Quantitative cooking
Completely silly, but still damn cool.
Labels: food, just for fun, science
Labels: food, just for fun, science
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.
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.
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.Labels: astronomy, basics, photometry
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).
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.
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.
Labels: astronomy, basics, photometry
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Fig 1. - Reflectivity curves for various silver coated liquids. PEG curve is shown for an attempted liquid deemed not suitable and not discussed in this post. As discussed in the paper, the most promising is the ionic liquid with an initial chromium layer (5nm) followed by a 30nm silver coating. Curves only extend to 2.2 μm due to instrumentation limitations. (Borra 2007) .

Fig 2. - Three-dimensional map of a 1.25 cm2 section of the 5nm chromium/30nm silver mirror deposited on an ionic substrate. Peak to valley distribution is 0.0373 μm. (Borra 2007)

Fig 2. - Reflectivity of Li(NH3)4. Measured points from McKnight and Thompson (1975) at 195 K. Theoretical curve is shown for 93 K. (Burns 2008)
Labels: astronomy, bpr3, journal summaries