Download Lecture 14

“You really should keep a personal log.
Why bore others needlessly?”
The Doctor, Star Trek Voyager
Announcements
Midterm in one week.
Draft of your paper
A rough draft of your paper will be due on March
23.
This draft does NOT need to be complete. However,
it should include ALL of the references you plan to
use and outline ALL of the sections you think your
paper will include. The more complete it is, the
more I can comment.
It will be worth 25 points.
Star formation
The basic idea is that stars form from the widely
dispersed clouds around the galaxy.
Both the gas and stars in the Milky Way are not
evenly distributed.
So we start with the ISM
The ISM
The ISM comes in different densities and
temperatures.
However, since H is the most abundant atom by a
longshot, we can concentrate on that.
H can be ionized, neutral, or molecular (H2).
The ISM
The number density of the ISM depends on what
form H takes. If H is ionized, then nISM=2nH or if H
is molecular, then nISM= ½nH.
The ISM
But nH does give a good indicator of the mass
density, r. So for any sample of ISM, r~nHmH.
Various types
of gases
distinguished
By number
density and
temperature.
Note the general
trend in this plot.
The cold gases tend
to be more dense
and the hotter ones
less dense.
And the ranges;
from 100/m3 to
1017/m3 and from
10K to over a
million K.
We will explore
these different types
of gas.
Starting here.
Intercloud Medium
The intercloud medium is the diffuse gas that
accounts for most of the volume of the ISM. It is the
gas between the stars and all other type of ISM are
within this one.
Hot Intercloud Medium
The hot intercloud medium is very widespread, but
very diffuse. This is ionized H.
This medium is highly transparent
Warm Intercloud Medium
Same as the hot stuff, but neutral H. Still very
diffuse.
This medium is optically transparent.
Typical densities are 1 H /cc (a nice number to
remember!)
This is the gas that makes the 21cm radio line.
We use it to map galaxies.
Interesting note
The 21cm line cannot be produced in Earth-based
labs as our vacuums cannot get low enough, so
collisions dominate and lab atoms de-excite prior to
emitting 21cm photons.
Intercloud medium
But this gas is not involved directly in star
formation. So we are not so interested in it now.
The rest
The other types are compact, but are either
associated with stars (planetary nebulae and
supernova remnants) or are not (the ones we're
interested in now)
Those associated
with individual stars
And those we're
interested in now.
Diffuse clouds.
Diffuse Clouds
These regions are cold and of moderate density. You
can see stars through them at visible wavelengths
and so are typically not apparent.
H is both neutral and in molecular form.
These typically have temperatures of 30 – 80 K and
number densities of 100 – 800 /cc (divide by a
million to get mks units) and masses of 1 – 100 solar
masses with sizes of 3 - 100pc.
Diffuse Clouds
H2 is not easily mapped (diatomic molecule), but
typically where you find H2, you find CO, which
can be.
Dense clouds
Dense clouds
Unless very thin, these are opaque at visible and UV
wavelengths.
These are therefore often called dark clouds.
Dense clouds
Most of this gas exists in molecular form.
The clouds are usually mapped in CO, HC, or OH
molecules.
Temperatures are 15 – 50 K, n~ 500 – 5,000/cc, and
masses of ~3 – 1000 solar masses with sizes of 0.1 –
20pc.
So ALL dense clouds are also molecular clouds.
Part of Orion mapped
in CO.
Regions of dense
clouds are usually
surrounded by diffuse
clouds.
HII regions. These
are again regions of
ionized H, caused
by very hot O or B
stars.
HII regions (aka Stromgren spheres)
UV photons from hot stars ionize the H in the
nearby cloud. This creates bubbles of HII gas. These
spheres are called Stromgren spheres. At the outer
boundary, there is some recombination.
With the short lifetime of massive, UV-creating
stars, the size of Stromgren spheres often reaches a
limit.
Other times, it can break out.
The pretty
pictures are
caused by
recombination
at the boundary
regions, where
the electron
cascades down
through shells.
This is the n=3
to 2 transition
(Ha).
A beautifully complex
slice of the Orion nebula.
Giant molecular clouds
These consist of diffuse and dense clouds that span
large regions.
Attributes are typically T~20K, n~100-300/cm3,
m~10-10,000 solar masses and sizes are around
50pc (but up to 100pc).
Thousands of these are
known in our galaxy.
Most in the spiral arms.
Orange are
GMCs,
green is an
HII region,
Pink is an
SNR.
Scale is
1500 light
years per
side.
You can see how GMCs trace the spiral arms (or
is it the other way round?).
Dense cores or Bok globules.
These are dense regions inside GMCs which have
the densest gases. T~10K, n>104/cm3, m~1-1,000
solar mass and r~1pc.
Dense cores or Bok globules.
Infrared surveys reveal that these are regions of
active star formation
These regions are usually
associated with OB
associations. Another
indication of their youth.
How dense is dense?
Space is pretty empty and so comparing a giant
molecular cloud to space, it seems pretty dense.
However, even the densest cloud is about a million
times less dense than the best vacuum we can create
on Earth.
They make up for it in volume.
Dense clouds
These make up about 45% of the total mass of the
ISM.
Connections between clouds and star
formation.
1) We see young stars near clouds.
We only see OB associations near clouds and never
alone. And of course these are the stars with the
shortest lifetimes, and so cannot travel as far from
their birth place.
Or even still
embedded in the
gas.
We see large regions of dust surrounding very young stars
These are often called cocoon nebulae, as they surround
and hide the star inside. They are heated to 100s of K.
HR diagrams of these regions also show that
while massive stars have reached the MS,
most stars have not.
Theoretical isochrones date regions like this
at a few million years (Orion is 1 million)
The basics of star formation
Gravity acts everywhere and on/from every particle
with mass. As such, even though the density is very
low, each particle does pull on other particles.
While these forces are very, very, VERY small, we
cannot ignore them.
1) Because there are no other large masses around,
and 2) because taken as a whole, the clouds can be
very massive.
Gas balance.
James Jeans sorted a lot of this out in 1902.
Here are the basics:
1) Ignore galactic rotation and magnetic fields
2) Put the cloud in hydrostatic equilibrium (a
balance between gravity and pressure)
3) just overcome the pressure.
Volume is area
x radius
Pressure is
force over area.
Gravitational force is GM2/r2
Density is M/V ~M/r3
Higher pressre → expansion (stability against
contraction).
Higher density → contraction (gravity wins).
Higher pressre → expansion (stability against
contraction).
Higher density → contraction (gravity wins).
The virial theorem
The virial theorem describes the condition of
equilibrium for a stable, gravitationally bound,
system:
2K + U = 0
Where K is the kinetic energy of the gas and U is the
gravitational potential energy of the gas.
The virial theorem
2K + U = 0
If twice the kinetic energy of a molecular cloud
exceeds the gravitational potential, the cloud will
expand.
If the internal kinetic of the cloud is too low, the
cloud will collapse.
The virial theorem
2K + U = 0
The boundary between those two cases is the critical
condition for stability.
Deriving the Jean's criterion.
The gravitational potential energy of a spherical
cloud of constant density is:
The gravitational potential
energy of a test particle of
mass dmi at a distance r
from the center is
Deriving the Jean's criterion.
The gravitational potential energy of a spherical
cloud of constant density is:
The mass within the shell
of dr is dm=4pdrr which
makes the potential energy
Deriving the Jean's criterion.
The gravitational potential energy of a spherical
cloud of constant density is:
To sum all the potential
energy, integrate over the
entire cloud
Deriving the Jean's criterion.
The gravitational potential energy of a spherical
cloud of constant density is:
At uniform density, we can
integrate over the total
mass, which is (4/3)pr3r
Deriving the Jean's criterion.
The gravitational potential energy of a spherical
cloud of constant density is:
Substituting back to M, this
becomes.
Which is the gravitational
potential energy of a uniform
sphere.
Deriving the Jean's criterion.
The gravitational potential energy of a spherical
cloud of constant density is:
Where Mc and Rc are the mass and radius of the
cloud.
Deriving the Jean's criterion.
The internal kinetic energy of a spherical cloud of
constant density, ideal gas is:
Where N is the total number of particles. We may
rewrite N as
where m is the mean molecular weight and then
Deriving the Jean's criterion.
Putting it back together, we have
Yet we can also eliminate Rc using the initial mass
density of the cloud ro.
Deriving the Jean's criterion.
And finally, we can get the Jean's mass and the Jean's length
So the conditions
for cloud collapse
are Mc>MJ or
Rc>RJ.
Example 1
A typical diffuse cloud has T=50 K, n=5x10108/m3
which, if entirely composed of H, is
ro=nHmH=8.4x10-20kg/m3. Then m=1 too.
mH=1.67x10-27kg, G=6.67x10-11, k=1.38x10-23.
What then is the Jean's mass?
Example 1
A typical diffuse cloud has T=50 K, n=5x10108/m3
which, if entirely composed of H, is
ro=nHmH=8.4x10-20kg/m3. Then m=1 too.
mH=1.67x10-27kg, G=6.67x10-11, k=1.38x10-23.
What then is the Jean's mass?
The pressure from the
large star on the left has
caused the four stars on
the right to condense
from their proto-cloud.