1. Great Barriers in High Mass Star Formation, Townsville, Australia, Sept 16, 2010 Patrick Koch Academia Sinica, Institute of Astronomy and Astrophysics (ASIAA) Taiwan Magnetic Field Properties in High-Mass Star Formation from Large to Small Scales: The Evolving Role of Magnetic Field and Turbulence from a Statistical Analysis from Polarization in collaboration with Ya-Wen Tang & Paul Ho pc

2. Content: (1)Introduction - dust polarization - turbulence versus magnetic fields (2) Method - Polarization beyond Imaging - dispersion function (3) Case Study - W51 e2/e8 and Orion BN/KL (4) Summary References: - Koch et al., 2010, ApJ, 721, 815 - Tang et al., 2010, ApJ, 717, 1262 - Tang et al., 2009, ApJ, 700, 251 → Poster # 28, session B

3. Introduction - Motivation Key Questions: (1) magnetic field or turbulence dominated? (or mixed?) (2) evolution with scale?  In theory: B field and turbulence can both provide support against gravitational collapse, possibly explain low star formation efficiency  Observationally: percentage of linearly polarized dust emission is low, ~ a few % of dust total intensity  High mass star formation regions: strong dust continuum emission, therefore observable

4. Method: linear polarization from thermal dust emission B Polarization Molecular cloud CO H2H2 CS dust paramagnetic, elongated, rotating… “in most cases, grains are aligned with B field” (Lazarian 2007) See review by Roberge 2004 for alignment mechanisms n H 2 ~ 10 4-7 (cm -3 ) T ~ 10 (K)

5. Method (1)... unfortunately, dust polarization only gives plane of sky projected magnetic field direction, but not the strength... Question: what is a good measure to „characterize turbulence“ from polarization data? Fact: polarization observations can be messy and complicated... expanding shells, swept-up structures, shocks, etc... → standard deviation is generally not a fair measure! e.g. G5.89-0.39 (Tang et al. 2009b)

6. Method (2) dispersion function ≠ dispersion Fact: polarization observation can be messy and complicated... expanding shells, swept-up structures, shock, etc........, yes, but typically they have characteristic scales larger than turbulence → need a scale-dependent measure: dispersion function (=structure function of 2nd order) Φ: position angle scale disp. large scalesmall scale

7. Method (3) Idea: use dispersion function in scale=0 limit to derive ratio between turbulent to mean magnetic field strength (Hildebrand et al., 2009; Houde et al., 2009)  assume: B = B 0 + B t  develop auto-correlation function  expansion of dispersion function model independent! (Hildebrand et al., 2009) scale disp. large scalesmall scale b turbulent / mean field ratio:

8. Case Study (1) - W51 e2/e8: some facts  distance ≈ 7 kpc  5 Ultra-compact HII regions ( ☆ )  collapsing phase, locally in e2 and possibly also e8 (Ho 1996; Zhang 1997), with M gas ~200 M ⊙  previous BIMA B field measurement at 1.3 mm exhibits uniform B field morphology Color scale: 1.3 mm continuum White segments: B field direction (Lai et al. 2001)

9. (Tang et al., 2009; Poster # 28, session B) …W51 – zooming in - BIMA @ 1.3mm (θ ~ 2.3 ’’ ) SMA @ 0.87mm (θ ~ 0.7 ’’ ) - small scale structures resolved - likely decoupled from larger scale field in envelope

10. …W51 – dispersion functions (1) with higher resolutions: increasingly larger values at smallest scales and steeper slopes (2) some irregularities at larger scales: hourglass-morphology at larger scales (3) possible bias: gravity

11. Vaillancourt et al. 2008 (Tang et al., 2010; poster #28, session B) 0.26 pc SHARP 350, 450 μm - SHARP @0.35 / 0.45 mm (θ ~ 13’’ ) : uniform field structure at largest scales - SMA @ 0.87mm (θ ~ 0.9’’ ) : complex but smooth structure SMA B field Case Study (2) – Orion BN/KL

12. …Orion BN/KL: zooming in with 2 mpc resolution 0.87 mm: SMA (Tang et al., accepted) 1.3 mm and 3 mm: BIMA (Rao et al. 1998) 0.87 mm: SMA (Tang et al., 2010) 1.3 mm and 3 mm: BIMA (Rao et al. 1998) → dispersion functions: general trend from W51 confirmed SMA, θ~0.9’’ SMA, θ~2.8’’ BIMA, θ~3.4’’ BIMA, θ~7’’

13. …putting it all together: combining scales (Koch et al., 2010) pc  technical aspect: beam integration correction  Houde et al. 2010: correction factor ~1/N (N: number of turbulent cells sampled by beam)  in our observations: N ~ 120 to a few

14. Turbulence – Magnetic Field Evolution  close to constant turbulent / mean field ratio  ratios: 0.4 (Orion), ~ 1 (W51 e2 / e8)  hint of a decrease toward smaller scales  source specific differences

15. …and: more to learn from polarization:  polarization correlation length:  symmetry properties, characteristic structures,...:

16. Summary and Conclusions (1) case study of the role of magnetic field and turbulence as a function of physical scale: - Orion BN / KL: 5 observations (θ ~ 13’’- 0.9’’, i.e. 40 – 2 mpc) - W51 e2 / e8:2 observations (θ ~ 2.3’’ and 0.7’’, i.e. 69 and 21 mpc) (2)statistical analysis: (model independent!) dispersion function in scale=0 limit measures turbulent / mean field ratio (3)ratio close to constant, with a slight decrease toward smaller scales (taking into account beam integration) (4)detected field morphologies sample various stages of star formation (envelope, cores) Therefore, ratio over scales measures evolutionary trend (5)smallest resolved scales close to ambipolar diffusion (~ 2 mpc) (6)...more to learn from polarization