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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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HI - atomic hydrogen - 21cm T ~ 0.07K
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
faster chemical reactions shielding from radiation increased survival and yet... • cloud structure: • higher densities • higher extinction • lower temperatures
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 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
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 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.
In terms of the mass density 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:
Free-Fall Time 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 rotation Rotation & effect on collapse
Bally, O’Dell & McCaughrean 2000 AJ 119, 2919 Sterrenformatie - Orion
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 • 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(4rs3/3) the stromgren radius: • > NUV = np2(4rs3/3) 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.
