- #1

Ellie Snyder

- 8

- 1

## Homework Statement

The nuclear reactions in a star’s core are very sensitive to pressure and temperature, so high mass stars have much higher luminosities. The luminosities of massive stars have been observed to obey the following scaling relationship with mass (M):

Lstar = (34.2)*M^2.4, where M, L have units of MSun, LSun.

The Eddington limit is the maximum luminosity an object (such as a star) can achieve and still retain a balance between the outward force of energy from the center and inward pull of gravity. The following formula is for the Eddington Limit (LEdd), i.e., the luminosity which stops the inward pull of gravity:

LEdd = (3.2*10^4)*M, where M, L have units of MSun, LSun.

a. Using these two equations, calculate the maximum mass of a star in solar units.

b. A bright quasar has a luminosity of about 10^13 LSun. The source of its power is a supermassive black hole that attracts surrounding gas into a hot (~10^6 K), compact accretion disk which radiates light. If the quasar is to continue attracting gas into its central black hole, what is its minimum mass?

## Homework Equations

Lstar = (34.2)*M^2.4

LEdd = (3.2*10^4)*M

## The Attempt at a Solution

a. Solved for M in the Lstar eqn to get (Lstar/34.2)^1/2.4 and plugged that into the LEdd eqn. Got 7344.7Lstar^1/2.4, and plugged that in for LEdd to get an M of 0.2295Lstar^1/2.4, which is obviously preposterous. I guess I'm not sure how to relate the equations to solve for M.

b. Waiting to attempt this one until I have a better understanding of a.