Lab 1: Astrometry & 3-Color Imaging

Transcription

1 Astro 101: Observational Astronomy Fall 2009 Lab 1: Astrometry & 3-Color Imaging Name:... 1 Observations 1.1 Objectives During this lab you will learn the basic observing techniques of locating objects in the sky and taking images using different filters. You will use an SBIG STL-11000M camera mounted on 14 Celestron telescopes at Brackett Observatory (BO). The tech specs for the camera can be found on our website (both homework and lab pages). During the first part of the lab, you will take an image of the sky around one of the known high proper motion stars. Then you will compute an astrometric solution for your image and calculate the velocity of your target in the plane of the sky. During the second part, you will obtain multi-band images of your favorite astronomical object(s), perform some basic image processing and create a color image of your target. You will be using the Sky computer program to run the telescope and another program, Maxim DL, to operate the camera. It is a good idea to familiarize yourself with the basic workings of Maxim DL before the start of your lab. In particular, check out the online manual at (go to Contents Tutorial CCD Imaging Tutorials). You will be meeting at the Brackett Observatory on Tuesday (Sept 15) or Thursday (Sept 17) at the time specified by your instructor. It should take you about hours to complete both sections of this lab. The Observatory is located at the East end of 4th street, next to the Greek theater on Pomona campus. Make sure to bring this manual, your finding charts and airmass tables (see 1.2), a lab notebook (any square-lined notebook will work), a USB flashdrive, a calculator and a small flashlight if you have one. 1.2 Preparation: Finding Targets After you ve completed homework #1, copy the relevant information into the table below: Optics/ f eff Plate Scale Pixel Scale FOV) Camera (meters) ( /mm) ( /pixel) (degrees) Celestron/ SBIG STL Table 1: Effective focal length, plate scale, pixel scale and field-of-view (FOV) for the optics/camera configuration used in this lab. Now that you know the field of view for the camera you will be using, you can pick your targets. For Part I (astrometry, see 1.3.2) you need to pick a field that contains one of the stars in Table 2, chosen from the Hipparcos Catalog. I picked these stars since they have been measured to have high proper motions, which you will be measuring in this lab. 1

2 HIP# RA DEC V π (mas) Table 2: High proper motion stars chosen from Hipparcos catalog. The columns are Hipparcos catalog number, RA (J ), DEC (J ), V magnitude and parallax angle in units of milli-arcseconds. For Part II (3-color imaging, see 1.3.3) choose your favorite nebula, galaxy or star cluster. The Messier catalog (on our course website go to Astrophysical Resources) is a good starting point, but you are certainly not restricted to it. For best results, consider the angular size of your object and the FOV of the camera. The sky background at BO is very high, so you will do best with an object close to zenith since this minimizes the amount of atmosphere you will have to look through. Your calculations for homework problem #1 should give you a good idea which range of RA and DEC to consider in your target search. You might find it useful to know that the longitude and latitude of Claremont is 118 degrees West and 34 degrees North. The September issue of the Sky and Telescope, available at or as a hardcopy outside my office, can also provide you with the information on what the sky looks like for a specified date and time. Note down the constellations close to zenith these are the best locations for your targets. Once you identified your target(s), as a sanity check, you should confirm their visibility by going to Astrophysical Resources Almanac Tools Hourly Airmass Tables on our website. Make sure you set the location or simply choose Palomar Observatory (it s close enough) from the drop-down Observatory menu; choose the correct date and choose the correct epoch. This calculator will give you HA and sec(z), where z is the zenith distance, for your object as a function of local time. You should aim for sec(z) < 1.3 (to stay close to zenith), during your scheduled observing time slot. As a last step create finding charts using the Palomar Digital Sky Survey (POSS, go to Astrophysical Resources Palomar Observatory Sky Survey). For this task you can choose either GIF or FITS format; the latter can be viewed using command ds9 available on astro computers. To locate your astrometry target on the finding chart, download images from POSS1 (released in 1957) and POSS2 (released in 2001); make sure to set epoch to J2000 for both. When comparing the two images, you should be able to clearly identify your target as the only moving star on the image. Your finding chart should be slightly larger than the FOV of your detector, but make a note of the image size you used. Finally, write down relevant information for all your targets, filling in Table 3. Print out your finding charts (be sure to invert the image, i.e. you want black stars on white background to save ink), circle your targets and record your airmass information. You are now ready for your observing 2

3 run. Target Angular Size RA (Epoch) Dec (Epoch) Transit Time Table 3: Potential targets 1.3 Procedure for Data Collection The Night Sky At some point in the evening, step outside and take some time to orient yourself on the sky. When observing from inside the dome, you will find that this preliminary orientation is very useful. Take note of the sky conditions and when finalizing targets be mindful to avoid regions near incoming cloud cover (for obvious reasons). In general you would also need to avoid the moon (which will brighten your sky background and limit the depth of your observations), but it is nearly new the third week of September. Since it could be hard to identify stars through the slit in the dome you may need to step outside periodically to ensure that you are looking at reasonably dark and clear patches of sky. When you step outside, you will find that north is toward the mountains and west is toward College Ave. I recommend you use a finding chart (again Sky and Telescope is a good resource) or preferably a desktop planetarium (eg. The Sky, Starry Night or Voyager) to help orient yourself. Toward the north, about a third of the way up the sky is Polaris. Around it you can normally find the Little Dipper (Ursa Minor), Cassiopeia and Cepheus. In the early evening, you may also be able to see the Big Dipper (Ursa Major) fairly low on the horizon, but it will set a couple of hours after sunset. In the early evening, the Summer Triangle is nearly overhead. The three stars that form it are Deneb (α Cygni), Vega (α Lyrae) and Altair (α Aquilae). The first two make up the base of the triangle (Deneb to the east and Vega to the west) and Altair points toward the south. The constellation Cygnus, the Swan (also called the Northern Cross) lies inside the Triangle. If you follow the line from Deneb to Altair, just above the southern horizon you should be able to see the characteristic tea-pot shape of the constellation Sagittarius. The center of our Galaxy lies in this constellation. In addition to the bright stars that compose the major constellations, the brightest visible object in the sky can be found toward the East. This is Jupiter Part I: Astrometry You will be using two different software packages: The Sky, which controls the motions of the dome and the telescope, and Maxim DL, which controls the camera. Browse through the online tutorial for Maxim DL ahead of time, but our lab instructor will help guide you through these programs. 3

4 You will start by opening the dome, removing covers from the telescope and connecting and cooling the camera. Point the telescope to your first target field using The Sky. For the first part of this lab, it does not matter which filter you choose to use. To minimize exposure time, it makes sense to select the Clear position, but this is up to you. Take an image with exposure time of several seconds. As a first step you will need to focus the camera, aiming to minimize the angular size of the stars on your image. With the present setup you will have to do this manually. The most efficient way to do this is for one person to take a series of images (use the Maxim DL focus option) while the second person manually adjusts the telescope focus. You might also have to adjust your exposure time to make sure that the star which you are using to judge the best focus position is not saturated 1. The saturation limit for this camera is about 50,000 counts. To be on the safe side, you should stay below about half this number, i.e. 25,000 counts. Once the you ve done your best to choose the best focus position, compare the image to your finding chart. Make sure you are looking at the correct field! Move the telescope as necessary to center your target. Keep in mind that the orientation of your image may be different than that of the finding chart. When you recognize your star field, note the north and east directions for your images and list this in your log. Now you are ready to take data. For this lab you should choose the Autodark correction mode when to eliminate the dark current from your images. Also, make sure to save all your images as fits type! It is a good idea to save all images that you take, regardless of their quality. Note that when you take images in sequence mode, they will automatically be written to disk; otherwise, you need to manually save them. For every image saved, you should to create a record in your notebook. At minimum, you have to record: 1. file name/number, 2. target coordinates or name, 3. time of observation, 4. exposure time, 5. filter (in this case clear ), 6. whether or not a dark image was subtracted. It is also good practice to note any changes in observing conditions (e.g. cirrus clouds) and your comments on the image quality (e.g. bright stars are saturated; clouds rolled in; focus sucked: FWHM 3.0 arcsec). The recording works best if one person is controlling the telescope and another is taking notes. You should switch tasks midway through the observing session. Experiment with different exposure times, examining each image with Maxim DL. You will want to maximize the number of stars you can see on your image without saturating the brightest stars. Once the star is saturated, the precision with which you can later locate its position decreases. (Think why this is true.) Once you are happy with your pointing and exposure times, take a set of ten exposures of your field that you can later co-add to improve signal-to-noise and remove cosmic rays (if desired) Part II: 3-Color Imaging For this part you will be taking images of your target through different color filters. In general it is a good idea to focus the camera separately for every filter. For this lab, you can probably get away with a single focus position it is a good idea to check. Once the camera is focused, find your target and experiment with the exposure times. Make sure you are saving your images and record all the relevant information on your log sheet. When 1 If your target field does not have many bright stars, you might want to focus the telescope by pointing to a relatively dense stellar region. An open cluster (e.g. the Wild Duck cluster, M11) might be a good choice. 4

5 you find the best exposure time, take a series of exposures in all three filters. You d like a minimum of 3 exposures per band, but 5-10 is preferable CCD Calibration As a final step, you now need to take flat field images. The idea here is that you want to observe an extended source that is spatially uniform (i.e.. flat) over the scale of your detector. You will use this image to determine the instrument response function. The standard approach is to take exposures of the twilight sky, since it is bright enough that flux from stars or other point-like sources are generally negligible. The challenge with twilight flats is that, as the name suggests, they need be taken during a relatively narrow window in time, either just after sunset or just before sunrise. For the purposes of this lab we will take an alternative approach, since the night sky in Claremont is bright enough that you can get away with taking nighttime sky flats. (Aside: This IS the standard approach for taking near-ir images. What does this suggest about the near-ir night sky vs. star brightness?) Try to aim lower towards the horizon away from really bright stars and take 4-5 images in each filter at slightly different locations on the sky. When these images are combined during data analysis, you can eliminate the stars by taking a median value for each pixel, so that the (hopefully!) uniform sky background will serve as your flat. Before you leave for the night, make sure that all your data is stored in a single directory. Transfer all the files onto your flashdrive; this is the most efficient method of transporting it to HMC. 5

6 2 Data Analysis While the data is collected with the help of your lab partner, the subsequent analysis and writing of the report should be done completely on your own. 2.1 Data Access The data you collected during the observing sessions will be on your flashdrive and should be downloaded onto one of the astro cluster computers. It is a good idea not to save the files into your home directory. The best thing to do is to make separate directories for each lab and then each observed target (the Linux command is mkdir directory name ) and copy the appropriate associated data files into each. It will be very helpful if you also put a text file in each directory (I typically name such files README), which serves as an electronic log file. At the very least it should give the date of your observation, the equipment used and the target(s) observed. In the best case, your README file will contain the entire copy of your log file; this will considerably simplify your data analysis and make it easier to share data between lab partners. 2.2 IRAF Initialization Before you begin with IRAF, I strongly recommend that you read through the Unix and DS9 parts of the Software User Guides on the course page. In this course you will be doing most of the data analysis using the Image Reduction and Analysis Facility (IRAF) software package developed and maintained by the the national Optical Astronomy Observatories (NOAO). However, the first time you start up, you will need to perform the following initialization step. To initialize IRAF, follow the directions on the course web page under Software User Guides. First click on IRAF Startup, scroll down to Getting Started and follow the instructions to set up your IRAF directory and login file. After you ve started IRAF, you will see a list of packages loaded automatically. If any from the list below are missing, type in their names to load them, as you will need them for this lab. images imred ccdred imcoords mscred mscfinder astutil 2.3 Astrometric Solution You are now ready to find the astrometric solution for your data, i.e. a mapping between the (x, y) pixel coordinates on your image and (α, δ) equatorial coordinates on the sky. To do this you will use the IRAF routine ccmap, which is part of the imcoords package. As you will see this is a fairly manual method for computing your astrometric solutions. Once you obtain a a rough solution with ccmap, you will then use msctpeak to obtain a refined solution Creating Coordinate List The astrometric solution will be computed using a list of known coordinates for several (4-6) stars on your image. The coordinate list needs to be an ASCII file, which you can create by using an emacs text editor (see Software Users Manual for Emacs help). The format of the list is somewhat flexible, but it must contain at least four columns that contain the x & y pixel coordinates and the 6

7 α (right ascension) & δ (declination) astrometric coordinates for each star. As an example, I ve created the following list for one of my own images: :21: :23: :21: :25: :21: :24: :21: :21: :21: :22:25.6 The first column here is simply an index number; the next two are x & y pixel values and the last two are R.A. and Dec. To get the best possible solution, your stars should be distributed more or less evenly throughout your image. Below I suggest one procedure for creating your coordinate list, it is neither the most efficient nor most accurate approach but for this application it will serve its purpose. I encourage you to take alternate routes if you are comfortable doing so. However, if you do, please make sure to describe and justify your method. Step 1, Identify a reference star sample: Display your image on ds9 by either: a) loading an image directly (type ds9 imagename & on the command line); or b) using the display command in IRAF (if you choose to use display remember to first start a fresh ds9 session from the IRAF prompt.). Identify and label a set of bright non-saturated stars that are well distributed over the entire image. The easiest way is to overlay circles (mouse left-click) on your selected sources and then label them 1 through N, where N is something like 4-6 (double-click on any given circle to bring up its label dialog window). These should be bright but not saturated and well distributed over the entire image. DO NOT include your proper motion target in this list! Think why this is a bad idea. It is important that you center your sources carefully since with you will not be implementing an additional centroid fit. While you make your measurements, try to estimate the uncertainty of your eyeball centroids. What would you estimate for your 1 σ uncertainty? Convert this into arcseconds and discuss how this might impact your astrometric fit. Once you have marked a set of stars you are happy with, you can list all of your targets by selecting List Regions under the Region menu option. For each circle you overlaid, you will see one line item with x/y pixel information, radius (default unit: pixels) and the text label. You should save this info to an ACSII file using the Save Regions option and then edit it with an emacs text editor. A simple emacs macro will simplify this process considerably. Alternatively, you can use imexamine to determine much more precise positions for your reference stars (see the course web page for a description of imexamine). Start by displaying the image and picking the reference stars as described above. Then type imexamine at the IRAF command prompt. For all of your marked stars, use the r keystroke command to examine their radial profile and check for saturation. For unsaturated stars you can then use a keystroke command to measure their precise (x, y) coordinates. Copy the values into your coordinate file, either manually or by using an the imexamine log feature and do the final editing in emacs. Step 2, Determine astrometric coordinates: To get the (RA,DEC) coordinates of your stars from astronomical catalogs you need to first identify them, which is actually not so easy to do for a relatively dim garden-variety field star. Instead I suggest you obtain approximate coordinates using the POSSII database. Download a POSSII image (make sure to specify epoch J2000!) that has roughly the same size as your data image and is centered on your 7

8 object, just like you did when making finding charts. Make sure that you can read off (α, δ) coordinates of the cursor position. Equatorial J2000). This seems to only work if you are loading you image directly into ds9, without going through the IRAF display command. Since you do not necessarily know which way is North, you may need to flip and/or rotate POSS image (in ds9 use Zoom button) to match it to your data. This is an exercise in pattern recognition. Once you have matched them up, read off the coordinates of your reference stars and include them in your ASCII coordinate file. You can also use imexamine to get more precise coordinates. Before starting this routine, type epar imexamine at the command prompt, move down to wsc parameter using the key and type world followed by Enter key. Exit this task by typing Cntr-d. Now imexamine will produce the actual (RA,DEC) and not just column and row coordinates Reference Point of the Image For the last step before running ccmap you need to determine the coordinates near the center of your image. You can make this estimate using POSS and simply picking a star near the center of your field Setting CCMAP Parameters Now you will modify the parameters of ccmap prior to running it. Before you do this, take a look at the help pages for ccmap. You can bring this up in IRAF with the command: help ccmap. This will give you an overview of the IRAF task and it will define all of the input parameters you are about to set. Type epar ccmap and set: input to the name of the coordinate file you just created database to coordinate file name.db images to the name of your image file results to image file name.results (this is the file in which the summary of the results will be written) xcolumn to 1 ycolumn to 2 loncolumn to 3 latcolumn to 4 refpoint to user lngref to α (RA) of the image center latref to δ (DEC) of the image center (don t forget the sign) update to yes (this will allow ccmap to update the header of your image to include the info about the astrometric solution) interac to yes (this will run ccmap in interactive mode). 8

9 2.3.4 Running CCMAP Now type ccmap. The program will be running in the interactive mode, and first the mapping function for the astrometric solution will appear. The plate solution has the form xi = f(x, y), eta = g(x, y), where xi = α, xi = δ. To check that the program worked well, use the keystroke commands x, r, y, s to see the residuals for xi vs. x, xi vs. y, eta vs. x and eta vs. y, respectively. What kind of residuals are you getting? What do you think are the primary contributors to these residuals? You can type? to get a list of all the keystroke commands. If all looks well, type q to save your solution and quit Check the Results b Check the file image file name.results to see the computed plate scale (in arcseconds per pixel) and the fit values of α and δ for the stars in your coordinate list. Check that the difference between the input and fit coordinates is not too large. Look at the header of your image file to make sure that the astrometric solution has been recorded there; use the command imhead file name long+. Finally, display your image file in ds9 and make sure that you can read off (α, δ) coordinates of the cursor position. Again, this seems to only work if you are loading you image directly into ds9. Turn on the coordinate grid box (Analysis Display Coordinate Grid) and set the coordinate type to equatorial (Analysis Display Coordinate Grid Parameters Coordinate Equatorial J2000). Finally, invert the color map on your image (Color Invert Colormap) to save ink, save your image to a postscript file, so that you can include it in your report. You can also test your astrometric solutions by running imexamine on your modified image file Refining your solution The approach outlined above is fairly manual, since you need to record RA/DEC and pixel coordinates for each star you want to include in the solution. We got a very rough solution using a half-dozen stars, however, if we are interested in a better solution that included distortion terms for instance, we would need many more stars and this manual approach quickly becomes prohibitive. An alternative is to compute a preliminary solution using the method above and then improve on it using the IRAF task msctpeak with a more complete star catalog list that msctpeak will try to match automatically to your image. Such a list can be retrieved online at the ESO Guide Star Catalog (GSC) page ( or USNO Catalog of Astrometric Standards (USNO A-2.0) page ( You may need to experiment a bit to find the correct magnitude limit to retrieve, so that you have not too many and not too few stars. You will need to download the output file and edit it using a text editor like Emacs to place RA and Dec in the first two columns in the following format: (hh:mm:ss deg:arcmin:arcsec). Just as with your first list, try to exclude your proper motion target star. Msctpeak takes this input coordinate file and the FITS image you are working on and tries to match up the sources in your input list automatically. Depending on how well you did in the rough solution above, msctpeak might need a nudge, so make sure you do this in interactive mode. When you run MSCTPEAK, it should load your image in DS9 (so make sure you have a DS9 window running) and overplot blue circles from the GSC catalog on your image. If your solution is OK, these should fall on or near what look like real stars. These coordinates are overlaid based on your current solution, so what you want to do is refine this. If the blue circles are close to real stars, then just type a then j. This will apply to ALL star, the J command, which is recenter the circles on the nearest detected star. If they are not close, you will need to use the K command (see below and experiment). Once they look well centered, type F, which will do a fit and open 9

10 a new graphics window that will let you look at the fit and its residuals. You can look at various residual plots with the keystrokes x,y,s,r and also delete and undelete points that look really bad. Do the RMS values you are getting look reasonable? Record these values so you can use them to estimate the uncertainty in your final proper motion velocity measurements. You can also increase or decrease the order of your fit. Once you are happy with your fit, type Q to save and quit. To get a full list of keystrokes, type?. Here is an abbreviated list: - IN IMAGE WINDOW - keystroke a ; keystroke j (will center blue circles) - keystroke a ; keystroke k (will center blue circles on cursor) - keystroke f (will do fit) - keystroke q (to quit after FIT) - IN FIT WINDOW: - keystrokes x,y,s,r show fit - keystroke d,u delete/undelete - keystroke f/g fit/show fit - keystroke q to quit The advantage of doing this in two steps is that it minimizes the manual labor since we are only using 4-6 stars for the rough solution. Also, since the refined solution will use as many stars as are detected you should be able to compute a better solution. Check as described in above that the solution has been saved in your image header. At this point you can also determine the plate scale and FOV of your detector. 2.4 Proper Motion Measurement We are now ready to measure the proper motion of our target. Your newly calculated coordinate solution allows you to determine its present day epoch J2000 coordinates. Its J coordinates measured by Hipparcos satellite are given in Table 2. Your task is to calculate the total displacement of the target star in RA and Dec and convert these results to speeds measured in milli-arcseconds per year. If you find yourself needed to convert coordinates from one epoch to another, you can either do this manually, or using the task precess in IRAF. Type help precess and look at the examples to figure out the syntax for this task. A way to get a longer baseline for your measurement is to use the coordinates from the POSSI image for your target. The major uncertainly there is the time when the image was taken, since the survey took 7 years to complete ( ). Describe your calculations in the report; do not forget to discuss the uncertainties in your results Color Imaging You will use IRAF+DS9 to produce color images from your 1-meter observations. There are three primary steps for combining images: 1.) Initial reduction of the raw frames; 2.) alignment and co-addition of all images for a given filter; 3.) combination of the co-added frames into a single color image. The first two reduction steps will be performed with IRAF, the last step with DS9. 10

11 2.5.1 Initial Reduction The combined image will look better if you perform some initial reduction steps of bias-subtraction, dark-subtraction, flat-fielding and hot-pixel masking. The first two steps have already been done for you if you chose to do automatic dark subtraction during your observing run. The third step can be done now. All of these steps are non-essential for performing astrometry (but will be in future labs), so we leave them as optional for this lab. If you would like to create a flat-field image, follow CCD Reduction Combining Flats guidelines under Software Users Guides link on our webpage. Keep in mind that you will need a different flat for each filter. Once the flats are created, use the task imarith to divide each of your images by the relevant flat Aligning/Combing with IRAF/DS9 Aligning the Images Chances are the pointings for your images taken in different filters are not exactly the same. To correct this you will use the command imalign. First you will need to pick the image to serve as a reference all the other images will be shifted to match this one. Next create a file that contains a list of registration stars. This step is similar to what you did for computing the astrometric solution, except now only (x, y) coordinates are important. Pick several (say 5) stars that are well spread out on your reference image. Use imexamine to determine centroid positions of these stars. Copy these position coordinates into a file called, say reference file name.coords. Put x and y coordinates in columns one and two respectively. Now modify the parameters of imalign and set: input to R band image, V band image, B band image (this has to be a comma-separated list); all the images will be shifted to match the first one) reference to reference image coords to the name of the coordinates file you just made output to R band image.out, V band image.out, B band image.out (a comma-separated list of shifted images) This program will shift the images to match the reference image and trim all of them to include only the overlapping region. Combining the Aligned Images There are IRAF tasks that allow you to combine multiple images into a single tri-color image (eg. export is designed to give the user complete control over the color levels of the 3-color image and run quickly in batch mode). Unfortunately, they tend to sacrifice usability for control. A powerful but more interactive and user-friendly method for producing color images is to use ds9. To do this, first start a fresh ds9 session with the RGB option selected: ds9 -rgb & This will bring up your normal ds9 window along with a small RGB channel control window. In RGB mode, ds9 will allow you to load different images into 3 different color channels, and will combine them on the fly. By default, ds9 expects you to load the red channel image first do so with the File/Open option. Next, select the green channel in the RGB control window and load the green image. Repeat for the blue image. Once all three image files are loaded ds9 should display a single color image. You can and should experiment with the scale and colormap parameters of the three images individually until you come up with a color image that you are happy with. Unless you are trying to create a true color image, in which you would try to map the individual filters to the response function of the eye you don t need to worry too much about the exact color mapping function. The creation of tri-color images is a bit of an art and as such, they are rarely used 11

12 for quantitative purposes. That said, they do serve the powerful purpose of highlighting physical features that are best (and sometimes only) identified by their differential colors. If you have loaded your three channels properly, the RGB colors should map to your red/green/blue filtered images, which by itself already conveys important information about the object. Try to choose your scale and color map that will draw out some physical feature of your image that is not as obvious from a single band image alone. In your write-up, describe your scaling choices and what you are trying are trying to illustrate with this choice. Images can be saved with multiple image formats using the Save as... option under File. To create a more printer friendly version of your image, you should use the File/Print option to print to a postscript file. RGB/Level 1 should be should be sufficient. 2.6 Report Format I expect your final report will be 4-6 pages in length. You should divide your paper into two sections devoted to the two parts of this lab (astrometry and 3-color imaging). Each section should be divided into three subsections: Observations. Here you will describe the instruments you used and include your observing log in a table form including time, exposure length, filter (when applicable) and target information; Data Analysis. This will contain a brief description of the data analysis steps. Results. This is the most important section. It should contain all of your numerical results and the appropriate images. For the astrometry part please comment on how well the fit coordinates for your reference stars agree with the coordinates you provided, as well as on how your plate scale and field of view compare with the values you found in your homework. Report how you calculated the proper motion for your target star and quote your results with uncertainties. For the 3-color imaging part describe the overall colors of the features on your image and discuss these based on your knowledge of astrophysics. Whether you observed a nebula, a galaxy or a star cluster you should provide a physical interpretation of the colors in the image as much as you can. You will find g, r, i-band sensitivity curves in Gunn et al (ApJ, v116, 3040), which is conveniently linked at: Note that all tables and figures should be numbered and should have captions describing their contents. If you have any questions regarding the format of the report, or about what should be included in it, please come talk to me. Please submit your report by sending it to Ann Esin@hmc.edu as a PDF file or by handing it to your instructor in person. 12