Background: The Big Bang
P = d ´ T = M/R3 ´ (1/R)??
Based on the Hubble redshift observed for distant galaxies, the Universe is believed to have started out, about 15 billion years ago, as a very small, dense, hot blob, which expanded violently outwards in all directions, in an explosion which we call the Big Bang. In the first few moments of the expansion, the temperatures and densities were so high that matter as we know it could not exist. As the expansion proceeded, temperatures and densities dropped very rapidly, and within a very short time, the primordial stuff of the Universe was transformed into hydrogen nuclei, electrons, photons, and neutrinos. For a little while after this, hydrogen was fused into helium through the same proton-proton cycle still used in stars like the Sun, until only 3/4 of the weight of the Universe remained as hydrogen, and 1/4 was helium. Not much later, as the expansion cooled off the gases, the temperature dropped so that hydrogen fusion could no longer occur, and the gas simply expanded more and more, causing temperature and density to continually decrease. For a few hundred thousand years the gas was so dense that photons of light were continually running into other particles (the gas was opaque, as in the interior of a star), but as the gas expanded, the light was able to move further and further without interference. Eventually the gas became so rarefied that most light could keep going through space forever without running into anything. The early stage where the Universe was opaque, and light could not get very far, is referred to as the Cosmic Fireball. Once the Fireball had expanded to the stage where it became transparent, and light could travel freely through the Universe, the Big Bang was over.
Background: Origin of the Galaxy
Eventually, as the hot gases from Big Bang cooled, electrons combined with protons to
make neutral hydrogen gases, and gravity began to pull gases together, forming galaxies, and within the galaxies, stars.
When the gases that become our Galaxy were still spread out over hundreds of thousands of light years, the density would have been relatively low, making it difficult to get denser clumps of gas which could form into stars. The large distances between halo stars (low star density) presumably mirrors the low formation rate at that time.
As the gases contracted towards the center of the Galaxy, they became denser, making it easier to get dense clumps of gas which could form clusters of stars. The smaller distances between stars closer to the nucleus presumably mirrors the higher formation rate at that time.
As the gases contracted to form the nucleus of the Galaxy, the still greater gas densities made star formation faster and faster, so there are more and more stars closer and closer to the nucleus.
At the end of the formation, large amounts of gas may have formed into huge numbers of stars, or they may have collapsed to supermassive black holes. Most of the stars in the Galaxy probably formed within a billion years or two after the start of the Galaxy's formation, over 12 billion years ago. Since then, star formation has been much slower, since most of the gas had already been turned into stars. There are very few places where there is much gas left to make into new stars (mostly in the spiral arms).
Stars formed during this early stage have very few heavy atoms in them, while stars formed later on have more and more heavy atoms in them, because the heavy atoms are not formed in the Big Bang, but in massive stars. During the formation of the Galaxy, there was a lot of gas left, and very few stars, even massive ones, had had time to die and spread their ashes around. Later on, there was less gas left, and more ashes from dead stars, so the ratio of heavy atoms to light ones gradually increased (to about 4% by weight today).
Background: Structure of the Galaxy
The Sun is about 25000 light years (LY) from the center of our galaxy. The nucleus of the Galaxy is roughly spherical, about 10000 LY in diameter, and contains about 100 billion solar masses. Superimposed on this is a flattened rotating disk which is about 100000 LY in diameter, 2000 LY thick, and also contains about 100 billion solar masses. Superimposed on both of these is the halo, which is roughly spherical, between 200000 and 500000 LY in diameter, and contains between 100 billion and 500 billion solar masses. Our Galaxy probably looks very much like the Andromeda Galaxy, but is probably only 70-80% as large.
Most of the stars in the galaxy are very old, which means they are very faint, since bright stars cannot last very long. In the nucleus, the stars are only a few light weeks or months apart, but in the disk they are several light years apart, and in the halo they are tens of light years apart. Because the stars are thickly clustered in the nucleus, even though they are individually faint, their combined light can be easily observed, even at the distance of other galaxies. But in the disk and halo, the larger distances between the stars mean that even their combined light is usually too faint to observe.
There are, however, regions in the disk of the Galaxy which contain large amounts of gas and dust, out of which new stars are continually forming. Some of these stars are massive, hot, large, bright stars, and they light up the space around them, making it easy to see the regions where they have just formed. The places where gas and dust are common usually have a spiral distribution, so they are called spiral arms. In these regions, new stars can continually form out of the gas and dust, or Interstellar Medium.
Initial Conditions For Forming Stars: The Interstellar Medium
Clouds of gas and dust in interstellar space are very large (often tens or hundreds of thousands of AUs in size), but very rarefied, with only a few tens or hundreds of atoms (mostly hydrogen and helium) per cubic inch. Considering that a cubic inch of air contains almost a billion trillion molecules of nitrogen and oxygen, a typical interstellar cloud has almost nothing in it at all. In fact, if you were inside such a cloud, unless you had sensitive measuring devices, you wouldn't be able to tell that it was even there. However, despite the small amount of material in any given area, the clouds are so large that they can contain substantial masses, comparable to, or even larger than, the mass of our Sun.
In order to form a star, something has to happen to make this incredibly large, incredibly thin gas collapse to a very small, very dense object: a Main Sequence star. That requires some kind of force which can compress the gas, and make it smaller and smaller.
Sometimes, the force that accomplishes this is simply the force of gravity. If, in some way, gravity can overcome whatever forces keep the cloud at its current size (to be discussed in more detail below), then, as the cloud decreases in size, the gravitational force will increase, since it depends upon the inverse square of the distance between the various parts of the cloud. As the cloud shrinks, the various parts get closer together, so the gravitational attraction between them increases. As this happens, it should become easier and easier for gravity to pull things still closer together, and if there weren't any other problems, the cloud would shrink, faster and faster, as its parts pull closer and closer together, and exert larger and larger forces on each other.
The only trouble with this idea is that there are various problems to overcome. One of them is a tendency for the cloud to rotate, faster and faster, as it gets smaller. However, that has been dealt with earlier (in the discussion of the origin of the Solar System), and in any event, is not a serious problem until the cloud becomes much smaller than its original size. There can also be problems with a gradual increase in the magnetic field which runs through interstellar space. Although it is very, very weak, it will become stronger as the cloud contracts, and it can, to a certain extent, oppose the contraction of the cloud, as well. However, to a certain extent, as in the case of rotation, the magnetic field simply makes the cloud contract in certain ways, rather than preventing it from contracting at all, and in any case, the physics involved is well beyond what can be easily explained at an introductory level, so we will ignore it, as well, in this "simple" discussion.
There is, however, one problem which cannot be ignored, in discussing the formation of stars, namely the fact that, in addition to gravitational forces which are trying to contract the cloud, there will be an internal pressure, due to the motions of the gas particles, which is trying to expand it. This pressure will be extremely small at any given place, because it depends upon the density and temperature of the gases, which are both very low. As already mentioned, the gas is millions of trillions of times thinner than air, so the density is incredibly low, and the temperature of a typical interstellar cloud is also very low, typically no more than 100 Kelvins above absolute zero, or more than 250 degrees below zero, on the Fahrenheit scale. With both a low density and a low temperature, the gas pressure is very close to zero, so it would be easy to ignore it, at first thought.
However, although the gas pressure is very low, it should be remembered that since the cloud is very large, its gravity is also relatively low. Even if it has a mass like that of the Sun, since it is millions, or even tens of millions, of times larger than the Sun, its gravity would be that amount SQUARED, or many trillions, or hundreds of trillions, of times less than the Sun's gravity. As a result, BOTH the gas pressure and the gravity are very small, and in point of fact, under normal circumstances, they must be more or less equal. If this were not true, then clouds would always be fairly rapidly contracting to form stars (if gravity is larger than gas pressure), or expanding into nothingness (if gas pressure is more than gravity). The fact that, over 12 billion years since our Galaxy began, there are still regions, such as the spiral arms of the Galaxy, where as much as half the mass is in the form of clouds of gas and dust, means that most of the time, interstellar clouds must be in a state of quasi-equilibrium in which gas pressure and weight are more or less in balance.
Why It Is Hard For Interstellar Clouds to Form Into Stars
Now, let's suppose that we think about contracting a cloud again, taking into account the fact that initially, the gas pressure may be approximately equal to the gravitational force which is trying to contract it. As the cloud gets smaller, the gravity will increase, but so will the pressure. In fact, under normal circumstances, the pressure will increase considerably. For one thing, the density of the gas will increase as the inverse CUBE of the radius, since density is mass divided by volume, and volume goes as the cube of the radius, presuming the overall shape and structure of the cloud changes in a more or less uniform way. For another, when you compress a gas, the work that you have to do to fight the internal pressure is converted into an increase in the energy of motion of the gas particles, or an increase in the temperature of the gas. The exact amount of the increase depends upon the nature of the particles. If they are simply pieces of atoms, with no internal structure, all of the work done on the gas is turned into an increase in the heat and temperature, but if they are complex objects such as molecules, part of the energy may be converted into internal motions and energy, and part into external motions, and heat. Regardless of the details, however, if nothing else complicates matters, compressing the cloud to a smaller size would result in an increase in its temperature. As a result, the pressure could be expected to react to a decrease in size approximately as shown by this equation (note that all constants and other complications are ignored -- this is just to show the basic concepts):
The ?? on the Temperature part of the equation represents the uncertainty as to how the temperature would increase, but in general, we can expect the pressure to depend on (approximately) the mass of the cloud, and the inverse FOURTH power of the size of the cloud. If we compare this with gravity, which depends upon the square of the mass, and only the inverse SQUARE of the size of the cloud, we can expect a change of force something like that shown in this diagram:
In this diagram, the size of the cloud increases towards the right, and the force that is under discussion increases towards the top (those of you who love mathematics will note that the scale for each quantity is logarithmic, so that exponential relationships are shown as straight lines). As you can see, as you go toward smaller sizes (on the left), gravity increases rapidly, but the pressure increases even more rapidly. In fact, for each 1% decrease in the size of the cloud, gravity will increase by 2%, but pressure will go up by around 4%, or about twice as fast. Because of this, unless something can be done to prevent the pressure from increasing as the cloud contracts, gravity will not be able to overcome the pressure, and the cloud will not contract to form a star.
Ways of Overcoming the Pressure
Of course, despite the fact that it is difficult for clouds to contract to form stars, hundreds of billions of stars now exist in our Galaxy, showing that somehow, any problems which prevent their formation must be overcome, so somehow, the problem of overcoming the pressure must be solvable, and easily solvable.
One way in which this can occur has to do with the fact that, in the spiral arms, there are hundreds of thousands or even millions of clouds clustered together in some areas. As they gradually move around, they can collide, and merge. There can be a number of effects associated with such collisions, but to keep things relatively simple, let's just presume that two or more clouds very slowly pass through each other, and, for a while, are essentially a single cloud. The gas pressure inside the combined clouds is proportional to the overall mass, so it will go up by however many times the overall mass increases, but the gravity is proportional to the mass SQUARED, so it can temporarily become much larger than the pressure, depending upon how much mass becomes concentrated in one area or another. This would allow the combined clouds to, at least in some of their denser areas, start collapsing toward considerably smaller sizes, and considerably higher densities, as the gravity pulls things in, closer and closer, denser and denser, as originally discussed, a little while ago.
Of course, as the size of a given part of the combined clouds decreases, and the density increases, the pressure within that region will tend to increase, and as already discussed, will in fact increase much faster than the gravitational force, but if the gravitational force starts out considerably larger, it may take a while for the pressure to catch up, and as described below, by then, things may have changed considerably. So this method of getting stars started will at least get us over the first hurdle.
There is also another way of getting things started, which depends upon the fact, discussed much later here, but which you have hopefully already become aware of, from reading your textbook, that massive stars tend to form very quickly, and when they do, become extremely hot, and extremely bright, lighting up, and heating up, large areas all around themselves. If, in a region with many, many clouds (that is, in one of the spiral arms of the Galaxy), a number of massive stars can form and begin to light up, and heat up, the surrounding gas, the gas can very quickly increase its temperature, from less than a hundred Kelvins to more than ten thousand Kelvins. This increase in temperature increases the pressure inside the gas by more than a hundred times, and such HII regions, as they are called, begin to expand outward, quite rapidly, blowing the gas which is so heated away from the massive, bright stars.
If there is nothing in the way of the expanding, heated gas, it will just expand out into space, and eventually become too thin to notice. But if it is expanding into a region filled with cooler clouds of gas, it will press against them, eating away at their outsides (since the expanding gas is hot, it will gradually heat up and eat away at the cooler gas), and at the same time, compressing them with a force that is as much as a hundred times greater than the internal gravity and pressure of the denser clouds. We can, in fact, see many emission nebulae, as the hot, glowing gas lit up by the massive, bright stars are called, in which cold, dark clouds of denser material are being compressed by the expanding, heated gas. Depending upon the shape of the colder, denser material, we call the darker region "dark globules," or "elephant-trunk" structures. The Horsehead Nebula, the Cone Nebula, and the Eagle Nebula are all examples of elephant-trunk structures, and you can easily see, in many of the photographs of emission nebulae in the book (a favorite kind of illustration, because they are so pretty), small dark blobs, or dark globules, which are surrounded by, and being compressed by, the heated gases surrounding them.
Since the heated gas may have a pressure which is as much as a hundred times the internal pressure of the colder, darker gases that they are pressing on, they can force the colder clouds of gas to rapidly contract. As the clouds contract, their own gravity will of course increase, and the external forces, added to the internal gravitational forces, can force the clouds to contract much faster, and much further, than a simple gravitational collapse would allow.
If these methods won't work, there is also another, even more spectacular way of forces clouds to become stars. When the massive stars already referred to end their lives, they usually do so in spectacular explosions, referred to as supernovae. In these fiery explosions, huge amounts of gas can be ejected into space at tremendous speeds. When these gases collide with clouds of gas, they can violently compress the clouds, with forces far larger than any so far discussed. Because of this, it is not unusual to see, within arcs of gases which were ejected by supernovae, knots of hot, bright stars which formed as a direct result of the impact of the expanding supernova gases with cooler, denser clouds.
The expansion of gases near young, hot stars of high mass, and the violent expansion of gases by the death of high-mass stars, can be so effective in helping clouds of gas turn into stars that as many as half of even the high-mass stars may be formed in such a way, and almost all low-mass stars, such as the Sun, have at least some kind of help of this sort. (Note in passing: In discussions of the origin of the Solar System, and the melting and differentiation of the planets, it was mentioned that there must have been a large amount of short-lived radioactive elements in the gases which made up the cloud which became our Solar System. This suggests that not only was the Sun helped to form by the explosion of another, more massive, star, but that a substantial minority of the heavy elements in our Solar System may have actually been created at the time of the death of that star, and mixed in with the materials which were in the already existing, cloud. So, in several ways, we may well owe our existence to the death of a massive star.)
Breaking the Relationship Between Temperature and Cloud Size
In order for a cloud of gas to form into a star, the tendency of pressure to rise faster than gravity and external forces must be overcome. Stars are millions of times smaller than interstellar clouds, and even if external forces and gravity are originally hundreds or thousands of times greater than the gas pressure, as the cloud contracts the pressure should rise dramatically, and catch up with the compressional forces when the cloud has contracted only a few dozens of times. So how can clouds turn into stars? We know that somehow, this problem must be fairly easily solved, because there are hundreds of billions of stars. How is this accomplished?
One of the key problems in forming stars is that the temperature of the clouds tends to increase as they are compressed. If we could somehow stop this from happening, it would be much easier to form stars, because the pressure wouldn't rise as quickly, and the compression could continue for a longer period of time, pushing the cloud much closer to stellar size. As it turns out, the difference between the way in which the gas in the clouds interacts with light, and the way in which the "dust" (a mixture of silicate grains, carbon compounds, and ices) interacts with light, is the key to the problem.
When clouds are spread out, most of the material in any given region is gas. Typically, a cloud might contain a few dozen, to a few hundred, atoms (mostly of hydrogen and helium) per cubic inch, but only a few dust grains per cubic mile. The reason for the difference is party that the materials which make up the dust are rare -- amounting to only a tiny fraction of one percent of the total number of atoms -- and partly that each dust grain, although microscopic (studies discussed in the text show that the most common dust grains are about 1/50000th of an inch in size), consists of many billions of atoms, whereas the gas consists mostly of individual atoms, or molecules containing only a few atoms. Since the dust grains require huge numbers of atoms, each of which are relatively rare, the dust grains are far less common than the gas particles.
The gas particles only absorb certain types of light which pass through the cloud -- mostly, ultraviolet light, corresponding to wavelengths which hydrogen and helium atoms can absorb, when in their "ground" states. Such light is quite rare in interstellar space, partly because all light is rare (the stars are mostly far away, and pretty faint), and partly because only hot, bright stars, which are not as common as ordinary stars, because they don't last very long, can give off such ultraviolet radiation. As a result, most of the light from the distant stars, which is visible or infrared light, passes right through the gas, as if it weren't even there. There is a very small absorption of specific wavelengths by rarer atoms and molecules of gas (refer to the discussion of interstellar absorption lines in the text), but the vast majority of the light which passes through the clouds literally just passes through them, at least as far as the gas component of the clouds is concerned. In other words, the gas in the clouds does a pretty poor job of blocking, or absorbing, the light passing through it.
Now, you might expect that if the gas doesn't absorb much light, it would be relatively cold, as it is the light absorbed the gas that is primarily responsible for what little heat that the cloud has. But remember the example of Venus. Venus reflects most of the sunlight which falls on it, so much, in fact, that if the light which did make it through the clouds, to the surface, were absorbed and emitted in a normal equilibrium, Venus wouldn't be much warmer than the Earth, despite being considerably closer to the Sun. However, Venus is much hotter than you'd expect, because, as hard as it is for light to reach the surface, it is even harder for the infrared radiation emitted by the surface to get out, as a result of the runaway greenhouse effect caused by the atmosphere of Venus. In a similar way, if we want to understand the heat balance of interstellar clouds, we must consider not only how they absorb light, but also how they get rid of it.
Now, it is very difficult for the clouds to absorb heat, because they can only absorb tiny amounts of the visible light passing through them, and although they are pretty efficient at absorbing certain types of ultraviolet light, that kind of light is quite scarce in interstellar space. However, as hard as it is for the clouds to absorb light, it is even harder for them to get rid of it.
As you can read in the text, the hydrogen and helium atoms which make up the bulk of the gas are normally stuck in their so-called "ground" state. In this state, they can only emit radiation by colliding with each other at very high energies, which would correspond to temperatures thousands of times higher than the actual temperature of the gas. As a result, they shouldn't be able to get rid of any of the heat that they've absorbed, and although they absorb very little at any given time, they should gradually heat up.
Eventually, as the gas increases in temperature, collisions of gas particles will put some of them into "excited" states which can emit radiation. For complex atoms, such as iron or calcium, which have complicated structures, and complicated energy level diagrams, small amounts of radiation can be given off, once the gas is relatively hot. But these atoms are rare, and at the low temperatures in the interstellar clouds, give off radiation in only small amounts. Most of the radiation is given off by complex molecules, and by a particular radiation due to hydrogen atoms, called the 21-centimeter radiation, because that is the wavelength of the radiation.
The 21-centimeter radiation represents a substantial fraction of the radiation by interstellar clouds of gas, and in fact, is sufficiently strong that we use it to map the distribution of such clouds of gas in interstellar space. But the radiation is only given off once in a great while. To emit it, a hydrogen atom which is in its ground state must bump into another one, which doesn't happen very often, and end up in a very slightly energized version of the ground state. The ground state turns out to consist of two extremely close energy states, differing by an incredibly tiny amount of energy, according to whether the electron going around the nucleus has a "spin" which is parallel to, or anti-parallel to, the "spin" of the nucleus. Switching from one of the two spin states to the other one involves the absorption (through collision) or the emission (through a 21-centimeter photon) of that very tiny amount of energy. Since the energy involved is so small, it takes over a million 21-centimeter radiations to get rid of the energy absorbed from a single ultraviolet photon, and the rate at which the 21-centimeter radiation is emitted is quite small, because the collisions which put the hydrogen atoms into the correct energy state to emit it, are very rare.
To summarize this long, complicated story, the gas has a hard time absorbing light, and an even harder time getting rid of it, and as a result, is much warmer than you might expect, given the tiny amount of light falling on a typical cloud. In fact, if the cloud absorbed and emitted heat in an easy, effective way, it would probably have a temperature no more than a few degrees above absolute zero, whereas usually, the gas temperature is around a hundred degrees above absolute zero, or even higher. This is very cold by our standards, since we live on a world where temperatures are more than 500 degrees above absolute zero, but still very hot compared to what we would expect, if the clouds were in "equilibrium" with the light running through them.
In addition to the gas, however, we also have the small number of dust grains which are scattered throughout the cloud. The dust grains do not absorb light in the same way as the gas particles. They absorb, or scatter, it more like ordinary bits of solid material, and although, because of their small sizes, they have a much harder time interacting with light, especially longer wavelengths of light, they can interact with the light much more effectively than the gas particles. To see how this works, suppose that you were in the middle of one of these clouds. You would absorb starlight, at a very small rate, because the starlight falling on you would be quite faint, and radiate heat, because you are warm, at a much greater rate. Both the absorption and emission would proceed at a rate comparable to that of a so-called "black body", because you are made of solid materials, which are good at absorbing and emitting light. As long as you were relatively warm, the starlight that you were absorbing, although absorbed fairly well, would be far less than the heat your body was radiating, and you would cool off. However, as you got colder and colder, the rate at which your body would radiate heat would gradually decrease, and when you got cold enough, it would be equal to the rate of absorption of starlight, and you would stop cooling off. This would happen, in most places in interstellar space, when your temperature was less than 10 degrees above absolute zero.
Now, the dust grains in the interstellar clouds can't absorb and radiate heat as efficiently as you can, because they are microscopic, and have trouble interacting with light waves which are bigger than they are (which is most of them). So they might not stabilize at quite the same temperature that you would, because their heat balance wouldn't be quite as efficient as yours. However, they would stabilize at a much lower temperature than the gas surrounding them, because they are much more efficient at absorbing and emitting light, and would be closer to the expected equilibrium temperature for objects in interstellar space.
The result of all this is that you can think of a typical interstellar cloud as consisting of a huge amount of relatively hot gas, and a very tiny amount of relatively cold dust grains. The dust grains, being made mostly of ices (because that is the most abundant materials making them up), are literally dirty pieces of ice, and, compared to the gas, ice cold, as well.
Now, when the clouds are spread out over tens or hundreds of thousands of AUs, there are so few dust grains per cubic mile that any given gas particle is hardly ever going to run into an ice grain, and so the fact that the ice grains are much colder than the gas is of relatively little importance. But what would happen if the cloud were compressed, either by its own weight, or some external force, to a size which is many times smaller -- say, ten times smaller than its original size?
In that case, the density of the cloud would increase by a thousand times, meaning that each part of the cloud would have a thousand times as many gas particles, AND a thousand times as many dust grains, per unit of volume. Under those circumstances, collisions between the gas and dust particles would occur a thousand thousand, or a million, times more frequently. If, at the large size that it started out at, collisions with the dust grains were robbing the gas particles of only a tiny fraction of one percent of their heat, as the cloud contracted, and became denser and denser, the dust particles would gradually have a better and better chance to steal heat from the gas, and radiate it away. Because of this, as a cloud compresses, although it should get hotter and hotter, because the compression of the gas pumps heat energy into it, the ability of the dust grains to steal heat away from the gas can become so much more important that, instead of heating up, the gas actually decreases in temperature.
If this idea is correct, then clouds which have been compressed to a much smaller size, instead of being a hundred degrees above absolute zero, should be much closer to absolute zero. And in fact, when we observe compressed clouds, referred to as dark globules, because they look like dark little blobs, or as protostellar clouds, because we believe that they are well on the way to becoming stars, we find that they are indeed, in most cases, much colder than typical interstellar clouds, and in some cases, the outer parts of these dark globules are only a few degrees above absolute zero.
A Cloud Collapses, and a Protostellar Cloud Begins
The way in which stars start out is, therefore, like this. Either as a result of the merger of several clouds, or some external force, involving the life or death of a nearby massive star, a cloud begins to contract. As it does so, the increasing density allows the dust inside the cloud to steal the heat energy of the compression from the gas, and radiate it into interstellar space, preventing the cloud from heating up, and in fact, causing it to cool off. This allows the compressional forces to remain substantially higher than the internal pressure for a long period of time, and over a period of a few tens or hundreds of thousands of years (depending upon how violent and rapid the collapse is), the cloud shrinks from several tens or hundreds of thousands of AUs, to a much, much smaller size.
Throughout this collapse, the gas in the cloud is, in a sense, in "free fall", or "accelerated free fall", pushed inward by forces much, much greater than the pressure. But, as it turns out, this state of collapse cannot continue forever, as eventually, the pressure will rise, catch up with the compressional forces, and stop the collapse, at a stage of formation which, as mentioned above, is referred to as a dark globule.
To see how this works, consider what the cloud would look like, if we could speed up time by hundreds of thousands of times, and watch it collapsing. At first, it would be spread out over a vast space, and be relatively transparent, because the gas allows most light to go right through it, and the dust is too spread out to affect the light much, either. But as the cloud collapses, it would become denser and denser, and it would gradually become more and more opaque, meaning that the light of distant stars would have a harder and harder time getting through it.
Hopefully, you will remember that we refer to idealized radiation, such as that given off by stars, as "black-body radiation", because, as discovered by Kirchhoff, if an object is a good absorber of heat and light, it is also a good emitter of heat and light, and since nothing can absorb light energy better than a black object, which absorbs all the light falling on it, such an object, when radiating light, would be more efficient than any other kind of object, as well.
Now, when the gas cloud is spread out, and most light just passes right through it, it is obviously not a very good absorber, and so, it is not a good emitter, either. The gas does a lousy job of absorbing and emitting light, and the dust, hardly any better a job of it. But as the cloud shrinks, it will become harder and harder to see through. The gas still doesn't do a very good job of interacting with light, but the dust, as it becomes more and more thickly concentrated, does a better and better job, until it is so good at blocking light, that you can't see stars through the cloud, at all (refer to the discussion of interstellar extinction and reddening in the text for more about how the dust blocks the light of distant stars). But if the dust is doing a better and better job of blocking the light of stars -- that is, if it is acting more and more like a "black body" -- then it must also be doing a better and better job of radiating away the heat of the cloud -- that is, it must be stealing heat from the gas, and radiating it into space, and pushing the cloud to lower and lower temperatures, more and more efficiently.
Because of this, as the cloud gets denser and denser, and darker and darker, approaching the "dark globule" stage, it should gradually cool, more and more, until it is close to absolute zero, as already discussed. But there is a limit to how far this can go, because, as the cloud gets denser and denser, there will come a time when the dust is so good at blocking light that it not only prevents the light of distant stars from passing through the cloud, but it also prevents the heat which is being radiated away by dust near the center of the cloud from escaping. When this happens, the cloud will begin to alter its structure, becoming more and more like a star, with higher temperatures in the middle, and lower temperatures near the outside, and, as heat flows from the dense, opaque, central regions, toward the less dense, less opaque, outer regions, we develop a structure which is hotter and denser in the middle, and less hot, and less dense, outside.
Quasi-Equilibrium Contraction: Differences Between Massive and Low-Mass Clouds
Once the temperature begins to rise in the core of the contracting cloud, meaning, once it is a dark globule, and heat radiated by the center cannot just escape to interstellar space, but must struggle to get through the intervening gas, the collapse of the cloud will begin to slow. For some clouds, which have large external forces, the cloud may already be about the size of our Solar System when this happens. For others, the cloud may be somewhat larger than our Solar System. But in all cases, it will be substantially larger than a star, so there is still quite a bit of development left, before the star that the cloud will eventually become, has finally been formed.
In the interval between the initial collapse, and the final formation of the star, the central part of the cloud will undergo a relatively slow, more-or-less steady contraction, in which, at any given time, the internal pressure, caused by the extreme density increase which resulted from the initial collapse, and the relatively high temperatures created when the dust became too thick for the internal heat to easily escape, becomes essentially equal to the external forces, and any intrinsic gravitation force, and, if the heat of the core could be held onto, the cloud would stop getting smaller, and would remain more or less stable, at a relatively large size.
Now, despite this suggested possibility, it is not actually possible for the cloud to remain constant in size at this point. For one thing, there may be more gas, further out, which is still collapsing towards the central core, and has not yet become so dense and opaque that its temperature is substantially increasing. In addition, the core will now be relatively hot, and radiating energy (primarily infrared radiation) at a fairly substantial rate, and unless that radiation energy is somehow replaced, the gas in the core of the protostellar cloud, or dark globule, will cool off, reducing the pressure, and allowing the compressional forces to win, and force the cloud to still smaller sizes.
As it turns out, however, things don't work quite exactly that way. It is true that, as heat is radiated away from the core, there is a tendency for the gases to cool off, and for the compressional forces to push the cloud to still smaller sizes, but in the process, energy is created, and the gas, instead of cooling off, actually gets hotter. We refer to this stage of the star's formation as a gravitational contraction, and the heat generated by the contraction will not only replace the lost heat, but actually add to the store of heat in the central core of the cloud, so that instead of cooling off, it gets hotter, and hotter.
The rate at which the core gets hotter strongly depends upon the mass of the cloud, because, the more massive the cloud is, the greater the gravity it has, and the greater the force that it exerts on itself, as it contracts. But, according to the laws which govern all heat engines (automobile engines, refrigeration units, air conditioning, etc), the compression of the gas will create an amount of heat which is proportional to the force which is compressing the gas. If the gas is compressed by only a small force, only a small amount of heat will be generated, and the gas will become only a little hotter, whereas, if the gas is compressed by a large force, a much larger amount of heat will be generated, and the gas will become considerably hotter.
The result of this is that a relatively massive cloud will, as it contracts, generate far more heat, and become considerably hotter than, a less massive cloud, which has a smaller gravity, and a smaller compressional force, as a result of its lesser mass, and because of that, as clouds of different mass contract, the more massive ones will, at a given stage of the contraction, be hotter at a given size, or bigger at a given temperature, and, in either case, end up much brighter, radiating heat away into space at a much greater rate. A cloud which is going to become a low mass star might take a million years, slowly radiating heat away, to shrink from a given size and temperature and brightness, to a particular smaller size and temperature and brightness, while a cloud which is going to become a high mass star, because it is much hotter at any given size, is much brighter at any given size, and radiates heat away much more rapidly, causing it to shrink much more rapidly. This effect is so dramatic that if one cloud has as little as ten times the mass of another one, it can shrink as much as a hundred times faster, becoming, in this example, substantially smaller in just a few tens of thousands of years, instead of in a million years or so.
This tendency of massive clouds to generate larger amounts of heat, from their greater gravitional compressions, to become brighter, as a result, and to shrink towards stellar status far faster than less massive stars, is one of the critical differences between stars of different masses, and causes them to form at different rates, and to become different kinds of stars. Over a period of only a few tens of thousands of years, a very massive cloud may collapse, undergo a relatively rapid contraction, and become, finally, a very hot, very bright, upper Main Sequence star -- a star with a brightness of tens of thousands, hundreds of thousands, or even a million times the brightness of the Sun. Meanwhile, a less massive object, like the cloud that became the Sun, may take several millions of years to slowly contract, always cooler, smaller, and fainter, at any given stage, than the more massive object, and finally become a relatively ordinary, Sun-like star. Still less massive clouds, which end up as stars with only a fraction of the mass of the Sun, would be still cooler, still fainter, and shrink still more slowly, as they struggle to become the very small, relatively cool, very faint lower Main Sequence stars.
Please note that you can actually see the effects on this in the diagram in the text which shows the way in which stars approach the Main Sequence. That diagram, which shows evolutionary paths, as they are called, for stars which are approaching the Main Sequence, shows that the high mass stars form relatively quickly, and are always relatively big, relatively bright, and relatively hot compared to the lower mass stars, which form much more slowly.
Summary of the Preceding
To summarize what we have already covered, clouds are forced to contract by the merging of several clouds, or external forces created by massive stars which, because they form easily and quickly, form first in a region full of clouds of gas and dust, and, as they live out their lives and die, trigger the formation of other stars, massive and not so massive.
The initial stage of the formation of stars is always relatively rapid, involving a decrease in the size of the original cloud of several dozens, or even hundreds, of times in size. During this collapse, the dust in the cloud, as it becomes more and more thickly concentrated, steals heat from the gas, lowering its temperature, and allowing the collapse to continue. Within a few tens or hundreds of thousands of years, the cloud is much smaller, and doomed to become a star.
Towards the end of the initial collapse, the dust becomes so dense that, in the core of the collapsing cloud, heat and light can no longer escape, and the temperature begins to rise, and pressure begins to rise quite rapidly, and the core of the cloud becomes more like a cool star, than like a cloud, and the collapse begins to slow. At first, the compression of the cloud by additional gases falling in from the outside may continue the collapse, but eventually, the central core will become a more or less stable object, which continues to contract, much more slowly, only because it is slowly radiating heat away, through the surrounding layers of gas and dust.
This somewhat slower, quasi-equilibrium contraction is relatively fast for massive objects, because their weight, squeezing the gas of the cloud, generates large amounts of heat, making the cloud relatively hot, and relatively bright, for its size, causing heat to pour out of the central regions at a prodigious rate, and causing the cloud to contract to smaller sizes at a relatively rapid rate, and in fact, in times still measured in only tens or hundreds of thousands of years.
For less massive objects, however, the lesser gravitational force contracting the object means that the gas doesn't get nearly as hot, and heat moves from one layer to another much more slowly, causing the contraction to be much slower. Depending upon how low the mass of the contracting cloud is, it may take millions, or even tens of millions, of years for the cloud to finally shrink enough to become a star.
Protostellar Clouds vs. Protostars
Up to this point, we have been discussing objects which are relatively cool, even if considerably heated relative to their initial temperatures, and as a result, are giving off mostly, if not exclusively, infrared radiation. Such objects are sometimes referred to as protostellar clouds, to distinguish them from the next stage of stellar formation. That stage involves objects which have become so hot that they give off not only infrared, but also visible, radiation, and we refer to those objects as protostars. They are, if not still completely obscured by the gas and dust surrounding them, now visible as stars, but are not yet stable objects. Thus, they are stars, visible objects, shining by their own light, but not being stable objects, they are "proto"-stars. The next part of this "outline" (part 2a) discusses how protostellar clouds become protostars.