Slow Contraction of Protostellar Cloud
Once the cloud is so dense that the heat which is being produced in its center cannot easily escape, pressure rapidly rises, and catches up with the weight, or whatever external force is causing the cloud to collapse, and the cloud becomes stable, as a protostellar cloud, which refers to the fact that it is now destined to become a star, or a dark globule, which refers to the fact that it is a small, dark blob.
Although the blob is now somewhat stable, it cannot be stable in the same way that it was prior to its initial collapse. At that time, it was so spread out that the gas was in control of its temperature, and it could be warmer than one might expect, because the heat absorption and emission of gases is quite complex, and does not require the same sort of balance that one would expect from a so-called "black body."
Now, however, the cloud is a black body. It is dark, and the dust within it absorbs and emits radiation fairly efficiently, so that it cannot maintain a temperature higher than that which one would expect in interstellar space (just a few degress above absolute zero). Instead, as it radiates heat away (moderately slowly, from the core to the surrounding layers, from there to the surface, and from there, into space), it should cool off. But it can't cool off, because its heat is what holds it up against its compressive forces, and so, instead of cooling off, it contracts to a smaller size.
In this contraction, weight increases, but density and temperature also increase, and in particular, the temperature inside the cloud increases, because the heat generated by its gravitational compression is greater than that which is radiated away (it has to be greater, because at the smaller size, gravity is stronger, so both density and temperature have to increase, in order to balance the stronger force of gravity).
Over the next few tens of thousands or millions of years (as you will see below, the time involved depends upon the mass of the cloud), the cloud is in a state of pseudo-equilibrium, in which, if it were possible to stop its heat radiation, it would be stable, but because heat continues to slowly escape it, it slowly contracts, with weight and pressure in balance, but weight gradually winning the war, as it compresses the cloud to smaller and smaller size. During this stage, we refer to the decreasing size as a contraction, rather than a collapse, because it is much slower, and because weight and pressure are more or less in balance. In the first stage of formation, the decrease of size is very rapid, and compressive forces completely overwhelm the pressure of the gas, and we say that the cloud is collapsing. In the second stage, where things are more in balance, and proceed more slowly, we say that the cloud is contracting.
The rate at which the contraction proceeds is strongly dependent upon the mass of the cloud, or more accurately, since gas may still be falling onto the outer portions of the cloud, the mass within the region where the cloud is more or less stable. If we were to compare two clouds of similar structure and size, but with different masses, the more massive cloud would have a larger density, a greater weight, and, in order to be stable, would require a greater internal pressure, to balance that weight. The higher density would help provide that greater pressure, but as it turns out, the temperature would also have to be higher, in order for the more massive cloud to be equally stable. To a first approximation, if one cloud is ten times more massive than the other one, the more massive cloud would be ten times denser, weigh a hundred times more (because gravity goes as the square of the mass), and require a pressure a hundred times greater, to balance that higher weight. To achieve the higher pressure, the more massive cloud would have to be not only ten times denser, but also ten times hotter than the less massive cloud.
Example of how different mass clouds' properties differ
More massive clouds are denser, hotter, brighter, and shrink faster
As it turns out, this is not a problem, because the heat that is generated by a cloud as it contracts is proportional to the force that is compressing it, which is its weight, in this case (the fact that greater forces generate more heat is a well-known principal of heat mechanics). Since the more massive cloud weighs a hundred times more than the less massive cloud, it will generate a hundred times more heat. This heat will be distributed over ten times as much material, so it won't make the material a hundred times hotter, but will instead make it (100 times as much heat)/(10 times as much mass), or ten times hotter, which is exactly what is needed, in order for the cloud to be stable.
In other words, regardless of the mass of the cloud, it can be stable, but heavier clouds will generate more heat as they contract, and become hotter, while less massive clouds will generate less heat as they contract, and become less hot. This is, as it turns out, the fundamental reason why massive stars are bigger, brighter and hotter than less massive stars. During every stage of their formation, as they compress themselves under their own weight, they generate far more heat than less massive stars, and as an inevitable result, become hotter at a given size, or bigger at a given temperature, and, in either case, brighter.
It is the brightness that determines how long it takes the cloud to contract. If it were to take a one-Solar mass star a million years to contract through a given size range, a ten-Solar mass star would accomplish that same contraction much, much faster. Since it would be about ten times hotter, at any given stage of its contraction, as described above, it would generate, according to the laws of black-body radiation, ten to the fourth power, or ten thousand times more radiation, and be ten thousand times brighter than the one-Solar mass star. Now, it is true that a given contraction by such a star would generate a hundred times more heat, per unit of distance contracted, if that heat is radiated away ten thousand times more rapidly, it would last for only 1% of the time, or, in this example, only ten thousand years.
In other words, as the protostellar clouds contract, ones which happen to have large masses will be forced, by their larger gravity, to higher temperatures and greater brightnesses, than ones with smaller masses. Since it is the radiation of their heat that keeps the clouds contracting, the much faster rate of radiation by more massive clouds causes them to shrink much faster -- still not as fast as in their initial collapse, but far, far faster than the less massive clouds. As a result, less massive clouds, destined to become stars like the Sun, or less massive stars, may take millions, or tens of millions of years, to contract to very small sizes, and become somewhat starlike, while much more massive stars can do the same thing in just tens of thousands, or hundreds of thousands, of years.
SUMMARY OF SLOW CONTRACTION
Very slow equilibrium contraction, with pressure and weight in balance
Starts at 1000 to 10000 AU size, ends at a few AU's size
Different for different masses:
Massive stars are bigger, hotter and brighter than low mass stars during this contraction
Contraction is very fast (tens or hundreds of thousands of years or so) for high mass, high luminosity stars,
Very slow (millions of years) for low mass, low luminosity stars, like the Sun.
From Protostellar Cloud to Protostar
In the simplest sort of discussion, we could pretend that the slow contraction just discussed could continue until the star reached the Main Sequence, and in fact, most of the time involved in doing that does involve a slow contraction at least similar to that. However, there is an event which occurs partway through the slow contraction which separates the formation of the star into two parts: one part as a relatively cool, infrared object, called a protostellar cloud, and the other part as a relatively hot, visible-light object, called a protostar.
The event which separates the two is a relatively sudden collapse caused by the ionization of hydrogen.
During the contraction of a dark globule, or protostellar cloud, heat generated by the compression of the cloud only slowly leaks from the center of the cloud, to the surrounding layers, to the surface of the cloud, and then into space, because the dust contained within the cloud blocks the outward flow of radiation. However, when the central temperatures exceed a thousand degrees, the dust begins to vaporize, and when they exceed two thousand degrees, virtually all of the dust has been vaporized. The vaporization of the dust makes the central regions less opaque (meaning, that it is easier for the radiation to escape), and they contract more rapidly than they had been contracting. The heat released by their contraction, and the contraction of the surrounding regions (which must also contract, with the central region) rapidly increases the temperature of those surrounding regions, and dust begins to vaporize within them, as well, causing them to radiate heat more quickly, as well.
Within a fairly short period of time, most of the central area of the cloud is contracting considerably faster than it had been, and heating up, as a result, considerably more rapidly. At first, this faster contraction still involves a balance, more or less, between the internal pressure of the cloud, and the compressive forces squeezing it to smaller and smaller sizes, and should, therefore, be called a contraction, even though it may be several times faster than it was. But as the temperature rises, a catastrophe occurs which makes the contraction even faster, and turns it into a virtual free-fall.
This catastrophe is the ionization of hydrogen gas and, later, helium gas. When a gas ionizes, the electron (for hydrogen) or electrons (for multi-electron atoms) is/are stripped away from it, turning it from a normal gas, into a plasma. For most purposes, unless there are strong magnetic fields present, the behavior of a plasma is essentially the same as that of a normal gas. In fact, the Sun and virtually all other stars consist almost entirely of plasma, but in discussions of their structure, we generally treat the behavior of their material as though it were a perfectly normal gas. However, there is a thing which happens when turning a gas into a plasma, which is similar to things which happen when a solid is turned into a liquid, or a liquid into a gas, and for this reason, we sometimes consider a plasma to be quite different from a gas, and call it a fourth state of matter (the first three states being solid, liquid, and gas).
The thing that happens when one state of matter is turned into another is referred to as a phase change. The melting of ice (or the reverse freezing of water), the boiling of water (or the reverse condensation of steam), and the ionization of hydrogen are phase changes.
In a phase change, an odd thing happens, which does not happen when you are dealing with matter which is not in a phase change. Namely, the temperature is insensitive to changes in the heat of the material. Normally, when you heat a material, it becomes hotter. That is, if you pour heat into it, its temperature rises. However, during a phase change, the temperature does not change -- it remains constant, until the change is completely done. This is why it is useful to use boiling water to cook things. While the water is boiling, no matter how much heat you pour into it, its temperature doesn't increase -- the rate at which the water is boiling may increase, but the temperature remains constant, which makes for a better control of the cooking conditions. In a similar way, when hydrogen ionizes, the temperature of the hydrogen gas/plasma remains fixed, at the temperature required for the phase change, which is approximately 10 thousand Kelvins (a little less than 20 thousand Fahrenheit degrees).
When the hydrogen in the rapidly contracting cloud reaches this temperature, it begins to change from a gas to a plasma. As a plasma it consists of two particles per hydrogen atom, the nucleus (usually a proton), and the electron that used to go around the nucleus. For the purposes of gas physics, this will double the number density of the particles, which will gradually increase the pressure to twice the pressure that existed prior to the ionization of the hydrogen, but the temperature will remain fixed throughout the phase change, and as a result, the pressure doesn't go up quite as much as it "ought" to, and the weight of the cloud gradually begins to outpace the pressure.
As long as a contraction increases the weight, the density, the temperature, and the pressure inside the cloud, it can contract more or less stably, albeit at a rate which depends upon how fast the light produced by the high temperatures can leak out of the cloud. Once, however, the temperature becomes stuck, and only the weight and density increase, the pressure will fall behind the weight, and the cloud will go into free fall, collapsing to a much smaller size at essentially the rate that an object would fall under the influence of gravity, without much opposition from the internal pressure.
The time required for this to happen is surprisingly short, because, by the time hydrogen is ionized, the cloud is relatively small (only a few AUs in size, depending upon the mass of the region that we are talking about), and the gravity is relatively large, compared to earlier stages of the star's formation. For the Sun, ionization would begin when the central regions have shrunk to about the size of the orbit of Jupiter, and it would take only a few years for those regions to free fall to a size less than the orbit of Mercury. For larger stars, which are hotter at a given size, or bigger at a given temperature, the ionization would begin at a larger size, but because of their greater mass, they would have a greater gravity, allowing them to shrink to smaller sizes in hardly any more time. As a result, it takes less than a decade for the ionization of hydrogen to spread throughout the central regions of the collapsing cloud, and for the cloud to contract to only about a tenth of its former size, regardless of the mass of the cloud.
Prior to the start of hydrogen ionization, the cloud is relatively large, and relatively cool, and gives off only infrared radiation, so it is "invisible" to ordinary telescopic observations. As it collapses, however, huge amounts of energy are used to convert ordinary hydrogen gas in hydrogen plasma, and the energy "wasted" in this way means that it will require a huge increase in temperature to overcome the effects of the collapse.
The temperature of the cloud remains stuck at the hydrogen ionization temperature until all of the hydrogen is ionized. The energy required to do this is so great that if, somehow, the gas could avoid becoming ionized, and simply become hotter, the temperature would increase to over a hundred thousand degrees. This means that if the ionization had not occurred, the pressure in the gas would have increased by a factor of ten (as a result of the temperature increase), whereas the actual pressure increase is only by a factor of two (as a result of the conversion of hydrogen atoms into two separate pieces). Eighty percent of the heat energy is wasted, as far as the pressure is concerned, and in order to overcome the effects of this phase change, we must have, after the phase change is completed, a huge rise in temperature, to several hundred thousand degrees, to provide enough pressure to stop the collapse, and make the contracting cloud more or less stable again. Because of the rapid collapse of the cloud, it doesn't take very long for the temperature and pressure to increase to the values needed to stop the collapse, but because of the huge temperature change (from ten thousand degrees to several hundred thousand degrees) the whole nature of the object drastically changes.
Prior to the beginning of the collapse, the cloud was relatively large, relatively cool, and incapable of radiating anything other than infrared radiation. Towards the end of the collapse, the cloud is much smaller, and much hotter, and radiating huge amounts of visible, as well as infrared, radiation. Because of this, it has become an essentially different kind of object -- a protostar.
Despite the change in size and temperature, and the resulting change in the nature of the radiation coming out of the cloud, after pressure catches up with weight, the protostar is in many respects quite similar to the protostellar cloud that it was before the collapse. Pressure and weight are once again in equilibrium, but the loss of heat from the protostar causes gravity to slowly win the battle, and the star slowly contracts, in almost exactly the same way as before, with more massive stars being bigger, or hotter, or both, and in any event brighter than, less massive stars, and as a result, contracting considerably more rapidly. As a result, the ionization of hydrogen, although it drastically changes the nature of the material inside the forming star, is in some ways merely a footnote in the long, relatively slow contractive phases which precede it, and follow it. However, there are substantial differences in the detailed nature of the contraction which precedes the collapse, and that which follows the collapse, and of course, there is a huge difference in the appearance of the object. Prior to the collapse, it is, other than in infrared radiation, an invisible object. Afterwards, depending upon the amount of gas and dust which still surrounds it, and may still be falling onto it, and increase its mass, it may still be invisible, hidden by the surrounding material, or it may shine brightly, as a red giant, subgiant, or supergiant, depending upon its mass.
The ionization collapse of protostellar clouds: Prior to the ionization of hydrogen (and helium), protostellar clouds of different masses contract toward smaller sizes, but greater densities, temperatures, and luminosities. This occurs rapidly for high mass objects, which are always hotter, bigger, or both, and as a result, brighter than low mass objects. As they approach the Hayashi Forbidden Zone (the pink area to the right of the Hayashi Line (100% convection), they begin to ionize their hydrogen, then their helium, and suffer a free fall to much smaller size. At the end of their collapse, 5 to 10 years later, they are 10 to 20 times smaller, almost totally ionized gas (plasma), and much hotter, inside and out. They are also in violent vertically mixed motion, as evidenced by the fact that they are on or near the 100% convective Hayashi Line, at the end of their collapse. They are now protostars, glowing visibly, but still unable to produce energy save by gravitational contraction.
SUMMARY OF IONIZATION COLLAPSE
Extremely fast collapse (5 to 10 years), with pressure much less than weight
Starts at a "few" AU's size, ends at a "few" tenths of an AU size
Massive stars much bigger at both start and end than less massive stars.
Infrared object prior to collapse, visible red giant/subgiant/supergiant after collapse
Next: From Protostars to the Main Sequence