Pre Main Sequence Evolution 

So how do the observable properties of a protostar behave as it collapses?

We can calculate both the luminosity of the collapsing cloud, as well as its temperature (once it becomes optically thick). So we can place it on the H-R diagram. Since its structure is changing, T and L change, so its position on the H-R diagram changes. We can calculate how it moves on the H-R diagram -- this is called an evolutionary track.
 

Let's look at a 1 Msun protostar:

At the point where the collapsing cloud becomes optically thick, it has a high luminosity and a low temperature.
Question: what is the luminosity of a 1 Msun protostar which has collapsed to R=500 Rsun, if most of the energy is liberated in the last 100 years of the collapse?

Answer: Remember that the energy radiated during a collapse to size R is

And if that energy is given off in the last 100 years of the collapse, the luminosity is

Remember this luminosity is from gravitational contraction alone - no nuclear reactions!

So what part of the H-R diagram does this protostar live in?

At the point where the protostar has reached adiabatic contraction (that is the gravitational energy heats the star), the collapse slows considerably -- it has achieved quasi-static equilibrium.
The rate of collapse depends on the rate at which the protostar can radiate the energy of collapse, which is much longer (~ 107 years) than the free fall time.
 
Low mass stars contract and drop in luminosity, until the interior opacity drops and the energy comes flooding out, resulting in an increase in surface temperature and luminosity.

High mass stars have low opacity to begin with (because of high temperatures) and simply heat up as the contract.
 
 

Contraction Times:

  • 9 Msun: 150,000 years
  • 5 Msun: 575.000 years
  • 2.25 Msun: 5.8 million years
  • 1 Msun: 50 million years

    • 0.5 Msun: 150 million years