Variable Star Photometry Photometry One of the most basic of astronomical analysis is photometry, or the monitoring of the light output of an astronomical object. Many stars, be they in binaries, interacting, or pulsating, change their brightness over time. We can learn much about the physical processes going on in a star by monitoring its changes in brightness. The typical data set used for photometry contains a series of images taken over time. The brightness of the star, when extracted from each image along with the time of the observation, allows you to create a light curve describing the brightness over time. The type of photometry discussed here is called relative photometry. The brightness of the variable star is compared to two or more other stars in the CCD image that are assumed to be constant. We determine the counts coming from each star by calibrating each image each image and removing the counts coming from the sky background. Step 1: There are data sets saved in the directory photometry in the data directory for your computer or on the CCD Observations page at the class web site. Start AIP4WINV2. Go to the photometry/terskol directory. The bias files start with BIAS, the flats start with FL, and the darks start with DARK. The data images start with GD. Open one of the GD images. The pulsating star is the bright one near the center of the image at X=252 and Y=333. Click Measure Statistics Image. 1. What do you notice about the size of this image? 2. What is its width and length in pixels (look at the fits header)? This is important for the calibration routine to work properly. 3. Click on Edit Fits Header. a. What are the Min and Max values for this image? b. Click the Camera tab. What is the exposure time for this image? c. What is the midpoint (the time of the middle of the observation)?
This is a test image showing the structure of the photometry apertures. This is not an image of GD358. Step 1a: Testing the Suitability of a Star for Photometry. You can test a star to determine if you will get good photometric results. You need to determine three values: 1) the size of the photometry aperture (aperture_radius in the above image), 2) the size of the inner sky annulus, (aperture_innersky) and 3) the size of the outer sky annulus (aperture_outersky). The idea is that we determine the number of photons in the aperture_radius (star+sky) and determine the sky contribution from the annulus defined by aperture_outersky and aperture_innersky. The sky contribution is then subtracted from the photons in the aperture_radius, leaving the observer with just the photons coming from the star itself. 1. Open the Single-Star Photometry Tool (under Measure Photometry Single Star). A window will pop up. Click on the Settings tab. You will see controls setting the inner and outer radii for the photometry aperture. The first setting is for the photometry aperture, the second for the inner radius of the sky annulus, and the third for the outer radius of the sky annulus. The photometry aperture will include the star plus some sky counts. It is important that the inner radius be large enough to include all the light from the star, but not too much sky. The outer radius determines the size of the sky annulus. It is important to get a good measurement of sky because the sky can be variable, even over short timescales (like minutes or even seconds). To start, set them for 7, 10, and 20 respectively. 2. Click on the Result tab. Make sure the Show Analysis box is checked. Click on GD358 in your image. The Result window will contain the photometric results for this image. a. Record the x and y coordinates, the peak pixel value, the Star-Sky value, and the Sky value. These results are in Analog to Digital Units (or ADUs).
3. A new window will have appeared when you clicked on GD358. This window contains two important plots. The first is called Profile. It plots distance from the center of GD358 (in pixels) along the x axis, and counts in the y axis. The counts will be high for pixels receiving light from GD358, and fall to the background (sky) value. Each thin green vertical line is one pixel, and the thick green lines mark the apertures you chose for this initial look. You can use this to determine the best size of the inner aperture (the photometry aperture). If you look at the yellow fit, you will see that the counts (the y axis) are high close to GD358 and fall off as you move from the star. But the counts never go to 0. The level region indicated domination by photons coming from the sky. When you are selecting aperture sizes, you want to pick a size for the aperture_radius (or star aperture) that includes all the counts from the star. You want to pick sky raddi that are large enough that they do not include and counts from GD358, but also do not include other stars. a. Do you think you can make the aperture smaller than 7 and still include all the light coming from GD358? b. What size aperture would you use? 4. The second window shows a plot of the photometric curve of growth (differential magnitude versus aperture radius) of the selected star. You can also use this to select your inner aperture. The inner aperture should not be smaller than the size where the differential magnitude first flattens out. a. What size would you choose for the aperture_radius based on this plot? b. Does this plot agree with your results from the Profile plot? 5. The inner sky annulus is typically made slightly larger than the photometry aperture. The outer sky annulus is usually twice the inner sky annulus. Step 1b: Setting up the calibration routine. Set up the calibration routine. Check the size of your calibration frames! Calibration frames must be the same size as your images. If the calibration frames are not the same size, click Transform Resample to change their sizes to match the images. Click Calibrate ->Setup ->Advanced. Choose the frames to create your master bias, your master thermal frame and your master flat frame. Make sure Automatic Dark Matching is checked. 1) Why should Automatic Dark Matching be checked? 2) Check the size of your calibration frames! They must be the same size as your images. You may need to resample the calibration frames (under Transform in AIP). Step 2: Click Measure ->Photometry->Multiple Image. The Multi-Image Photometer window will pop up. If you want the images to be calibrated (subtract bias, dark, divide by the flat) as you go, make sure Calibrate Images is checked.
Step 3: Select the files to be measured. Make sure you have looked through some of the images, especially the ones at the beginning and at the end, to make sure they are all good (ie no biases saved as images). Step 4: Click the settings tab. Input the radii values you determined above. This is a selection that requires some thought. To review, you want the final measurement for each image to contain just the counts from the star. But when you measure the counts in a given circle with radius R, these counts are star+background. Therefore you need a measurement of the background counts to subtract. The best place to measure the background is right near the star itself. When you select the In radius, you are selecting the size of the radius that the star+background measurement will come from. Make sure you choose a number large enough to include the entire star image, but not too much background. When you choose the outer radius for the sky annulus, you are selecting the area to measure the background. Be very careful in crowded star fields. 1) Why do you think you should be careful in crowded star fields? Step 5: In the next step, you will be selecting the variable and comparision stars. The first, called V, is your suspected variable, in this case GD358. The remainer are comparison stars. Choose 4 additional comparison stars. Try not to pick ones close to the edge of the image. The program will attempt to track these stars from image to image. The star images might drift from image to image, so you need to give the program a pixel range in which to search for the stellar image. Step 6: Once you have selected your files, the first image will appear. Click on GD358, and a yellow photometry aperture and sky annulus will appear around GD358. Click on 4 more suitable comparision stars. Step 7: Click on the Report Tab. Select file on hard disk as your method of saving the output. Step 8: If you think everything is set up okay, return to the setup tab and click Execute. Each image will appear on the screen, the stars identified, and their relative magnitudes and counts logged. When finished, a graph will appear showing the data for the variable star minus the comparison star, and the Check star minus the Comparison star. The graph is an example of a light curve. 1) If conditions are ideal, what do you think the result of the Check star minus the Comparison star should be? 2) How could you use the measurements of the variable and comparison stars to determine if the suspected variable is indeed changing its brightness? 3) Open the images number 2 and 699. Look at the fits header and record the observation time (TIME-OBS) for each image. How long of a time do the observations span? 4) Can you roughly determine the pulsation period of this star?
Step 10: Repeat steps 1-9, using an inner radius that is 2 pixels smaller than the one you started with. 1) Look at the resulting graph. Look at the scatter in the graph. Do you think this is a more significant result than your first light curve? Step 11: Repeat steps 1-9, using an inner radius that is 2 pixels larger than the one you started with, and an outer radius that is 2 pixels larger than the one you initially picked. 1) Look at the resulting graph. Examine the scatter in the graph. Do you think the noise is lower in this result? 2) Compare the results from the three different light curves. Which do you think gives you the best results? Asteroid Photometry Repeat steps 1a -9 using the asteroid data. Use files 1-375. The purpose of these observations is to measure the asteroid s rotation period. The asteroid is at x=132, y=159. Make sure you select this as your V. 1) If you are using the asteroid data, what special problem do you think you might encounter? Why won t C offset work in this instance? 2) Do you observe any changes in the asteroid s brightness? 3) Open images 1 and 375. Look at the fits header and record the observation time (TIME-OBS) for each image. How long do the observations span? 4)What can you determine about the asteroid s rotation period? Save your photometry files to a diskette! If you are using a computer with Excel, load them into Excel. The Sky With Excel, plot the sky counts column in your output file. Describe what you see.