Wednesday, November 22, 2006

Coordinate Calibration

The coordinates used by astronomers are referred to as "RA" and "dec." RA, or right ascension, tells us when an object will be viewable and is measured in hours (and minutes and seconds). It is set so that the RA of the sun on the March equinox (the first day of spring in the northern hemisphere) is 0 hours; the RA of the sun on the September equinox (the first day of autumn in the northern hemisphere) is 12 hours. Each month, the sun (and thus the sky) moves by 2 hours in right ascension. Since astronomers generally like to look at the sky at night, when the sun is not up, this means that objects with an RA near 12 hours are best viewed around March, while objects with an RA near 0 hours are best viewed near September.

The other coordinate is the declination, or "dec." The declination of an object, measured in degrees, is just the projection of the lattitudes on Earth onto the sky. For example, Columbus, OH is at a lattitude of 40°, so any star or galaxy directly overhead will have a declination of 40°. It also means that the so-called North Star, Polaris, which has a declination of 90°, will always be 40° above the horizon in Columbus.

RA and dec are designed so that by simply knowing an object's coordinates, an astronomer can tell you whether or not the object will be viewable from a certain location, and, if so, when. For example: can the center of the Milky Way (theoretically) be observed from Columbus, OH? NED tells me that the coordinates of the supermassive black hole (Sagitarrius A*) right at the center of the Milky Way are 17h45m40.0s -29d00m28s. The second set of numbers there is the declination: -29°. Columbus is at 40°, which means that the Galactic center will be 40°+29°=69° down from the zenith (the "zenith" is a fancy word for "straight up"). 90° is all the way down to the horizon, so when the Galactic center is "up," it won't get very far off of the horizon, and you'd be hard pressed to find someone to let you tilt their large telescope over that far. This is why the Galactic center is more commonly observed from the southern hemisphere, such as at one of the many observatories in Chile.

So when is the Galactic center observable? Well, the RA is at 17 hours and 45 minutes—let's call it 18 hours. 18 hours is halfway between 12 hours and 0 (=24 hours), so the Galactic center is best viewed halfway between March and September, also known as June. Luckily, this is also when the nights are the longest in Chile (Chile being in the southern hemisphere and thus June being in winter), and so when the Galactic center is up, it's observable for a long time.

This is all fine and dandy, but once you have an image of the sky, how do you know what the coordinates of all of your objects are? The standard way is to compare the locations of the objects on your image to the locations of objects in some catalog where they have measured this very carefully (known as astrometry, or "the measure of the stars"). Generally, you have a pretty good idea of where the telescope was pointing when the image was taken, and thus the coordinate of the middle of your image. You also generally know what the pixel size of your image is. When astronomers talk about "resolution," they don't mean a number of pixels (like 1600x1200) like you hear people talk about with normal digital photography. Instead, astronomers talk about how large a single pixel is on the sky.* For example, the pixel size of ACS, the newest camera on the Hubble Space Telescope, is 0.04" (the " is arcseconds; there are 3600 arcseconds in one degree). Ground-based telescopes generally have pixel sizes varying from ~0.2" to several arcseconds; HST has a smaller pixel size because there is (basically) no atmosphere in space, making it possible to resolve smaller objects than can be resolved from the ground.

Like with a map, it's a fairly straightforward procedure to go from one known position, a certain scale, and a sense of direction (given by the "known" stars in the catalog) to a set of coordinates for all of the objects in the image. Well, sort of. The first problem with this analogy is that, generally, when we make maps of things like cities or continents, we actually "know" where the things are we're mapping: we can physically go there, pull out a ruler, and measure the distances between buildings or whatnot. This doesn't really work when we're talking about stars thousands of lightyears away. And what if the resolution of our catalog is worse than of our data, and where they saw one blobby thing we see three or four stars? Which position do we believe or use for calibration? The second problem is that the sky is not flat, and, in general, the projected size a telescope "sees" at the edge of an image is not going to be the same as it "sees" at the center. If we want really precise astrometry, then these slight changes have to be modeled accurately.

And yet, deciding the coordinates for an object is massively simpler and less convoluted than trying to decide how "bright" it is ...

* More precisely, the resolution is given by the size of the smallest object that can be fully resolved, which is larger than one pixel and depends on many different factors, but that's a little too complicated for now.


Vincent said...

Nit: Polaris has a declination of approximately +90 (according to SIMBAD, +89 15 50.794).

mollishka said...

Quite so. Fixed; thanks for the catch.

Stephen said...

Nit. Polaris ranges from 39.3 degrees to 40.7 degrees from Columbus Ohio. The 44 minutes and nine seconds it lies from true North is bigger than the full moon. So, like a broken clock, Polaris is true North twice a day (at least from the Equator and North).

A friend was setting up the pier for his new observatory. He knew the magnetic offset for true north, and decided to use a compass when setting the pier in concrete. When everything had set, he tested it one night - only to discover that he was more than five degrees off.

It turns out that he uses magnets to relieve arthritic pain in his ankles (it works for him... i'd need at least double strength plecebo). That messed up his compass. After breaking up the concrete, the new idea was to wait for a transit (12:07 am on 11/22 in Columbus) and mark a line with string. The next day, he poured new concrete. He's been happy with it since.

The Polaris transit comes at 8 pm on January 23rd. That's a good time to get your kids out and mark up true north on your lawn with a couple of sticks. Maybe i'll get my son to help me mark my driveway.

Stephen said...

ACS's 0.04" per pixel is also close to HST's diffraction limit. As far as i can tell, this wasn't the design of earlier cameras because in the technlogy of 1990, 800x800 isn't much sky at 0.04" per pixel. And, 800x800 was a HUGE image on your computer.