Photometry of Asteroid 107 Camilla

This paper describes the results of observations of asteroid 107 Camilla intended to experimentally verify its accepted rotational period. Measurements were made of its R band magnitude at various points throughout the night in order to plot a lightcurve that could be used to derive the asteroid's rotational period. This report explains that until the quality of the seeing conditions degraded to the unusable level, we were able to obtain data that seems to agree with the previous studies of 107 Camilla's rotational period.

1. Introduction

Because of their close proximity to the Earth, asteroids make for interesting observational targets. Their relative nearness makes them highly probably candidates for manned and unmanned exploration in the near future. The orbital properties of several groups of asteroids make them rather dangerous objects, as they have high probabilities of impacting larger planetary bodies (shown by Bottke and Greenberg), including Earth, where they would certainly cause some degree of destruction with the possibility of altering the level of habitibility the planet holds for humanity.

The Yarkovsky effect discovered by Polish engineer I.O. Yarkovsky around 1900 is a phenomenon of rotating bodies springing from their rotation while being heated by radiation on one side. The rotation causes the dusk side of the asteroid to be hotter than the dawn side because it has absorbed more radiation at any given time. This results in an uneven radiation pressure from escaping thermal radiation emitted by the asteroid, and can thus result in a change in the direction of the asteroid's motion. This provides a potential way to avoid asteroid collisions with the Earth. If advance warning is given, an asteroid could be painted to change its reflectivity and thus alter its motion through the Yarkovsky effect.

We see that the Yarkovsky effect alone gives us a good reason to study asteroid rotational periods. An equally valid reason for such studies is to compute the distribution of angular momentum amongst the various compositional and orbital groups of asteroids and thus make inferrences about their origins and relationships.

The typical method for computing asteroid rotational periods is to use measurements of their magnitude over time to plot a lightcurve, and derive the period of the lightcurve as the period of the asteroid. This works well because most asteroids are not perfectly spherical, but are rather more potato-shaped and so reflect a changing amount of light towards the Earth proportional to the asteroid surface area facing the Earth at a given time. Storrs et al. have shown asteroid 107 Camilla to have a small moon, but its size and reflectivity should make its contributions to the lightcurve we observe negligibly small.

The rotational period of asteriod 107 Camilla was last computed using this technique by De Angelis in 1995. The observational equipment and timeframe of that study was of much better caliber than that available to us, and thus we hoped only to verify and not improve upon its results. This sort of work had not been previously attempted on the Great Ohio Telescope, and so we picked 107 Camilla as it seemed an easy target due to its brightness, period, and change in magnitude. 107 Camilla has an absolute magnitude of 7.12 (for asteroids this is the apparent magnitude they would have if viewed from the Sun at a distance of 1 AU away). Its rotational position and distance from Earth in mid-May gave it an apparent visual magnitude of 12.29, which was well within the bounds of easy detection by our equipment. Its previously measured and accepted rotational period was 4.844 hours, which was a short enough time that we should've been able to capture over a full rotation's worth of data during the course of a single night of observation. The amplitude of its variations in magnitude as previously measured has been between 0.32 and 0.52 magnitudes as indicated by Minor Planet Lightcurve Parameters database maintained at Harvard. This variation in magnitude should be well within the limitations of our equipment to detect.

Figure 1 depicts a sine curve of a period and amplitude based upon previous measurements of 107 Camilla's lightcurve. This curve is based on the equation:

Figure 1. The form of the sine curve we expected to observe.

2. Observations

The asteroid 107 Camilla was observed using the 0.25 meter Great Ohio Telescope on 2002 April 26 UT. The sky conditions started out clear, but degraded throughout the night as clouds moved in, eventually making data acquisition impossible. We were able to get sets of measurements during four time periods before the clouds ended our night, taking a total of 28 frames containing 107 Camilla. All of these exposures were 15 seconds long and taken in the R band. In addition, we took 9 flat fields of the dusk sky, 9 flat fields of the dawn sky, 11 zeros, and 7 darks of 15 seconds. We used values from the GOT manual of 11.8 electrons for the readnoise and 2.9 electrons per ADU for the gain in all images. The 15 second object frames were short enough to avoid the need for the telescope autoguider and problems associated with it, yet long enough to have attained very good signal-to-noise ratios had the clouds not interfered with our plans. There would have been ample time to have taken fifth and sixth sets of measurements before daylight, but the sky conditions were unusable and prevented clear images from registering on the CCD.

Figure 2 depicts the degradation of our seeing conditions due to the incoming clouds using the error values obtained from the aperture photometry of one of the stars in our field as explained in the next section, and serves as a motivation for some of the additional reductions we were forced to make because of the plague of clouds. The values shown in Figure 2 are the intenal statistical errors of our data. The first set of measurements was taken in a sky with only sparse fleeting clouds, in the second set, cloudiness was slowly increasing, and by the third and fourth salvos fogginess had rapidly taken over the sky, obscurring all but the brightest stars from naked eye observations.

Figure 2. - Error as a function of time. Small crosses represent errors from individual frames, while the larger "X"s represent the average error during each of the four flights of measurements.

3. Reductions

Data reduction was performed using several tasks of the IRAF software package in the following order:

1. Three of the zero frames were thrown out for having spikes in the maximum and standard deviation values as reported by the imstat tast, and the remaining eight zeros were combined into a single frame.
2. The seven darks were combined and then zero corrected.
3. The flats were then both dark and zero corrected and the object frames dark corrected against the combined images.
4. The flats were combined and used to perform flat-field division on the object frames.
5. Upon examining the fully corrected object frames, we decided to throw out one because it was apparently taken using the CCD's focus mode and was at a lower resolution than the rest of the images. Additionally, two of the images taken in the latest salvo of exposures were too obscured by clouds to be useful, so they were thrown out as well, leaving us with 25 object frames to analyze.
6. Aperture photometry was performed on the asteroid 107 Camilla and five other nearby stars. The apparent magnitudes of these stars as reported by the XEphem software tool is displayed in the following table:

   Star	Magnitude
   GSC 5611-0158	11.96
   GSC 5611-1049	13.82
   GSC 5611-0639	12.95
   GSC 5611-0997	10.46
   GSC 5611-0614	12.60

   The aperture photometry was carried out using the IRAF phot task. Plots of the point spread function of stars in the images gave us the FWHMPSF setting of 7 pixels. The annulus used to compute the sky brightness was set to a radius of 20 pixels and a width of 3 pixels. Since we were only concerned with the relative brightnesses of objects each frame and not between frames, we didn't attempt to compensate for the differing airmasses that exposures were taken through over the night. This procedure was carried out for each of the 25 frames.

4. Results

We constructed the lightcurve for asteroid 107 Camilla shown in Figure 3 using the difference between its magnitude and the average magnitude of the five stars in each frame. The error bars are rather large throughout, because they represent the error of all six magnitude measurements as reported by the IRAF phot task. Despite the lack of accuracy, the results are at least consistent within each group of exposures.

Figure 3. Magnitude difference between asteroid 107 Camilla and the average magnitude of the five other stars in each frame over time. Green "X"s represent the average values in each set of measurements.

The large error bars in Figure 3 aren't very desirable for accurately fitting a curve to, as they lead to several ambiguous solutions. As Figure 4 shows, the average magnitude of the five stars also modulated fairly wildly after the first set of images were taken. The third set was especially inconsistent, with variations of over a full magnitude. Ideally, we would've liked to see this value remain fairly constant over the night, as the goal in using the average of five stars was to minimize oddities that would arise from using individual stars such as differing degrees of light extinction due to a star's color. It should be noted that the values in Figure 4 do not account for the fact that the measurements were made through different airmasses. This would push the data from the beginning of the night and the end of the night even further apart, as the object was low in the sky (observed through a greater airmass) during the first set and rose to higher positions (less airmass and light extinction) in the rest of the sets.

Figure 4. As the course of the night progressed and the cloud cover increased the opacity of the atmosphere, the average magnitude of the five stars became fainter and much less steady between frames. Large "X"s represent the averages in each of the four sets of measurements.

As alternatives to the lightcurve presented in Figure 3 using the average of five stars magnitudes as a comparison, we also present Figure 6, which contains lightcurves of asteroid 107 Camilla using the five individual stars as comparisons. In the next section, we shall use these as a sort of "sanity check" for our attempts to generate offset and phase angle parameters to match the accepted rotational period of 107 Camilla to our data. The similarity in the lightcurves shown in Figure 6 shows that our results were consistent within each group of exposures.

	Figure 6. Alternative lightcurves based on comparisons to single stars.

5. Discussion

Matching the sine wave presented in Figure 1 with the lightcurve we observed in Figure 3 is a difficult task due both to the limited scope of time the measurements we took covered, the burstiness of the measurements, and the high degree of observational error. When we planned the project we expected over seven hours of good seeing to record data during, but reality gave us four hours through clouds. Despite this, we were able to map a curve of the accepted form onto our observational data. The magnitude values calculated during the fourth set of measurements may be poor due to the low counts of photons which were recorded by the CCD.

In order to best fit the curve of the desired form to our data, we wrote a C program to generate phase angle and offsets that minimized the reduced chi squared value over a given set of data points. We inputed the sine function of Figure 1 into this program along with the average magnitudes for the first three sets of data to produce Figure 7. Figure 8 was produced in the same way, except using all 20 individual measurements fromt the first three sets of data as input rather than the averages. The agreement of both the output values (3.7% in phase and 8.2% in offset) gives us confidence that these values give the near optimal fit to our data.

Figure 7. A sine function with magnitude 0.26 and period 2.422 that minimizes the reduced chi squared value over the three averages.

Figure 8. A sine function that minimizes the reduced chi squared value over all 20 observations.

	Figure 9. The sine function of Figure 8, applied to the alternative lightcurves of Figure 6.

We think that the equipment used was sufficient for the task of confirming the rotational period of 107 Camilla (and other similar asteroids), as long as the weather conditions are pleasant for observing and the time frame covered by the measurements is suitably long. We conjecture that given several nights of observation, asteroid rotational periods can even be independently calculated to a decent degree of accuracy.

Acknowledgements

I would like to thank Tom Statler for all of his guidance in performing this project, as well as the other members of the ASTR 410/510 class who made excellent companions for learning the intricacies of the equipment and the data reduction process with.

References