A Method for Asteroid Light Curve Determination Using Standard Star References
by John Menke, February 2003
A major problem in asteroid light curves is that the reference star(s) on the image frame change from night to night as the asteroid moves. This and other effects result in data from successive nights having inherent offsets in magnitude that must be eliminated to allow combining the data into smooth curves. While one can simply "adjust" the data sets as necessary, it is certainly desirable to minimize the adjustments by taking the necessary data and computing the proper corrections. The larger the ad hoc corrections that must be made, the more difficult is will be to detect very slow low amplitude periods or the presence of other harmonics in the light curve signal.
The popular program MPO (by Brian Warner) implements this general approach in its software. The purpose of my work was to develop a reasonably simple method that users of other software would be comfortable with, and that is easy for new observers to master.
The method I describe here allows the user to make most images with no filter thus allowing access to the faintest objects. The method requires the user to make only a single set of filtered images of the asteroid field and a nearby standard star field. A simple analysis of these images provides the calibration factors that can be applied to UN-filtered images to allow night to night calibrations that in effect allow for both the instrumental calibration and the reference star:asteroid color difference. I am currently adding software also to correct for the magnitude change as the asteroid moves in its orbit.
In this method, virtually any software can be used for image taking and analysis. I find use of a spread sheet to be the simplest analytic tool, as it is easy to tailor the analysis and graphs to meet the needs of the particular case. The calibration method I describe is easy to include in an observing program, and adds only about five minutes to the data taking and data analysis (Steps 3 and 6 below) for each night’s data.
I have a C11 operated at f/6.3 (1 pixel=1 a-sec) on an AP1200 mount. The camera is an ST7E, with a color filter wheel containing BVRI and a clear (non IR blocking) filters. The system is in a remote dome using Digital Dome Works on a ProDome PD-10, 400 feet from house, normally operated by remote computer over a simple network. (Other connections work as well — I once initiated an evening's image taking using PCAnywhere and a laptop from a Kinko’s phone connection in downtown Washington, DC.)
I control the scope with TheSky® and use MaximDL® for taking and measuring images. I normally start a run (turn on equipment, start software, calibrate scope, etc.), then run automatically with occasional checks for focus, etc., and to make the standard field images. I let the DDW close the dome before sunrise and automatically stop the scope tracking, then I park the scope after I get up the next morning!
Method Summary1. Determine asteroid and standard star fields. I load asteroid elements into TheSky, making it easy to select the desired asteroid. I also loaded the Landolt stars with special symbols into TheSky. This makes it very easy to spot the nearest Landolt stars to the asteroid. I generally pick a Landolt field in which there are 3-6 Landolt stars within the CCD field. If there are no Landolt stars near to the asteroid, I can pick a suitable, non-variable star near the asteroid region and calibrate on that in a two step process against a Landolt field. I find that the graphical interface of TheSky is a real advantage in these operations. I normally run without active guiding.
2. Take Images. I usually run sequences of 60 second images with clear non IR blocking filter as I want all the light I can get. I usually use an initial dark field in automatic subtraction. I will begin the run as soon as the asteroid is up to 20deg or so and I run the scope unguided. A typical night may have 400 images. I usually don’t flat field correct, as experience and measurement that on my camera there is less than .01 mag error present. My experiments show that flat fields are very difficult to do better than .01 mag, so that improvements by flat fielding are not worth the effort.
3. Take Reference images. At least once during the night, and especially near the time of transit, I will take the reference images used for calibration. I will interrupt the clear image sequence, and shift to a V-filter, and will take a 240 sec. image of the asteroid field. Still with a V-filter, I then slew the scope to the selected Landolt field where I take a 240 sec image. With 240 sec images the star images are still reasonably round, although the asteroid may be somewhat elongated. I then return to the clear filter sequence. Note that you use the same Landolt star field each night—usually the asteroid is moving slowly enough that this introduces no problem.
4. Read Images. Maxim requires that the user select a reference star on the image field, and all measurements are made relative to it, thus losing the absolute brightness information. One result is that you cannot inspect the data to determine presence of clouds, haze, etc. However, a plug-in is available that allows you to imprint a standard digital reference star on all the open images. When measuring the images, you choose this as the "reference" star, then select as objects the asteroid and 2-4 other stars in the image field to use as the real reference and check stars. Finally, I set the Maxim photometry calibration to a standard setting for all photometry work (I use 60 sec=100,000 units=10.0 mag). By always using the same setting, I can always compare results between data sets. So the sequence is to select a batch of image files (eg, 50 or 100), imprint the digital reference, go into the photometry mode and select the reference and objects, and let Maxim read the images. Of course, one checks the on-line plot to assure that the reading has been done correctly, bad images deleted (eg, asteroid too close to a star), and the like, then one saves the data (as a comma separated file CSV). This process takes about five minutes for a batch of 100 images, so 400 images might result in 5 or so CSV files of intensity data. Note: I find it essential to do a "print screen" image of the photometry screen so I have a record of which objects in the image correspond to which object number. This makes it easy to have all the CSV files use the same nomenclature, and allows me to document what I did.
5. Analyze Run. I then import the CSV data into a spreadsheet. I open each CSV file with Wordpad, then copy and paste each one into an Excel worksheet. I do this in order, pasting successive data sets in the same columns. For convenience, I subtract a constant from all the Julian Days to make smaller JD numbers.
6. Calibrate. I now read the filtered images to get the necessary calibration factors. In Maxim, I use the desired data set (usually from near the transit time), open the asteroid V field image, the Landolt V field, and the immediately preceding clear asteroid field images. For this work, you do not need to do the digital reference star.
- The first step is to graph the raw data (the graph is an x-y graph, JD vs brightness). I generally choose the asteroid, the star I have chosen as the real reference star, and at least one additional star as a check star (to verify that the reference is not a variable). The graph will show immediately the presence of clouds, haze, or other problems in the data set, as well as the general effect of extinction as the asteroid rises, transits, and sets.
- The second step is to take the difference between the asteroid and the reference star(s), and graph the results. This is the raw light curve of the asteroid, ie, not yet calibrated. At this point, you may see that some data points are simply wrong—clouds were very dense, an error in imaging, etc. You can now delete these lines of data from the spreadsheet list (unfortunately, Excel does not simply allow you to label the lines of data to be ignored). Interestingly, I can often get good data (ie, .01-.02mag precision) data even in the presence of 1-2 mag of clouds or haze.
- Using TheSky, I identify the Landolt stars in the image and write down their V-brightness values (or print out a chart with the values as you will use this over and over). Then I measure the instrumental brightness of each Landolt star and write down the value. Subtract the measured from the catalog values, and average the results to get the V-offset. This is the value to add to the measured V-values that gives the "real" values.
- Using the Asteroid V-field, measure and write down the asteroid (Av) and reference star (Rv) magnitudes.
- Using the asteroid clear field, measure and write down the asteroid (Ac) and reference star (Rc). By hand, or on the spreadsheet, compute C=Av-Ac-Rv+Rc. This number is the color difference correction between the reference star and the asteroid (each night’s reference star may have a different brightness AND color!). We now have the V-offset and the Color C offset. Simply add these to the raw asteroid brightness values in the spreadsheet to obtain the calibrated values. This technique accounts for the major night to night offsets.
7. Mix Data. I find that it is best to use a different worksheet (within the same workbook) for each night of data. I copy and paste the JD and calibrated magnitude data from each sheet onto a Master sheet.
- I then graph the data from beginning to end. This shows the successive nights of data and no data.
- To determine the period of the asteroid I use a graphical folding technique. Assign a tentative value for the rotation period (ie, an estimate based on visual examination of the data) to a spreadsheet cell. Using this value for the period P, I compute the relative phase in days of each JD value using the formula Phase=JD-(INT(JD/P)*P). I then plot the phase (X-axis) vs the magnitude. You will usually see a series of segments of the light curve, with high and low misaligned pieces, with some parts of the "curve" having multiple data points, and others having none. You try different values for the period and choose the one that gives the smoothest curve (remember, the rotation curve has two peaks and valleys, the light curve just one of each). If there are vertical (magnitude) offsets among the data, you have either residual errors in the calibration or original measurements, or you may have discovered a true modulation of the light curve (eg, tumbling asteroid). If desired, it is easy to add a deliberate offset to produce a smooth combined data curve.
8. Use Other Programs. With the data in spread sheet, it is easy to export a text file with the JD and best estimates of the magnitude of the asteroid. This can be imported into Canopus (part of MPO) or other programs for comparison or further analysis.