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PHYSICS 1112    SPRING 2000
Astronomical CCD Imaging and Analysis

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PURPOSE: In this lab, we will do some simple analysis of digital images obtained with a CCD camera on the 16-inch telescope in the Marrs McLean Observatory. The CCD imaging technique will be briefly outlined, and then you will make simple measurements on images of seven very different objects, ranging from our solar system to billions of light-years distant. With some additional information that will be provided, you will be able to calculate some basic physical parameters of these astronomical objects. This isn't meant to be really hard - it's meant to be fun and to show you how easy it really is to learn a lot about the universe by applying basic physical ideas. In a companion lab, you will learn about some powerful techniques for suppressing noise in digital images.

camera.jpgCCD IMAGING: A CCD, or "charge-coupled device", camera is an electronic camera. The heart of the CCD is a semiconductor chip that contains an array of pixels. Each pixel is essentially an "electric potential well" in which charge accumulates in direct proportion to the number of photons (particles of light) that strike the pixel during an exposure. The accumulated charge can then be "read out" line by line across the whole array, giving you a stored digital image on a computer that can be processed and analyzed to your heart's content. The "quantum efficiency" of a CCD - that is, the percentage of incident photons it detects - can, in some of the best recent models, exceed 90%; the human eye and photographic film come in at only 1% or so (although it is possible for the human eye to detect a single photon, which is a different matter). So not only do CCDs provide digital images that can be readily processed, they are extraordinarily sensitive and thus capable of detecting extremely faint objects. Our CCD at Trinity is simply attached near the focal plane of our large telescope in the dome, and is controlled by software on a laptop computer.

IMAGE ANALYSIS: The software package you will be using is called "CCDOPS". To start it on a computer in the PGM lab, you select:
"Start" - "Programs" - "Sbig" - "CCDOPS".
You can close the "Tip of the Day" window. Then, on the Menu Bar, you select "File" and "Open", and make sure the directory is set to "Ccd". You will need to set "Files of type" to "All files". You then select a file and "Open" it, followed by a click in the "Image Parameters" window. If the image is too small for you, you can choose "Utility" - "Enlarge Image 2X". There should be a "Contrast" window open; in addition, you should open a "X Hair" window by choosing "Display" - "Show Crosshair". Now for a few words about these windows:
"Contrast": The actual intensity values of the pixels can range from 0 to 65535 (that's 216, in case you hadn't noticed). But CCDOPS attempts to automatically set a background ("Back") and "Range" of pixels to display: pixels less than "Back" appear black, pixels greater than "Range" appear bright white, and pixels inbetween appear various shades of gray. You may want to adjust the "Back" and "Range" values for some, but not all, of your images.

"X Hair": We're going to make sure the "Box" is set appropriately, and then make use of the "Pixel Data", "Magnitudes - Absolute" (which is actually a bad name, because the magnitudes are "apparent", but don't worry about that), and "Geometry - Sep(aration)" options at various stages. The magnitude is a funny logarithmic measure of intensity (formula given a little later below); magnitudes have been used historically, and are essentially a ranking of brightness - first magnitude stars are the brightest, fifth magnitude is about the naked-eye limit, etc. The magnitude will be correctly calculated if (1) you click on the background somewhere (you'll see the "Box" displayed) and then center the cursor on the object whose magnitude you want to measure. To measure separation between two points, you place the cursor at the first point and type "S", then you move the cursor to second point and read off the angular separation.

Oh... when you're done with an image, you close it by just clicking on the "X" button at the upper right corner of the image window.
jupiter.gifObject #1 - Jupiter: Open jupiter.ccd. Measure the angular diameter of Jupiter in arcseconds and convert it into radians using 1 radian = 206,265". Then, using the fact that the distance between Earth and Jupiter on the date of observation was approximately 6x108 km, use a little simple trigonometry to calculate the linear diameter of Jupiter in kilometers. HINT: For a small angle q in radians, q = sinq = tanq.


sirius.gifObject #2 - Sirius: Open sirius.ccd. What you see is not an image of the brightest star in the sky itself, but rather its spectrum that was recorded by passing the starlight through a diffraction-grating spectroscope on its way to the CCD. It's black-and-white, of course, but violet is on the left and red is on the right. In fact, a quick calibration using the leftmost line (a violet Balmer line) and the rightmost line (due to atmospheric oxygen) shows that the wavelengths of the vertical absorption lines you see in the spectrum can be found from the following function for wavelength l vs. x pixel number x:
l (nm) = 0.526x + 397 .
There are four Balmer absorption lines visible in the spectrum of Sirius. You are already familiar with the blue-green Hb 486 nm line. Can you identify which one it is? Convince us by specifying its pixel number x.

albireo.gifObject #3 - Albireo: Open albireo.ccd. Albireo is thought to be a binary star, in which the two stars slowly orbit one another; this is actually quite a common occurrence. Try a couple of different things here. First measure the magnitudes of each star. Then convert the magnitudes, m, into actual intensities, I, (in W/m2) using the formula:
I = (2.7x10-8)x(10(-m/2.5))    (intensity in W/m2).
Spectroscopy of the two stars shows that the brighter one is an orange K giant with a luminosity, or power output, LK = 4x1029 W, and the dimmer one is a blue main-sequence ("regular") star with LB = 3x1028 W (it's a beautiful sight in the telescope - striking color contrast). Now, since the inverse-square law says that:
I = L / 4pr2
You can now calculate the distance r to each star. The two values of r may be slightly different; just in case this happens, let's agree to split the difference and average the two values and call the distance ravg.

Now the second exercise begins by measuring the angular separation between the stars. Using the distance ravg, you can find the apparent linear separation a between the stars (apparent because we don't know if the stars lie in the plane of the sky or not). Convert this to astronomical units (AUs) using 1 AU = 1.5x1011 m. Assuming the separation you measure is the true separation, and assuming the total mass of the stars is about 2 solar masses, use good old Kepler's Third Law -
P2 = a3/ M   (P in years, a in AUs, total mass M in solar masses)
to find the orbital period P of the binary system. Do you think you want to wait around for the stars to move?!

szcas.gifObject #4 - SZ Cassiopeiae: Open szcas.ccd. Your will see a star field. The brightest star on the left is the pulsating variable star SZ Cas. Stars like this are incredibly useful, because there is a tight correlation between period of pulsation and luminosity, and because they are very luminous giant stars. So, you can see them to great distances - like in other galaxies - and, by observing the period and using the inverse-square law, determine their distances. SZ Cas is in our Milky Way Galaxy, but to illustrate the method, find its magnitude m and intensity I. More detailed observations show its period to be 13. 6 days, which puts its luminosity at about L = 4x1030 W. Find the distance r to SZ Cas, this time giving your answer in light-years, where 1 ly = 9.5x1015 m.

m1.gifObject #5 - M1: Open m1.ccd. This is Professor MacAlpine's famous Crab Nebula, the remnant of a supernova explosion that was observed on Earth in 1054 A.D. Measure the angular size of M1 (you can do it across the major and minor axes - i.e., the long way and the short way, and average these if you like). Using its distance of 6500 ly, find the linear size of M1. Finally, assuming that the glowing gases you see have been expanding at a constant rate since 1054 (as observed on Earth), calculate the speed of the gases ejected in the supernova explosion.

m51.gifObject #6 - M51: Open m51.ccd. This is the beautiful spiral galaxy known as the Whirlpool Galaxy (with an irregular companion to the left). We really took this picture here - no kidding. If you go to "Display" - "Color Table" and choose "Rainbow", and then play with the "Back" and "Range" a little in the "Contrast" window, you can bring out detail in the spiral arm structure (just for fun). Measure the angular size of M51. Using its distance of 15 million light-years, calculate the linear size of M51.


3c273.gifObject #7 - 3C273: Open 3c273.ccd. This is apparently just a field of stars, but one of the stars is a quasar at a great distance from Earth: it's the "quasi-stellar" (hence the name) object to the lower left. And again, we're not joking, we really made an image of this quasar from the roof of MMS. Since you've already learned about quasars and how their redshifts tell you their distances in an expanding universe, we'll just tell you that the redshift z = 0.158 for 3C273 puts it at a distance of about 2 billion light-years (which is technically known as its luminosity distance). Measure the magnitude m for 3C273 and find its intensity I. Now calculate the luminosity L of 3C273, giving your answer in terms of the solar luminosity Lsun = 4x1026 W.