Chapter 13: Taking the Measure of Stars Stars 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 Distance is an inverse square relationship 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 luminosities The 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: b v – b b or b u –b v or some other combination

Temperature isn’t all there is to the luminosity of a star If 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 L is the luminosity of the star in watts, T is the temperature in Kelvin, R is the radius of the star and  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 Luminosity Class

So we now have several ways to get temperature We still need a way of finding the diameter of the star

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 1 st 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 Mass The 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 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

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

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.