siblings' formation,
but its
own. Close to the wind axis, infalling material is beaten
backward; however, the wind cannot entirely shut off accretion, as it
is fed by the flow of material through the accretion disk. Our model
for this process, which relies on the
theory for magnetized cores developed by Zhi-Yun
Li and Frank Shu, predicts that protostellar winds regulate the efficiency
with which an unstable core can collapse to form a star; however,
ultimately, the stellar mass is determined by the size of the initial
core. For this reason, the core mass function is reflected in the
stellar initial mass function with very little change in slope. Our
conclusions therefore resemble those of
Nakano, Hasegawa, & Norman, except that we derive significanlty
higher efficiencies because we account for the collimation of the
stellar wind (and possible flattening of the magnetized core). Our theory is
distinctly different from a number of other
models found
in the literature;
the differences should have observational consequences that will
allow it to be tested.
The original motivation for this project, as described above, is to
study the effect of protostellar outflows on the evolution of a
stellar cluster-forming clump. This requires an investigation of the
dynamics of such a system:
the gas; its internal magnetic field and turbulent support; turbulent
decay; star formation; and the effects of protostellar winds,
turbulent re-generation and gas expulsion. I incorporated these
elements into a suite of numerical models in the last chapter of my
thesis. As my goal was to investigate in gross detail the dynamics of
the star-gas system, I considered only a spherical, non-rotating
clump, and included a number of contributing terms (such as the
gravitational potential of the embedded stars) in an approximate
manner. However, using the virial equation as an equation of motion, I
was able to explore for which conditions the system tends to sit
stably near its equilibrium (as assumed by
McKee 1989 and
Bertoldi & McKee 1996), for which it undergoes overstable
oscillations, and for which it becomes unstable to collapse. Two
components appear to dominate this behavior: the rapidity of turbulent
decay (fast decay leads to collapse), and the "noise" introduced by
the discreteness of star formation. For further explanation, go to the
technical
overview on this subject.