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.