Dinamica del Gas nelle Galassie
II. Star formation
• Overview on ISM
– • Plasmas
– • Charge neutrality, infinite conductivity; Field freezing; Euler equation with magnetic force; Magnetic
Pressure and tension; Magnetic virial theorem; Shocks with magnetic field.
Stability of clouds
– • Molecular clouds: composition and properties. Isothermal sphere, Lane-Emden equation; Bonnor-Ebert sphere and mass; Analysis of stability; Effect of
rotation; Effect of magnetic field; Hydromagnetic waves; The role of turbulence.
Collapse of clouds – Free-fall time; Self-similar collapse; Ambipolar diffusion, magnetic braking.
- The Formation of Stars, Stahler & Palla, Wiley-VCH - The Physics of Astrophysics, F. H. Shu, University Science Books
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Molecular clouds
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Location of GMCs
Strahler & Palla, 2006, W-VCH
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IR allsky
Ophiucus
Cygnus
Rosette
Orion
Taurus
IRAS 12-100 micron
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Orion
nebula
Distance from Sun ~ 400 pc
CO map outer contours
dots = CO peaks
Shaded loop = UV emission
Maddalena et al. 1986
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CO J=2-1
Orion A
Optical multicolor
Maddalena et al. 1986
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Rosette cloud
CO J=3-2 peak emission map. O stars are shown as triangles.
Squares show the locations of the outflows found in the region.
Dent et al. 2009, MNRAS
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Dense cores
T ~ 10-15 K, n ~ 2x103 - 2x105 cm-3, sizes < 1 pc
More than 50% have associated IR sources
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Properties of molecular complexes
Type
n
(cm-3)
L
(pc)
M
(MO)
T
(K)
cs
(km/s)
σobs
(km/s)
GMCs
102
50
105
15
0.25
2
Dark clouds
103
1-10
102-4
10
0.2
1
Dense cores
104
0.1
10
10
0.2
0.3
Filippo Fraternali (Unibo)
vrot
(km/s/
pc)
Dinamica del gas – AA 2013-14 – part 2
<0.05
B
(µG)
vA
(km/s)
10
1.5
<0.1 10-30
0.5-1.5
~30
~0.4
<~1
10
Composition of
MCs
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Composition of MC
Aul = radiative de-exitation coefficient
Strahler & Palla, 2006, W-VCH
For n >> ncrit -> LTE
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Orion B - CO vs CS
CO - moderately high density
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CS -> High density regions
Lada et al. 1992
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Dense cores
Elongated
(mostly
prolate)
whether or
not they
harbour an
embedded
star
Myers et al. 1991
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HI envelops
Rosette MC
CO J=1-0
+
HI envelop (dashed) Filippo Fraternali (Unibo)
Blitz & Thaddeus 1980, ApJ
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Heating & cooling
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H2 formation and maintenance
Strahler & Palla, 2006, W-VCH
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Cooling inside MCs
Rotational transitions:
12CO, 13CO
O2, H2O etc.
Tielens 2005, CUP
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Heating of MC vs CNM
CR = cosmic ray ionization
decay of turbulence
grav = gravitational heating
ambipolar diffusion
d-g = collision with dust-grains
Tielens 2005, CUP
pe = photo-electric effect
CR = cosmic ray ionization
CI = photoionization of Carbon
X-ray ionization
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Stability of clouds
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MCs are rather stable
tff ~ (G ρ)-1/2
MC blown away by stellar
winds
O stars
From the stellar cluster age
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Bonnor-Ebert mass
unstable
Boyle’s law: stable
Bonnor 1956
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Coalsack G2 dense core
Extinction map
Bonnor-Ebert sphere with ξ=5.8
Lada et al. 2004, ApJ
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Barnard 68
Alves et al. 2001, Nature
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Equilibrium of rotating clouds
β = Ω02 R03/ 3GM
Along R
Ω0, R0 of the
initial sphere
from which the
cloud has
contracted
Along z
Isothermal sphere
Strahler 1983, ApJ
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Critical mass with rotation
β = Ω02 R03/ 3GM
unstable
For comparison:
Bonnor-Ebert sphere
unstable
Strahler 1983, ApJ
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Velocity gradients?
A clear case L1495
Typical β = 0.02 (very low)
Gradient ~ 3 km/s/pc
Goodman et al. 1993, ApJ
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Magnetostatic equilibrium
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2013-14
& Palla,
– part2006,
2 W-VCH
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Critical mass with Magnetic field
α = B02 / 8 π P0
B0, P0 of the initial homogenous sphere from
which the cloud has contracted
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Tomisaka et al. 1988, ApJ
Strahler & Palla, 2006, W-VCH
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Problems with Magnetic field
Magnetic field orientation non coherent
(evidence for MHD waves?)
Dense cores are not too
elongated but probably
prolate!
Loren 1989, ApJ
Goodman et al. 1990, ApJ
Myers et al. 1991
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Large velocity dispersion
CO J=1-0
Taurus cloud complex
Channel maps at different velocities
Mizuno et al. 1995
σoss ~ 1-2 km/s
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Non-thermal kinetic energy
Equilibrium between non-thermal kinetic
energy (T) and gravitational energy (W)
2o Larson’s law αvir ~ 1
log Kturb /|W|
GM ~ σ2 L
Larson 1981; Stahler & Palla 2006, W-VCH
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Turbulence achievements
Supersonic turbulence predicts
If dense cores are the products of turbulence
then one expect a power-law spectrum
σ ∝ L 1/2 1o Larson’s law
σ (velocity dispersion) ∝ S0.4 (size)
Clumps in Rosette MC
Williams & Blitz 1994, ApJ
Solomon et al. 1987
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Pre-stellar cores and IMF
Ward-Thompson & Whitworth, CUP
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Different IMFs
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Summary SF & turbulence
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McKee & Ostriker 2007, ARA&A
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Collapse of clouds
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Dense cores
with and
without stars
R = radius of the cloud
Benson & Myers 1989, ApJS
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Self-similar isothermal collapse
Basic equations
Self-similarity
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a = cs (sound speed)
Solution
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Shu 1977, ApJ
40
Inside-out collapse
Similarity variables: x = r / cst
v(x) = u(r,t) / cs
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a
b
Shu 1977, ApJ
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Simulations of collapse
(“core” = protostar)
Mass accretion
Non-dimentional
variables:
ρ / ρc
Density profile
Foster & Chevalier 1993
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Deformation of field lines
Initial field is rather uniform
NGC 1333 IRAS 4A
B0 ~ 0.5 mG
tcoll ~ few 104 yr
Frau et al. 2011, A&A
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From dense cores to stars
Optical-IR spectral energy distribution
i = 0
i = 0
i = 90
i = 90
i = 0
i = 90
i = inclination along the line of sight
Lada 1999, Kluwer
Hogerheijde 1998
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Formation of protostars
Strahler & Palla, 2006, W-VCH
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SF on the large scale
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Star formation indicators
Kennicutt et
al. 2008
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SFR vs galaxy type
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Kennicutt 1998, ARA&A
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HI distribution vs optical/UV
Sancisi et al. 2008, A&ARv
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HI and Molecular clouds in M33
Engargiola et al. 2002
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The Kennicutt-Schmidt (K-S) law
Kennicutt 1998
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“Local” K-S law
Leroy et al. 2008
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Local K-S law
21 galaxies
THINGS
Slope change?
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