# How much star can star fusion fuse if star fusion can fuse hydrogen?

During stellar nucleosynthesis a star will convert a portion of its hydrogen atoms into helium. Is there a constant of how many tons of hydrogen is converted based on the mass of the star? Is it based on a percentage of the star's mass? Or can it vary? A Nasa blurb stated that 600 million tons of hydrogen per second are consumed by our own sun. Is there a mathematical formula that can tell you how much any star would consume and convert to helium?

• Now I wonder if class WC stars are full of woodchucks chucking wood... – Mike G Sep 10 '16 at 1:32

There's a rough equation based on a star's mass but the age and metalicity of the star are factors too. As large stars grow older they grow hotter on the inside and as they grow hotter, they fuse hydrogen faster, but they also become less massive over their lifetimes and have less and less hydrogen over time, so there's two opposing factors.

A rough equation is found here:

http://www.astronomynotes.com/evolutn/s2.htm

a star's luminosity increases with mass as $(\text{the star's mass})^p$. The value of the exponent p varies between 3 and 4. For the rare massive stars (M* > 30 Msun), p = 3 and for the more common low-mass stars (M* < 10 Msun), p = 4

Loosely speaking, the luminosity is roughly equivalent to the rate of hydrogen fusion though the hydrogen fusion takes place inside the star and it takes some time for the energy to make it's way to the outside of the star and radiate away, the age of the star is far greater than the time it takes the newly created energy to escape, that it's still a pretty good ratio direct, luminosity to hydrogen fusion rate.

A star with 2 solar masses is about (4th power) 16 times as luminous, which means it fuses hydrogen about 16 times as fast. When you get into significantly larger stars, the 4th power rule gradually becomes the 3rd power.

But as far as age being a factor, our Sun during it's main sequence will be about twice (or a bit more than twice) as luminous when it's 8 or 9 billion years old as it was when it was 1 billion years old, which corresponds to a gradual doubling of hydrogen fusion rate. This happens (basically) because the core retains heat and more heat makes fusion more likely to happen, even as the amount of hydrogen is significantly lower in the later stage of it's main sequence than the early stage.

• I always found the mass-luminosity relations for stars to be a bit circular. If you know the luminosity and want to determine the mass, you need to pick the right equation with the right power $-$ which requires knowing the mass. But that's how science works sometimes I suppose. – zephyr Sep 8 '16 at 12:31
• @zephyr so do anomalies exist where the body should be fusing hydrogen at a faster rate, but the fusion seems stunted? Or the other way around, where fusion seems to be accelerated and should not be? – El Bromista Sep 12 '16 at 23:25