From Interstellar Clouds to Protostellar Clouds
Interstellar Cloud
     (tens or hundreds of thousands AUs across)
     relatively stable, because pressure is more sensitive to the size
     relatively hot, because temperature is controlled by gas, which is a poor absorber/emitter
Start of Collapse
     merging of clouds or external forces temporarily overcomes pressure
     as the cloud collapses, density increases, and dust steals heat from gas and radiates away
     as a result, temperature goes DOWN, instead of up, and pressure can't keep up with compression
RESULT
     RAPID COLLAPSE, with weight or external force much larger than pressure
     10's of thousands, or 100's of thousands of years, depending upon compressive forces
     Decrease of 99.9% or more in diameter, increase of billions of times in density
End of Collapse
     as cloud collapses, density increases, making it darker and darker
     since darker objects are better and better absorbers, this means dust is radiating heat better
     BUT ONCE the cloud is so dark you can't see through it, or even out of it, heat can't escape
     Temperature begins to rise, increasing pressure, and collapse must eventually slow and stop
     AT THE END OF THE COLLAPSE, WE HAVE A DARK GLOBULE (descriptive of appearance)
     OR PROTOSTELLAR CLOUD (descriptive of the fact that although not collapsing, is fated to be a star)
Protostellar Clouds
     100's or 1000's of AUs in size, instead of 10's of thousands or 100's of thousands of AUs
     billions or trillions of times denser than interstellar clouds
     opaque (dark), instead of transparent
     temperature controlled by dust, not gas
     AS A RESULT, heat generated by the collapse leaks from layer to layer, as in a star, and is lost
     this causes a slow, QUASI-EQUILIBRIUM contraction of the cloud to smaller and smaller sizes

From Protostellar Clouds to Protostars
Slow Contraction
     Heat leaks from layer to layer, within the cloud, and escapes
     This should cool off the cloud, which should reduce the pressure
     Instead, the cloud contracts, increasing the density, temperature, pressure AND WEIGHT
     and a new balance is struck, at a smaller size
Rate of Contraction Depends Upon Mass
     More massive clouds weigh more, and compress their gases harder, making them hotter
     The higher temperatures and densities in massive clouds allow them to be just as stable as
     less massive clouds with lower temperatures and densities
     BUT the higher temperatures make them brighter, so they throw away their heat much faster
     (approximately as the square of their mass)
     and as a result, they contract much more quickly
Summary of Contraction Stage
     Massive clouds are hotter, bigger and brighter than less massive ones
     As a result, they contract much faster
     Contraction accomplished by a low-mass star in millions of years
     May occur in higher-mass stars in only tens of thousands of years
     SO THE MORE MASSIVE STARS FORM SOONER
     Throughout the contraction, pressure and weight are in balance
     Sizes decrease from 100's of AUs (or more) to tens of AUs (or less)
     in tens or hundreds of thousands of years for massive stars
     in millions of years for lower mass stars
Accelerated Contraction and Collapse
     As the clouds contract and heat up, dust begins to vaporize in the core
     When about 10 AUs across for Solar masses, bigger for bigger masses, smaller for smaller masses
     This causes an increase of the rate of contraction (heat escapes faster, without dust to block it)
     As the temperature reaches 10 thousand Kelvins, hydrogen ionizes
     This uses up the heat of contraction WITHOUT INCREASING TEMPERATURE
     This allows weight to become much larger than pressure, causing a RAPID collapse
     IN ONLY 5 to 10 years, protostellar cloud collapses by a factor of 10 in size
     For Sun, from 10 AUs to about 1 AU, for more massive stars, from 20 or 30 AUs, to 2 or 3 AUs (diameter)
     IN THE EARLY STAGES OF THIS COLLAPSE, TEMPERATURE IS STUCK AT 10 thousand degrees
     ONCE ALL HYDROGEN IS IONIZED, temperature rises rapidly and the collapse is stopped

From Protostars to the Main Sequence
Resumption of (Slow) Contraction
     Once temperature and pressure catch up, PROTOSTAR resumes contraction.
     PRIOR to ionization collapse, had very large, but relatively cool, INFRARED object (protostellar cloud).
     AFTER that, have much smaller (although still much bigger than normal star), much hotter, VISIBLE object (protostar).
     Otherwise, contraction continues in nearly the same way as before -- massive stars brighter and faster, less massive stars fainter and slower
     HOWEVER, there is a big difference in the details, now...
Contraction Resumes: The Struggle Between Density and Temperature
     Prior to protostar stage, as clouds contracted, large and small masses contracted in similar ways, albeit at different rates
     In fact, differences in the details of how they got started (external forces, etc) might make more of a difference than anything else
     NOW, however, the gas is getting so dense that it is hard for light to get out of the interior
     HOW HARD depends upon density and temperature
     Increasing density, as contraction occurs, or as you go toward the center, make escape of light harder
     Increasing temperature, as contraction occurs, or as you go toward the center, creates more light
     In very small stars, which have to contract a lot to get just a little hotter, density increases faster than temperature
     As a result, even though more light is trying to get out, less and less does, and the star gets fainter as it contracts
     So, even though it is getting smaller, it doesn't have to increase its temperature
     (In the H-R Diagram, its evolutionary path is nearly straight down)
     In very large stars, which get much hotter by contracting just a little, temperature increases faster than density
     Even though the star is getting smaller and denser, and it is harder for light to escape, more and more manages to do so
     With the surface getting smaller, but the brightness going up, the surface temperature increases
     In the H-R Diagram, the star moves to the left
     Intermediate mass stars, like the Sun, move downwards at first, like low mass stars, then to the left, later on, like high mass stars
(Alternate version of summary)
     All protostars get smaller as they “approach” the Main Sequence. How they approach it depends upon how the density and temperature inside the protostar change, as they contract.
     HIGH MASS STARS: Generate a lot of heat from a small contraction (because their large mass creates a large gravity, in comparison to their size, and heats up the gas a lot). So a given contraction in size results in a BIG temperature increase, and a SMALL density increase.
     LOW MASS STARS: Generate little heat from a small contraction (because their small mass creates little gravity, in comparison to their size, and doesn’t heat up the gas very much.) So a given contraction results in a SMALL TEMPERATURE increase, and a BIG density increase.
     IN A HIGH MASS STAR: Density goes up a little, but TEMPERATURE GOES UP A LOT. So the amount of light escaping stays the same, or goes up. THE SURFACE MUST ALSO GET HOTTER TO DO THIS, so star moves TO THE LEFT in the HR Diagram
     IN A LOW MASS STAR: Temperature goes up a little, while DENSITY GOES UP A LOT. The amount of light escaping goes down and down, so the surface temperature doesn’t have to change, and the star moves DOWN in the HR Diagram
Convection
     If the star gets/stays very dense, in comparison to its temperature, so that it is hard for light to get out, the gas suffers vertical mixing, or convection
     For stars that have just become visible, the entire star is in turbulent motion
     For stars that then move DOWNWARDS in the H-R Diagram, the entire star REMAINS convective
     But for stars that move to the LEFT, the internal/surface temperatures are increasing faster than density, and the convective zone shrinks toward the surface
     This means that if a star moves well to the left, before reaching the Main Sequence, it is NOT thoroughly mixed
     whereas, if it moves more or less downward to the Main Sequence, it is thoroughly mixed
     This affects the lifetime of the stars, and the way they die

Moving to the Main Sequence
     As the star's interior becomes hotter and hotter, nuclear fusion begins in the core
     At first, this produces very little heat, and doesn't affect the contraction
     but as the temperature continues to increase, fusion creates more and more energy, and eventually this energy partially replaces the heat loss at the surface
     This causes the contraction of the star to slow, so that the fusion reactions, instead of going faster and faster, increase more and more slowly
     As the fusion energy production approaches 100% of the heat loss, the contraction of the star slows, and finally stops
     When that happens, energy is being created in the core, and flowing from layer to layer, at the same rate as it is being lost, so the star remains in a perfectly stable state for however long the fuel can last
     Any 'error' in the rate of energy production causes the gas in the core to expand or contract in such a way as to cancel out that error, maintaining a steady rate of energy production

The Mass-Luminosity Diagram and the Lifetimes of Main Sequence Stars
Formation Times and Main Sequence Lifetimes
     Protostar contraction to the Main Sequence, like the pre-visible protostellar cloud contraction, is fairly rapid for large mass stars, and fairly slow for lower mass stars
     As a result, massive stars can go from the initial cloud collapse, all the way to the Main Sequence, in just a few 10's of thousands of years
     Lower mass stars, unless forced to contract faster by violent external forces, will take millions of years
     THIS DIFFERENCE IS DUE TO THE FACT THAT MASSIVE STARS ARE ALWAYS BIGGER, HOTTER AND BRIGHTER THAN LESS MASSIVE STARS, AT THE SAME LIFE STAGE
     This is ALSO true after the stars reach the Main Sequence. Massive stars have more fuel to burn, but they burn it far faster, so they last only millions of years, compared to many billions of years for stars like the Sun, and trillions of years for very low mass stars.