Magnetic Fields and Star Formation: Zeeman Studies

1. Magnetic Fields and Star Formation: Zeeman Studies Dick Crutcher University of Illinois

2. Measuring Important Parameters: M/ & turb M/: ratio of gravity to magnetic fields • Uniform disk Nakano & Nakamura 1978 Ciolek & Mouschovias 1994 critical subcritical  • Observing M/ supercritical •  definition turb: ratio of non-thermal kinetic to magnetic energy • turb calculation

3. Scaling of B with : B   Equilibrium between gravity, kinetic & magnetic energy Spherical collapse, implies weak magnetic field B  2/3 B  1/2

4. Zeeman Effect V = LR  (dI/d)Zcos  line of sight B only, Blos= Btotcos Species Wavelength n(H) traced H I 21-cm 10 – 103 cm-3 OH 18-cm 103 – 104 cm-3 CN 3 mm 105 – 106 cm-3

5. Major Zeeman Data Sets (with Blos, N, n, r) Data Set Measurements of Blos ------------------------------------------------------------------------- 1. Compilation 27 Crutcher 1999 2. Arecibo H I Millinium survey 69 Heiles & Troland 2004, 2005 3. Arecibo OH dark clouds 34 Troland & Crutcher 2008 4. IRAM CN 11 (+ 3 included in #1) Falgarone, Crutcher, & Troland. 2008 TOTAL 141

6. Arecibo Dark Cloud OH Zeeman Blos=26 4 µG Blos=+14  4 µG Blos=+11 2 µG Troland & Crutcher 2008

7. CN Zeeman Examples OMC1 W3OH BLOS = +1.1  0.3 mG BLOS = 0.36  0.08 mG LSR Velocity (km/s) Crutcher et al. 1999 Falgarone et al. 2008

8. Results for Field Strength Crutcher et al. 2008

9. Results for Field Strength

10. Results for Diffuse and Molecular Clouds Mean Values H I Clouds OH Clouds CN Clouds nH (cm-3) 54 3.2 1034.5 105 turb1.3 2.4 2.9  (M/ wrt critical) 0.06 2.1 3.0

11. PDFs of Btot &Blos Lazarian & Goncalves 2007 Heiles & Crutcher 2005

12. Bayesian Analysis • Data and their uncertainties are the priors • Fully probabilistic model with unknown parameters • Model interpreted as a pdf over the model parameters given the priors through use of Bayes’ theorem • Evidence P(d|M) computed by integration over the probability density of different parameters, or by Monte Carlo simulations. Priors (data): Models: unique, numerical, uniform pdf for BTOT Crutcher et al. 2008

13. Initial Results for H I & Molecular Zeeman H I B1/2 = 6 G Unique : Numerical : Uniform = 1 : 0.4 : 2 OH & CN B1/2 = 0.64 n1/2 G Unique : Numerical : Uniform = 1 : 103: 104

14. Bayesian Analysis with Sophisticated Model Priors (data): The model: Crutcher et al. 2008

15. Preliminary Results of Bayesian Analysis Crutcher et al. 2008

16. Preliminary Results of Bayesian Analysis Crutcher et al. 2008

17. PDFs of Btot &Blos Heiles & Crutcher 2005

18. Observed PDF ofBlos

19. Tilley & Pudritz (2008) Simulation

20. Testing M/ Change from Envelope to Core Testing ambipolar diffusion driven core formation & star formation Vazquez-Semadeni et al 2005 Ciolek & Mouschovias 1994 Dib 2006 

21. Testing M/ Change from Envelope to Core Measure differential M/ between core and envelope: Hakobian & Crutcher 2008

22. Conclusions • Magnetic fields are highly significant and probably crucial to understanding the central physics of star formation. In at least some cases, M/ is ~ critical in molecular clouds. • Total strength of B seems to range from near zero to maximum value in molecular clouds; smaller values of Btot would imply highly supercritical cores. • Slope of B vs. n is about 2/3, consistent with collapse with magnetic fields not dominate. • Preliminary:Increase in M/ from envelope to core required by ambipolar diffusion is apparently not seen. • Speculative:Will present subcritical unbound H I clouds form future dense molecular clouds? Perhaps present H I and molecular clouds are contemporary, formed at the same time in turbulent flows.