MAIN SEQUENCE STARS: LIFETIMES

What Does Lifetime Depend Upon?

On the Main Sequence, the life time depends upon two things- the amount of "fuel" the star has... its mass, and the rate at which it consumes the fuel... its luminosity. So, how do the lifetimes depend upon these two quantities?

The More Fuel, the Longer the Lifetime

The more fuel, the more supply of material for fusion the star has and so the longer the star can live. The fuel is hydrogen atoms and the number of hydrogen atoms is greater in high mass stars than it is in lower mass stars. Thus, the higher the mass of the star, the longer its lifetime can be.

Amount of Fuel = Mass

The Faster the Fuel is Consumed, the Shorter the Lifetime

The faster the star generates energy, the faster it consumes its fuel. The faster it consumes its fuel, the shorter will be its lifetime for a fixed amount of fuel. The rate of fuel consumption for a star is its luminosity (because the amount of energy radiated by the star equals the rate energy is created in the core). But, luminosity is mass dependent! From the mass-luminosity relation we can state the following:

Rate of Fuel Consumption = Luminosity = Mass^3.5

Putting These Two Competing Effects Together

In short, the life time is directly proportional to the amount of fuel and inversely proportional to the rate of the fuel consumption.

Lifetime = (Amount of Fuel)/(Rate of Fuel Consumption)

or

Lifetime = Mass/Luminosity

or

Lifetime = Mass/Mass^3.5 = (1/mass)^2.5

This equation states that the larger the mass of the star, the shorter the lifetime. This is because the fuel consumption gets huge for the more massive stars. Even if massive stars have more fuel, the consume it at such intensely high rates that they don't live as long as lower mass stars. The sun will live on the main sequence for 10 billion years. Lower mass stars live longer than the sun. Higher mass stars live shorter than the sun.

Back to the Main Sequence

So the Main Sequence is also a lifetime sequence! As mass goes up, temperature goes up, size goes up, luminosity goes up, lifetime gets shorter!

"O" "B" "A" "F" "G" "K" "M"

(All Stars)
<---------------- increasing temperature

(Main Sequence only)
<---------------- increasing mass
<---------------- increasing size
<---------------- increasing luminosity
----------------> increasing lifetime

Introducing Stellar Evolution

When main sequence star get old and start their dying process, their sizes increase and temperatures decrease (they cool as they expand). Because the size increases, the luminosity increases... so a star moves to another position on the HR diagram (to the right and upward). If we track this process for a star as it goes through its dying process, we could see how it changes position on the HR diagram as time passes. The locus of points (curve through each data point) we would draw on the HR diagram is called an evolutionary track. We will discuss stellar evolution in the following lectures.