Paying the Power Bill

Our sun emits an incredible 4 x 10^26 Watts of energy. That's 400 trillion trillion W of power being radiated into space. How does our sun "pay" this enormous energy bill? While on the Main Sequence stars are busily turning Hydrogen into Helium. This occurs in the core of the star and proceeds until about 10% of the star's Hydrogen is converted to Helium. This defines the main sequence lifetime phase for a star.

How to Turn Hydrogen into Helium

Basic Stellar Structure

The structure of a star is governed by 4 basic principles:
  1. Hydrostatic Equilibrium
  2. Energy Transport
  3. Continuity of Mass
  4. Continuity of Energy

Mass - Luminosity Relation

Putting the pieces together: We now know: If we use our knowledge we can construct a very simple relationship between the mass of a star and its intrinsic brightness or luminosity. In fact:

Mass is the single most important parameter that determines the life and fate of a star.

Click here to see a graphical depiction of the mass-luminosity relationship.which can expressed using the formula:

 

Converting Between Absolute Magnitude and Luminosity

In most of what we have done previously we have talked about absolute magnitude as a measure of intrinsic brightness. You should recall, however, our discussion of brightness factors early in the course. There is a simple way to convert between magnitude difference and brightness or luminosity. You can either use the brightness factor graph from lecture 2 or choose one of the following:

Life Expectancy - Mass Relation

A star will live as a main sequence object as long as it can use either the p-p or CNO process to convert hydrogen into helium at its core. This depends on two key points: This can be expressed in equations as:
and graphically as:
and using a javascript calculator agecalc

Example:

Over the Christmas break you will attend lots of parties. Late at night as you leave one of the parties look up - Orion will be high and in full view - a beautiful sight!. If that isn't enough - astound your friends with the following! (warning: when word gets out that you know all this stuff lots of people will invite you to their parties just to amaze them - it's hard work being an astronomer!)

Solution:

First, convert 1340 ly into pc so that we can use the distance modulus graph. That's easy since 1 pc = 3.26 ly we now kow that Alnilam is 1340/3.26 = 411 pcs away. Now consult your graph. From this we can estimate the distance modulus (m-M) to be 8.1. We want to know what M is for Anilam so just rearrange the equation
m-M=8.1 or M = m-8.1 which becomes: M = 1.65-8.1 = -6.5 (rounding):
Next click on the appropriate conversion graph to get the luminosity of Alnilam. This icy blue star shines at a prodigious rate - about 40 thousand times the Sun!
Now that we know the luminosity we can determine the mass for Alnilam. Using the Mass-Luminosity relation we know that L = M^3.5. It is easier to work with this graphically so click on the following version of the mass-luminosity graph:
From this we learn that Alnilam has a mass of about 21 solar masses. How long will it live? The time-mass graph indicates that this star will live only 1/50 000 th as long as the Sun or about 5 million years!.

Then What?

This example leads us to our next lecture. What happens to a star as it runs out of its central supply of Hydrogen? This is a fascinating question to explore and one whose answer depends very much on the mass of the star.
Spectral Type vs Main Sequence Lifetime
Spectral Type Main Sequence Lifetimes
O5 1 million
B0 5 million
B5 80 million
A0 1 billion
F0 3 billion
F5 5 billion
G0 9 billion
G5 10 billion
K0 20 billion
K5 40 billion
M0 200 billion
M5 300 billion

Time toTake a Quiz!

If you are ready, click on "Big Al"  to take a 20 question multiple choice quiz. It should take about 10 minutes and provide you
with an evaluation of your comprehension of the past 6 lectures.  Don't forget to "register" the quiz so that I have a record that you have completed it.

Assignment 3

Seeds: Chp 12;all
Kaufmann: Chp 21; pgs 384-396