Star and Planet Formation Sommer term 2007 Henrik Beuther & Sebastian Wolf 16.4 Introduction (H.B. & S.W.) 23.4 Physical processes, heating and cooling, radiation transfer (H.B.) 30.4 Gravitational collapse & early protostellar evolution I (H.B.) 07.5 Gravitational collapse & early protostellar evolution II (H.B.) 14.5 Protostellar and pre-main sequence evolution (H.B.) 21.5 Outflows and jets (H.B.) 28.5 Pfingsten (no lecture) 04.6 Clusters, the initial mass function (IMF), massive star formation (H.B.) 11.6 Protoplanetary disks: Observations + models I (S.W.) 18.6 Gas in disks, molecules, chemistry, keplerian motions (H.B.) 25.6 Protoplanetary disks: Observations + models II (S.W.) 02.7 Accretion, transport processes, local structure and stability (S.W.) 09.7 Planet formation scenarios (S.W.) 16.7 Extrasolar planets: Searching for other worlds (S.W.) 23.7 Summary and open questions (H.B. & S.W.) More Information and the current lecture files: and s:

Summary outflows HH211, Gueth et al Force vs. L

Clusters and the Initial Mass Function (IMF) M sun Muench et al Shu et al. 2004

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

Star cluster NGC x 6 pc 1 pc diameter stars between 0.5 & 120 M sun Stolte et al. 2006

Mass segregation NGC3603 Stolte et al. 2006

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

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

Pre-stellar core mass functions Motte et al. 1998

Pre-stellar core mass functions II Johnston et al Orion B South Constant TT from Bonnor-Ebert fits M -0.5 M -1.5

Gravitational fragmentation Klessen et al Initial Gaussian density fluctuations - With the Jeans mass:  M J = 1.0M sun (T/(10K)) 3/2 (n H2 /(10 4 cm -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.

(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- scale driving - Turbulence produces complex network of filaments and interacting shocks. - Converging shock fronts generate clumps of high density. - Collapse when the local Jeans-length  J = (  a t 2 /G  0 )] 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 - 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 … Histogram: Gas clumps Grey: Jeans un- stable clumps Dark: Collapsed core

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 Distance of gas that is ultimately accreted.

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

General properties (maybe) governing the IMF or fragmentation or fragmentation - 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! - 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.

Characteristic mass defined by thermal physics Larson 1985 Tempereature variation with increasing density - At low densities, temperature decreases with increasing density, regions can cool efficiently via atomic and molecular line emission. --> decreasing M J suggests that fragmentation may be favoured there. - With further increasing density gas thermally couples to dust and clouds become partially optically thick. Cannot cool well enough anymore --> temperature increases again. --> M J 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 M sun. - Jeans mass depends on T: M J = m 1 a t 3 /(  0 1/2 G 3/2 ) = 1.0M sun (T/(10K)) 3/2 (n H2 /(10 4 cm -3 ) -1/2 - The number of bound fragments is generally similar to the number of Jeans-masses within the cloud.

The IMF in extreme environments - 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! Stolte et al. 2005

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

12 clumps within each core Integrated masses 98M sun (south) 42M sun (north) --> 80 to 90% of the gas in halo Clump masses 1.7M sun to 25M sun Column densities cm >A v ~1000 Spatial filtering affects only large scale halo on scales >20’’ Fragmentation of a massive protocluster 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 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.

Massive Star Formation - Why important? - Although few in numbers, L  M 3 they inject significant amounts of energy into ISM during their lifetime (outflows, radiation, supernovae). - They produce all the heavy elements. - Low-mass star formation is strongly influenced by massive stars. - Massive stars exclusively form in clusters. - Short Kelvin-Helmholtz contraction time: t KH =3x10 7 yr (M * /1M s ) 2 (R * /1R s ) -1 (L * /1L s ) -1 For 60M s, 12R s and L s we find: t KH ~ yr --> no observable pre-main sequence evolution. - Radiation pressure important constraint.

Eddington luminosity and limit The Eddington luminosity/limit gives the upper limit on the luminosity a star can have before it becomes unstable and blows away the gas again. - Assumptions: spherical symmetry and fully ionized hydrogen. --> Radiation exerts force mainly on free electrons via Thomson scattering  T =(q 2 /mc 2 ) 2 (q: charge, m: mass particle) - Outward radial force equals rate at which electron absorbs momentum:  T S/c (S: energy flux) --> In effect radiation pushes out electron-proton pairs against total gravitational force GM(m p +m e )/r 2 = GMm p /r 2 - With the flux S = L/4πr 2, the force equilibrium is: GMm p /r 2 =  T L/(4πr 2 c) --> The Eddington luminosity: L Edd = 4πGMc (m p /  T ) = 4πGMc/   (with  =  T /m p mass abs. coefficient) = 1.3 x (M/M sun ) erg/s or L edd [L sun ] ~ 3 x 10 4 (M/M sun ) - If L > L edd then - accretion stops if L provided by accretion - Gas layers pushed out and star unstable if provided by nuclear fusion. - Scaling relations for massive (proto)stars: L  M a with 2<a<4

Radiation pressure - In contrast now the radiation pressure of the central massive (proto)star on the surrounding dust cocoon. Same relation: L/M = 4πGc/   (  : mass abs. Coefficient) - While  is very low for the fully ionized H plasma (  ~0.3cm 2 g -1 ), at the dust destruction front (T~1500K) it is considerably larger with  ~10cm 2 g > L/M ~ 10 3 [L sun /M sun ] --> In spherical symmetric accretion models, accretion is expected to stop as soon as the luminosity is approximately 1000 times larger than the mass of the protostar. --> No problem for low-mass star formation. --> The critical ratio is reached for stars of approximately 11M sun. Since more massive stars are know, the assumption of spherical accretion has to be wrong and other processes are needed.

Two competing massive star formation scenarios Modified low-mass star formation: - Increase accretion rates a few orders of mag. - 2D disk geometry helps accretion processes. - Radiation pressure can escape through outflow cavities --> flashlight effect Wolfire & Cassinelli 1987, Jijina & Adams 1996, Yorke & Sonnhalter 2002, Norberg & Maeder 2002, Keto 2002, 2003, Krumholz et al. 2005, Banerjee & Pudritz 2005 Coalescence and competetive accretion: - Massive stars form only in clusters. - The cluster potential favours accretion toward objects in the cluster centers. - All kinds of protostellar entities may merge. Bonnell et al. 1998, 2004, 2004, 2007, Stahler et al. 2000, Bally & Zinnecker 2005 Pudritz & Banerjee 2005 Bally & Zinnecker 2005 Bonnell et al How to differentiate between both scenarios? - Molecular outflows and accretion disks. - Fragmentation and global collapse.

Summary - The most widespread mode of star formation is clustered. - The IMF is almost universally valid, Salpeter-like for >1M sun, characteristic mass plateau around 0.5M sun. - Mass segregation in clusters. - Cloud mass distributions versus pre-stellar core mass distributions. - Gravitational fragmentation. - Gravo-turbulent fragmentation. - Competitive accretion. - General features of the IMF. The plateau at 0.5M sun maybe explicable by thermal physics. - Order of star formation. - High-Mass star formation - Importance - Problems - Possible solutions

Star and Planet Formation Sommer term 2007 Henrik Beuther & Sebastian Wolf 16.4 Introduction (H.B. & S.W.) 23.4 Physical processes, heating and cooling, radiation transfer (H.B.) 30.4 Gravitational collapse & early protostellar evolution I (H.B.) 07.5 Gravitational collapse & early protostellar evolution II (H.B.) 14.5 Protostellar and pre-main sequence evolution (H.B.) 21.5 Outflows and jets (H.B.) 28.5 Pfingsten (no lecture) 04.6 Clusters, the initial mass function (IMF), massive star formation (H.B.) 11.6 Protoplanetary disks: Observations + models I (S.W.) 18.6 Gas in disks, molecules, chemistry, keplerian motions (H.B.) 25.6 Protoplanetary disks: Observations + models II (S.W.) 02.7 Accretion, transport processes, local structure and stability (S.W.) 09.7 Planet formation scenarios (S.W.) 16.7 Extrasolar planets: Searching for other worlds (S.W.) 23.7 Summary and open questions (H.B. & S.W.) More Information and the current lecture files: and s: