Sub-mm/mm astrophysics:
How to probe molecular gas
Yasuo Fukui
Nagoya University
Summer School
The Gaseous Universe
Oxford, 21-23 July 2010
1
Outline
Lecture 1 “Sub-mm and mm observations of molecules”
Molecular vs. atomic gas/ radiative and collional porcesses /
rotational energy levels/ sub-mm transitions/ time scales/
cooling and heating/ chemical processes
Lecture 2 “Sub-mm diagnostics; density and temperature”
LVG approximation and its application to three high
temperature regions
N159 and other GMCs in the LMC/ Westerlund 2 super star
cluster/ Galactic centre loops
Lecture 3 “Giant molecular clouds (GMCs)”
GMCs/ star formation/ resolved GMCs in the LMC and M33/
three GMC types/ GMC lifetime/ GMC formation/ HI
filaments/ shells or spiral density waves/ difference between
disk and center of a galaxy
2
Lecture 1
Sub-mm and mm
observations of molecules
3
ISM between stars
• We have interstellar medium ISM among stars
• ISM consists of gas and dust
Mgas/Mdust is 100, Dust grains include most of the heavy
elements, abundance ratio; H:He:CNO = 1:10-1:10-4
• Gas consists of neutral and ionized components
Here with an emphasis on neutral gas because neutral is
dominant, related to star formation and ultimately galactic
evolution,
Ionized gas is minor in mass and probes UV radiation field, PDR
• Neutral consists of molecular and atomic gas
– 1951 discovery of 21cm HI
– 1970 discovery of 2.6mm CO
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Molecular vs. atomic
• HI gas is less dense, average is 1 cm-3 with a
range of 0.01cm-3 to 100 cm-3, temperature
average is 100K with a range of 20–3000 K
• Molecular gas is dense, average is 1000 cm-3,
up to 107 cm-3 or higher
• Temperature is low, 10–20 K in the disk, can
be higher in high-mass star forming regions
• but is higher in the Galactic center, 30–300 K,
due to not-well known heating
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Some chemistry
• HI is converted into H2 on grain surface because
gas phase reaction is very slow, exception the first
stars form without dust grains
• H2 is readily dissociated if Av is small,
less than ~ 0.2 mag
• but can survive if Av is more than 1 mag
• Other molecules are often formed via ion neutral
reactions
• At very high densities more than 107cm-3
molecules freeze onto dust grain surface
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Radiative transitions
The Einstein coefficients
• (a) Spontaneous emission: A21n2
• (b) Photo absorption:
B12Iνn1
• (c) Stimulated emission:
B21Iνn2
(Electric dipole transition)
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Collisional Excitation
Excitation
De-Excitation
• C coefficient :
(N: density, σ: cross section, v: velocity)
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Excitation temperature
• For non-LTE case (more realistic in molecular cloud),
we can define the “Excitation temperature” as
follows;
(＊Especially, Tex of the spin excitation (e.g. HI 21cm line)
is called “Spin temperature”, Ts)
• Brightness temperature
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Detailed balancing
• Ex. Simple two level system rate equation
• Collision dominated
• Radiation dominated
Critical density
• When Iν → 0
• Critical Density:
• ncrit << n(H2) :
• ncrit ~ n(H2) :
• ncrit >> n(H2) :
LTE
excited but subthermal
unexcited
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My recommendation
• Keeep physical constants in mind
• Ready to make order-of-magnitude estimate
Planck const.： h = 6.63×10-27 erg s
Boltzmann const.： k = 1.38×10-16 erg deg-1
1 eV = 1.60×10-12 erg（e.g., 1eV~kT => T〜104 K)
electron mass： me = 0.911x10-27 g
proton mass： mp = 1.67x10-24 g
etc.
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Non-LTE case (Photon trapping)
• Photon escape probability, β (0 ≤ β ≤ 1 )
• Effective A coefficient: A21 → A21β
• Effective critical density: ncrit = A21/C21 → A21β/C21
• Large Velocity Gradient (LVG) model
Molecular cloud
(Castor 1970; Goldreich & Kwan 1974)
- Spherical
Velocity
- Slab
Tk, n(H2)14
Heating processes
• Based on the ionization of ISM components by an
energetic radiations. Then, electrons quickly (~1Myr)
interact with the ISM and thermalize.
– Cosmic rays; heat gas to 10 K (Black 1987; Lequex 2002)
– Photoelectric effect on small dust grains and PAH
(Watson 1972; de Jong 1977; Draine 1978; Bakes & Tielens 1994)
– Ionization of atoms and molecules (e.g., HCO+)
froze-in condition is good approx. MHD
– X-ray
– Chemistry
– Mechanical heating
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Cooling processes
Cooling by line radiation processes is dominant.
Proportional to n2.
• Atomic gas
– Forbidden lines. (< few 1000 K, e.g., CII)
– Lyman α (> few 1000 K)
• Molecular gas
Cooling by the line radiation from molecules
– CO, H2O and other molecules
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Thermal equilibrium curve
WNM
CNM
Unstable
Wolfire et al. 95
criterion for instability:
P 
  0
 L 0
(Field et al. 69, Wolfire et al.1795)
Heating and Cooling processes
for the thermal equilibrium curve (NW~1019 cm-2)
Atomic gas (solid lines: cooling, broken lines: heating)
Wolfire et al. 199518
Tk = 40 K
Molecular cooling
• CO is the dominant cooling
line for low n and T
• H2O and other molecules are
dominant for n > 106 cm-3 and
T > 200 K
Goldsmith & Langer 1978
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Temperature and density
balance of atomic gas
(Goldsmith et al. 2007)
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Temperature
•
•
•
•
•
kinetic temperature (Maxwell distribution), Tk
excitation temperature, Tex
radiation temperature, Planck law, Trad
color temperature, Tc
dust temperature, Td
These temperatures are generally not the same
Collisional coupling between dust and molecules
at density higher than 104 cm-3, Tk equal to Td
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Excitation 1
Upper state
•
•
•
•
Lower state
Electronic state (1-104 eV)
Vibration (10-2-10-1 eV)
Rotation (10-3-10-2 eV)
Spin (~10-6 eV)
104K ~ 1eV
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Excitation 2
• Hydrogen molecules are not observable in radio. Too
high energy levels. Only in absorption.
• Carbon monoxide CO and others can be observed
rotational energy levels, high excitation vibration.
cf. electronic, spin-spin interaction
• Sub-mm transitions
generally higher excited states
ratio between J and J’ gives
density/tempearture.
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Molecular cloud
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Goldsmith 1987
Time scale 1
• Crossing time scale
– Velocity width (5-10 km/s): dv
– Molecular cloud size (1-100 pc): r
＝ 105 – 107 yr
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Time scale 2
• Free fall time
a：initial radius, ρ(0) : initial density
n : initial number density, n = n(H) + 2n(H2)
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Time scale 3
• Cooling time
shorter than its dynamical time
isothermal is a good approximation
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Time scale 4
How frequently do molecules meet?
• C(s-1) = n (cm-3) s (cm2) V(cm/s)
n(density) ~ 103 cm-3
s(cross section) ~ πa2 ~ 10-16 cm2
V(velocity) ~ 105 cm s-1 [mV2 ~ kT]
t ~ 1/C ~ 108 [s] ~ 1 [yr]
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Time scale 5
• Formation time scale of H2
(Hollenbach & Salpeter 1970; Jura 1974)
γ：sticking probability for incident H atoms.
<v2>: mean thermal velocity of H atoms.
<σg>: average grain cross section.
n1, n2 & ng: number density of HI, H2 and grains, respectively
[yr]
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Time scale 6
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Koyama & Inutsuka 2000
Formation of H2 in gas phase
• Permitted processes in warmer regions
H+ + H → H2+ + hν
H2+ + H → H2 + H+
e- + H → H- + hν
H- + H → H2 + e-
In very dense regions(> 108 cm-3), 3 body reaction
3H → H2 + H
2H + H2 → 2H2
This process is important in the early Universe.
Very dense & hot HI cloud → molecular cloud
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