ISM & Star Formation. The Interstellar Medium. HI - atomic hydrogen - 21cm. T ~ 0.07K. not very optimistic. Interstellar Molecules. OH 18cm H 2 O 1cm NH 3 1cm. In 1969, CO at 2.6mm - high abundance. Estimate rate of formation: R form = n C n O v
T ~ 0.07K
In 1969, CO at 2.6mm - high abundance
Estimate rate of formation:
= 10-15 cm-3/s
nC density C atoms
nO density O atoms
v average thermal speed
geometric cross section
105cm/s at 100K
size of atom
Estimate rate of destruction
e.g. photodissociation, tdis ~ 103yrs -> Rdis= nCO/tdis
-> nCO=10-15cm-3/s . tdis = 3.10-5cm-3
Since nH~3.10-3 nCO/nH ~ 3.10-6
Chemical reactions can take place on dust grain surfaces
-> formation of H2
Vibrational transitions -> infrared
Rotational transitions -> radio
balls on springs
quantisation of angular momentum
indirect presence of H2
Need to calculate the rate at which various processes occur in different conditions
Model calculations predict the strength of various molecular
lines, which can be compared to observations.
The models are adjusted until agreement is found.
The model is then used to predict the results of new
observations and the process continues
Most abundant: 10-4 or 10-5 times HI abundance
easy to excite and to observe - allows us to estimate cloud
masses and kinetic temperatures.
other elements ~ 10-9 times HI
See internal motions in the molecular clouds (line broadening):
collapse, expansion or rotation... also turbulence.
CS and H2CO
carbon sulphide & formaldehyde
Rarer molecules, harder to excite than CO, they trace the very
dense part of clouds
Determining mass is tricky because we are looking at trace
constituents (10-6 of H2) - and abundance may vary, and also
cloud may not be dynamically relaxed.
Density fluctuations are constrained to have a minimum mass because the conditions are such that thermal pressure of matter can balance gravitational collapse.
That is the equilibrium of the force of gravity (GM2/R) and the force exerted by the thermal movement, or kinetic energy (3/2NkT) of the particles inside a cloud of gas.
In term of the total energy we have the following three cases that define dynamical stability:
In the case of galaxy clusters the kinetic energy refers to the motion of individual galaxies. In the case of a clump of gas, it refers to the motion of the individual gas particles, the atoms. Thus, for a parcel of gas, assumed to be ideal,we can write the condition for collapse as:
From the Jeans\' condition we see that there is a minimum mass below which the thermal pressure prevents gravitational collapse:
The number of atoms corresponding to the Jeans\' mass is given by:
where is the mean molecular weight of the gas and mp is the mass of the proton.
combiningequations 77, 78 and 79
As expected, high density favors collapse while high temperature favors larger Jeans\' mass. In units favoured by astronomers the above condition becomes:
a(r) = GM(r)/r2 = G(4/3)r3r2 = (4/3)Gr
if the acceleration of the particle stayed constant with time, then the free-fall time, the time to fall distance r, would be:
tff = [2r/a(r)]1/2 ~ 1 / (Gassuming (3/2)1/2 ~ 1
free-fall time is independent of starting radius, however as the cloud collapses the density increases, and so the collapse proceeds faster.
If the cloud is rotating then the collapse will be affected by the fact that the angular momentum of the cloud must remain constant.
The angular momentum L is the product of the moment of inertia and the angular speed:
L = I
for a uniform sphere the moment of inertia is:
I = (2/5)Mr2
Conservation of angular momentum:
I00 = I0) = (r0/r)2
looking at a particle distance r from centre of collapsing cloud, the radial acceleration now has two parts: a(r) associated to change in radius and the acceleration associated to the change of direction r2
GM(r)/r2 = a(r) + r2 -> a(r) = GM(r)/r2 - r2
The effect of rotation is to slow down collapse perpendicular to axis of rotationRotation & effect on collapse
The virial theorem tells us that for a stable, self-gravitating, spherical distribution of equal mass objects (stars, galaxies, etc), the total kinetic energy of the objects is equal to minus 1/2 times the total gravitational potential energy. In other words, the potential energy must equal the kinetic energy, within a factor of two.
We can thus relate the luminosity of a contracting cloud to its total energy:
E = (-3/10)GM2/R
The energy lost in radiation must be balanced by a corresponding decrease in E. The luminosity L must equal dE/dt.
dE/dt = 3/10 (GM2/R2) (dR/dt) or dR/dt = 10/3 (R2/GM2) (dE/dt)
The fractional change in energy is equal to the fractional change in radius.
Once the cloud is producing stellar luminosities it is called a protostar. When the pressure in the core is sufficient to halt collapse the star is on the Main Sequence.