#### Transcript Free-fall time

```The Interstellar Medium
Physical Astronomy
Professor Lee Carkner
Lecture 12
Questions
 The corona has a number density of
~1011 m-3 and a temperature of ~1
million K. What is the gas pressure in
the corona?
 P=nkT=(1011)(1.38X10-23)(106) = 1.38X10-6
Pa
 What would the magnetic field have to be
to equal that pressure (in Gauss)?
 Pm =B2/2m0, B = (2m0Pm)½ = [(2)(4pX107)(1.38X10-6)]½ = 1.86X10-6 T = 0.02 G
Star Formation

The gas is mostly hydrogen and fills most of the mass
and volume
The dust is mostly silicates (some ices) and accounts
for most of the extinction

Jeans Criterion
Assume the cloud has a balance between the
outward thermal kinetic energy (K) and the
inward gravitational energy (U)

U = (3/5)(GM2/R)
K = (3/2)NkT

R = (3M/4pr)1/3
If the cloud’s mass is greater than the Jeans
mass MJ it will collapse
MJ = (5kT/GmmH)3/2 (3/(4pr))1/2
Free-Fall Time

RJ = ((15kT)/(4pGmmHr))1/2
We can find an estimate for the time it takes the
cloud to collapse if we make some assumptions

Free-fall time depends only on density
tff = (3p/32Gr)1/2
Other Factors

Other include

The perturbation that starts collapse

Rotation

Magnetic fields
Magnetic Pressure

Field “freezes in” to the cloud and get compressed
and thus stronger as the cloud collapses

MB = cBpR2B/G1/2

Can also write in terms of Msun, nT and pc
MB ~ 70 Msun (B/1nT)(R/1pc)2
Parts of the ISM
 Coronal gas

 T = 106 K, n <104 m-3
 Intercloud Medium

 T ~ 104 K, n ~ 105 m-3
 H II regions

 T ~ 104 K, n ~ 103 m-3
 H I regions

 T ~ 100 K, n ~ 107 m-3
 Molecular clouds
 Very cool, dense clouds
 T ~ 10 K, n ~ 109 m-3
Extinction

 Can parameterize as an
the extinction, Al
ml = Ml + 5logd + Al

 Dust grains preferentially
scatter short wavelengths,
causing reddening
 Blue light dimmed more than
red
Extinction Curve

 Can’t fit curve with just
normal dust grains

 Might be due to carbon
molecules such as graphite
and polycyclic aromatic
hydrocarbons (PAH)

 Sizes from microns to less
than a nanometer
Hydrogen
 Hydrogen near sources of
become ionized (H II)

 Might produce pink emission nebula
 Most hydrogen is un-ionized (H I)

 Might produce blue reflection nebula
 In dark cores of clouds,
molecular H2 can be produced

 Might produce black dark nebula

rS ~ (3N/4pa)1/3 nH-2/3
N is the number on ionizing photons per
second produced by source star

a is the recombination coefficient (~ 3.1 X
10-19 m3/s)
nH is number density of hydrogen (~108 m-3)
Chemistry
 Molecules can form both on
dust grains and in the gas
phase

 Molecules mostly composed of
CHON elements

 Many molecules have strong
mm transitions and are used to
map molecular clouds

Next Time
Test #2
Same format as Test #1
Covers lectures 7-12
For first class after break (Jan 10)