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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  

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interstellar molecules

not very optimistic

Interstellar Molecules

OH 18cm

H2O 1cm

NH3 1cm

In 1969, CO at 2.6mm - high abundance

Estimate rate of formation:

Rform= nCnOv



= 10-15 cm-3/s

nC density C atoms

nO density O atoms

v average thermal speed

 geometric cross section

10-3cm-3

Cosmic abundance

10-3cm-3

105cm/s at 100K

10-16 cm-2

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

and yet

faster chemical reactions

shielding from radiation

increased survival

and yet...
  • cloud structure:
  • higher densities
  • higher extinction
  • lower temperatures
interstellar chemistry
Interstellar Chemistry

Chemical reactions can take place on dust grain surfaces

-> formation of H2

Vibrational transitions -> infrared

Rotational transitions -> radio

Collisional transitions

balls on springs

quantisation of angular momentum

indirect presence of H2

physical conditions
Physical Conditions

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

slide8
CO

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.

the jeans mass
The Jeans Mass

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:

slide12

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.

slide13

In terms of the mass density 

combiningequations 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:

free fall time
Free-Fall Time

a(r) = GM(r)/r2 = G(4/3)r3r2 = (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 / (Gassuming (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.

rotation effect on collapse

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:

I00 = I0) = (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 r2

GM(r)/r2 = a(r) + r2 -> a(r) = GM(r)/r2 - r2

The effect of rotation is to slow down collapse perpendicular to axis of rotation

Rotation & effect on collapse
protostars
protostars

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.

hii regions
HII regions
  • In equilibrium in an HII region there is a balance between ionizations and recombinations: free electrons and protons collide to form neutral HI however the UV photons from the stars are continuously breaking up these atoms.
  • If NUV is the number of UV photons per second from a star capable of ionising hydrogen - this is the ionisation rate: Ri = NUV
  • The higher the density of photons and electrons the greater the rate of recombination: Rr = nenpV V is volume, and depends on temperature.
  • For the volume we can substitute a sphere of radius rs: Rr = np2(4rs3/3) the stromgren radius:
  • > NUV = np2(4rs3/3) or rs = (3/4)1/3(NUV)1/3 np-2/3
  • The size of an HII region depends upon the rate at which a star gives off ionising photons and the density of the gas.
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