1. 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 (E. Schinnerer) More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ss06.html beuther@mpia.de

2. Summary Clusters and the IMF - 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. - 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 0.5M sun maybe explicable by thermal physics. - High-Mass star formation differences? - Order of star formation.

3. 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-Helmhotz 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 10 5.9 L s we find: t KH ~ 11000 yr --> no observable pre-main sequence evolution. - Radiation pressure important constraint.

4. 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 10 38 (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

5. 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 -1. --> 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.

6. Possible ways out - Decrease mass absorption coefficient . - Deviate from spherical symmetry. Disks are known for low-mass star formation. High accretion rates necessary. - Coalescence of low- to intermediate-mass stars at the center of extremely dense massive protoclusters. - Competitive accretion caused by the cluster potential.

7. Change of mass absorption coefficient  Yorke 2004 Wolfire & Cassinelli 1987 -  can be changed if: - radiation field is shifted from optical to far infrared - dust composition changes significantly: - reduce dust-to-gas ratio - reduce grain sizes  : radiative to gravitational acceleration.

8. Accretion rate dependence Wolfire & Cassinelli 1987 Beyond dust destruction radius In spherical gravitational infall gravity governs accretion rate. dM/dt ~ 4πr 2  v with 1/2mv 2 = GMm/r --> v = √2GM/r Hence to overcome the radiation pressure to form more massive stars larger accretion rates are necessary. However Eddington limit sets upper boundary.

9. Turbulent accretion: scaling up low-mass sf - A 100M sun star forms in ~10 5 yrs --> average accretion rate ~10 -3 M sun /yr - Standard low-mass accretion rate: dM/dt ~ c s 3 /G ~ 2x10 -6 M sun /yr. - To form massive stars McKee & Tan (2002, 2003) developed “turbulent core model”, in which massive stars form within gravitationally bound cores supported by turbulence and magnetic fields. --> The turbulent support raises the sound speed c s and hence dM/dt. dM/dt ~ 0.5x10 -3 (M final /30M sun ) 3/4  cl 3/4 (M/M final ) 0.5 [M sun /yr] t ~ 1.3x10 5 (M final /30M sun ) 1/4  cl -3/4 [yr]  cl : cloud surface density ~ 1g cm -2

10. Forming massive accretion disks Yorke & Sonnhalter 2002 - 2D frequency-dependent hydrodynamic simulations reveal that short-wavelength radiation (most effective for radiative acceleration) can escape in the polar directions. Long-wavelength radiation is more or less isotropic. - In these models radiation driven outflows in the polar direction and disks in the equatorial direction are forming. --> These models imply that massive stars may form in a similar fashion as low-mass protostars due to disk accretion. Yorke & Sonnhalter 2002 Other lines: Non-accreting protostars

11. Protostellar cavities reduce radiation pressure Models for different outflow angles and cavity shapes. Black: grav. force Col: rad. force for varying degrees from north (  ) and opening Angles (  0 ) Krumholz et al. 2005 - Protostellar outflows produce cavities which can work as valves releasing large fractions of the radiative pressure. - Away from the outflow cavity, gravity still overwelms radiation.

12. Radiative bubbles and instabilities 1.5x10 4 yr 1.65x10 4 yr 2.0x10 4 yr 21.3M sun 22.4M sun 25.7M sun - 3D radiation hydrodynamic simulations, starting with 100 to 200M sun cores. - First, until approximately 17M sun protostellar mass: smooth accretion flow, low angular momentum gas accretes directly on protostar, high angular momentum gas forms Keplerian accretion disk. - From 17M sun upwards, radiation pressure stars driving out gas, bubbles form. Further infalling gas moves along the bubble walls and falls onto disk. - At ~22M sun bubbles become Rayleigh-Taylor instable and collapse again. This happens when radiation force gets too low and the bubble walls encounter net gravitational force. (Rayleigh-Taylor instabilities naturally occur when heavy fluids (gas) are accelerated by light fluids (radiation).) - Mean accretion rate 2.8x10 -3 M sun /yr - No further fragmentation likely due to the heating from accretion/nuclear L. Krumholz 2005

13. Trapped hypercompact HII regions - Stars >~ 10M sun produce enough UV radiation to ionize the surrounding gas. - Since the temperature of the ionized region is about 100 times larger than that of the molecular gas (10000 vs. 100K), the pressure of the small HII region should be 100 greater as well (P=  a T 2 with a T  √T for ideal gas): --> Expansion of hypercompact HII region could stop accretion. - Possible solution: if size of HCHII region is below sonic radius where the necessary escape speed is larger than thermal sound speed of ionized gas. This can happen if the accretion flow is dense enough that the radius of recombination were smaller than the sonic radius. - Keto (2002, 2003) included gravity in classic expansion models of HCHII regions and found that a steep density gradient and accretion flow can be maintained in the ionized gas confining the HCHII to the required small sizes. Accertion solution Free-fall with n  r -3/2 And hydrostatic equlibrium With n  exp(2r s /r) Sonic point Keto 2002 ionized neutral Sonic point

14. Coalescence and merging Bally & Zinnecker 2005 Bonnell et al. 1998 - Required (proto)stellar densities of the order 10 6 to 10 8 stars per pc 3. - Very explosive events expected. - Collimated outflows and jets can barely survive. - The IMF should have a dip at intermediate masses.

15. 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.

16. Single-dish maps of massive outflows - Early observations claimed different collimation degrees for massive outflows --> different formation? - Then single-dish data taking into distance and spatial resolution were consistent with low-mass outflows. - Outflow-mass scales with core mass. - Many outflow properties scale over many orders of magnitude. - Outflow force implies non-radiative outflow driving. - High outflow rates imply high accretion rates. Force vs. L Outflow rate vs. L Beuther et al. 2002 Wu et al. 2004, 2005

17. Collimated massive jets and outflows Beuther et al. 2002 IRAM 30m data Grey: 1.2mm Contours:CO(2-1)

18. An evolutionary scenario - Outflows are ubiquitous phenomena - Jet-like outflows exists at least up to early-B and late-O-type stars - The observations suggests tentatively an evolutionary scenario

19. Disks in Massive Star Formation Theory: Flattened rotating disk-structure with a Keplerian velocity profile and a mass that is usually dominated by central star. Observation: Velocity gradient perpendicular to the outflow. Offset [‘’] Velocity [km/s] Best current example IRAS20126+4102, Cesaroni et al. 2005 The data imply a 7M sun central source. It may still be in its main accretion phase because L~10 4 L sun can be well explained by accretion Luminosity: L acc = G(dM/dt)M * /R *.

20. The disk-outflow system in Orion-source I

21. Potentially disk-tracing molecules IRAS 20126+4104: CH 3 CN & C 34 S Cesaroni et al. 1997, 1999, 2005 G29.96: HN 13 C(4-3) Beuther et al., in prep. IRAS 18089-1732: HCOOCH 3 Beuther et al. 2004, 2005 IRAS 23151+5912: CH 3 OH v t =1 Beuther et al., in prep. G24.78 & G31.41: CH 3 CN Beltran et al. 2004, 2005 Moment 1 for HN 13 C(4-3)

22. 12 clumps within each core Integrated masses 98M sun (south) 42M sun (north) --> 80 to 90% of the gas in halo Core masses 1.7M sun to 25M sun Column densities 10 24 cm -2 -- >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

23. Hot core chemistry Beuther et al. 2004, 2005

24. Summary - Massive stars are very important for energy budget and nucleosynthesis. - They form exclusively in a clustered mode. - They have very short Kelvin-Helmholtz contraction times and hence no optically observable pre-main sequence evolution. - Large radiation pressure has to be overcome. - Two main proposals: (1) scale up low-mass star formation scenario (turbulent core model) with accretion disks and enhanced accretion rates. (2) Turn more dynamical, competitive accretion, coalescence and merging. - Current observations support the accretion model, collimated outflows and disk-like structures have been found. Fragmentation is also indicative of large, massive bound cores from early on. - No current evidence for coalescence and merging. Seems not necessary but may exist is selected sources. - Current debate largely between “turbulent core” and “competitive accretion” people. Observational discrimination necessary, e.g., are largest fragments stable? Do we find global collapse? - Chemistry interesting additional feature of Hot Molecular Cores.

25. 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 (E. Schinnerer) More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ss06.html beuther@mpia.de