Lecture 25 - Molecular Clouds and Star Formation (3/20/96)

Seeds: Chapter 9

1. Atomic Hydrogen Clouds
   • Neutral hydrogen atoms (ionization state H I) make up about 22% of the interstellar medium.
   • These clouds range in density and temperature from 3000K at 0.3 atoms/cm^3 for warm clouds to 100K at 50 atoms/cm^3 for cold clouds.
   • The primary way of identifying clouds of H I is through the 21 cm line.
   • The hydrogen line at a wavelength of 21cm in the radio spectrum is caused by a slight energy difference between states of the hydrogen atom where the proton and electron spins are aligned or opposite.
   • If you remember our discussion of the hydrogen energy levels and quantum numbers, then you will remember that particles like electrons and protons have a property called spin (quantum number s = +/- 1/2) which is analogous to picturing the particle as a little spinning top.
   • Because the proton and electron are electrically charged, the spin means that they act as little magnets. Because they are charged oppositely, their magnetic poles are aligned oppositely with respect to the spin in the electron versus the proton (if their spins are aligned, then their magnetic poles are opposite).
   • If you've played with magnets, then you know that they like to be oriented oppositely - the opposite poles attract and the like poles repel.
   • Thus, if the spins of the proton and electron in the hydrogen atom are aligned (poles opposite), then there is a tiny extra attraction which is like decreasing the energy of the ground state level (making the electron slightly more bound).
   • If the spins of the proton and elecron are opposing (poles aligned) there is a tiny repulsion, which is like increasing the energy of the ground state level.
   • The energy difference between these two configurations of the ground state is tiny: the photon wavelength to excite this transition is 21cm, compared to 121.6 nm for the transition from the ground state to the next higher electron level. Q: How many times smaller is this energy difference? What is this difference in electron volts (eV)?
   • If a photon of wavelength 21cm is absorbed or emitted, the spins flip relative to each other.
   • The emission (and absorption) of the 21 cm line by clouds of hydrogen can be observed with large radio telescopes. The line was predicted by the Dutch astrophysicist van der Hulst in 1945, and first observed by Ewen and Purcell of Harvard in 1951.
   • The 21 cm emission has been used to map out the H I clouds in our galaxy, and to detect H I in other galaxies.
2. Molecular Clouds
   • If a cloud is cold enough, then the atoms have the chance to come together and form molecules. This is able to happen in clouds with temperatures of roughly 100K or less.
   • These clouds tend to be buried deep within atomic H I clouds.
   • These are the coldest (10K - 100K) and densest (10^4 - 10^5 atoms/cm^3) clouds.
   • These clouds are made up mostly of molecular hydrogen (H2), which is two atoms of hydrogen bound together. The dissociation energy for H2, the energy needed to break apart the molecule, is 4.48 eV.
   • Carbon monoxide CO is also seen in clouds. CO has a dissociation energy of 9.6 eV, and it thus hardier than H2.
   • There are many other diatomic (two-atom) molecules found in molecular clouds, such as C2, CO, CN, CH, CS, SO, SiO, OH, etc.
   • More complex molecules like H2O (water!), HCN (cyanide!), H2S, as well as alcohols and molecules with more than 13 atoms have also been seen in these clouds! As of the end of 1993, over 93 different molecules have been seen in the ISM. That number has increased in the years since then.
   • The presence of these molecules has been identified by observing molecular lines, which like the atomic lines like the Balmer series of hydrogen, correspond to energy levels in the molecule.
   • The molecular energy levels correspond not to electron orbits like in atoms, but to vibrations and rotations of the molecule.
   • Vibrational lines are the most energetic, with typical wavelengths of 0.1 mm or shorter. For H2, the series limit is 4.48 eV (277 nm), with the "alpha" transition at 2275 nm, or 2.275 microns, in the far-infrared. The CO "alpha" vibrational transition is at 4.6 microns.
   • Rotational Lines are lower in energy, and thus come out in in the millimeter wave range. It turns out that to get a rotational transition, you need two (or more) atoms of different mass in the molecule - H2 has no rotational transitions, because it is symmetric! The "alpha" rotational transition for CO is at 2.7 mm, this is one of the primary lines used to map out molecular clouds.
   • Because the molecular clouds are the coldest and densest of the gas clouds, they are the places where stars are formed. They are in many ways "stellar nurseries".
3. The Orion Molecular Cloud
   • One of the most spectacular and nearest large molecular clouds is the Orion Molecular Cloud, which covers much of the constellation of Orion, and contains the bright diffuse Orion Nebula.
   • The cloud is at a distance of 460 pc from us, and extends over 30pc in size. The total mass of molecular gas in the cloud is around 2 x 10^5 times the mass of the Sun.
   • The oldest stars formed out of the cloud are near the shoulder of Orion, and are around 12 million years old. The youngest stars that we see are in the center of the Orion Nebula itself, and are about 2 million years old. The sun is about 4.5 billion years old in comparison.
   • Star formation in Orion uses less than 25% of the gas in any given region, there rest is blown away.
   • Because there seems to be a pattern to the ages, with the oldest stars farthest away from the nebula, we believe that there is progressive star formation where the formation of the first stars triggers the next stars to form. Thus, star formation sweeps through the cloud like a forest fire!
   • Note that the Sun itself was not formed with the first stars, its formation was triggered later on! In fact, basically all of the elements heavier than helium were formed in stars, then blown out in supernovae. Our bodies are made up of stuff that was cooked in long dead stars!
4. Under Pressure: The Ideal Gas Law
   • We have established that clouds will collapse under gravity until something stops the contraction. Some sort of pressure will do so - magnetic, radiation, or thermal gas pressure can do this.
   • To determine the pressure of a gas at a given temperature and density, we use what is called the ideal gas law. It is called an "ideal gas" law because it assumes the gas atoms or molecules are perfect elastic little spheres (not the "ideal" gas law because the law itself is perfect and just!).
   • By considering how atoms at velocity bounce off the walls of a container transmitting momentum, and remembering the definition of temperature as average velocity, and the definition of pressure as force per unit area, we get the relation: p = n k T where n is the number density of atoms/molecules, and k is Boltzmann's Constant .
   • What does this formula mean? First note that if you compress a gas holding the temperature T constant, you find that the pressure is inversely proportional to the volume - it takes force (pressure) to compress a gas.
   • Also note that if you take a gas in a container at constant pressure, say sitting at sea level at standard atmospheric pressure (10^5 N/m^2 = 14.7 pounds/square inch), then the density is inversely proportional to the temperature (volume proportional to the temperature.
   • What happens under gravity? The question of how the pressure, density and temperature of a gas behaves under gravitational contraction is at the core of the star formation problem. Because it is not under constant density, pressure, or temperature it is more complicated than we are prepared to derive quantitatively. Therefore, I will describe qualitatively the picture we have for star formation.
   • If we have two clouds in pressure equilibrium, that is co-existing at the same pressure p, then they can live in harmony as the pressures are balanced. If they had different pressures, then the lower pressure region would be compressed by the higher outside pressure until it reached equality with the other pressure.
   • The gas law tells us that for the regions 1 and 2: n_1 T_1 = n_2 T_2 This is why cold clouds are denser than hot clouds at the same pressure in the ISM.
5. Gravitational Heating
   • As clouds contract under gravity, some of the gravitational potential energy gets turned into kinetic energy of the gas, which in turn gets turned into heat.
   • This is exactly analogous to the calculation we made for the kinetic and potential energies in the atom, we just use the masses instead of charges in the potential: E = mv^2/2 - GMm/r
   • Thus, as the cloud contracts r gets smaller and thus the potential energy more highly negative, to keep the total energy E the same, the kinetic energy gets more highly positive.
   • About 1/2 of the heat is radiated away from the cloud at its surface, the rest raises the temperature in the center of the cloud.
   • The more massive the cloud is, the more potential energy it has, and thus the hotter it gets in the center.

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