The Astronomy Mega Thread (More than 50 pages of info!)

[VoijaRisa]

TABLE OF CONTENTS
Introduction

The Nature of Light
- 1a: What is Light?
- 1b: Where does Light Come From?

On Astronomical Imaging
- 2a: Light's Impediments
- 2b: Light Detection
- 2c: Image Calibration
- 2d: Astrophotography

Making Sense of Data
- 3a: The H-R Diagram
- 3b: Main Sequence Turn Off
- 3c: Spectroscopy
- 3d: Radial Velocity

Stellar Evolution
- The Big Picture
- Model Evolutionary Tracks
- Isochrones
- The Effects of Convection
- Nucleosynthesis
- Variables and Asteroseismology
- Supernovae Products
- Hidden Creation

Galaxies
- Spiral Structure
- Galactic Evolution
- The 81 Group

Various Topics
- Four Misconceptions About the Big Bang
- Pluto's Demotion from Planethood

[VoijaRisa]

Intro:

Although many people consider it to be one of the easier sciences out there, Astronomy poses its own unique challenges. One of the greatest among them is that, in most cases, direct experimentation is impossible. Even at the speed of light, it would take a little over 4 years to reach the nearest star. Even the furthest space probe we’ve ever launched (Voyager 1, launched in 1977), is only a “measly” 17 billion kilometers from Earth. At the speed of light, it would only take about 16 hours to go that far. Paltry compared to the 4 light years it would take to reach our nearest stellar neighbor.

Thus, by the very nature of these distances, astronomers can’t very well go to distant bodies to explore and study. Anything outside of our solar system is out of bounds for the time being. So instead of going to them, we sit back and let objects send us information.

Yet this seemingly laid back approach belies several questions that bear further exploration.

The first is: “what sort of information?” The second, “how to we receive it?” Also, “How do we interpret it?” We can also ask, “How do we match it to theory?”

It is the answers to these three questions that I intend to explore for you in this, my next series of science minded posts. Hopefully this will enlighten you to how astronomers collect the data we need and how we can make the claims we do about places we’ve never been.

This series of posts is taken from a series of posts in my blog. I am reposting it here because I know many people on Gaia have interests in Astronomy but have difficulty finding simple, yet in depth information.

I teach introductory Astronomy labs at the University of Kansas and know how scattered things can be, so I hope this is coherent. While I intend to provide a great deal of information in this thread, it's always hard to know how to organize things. The first section is devoted to an introduction of data acquisition. The hope is, that with this I can then have a basis to discuss particular topics using the tools I've explained previously.

Currently, I've already written a good section on the basics of stellar evolution which is why I've made it the next section. At the present time, however, there are no more topics I have currently written on. As such, if anyone has specific questions on a topic, I'll be happy to add additional sections. Just give me a topic.

[VoijaRisa]

Part 1a: What is Light?:

As previously mentioned, in astronomy, there are very few circumstances in which astronomers can obtain physical samples with which to work. Instead, our work relies primarily on objects transmitting their secrets to us in another form.

This form is electromagnetic radiation, or, as it is most commonly known, light. For those that remember, the light that we see with our eyes is just a small part of a much larger spectrum of light that we cannot see.

Figure 1
Source

Looking at the above diagram, you are probably familiar with several other of the types of electromagnetic radiation listed. The low energy radio waves are the ones that we pick up our cars on the way to work (assuming of course you're not listening to a CD or something else).

You're probably also familiar with microwaves. However, this title encompasses a much broader range of light than what your microwave oven actually uses (microwave ovens use a very specific frequency that excites water molecules to heat your food while other frequencies won't).

Infrared radiation is most commonly known as heat. When heat is not transferred through direct contact, this is the method that is generally used.

Visible radiation is what we see with our eyes.

Beyond that is the ultraviolet. Bees see in this region of the spectrum, which is why flowers and are frequently marked differently when viewed in this region, in order to indicate where the pollen is:

Figure 2
Source

X-rays are what we use to see through soft tissue and take images of bones. I just had a few of these at the dentist a few hours ago.

Gamma rays are much rarer as they are only generated in high energy reactions. They are quite dangerous as they can cause cancer, but fortunately, our atmosphere shields us from the cosmological sources.

Past gamma rays, and not featured in this image, is the enigmatic cosmic rays which are even more powerful, but extremely rare.

So that's a quick overview of each different region. However, this does not answer the question of what's behind all this radiation? To answer this in a complete manner requires a look at over 200 years of physics history.

Early experiments into how light works revealed that light is a wave. A classic experiment demonstrating this was done in the early 1800's in which light was passed through two narrow slits and projected onto a screen.

If you don't already know the result of this experiment, take a moment to think about what you'd expect. Inuition would tell you it should be like shining two spotlights nearby eachother. Where they overlap, you should have a brighter spot, whereas where they don't, it wouldn't be as bright.

As you might suspect though, this isn't the case. It turns out, that when the slits are made narrow enough, a strange pattern emerges:

Figure 3
Source

In this pattern, we see that there is a series of light and dark bands, which is brightest towards the center, and fades as you move away in either direction.

This pattern is indicative of waves. When a wave from the right slit would interact with the wave of light from the other, the two waves merge. When they merge in such a way that the crest of one wave matches with the crest of another, then it makes a bright spot. When the crest meets a trough, they cancel out and that point on the screen is dark.

So the wave theory of light was established. However, if light was a wave, waves, like water waves and sound waves, need a medium through which to travel. That means that there should be something beyond our atmosphere though which the wave could propogate. This mysterious medium was dubbed the "ether".

Unless you're really into science, most of you reading this have probably never heard of this ether. It's likely you don't remember everything from science class, but this term is probably one you've never even heard (unless you play a lot of roleplaying games).

So why don't we teach about this ether in science courses? The reason is that it was eventually discredited in the early 1900's by a team of scientists known as Michelson and Morely. These two attempted to determine the properties of the ether. Since the Earth travels around the sun, the Earth should be moving through this ether. Therefore, waves should be deflected in some measureable amount as they were swept away by the current relative to the moving Earth.

However, their experiment was completely unable to detect any sort of variation. No matter how many times they tried their experiment, the results always showed the waves propagating at the same speed, roughly 3 x 10^8 meters per second.

The puzzle seemed unsolvable and it would take a genius like Einstein to solve it. In fact, it was Einstein that solved it. Although most people known Einstein for his famous equation, E = mc^2, and his laws of relativity, his nobel prize was actually awarded the prize "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect."

Huh? Photoelectric effect?

Since a comprehensive explanation would take quite a bit of time and space, I'll cut to the chase on this one and just say that this effect shows that light comes in discreet "packets". This indicates that light is a particle with a fixed energy. This particle, which travels at the speed of light and has no mass, was called the photon.

So which is it? Is light a particle, or a wave?

In reality, it's both. This discovery, and similar ones that showed all subatomic particles exhibit this wave/particle duality, gave rise to the entire field of quantum mechanics.

But that's beside the point for this post. For this topic, it's just important to understand that light can be thought of as either, and while neither is wrong, one may be more convenient than another for explanation.

[VoijaRisa]

1b: Where Does Light Come From?

In my last post on this topic, I gave a very abbreviated overview of the nature of light and pointed out that it is both a particle that carries discreet energies in the form of a photon, yet also exhibits the interference patterns characteristics of waves.

Yet, in this, I made the assumption that the light, in whatever form it is, already existed. But that light had to come from somewhere. And that's the topic of this post.

In short, light comes from atoms. That's the quick answer, but before I try to give the more complete one, let's review some basic concepts that you may or not remember from high school.

Figure 1
Source

This is the basic model of an atom with which you're probably familiar.

In this we see the nucleus (although represented millions of times too large) which contains protons and neutrons (the red and blue balls in the center). Around the nucleus is a swarm of electrons. In a normal atom, the number of negatively charged electrons is the same as the number of positively charged protons which makes the atom neutral.

However, while you're probably familiar with this model of the atom, it's also very outdated. While it's easy to picture electrons orbiting in that manner, it's actually incorrect.

With pretty little circular orbits like that you'd expect that you could just make the orbit a little larger and still have no problems. There shouldn't be any preferred orbits. But as you're probably expecting by now, that's not the case.

In fact, electrons are only able to be in very specific orbits which are conveniently called "orbitals". And not all orbitals are created equal. In fact, none of them are.

To get a better feel for this, let's take consider the simplest case we can; the hydrogen atom. This atom has a single proton in the nucleus, and is orbited by one electron. Can't get any simpler than that.

The smallest orbit that an electron is called the "s orbital". When electrons are in this state, they have the least amount of energy possible, which is why this level is often referred to as the "ground state". The s orbital is able to hold at most, two electrons.

Beyond the s orbital, the next smallest orbit that electrons can possess is called the "p orbital". When electrons are in this orbital, or any other besides the s orbital, they're said to be excited which basically means they have extra energy (kinda like that excited little kid who'd never been on an airplane before that I sat next to this morning). But unlike hyperactive children, these electrons don't have energy in the sense that they're bouncing off the walls.

Instead, you can think of this energy as a sort of potential energy. Potential energy is something that you're probably quite familiar with, even though you may not realize it. The most common instance we see of it, is with objects that are raised some distance from the ground. If an object is raised, it accumulates potential energy due to it's height. The higher an object is, the more potential energy it has.

If you want to see just how much potential energy an object has in a case like this, drop it. The potential energy will be converted to kinetic energy (energy of motion). Common sense will tell you that a rock dropped from the top of a cliff is going to end up hitting the ground a lot harder than that same dropped from your hand.

The reason for this is that the rock dropped from the higher point had more potential energy. Since energy must be conserved, when the rock falls, it has to convert that energy to kinetic energy.

The same sort of thing happens with our little electron. If we have an electron in the p orbital, that's like having the rock raised off the ground. However, just as a rock will fall if unsupported, so too will an electron. If that electron is in the p orbital and there aren't two electrons filling that s orbital to support it, then that electron will fall back down to the s orbital.

Since the p orbital was the one with higher energy (the excited state), that means that the electron is going to have to convert that potential energy into another form. But instead of picking up speed like our hypothetical rock, the electron does something a little different; It spits out a photon.

This photon will have the exact same energy as the electron lost as it fell down.

But remember how light can't just be thought of as a particle? Here's a great place to think of it as a wave again. Waves are described by two main properties: their amplitude (the height of the wave) and their wavelength (the distance between successive waves). What important to know here is that the smaller the wavelength, the higher the energy of that wave is.

That means that if you have a really energetic photon/wave, it will have a very short wavelength. These are things like x-rays, gamma rays. They have lots of energy and can do serious damage to your cells the same way a highly energetic kid can do serious damage to a china shop. That's the reason you try to limit your exposure to such wavelengths. On the other hand, if there's a small change in the energy, the wavelength will be long giving you things like micro waves and radio waves.

If you're really following everything here, what you should realize is that these falling electrons are responsible for creating photons of every sort we observe; from radio waves to cosmic rays. In reality, it's all dictated by a rather simple formula that gives the energy of a photon in relation to its wavelength:

http://s94958815.onlinehome.us/angryastronomer/ephot.gif

In which lambda is the wavelength, c is the speed of light (3 x 10^8 m/s), and h is just a number, known as Planck's constant (6.6 x 10^-34 m^2*kg/s).

However, you might have spotted a problem here. So far we only know that the electron can go from the p orbital to the s. Every time this happens, it will release a consistent amount of energy, which would correspond to a single wavelength. That means the entire universe should be monochrome! This obviously contradicts what we see since the world is filled with pretty colors and all those other wavelengths that we can't even see with our eyes.

You're probably expecting that there must somehow be more transitions with different energies. And you'd be right. Beyond the p orbital, there are several more including the d and the f orbitals.

So when you start putting everything together, you'll eventually start getting a picture like this:

Figure 2
Source

In this schematic diagram, you'll see the ground state at the bottom. Above it is each excited state. What you'll notice is that each next excited orbital is closer to the previous one than the one before it. Thus, they start to bunch up. Eventually they bunch up so much, they're not really going anywhere, hence that top line labeled with the infinity symbol.

We'll come to that in a moment, but for now, what you may be realizing is that, even with all these additional orbitals, we still haven't figured out how to get every different wavelength out there. Since there's only those discreet transitions it can make, it can still only produce photons at very specific wavelengths. We haven't solved the problem at all!

But that's where that last line with the infinity symbol comes in. What that line represents is the "ionization energy" for hydrogen. If an atom is ionized, that just means that it's lost an electron somehow. That means the atom as a whole will have more protons than it does electrons and it need to find a new electron to be neutral again.

Fortunately, electrons aren't too hard to find. And when an electron falls into one of those orbitals from past that ionization line, it can fall from any distance. That means it can fill in all those "gaps" that electrons jumping from all those bound orbitals just can't do. So now, we can successfully explain light of any wavelength out there!

[VoijaRisa]

2a: Lights Impedements (Reddening, Absorption, and Extinction)

In the past few posts in this topic we learned that light is created when electrons fall down and have to give off their extra energy in some form. The light travels as a strange particlish wavy thing and then travels billions of miles to come twinkle in our night skies.

But for all that work, it's all in vain if we can't do something with it. So in this post we'll explore the history and challenges of detecting light from outside our planet.

The first challenge comes before the light even gets to our solar system. While for the most part, space is a damn near perfect vacuum (having only a few atoms per cubic kilometer), some areas are less vacuous than others.

Such things as nebulae (clouds of gas and dust) can obstruct the light of a star in its travel. Ultimately, there's not too much that can be done about this since it's hard to gain a clear picture of how big such a nebula is so that we can subtract out the effects.

However, we can recognize that the effects are present. Since most nebulae are made primarily of the most common element in the universe (hydrogen) we recognize that hydrogen will allow certain wavelengths to pass easier than others. The longer the wavelength, the less effect passing through these clouds will have. For the visible part of the spectrum, that means that red light will pass through relatively easily while blue light will be cut down. Thus, the star will appear redder. Not surprisingly, this effect is known as "interstellar reddening".

Depending on where we're looking in the galaxy, such nebulae may or may not be common. In our galaxy almost all nebulae are found in the plane of the galaxy which is that faint band of light in the sky known as the Milky Way. Therefore if we're looking at stars in this reason, we can expect that they will exhibit much more reddening than stars further from that plane.

These nebula become so thick in the Milky Way that after a relatively short distance, stars are completely blocked in the visible. Therefore, to "see" these stars, astronomers must use longer wavelengths such as infrared and radio.

However, much more importantly, there's another region of gas that's far more important: Our atmosphere.

Although our atmosphere is much thinner than any nebulae, its effects are much more pronounced because it is millions of times more dense and is constantly changing. Additionally, the chemical composition is very different. Unlike the rather simple dimming of hydrogen clouds, our atmosphere's blocking is much more complex as this diagram shows:

Figure 1

What this diagram is showing is how far different wavelengths can penetrate our atmosphere. What we can see is that short wavelength radiation like gamma rays and x-rays don't get through the atmosphere at all.

The rainbow you see at the top is the visible part of the spectrum. Just to the left, you'll notice that a tiny bit of radiation is able to get through. This is ultraviolet radiation. It's the stuff that gives us tans and causes cancer. It's a damn good thing our atmosphere does a pretty good job of blocking it.

However, on the other side of the visible spectrum, you'll notice things get much more complex. Just to the right is the infrared. Various parts come right through while others are blocked completely. This choppy pattern extends into the microwave as well.

The next big dip that all radiation can get through is in the radio part of the spectrum. This is the range in which radio and TV stations send their signals. Yet longer wavelengths radio waves are blocked.

So our atmosphere does some funky blocking stuff. In the visible part of the spectrum, we can see that even at its best, it's not quite 100% that gets through. Somewhere around 10% is still blocked. Thus, if we want to know how bright a star really is we're going to have to take this into account.

But this is only if you're looking straight up that that's how much light is blocked. And how often is a star straight up? This means that when worrying about how much light our atmosphere kills off, we have to consider where in the sky that object is at any given time.

You're probably familiar with just how much of an effect this is. Perhaps the most commonly seen, and also the most dramatic effect of this is the moon on the horizon:

Figure 2
Source

As with light passing through nebulae, our atmosphere tends to scatter blue light more (hence the reason the sky is blue). Thus, the moon looks redder the more atmosphere it has to go through.

This effect is known as "atmospheric extinction" and as you've seen it depends not only on the wavelength of light, but also on the amount of air it's having to go through. So that's all one big mess.

But wait! There's more!

As I mentioned briefly, our atmosphere is constantly changing. It's being blown around by all sorts of winds and acts as an ever changing lens. However, because the light was already a perfect point before entering the atmosphere, this ethereal lens can never improve upon that and thus, can only reduce the quality of the image by blurring it out.

Obviously, the more atmosphere light has to travel through, the more it's going to be blurred. How blurred something is, is called the "seeing" in astronomy. This (as well as the absorption mentioned previously) is why observatories are placed at high altitudes. Yet even at these locations, the best seeing is generally about half of an arcsecond. I assume most of you aren't familiar with an arc second so let me digress for a minute to explain:

If the entire sky, including that below the horizon is pictured as a sphere and divided into 360º, then each degree is divided into 60 more segments, these are called arcminutes. If each arcminute is divided into 60 more segments, then these are arcseconds. That means 1 arcsecond is 1/360 of 1º. That seems like it's still very tiny and there's no room to complain.

However, let's put that in perspective: If the moon is a half of a degree, that means it's 1800 arcseconds across. In my moderate size telescope (8" mirror) I can quite easily magnify the moon by 20 times. This means that my field of view is about 1/3 the width of the moon, or 600 arcseconds. So if the seeing was good enough as the .5 arcseconds figure, then any details larger than 1/1200 of that field of view would be visible. Not too bad.

However, only at some of the best observatories in the world (like the ones on Muana Kea) get this sort of benefit. In a normal suburb the seeing can often be much poorer due to lower altitudes, air currents due to the uneven cooling of cities, as well as a much higher amount of pollution. Thus, we can expect things to be blurred to a size of 10-20 arcseconds.

That means that in my magnified moon, anything larger than 1/60 to 1/30 the width of my field of view is going to be blurred. That's quite noticeable. That's why magnification in amateur telescopes is ultimately rather pointless. Due to the turbulence of the atmosphere, there is just a limit to how clear of an image you can get, no matter how big your telescope is.

So now we have light that's being dimmed by nebulae and our own atmosphere, and then blurred. Things aren't looking too great here for getting good data.

And that's only nature getting in the way. In my next post, I'll go through some of the history assosciated with astronomical imaging, and then discuss how various difficulties can be overcome with modern instrumentation.

[VoijaRisa]

Astronomical Data - 2b. Light Detection

In my last post on this topic we learned several challenges for light to reach us. Aside from possible interstellar clouds that obscure our signal, there's also a significant distortion and dimming from our own atmosphere. But the fun doesn't stop there!

In this post we'll explore the final step of astronomical observations: the detection and the problems associated with it.

The first device used to observed starlight was undoubtedly the human eye. In some ways this tool is far superior than any other in use today, yet in many others, is extremely difficult.

Around 150BC, Hipparchus, a Greek astronomer, developed a system using the unaided human eye in which he classified the brightness of stars. The system places stars in categories called magnitudes. Brightest stars he gave a magnitude of 1. The faintest he could observe he gave a magnitude of 7.

Surprisingly, the human eye works well at determining what category stars should be placed into. The problem with this system is that the human eye doesn't work linearly. That means that if star A is twice as bright as star B, then the human eye doesn't actually A as twice as bright as B. The reason for this is that the human eye uses a logarithmic scale. Accordingly, the magnitude scale is logarithmic as well, making the system rather difficult.

The magnitude system is even more frustrating when you stop to consider that it runs backwards! Bright stars are smaller numbers. Thus, when you graph things using the magnitude system, you generally have to flip the Y axis over. Over time, revisions were done to the magnitude system so that there was a strict mathematical definition of magnitudes. However, it still remains largely the same.

This standard of naked eye observing was common for many centuries. During the Middle Ages, calls for astronomical predictions increased, and astrologers (the forerunners of astronomy) began developing new instruments to more accurately measure the position of stars and planets.

One important person amongst these people was Tycho Brahe who was an extremely interesting character. Apparently he was a rather convivial fellow who enjoyed drinking and dueling. In fact, he had at some point lost his nose in a duel and had it replaced with a brass one.

Legend has long held that Brahe met his death thanks to his other addiction. During a dinner with royalty in Prague in 1601, he supposedly drank too much. Yet due to the rules of ettiquite, he was not allowed to leave the table until the host left. After drinking too much wine, his bladder eventually burst. However, more recent investigations have shown that he most likely died of mercury poisoning.

Yet although his lifestyle was unconventional, he did make excellent contributions to astronomy. His observatory housed large sextants with which he could measure the position of celestial objects to far greater position than any other at the time. Amongst his discoveries was the discovery of a "novae", or "new star" in Cassiopeia. This destroyed the long held belief that the heavens were static and unchanging.

However, Tycho did not release his data. Upon his death, his apprentice Johannes Kepler used his data to lend strong support to the heliocentric model.

The next major revolution came with the development of the telescope. Although its development is generally attributed to Galileo, this is incorrect. The telescope had already been in existance, but Galileo made several improvements and was the first to make recorded astronomical observations using it. Among them was the realization that there were many small craters on the moon as well as stars too faint to see to the unaided eye.

For many years, observations were done by hand:

Figure 1

This continued until the invention of photographic film the mid 1800's. This allowed for major revolutions in the astronomical field. The main advantage that film has over the human eye, is the ablility to do long exposures, and thus, bring out detail that would otherwise be lost.

New nebulae that were far too faint to see even with powerful telescopes were suddenly discovered as well as millions of new stars. Photographic film is also very useful because it allows for very large fields of view.

However, photographic film wasn't without problems. One of the largest was a property known as the "quantum efficiency". Don't be intimidated by the big word. It really just means what percentage of incoming light is actually turned into an image. With standard photographic film today, less than 5% of light that falls on the film actually goes towards making the image.

For standard use everyday, this isn't a problem because there's millions of photons streaming into your camera. However, when every photon is precious, only getting a few precent is a sore deal. Eventually, techniques were developed that increased the quantum efficiency to closer to 10%. But these techniques were difficult and extremely expensive.

Due to the poor light sensitivity, this means that exposure times will have to be relatively long. Since the Earth is constantly turning, this means that the telescope will have to track the night sky perfectly, until the image is finished.

Another problem with film is that its quantum efficiency is different at different wavelengths. Thus, film was great for making pretty pictures, but made extracting numerical data extremely difficult.

Similar to the human eye, photographic film is also non-linear. For certain brightnesses, it performs quite well, but after a certain point, no matter how much you increase the light falling on a given part of the film, the image will not appear any brighter in the result. Again, this non-linearity makes extracting data difficult.

By the 1970's a new type of device known as a Charge Couple Device (CCD). These are the receptors used in most digital cameras today. One of the largest advantages of CCDs is that they have extremely high quantum efficiency. Even a cheap CCD will often be above 60%. The tens to hundred of dollar astronomical grade CCDs will have quantum efficiencies of closer to 90%! Higher quantum efficiency means less exposure times which means its easier to track, as well as the ability to do more science in one night!

Figure 2

Another major advantage is that CCD cameras are very linear! Doubling the brightness of an object doubles the output value the computer reads out.

So what are the disadvantages?

One of the main ones is that CCDs are very expensive. This stems from the fact that they're also very hard to produce. The difficulty in producing them leads to small sizes. Thus, only images of small sections of sky can be taken. To solve this problem, several CCDs can be glued together side by side. But if one CCD is expensive, an array is even worse.

The next is that CCDs take a long time to "read out". This means that getting the image from the CCD camera onto a computer takes quite awhile in comparison to film which is just a sort of *snap* next frame. If you've ever downloaded a full resolution image from a digital camera to your computer, you'll know that this can take a few seconds. However, because of how CCDs work, astronomical CCDs take even longer because we're worried about preserving every bit of data. Additionally, the images for astronomical CCDs are much larger in size than those for a digital camera.

Lastly, CCDs are very "noisy". To explain this problem, we'll have to first take a look at how CCDs work.

A CCD in essence is just a very large grid of (generally) silicon. When a photon comes and hits an atom in one of the boxes in the grid, it will knock off an electron. Thus, that box will have an electron floating in it. The more photons strike a box, the more free electrons.

Once the exposure is done, the CCD counts how many electrons are in each box. The number is then displayed on a computer as a brightness of that box.

One of the problems with this is that, to read how many electrons are in each box, the box must move to the counter. If we're not careful, electrons can spill out during this process, hence the reason astronomical CCDs move the boxes slowly where digital cameras run the boxes over as fast as they can.

However, photons hitting the silicon isn't the only way to get an electron. On a microscopic level, atoms are always bouncing around. The hotter something is, the more they bounce. Occasionally, when two atoms bump into one another, this collision will knock off an electron. The result of this is an extra electron that looks like it came from a photon, when in reality, it had nothing to do with it. This sort of noise is called a "dark current" since the CCD will read like it's getting light even when the shutter is closed.

Another source of noise is what's called "bias". If a CCD were cleared and then immediately read out without having any exposure time, it would still read some signal just due to electronic circuits not being perfect.

The third source of error in CCDs is imperfections in the equipment. When making CCDs, it's impossible to make each of the boxes the exact same size given that each box is only a few microns across. Inherently, if one box is larger than the one next to it, it will collect more photons than its dimunitive neighbor. However, when displayed on your computer, each pixel on your monitor is the same size. Thus, the pixel corresponding to the smaller box will be darker than it should be if the boxes on the CCD were perfect, while the bigger boxed pixel will appear brighter.

Additionally, problems in the equipment arise due to dust in the optics. Dust will cast a shadow onto the CCD. Since the dust is out of focus, this will cause it to appear as a darkened doughnut shape on the image.

So by this point, we have gas and dust in space blocking light, our atmosphere absorbing and blurring the light, the CCDs reading non-existent light as well as unevenly distributing what light it finally receives...

How do we ever get anything useful!?

[VoijaRisa]

Astronomical Data - 2c: Image Calibration

So far in this series on Astronomical Data, we've explored the origins of light (hip-hoppin electrons) and its strange phyicality (a wavy particle thing).

In section two, we've discussed some of the troubles light has in getting to observers once. Natural sources, like gas and dust clouds and our atmosphere are the first challenge.

Next up there's all sorts of difficulties in the CCD chip between imperfections in the size of each box, heat induced noise, and just a general electronic noise.

So the question after all this was, with all this distortion, how ever can we get any useful data?

The answer is that we have to correct for as many of these as possible. Thus, we'll now explore what methods go into this.

Because it's more straightforward, I'm going to start with the nature of correcting for problems with CCDs before going into the effects caused by nature.

If you recall there were three main problems with a CCD that need to be fixed:

1. Certain photon collecting boxes were more sensitive than others (because they're bigger) while others are less sensitive (because they may have dust or other obscuring material.

2. General motion of atoms can bump off electrons giving false signals.

3. General electronic noise.

To explain how this cleaning process works. Let's start by looking at a raw image

Figure 1

Looking at this, you’ll probably notice quite a few things. One thing is that the background sky isn’t actually black. This is a result, primarily of the general electronic noise and/or the bumped off electron noise. Another thing that should stand out is that there are some dark doughnut looking things. The highly technical, jargon filled, and oh so scientific term for these are “doughnuts”. As mentioned earlier these are a result of out of focus dust particles somewhere in the system.

What may not be so obvious is that certain regions are slightly brighter than others. You might also not notice (depending on your monitor settings and how zoomed in on the image you are), that the pixels right next to each other in the sky where it should be even, certainly aren’t.

All of these in some way or another are (probably) due to the three items I’ve mentioned before (I’ll discuss a few other sources of noise that aren’t always present towards the end).

So since there’s three main causes of noise, it makes sense that there will need to be three steps in the cleaning process.

Since those dust doughnuts really stick out, we’ll start with those. To correct for this, astronomers take what’s known as a “flat frame”. If you remember back on day 9 of my internship, we went to the observatory and I posted an image of a white square inside the telescope dome.

This white square is evenly illuminated (well, as best as possible) by an out of focus slide projector across the room. We then take an image of this flat field using the telescope.

The result is something like this:

Figure 2

Now those dust doughnuts really stand out. This will allow astronomers to fix all those dust doughnuts as well as any individual pixels that are slightly more or less sensitive than others. The trick is “how?”

The first thing that must be done is to figure out what the average value is supposed to be. So a computer program takes each pixel and finds the average. Keep in mind that a fairly low end astronomical CCD can be 2048 pixels^2 (ie, 4.1 megapixels). If it weren’t a computer, that’d be quite the task.

The next is to compare the value of each pixel on this flat frame to the average. If it ends up higher, that means that individual pixel is, for one reason or another, too sensitive. If it’s too low, that means the pixel was under sensitive (either because it’s box on the CCD was smaller, or there was dust blocking it, etc…)

So now we can play Goldilocks with each pixel and see whether it’s too sensitive, not sensitive enough, or juuuuust right. But what’s better, is that for those that are off, we also now know by how much!

Taking this information, we then apply it to the actual image taken of whatever object we happen to be looking at. Pixels that were darkened will be brightened by the amount the flat field told us they were below the average. Pixels that are too bright will be dimmed similarly.

One problem down!

Problem #2 was that, as atoms move around, they’ll bump into one another, knocking off an electron which gives a false signal.

The easiest way to stop this from happening is to stop it before it starts and just keep those atoms from moving! To do this astronomers cool the CCD to extremely low temperatures using liquid nitrogen (which is also good for blowing up watermelon).

In doing this the amount of electrons that get bumped off is something like one per hour. Statistically not even worth mentioning.

However, for smaller, non-professional grade telescopes this isn’t an option for multiple reasons. First off, liquid nitrogen isn’t something you can just pick up at the grocery store. But even if you could get a hold of some, the equipment necessary costs tens of thousands of dollars. Lastly, the equipment is also very heavy, hence it can only be used on telescopes large enough to lug it around.

So how do astronomers using smaller telescopes deal with this problem?

The idea is very similar to what’s done with a flat field image. This process is known as a “dark frame”. A dark frame is essentially an image taken without the shutter open. They’re taken for the same amount of time that the actual image is taken for. As with anything else, several are taken and then averaged so we get a better idea just how much thermal noise there is. Dark frames aren’t nearly as fun looking as the flats.

As with the flat frame, the extra readings, as determined by the dark frame, are subtracted out.

So that only leaves one source of noise: The random electrical noise.

While I didn’t state it earlier, this feature is actually controlled by the manufacturer. The reason for this is rather technical but some small amount does need to be present to be able to analyze the uncertainty in measurements. However, for the main image processing it does need to be subtracted out like the thermal noise.

Therefore, another image is taken, called a “bias frame”. This time, the shutter is left on, and the exposure time is 0. This means that there’s no thermal noise involved and any electrons there are just from electrons seeping in because it’s an electronic device.

So by taking another image, we can figure out how much noise there is and subtract that amount from each pixel. Again, the image isn’t very exciting, and generally looks like this:

Figure 3

So now with these three sources of noise, we’re almost ready to start actually analyzing the image!

But wait! There’s more!

Aside from electronic noise, there’s one more source of outside error that I haven’t mentioned. I left it for now because it’s actually one that’s corrected in the computer as well. To present it, we’ll jump back to the earlier post regarding where light comes from.

You’ll recall that a photon pops out when an electron falls into a lower orbital from a higher one. This is where light in stars comes from. There’s lots of atoms with jumping electrons there.

You might find this a bit hard to swallow, but there’s another place that has atoms: Our atmosphere. Shocking isn’t it?

While these atoms aren’t generally heated to as high a temperature as a star, there is enough heat to cause electrons to get bumped up and then fall back down. This is known as fluorescence. The more atmosphere you’re looking through, the more light you’ll get from it. This is the reason that distant hills look washed out.

So even at night, there’s small amounts of light generated by our atmosphere that we need to take into account. Thus, we will generally measure how bright the empty areas are, and subtract that from everything.

Let’s review what we’ve fixed so far today:
1) Under or over sensitive pixels using “flat frames”
2) Heat induced thermal noise by cooling with liquid nitrogen or subtraction of “dark frames”
3) Electronic noise with “bias frames”
4) Sky noise via average subtraction

With these four corrections made, the only thing left in the image should be light coming from the star! No dimming or brightening involved.

However, there’s a few more problems that may need to be taken into account that I’ll go over now.

The first is dead pixels. Sometimes the buckets collecting the photons are just broken and don’t work. In the end, there’s nothing that can really be done about this. What’s generally done is to take an average of all the frames immediately adjacent to them and just assume that would be the approximate value. Not a perfect solution, but the best that we can do.

Another rare, but rather annoying occurrence is that the CCD can be struck by what’s known as a cosmic ray. These ultra-high energy particles stream right through your body all the time. They’re extremely small, so chances are, they’ll go right through. However, sometimes they do hit.

If they do, it completely destroys the atom it strikes, sending a shower of particles everywhere. The scattered particles strike more atoms and make an even bigger mess.

The end result is thousands of electrons suddenly falling into the collecting boxes in the CCD. This means that the readings for those boxes will be extremely high. In fact, so many electrons are generally splattered into the boxes, that those boxes overflow. The technical term for overflowing is “saturating”.

As with before, there’s nothing that can be done about this. Hopefully such strikes will be in an area of the CCD not important to the area being studied. But if it is and it made big enough of a mess, that entire exposure is a wash.

So with all that, I hope you have a bit more of an understanding, and possibly appreciation, for all the work that goes into taking an image, and getting it ready to be analyzed. It’s not an easy task. But with a bit of work, that initial image will finally look something like this:

Figure 4

No dark doughnuts. No grey sky.

[VoijaRisa]

Astronomical Data 2d. - Astrophotography

In this post, I’m going to take a brief deviation from the strict science behind astronomical data acquisition and discuss a related topic: Making pretty pictures.

Even if you’re not into astronomy, you’ve probably seen some stunning pictures like the pillars of creation. But what you probably haven’t stopped to consider is what was involved from taking those images to having an image worthy of display. So in this post, I’ll be giving a brief introduction to the art of astrophotography.

The first step is, predictably, choosing an object to photograph. The Messier catalogue has large number of objects that are favorites.

So once a target is selected we just have to find it. There’s various ways to go about doing this, from star hopping, to using coordinate systems, or just plain making the telescope figure it out in the cases of some newer ones.

Now that we have an object in the view of the telescope, it’s time to take a picture! Hooray! So we grab our digital cameras, hold it up to the eyepiece and snap a picture.

Chances are, if you get anything, it will either look like a big blur or streaked.

Nuts. So what went wrong? One of the first problems is focusing the image from the telescope onto the film or CCD. For amateurs, there are a number of devices specially designed to make the process simple. In professional observatories, the instrumentation packages are designed in such a way that the image should already be pretty close to focused.

The next problem is getting the camera to hold still. This is the reason that holding a camera up to the eyepiece of a telescope is extremely difficult. Chances are you don’t have anywhere near steady enough hands to do this. I know I don’t and I have no problem moving my mouse to pixel perfection. To fix this problem, the camera needs to be attached to the telescope and the shutter is triggered by remote.

Again, there are a number of methods available. Most SLR cameras on the market have adaptors built that are relatively inexpensive. For these cameras a cable release is also used. With astronomical CCD cameras, they’re built to go right on the telescope, and a computer program triggers the “shutter.”

So now we have the camera set up to expose. But how long do we leave the shutter open for?

This is entirely dependent on the object you’re trying to photograph, the equipment, and the intent. For very bright objects like the sun (with a proper filter) a 1/64 exposure is more than long enough. For the full moon, about twice that is necessary. For a thin crescent moon, good exposure times may be closer to 1/4 second. Planets will be in the range of a few seconds on film.

However, for the faint nebulae and the really fun deep sky objects, exposures of minutes to hours are required.

This introduces a new problem: tracking. Since the Earth is turning, it seems like the sky doesn’t hold still and spins overhead. If you have a telescope that doesn’t track that motion, the images will turn out streaked! If done intentionally, this can be a very cool effect:

Figure 1
Source

However, if your goal is to get sharp images, the telescope must be able to follow these motions.

So assuming everything is done correctly, you should now have a nice astronomical image! However, if you’ve used a CCD, it’s in black and white since CCD’s don’t do color.

“But wait!” you’re thinking. “My digital camera does color and that’s a CCD, right?”

Yes, it is! But there’s a trick. Each pixel on the CCD is black and white, but sensitive only to a certain color: red, blue, or green. They’re arranged in a pattern like this:

Figure 2
Source

Each one is very small, and the computer then averages each pixel with its neighbors to determine what color there is.

Not a bad trick. So why don’t those silly astronomers get a clue and do this too? In scientific astronomy the reason is because we don’t care about color images. In fact, we frequently only want to look at light from just one wavelength. But that will all be covered in my next post.

For amateur CCDs that are only going to be doing photography, many are color in this manner. However, it’s cheaper to have CCDs that are black and white so many amateur cameras are still black and white.

So how do astronomers get those color images out of a black and white image?

They go into Photoshop and get out the paint tools of course.

No. I kid. Astronomers use a trick similar to the one for color cameras. However, instead of taking one image, they take three or four. One will be taken through a red filter, another through green, and another through blue. A fourth one is frequently used with no filter to get luminance information across the whole spectrum.

Since things outside our solar system don’t generally have any perceptible motion over a few nights, we can get away with taking these images in different filters at different times. Each image is then recombined digitally to produce a color image (after the calibrations to remove noise that I talked about in my last post on this topic). There are several programs out there to do this. My personal favorite is Photoshop with the FITS Liberator plug in available from the ESA (astronomical images are stored in .fits format which is uncompressed and also has another file embedded that stores information about exposure time, location image was taken, and many other things, as opposed to .jpg format which inherently has compression artifacts).

The trick here is that the person processing the images can do a lot of customization from here. I’m partial to red nebulae, so when I do this sort of processing, I tend to put more emphasis on the red filter. When doing star clusters, I think they look prettier sort of bluish.

Thus, there’s a lot of customization involved in processing astronomical images. Two people can be given the same set of images can end up with very different results. Ultimately, this means that no astronomical image you see is “true color”. That would include those taken with “color cameras” since they are more sensitive to certain colors of light than others which lends an inherent favor to certain colors (generally red).

Is it possible to generate a truly “true color” image. Sure. If images are corrected for the biases proffered by the CCD, and not given any preference by the person doing the processing, it’s possible. However, such images are very boring to look at. The images generally come out very grey. So in the end, having a little bit of artistic license is a good thing.

[VoijaRisa]

3a. – The H-R Diagram

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 blog post 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.

Figure 1

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 <b>apparent magnitude</b>. 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.

Figure 2

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.

Figure 3

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.

Figure 4

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.

[VoijaRisa]

3b. – Main sequence turnoff

In my last post, I discussed a wonderfully important tool in astronomy known as the HR diagram. We saw how it gave a wonderful relationship between temperature (or color, or mass) and the luminosity of the star. Additionally, it could also help determine the radius of a star.

So all in all, it’s a pretty nifty little tool. But at the end of my post, I pointed out that, if a HR diagram was composed for a cluster instead of for a number of random, unrelated stars, it gave could also give us the age!

To explain this, I’ll start off by giving away the underlying reason: Massive stars evolve faster. This runs a bit counter to what one might expect.

Most people are aware that stars convert hydrogen to helium in their cores. So you’d expect with more massive stars, there should be a lot more hydrogen to have to use up and those little bitty red stars down in the bottom right hand corner of the HR diagram should burn out pretty quickly.

However, the opposite is actually true. Massive stars are the rock legends of astronomy: live fast, die young, and go out in a blaze. Meanwhile, their diminutive little brothers will putter along for billions of years.

So what causes massive stars to die out so quickly?

The reason is that fusion occurs more rapidly at higher temperatures and at higher densities. Massive stars have both of these quantities in excess. Their mass squeezes the core to immense pressures and temperatures.

If you think about it, this should make sense now. If fusion is caused by two hydrogen nuclei ramming into one another fast enough to stick (ie, fuse) then there’s going to be a hell of a lot more collisions in a tightly packed stellar nuclei. Additionally, when it’s really hot, atoms bounce around a lot more and with greater momentum.

Taking these two together, it’s not a huge challenge to see why massive stars burn their fuel and die faster.

But what does that have to do with the HR diagram?

If you remember in the last post, I pointed out that very special place called the “main sequence” on which stars spend the vast majority of their life. As stars begin to exhaust their fuel, they swell up and become giants.

So let’s take a look at that HR diagram I posted before and see exactly what’s going on here:

Figure 1

Looking at this, we can see the main sequence running from the upper left to the lower right across the diagram. The giants appear in the upper right. As the star swells up, it moves across the diagram heading up and to the right.

But remember that more massive stars do this before less massive ones.

Keep that in mind for a minute, as we’ll come back to it. For now, we need to discuss the other half of the situation: the cluster.

Clusters are very special little things. They’re accumulations of stars that are all gravitationally bound. They’re like a mini galaxy in a way. However, they have some very special properties which is what makes them special: They all formed from the same cloud at the same time.

That means for all intents and purposes, the stars will all be the same except for one property: Their mass.

When a cluster forms, there will be some of those massive stars we discussed earlier, and some medium ones, and some runts of the litter. Thus, if it’s a nice young cluster, all stars should be on the main sequence but scattered along the whole thing.

But give that cluster a million years and things start happening. Those giant massive stars will expend all their fuel and start drifting off the main sequence. But remember where massive stars are on the HR diagram? They’re to the upper left.

What this means is that, as stars swell up to giants, it will start at the upper left of the main sequence and slowly work its way down to the less massive stars.

Thus, by seeing where stars are turning off the main sequence, we can determine age!

This method is commonly referred to as “main sequence turnoff” and is one of the few indicators of age available in astronomy. It’s certainly the most reliable.

At this point, I’m thinking spectroscopy sounds like a very good next topic. There’s a number of other topics I’d like to discuss and don’t technically require an understanding of spectroscopy, but since spectroscopy predates many of them, I think it will help put things in a historical context which can be a good thing.

[VoijaRisa]

3c. - Spectroscopy

In today’s post, we’ll be exploring another astronomical technique known as spectroscopy in which astronomers can use light to determine chemical composition.

If you’ve forgotten where light comes from, you might want to go back and reread my earlier post on where light comes from since we’ll be referring back to that quite a bit in this post. Assuming you do remember, let’s take an expanded look at all that.

You should recall that we can get the entire continuous spectrum of light (ie, the entire rainbow including what lies beyond just the visible part) due to electrons falling into orbitals from outside the atom. Since they can fall any distance, that’s what makes it possible to have every wavelength thus making the spectrum complete.

However, in this scenario I made a few assumptions that you may or may not have caught.

The first is that there are slots for the electrons to fall into. If the electron is already neutral (ie, has as many electrons as there are protons in the nucleus) then the atom won’t readily accept any more.

The second is that, if an atom is needing an electron to become neutral, that there’s actually some nearby to fall in.

On the surface of stars, this isn’t a bad assumption. The heat causes atoms to become ionized (lose their electrons) and since the star is relatively dense, those electrons are right nearby to fall into another atom, give off a photon, and then get ionized again.

But in case you haven’t noticed, stars aren’t the only thing in the galaxy. So, as you might be anticipating, continuous spectra aren’t the only kind.

Let’s consider another case in which we have a low density gas that’s warm but not warm enough to actually ionize the atom (for the time being, stick with the hydrogen model in your mind since it’s easiest). In this, since the atom will be imparted with some energy, but not enough to ionize it, the electrons will jump up orbitals and fall back down, emitting a photon.

But since, as I discussed in the previous post, the orbitals have discreet energies, the photons emitted will be confined to those energies as well, and thus, only certain wavelengths. So for hydrogen, here’s what that looks like in the visible part of the spectrum:

Figure 1

Since hydrogen is the most plentiful element in the universe, we see this pattern popping up almost everywhere. However, what happens if we have other gasses in the same condition?

In that case, we get different lines being emitted due to different atomic configuration. Here’s a few more:

Figure 2

As you can see each element has a unique configuration of lines. I generally compare this to a barcode that’s unique to each different element. Thus, if astronomers can put the light from one of these low density, warm clouds through a spectrum and see a pattern that conforms to one of these, they’ll know what element is present. This isn’t always as easy as it sounds for many reasons. One of the major reasons is that there’s frequently more than one element present in what we’re wanting to look at, so sorting things out can get difficult. Another (which we’ll explore later) is that such lines aren’t always where they’re supposed to be due to a few different reasons.

But assuming that things can be sorted out, an accurate determination of chemical makeup can be determined! This type of spectra, one with distinct lines, is called an emission spectra. So keeping all that in mind, let’s take a look at another scenario.

In this one, let’s allow the cloud of gas to be nice and cold heat isn’t causing any electrons to jump up into higher orbitals. In this case, density is unimportant since the atoms already have their lower energy levels filled and aren’t accepting electrons.

But now let’s imagine that we put a source that emits a continuous spectrum behind it so this cloud is in the way. In this scenario, light from the continuous spectrum source will have to pass through the cold cloud. Here’s where something special happens.

If a photon happens hit an atom of the cold gas, it can get absorbed. But only if it’s of one of the specific energies that corresponds to one of those jumps between orbitals. If that happens, and the photon is absorbed, then the electron will take that energy and hop up.

Of course, since that’s a higher energy level, it will fall back down, emitting a photon of the exact same energy as the one it absorbed.

So what? Photon absorbed and given right back off. What’s the big deal?

The trick here is that, the photon that is given off can be given off in any direction. The chance that it will happen to go straight towards the observer is pretty slim. Thus, the observer no longer sees light at the wavelength that corresponds to that energy!

So now instead of having a continuous spectrum, the observer will see one that has lines subtracted from it at the same wavelengths that the gas the light was passing through would emit if it were hot.

Where do we see this? The major place is in stars.

Yeah yeah, I know I said stars have continuous spectra earlier. And they would. If it weren’t for the fact that they don’t have solid surfaces and just slowly fade into a sort of extended atmosphere. That atmosphere is (relatively) cool, and thus, will absorb pieces of the continuous spectrum generated lower in the star.

So what’s this called? As you might expect, it’s called an absorption spectra.

Let’s take a look at one.

Figure 3

Want to take a guess what star this is?

It’s the Sun! And wow is that a lot of absorption lines! Some of the most prominent ones are caused by hydrogen and helium. Some of the other, fainter ones are caused by trace gasses in the Sun’s atmosphere, but most are caused by our own atmosphere.

As a brief aside, you’ll also notice that the spectrum is brightest in that yellow green area as I pointed out in a few other posts.

Incidentally, the late mid 1800’s was the first time the solar spectrum was examined. At that time, astronomers first determined that the sun was made mostly of hydrogen and were able to pick out many other elements. However, some prominent lines couldn’t be explained. Thus, the presence of a yet undiscovered element was inferred. This element was named Helium after the Greek word for sun, Helios. Helium was later discovered on Earth.

So let’s do some recapping before we go any further:

We’ve now looked at three types of spectra: continuous, emission, and absorption.

With a continuous spectrum or absorption spectra, we’ll be able to find the wavelength where the most light is given off (as I pointed out in my last post), which can give us the temperature of the star.

Emission spectra and absorption spectra are useful because the pattern of lines tell us what chemicals are present.

Continuous spectra come from hot, high density gasses.

Emission spectra come from low density, warm gas.

Absorption spectra come from continuous spectra passing through cool gas.

But the fun doesn’t end there!

Let’s take another look at that absorption spectra. But this time, let’s do it in a graphical form:

Figure 4

The blue line here is what the continuous spectrum would look like for this star if there weren’t the deep absorption lines present. Those very deep ones at ~430, ~480, ~520, and ~655 nm are those caused by hydrogen we looked at earlier.

You’ll notice they’re pretty damned deep. However, the other ones aren’t so deep. The reason has to do with the abundance of each element in that star’s atmosphere. Since there’s a lot of hydrogen in stars, it makes sense that the hydrogen lines be the deepest.

So by looking at how deep each line is astronomers can figure out the ratio of elements which is a pretty nifty trick.

These absorption lines can also be used in other ways. Another use is that they reveal the presence of magnetic fields thanks to an effect known as the Zeeman effect which causes the spectral lines to split into two if there’s a magnetic field present.

In my blog, I posted about the solar telescope at Mt. Wilson. It looks for this spectral line splitting at thousands of different points on the face of the sun, which allows the astronomers working on that project to essentially map the magnetic field.

So that’s it for this post. In my next post, we’ll look at some other uses of these lines to determine other quantities, but since it will require another bout of background explanation, I’ll save that for the next post.

[VoijaRisa]

3d. - Radial Velocity

As we’ve seen in previous posts, light is able to give many wonderful pieces of information such as temperature, color, brightness, age, and chemical composition. But now we’ll explore how light is able to give us a property known as radial velocity.

First off, what is radial velocity? In short, it’s the speed of an object towards or away from the observer. Whether or not you realize it, you’re already familiar with a very common use of this: Doppler radar. This device uses radar pulses which are reflected by water vapor and then their speed, towards or away from the detector, is measured.

But how?

The answer is actually right in front of your eyes. It’s due to something known as the Doppler effect. It sounds pretty exotic but again, it’s something you’re most certainly familiar with. If you’ve ever listened to a train passing as it blows its whistle, you’ve heard the Doppler effect. As the train approaches you, the pitch of the whistle seems higher but drops off as it speeds past. If you can’t picture what I’m talking about try here.

So now that we know what the Doppler effect is, what causes it? You’re probably well aware the sound is actually a wave. We’ve already had a good look at what waves are and how they’re characterized for light, so we’ll apply some of the same concepts here before moving on.

With sound, the pitch of something like a train whistle depends on the distance between successive waves, called the wavelength. If you have a long wavelength, this would be a low pitch sound. If there’s a short wavelength, this is a high pitch.

A train whistle has a single tone, so the distance between waves should be constant which means a constant pitch. If you stand by a train that’s holding still as it blows its whistle, you’ll realize this is true.

But let’s imagine that the train is now moving towards you. The crest of one wave is emitted. In the time before the next one is emitted, the train moves towards you, catching up a bit to the wave it just gave off. Thus, when it gives off the next one, it will be closer to the previous one than if the train was remaining stationary. This gives the sound that you’d hear a shorter wavelength, and thus, a higher pitch.

The opposite is true if the train is moving away from you. Since the train is moving the opposite direction of the wave that you’re hearing, each successive wave takes longer to reach you, meaning a longer wavelength, and therefore, a lower pitch.

Here’s a nice image to sum that all up:

Figure 1
Source

So how does that have anything to do with light?

Conveniently enough, light is also a wave and the same rules apply. If an object that’s giving off light is moving towards you, the wavelength gets shortened. With light, this means that it looks bluer. If it moves away, the opposite is true and it looks redder.

But how do we tell if that observed color is due to the actual color of the star, or if it’s due to some sort of shift? To figure this out, we’ll need a reference point that we know what the wavelength should be.

Fortunately, this isn’t too hard. In my last post concerning spectroscopy, we explored types of spectra called absorption spectra in which dark lines were taken out. These lines were due to transitions of the electrons in atoms. Since these transitions have a fixed energy, that means they have a fixed wavelength.

Unless something happens to shift that wavelength that is.

The easiest absorption lines to find generally are two prominent ones due to hydrogen, known as the Hα and the Hß lines. When the source is at rest with respect to the observer (neither moving towards or away) these lines appear at 656.3 nm and 486.5 nm respectively.

So since we know where these lines should be, we can compare them to where they are. The further they’re shifted, the faster the object is moving towards or away from us. If they’re shifted to the blue, it’s moving towards us. If it’s shifted towards the red, it’s moving away.

With this, we’ve examined many of the important tools that astronomers frequently use. With these tools, we can generate a huge number of facts about our universe. However facts are actually pretty useless in science. It’s what those facts mean that is important. To get this meaning, we have to tie facts together with something that is actually useful: a theory.

[VoijaRisa]

Stellar Evolution - The Big Picture

In early 2007, I had a rather lengthy post concerning stellar evolution. However, that post was mainly presented as a response to a rather absurd set of creationist arguments.

But instead of always doing things in response, I think it’s good to occasionally be more pro-active and cover topics in a more educational manner. So in this series of post I intend to first lay out the basic picture of stellar evolution, from the main sequence to death, and later, get into how this theory is derived and supported.

The first thing that I think is important to point out, is that, despite the equivocation of creationists, stellar evolution has absolutely nothing to do with biological evolution. It’s an entirely different theory based upon an entirely different body of evidence. Stars don’t have inheritable characteristics, and even if they did, they don’t reproduce, so the basics of biological evolution just don’t make any sense here.

Instead, “evolution” in the stellar sense refers to the colloquial definition in which it just means a change over time. But what sorts of changes? Well, changes could include such things as temperature, pressure, chemical composition, and a whole array of other features, such as mass, size, luminosity, most of which are determined by the first three.

Astronomers know these features change, albeit very slowly (usually).

I’ll discuss the rather sudden changes later on, but more important, is to begin to explain how we know stars are evolving even when we claim the timescales are hundreds of millions, to billions of years (far too long to witness in the entire course of human history), and the changes nearly imperceptible.

Perhaps the largest reason we know stars evolve, is because stars shine.

This seems like a very confusing statement at first, but if you think about it a bit more, it makes sense. A star shining means that it’s giving off energy. For stars like our sun, they’re giving off a lot of energy. The sun gives off just under 4 x 10^26 Joules of energy per second.

In 2000, the US consumed 1 x 10^20 Joules of energy. This means that, in 1 second, the sun generates enough energy to last the US 4 million years. That’s a lot of energy!

And it’s got to come from somewhere.

To figure out where, we start off by looking at what’s available. By looking at the spectra of the sun, we know it’s about 75% hydrogen, 24% helium, and 1% everything else (if you need a refresher on what spectra are, go here). This rules out a lot of possibilities of where the energy comes from right off the bat.

Early ideas suggested that the sun was a ball of fire. However, fire requires the presence of oxygen. Thus, that’s right out. Additionally, there’s just not enough chemical energy available to sustain the sun for the amount of time we’ve known the solar system to exist.

The sun shrinking under its own gravity and exchanging gravitational potential energy for other forms was another possibility. But the sun’s not shrinking fast enough to account for the energy generation of the sun and again, the timetable doesn’t fit.

So astronomy required something that generated a lot of energy using hydrogen and could be sustained for billions of years. Fusion fits the bill perfectly. It also fits well because, when physicists realized that fusion will emit neutrinos and we went looking for them and found them (although only 1/3 the predicted number originally. For more on the missing neutrino problem, go here).

Now that we know that fusion is the source of energy generation for the sun and other stars, we can start to ask what the consequences are.

One consequence that fusion has is that it converts hydrogen into helium. This means that there’s going to have to be a change in chemical composition. Why? Because it shines. If it didn’t, there would be no need for fusion to change the chemical composition and there wouldn’t be any evolution.

Another side effect of this, is that, give it long enough, and you’ll use up all your hydrogen. When that happens, it means you’re not going to have much energy generation anymore. This doesn’t mean the star stops shining all the sudden. It takes light a long time to work its way to the surface and escape due to the fact that it’s going to be scattered off lots of particles along the way. But this does mean that the brightness is going to change. Again, the star evolves.

Aside from sustaining the luminosity of the star, the out flowing radiation has another important effect: It provides pressure to keep the star from collapsing in on itself. With this pressure gone, the star will inevitably contract. This happens relatively slowly, but due to the large mass of stars, and the large radius, this can generate a lot of energy.

And it does. This energy primarily goes into the interior of the star (since that’s what’s being squished). The extra energy heats the interior until some of the hydrogen outside of the core can begin fusion (known as H-shell burning). This supports the star somewhat, but doesn’t quite halt the slow contraction.

Rather, the core continues getting squeezed, and heated, until the point at which it gets hot enough that the Helium atoms can begin fusing. Again, the star has a strong energy source supporting it. This extra energy pushes back against the matter on top of it, causing the star to poof up into a red giant. It eventually stabilizes, and becomes something like a normal star again.

Eventually, the helium too runs out. If the star is massive enough, more cycles of contraction, shells of fusion, and new forms of fusion in the core will occur. If not, the star will go through one last bit of the cycle, where the outer layers are pushed out and released as a planetary nebula.

For those more massive stars, the cycles can continue until iron is built up in the core. This is one of the points where things happen fast.

Out of all the forms of fusion, Hydrogen is the most efficient. Each successive cycle is less so. By the time you hit iron, you’re barely getting energy out of it. With iron, you get none at all.

Once iron builds up to a critical mass in the core, it very suddenly collapses in on itself. Several suns worth of mass crashes down, releasing more energy in that act, than the rest of the entire galaxy it lives in. This is known as a supernova.

So that’s the basic story of stellar evolution. But at this point that’s all it is. In my next post, I’ll get more into how this theory of stellar evolution is all determined, both by mathematical modeling and comparisons of those models to direct observations.

[VoijaRisa]

Stellar Evolution - Model Evolutionary Tracks

In my last post, I went through a quick version of the life and death of stars. Here, we’ll explore a bit more of the current understanding of all this. Namely, how do astrophysicists support the stellar evolution theory, when we can’t actually create stars in labs and fast forward time to watch the process unfold before our eyes, or even resolve the surface of more than a handful of stars aside from our sun?

Let’s start off with what we can observe pretty directly. As I’ve mentioned before, looking at the spectra of stars, we can learn what they’re made of, at least at the surface. As you’re probably aware, stars are gigantic balls of primarily hydrogen. There’s about 20% helium, and 1% other stuff.

Another property we can obtain pretty directly is the mass of a number of stars. To do this, we look for stars in binary systems. From there, we observe the period of the stars around the center of mass. Using Kepler’s laws, we can derive the ratio of masses. But while the ratio is all well and good, we’d like to know the masses of each one independently.

Fortunately, nature occasionally provides us with the ability to make another set of observations, which fully solves the system of equations. About 50% of stars in our galaxy seem to appear in binary systems. Statistically, some of them will have planes of orbit that align with the Earth. That is to say that, from Earth, we the stars eclipsing one another. Such systems are known as eclipsing binaries.

The reason they’re useful is that as the stars orbit around one another they will be moving towards Earth for part of their orbit, and then heading away for another part. By measuring the doppler shift we can measure the precise speed with which the stars are orbiting.

Lastly, we can determine the ratio of sizes from the period of the eclipse. If, for the sake of example, we assume that one star is smaller, as it passes in front of the larger star, it will block the light from the larger causing a dip in the overall brightness as long as it’s in front of the other. As it passes behind the larger star, there will be another dip in brightness as the larger star blocks the light from the smaller. If you want to play with some computer simulations of these objects, try checking out StarLight Pro. It can be use for real life astronomy, but it’s fun to play with even if you don’t know what you’re doing.

Put all these observations together, do some math, and you can pop out information such as radii, and relative brightnesses. But these aren’t the only features we know. As I described in this post we can also determine surface temperature and distance.

So there’s three intrinsic quantities we have right there: Radius, chemical composition, and temperature (at least for the surface for the latter to).

This gives astrophysicists a starting point. From there we can start building models and make up our temporal limitations through mathematics.

We start off with a mathematical model of a big giant ball of hydrogen not doing much of anything. From there, we plug in known physical laws; things like gravity, the ideal gas law, laws governing radiative transport, etc…

I don’t intend to go into the math here, as there’s not nearly enough room. After all, my entire astronomy course for fall of '06 was just doing the basics of all this math for the atmospheres of stars.

So cutting all of that out, let’s talk about some of the things these models predict that we can confirm observationally.

One of the things that the models make perfectly clear is that stars do indeed evolve over time. It also makes it clear that the more massive the star, the faster it will evolve and die. Observationally, this should mean we see less high mass stars than we do low mass ones. They’re simply not around long enough for us to see many. This is something we observe very distinctly.

Another extremely important prediction of these models is to let us know how these stars will evolve across the H-R diagram. The models tell us that stars will spend most of their life (~90%) of their lifetimes all along a single line we call the main sequence. Thus, when we look around, we should see that same amount of stars on this line. If you look at this H-R diagram that line jumps out as the diagonal conglomeration running from the upper left to the upper right.

From there, we can ask what happens when stars run out of the hydrogen in their cores and begin their deaths. If we take sample stars of various masses and chug through the math, we can generate tracks on the H-R diagram for these various stars. Let’s take a look at one of those:

Figure 1

The main sequence isn’t drawn in on this graph, but you can get a feeling for where it is. Again, it’s running from the upper left to the lower right, going through those filled circles labeled 1 on each track. The masses are listed next to those points in units of solar masses (the circle with the dot in it is the symbol for Sun).

Let’s look at some of those other points for a minute. The points labeled one are when hydrogen fusion first starts in the core. This marks the beginning of the star’s life and is known as the “Zero Age Main Sequence” or ZAMS.

From there, the stars are slowly evolving to point two, which is where the core runs out of hydrogen. As we can see, this evolutionary process requires that the main sequence have some width to it. If you look back at that H-R diagram I linked to earlier, you’ll see this is precisely the case.

From points two to three, this is the phase of contraction until the point where the area outside the core gets hot enough to initiate shell fusion of hydrogen. This kicks the star over to point five pretty quickly in astronomical time scales (something like 1% of the time the star spent on the main sequence). So here we have another prediction: We shouldn’t see many stars in this region of the H-R diagram. Again, observations confirm this. This sparsely populated region is known as the Hertzsprung Gap.

The rest of the points start getting horribly complicated so I’ll skip out on those, although that's not to say that complicated means impossible. However, it should be noted that we can’t watch a single star go along these tracks. Fortunately, there’s another way to plot the data that gives us a whole different way to analyze the data. In this plot, we looked at position on the H-R diagram for different stars across time at constant masses.

Alternatively, we can look at position on the H-R diagram for different stars across mass at constant time. Such diagrams are known isochrones (meaning same time) and I’ll explore them in my next post.

Recapping what we learned from this post, a good number of predictions can, and are, made based on these mathematical models based on an extremely solid understanding of physical laws. The observations, thus far fit very well, so stay tuned to see how well they stack up for other tests.

[VoijaRisa]

Stellar Evolution - Isochrones

In this post on stellar evolution, I’ll be discussing what are known as “isochrones”. In my last post we looked at evolutionary tracks on the H-R diagram for constant masses across time.

Isochrones are the opposite. They are plots of on the H-R diagram at constant time across all masses. Another way to think of this is to take thousands of stars, of varying masses, get them started at the same time, wait some millions of billions of years, come back, and see where they lie on the H-R diagram.

As I pointed out earlier (and common sense should tell you even if I didn’t), we can’t create stars in labs and we most certainly can’t just sit around for billions of years to see what happens. Instead, our chief tool is modeling. Astronomers will make a model, applying all applicable physical laws, such as the ideal gas laws, gravity, and the like. Models can then be fast-forwarded to any point in time, and then checked against observations and refined.

Figure 1

So let’s start by taking a look at a basic isochrone. Figure 1 shows a typical H-R diagram with hot, blue stars to the left, and cool red stars to the right. Going diagonally from the upper left to the lower right, we can see a large section of the main sequence. Branching off from that are three trails which represent the distribution of stars after 10^8, 10^9, and 10^10 years. What we learn from this is that, as this conglomeration of stars ages, stars will “peel off” the main sequence, starting with the massive stars in the upper left. The turn off will then work its way down the main sequence with the path it takes from there changing as it does.

That’s all well and good of course, but now how to test this aspect of the models? To apply some data to these, we need a large number of stars that all formed at very nearly the same time, but at a variety of different masses. Fortunately, nature provides a wonderful opportunity to find just such things: clusters.

Clusters form from a single cloud so the chemical composition is the same for all stars involved. The formation occurs relatively quickly in astronomical time scales, so now we have everything we need to be able to see if models can accurately reproduce the observed shape that nature creates.

So let’s take a look at a few and see how they do:

Figure 2

Figure 2 is a set of isochrones for the globular cluster m92. The scale is different than the isochrone I presented and it actually covers a lot more area of the H-R diagram than mine. You’ll notice that the isochrones are only plotted for the part near the main sequence and one part later while there are data points that continue past the end of the theoretical tracks. The reason for this is that the tracks tend to merge as they approach that upper line which is known as the red giant branch (RGB). Thus, there’s no real point in plotting it over there.

What we can see is that this cluster fits the shape of these particular isochrones very nicely. It’s not perfect though. Many effects, such as unresolved binaries, slight differences in chemical composition, unusually fast rotations, and other things, contribute to the scatter. But overall, the data fits the isochrones pretty well.

Figure 3

47 Tucanae is another globular cluster (visible only from the southern hemisphere) which has a very nice fit with the theoretical models.

This sort of fitting is one of the goals of the research I participated in in the summer of 2006.

Our data wasn’t nearly as pretty though. Part of the reason is that we were studying an open cluster, which by definition has far fewer stars, but also because there was interference from an interstellar cloud which caused reddening and extinction.

But general shape matching isn’t the only thing that we should be able to predict based on isochrones. As with the evolutionary tracks, we should also see gaps where stars don’t spend much time. Again, we should, and do, observe the Hertzsprung Gap.

Another feature that we should observe and is one I’ve used, is known as the Red Giant Clump. This is a particular point near the RGB where stars slow down in their evolution for a time and tend to bottleneck. This happens at a fairly consistent color and luminosity, which gives it a feature astronomers can exploit to make corrections.

Are models perfect? Absolutely not. Models are still limited by what we’re able to realistically calculate. As computing power improves, we are able to take more and more into consideration, which should bring our models into better agreement with the data.

One example of this is that models are now beginning to consider a feature known as convective core overshoot. In this, convection that occurs in the interior of some stars, is able to provide the core with additional hydrogen, thus slightly changing the evolutionary features of the star.

So as with the evolutionary tracks I mentioned in my previous point, our main test of these theoretical models are to check where stars should and shouldn’t be, where they clump, and where they go, to observations of reality. If they match, we gain confidence in our models.

As you might expect, the general shape isn’t the only feature of models that we can test. In my future posts on stellar evolution, I’ll briefly discuss other properties of stars for which we can hold models accountable.