Best Observing Season: any

Level: Intermediate to Advanced

Learning Goals: The student will find the rotation period of an asteroid.

Terminology: light curve, opposition, photometry, rotation period

Software: Photom, Camera, Megastar, MaxIm, Axum, Graphical Analysis or another graphing program.

Archive Image Directory: asteroid/rotation

Archive Image List:. freia*.fts

References: Kowal, C. Asteroids; The Astronomical Almanac

Background and Theory

While more than 9,000 asteroids are now catalogued, only a few hundred have measured rotational periods. Typical rotational periods are 5-15 hours, so it often possible to obtain an entire light curve cycle in a single evening for an asteroid near solar opposition. The amplitude of the light curve varies with size, with the large asteroids having smaller light variations since they tend to be more nearly spherical. For asteroids with diameters less than 100 km, the light curve amplitude is typically  0.1-0.3 magnitude or even larger (e.g. Harmonia, at right), depending on the degree of irregularity of the asteroid’s shape. 

Determining the rotational period of an asteroid involves careful monitoring of the apparent magnitude of the asteroid over a large enough time interval to determine the period unambiguously. This will typically involve several nights of observing using aperture photometry with nearby field stars as magnitude references.

Note: Portions of this lab will require both Camera and Photom, which you may not be familiar with.  Consult Appendix C and with your instructor for details on using these programs.

Procedure

Observing

1.    In order to measure the complete light curve in a single evening, choose an asteroid near opposition, one with a well known short period (<9 hrs) and a large light curve amplitude. To find asteroids near opposition:

a)      First, determine the approximate celestial coordinates of the Sun on the expected observing date using either Starry Night or by looking at section C of the Astronomical Almanac. To determine the opposition position, add (or subtract) 12^h to the solar right ascension and change the sign of the declination. For example, on October 15 the sun is at a = 13^h18^m and d = - 8°, so solar opposition direction is a = 01^h18^m and d = +8°.

b)      Run Megastar.  Set the date and time by selecting Options then Date-Time. Then remove all stars (Stars/Remove) and all non-Stellar objects (NSOs/Filter by Type/All Off) from the display. Click on Solar Sys/Show Asteroids to display the asteroids.  Click on Field/Center Coordinates and enter the coordinates of opposition from step 1A. Check under Field/Field Size to make sure that you are looking at a reasonable search field (about 15°). There should be several dozen asteroids displayed.  If you see only a few, check the magnitude filter under Solar Sys/Magnitude Filters.  This should be set to about 13.0.  To minimize clutter, turn off the date and time in the labels by choosing SolarSys/Label Options and turn off date and time.

c)      In general, you will want to choose low numbered (<1000) asteroids, as these tend to be the brightest (they were discovered first). Click on each asteroid. A pop-up window will appear which give the apparent magnitude. Write down all asteroids by number with magnitudes V=13.0 or brighter. You may want to use the arrow keys to move a field right/left or up/down to search for candidates.

d)      Check the Upsalla astronomical observatory website: http://www.astro.uu.se/planet/rotast_eng.html for a list of asteroid rotation periods.  The website gives the asteroid number, the period, and a code which indicates how well that period has been determined.  You may choose one with a well known (a or b code) period which is less than 8h and with a magnitude variation greater than 0.2 magnitudes that is on your observing list from step c.  Alternatively, you might want to try observing an asteroid with an unknown or poorly determined period (class c or d).  Be aware that if you choose an asteroid with a c or d code, you may not see any variation if the period is too long or the modulation of the light curve is too shallow. 

2.    Prepare an observing file (see the Appendix, Guide for Remote Observers). Specify ‘asteroids’ as the catalog. The asteroid designation must be given as a number (e.g. ‘201’). Make sure there is a relatively bright star in the same field as the asteroid to use as a magnitude reference.  Use a clear © filter to maximize sensitivity. An exposure time of 60 seconds should be adequate for asteroids with apparent magnitudes 10<V<13. For other ranges, adjust the exposure accordingly. Make certain the asteroid itself is not overexposed.  Schedule enough time to cover at least one period (typically 8 hr or so), sampling every 20 minutes.  The hastart keyword is used to schedule the observations at the appropriate time with respect to the asteroid’s transit time.  For example, if an asteroid transits at midnight, an hastart time of 04:00:00 would start the imaging at 8 pm.  Repeating this 24 times would result in an eight hour imaging run ending at 4 am.

Image Analysis

1.    Before analyzing all images, choose a few sample images to examine.  This is best done using the program MaxIm.  Use the position given in the header to display a finding chart using program Megastar.  Both MaxIm and Megastar can be run in separate windows and the image compared with the sky display.  Identify the asteroid in the field.  Notice that images taken several hours apart will show the asteroid shifted relative to the field.

2.    You can use MaxIm to blink between images taken several hours apart to show the asteroid’s motion. To do this, open all images to be added to the blink movie.  You will likely need to align your images.  To do so, use the Align tool described in the MaxIm portion of Appendix C.  Select View/Blink from the menu.  Either add the images in order one at a time, or press the Add All button and then the Move Up/Down buttons to put the images in proper order (if necessary.)  Press the OK button then press Play.  The stars should remain fixed and the asteroid should move.   

3.    Load one image of the asteroid into Camera.  Make a note of the image name.  Identify the Guide Star Catalog stars in the field by choosing Options/Mark Stars Once.  This will put a box around every star from the GSC in your field of view.  Click on the asteroid and at least three bright stars in the image.  Record the R.A. and Dec. of all these objects.  The stars will be used to perform differential photometry on the asteroid.

4.    Load a second image of the asteroid, make a note of the image name, and mark the GSC stars.  Find the asteroid again and record it’s RA and Dec in this image.

5.    The easiest way to perform photometry on a large set of images is to use Photom (part of ATFTools).  This program performs differential photometry on all of the images, comparing the variable and check stars to a calibrator star, whose magnitude is arbitrarily set to zero.  Differential photometry is done by first making a circle around a star (or asteroid or other (small) bright object) and adding up all of the ADU counts within that circle.  The sky background brightness is subtracted from this total, and the resulting ADU counts are set equal to a magnitude (in this case zero).  The magnitudes of other stars in the field are determined relative to this star by comparing ADU counts.  One problem with this method is that it is possible to choose a variable star as your comparison star.  If this is the case, then the calibrator star’s variability will contaminate the results.  To eliminate this possibility, at least two check stars are chosen, and analyzed in the same way as the variable star.  These check stars should show zero variability with time.  If these stars show variability, a new set of calibrator and check stars are chosen, and the photometry repeated.  Fortunately, in Photom, the whole process is automated, and you do not need to do all of the arithmetic by hand.

6.    Click on the Photom icon, or choose it from the menu.  (Note: Photom and Fphotom are not the same thing!)  Fill in the target object boxes, and the calibrator star boxes.  Also fill in the position of the asteroid in two different images. Pick aperture photometry parameters (the defaults are usually fine).  Make sure that the Run Now option is enabled.  Click on Ok when you are finished.  This runs Photom on your image list.

7.    After running Photom, the resulting text file can be imported into a scientific spreadsheet program (e.g. Axum, Graphical Analysis) and the data plotted.  You may need to strip out excess information from the file. Make a plot of your target (variable) star’s magnitude versus Julian Date.  Also make a plot of each of your check stars versus Julian Date.  All of the plots of your check stars should be constant with time.  Be sure to include the error bars.  The magnitudes of the errors are given in the Photom output file.  A sample plot of an eclipsing binary is shown below.

8.    Finally, to form an estimate of the period, find the times of two different locations on the graphs where the light curve is approximately the same.  For example, find two peaks of the same height, and find the times of these peaks.  Subtract the smaller time from the larger time.  The resulting time is the period.

Research Project

Most asteroid periods have not yet been measured. A very worthwhile observing project would be to choose a set of asteroids near solar opposition which could be monitored using the same technique as the above project.  To avoid choosing asteroids which already have well determined periods and light curves, the following references should be consulted:

·        Check the compilation of measured light curve parameters in the table at Uppsalla referenced above.

Check the WWW home pages of the European asteroid node (http://129.247.214.46) or the University of Maryland’s Small Bodies Node: (http://pdssbn.astro.umd.edu)