Star Cluster Formation and the Origin of Stellar Properties. Matthew Bate University of Exeter

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1 Star Cluster Formation and the Origin of Stellar Properties Matthew Bate University of Exeter

2 Typical molecular cloud (Bate et al. 2003) Denser cloud (Bate & Bonnell 2005) Jeans mass 1 M, Opacity limit 3 MJ, P(k)k -4 Jeans mass 1/3 M

3 Stellar Masses - Dependence on Initial Conditions Typical Initial Conditions 9 Times Denser Cloud Opacity-limited Minimum Mass 3 Times Greater Large-scale Turbulence P(k)k -6 Characteristic stellar mass depends on the cloud s mean Jeans mass (Bate & Bonnell 2005) Denser/cooler clouds produce more brown dwarfs and low-mass stars

4 What is the Origin of the IMF? Jeans Mass Ejection Competitive Accretion

5 Bate 2009a: 500 M cloud with decaying turbulence, 35 million SPH particles Follows binaries to 1 AU, discs to ~10 AU Forms 1253 stars and brown dwarfs - best statistics to date from a single calculation

6 Multiplicity as a Function of Primary Mass Multiplicity fraction = (B+T+Q) / (S+B+T+Q) Observations: Close et al. 2003; Basri & Reiners 2006; Fisher & Marcy 1992; Duquennoy & Mayor 1991; Preibisch et al. 1999; Mason et al. 1998

7 Star/VLM Object Separation Distributions Stars: binary, triple, quad separations Median separation: 26 AU VLM objects: binaries, triples, quads Median separation: 10 AU

8 Stellar Mass Distribution Competitive accretion/ejection gives Salpeter-type slope at high-mass end Low-mass turn over ~4 times as many brown dwarfs as a typical star-forming region Not due to sink particle approximation - results almost identical for different sink parameters

9 Additional Physics Star cluster simulations with radiative transfer (Bate 2009b) Radiative feedback dramatically decreases the amount of fragmentation Magnetic fields Star formation simulations (Price & Bate 2007) Magnetic fields inhibit gravitationally unstable discs and binary formation Substantially reduces the ratio of brown dwarfs to stars, in agreement with observations Removes the dependence of the characteristic stellar mass on the cloud s initial Jeans mass Star cluster simulations (Price & Bate 2008) Magnetic fields reduce the amount of fragmentation and the star formation rate Radiation magnetohydrodynamical simulations Star cluster simulations (Price & Bate 2009) Strong magnetic fields (plasma beta <1) and radiative feedback can give low star formation rates similar to those inferred from observations

10 Star Cluster Formation with Radiative Feedback Repeat Bate, Bonnell & Bromm 2003, Bate & Bonnell M molecular clouds, Decaying `turbulence P(k)k -4 Diameters 0.4 pc and 0.2 pc, Mean thermal Jeans masses 1 M and 1/3 M 3,500,000 SPH particles Sink particles Original calculations: Sink Radii 5 AU, gravity softened within 4 AU Radiative transfer calculations: Sink Radii 0.5 AU, no gravitational softening Radiative transfer No feedback from protostars Intrinsic protostellar luminosity unimportant Gives a lower limit on the effects of radiative feedback Accretion luminosity underestimated (energy liberated from 0.5 AU to stellar surface)

11 BBB2003: Typical molecular cloud Jeans mass 1 M, Opacity limit 3 MJ, P(k)k -4 BBB2003, but with Radiative Transfer

12 BBB2003: Typical cloud: Jeans mass 1 M, P(k)k -4 with Radiative Transfer Log Column Density Mass weight temperature (Log K)

13 Log Column Density BB2005: Dense cloud: Jeans mass 1/3 M, P(k)k -4 with Radiative Transfer Mass weight temperature (Log K)

14 Radiative Feedback and the IMF Radiative feedback reduces the number of objects by factors of 3-5 Radiative feedback brings the star to brown dwarf ratio in line with observations Observations suggest a ratio of 5 ± 2 Chabrier 2003; Greissl et al. 2007; Luhman 2007; Andersen et al Simulations: 25:5 ~ 5 Furthermore, dependence of the IMF on cloud density is removed K-S test on the two IMFs with radiative feedback shows them to be indistinguishable

15 The Apparent Invariance of the IMF Bate 2009b In the absence of stellar feedback, cloud fragments into objects separated by Jeans length Jeans length and Jeans mass smaller for denser clouds But, heating of the gas surrounding a newly-formed protostar inhibits nearby fragmentation Effectively increases the effective Jeans length and Jeans mass Effective Jeans length and Jeans mass increases by a larger fraction in denser clouds Show that this effective Jeans mass depends very weakly on cloud density Low-density Cloud Higher-density Cloud

16 Large-scale Simulations with Radiative Feedback Currently re-running Bate (2009a) with radiative feedback 500 M cloud, using 35,000,000 SPH particles Resolves opacity limit for fragmentation Follows: Results so far All binaries (0.02 AU) and discs to ~1 AU radius Recently reached 1.14 initial cloud free-fall times Formed 145 stars and brown dwarfs Original calculation at the same time: 403 stars and brown dwarfs

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19 Large-scale Simulations with Radiative Feedback Comparison of the IMFs obtained without and with radiative feedback Confirms Bate (2009b), Offner et al. (2009) Many fewer brown dwarfs Much better statistics

20 Large-scale Simulations with Radiative Feedback Multiplicity as a function of primary mass Smaller numbers so far, but consistent with observations If anything, multiplicities are somewhat higher with radiative feedback

21 Radiation Magnetohydrodynamical Simulations Price & Bate (2009) Hydrodynamical Mass-to-flux ratio: 10 Mass-to-flux ratio: 5 Mass-to-flux ratio: 3 Upper panels: Without radiative feedback Lower panels: With radiative feedback

22 Star Formation Rate Star formation rate decreases with Increasing magnetic field strength Radiative feedback Observationally Evans et al Spitzer c2d survey, 5 clouds ~3-6% SFR/t ff Numerical results 10-32% SFR/t ff Strongest field, with radiative feedback ~10% SFR/t ff

23 Conclusions Hydrodynamical/sink particle simulations Statistics now good enough that meaningful comparison can be made with observations Reasonable multiplicity, separation, eccentricity distributions Too many brown dwarfs, too few unequal mass stellar binaries Radiative feedback has a huge effect, even for low-mass star formation Inhibits fragmentation of discs and filaments near existing protostars Solves the over-production of brown dwarfs Removes or severely weakens the dependence of the IMF on the cloud s mean Jeans mass Magnetic fields have a significant effect on large-scales Strong magnetic fields (plasma beta ~1) Can produce large-scale voids and magnetic structures in the gas Decrease the star formation efficiency, bringing it into line with observational estimates Do not seem to alter stellar masses greatly; rather decrease rate at which objects form

24 The Future: Self-gravitating radiation magnetohydrodynamical simulations Statistics as good or better than observational surveys This work was conducted as part of: the EURYI scheme award. See the EC Marie Curie Research Training Network CONSTELLATION It was also partially funded by a 2003 Philip Leverhulme Prize The calculations were performed on the UK Astrophysical Fluids Facility (UKAFF) and the University of Exeter Supercomputer