From Interstellar Clouds to Protostellar Clouds
Begin With 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
Resulting in 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)
End With Protostellar Cloud
    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
    causing 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 at "surface"
    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 between compression and expansion 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 make them 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) so they contract much faster
Summary of (Slow) Contraction Stage
    Massive clouds are hotter, bigger and brighter than less massive ones
    As a result, they contract much faster
    A 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 (slow) 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 Kelvins
    Once all hydrogen & helium is ionized temperature rises rapidly and collapse stops
Protostars vs Protostellar Clouds
    PRIOR to ionization collapse, had very large but relatively cool INFRARED object (protostellar cloud)
    AFTER that have much smaller (though still much bigger than normal star), much hotter VISIBLE object (protostar)

From Protostars to the Main Sequence
Resumption of (Slow) Contraction
    Once temperature and pressure catch up, PROTOSTAR resumes contraction.
    Though now hot and visible, contraction resumes in much the same way as prior to ionization collapse
    massive stars brighter and faster, less massive stars fainter and slower
    HOWEVER, there is a big difference in the details, compared to earlier stages...
Contraction Resumes: The Struggle Between Density and Temperature
    Prior to protostar stage as clouds contracted, large and small masses contracted in similar ways, though at different rates
    Differences in the details of how they got started (external forces, etc) might make more of a difference than anything else
    NOW the gas is getting so dense that it is hard for light to get out of the interior
    HOW HARD depends on density and temperature
    Increasing density, as contraction occurs or as you go toward the center, makes escape of light harder
    Increasing temperature, as contraction occurs or as you go toward the center, creates more light
    In low mass stars, which contract a lot to get just a little hotter, density increases faster than temperature
    As a result, 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 surface temperature
    (In the H-R Diagram, its evolutionary path is nearly straight down)
    In massive 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 downward 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 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
Importance of Convection During Protostellar Contraction
    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 (protostars), 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 greatly 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
    As the temperature increases, fusion creates more and more energy, and eventually this 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.