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The Relation Between Interstellar Turbulence and Star Formation

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The Relation Between Interstellar Turbulence and Star Formation The Relation between Interstellar Turbulence and Star Formation Ralf Klessen The Relation between Interstellar Turbulence and Star Formation Habilitationsschrift zur Erlangung der venia legendi für das Fach Astronomie an der Universität Potsdam vorgelegt von Ralf S. Klessen aus Landau a. d. Isar (im März 2003) Deutsche Zusammenfassung: Eine der zentralen Fragestellungen der modernen Astrophysik ist es, unser Verständnis für die Bil- dung von Sternen und Sternhaufen in unserer Milchstraße zu erweitern und zu vertiefen. Sterne entstehen in interstellaren Wolken aus molekularem Wasserstoffgas. In den vergangenen zwanzig bis dreißig Jahren ging man davon aus, daß der Prozeß der Sternentstehung vor allem durch das Wechselspiel von gravitativer Anziehung und magnetischer Abstoßung bestimmt ist. Neuere Erken- ntnisse, sowohl von Seiten der Beobachtung als auch der Theorie, deuten darauf hin, daß nicht Mag- netfelder, sondern Überschallturbulenz die Bildung von Sternen in galaktischen Molekülwolken bes- timmt. Diese Arbeit faßt diese neuen Überlegungen zusammen, erweitert sie und formuliert eine neue The- orie der Sternentstehung die auf dem komplexen Wechselspiel von Eigengravitation des Wolken- gases und der darin beobachteten Überschallturbulenz basiert. Die kinetische Energie des turbulen- ten Geschwindigkeitsfeldes ist typischerweise ausreichend, um interstellare Gaswolken auf großen Skalen gegen gravitative Kontraktion zu stabilisieren. Auf kleinen Skalen jedoch führt diese Turbu- lenz zu starken Dichtefluktuationen, wobei einige davon die lokale kritische Masse und Dichte für gravitativen Kollaps überschreiten können. Diese Regionen schockkomprimierten Gases sind es nun, aus denen sich die Sterne der Milchstraße bilden. Die Effizienz und die Zeitskala der Sternentstehung hängt somit unmittelbar von den Eigenschaften der Turbulenz in interstellaren Gaswolken ab. Sterne bilden sich langsam und in Isolation, wenn der Widerstand des turbulenten Geschwindigkeitsfeldes gegen gravitativen Kollaps sehr stark ist. Überwiegt hingegen der Einfluß der Eigengravitation, dann bilden sich Sternen in dichten Gruppen oder Haufen sehr rasch und mit großer Effizienz. Die Vorhersagungen dieser Theorie werden sowohl auf Skalen einzelner Sternentstehungsgebiete als auch auf Skalen der Scheibe unserer Milchstraße als ganzes untersucht. Es zu erwarten, daß proto- stellare Kerne, d.h. die direkten Vorläufer von Sternen oder Doppelsternsystemen, eine hochgradig dynamische Zeitentwicklung aufweisen, und keineswegs quasi-statische Objekte sind, wie es in der Theorie der magnetisch moderierten Sternentstehung vorausgesetzt wird. So muß etwa die Masse- nanwachsrate junger Sterne starken zeitlichen Schwankungen unterworfen sein, was wiederum wichtige Konsequenzen für die statistische Verteilung der resultierenden Sternmassen hat. Auch auf galaktischen Skalen scheint die Wechselwirkung von Turbulenz und Gravitation maßgeblich. Der Prozeß wird hier allerdings noch zusätzlich moduliert durch chemische Prozesse, die die Heizung und Kühlung des Gases bestimmen, und durch die differenzielle Rotation der galaktischen Scheibe. Als wichtigster Mechanismus zur Erzeugung der interstellaren Turbulenz läßt sich die Überlagerung vieler Supernova-Explosionen identifizieren, die das Sterben massiver Sterne begleiten und große Mengen an Energie und Impuls freisetzen. Insgesamt unterstützen die Beobachtungsbefunde auf allen Skalen das Bild der turbulenten, dynamischen Sternentstehung, so wie es in dieser Arbeit ge- zeichnet wird. Summary: Understanding the formation of stars in galaxies is central to much of modern astrophysics. For sev- eral decades it has been thought that the star formation process is primarily controlled by the inter- play between gravity and magnetostatic support, modulated by neutral-ion drift. Recently, however, both observational and numerical work has begun to suggest that supersonic interstellar turbulence rather than magnetic fields controls star formation. This review begins with a historical overview of the successes and problems of both the classical dynamical theory of star formation, and the standard theory of magnetostatic support from both observational and theoretical perspectives. We then present the outline of a new paradigm of star formation based on the interplay between supersonic turbulence and self-gravity. Supersonic turbu- lence can provide support against gravitational collapse on global scales, while at the same time it produces localized density enhancements that allow for collapse on small scales. The efficiency and timescale of stellar birth in Galactic gas clouds strongly depend on the properties of the interstellar turbulent velocity field, with slow, inefficient, isolated star formation being a hallmark of turbulent support, and fast, efficient, clustered star formation occurring in its absence. After discussing in detail various theoretical aspects of supersonic turbulence in compressible self- gravitating gaseous media relevant for star forming interstellar clouds, we explore the consequences of the new theory for both local star formation and galactic scale star formation. The theory pre- dicts that individual star-forming cores are likely not quasi-static objects, but dynamically evolving. Accretion onto these objects will vary with time and depend on the properties of the surrounding turbulent flow. This has important consequences for the resulting stellar mass function. Star for- mation on scales of galaxies as a whole is expected to be controlled by the balance between gravity and turbulence, just like star formation on scales of individual interstellar gas clouds, but may be modulated by additional effects like cooling and differential rotation. The dominant mechanism for driving interstellar turbulence in star-forming regions of galactic disks appears to be supernovae ex- plosions. In the outer disk of our Milky Way or in low-surface brightness galaxies the coupling of rotation to the gas through magnetic fields or gravity may become important. The scientific content of this habilitation thesis is based on the following refereed publications. The corresponding sections of the thesis are indicated in parentheses: ◦ Heitsch, F., M.-M. Mac Low, and R. S. Klessen, 2001, The Astrophysical Journal, 547, 280 – 291: “Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbu- lence” (parts of §§2.1 – 2.6) ◦ Klessen, R. S., 2003, Reviews in Modern Astronomy 16, in press (Ludwig Biermann Lecture, astro- ph/0301381, 33 pages): “Star Formation from Interstellar Clouds” (parts of §1, §§2.3 – 2.6, parts of §6) ◦ Klessen, R. S., 2001, The Astrophysical Journal, 556, 837 – 846: “The Formation of Stellar Clusters: Mass Spectra from Turbulent Fragmentation” (§4.4, §4.7) ◦ Klessen, R. S., 2001, The Astrophysical Journal, 550, L77 – L80: “The Formation of Stellar Clusters: Time Varying Protostellar Accretion Rates” (§4.4, §4.5) ◦ Klessen, R. S., 2000, The Astrophysical Journal, 535, 869 – 886: “One-Point Probability Distribution Functions of Supersonic, Turbulent Flows in Self-Gravitating Media” (§3.2) ◦ Klessen, R. S., and A. Burkert, 2000, The Astrophysical Journal Supplement Series, 128, 287 – 319: “The Formation of Stellar Clusters: Gaussian Cloud Conditions I” (parts of §§4.1 – 4.4) ◦ Klessen, R. S., and A. Burkert, 2001, The Astrophysical Journal, 549, 386 – 401: “The Formation of Stellar Clusters: Gaussian Initial Conditions II” (parts of §§4.1 – 4.4) ◦ Klessen, R. S., and D. N. C. Lin, 2003, Physical Review E, in press: “Diffusion in Supersonic, Turbulent, Compressible Flows” (§3.1) ◦ Klessen, R. S., F. Heitsch, and M.-M. Mac Low, 2000, The Astrophysical Journal, 535, 887 – 906: “Gravitational Collapse in Turbulent Molecular Clouds: I. Gasdynamical Turbulence” (parts of §§2.1 – 2.6, §3.3) ◦ Mac Low, M.-M., and R. S. Klessen, 2003, Reviews of Modern Physics, submitted (astro- ph/0301093, 86 pages): “The Control of Star Formation by Supersonic Turbulence” (parts of §§1, 2, 4 – 6) ◦ Mac Low, M.-M., R. S. Klessen, A. Burkert, M. D. Smith, 1998, Physical Review Letters, 80, 2754 – 2757: “Kinetic Energy Decay Rates of Supersonic and Super-Alfvénic Turbulence in Star- Forming Clouds” (§2.5.1) ◦ Ossenkopf, V., R. S. Klessen, and F. Heitsch, 2001, Astronomy & Astrophysics, 379, 1005 – 1016: “On the Structure of Turbulent Self-Gravitating Molecular Clouds” (§3.4) ◦ Wuchterl, G., and R. S. Klessen, 2001, The Astrophysical Journal, 560, L185 – L188: “The First Million Years of the Sun” (§4.5) 6.44 Nicht `wie' die Welt ist, ist das Mystische, sondern ‘daß’ sie ist. 6.52 Wir fühlen, daß selbst, wenn alle ‘möglichen’ wissenschaftlichen Fragen beantwortet sind, unsere Lebensprobleme noch gar nicht berührt sind. Freilich bleibt dann eben keine Frage mehr; und eben dies ist die Antwort. (Ludwig Wittgenstein, Logisch-Philosophische Abhandlung) meiner Familie gewidmet CONTENTS 1 INTRODUCTION 1 1.1 Overview . 1 1.2 Turbulence . 3 1.3 Outline . 5 2 TOWARDS A NEW PARADIGM 7 2.1 Classical Dynamical Theory . 9 2.2 Problems with Classical Theory . 13 2.3 Standard Theory of Isolated Star Formation . 14 2.4 Problems with Standard Theory . 19 2.4.1 Singular Isothermal Spheres . 19 2.4.2 Observations of Clouds and Cores . 21 2.4.3 Observations of Protostars and Young Stars . 25 2.5 Beyond the Standard Theory . 27 2.5.1 Maintenance of Supersonic Motions . 28 2.5.2 Turbulence in Self-Gravitating Gas . 29 2.5.3 A Numerical Approach . 30 2.5.4 Global Collapse . 30 2.5.5 Local Collapse in Globally Stable Regions . 31 2.5.6 Effects of Magnetic
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