Star time on main sequence

[mathtrek]

Hi all, having difficulty with this problem:

A B0 star has a luminosity of ~ 16000 L(solar) and a mass of ~ 16 M(solar). Can you estimate the time on the main sequence for this star simply from considering the rest mass energy of the core of the star (~10% of the total, and fusion burns with an efficiency of about 0.7%) and its luminosity?

 

Not really sure where to start, am very new to Astro stuff...

[ajb]

I think the method is to concider how much mass is lost due to the nuclear reactions in the star per unit time. This you can estimate this from the luminosity using [math] E = m c^{2}[/math].

 

Let the rate of mass loss be [math]R[/math]. It has units of mass/time. You need to concider that the nuclear reaction is 70% efficeint when calculating this. Let the mass of fuel be [math]M[/math], which you know to be 10% of the total mass.

 

If you evaluate [math]T = \frac{M}{R}[/math] you will have an estimate of the lifetime of the star.

 

I will let you work out the numbers, but be careful of units.

 

Another method is to use the so called Mass-Luminosity relation. [math]L = m^{3.5} [/math].

 

As an example, the Sun's lifetime of 10 billion years.

 

Hope that helps.