Chapter 13: Taking the Measure of

StarsStars come in a wide range of temperatures, sizes, masses and colors. The constellation of Orion is a good example of the variety of stars

How can we learn about stars?Suppose you are an alien with three days to learn

everything you can about the human species

So too, we survey a large number of stars to learn

about their lives

We begin by trying to answer one of the

fundamental question in astronomy:How far away is that

star?

Parallax gives us a

geometrical method of measuring distance

We define the parsec in terms of a parallax angle

Unfortunately, parallax only works out to a few hundred parsecs. After that, the

parallax angle is too small to measure

Distance can affect how bright a star appears to us

Brightness Versus Distanceis an inverse square

relationship

24

LuminosityBrightness

r

The brightness-luminosity relationship is an inverse square relationship like gravity.

If we want to find the distance using this, we need to know the luminosity.

Stars don’t come in standard

luminositiesThe Sun is a little above average when it comes to luminosity. So, the question now is how to determine luminosity.

Stellar color tells us the temperature via the blackbody spectrum

Color Index

Why not measure the brightness in a few different color bands? If we take a ratio or difference between

two colors that should give us the temperature.

The Color Index is related to the Surface Temperature

Another common color index is the difference between two colors: bv – bb or bu –bv or some other

combination

Temperature isn’t all there

is to the luminosity of

a starIf this was the only factor then all hot stars would be bright while all cool stars would be dim. The temperature obviously has something to do with luminosity but there’s more too it than just temperature.

How large a star is also contributes to the

luminosity

Stars come in a wide variety of sizes

Some stars are huge while others, like white dwarfs and neutron stars, are tiny. Watch

YouTube Star Size Comparison video

If we know the temperature and the size we can calculate

the luminosity

2 44L R T L is the luminosity of the star in watts, T is the temperature in Kelvin, R is the radius of the star and s is the Stefan-Boltzmann constant. If we know the luminosity and brightness, we can determine the distance to the star.

A spectrum gives so much more information than just

three colors

It takes more time to take a spectrum but you get so much more out of it.

The problem with spectra is we don’t always get the peak

of the blackbody curve

If we get the peak we can determine the temperature directly.

The absorption lines come from the atmosphere of the

star

Which elements absorb best depends on temperature

By looking at which absorption lines are present we can find the temperature

Stellar Classification Scheme

While we get the classification from looking at the spectral lines, the stellar classification scheme classifies stars according to their

temperature

We can also

classify stars by size: the Luminosit

y Class

So we now have several ways to get temperature

We still need a way of finding the

diameter of the star

4

42

LDistance

L=4 R

brightness

T

What can we find out from studying binary systems?

Visible and X-ray images of Sirius A & B

Sirius is a winter star. It is the brightest star in the sky.

Getting the orbit of visual binaries takes time!

Recall Kepler’s 1st Law: planets move in elliptical orbits with the Sun at one focus. The stellar equivalent is that binary stars move in elliptical orbits around a common center of mass.

Binaries actually orbit a common Center

of MassThe two stars are

always on opposite sides of the center of

mass

The center of mass is always closest to the most massive of the two stars

Using Kepler’s Third Law we can find the combined

mass of the stars

3 3

1 22 2

( )

( )AU

years

A Orbital radiusM M

P Orbital Period

The mass will be in solar masses.

From the ratio of the size of their orbits we can get the ratio of their masses. With Kepler’s Law

and that ratio we can get the mass of each individual star

Binary stars are the only way we have of finding the mass of stars

Most binaries are Spectroscopic Binaries

Play with Binary Star Simulator at http://astro.ph.unimelb.edu.au/software/binary/binary.htm

If the two stars have different masses they move at different

speeds but have the same period

The star with the least mass moves the fastest and has the largest orbit

Sometimes we see the stars with their orbit edge on

We call these systems Eclipsing Binaries

When the orbits are edge-on, the light-curve shows dips

How long it takes to reach the bottom of the dip and how long it stays at the bottom gives the diameter of the stars.

Finally, we have every thing we need to determine the

distance

Eclipsing binaries give us the size of the stars

The spectrum gives us the temperature

2 44L R T 4

distance=L

brightness

The Hertzsprung-Russell Diagram is the most important diagram in

astronomy

The H-R diagram tells us a lot about the life of stars

Stars spend most of

their life on the Main Sequence

On an H-R diagram the

mass increases as you move

up the Main Sequence

Mass determines everything on the Main Sequence

Our task now will be to find out why mass means so much. We will start by studying the

closest star.