Transcript Document

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;
Orion GMC
• 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. 2001
Initial conditions: dense gas in GMCs
CO (n
≈103 cm-3)
CS (n ≈104 cm-3)
(E. Lada et al. 1991)
IR clusters
Star formation confined to dense gas (n >104 cm-3, AV > 10 mag).
About 10% of the mass in GMCs is characterized by n(H2) > 104 cm-3
This gas is organized into dense, gravitationally bound cores
Cores
stars
Cores with
with stars
HH 46-47 flow poking out of a globule, optical (DSS)
Spitzer Infrared Image: A. Noriega-Crespo (SSC/Caltech)
Cores without stars
0.44 mm
2.16 mm
Alves, Lada & Lada 2001
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 BonnorEbert Sphere Fit
Alves, Lada & Lada (2001)
An evolutionary sequence?
time
Shirley et al (2005)
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?
Energy densities in the galaxy NGC6946
R (kpc)
Beck (2003)
The ISM as a magnetized fluid
Galactic magnetic fields
L ~ kpc, B ~ 1-10 mG
Interstellar magnetic fields
L ~ 1 pc, B ~ 10-102 mG
Stellar magnetic fields
L ~ R8, B ~ 1-103 G
The ISM as a turbulent fluid
Supersonic line widths in molecular clouds:
evidence for turbulent motions
observed Dv ~ 2-4 km/s
thermal Dv very narrow:
example: CO at T=10 K
Dvth = 0.13 km/s
Turbulence as isotropic
“pressure” contributing to
cloud support:
Pturb ~ r Dvturb2
Falgarone & Phillips (1990)
Kolmogorov incompressible turbulence
Energy input
.
v2(l)
E(l) ~
l/v(l) = const.
v(l) ~ l1/3
dissipation by
viscosity
inertial range
Larson’s (1981) scaling law
sv (km/s) ~ (l/pc)1/2
1/2
sv ~ sl1/2
v~ l
svs~ l~1/3l1/3
v
Heyer & Brunt (2004)
Very little turbulence inside low-mass cores
Intrinsic FWHM (km/s)
Supersonic motions in the outer parts
Subsonic motions in the interior
thermal line width
distance from core centre
Barranco & Goodman (1998)
log E
molecular clouds
sonic scale
The ISM as a turbulent cascade
massive cloud cores
supersonic
subsonic
L-1
log k
energy source and scale not known
(supernovae, winds,
spiral density waves?)
ηK-1
dissipation scale not known
(ambipolar diffusion,
molecular diffusion?)
The modeling of this process requires
supercomputer simulations
AMR: Stone & Norman (1992)
SPH: Nordlund & Padoan (2002)
Formation of cores and stars in a turbulent cloud
molecular clouds are threaded by the Galactic
magnetic field
cloud cores and protostars are magnetized
Girart, Rao, Marrone (2006)
Lai (2002)
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)
Fundamental parameter for stability:
the critical mass-to-flux ratio
Chandrasekhar & Fermi (1953), Mestel & Spitzer (1956)
M/F > (M/F)crit can collapse
diffuse
clouds
molecular clouds
M/F < (M/F)crit
cannot collapse
B=0
Hennebelle & Teyssier (2008)
B ≈ 1/50 BISM
B ≈ 1/20 BISM
B ≈ 1/5 BISM
Catastrophic magnetic braking
no B field
with B field (B≈1/ 3 BISM)
Price & Bate (2007)
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)
Han et al. (2006)
Magnetic field strength in the Galaxy
Beck (2003)
Breg from Zeeman effect
in molecular clouds
Btot from synchrotron
emission of diffuse
gas (+ equipartition)
Let l = (M/F)/(M/F)crit = 2p G1/2(M/F)
pressure
subcritical, cannot collapse
l<1
supercritical, can collapse
l >1
volume
• 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 subcritical l < 1 to super-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. 2004 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.
Maxwell’s equations: a B field of 3 muG
requires e-i drift of only 10-3 cm/s
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.
Flux Freezing
Self-inductance
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.
Pressure Balance in Barnard 68
Pthermal / PNT = a2 / sNT2
Barnard 68 is a thermally supported Cloud!
~70% of all stellar systems are composed of single stars!
Inside-out collapse (Shu 1977)
cloud core
.
M*=0.975 cs3/G
static
envelope
infalling region
r(r) ~ r-3/2
v(r)~ r-1/2
accreting protostar
Inside-out collapse with rotation
infalling region
centrifugal barrier at
Rc=G3M*3W2/16cs8
star + disk
Shu, Terebey & Cassen (1984)
Magnetostatic cloud models
Li & Shu (1996),
Galli et al. (1999)
NGC 1333 IRAS 4A
Girart et al. (2007)
NGC 1333 IRS 4A
400 AU
Gonçalves, Galli & Girart (2008)
Rosette GMC
Roman PhD Thesis
Very little turbulence in low-mass cores
slos=0.02 km s-1
slos=0.03 km s-1
Tafalla, Myers, Caselli & Walmsley (2004)
Equipartition magnetic field strengths in M51
Fletcher,Beck et al. (2005)
NGC6946
(Beck & Hoernes
1996)
Formation of clumps in turbulent flows
Supersonic turbulence
produces strong density
fluctuations, sweeping gas
into dense sheets and
filaments
This process needs
continuos injection of
energy at the large scale
Nordlund (2002)
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:
<Btot> = 9 μG
Niklas 1995
Temperature profile
Crapsi et al. (2007)
Larson’s (1981) cloud-to-cloud scaling law
sv (km/s) ~ (l/pc)1/2
sv ~ l1/2
sv ~ l1/3
Solomon & Rivolo (1987)