What's relevant for star formation is the cold part of the interstellar medium, the part that can condense. This is a picture from Hershel Satellite, that is mapping particular giant molecular cloud in several different wavelengths. You can see that these clouds are nothing like spherical. They have this knobby structures, so all the dense spots, the dense clouds are where stars can form. The way we study is through millimeter wavelengths, mostly from planet Earth. And that's usually done with interferometers of telescopes, which have receivers in the range of wavelengths on the order of one to a few millimeters. Caltech, jointly with a few other universities, is operating one of these arrays. In California it's called CARMA for California, all right, for millimeter astronomy. And the world's biggest is now operating in Chile that's at the CARMA large millimeter array. There are others too. Interferometry is the popular way of doing radiostromy because it allows you to resolve things with separations of not limited by the resolution or any individual antenna. And they typical molecules that we see out there are, first of all, molecular hydrogen, atomic hydrogen being the most common thing. Molecular hydrogen is not likely to lag behind. But then, there'd be carbon monoxide, not dioxide, monoxide, and ammonium, and a whole bunch of other stuff including some very, very complex organic molecules. And it was very surprising why such complex organic compounds are found in interstellar space. But now astro chemistry's explaining most of these things fairly nicely. Actually that fact that there are large clouds of organic material in interstellar space, prompted thinking among some people that the life had originated in interstellar space and just got accreated on planet Earth. Now, I don't think this is likely to be correct, but there is plenty of organic material in the universe, and a lot of it ends on planets, too. So we now know from direct observations that star formation, like Orion Nebula. Famous picture of it. They're always associated with giant molecular clouds in all galaxies near us. This may not be the case with the very, very first stars and galaxies of but from most of the observed universe, this is a correct statement. And clouds are sitting there. Somehow they have to start collapsing and making stars. Usually that requires some physical cause to push them over a critical density limit and that could be, say, density wave was paralarm could be a shock wave super nova, could be just the tidal force between two passing bimolecular clouds. And then once you start collapsing them, they carry on and make stars. Here's a beautiful picture of individual clouds. These are remnants of a much bigger cloud that created those bright stars behind them, which have light reflected from dust fuzz around them, and plenty of red ionized hydrogen, but these are the densest cores that still haven't managed to evaporate. They're called Bok/Thackeray globulae, and they were seen in optical pictures before any of this was really clarified. So the question then is, why do these clouds collapse in the first place and make stars? And the process of this is called core collapse. And it's intrinsic to all physical systems that are bound by gravity. In fact, will be the case for any attractive interaction. And it works like this. So you have a cloud of gas and it's in some equilibrium. That means the thermal kinetic energy of molecules has to balance the gravitational potential energy, and this would generally be the case. It would be the highest in the middle. Cuz, you know, that's where most of the. So the cloud, or star for that matter, would be in electrostatic equilibrium if you have exact match between thermal pressure of the material and gravitational pressure pulls it down. All right, so think you squeeze it a little bit. That means the core of it will get a little hotter, it will emit more radiation. If this is long wavelength radiation that can go through this material, say long wavelength infrared that can penetrate dust clouds, it will escape, thus carrying away some kinetic energy. Because now some kinetic energy is being radiated away, the cloud shrinks some more. That brings it closer, again, to hydro-static equilibrium, which again leaves it at a slightly hotter core, which then shines more light and so on. And it's a runaway process. In case of stars, it's stops because a new source of energy opens up in the middle, the thermonuclear reactions, otherwise these clouds would collapse into black holes. But at some point, you start burning hydrogen into helium, that releases goodly amount of energy. And that more than compensates for the amount of energies being escaping from this collapsing proto star. So the core collapse leads into ignition of star in the middle and then all manner of other interesting physical things happen. Interestingly enough, the exact same things happens in globular star clusters. We can think of them as a gas cloud of stars. What serves as a source of energy there are binaries, but we'll get to that later. So some very basic physics of star information. So what's at play here? Obviously gravity that pulls things together, pressure has to balance it But other things that can also fight gravity are magnetic fields, because they're hard to squeeze, or just bulk motions, kinetic energy, in a different packaging. And so if you have one of these clouds, which is sufficiently dense to collapse, it collapses according to a free fall time scale. Which is, if you were to drop something at the outer most of shell, how long will it take to come to the middle? And because the shells inner to it are accelerated more than, there are more shell crossings, so all we need to do is take one more test particle at the edge of your cloud, such as it is and let it go. And expression for that's given here, and the time it takes to do it is also given here. And so you notice that time is inversely proportional to square of mean density, and that kinda makes sense cuz denser the cloud, we have stronger gravitational attraction, so it'll collapse faster. Okay? Now the other concept that's important here is called the jeans mass. And deriving the formula is beyond the scope of this class, but the physics is simple. You have thermal pressure that balances pull of the gravity. What is the minimum mass that will push this over and make cloud collapse? James Jeans was the first one to evaluate this and he came up with this formula. It's called Jeans Mass. It's a function of two variables, temperature and density. Now that little R inside, R G is gas constant from PV = RT, it's not radius. And the mu is the mean molecular mass in atomic units. So if you look at this formula, it says it's going to be proportional to temperature, three-halves powered, why that power? It doesn't matter. And that again kinda make sense, because if you have a hotter cloud, it will require more mass to push it over into a collapse. Contrary to that, if your cloud is denser, then you wouldn't need as much and the mass would go down. So be inversely proportional to this weak power of density. So plug in the typical numbers that we observe for interstellar clouds and assume it's more like molecular hydrogen, it doesn't really matter if you take a mix of carbon monoxide. And amazingly enough, it produces a value that's pretty close to the mass of our sun. Now most stars are actually less massive than our sun. There are many more low mass stars than high mass stars. And so this is kind of amazing, if you know the temperature and the density of the proto stellar clouds, characteristic mass of stars comes out. Now stars don't come in one mass. Stellar mass functions not the delta function and that's because the clouds are not perfectly uniform, etc, so there will be some range of densities and temperatures and anti-fields and god knows what else. But this is very simple application of thermodynamics and gravity in deciding how stars are made. Just as we define a mass, there's also a characteristic length and that's called the Jeans length that would be the typical scale of clouds under which things start to collapse. And so if we just solve it so that it's a function of radius and not temperature, not mass, you get formula, which is similar to the previous one, proportional to some weak power of temperature, again because cutter clouds, you need to have a bigger cloud in order to get enough mass to collapse. Then you're easily proportional to weak power of density, denser clouds will collapse sooner, so going back. And that happens over the, three, four time scale. Now typical sizes of these proto stellar clouds are in the tens of thousands astronomical units, so they're bigger than a solar system by far. And if you plug in the numbers you find out that for this example, it will take approximately half a million years for a stellar cloud to collapse. And that's good, because that's just barely shorter than the lifetimes of massive stars. Why is that important? Because stars are disrupting star formation. So it makes them high mass stars, very luminous. They do two things. First they shine the UV. They go ionize the gas. The gas will be too hot to partake in formation of stars, they'd be just too much kinetic energy in the gas. And as they do this, they essentially eat the dust, they evaporate the dust. And so you form a bunch of stars and at that point star formation is more or less over. These young stars will preclude any more stars being made in that same region. And so you often see these clusters, that they're embedded into these nebuli, and this is picture of Rosette Nebula, slight unusual coloring. I see a cluster of bright, young stars. There are many fainter ones as well, but it's the brightest ones that dominate this process. So this also tells you that stars tend to get made in clusters, in groups. The reason for this is that a given cloud will fragment into multiple pieces cuz you've seen them, they're not spherically symmetrical homogeneous, they have those complicated geometry with many little dense knots. Each of those can give rise to a star. And so more or less all of them will kind of do their thing simultaneously. And however many those dense cores you have, that's how many stars you're going to make. And then as soon as the big stars start shining, game over. So star formation is self regulating because these stars last millions of years and collapse processes half a million years or something, that means that there'll be a regulation. Once you start making stars you can't make new stars until those massive ones are gone, and then you can start making more stars. Well, so radiation is one thing, they ionize the gas. The second thing is they like to explode. And what that does in addition to ionization is this sheer kinetic energy that's been implanted now in the gas cloud. It's approximately 10 to the 51 ergs, for a typical supernova, and the shockwave just clears out the dust, swoops it out. And so this is where those bubbles you've seen in pictures of interstellar medium came from. Right? But they begin like this. And so, the moment first supernova goes off in your star forming regions, that's it. So stars eat clouds, first. They're made up of that material, and then once they're made, they just destroy the rest. And you can also have a shockwave from explosions. So this is a cartoon of what that might look like. And this is an actual picture of one such thing, taken with Hubble. So we have a pretty good idea how stars form. Now, stars do something else interesting and important, and that's highly relevant for formation of planets, which is stuff falls in, settles into a protostar. But if there is any angular momentum, that angular momentum cannot be radiated away. So the material which had excess angular momentum has to settle into the lowest energy state for a given amount of angular momentum as you'll probably recall when we were talking about the origin of Kepler's laws. That essentially means surface. And so material with too much angular momentum will settle into a thin disk around newly minted star, which is made out of stuff that didn't have much angular momentum. And this is artist's conception but we have actually seen the real things. Oops. Here we go. And these are obtained with Hubble in the Orion star forming complex. And they are not necessarily symmetric, but they really are little protostellar disks with young stars embedded in them. Another thing that they do, is they drive so called bipolar outflow. If there is any magnetic field, and usually there is some inside of that propostelic cloud, as it collapses it will get bunched up and threaded through this disk. This disk will keep spinning and tightening even more. That creates a preferred axis along which you can accelerate charged particles. This is very similar to what happens in quasars and active galactic nuclear, but a much lower energy scale. And so the protostar consists of, it's actually three pieces. There is this actual protostar in the middle, that's igniting and starting thermonuclear reactions, surrounded by a thin disk of leftover material which soaked up all the angular momentum. And then outflow that happens along the rotation axis. And that's not fantasy either, here we are. These are actual proto-stellar jets from young stars as observed with Hubble, but a lot of things.
