## Sunday, July 09, 2006

### Astronomical Data 3a. – The H-R Diagram

Now that we’ve taken a look at what light is, where it comes from, how we detect it, and how we calibrate things, we’ve finally set enough groundwork to begin to say what we can learn and how?

In astronomy almost all of the information comes from light, so you can probably guess there’s a lot we can learn. Using nothing but the properties of the light, astronomers can measure the velocity of objects towards us or away from us, magnetic fields, chemical composition, temperature, and more.

So in this next series of posts, we’ll explore how light yields all these secrets.

The first topic that I feel should be discussed, is one that I mentioned in my post yesterday about Mt. Wilson observatory. This is the Hertzsprung Russell Diagram (HR Diagram) which, as I mentioned, is fundamental to the understanding of all stellar evolution.

In its simplest form, an HR diagram is simply a plot of a number of stars with their brightness on the y-axis, and their temperature on the x-axis. Thus, to really discuss it, I’ll have to speak about both of these properties, so this post will be a two for one deal.

Before I get started at giving away the answers, and if you don’t already know them, try to take a bit of time to figure out what an HR diagram should look like and why it should look that way.

Where will stars lie? Will they all be clumped? Will there be a trend line? Or will stars be evenly distributed everywhere?

What properties of the star will determine its position? Size? Magnetic fields? Rotation? Age? Chemical composition?

Once you’ve outlined your hypothesis, keep it in mind as we go.

So let’s get started on figuring out how to build an HR diagram from observations. The first thing we must do is to choose which stars to observe. This is more important than you’d think at first, because we have to choose stars that we either know the distance to so that we can correct for the light becoming dimmer due to distance, or choose stars that are all at the same distance so we don’t have to worry about corrections.

It’s possible to do either. The best way to do the former (stars for which we know the distance accurately) is to look at the closest stars. For these the distance is known extremely accurately because it’s possible to use a technique known as astronomical parallax to determine their distance.

Effectively this technique is the same as holding a finger up at arms length and then closing each eye. By observing the apparent change in position in relation to extremely distant objects and knowing the separation between your to observing points (in this case your eyes), you can determine the distance to the object in question because you’ve just formed a very nice little triangle. From that, you can make a right triangle and we should all know about those guys from high school.

The same thing works in astronomy, except, instead of using our baseline as the distance between our eyes, we use one that’s 186,000,000 miles: the diameter of Earth’s orbit.

As you can see, we’ll observe a star with relation to background objects at one point, wait 6 months, and do it again. The lower part of the image demonstrates that the star will move. The amount it moves gives the “parallax angle” which can be used to determine the distance. Obviously, the further away a star is, the less it will seem to move, which makes the angle harder to measure.

With the launch of the Hipparcos satellite there are roughly 100,000 stars for which we have precise parallax measurements for. That’s a pretty damn good sample of stars for which we can to make our HR diagram!

The other option is to choose a grouping of stars that all have the same distance so we don’t have to worry about some being more dimmed than others due to distance. Fortunately clusters have lots of stars that are all at the same distance.

So now that we’ve figured out which stars to choose, it’s time to measure their brightness. Before the advent of CCDs, this was quite tricky using photographic film, or quite slow using photomultipliers (which can only do one star at a time).

But fortunately CCDs allow us to determine brightnesses of a whole field of stars at once! All we have to do is count up how many photons hit the CCD and we get its apparent magnitude. We can then take the apparent magnitude and put it on a standard scale which fixes all stars for the same distance (in the former case) which is it’s absolute magnitude (the magnitude of a star viewed from a distance of 10 parsecs).

If we’re looking at one of those clusters, then we don’t have to worry about correcting for distance and are finished with figuring out what we need for the y-axis.

The next trick is to figure out the temperature of the star. Fortunately, this isn’t hard either.

If you remember back to my post on where light comes from, it’s caused by electrons in higher orbitals falling down.

What I didn’t tell you is what determines how electrons get in those higher orbitals. There’s two primary ways: The electron can get excited by getting hit by another photon, or it can get bumped up in a collision with another atom.

Both of those two cases are directly related to what we need: Temperature.

For a given temperature electrons are most commonly bumped up to a single orbital, although not always. Thus, when you look at how much light is given off at every wavelength, there will be one at which it peaks.

So if we can find this peak, we can determine the temperature. There’s a few different methods for doing this, which I’ll go into in detail in a later post.

So now we’ve been able to get both temperature and brightness. We’re ready to construct our HR diagram!

Before I show you the image, think back to what your hypothesis was and see if you were right.

Before I go any further, I feel it’s important to point out that the x-axis runs backwards. Higher temperatures are to the left. The reason for this has to do with a convention on another property I’ll discuss later that is actually interchangeable with temperature.

This image is from the ESO, and I suspect it’s a plot of the nearest stars. Ones for clusters have a distinct difference which I’ll discuss in my next post on this topic.

Looking at this very quickly, you can tell that the stars do indeed fall along a main line running diagonally from the upper left to the lower right. This line is known as the main sequence and is where stars spend 90% of their lives while they quietly burn hydrogen into helium in their cores. The other clumps I’ll go into at a later time.

But let’s explore what this graph is telling us before going any further. Stars to the left are the hottest. To the right they are the coolest. Towards the top they are brighter than at the bottom. Thus, a star in the upper left hand corner, is a very hot, bright star.

Hotter stars are obviously going to be brighter. But why then, do we see some cool stars that are almost as bright that are very cool (towards the upper right)? If temperature isn’t causing them to be brighter, what is?

The answer is that these stars are just larger than the average star. Since they’re larger, that means that they have more surface area to give off light, which is why they seem brighter. So stars in the upper right are giants, while stars in the lower left are dwarf.

So what else can we figure out from this diagram? Another thing that we can plot on this graph is the color of the star. Yes, stars do have color. Our eyes aren’t terribly sensitive to these colors, but if you really pay attention, you’ll see it. The bright star Sirius (which is up for those of us in the Northern hemisphere tonight, just to the southwest of the extremely bright Jupiter) is a blue star. Meanwhile, the star straight up from Orion’s belt (visible in fall and winter), Betelgeuse, is a dingy red.

Since Wein’s Law I mentioned earlier tells us that the peak wavelength is dependant on temperature, color and temperature can be used rather interchangeably. Hot stars have their peak wavelength at shorter wavelengths (ie, blue) since their photons should understandably have more energy. The opposite is also true with cool stars being red (long wavelength). The Sun is actually somewhere in the middle, with its peak wavelength being a sort of lime green.

Incidentally, this is the precise wavelength to which our eyes have evolved to be most sensitive at. Since your eyes are extra sensitive to that wavelength of light, newer fire trucks are being panted that color so they’ll stand out. Awful color, but it sure is noticeable.

You may have heard terms like “Red Dwarf” before. Now you should be able to get an idea of where these come from. They’re positions on this diagram. A red dwarf would be a red star towards the lower right. “White Dwarves” would be ones that were closer to the blue end, but still very small.

So let’s take another look at the HR diagram with those features plotted as well.

Again, pay no attention to the x-axis where it speaks of Spectral Class. I’ll explain that when I start getting into chemical composition and the spectra of stars.

But here we can see more clearly how size and color progress, as well as how a few popular stars like Betelgeuse, Sirius, Vega, and others stack up.

But not pictured on here, and still not discussed is one more important feature that we can plot: Mass.

To figure out how that would figure in, let’s stop to consider why stars are, well, stars. Even without taking a hunch of courses in astronomy, you’re probably well aware that stars are accumulations of (mostly) hydrogen gas that’s hot enough to undergo nuclear fusion in its core. But why are they so hot?

The reason has to do with where they come from. Stars (and their respective solar systems) start off as giant clouds of gas, lightyears across. Eventually, the cloud collapses under its own gravity. Bur remember how I discussed gravitational potential energy when talking about electron orbitals? The cloud has a net potential energy as well.

As everything collapses from something light years across to only a few million miles, there is a huge release of that potential energy. It is converted (at least in part) to heat.

So where does mass factor in to all of this? The answer is that the more mass there is, the more gravitational potential energy it has. Thus, more mass leads to more energy converted to heat, which means higher temperature! Cutting out the middle steps, and reversing it, hot stars are more massive.

I couldn’t find an image with this plotted on it, so I’ll just let you use your imagination.

So that’s an introduction to the HR diagram. By finding a star’s temperature (which is synonymous with color and something called spectral class), and its luminosity, we can figure out the mass and the size!

Suddenly this two for one post deal became a 4 for 1. Not bad.

Since the HR diagram we looked at today was generated by the closest stars, next time I post on the topic of how we learn things in astronomy, I’ll talk about a difference in these for when we look at stars in clusters. This difference gives us another important feature of the stars in that cluster: Age.

I’ll probably get that up in a few days since tomorrow’s Monday and I’ll be heading back to work on research, meaning I won’t have as much free time.