Gestazione e travaglio delle stelle, tra turbolenza e campi magnetici Daniele Galli Osservatorio Astrofisico di Arcetri WIYN Image: T.A. Rector (NOAO/AURA/NSF) and Hubble Heritage Team (STScI/AURA/NASA)

The initial conditions: Orion GMC Orion Nebula (part of Orion GMC) From: CfA Harvard, Millimeter Wave Group

Initial conditions: the molecular gas Molecular gas is concentrated in the galactic plane; accounts for as much as ½ all interstellar matter; most of it is concentrated in GMCs, the largest and most massive objects in the Galaxy. Dame et al Orion GMC

Initial conditions: dense gas in GMCs About 10% of the mass in GMCs is characterized by n(H 2 ) > 10 4 cm -3 This gas is organized into dense, gravitationally bound cores IR clusters Star formation confined to dense gas (n >10 4 cm -3, A V > 10 mag). (E. Lada et al. 1991) CO (n ≈10 3 cm -3 ) CS (n ≈10 4 cm -3 )

HH flow poking out of a globule, optical (DSS) Spitzer Infrared Image: A. Noriega-Crespo (SSC/Caltech) Cores with stars

Alves, Lada & Lada  m0.44  m Cores without stars

Starless or Prestellar cores: condensations with no known internal luminosity source Visual image CO Emission 5000 AU

Density profile Extinction Map Radial Density Profile, with Critical Bonnor- Ebert Sphere Fit Alves, Lada & Lada (2001)

Shirley et al (2005) An evolutionary sequence? time

Final Thoughts Fundamental question: how does matter arrange itself within interstellar molecular clouds? The role of magnetic fields and turbulence is critical. Ultimate questions: why is star formation efficiency ~1%? how are stellar masses determined ?

Beck (2003) Energy densities in the galaxy NGC6946 R (kpc)

Galactic magnetic fields L ~ kpc, B ~ 1-10  G Interstellar magnetic fields L ~ 1 pc, B ~  G Stellar magnetic fields L ~ R , B ~ G The ISM as a magnetized fluid

The ISM as a turbulent fluid

Supersonic line widths in molecular clouds: evidence for turbulent motions Falgarone & Phillips (1990) observed  v ~ 2-4 km/s thermal  v very narrow: example: CO at T=10 K ’  v th = 0.13 km/s Turbulence as isotropic “pressure” contributing to cloud support: P turb ~  v turb 2

Kolmogorov incompressible turbulence Energy input dissipation by viscosity E(l)  v 2 (l) l/v(l) ’  v(l)   l 1/3 inertial range  = const.

Larson’s (1981) scaling law Heyer & Brunt (2004)  v (km/s) ~ (l/pc) 1/2  v ~ l 1/3  v ~ l 1/2  v ~ l 1/3

Barranco & Goodman (1998) Intrinsic FWHM (km/s) Very little turbulence inside low-mass cores distance from core centre thermal line width Supersonic motions in the outer parts Subsonic motions in the interior

molecular clouds The ISM as a turbulent cascade log E log k L -1 η K -1 energy source and scale not known (supernovae, winds, spiral density waves?) dissipation scale not known (ambipolar diffusion, molecular diffusion?) supersonic subsonic sonic scale massive cloud cores transfer

SPH: Nordlund & Padoan (2002) The modeling of this process requires supercomputer simulations AMR: Stone & Norman (1992)

Formation of cores and stars in a turbulent cloud

molecular clouds are threaded by the Galactic magnetic field

Lai (2002) Girart, Rao, Marrone (2006) cloud cores and protostars are magnetized

in agreement with theoretical core models: Li & Shu (1996), Galli et al. (1999) Shu et al. (2000), Galli et al. (2001)

Effects of the magnetic field: Suppress fragmentation Suppress rotation (magnetic braking) Chandrasekhar & Fermi (1953), Mestel & Spitzer (1956) Fundamental parameter for stability: the critical mass-to-flux ratio

molecular clouds diffuse clouds M/  > (M/  crit can collapse M/  < (M/  crit cannot collapse

B = 0 Hennebelle & Teyssier (2008)

B ≈ 1/50 B ISM

B ≈ 1/20 B ISM

B ≈ 1/5 B ISM

Price & Bate (2007) no B field with B field (B≈1/ 3 B ISM ) Catastrophic magnetic braking

Summary The fact: stars are born in turbulent and magnetized molecular clouds; To allow the birth of a star, a cloud must loose its turbulent and magnetic support: turbulence decay; magnetic field dissipation; For massive protostars, radiative feedback non negligible.

Star formation: radiation magnetohydrodynamics with self-gravity and turbulence. The worst one can have!

Han et al. (2006)

Magnetic field strength in the Galaxy Beck (2003)

B reg from Zeeman effect in molecular clouds B tot from synchrotron emission of diffuse gas (+ equipartition)

Let  = (M /  )/(M/  ) crit = 2  G 1/2 (M/  )  < 1  >1 volume pressure subcritical, cannot collapse supercritical, can collapse

Subcritical clouds where the dimensionless mass-to-flux ratio … < 1 cannot undergo gravitational collapse/fragmentation (Mestel & Spitzer 1956) Are HI clouds precursors to molecular clouds? (Allen et al. 2004)

The problem of star formation separates into: a) how proto-cloud cores evolve from sub- critical l 1 b) how supercritical cores subsequently gravitationally collapse and fragment

(a) Early investigations of these processes assumed conditions of laminar flow: possibly rotation, but no turbulence Nakano (1979), Lizano & Shu (1989), Desch & Mouschovias (2001): cores form by ambipolar diffusion

+) McKee (1989): far-UV radiation penetrates up to Av = 4, keeping trace elements ionized (t_AD > t_Univ.). In Ophiuchus, cores don’t exist where Av < 7 (Johnstone et al for Ophiuchus) -) the time-scale for core formation is too long by 1 order of magnitude in comparison with the statistic of low-mass cores with and without embedded stars. The inclusion of turbulent velocity fields alleviate the difficulty (Zweibel 2002; Li & Nakamura 2004)

-) difficult to form massive cores without turbulent flows

The ISM of galaxies is turbulent on almost all observable scales (Elmegreen & Scalo 2004) Turbulence drops to subsonic levels in cloud cores (Goodman et al. 1998) Magnetic field is coherent from sub-pc to kpc scales

Han et al. (2006)

Why Magnetic Fields? Q. Why no large scale electric field? A.Overall charge neutrality in plasma means that E is shorted out rapidly by moving electric charges. In contrast, the required currents for large scale B can be set up by tiny drifts between electrons and ions. Finally, once large scale B is set up, it cannot be shorted out by (nonexistent) magnetic monopoles, nor can the very low resistivity dissipate the currents in a relevant time scale. Maxwell’s equations: a B field of 3 muG requires e-i drift of only 10-3 cm/s

Flux Freezing In a highly conducting plasma cloud, contraction generates currents that make the magnetic field inside grow stronger, so that magnetic flux is conserved. The magnetic field lines are effectively “frozen” into the matter. Self-inductance

Pressure Balance in Barnard 68 P thermal / P NT = a 2 /  NT 2 Barnard 68 is a thermally supported Cloud!

~70% of all stellar systems are composed of single stars!

Inside-out collapse (Shu 1977) M * =0.975 c s 3 /G.  (r)  r -3/2 v(r)  r -1/2 infalling region accreting protostar static envelope cloud core r i =c s t

Inside-out collapse with rotation centrifugal barrier at R c =G 3 M * 3  2 /16c s 8 Shu, Terebey & Cassen (1984) infalling region star + disk

Magnetostatic cloud models Li & Shu (1996), Galli et al. (1999) NGC 1333 IRAS 4A Girart et al. (2007)

NGC 1333 IRS 4A Gonçalves, Galli & Girart (2008) 400 AU

Roman PhD Thesis Rosette GMC

Very little turbulence in low-mass cores Tafalla, Myers, Caselli & Walmsley (2004)  los =0.02 km s -1  los =0.03 km s -1

Fletcher,Beck et al. (2005) Equipartition magnetic field strengths in M51

Turbulent fragmentation Supersonic turbulence (ST) produces strong density fluctuations, sweeping gas into dense sheets and filaments Stars form when shock-generated density fluctuations reach sufficiently high densities time scale < interval between two shocks

NGC6946 (Beck & Hoernes 1996)

Formation of clumps in turbulent flows Nordlund (2002) Supersonic turbulence produces strong density fluctuations, sweeping gas into dense sheets and filaments This process needs continuos injection of energy at the large scale

The magnetic virial theorem implies the existence of a magnetic critical mass or a the critical mass-to-flux ratio Chandrasekhar & Fermi (1953), Mestel & Spitzer (1956), Strittmatter (1966)

Total field strengths Survey of 74 spiral galaxies: = 9 μG Niklas 1995

Temperature profile Crapsi et al. (2007)

Larson’s (1981) cloud-to-cloud scaling law Solomon & Rivolo (1987)  v (km/s) ~ (l/pc) 1/2  v ~ l 1/3  v ~ l 1/2