Quantitative cooking

All my finals are finished and I'm just working on doing my term paper for my nanotechnology course. I'm a gigantic procrastinator, so I haven't even chosen a topic until the day before it's due (not a problem since it's only a 4 page paper). In skimming possible topics though, I found this journal article which uses nanotubes to detect the presence of chemicals in chili and hot sauces, providing an accurate measure of just how spicy that food is.

Completely silly, but still damn cool.

3e - 2. More Photometry

Last time, I walked through the basic idea of photometry leaving off with the ever so epic cliffhanger that things are always harder than they seem at first. Nature may be able to be broken down into a series of simple principles, but the combining of those principles always serves to make life hard for us science types. We try to find ways to minimize some of those confounding tricks nature plays by making simplifying approximations, but we can't always get rid of them. And this is no less true in photometry.

So let's now take a look at what happens when we start putting a bit more reality into the discussion.

I'd said earlier, that stars behave like black bodies and showed a bunch of nice, pretty curves. That'd be a great way to do things if only there weren't that one little bit of the star that mucks the whole thing up: The atmosphere. Since it can absorb photons out of the nice, simple blackbody spectrum (forming the absorption spectra), we can't just ignore them and toss our photometric filters wherever we'd like. If we did, we might end up tossing one right over the calcium K line which would cut out a ton of the light we'd receive and make whatever filter we slapped over that wavelength give fainter readings than it should. No good!

Instead, the position of filters and photometric system is carefully chosen to avoid such potential pitfalls. We have the spectra for thousands of stars, and we know where lines will typically be. Thus, we can select regions of the spectra where there isn't absorption (or emission) lines and you have primarily a continuous blackbody spectra.


Well, hopefully. Depending on the photometric system you choose, the bandpasses that they're standardized for can either be wide, intermediate, or narrow band. The Johnson/Cousins system is a wide band system. In fact, it's so wide, the filters actually have a bit of overlap. In such a case, lines are unavoidable, but since you're also picking up continuum on either side, they're (hopefully) swamped by signal.

For smaller bandpass systems, this is less of a problem... so long as those lines stay where we can keep track of them. But they don't always do that. If the object we're looking at is moving towards or away from us, the entire spectrum can get shifted one way or the other. That's great if you're trying to do radial velocity measurements, but if it shifts a spectral line into one of your filters, it could be trouble! If that's the case, you'd probably have to use some other filter system to avoid the lines.

But this all assumes that you can avoid the lines. In hot stars, it's not too hard. Nearly all elements in such really hot stars are completely ionized so you don't have any electrons in the orbitals. As such, you don't tend to have very many absorption lines. However, the cooler the star, the more electrons fall into orbitals to do the absorbing and the more lines you get. If you start getting to really cool stars, it's not just atoms you have to worry about, but molecules which can absorb even more because they can store energy in vibrational and rotational states too. Thus, in the spectra of a cool star, lines are everywhere! No chance of avoiding them there. Thus, errors are much larger in cool stars than in hot ones.

And line problems don't end there! If you do have a star that has absorption lines, remember that that's taking out light from the spectrum. Since that light has energy, and energy must be conserved, that energy is going to manifest itself somewhere else. Since you can't get more energy out than you've put in with the absorption lines, that means that the bluer lines that are taken out (blue light is shorter wavelength and higher energy) will get broken down into more, longer wavelength (and lower energy) photons that will get remitted at a wavelength that's not absorbed. Thus, when you have something being absorbed, it can pop back out at longer wavelengths enhancing the signal in that part of the spectrum. Typically, this isn't a big problem for a few lines, but if you have a whole bunch of closely spaced lines (like you do in cooler stars) a line blanketing effect kicks in and it can cause some problems.

However, there can be times when you actually want to stick your filter right into an absorption feature. And example of this would be the atmospheric activity value that I keep seeing the research I've been working on. The idea behind it is that stars like the Sun have whopping great lines due to absorption from calcium (the H & K lines in the visible part of the spectrum). But for active stars, there's actually a tiny emission peak at the center of this great whopping dip. Thus, if you can measure that emission peak in relation to the depth of the absorption line, you can get a handle on the atmospheric activity. Thus, you can toss a nice intermediate band filter on the H or K line, and a narrow band filter on the emission bit and again, without having to go through all the time and trouble of getting complete spectra, you've got the information you need.

So it's not always bad, but there's still other challenges.

The next major one is that light, as it passes through our atmosphere and optics, ends up getting smeared out. Instead of stars being perfect, infinitely small points that only fill a single pixel on our cameras, the signal gets spread out. If we look at the brightness as a function of distance from the center of a star on our CCD, we'll get something that looks like the image to the right. In the center, the image is the brightest, but some of the light is smeared off in every direction, making it get dimmer and dimmer as you move from that central point. However, since that trail that's dropping off is still some of your precious photons, you can't just ignore them! You have to worry about that too.

This isn't really all that hard though. To see why, let's look at that same star plotted slightly differently. Instead of being a 2-D plot, this one is of the same star's intensity profile plotted in 3-D. The grid represents the grid of CCD pixels and the height above the plane is how bright the star looked on that pixel. We can see it's the same sort of thing that happened in the 2-D image; It's brightest at the top and trails off. But we can still deal with that because at some point, it's dropped off enough that you don't really lose much by just chopping it off and counting up what you have. Essentially, the star looks like a big hill and if you chop the hill off at the bottom and count up all the dirt in it, you can still do just as well as if all that dirt was in a thin narrow column. Crisis solved!

At least, until another star comes along. The method I just described (aperture photometry) works great for fields of stars in which the stars are relatively isolated. However, if you have two stars that are close enough together that the hill of one blends into the hill of another, then you can't just chop it off at that certain radius because you'll be getting dirt (light) from the other hill. And you can't ignore it in the parts where it overlaps because that's your signal! For just random sections of the sky, this isn't typically a problem, but in high density regions like the plane of the milky way and clusters, it becomes a huge problem.

Time for another trick. And this one's really sneaky. The idea is, since we're looking at a moderately small part of the sky, any atmospheric perturbations that are inflicted upon our field will be more or less the same. Since the light is going through the same optics, that should be the same too. Thus, the amount of distortion should be the same for all stars. What that means in more useful terms is that the shape of each hill should be the same. They should all be described by the same (Gaussian) profile. The only thing that's different is how tall or short the hill is. But the rate that the hill falls off is identical for every star.

So if we can figure out what that shape is, we can make a model hill that we just slide up and down for brightness. To find the shape (known as the point spread function) of the hill, you first need to find some isolated stars whose hills aren't being polluted by other nearby stars. The more stars like this you can build your model off of, the better the model, and the better the data. This method is called "Profile Fit" or "Point Spread Function" (PSF) Photometry. It's not too bad since computer algorithms will try to pick out those isolated stars. Unfortunately, they're not that great and you have to go through each one manually to confirm it's really isolated (and not on the edge of the CCD or anything). When I was doing this for my San Diego internship, the computer would find about 200-250 candidate stars. For each image. For each filter. It took two solid weeks of work to get good modeling stars. It's laborious (which is why the task is relegated to undergrads and data monkeys), but it's doable.

So there's some of the problems that astronomers face doing photometry and how they can sometimes be overcome. This is pretty much all there is to understand how photometry works and we do what we do. About the only thing I haven't gotten into very much is a more detailed explanation on just what else we can get out of various filter systems. There's more than just the temperature (for example, the DDO photometry system can give an indication of iron abundance), but that discussion requires delving into each photometric system independently and I'll save it for another post.

3e - 1. Photometry Basics

In one of my earlier posts I discussed the information that can be gleaned from the HR diagram, but what I didn't really discuss is how such diagrams are really constructed. I mentioned that it's necessary to either pick stars that you know the distance to (so you can correct for dimming due to distance) or stars in a cluster that are all at the same distance (so there is no variation).

But what I didn't mention is precisely how astronomers go about getting the information for the brightness and the temperature. If you've read my post on the HR diagram, I've mentioned one way: You find the peak emission and use Wien's Law to get the temperature.

But doing that requires getting the spectra of the star. And therein lies the problem. To get the spectra of a star, you have to pass it through a prism (or a diffraction grating as is more typically the case). But this means that instead of having a single dot on your image plane, you're going to have a band. And if you have lots of stars, you'll have lots of bands. And if you have lots of bands, they'll overlap and make a mess. So spectroscopy is slow because you have to do one star at a time. There's been some ways to get around this by using fiber optic cables at the image plane to intercept the light and send it to lots of different spectrographs, but such things have to be individually set up for every field you want to look at. What a pain!

And that's not the only thing that makes spectroscopy slow. Since you're spreading out the light that you're getting, this also means that the amount of photons hitting at any one point will be less. Your image gets fainter the more you spread it out into the rainbow!

So there's two major things that make doing spectroscopy slow work. It's good and necessary for getting things like the chemical composition, but if we really just want to make an HR diagram, isn't there a quicker way?

YES!

And that method is known as photometry. The trick of this is that instead of looking at all the wavelengths, it picks out just a few important ones and does the work that way.

The reason this works is that stars tend to behave pretty close to what's known as a "blackbody". What this means is that it gives off radiation in a certain way with a peak wavelength dependent on it's temperature. They're described by Planck's Law (setting the first derivative equal to zero and doing a few substitutions gives Wein's Law). But what's really important is that the wavelength or the color of the peak is determined by the temperature. It's easiest to explain with a diagram:

As you can see, the hotter stars peak off in the blue region, and have a greater luminosity. The cooler a star gets, the more red it's peak emission and the less energy it gives off (which is shown by the area under the curve or the first integral of the blackbody equation).

Like I've already said, through spectroscopy, you can get that entire blackbody curve (with the superimposed absorption and emission features). That's great, aside from the slow part. But how does only looking at a few specific points on that curve tell you what you need to know?

This is most easily demonstrated by example, so I'll just jump right in with the most common photometric system, the Johnson/Cousin system. This system has five filters:

U: Ultraviolet
B: Blue
V: Visual (green-yellow)
R: Red
I: Infrared

Each of these filters only allows light from a narrow range of wavelengths (known as a bandpass) to get to the detector. It's essentially looking at a series of five points along those blackbody curves I just showed.

So let's take that first blackbody curve, the one for a hot star, and put the filters on it (note: For some reason I didn't show the R filter. Also, the units are removed since for the purposes of illustration, all we need is a qualitative effect).

In this image, we can see that the filter doesn't intersect at equal luminosities. In the U filter, it's pretty low. It gets higher in B (which it should since we already said, it's a hot star), and then gets lower in the V, and is lower still in the I.

Now consider what happens if you take the difference between the luminosities of two filters. Most commonly done is the B-V so we'll use that for the example. If you do this, the B is greater than the V, so if you subtract it, you'll get a positive number. But remember, this is in luminosity and astronomers work in the magnitude system in which brighter stars are smaller numbers. It's backwards. So when talking in terms of magnitudes, a blue star will have a negative B-V.

So let's now look at a cool star on the same filters:

Here, if we try the same thing, and take the B-V luminosities, the star is brighter in the V than it is in B, so if you're talking about luminosity and take B-V, you'll get a negative number. Flip that around for magnitudes, and you get a positive number.

So already, you should be able to see the trend. In terms of magnitudes, a negative B-V means a hot star. A positive B-V means a cooler star. The more negative you get, the hotter it gets. The more positive you get, the cooler it gets.

This is great! It fixes both problems we had earlier. It doesn't spread the starlight out, so images don't take any longer to expose. Nor does it require you to put each star through a slit. You can do an entire field of stars at once! And this is, for the most part, exactly what I did for my research 2 summers ago. Using this basic principle, I worked out the H-R diagram for NGC 7142 (except that when we use photometry to replace the temperature, we call it a "color-magnitude diagram" or CMD). Of course, there were a few nuances that made it a bit more difficult than what I've just described.

But instead of going into all that now, I'll save that for another post.

Pareidolia: The big idea

If you've followed my blog at all, you've probably seen the entire series of posts on pareidolia (ie, when things look like other things). Phil Plait at Bad Astronomy has a pareidolia series too.

So what's the point of posting these things all the time? Is it to show how stupid people can be?

Not really. Trying to find patterns in things is part of our genetic programming. I'm certainly not going to fault anyone for doing it. However, what I can fault them for, is taking it far too seriously. The reason is, that it demonstrates a gigantic case of confirmation bias. Odd shapes turning into miracles only works when you've already had the image implanted in your mind.

This image (I'm linking to it because it's possibly NSFW depending on how you look at it) illustrates it perfectly.

If you haven't seen the image, don't scroll down anymore till you have unless you want to spoil the surprise.





I bet most of the people reading this blog saw the same thing I saw: A naked couple embracing. However, when the same image is shown to people that wouldn't have already been made aware of such things (ie, children) the image is of 12 dolphins (they're in the dark regions).

Brother Jed at KU: 5/6/08 - A whole lotta stupid

Brother Jed and his companions made a trip to the University of Kansas today. At one point, we managed to get his older, portly companion on the topic of the age of the Earth. I was there with a grad student in Geology. It quickly became apparent, that despite Jed's companions claims to formal training in Geology are grossly exaggerated and he presented either gross ignorance or outright lies.

For example, one of the claims this person made is that uplift due to plate tectonics has never been observed. This was directly refuted by the Geology student with numerous examples and a quick Google search returns just such measurements from Papua New Guinea's Finisterre mountains.

He also claimed that convection zones in the Earth which drive tectonic activity must be square. A thorough search for this information returned no results. Searching scientific journals returned no results. Even a check against common sense shows how silly this claim is. Just try drawing a square (not rectangle) inside a circle. It requires that the material MAGICALLY change direction with no forces acting on it far from the core. Talk about miracles!

This person also attempted to invoke polystrate fossils (ie, trees cutting through many layers of deposited sediment) as indicative of a young Earth. What he neglected to mention was that these fossils are only found in places where you should expect frequent deposition rates (ie, near rivers or regions of volcanic activity). When actually dated, radiological dating confirms this prediction. Rather, Jed's companion hypocritically dismissed this, after having just previously argued against uniformitarianism.

Many of the other arguments he presented are so poor, that the major Young-Earth Creationist organization, Answers in Genesis, suggests they not be used. Among them that Jed's companion invoked:
- Plate tectonics is fallacious.
- There are no transitional forms
- Paluxy tracks prove that humans and dinosaurs co-existed.
- Moon-dust thickness proves a young moon.

If many of this person's BEST arguments are refuted by even Creationist organizations and simply searching Google, I hate to think what this says of his intellectual honesty and scholarship concerning his other arguments. Nor is his character much better. When presented with contradictory evidence, this person did not provide a rebuttal, but instead chose to reply by calling us "Morons!" I was personally called a "moron" five times.

I never caught this person's name, whoever this Santa Claus look alike, fisher hat wearing jerk was, he's an embarrassment to an already embarrassing ministry. I seem to recall St. Thomas Aquinas having something to say on how disgraceful it is for Christians to show ignorance in science due to it suggesting that they are ignorant to truth in general. Perhaps Jed's companion should learn from him.

Pareidolia: n + 12

What's that in the uterus?! It's a fetus! It's a baby!

NO!

IT'S JEEEEEEEZUS!

And Pareidolia man flies off into the night. Those he leaves behind remain stunned and confuses....

Meanwhile, the mother states, "People say maybe my baby is gonna be blessed and maybe it is a good sign."

Yes. Dying people is such an awesome sign....

National Day of Prayer 2008

Yesterday was the National Day of Prayer for the silly minded people of the nation. Meanwhile, I made my annual trip to the blood bank and made a real donation.

And what have all the silly minded people been up to? Well PZ has more, but I find the irony of the one that got dressed up in a sack and ashes to pray getting caught making illegal financial transactions especially amusing. Oops.

Oh well. Shame prayer doesn't work.