Stellar luminosity

In this class, we will describe how bright a star really is by its luminosity.

The luminosity is how much energy is coming from the per second. The units are watts (W).

Astronomers often use another measure, absolute magnitude. Absolute magnitude is based on a ratio scale, like apparent magnitued. I think it is confusing.

The luminosity of the Sun is

L_sun = 3.9 x 10²⁶ W We will often measure luminosities of stars in units of the luminosity. That is, we might say for a certain star L_star = 5.2 x L_sun, meaning that the star has 5.2 times the energy output per second of the Sun.

Measuring luminosity

Since we can't go to a star to measure its luminosity, we have to be clever. If we know the distance to the star we can do it, because there is a simple relation between

the distance d to the star,
the apparent brightness b of the star, and
the luminosity L of the star.

The relation is

This relation is based on conservation of energy. Consider an observer a distance d from the star. How much energy crosses a square meter detector that this observer has?

All of the energy produced by the star per second must cross a sphere of radius d.
The study of geometry tells us that area of this sphere is 4 Pi d².
a 1 m² detector gets a fraction

(1 m²)/(total area)
of this.

Note that the brightness decreases proportionally to the square of the distance as one moves away from the star. This can be demonstrated experimentally in the laboratory.

We can write the relation so that it gives L in terms of b and d.

It is easy to measure the apparent brightness b (e.g. with a telescope and a CCD).
It is not so easy to measure the distance, but we have already seen something about how that can be done.
Putting these toghther, we get L.

Luminosities of stars

One finds

There are a few stars that are more luminous than the Sun.
- For instance, Betelgeuse has L ~ 14000 x L_sun.
Most stars are less luminous than the Sun.
- For instance, L_star ~ 0.001 x L_sun is not unusual.
There are lots more low luminosity stars than high luminosity stars.

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu