Sternentstehung - Star Formation Sommersemester 2006 Henrik Beuther & Thomas Henning 24.4 Today: Introduction & Overview 1.5 Public Holiday: Tag der Arbeit 8.5 --- 15.5 Physical processes, heating & cooling, cloud thermal structure 22.5 Physical processes, heating & cooling, cloud thermal structure (H. Linz) 29.5 Basic gravitational collapse models I 5.6 Public Holiday: Pfingstmontag 12.6 Basic gravitational collapse models II 19.6 Accretion disks 26.6 Molecular outflow and jets 3.7 Protostellar evolution, the stellar birthline 10.7 Cluster formation and the Initial Mass Function 17.7 Massive star formation, summary and outlook 24.7 Extragalactic star formation More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ss06.html beuther@mpia.de

Summary protostellar evolution The “first core” contracts until temperatures are able to dissociate H2 to H. H-region spreads outward, T and P not high enough to maintain equilibrium, further collapse until H gets collisionally ionized. The dynamically stable protostar has formed. - Accretion luminosity. Definition of low-mass protostar can be “mass-gaining object where the luminosity is dominated by accretion”. - Structure of the protostellar envelope and effects of rotation. - Stellar structure equations: follow numerically the protostellar and then later the pre-main sequence evolution. Convection and deuterium burning. End of protostellar/beginning or pre-main sequence evolution --> birthline. Pre-main sequence evolution in the Hertzsprung-Russel (HR) diagram. Connection of HR diagram with protostellar and pre-main sequence class scheme.

Clusters and the Initial Mass Function (IMF) Msun 32 10 1 0.1 0.01 Muench et al. 2002 Shu et al. 2004

General properties of the IMF Almost all stars form in clusters, isolated star formation is exception. Seminal paper 1955 by E. Salpeter: linear: dN/dM ~ M-2.35 log: d(logN)/d(logM) ~ (logM)-1.35 derived for stars approximately larger than 1Msun. - More detailed current description of the total IMF (e.g., Kroupa 2001): dN/dM ~ M-a with a = 0.3 --> 0.01 ≤ M/Msun ≤ 0.08 (brown dwarf regime) a = 1.3 --> 0.08 ≤ M/Msun ≤ 0.5 a = 2.3 --> 0.5 ≤ M/Msun - Characteristic mass plateau around 0.5 Msun - Upper mass limit of ~ 150Msun - Largely universally valid, in clusters and the field in our Galaxy as well as in the Magellanic Clouds . Shu et al. 2004

Star cluster NGC3603 6 x 6 pc 1 pc diameter 10 000 stars between 0.5 & 120 Msun Stolte et al. 2006

Mass segregation NGC3603 Stolte et al. 2006

Westerlund 1 Brandner et al. 2006

Deviations from the IMF I: Taurus Hartmann 2002 - Taurus: filamentary, more distributed mode of star formation. - The core-mass function already resembles a similar structure. Grey: 12CO Goodwin et al. 2002

Deviations from the IMF II: The Arches cluster Stolte et al. 2005

Cloud mass distributions Orion B South 13CO(2-1) Kramer et al. 1996

Pre-stellar core mass functions I Motte et al. 1998

Pre-stellar core mass functions II Constant T T from Bonnor-Ebert fits M-0.5 M-1.5 Orion B South Johnstone et al. 2006

Gravitational fragmentation Initial Gaussian density fluctuations With the Jeans mass: MJ = 1.0Msun (T/(10K))3/2 (nH2/(104cm-3)-1/2 one can in principal obtain all masses. - Unlikely to be the sole driver for IMF: - Initial conditions have to be very spatial and nearly always the same. - With the usual temperatures and densities, the most massive fragments are hard to produce. Klessen et al. 1998

(Gravo)-turbulent fragmentation I Freely decaying tubulence field Driven turbulence with wave- number k (perturbations l= L/k) Klessen 2001 Low k: large- scale driving High K: small- - Turbulence produces complex network of filaments and interacting shocks. - Converging shock fronts generate clumps of high density. Collapse when the local Jeans-length [lJ = (pat2/Gr0)] gets smaller than the size of fluctuation. - Have to collapse on short time-scale before next shock hits the region. --> Efficiency of star formation depends strongly on the wave-number and strength of the turbulence driving. --> Large-scale less strongly driven turbulence results in clustered mode of star formation. --> Small-scale srong driving results in more low-mass protostars and more isolated star formation.

(Gravo)-turbulent fragmentation II Histogram: Gas clumps Grey: Jeans un- stable clumps Dark: Collapsed core - 2 steps: 1.) Turbulent fragmentation --> 2.) Collapse of individual core Large-scale driving reproduces shape of IMF. However, under discussion whether largest fragments really remain stable or whether they fragment further …

Competetive Accretion - Gas clump first fragments into a large number of clumps with approximately a Jeans mass. Hence fragmentation on smaller scales. Then each clump subsequently accretes gas from the surrounding gas potential. Even gas that was originally far away may finally fall onto the protostar. Bonnell et al. 2004 Distance of gas that is ultimately accreted.

Simulation example SPH simulation. Initial conditions: Uniform density 1000Msun 1pc diameter Temperature 10K

Pre-stellar core mass functions III Motte et al. 2001

General properties (maybe) governing the IMF or fragmentation Rather general agreement that characteristic mass plateau must be due to the original fragmentation processes. At the low-mass end, fragmentation may not be efficient enough and dynamical ejection could help. - Are large, massive fragments stable enough to be responsible for the Salpeter tail of the IMF, or do large clumps further fragments that later competitive accretion sets the masses of the high-mass end? -- Initially, one would expect fragmentation down to the original Jeans-mass at the beginning of collapse. -- However, early accretion luminosity may heat the surrounding gas relatively far out --> This would increase the Jeans-mass and inhibit further fragmentation. --> Not finally solved yet!

Characteristic mass defined by thermal physics Larson 1985 Tempereature variation with increasing density - Jeans mass depends on T: MJ = m1at3/(r01/2G3/2) = 1.0Msun (T/(10K))3/2 (nH2/(104cm-3)-1/2 The number of bound fragments is generally similar to the number of Jeans-masses within the cloud. At low densities, temperature decreases with increasing density, regions can cool efficiently via atomic and molecular line emission. --> decreasing MJ suggests that fragmentation may be favored there. With further increasing density gas thermally couples to dust and clouds become partially optically thick. Cannot cool well enough anymore --> temperature increases again. --> MJ decreases slower, potentially inhibiting much further fragmentation. - Regime with lowest T should then correspond to the preferred scale for fragmentation. The Bonnor-Ebert mass at this point is about 0.5 Msun.

The IMF in extreme environments Stolte et al. 2005 - Low-mass deficiency in Arches cluster near Galactic center. The average densities and temperatures in such an extreme environment close to the Galactic Center are much higher --> Gas and dust couples at higher temperatures. --> Clouds become earlier opaque for own cooling. --> Larger characteristic mass for the fragmentation process!

Clustering around intermediate-mass stars - The clustering increases with the mass of the dominating sources.

Going to high-mass star formation Shirley et al. 2003 Williams et al. 2004 Reid et al. 2005 Beltran et al. 2006 Log[M/Msun] Cumulative mass functions from single-dish surveys of massive star-forming regions resemble Salpeter-IMF. But regions sample evolving clusters?!

Fragmentation of a massive protocluster 12 clumps within each core Integrated masses 98Msun (south) 42Msun (north) --> 80 to 90% of the gas in halo Clump masses 1.7Msun to 25Msun Column densities 1024cm-2 -->Av~1000 Spatial filtering affects only large scale halo on scales >20’’ Assumptions: - All emission peaks of protostellar nature - Same temperature for all clumps (46K, IRAS) Caveats: - Temperature structure - Peaks due to different emission processes, e.g., outflows? Beuther & Schilke 2004

Order of star formation Kumar et al. 2006 - Detection of a large fraction of embedded clusters around young High- Mass Protostellar Objects. Since the detected sources are largely class I and II, and the massive HMPO are still forming, it indicates that low- mass sources may form first and high-mass sources later.

Summary The most widespread mode of star formation is clustered. The IMF is almost universally valid, Salpeter-like for >1Msun, characteristic mass plateau around 0.5Msun. - Mass segregation in clusters. - Hertzsprung-Russel diagrams allow to estimate cluster ages. - Anomalous IMFs (e.g., Taurus or Arches). - Cloud mass distributions versus pre-stellar core mass distributions. - Gravitational fragmentation. - Gravo-turbulent fragmentation. - Competitive accretion. - General features of the IMF. The plateau at 0.5Msun maybe explicable by thermal physics. - High-Mass star formation differences? - Order of star formation.

Sternentstehung - Star Formation Sommersemester 2006 Henrik Beuther & Thomas Henning 24.4 Today: Introduction & Overview 1.5 Public Holiday: Tag der Arbeit 8.5 --- 15.5 Physical processes, heating & cooling, cloud thermal structure 22.5 Physical processes, heating & cooling, cloud thermal structure (H. Linz) 29.5 Basic gravitational collapse models I 5.6 Public Holiday: Pfingstmontag 12.6 Basic gravitational collapse models II 19.6 Accretion disks 26.6 Molecular outflow and jets 3.7 Protostellar evolution, the stellar birthline 10.7 Cluster formation and the Initial Mass Function 17.7 Massive star formation, summary and outlook 24.7 Extragalactic star formation More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ss06.html beuther@mpia.de