The Feedback Effects of Radiation and Protostellar Outflows on High Mass and Low Mass Star Formation Richard I. Klein UC Berkeley, Department of Astronomy and Lawrence Livermore National Laboratory Collaborators Andrew Cunningham (LLNL), Charles Hansen (UC Berkeley), Mark Krumholz (UCSC), Chris McKee (UC Berkeley), Stellar Offner (CFA) LLNL-PRES Frontiers in Computational Astrophysics Lyon, France October 11, 2010

2 Regimes of Importance in Radiation Hydrodynamics We consider 3 regimes of importance:  << 1, (streaming limit, weak coupling)  >> 1,   <<1 (static diffusion limit, strong coupling)  >> 1,   >>1 (dynamic diffusion limit, strong coupling) Dynamic Diffusion : In stellar interior optical depth from core to surface of sun  ~ 10 11, v conv >> c = 0.3 cm s -1 so   >>1 Static Diffusion : Outer accretion disk around a forming massive protostar

3 Regimes continued Specific opacity  /  ~ 1 cm 2 g -1,  ≤ g cm -3 for distances more than a few AU from star For a disk of scale height h ~ 10 AU, optical depth to escape is: The velocity is approximately the Keplerian speed:  The system is in static diffusion   <<1 by ~2 orders of magnitude

4 Outstanding Challenges of Massive Star Formation What is the formation Mechanism: Gravitational collapse of an unstable cloud; Competitive Bondi-Hoyle accretion; Collisional Coalescence? How can gravitationally collapsing clouds overcome the Eddington limit due to radiation pressure? What determines the upper limit for High Mass Stars? (120M sun  150M sun ) How do feedback mechanisms such as protostellar outflows and radiation affect protostellar evolution? These mechanisms can also have a dramatic effect on cluster formation

5 Theoretical Challenges of High Mass Star Formation 1. Effects of Strong Radiation Pressure and Radiative Heating —Massive stars M  20 M  have t K < t form (Shu et al. 1987) and begin nuclear burning during accretion phase Radiates enormous energy For M  100 M  however  dust >>  T But, observations show M ~ 100 M  (Massey 1998, 2003) Fundamental Problem: How is it possible to sustain a sufficiently high-mass accretion rate onto protostellar core despite “Eddington” barrier? Do radiation pressure and radiation heating provide a natural limit to the formation of high mass stars?

6 Theoretical Challenges of High Mass Star Formation (cont.) 2. Effects of Protostellar outflows —Contemporary Massive stars produce strong radiation driven stellar winds with momentum fluxes —Massive YSO have observed (CO) protostellar outflows where (Richer et al. 2000; Cesaroni 2004) If outflows where spherically symmetric this would create a greater obstacle to massive star formation than radiation pressure but, flows are found to be collimated with collimation factors 2-10 (Beuther 2002, 2003, 2004) Fundamental Problem: How do outflows effect the formation of Massive stars? How do outflows interact with radiation from the protostar? Do outflows limit the mass of a star?

7 Equations of Radiation Hydrodynamics ORION-RMHD-AMR Laboratory Frame Equations of Radiation Hydrodynamics (Mihalas & Klein 1982)

8 Equations of Radiation Hydrodynamics Cont. where , v, e and P are the gas density, velocity, specific energy and thermal pressure, and E, F and  are the radiation energy density, flux and pressure tensor (G 0,G) is the radiation four-force density in the Laboratory frame T ,  = —G 

9 Equations of Radiation Hydrodynamics Cont. cG 0 is the rate of energy absorption from the radiation field minus the rate of energy emission for the fluid  time-like component G is the rate of momentum absorption from the radiation field minus the rate of momentum emission  space-like components The radiation four-force to all orders of v/c:

10 Scaling Arguments Simplify Lorentz Transformations Using the pressure tensor with  =  0 and F we can simplify the radiation 4-force density and obtain the transformed 4-force:

11 Mixed Frame Equations of Gravito-Radiation Hydrodynamics to order v/c ( Krumholz, Klein & McKee 2007a) (Continuity) (Gas momentum) (Gas energy) (Poisson) (Radiation energy) (Flux-limited diffusion approximation) Equations exact to (v/c) in static diffusion regime.

12 Formation of a Massive Binary (Krumholz, Klein, McKee, Offner and Cunningham Science, 2009) Gravitational instability in disk  massive binary system 32 M  and 18M  and low mass star 0.1 M  at t= 44 Kyr Radiative feedback from massive binary results in highly asymmetric bubble formation and radiative heating supressing small scale frag.

13 Formation of a Massive Binary System (Krumholz, Klein and McKee, Science, 2009) Observations indicate most massive O-stars have one or more companions; binaries are common (> 59%) Gies 2008 Massive protostellar disks are unstable to fragmentation at R≥ 150AU for M * ≥ 4 M  (Kratter & Matzner 2006) Cores above ~ 20 M  will form a multiple through disk fragmentation. Higher mass systems form binaries earlier in their evolution (Kratter, Matzner and Krumholz 2008) Radiation driven Rayleigh- Taylor instability breaks Eddington Barrier( KKM ‘05, ‘09) Gravitational instability in disk  massive binary system 32 M  and 18 M  and low mass star 0.1 M 

14 Formation of Radiation Driven Bubble and Evolution of Radiative Heating of Protostellar Core

15 Evolution of 100 Solar Mass Turbulent Protostellar Core with Effects of Radiation Feedback on Fragmentation

16 Evolution of 100 Solar Mass Turbulent Isothermal Protostellar Core

17 Feedback Effects of Protostellar Outflows High mass protostars have outflows that look like larger versions of low mass protostellar outflows (Beuther et al. 2004) Outflows are launched inside star’s dust destruction radius Due to high outflow velocities, there is no time for dust grains to regrow inside outflow cavities. Grains reach only ~10 –3  m by the time they escape the core. Because grains are small, outflow cavities are optically thin. Thin cavities can be very effective at collimating protostellar radiation, reducing the radiation pressure force in the equatorial plane Krumholz, McKee & Klein, (2005) using toy Monte-Carlo radiative transfer calculations find outflows cause a factor of 5 – 10 radiation pressure force reduction Outflows may be responsible for driving turbulence in clumps

18 HMSF with Protostellar Outflows: Late Time Evolution t= 60 kyr (Cunningham, Klein, McKee and Krumholz 2010, ApJ to be submitted) 52 M  accreted through disk to protostellar system; 30% ejected into outflow wind  reduction in radiation forces in disk results in protostar still building mass Final evolution results in a massive primary with 35 M  and a massive secondary with > 17 M  Each has a protostellar disk of 4.5 M  and 2.9 M  respectively

19 HMSF with Protostellar Outflows in Turbulent Core : (Cunningham, Klein, McKee and Krumholz 2010, ApJ) Early evolution t= 12.8 Kyr results in a massive primary with 13.5 M  and a secondary with 2.3 M  forming in a highly asymmetric turbulent disk Outflow has large dynamical affect in sweeping out wide region of turbulent core as wind becomes entrained in turbulent filaments  Outflow cools core relieving radiation pressure resulting in formation of high mass star

20 Radiation Feedback, Fragmentation and Environmental Dependence of the IMF (Krumholz,Cunningham, Klein & McKee ApJ, 2010) Column densities L= 0.1, M=1.0, H=10.0 g cm -2 (Diffuse clouds such as Taurus, Perseus and Ophiuchus; typical galactic massive star forming regions; extra-galactic super star clusters) Surface density determines effectiveness of trapping radiation and accretion luminosities of forming stars (Krumholz, McKee 2008) As surface density increases, the suppression of fragmentation increases  (L) small cluster, no massive stars, depleted disks; (M) massive binary with 2 circumstellar disks and large circumbinary disk; (H) single large disk with single massive star  Higher surface density environments produce higher accretion rates and thus higher accretion luminosities from embedded protostars. Higher  environments lead to higher optical depths which trap resulting radiation more effectively

21 Cumulative Distribution Function of Stellar Mass t= 0.6 t ff (Krumholz, Cunningham, Klein & McKee ApJ 2010) (L) system consists of several low mass stars of roughly comparable mass; (M) most of mass in 2 stars forming binary; (H) comparable fraction of mass in single massive star

22 HMSF with Protostellar Outflows in Turbulent Core: Environmental Effects (Cunningham, Klein, McKee and Krumholz 2010) We consider the evolution of high mass cores with protostellar outflows with  = 0.25, 1.0, 2.0, 10.0 contrasted with no wind for  = 2.0 Lower density cases are less heated; inefficient trapping of radiation results in higher fragmentation, greater structure in disk and higher rate of multiplicity scale: (0.1r cloud ) 2 Comparison of wind (col 3) vs no wind (col 5) for  = 2.0 g cm -2 shows that winds reduce thermal support in disk resulting in unstable spiral disk structure; No wind case has more stable, coherent disk formation

23 Environmental Effects on Radiation Beaming in HMSF in a Turbulent Core (Cunningham, Klein, McKee and Krumholz 2010) Radiation beaming is most collimated for  = 10 g cm -2 where cavity is well confined  pole to equator contrast ≈ 7 (consistent with KKM 2005) For less dense cores, beaming effect is diminished. Flashlight effect is destroyed as core becomes more depleted by strong dynamical effects of winds in low density environments

24 Cumulative Distribution Function of Stellar Mass with Protostellar Outflows t= 0.5 t ff Lower surface density cases have a less concentrated gravitational potential and therefore show slower accretion per unit of free fall time than higher surface density which have a higher SFR High surface density  = 10 lacks a secondary companion. Lower surface density cores fragment to produce a secondary with greater than 1 M  Transition to high mass star formation appears to be shifted toward  =.25

25 Radiative Feedback in Low Mass Star Formation (Offner, Klein, McKee, Krumholz ApJ 2009) To assess effects of radiation on the formation of low mass stars we perform comparative simulations with RT including radiative transfer and feedback from stellar sources and simulations with an EOS to describe thermal evolution of the gas Initial conditions: 3D turbulent cloud with  mach = 6.6 and  ≈ 1 T i = 10K; L= 0.65 pc; = 4.46 x 10 —20 g cm —3 ; M total = 185 M  Turbulence continues to be driven with constant energy injection rate for one global free fall time ~ Myr Calculations performed with 2 resolutions and multiple levels of grid refinement (AMR): effective resolution where  x = 32 AU and 65,536 3 with  x = 2 AU

26 Cluster Formation in Driven Turbulent Cloud with Radiation Feedback show Local Environs Affected within 0.05 pc Column densityDensity weighted temperature Radiation pressure effects not significant anywhere in cloud since advection of radiation enthalpy is small compared to rate of radiation diffusion Star formation commences at t~.50 t ff T = K variation in cloud

27 Heating Rate due to Protostellar Sources, Viscous Dissipation and Compresion At t = 0 only source of heating is due to turbulent motions Viscous dissipation dominates heating prior to star formation After star formation commences protostellar output and accretion luminosity rather than compression and viscous dissipation is responsible for majority of radiative feedback At t ~ 1 t ff H proto > 10 H visc ; H proto ~ 10 3 H comp

28 Stellar Mass Distribution of Star-disk System at 1t ff Large temperature range in the RT simulation has profound effect on stellar mass distribution Increased thermal support in protostellar disk acts to suppress gravitational disk instability and secondary fragmentation In the core Protostellar disks in the NRT simulation suffer high rates of fragmentation  SFR ff (NRT) = 13% SFR ff (RT) = 7% good agreement observations ( Krumholz and Tan 2007 )

29 Low Mass Cluster Formation with Radiation and Protostellar Outflow Feedback (Hansen, Klein, McKee 2010) If a weak wind shock interacts with an already fragmenting filament, it will lead to more fragmentation If it interacts with a marginally gravitationally bound filament, it can initiate collapse If it interacts with a low density filament, the extra compression can eventually lead to more fragmentation when that filament finally does collapse If a strong shock hits a filament, it can move a mass of gas away and then that can collapse. Winds interacting with filaments lead to enhanced star formation Lower mass stars form due to enhanced fragmentation and outflow loss results in lower luminosities and lower heating  less thermal support so higher fragmentation  = 6.5 L  ; Lmed = 1.7 L  Obser. ~ 5.3 L  ; Lmed ~ 1.5 L  C2D sample Dunham, Evans 2010

30 Velocity Dispersion of Gas in Low Mass Cluster Formation with Protostellar Outflows: Where Does the Wind Deposit energy? With winds, low density gas is accelerated to higher velocities than high density Winds deposit enough energy to prevent the turbulent decay of high density gas  maintains a fairly constant Mach number Without winds, infalling dense gas surrounding most massive stars speeds up due to steepening of gravitational potential well No WindsWinds

31 Stellar Mass Distribution: Effect of Protostellar Outflows Protostellar outflows in low mass clusters result in shift toward larger production of low mass stars IMF Wind outflowIMF No outflow

32 Conclusions High Mass Star Formation 3-D high resolution Rad-Hydro AMR simulations with ORION demonstrate: Two new mechanisms to overcome radiation pressure barrier to achieve high mass star formation  high mass binary system —3-D Rayleigh-Taylor instabilities in radiation driven bubbles appear to be important in allowing accretion onto protostellar core —Protostellar outflows resulting in optically thin cavities promote focusing of radiation and reduction of radiation pressure  enhances accretion —Radiation feedback from accreting protostars inhibits fragmentation (KKM 2007) —Outflows dynamically effect larger volume of core and may result in lower ∑ threshold Low Mass Star Formation —Inclusion of RT has a profound effect on temperature distribution, accretion and final stellar masses —Heating by RT stabilizes protostellar disks and suppresses small scale frag —Vast majority of heating from protostellar Rad. Not comp or visc. dissipation —For low mass SF, heating is local so, no inhibition of Turb. Frag. Elsewhere —Outflows interact with filaments enhancing small scale multiplicity High surface density environments produce higher accretion rates and higher accretion luminosities as well as more effective trapping of radiation  higher efficiency in Massive Star Formation