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Theory of Star Formation ANRV320-AA45-13 ARI 16 June 2007 20:24 V I E E W R S First published online as a Review in Advance on June 25, 2007 I E N C N A D V A Theory of Star Formation Christopher F. McKee1 and Eve C. Ostriker2 1Departments of Physics and Astronomy, University of California, Berkeley, California 94720; email: [email protected] 2Department of Astronomy, University of Maryland, College Park, Maryland 20742; email: [email protected] Annu. Rev. Astron. Astrophys. 2007. 45:565–686 Key Words The Annual Review of Astrophysics is online at accretion, galaxies, giant molecular clouds, gravitational collapse, astro.annualreviews.org HII regions, initial mass function, interstellar medium, jets and This article’s doi: outflows, magnetohydrodynamics, protostars, star clusters, 10.1146/annurev.astro.45.051806.110602 turbulence Copyright c 2007 by Annual Reviews. All rights reserved Abstract 0066-4146/07/0922-0565$20.00 We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating overdensities to initiate gravita- tional contraction or collapse, and countering the effects of gravity in these overdense regions. The key dynamical processes involved in star formation—turbulence, magnetic fields, and self-gravity— are highly nonlinear and multidimensional. Physical arguments are used to identify and explain the features and scalings involved in star formation, and results from numerical simulations are used to quantify these effects. We divide star formation into large-scale and by University of California - Berkeley on 07/26/07. For personal use only. small-scale regimes and review each in turn. Large scales range from galaxies to giant molecular clouds (GMCs) and their substructures. Annu. Rev. Astro. Astrophys. 2007.45. Downloaded from arjournals.annualreviews.org Important problems include how GMCs form and evolve, what de- termines the star formation rate (SFR), and what determines the initial mass function (IMF). Small scales range from dense cores to the protostellar systems they beget. We discuss formation of both low- and high-mass stars, including ongoing accretion. The devel- opment of winds and outflows is increasingly well understood, as are the mechanisms governing angular momentum transport in disks. Although outstanding questions remain, the framework is now in place to build a comprehensive theory of star formation that will be tested by the next generation of telescopes. 565 ANRV320-AA45-13 ARI 16 June 2007 20:24 1. INTRODUCTION Stars are the “atoms” of the universe, and the problem of how stars form is at the nexus of much of contemporary astrophysics. By transforming gas into stars, star formation determines the structure and evolution of galaxies. By tapping the nuclear energy in the gas left over from the Big Bang, it determines the luminosity of galaxies and, quite possibly, leads to the reionization of the Universe. Most of the elements—including those that make up the world around us—are formed in stars. Finally, the process of star formation is inextricably tied up with the formation and early evolution of planetary systems. The problem of star formation can be divided into two broad categories: mi- crophysics and macrophysics. The microphysics of star formation deals with how individual stars (or binaries) form. Do stars of all masses acquire most of their mass via gravitational collapse of a single dense core? How are the properties of a star or binary determined by the properties of the medium from which it forms? How does the gas that goes into a protostar lose its magnetic flux and angular momentum? How do massive stars form in the face of intense radiation pressure? What are the properties of the protostellar disks, jets, and outflows associated with young stellar objects (YSOs), and what governs their dynamical evolution? The macrophysics of star formation deals with the formation of systems of stars, ranging from clusters to galaxies. How are giant molecular clouds (GMCs), the loci of most star formation, themselves formed out of diffuse interstellar gas? What processes determine the distribution of physical conditions within star-forming regions, and why does star formation occur in only a small fraction of the available gas? How is the rate at which stars form determined by the properties of the natal GMC or, on a larger scale, of the interstellar medium (ISM) in a galaxy? What determines the mass distribution of forming stars, the initial mass function (IMF)? Most stars form in clusters (Lada & Lada 2003); how do stars form in such a dense environment and in the presence of enormous radiative and mechanical feedback from other YSOs? Many of these questions, particularly those related to the microphysics of star formation, were discussed in the classic review by Shu, Adams & Lizano (1987). Much has changed since then. Observers have made enormous strides in characterizing star formation on all scales and in determining the properties of the medium from which by University of California - Berkeley on 07/26/07. For personal use only. stars form. Aided by powerful computers, theorists have been able to numerically model the complex physical and chemical processes associated with star formation in Annu. Rev. Astro. Astrophys. 2007.45. Downloaded from arjournals.annualreviews.org three dimensions. Perhaps most important, a new paradigm has emerged, in which large-scale, supersonic turbulence governs the macrophysics of star formation. This review focuses on the advances made in star formation since 1987, with an emphasis on the role of turbulence. Recent relevant reviews include those on the physics of star formation (Larson 2003), and on the role of supersonic turbulence in star formation (Mac Low & Klessen 2004, Ballesteros-Paredes et al. 2007). The re- view by Zinnecker & Yorke (2007, in this volume) provides a different perspective on high-mass star formation, while that by Bergin & Tafalla (2007, in this volume) gives a more detailed description of dense cores just prior to star formation. Because the topic is vast, we must necessarily exclude a number of relevant topics from this review: 566 McKee · Ostriker ANRV320-AA45-13 ARI 16 June 2007 20:24 primordial star formation (see Bromm & Larson 2004), planet formation, astrochem- istry, the detailed physics of disks and outflows, radiative transfer, and the properties of YSOs. We begin with an overview of the basic processes and scales in turbulent, self-gravitating, magnetized media, and we then review both the macrophysics and the microphysics of star formation. 2. BASIC PHYSICAL PROCESSES 2.1. Turbulence As emphasized in Section 1, many of the advances in the theory of star formation since the review by Shu, Adams & Lizano (1987) have been based on realistic evalua- tion and incorporation of the effects of turbulence. Turbulence is in fact important in essentially all branches of astrophysics that involve gas dynamics, and many commu- nities have contributed to the recent progress in understanding and characterizing turbulence in varying regimes. [Chandrasekhar (1949) presaged this development, in choosing the then-new theory of turbulence as the topic of his Henry Norris Russell prize lecture. Here, we concentrate on the parameter regimes of turbulence applica- ble within the cold interstellar medium (ISM), and the physical properties of these flows that appear particularly influential for controlling star formation. Our discussion provides an overview only; pointers are given to excellent recent reviews that summarize the large and growing literature on this subject. General refer- ences include Frisch (1995), Biskamp (2003), and Falgarone & Passot (2003). A much more extensive literature survey and discussion of interstellar turbulence, including both diffuse-ISM and dense-ISM regimes, is presented by Elmegreen & Scalo (2004) and Scalo & Elmegreen (2004). A recent review focusing on the detailed physics of turbulent cascades in magnetized plasmas is Schekochihin & Cowley (2005). 2.1.1. Spatial correlations of velocity and magnetic fields. Turbulence is defined by the Oxford English Dictionary as a state of “violent commotion, agitation, or disturbance,” with a turbulent fluid further defined as one “in which the velocity at any point fluctuates irregularly.” Although turbulence is, by definition, an irregular state of motion, a central concept is that order nevertheless persists as scale-dependent by University of California - Berkeley on 07/26/07. For personal use only. spatial correlations among the flow variables. These correlations can be measured in many ways; common mathematical descriptions include autocorrelation functions, Annu. Rev. Astro. Astrophys. 2007.45. Downloaded from arjournals.annualreviews.org structure functions, and power spectra. One of the most fundamental quantities, which is also one of the most intuitive to understand, is the root mean square (RMS) velocity difference between two points separated by a distance r. With the velocity structure function of order p defined ≡| − + |p ≡ 1/2 as Sp (r) v(x) v(x r) , this quantity is given as v(r) [S2(r)] . The autocorrelation function of the velocity is related to the structure function: A(r) ≡ · + =||2− / v(x) v(x r) v S2(r) 2; note that the autocorrelation with zero lag is =||2 = ≡| |2 A(0) v ,asS2(0) 0. The power spectrum of velocity, P(k) v(k) ,is the Fourier transform of the autocorrelation function. For zero mean velocity, the 3 2 velocity dispersion averaged over a volume , σv() , is equal to the power spectrum www.annualreviews.org • Theory of Star Formation 567 ANRV320-AA45-13 ARI 16 June 2007 20:24 = π/ integrated with kmin 2 . If turbulence is isotropic and the system in which it is observed is spatially symmetric with each dimension ≈, then the 1D velocity dispersion along a given line of sight√ (a direct observable) will be related to the 3D velocity dispersion by σ = σv()/ 3. Analogous structure functions, correlation functions, and power spectra can also be defined for the magnetic field, as well as other fluid variables including the density (see Section 2.1.4).
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