KBNC Asteroid Lightcurves
Between 2008 and 2011, Dr. Ted Bowell directed a Lowell research program called the "Near-Earth Asteroid Photometric Survey" or NEAPS. During that interval, Lowell astronomers observed about 300 near-Earth asteroids and obtained lightcurves and corresponding rotational periods for a significant fraction of those. The astronomers noticed that there were several observational biases at work. One of the most obvious was that they tended to abandon asteroids that had long rotational periods. The long period asteroids took many days and even weeks of observational time. If bad weather, Moonlight, or other observational problems arose, astronomers would abandon the slowly rotating asteroids in favor of those with shorter rotational periods.
By organizing several world-wide amateur astronomers into a research group, we hope to overcome the problems associated with long period lightcurves. With a world-wide observing base, we can potentially get 24-hour observational coverage on an asteroid, we can often avoid weather problems, and we can complete observations before an asteroid becomes unobservable.
The Amateur Astronomer's Lightcurve Community
Amateur astronomers have been quite active in obtaining lightcurves for asteroids. Brian Warner has been a leader in this effort. He publishes a web site dedicated to the amateur astronomer who wants to find asteroid lightcurves. If you are considering a project in this arena, Brian's web site is essential reading. Brian has also published a book, "A Practical Guide to Lightcurve Photometry and Analysis" which will provide the guidance you need to understand how perform good photometry of asteroids. Brian has also written software for lightcurve analysis. It is called "MPO Canopus". This software performs the required photometry on each image and it provides major assistance in lightcurve analysis.
The Minor Planet Bulletin is the journal in which many asteroid lightcurves are currently published. I encourage you to read some of the recent issues, not only to see the lightcurves, but to learn of the contributors, their equipment, and collaborations. More than half of the current contributors are amateur astronomers. Many of the contributors participate in formal and informal collaborations, as the need arises.
Briefly, asteroid lightcurve observers will need a good telescope on a good mount. The mount should be capable of computer controlled pointing and tracking. Observers will need a camera, preferably a CCD camera. The camera should also be computer controlled, or at least it should have a computer interface for capturing images. Our preferred image format is FITS. Most astronomical software expects FITS format.
Anyone new to this field will quickly find that the bright asteroids have been well observed and their periods are often known to a fraction of a second. That leaves the fainter asteroids for our project. We should have equipment that can provide good photometry of r' = 16 mag asteroids (and brighter) with a one minute exposure. We need a rather short exposure time because asteroids move and their signal does not accumulate on a single spot in the camera for very long. Let's extrapolate from our experience with a 60cm Schmidt telescope. Under ideal conditions, that telescope can get a barely adequate signal to noise ratio at r' = 18 magnitude in about one minute. The table below indicates, in very rough terms, what smaller telescopes might expect.
|Aperture Size||Exposure Time||Limiting Magnitude (r')|
Main belt asteroids move at about 0.25 deg/day at opposition. This rate translates roughly to 0.625 arcsec per minute. So if we take a one minute exposure, the asteroid will probably remain located on the same set of pixels. However, near-Earth asteroids typically move much faster. Motion of 2.5 deg/day is common and some move even faster. At 2.5 deg/day, the asteroid will move 6.25 arcsec in a one minute exposure. Depending on the Full Width - Half Max (FWHM) of your system, this much motion could make the signal to noise ratio too low for good photometry or even for asteroid detection.
Aside 1: Pixel Scale If your telescope has a focal length, f, and your camera has a pixel width, p, (both in the same units), your pixel scale, θ, will be
Example: The focal length of a telescope is 1.1 meters. The pixel size of the camera is 12 microns (12 x 10-6 meters). Then the angle observed by a single pixel (pixel scale) is 6.25 x 10-4 deg/pixel or 2.25 arcsec/pixel.
Aside 2: Full Width - Half Max (FWHM) Most stellar objects are so far away that they are, essentially, points. However, when they appear on your image, they have a finite size both in spatial extent and in amplitude. So if we "cut" the stellar image through its center and plot the intensity as a function of position along the cut, we get a spike. Theoretically, we know that the spike should be well approximated by a Gaussian function. Since the CCD is arranged in pixels, the spike is not a continuous function but much like a histogram. However we can still approximate it with a Gaussian function. The FWHM is the width of the Gaussian halfway between its minimum value and maximum value. The smaller the FWHM, the better. The FWHM depends on the quality of the optics of your telescope, the quality of your mount, and the weather. Good values for the FWHM for Earth-based telescopes are less than one arcsec. Amateur telescopes seldom achieve this value but they come close at 4 to 5 arcsec.
A related problem is mount motion, camera motion and telescope flexure. The mount must be stable enough to keep the image from moving over the CCD. The camera mount must also be very stable so the camera will not move in relationship to the telescope. Finally, the telescope tube must be rigid enough so that the camera does not move with respect to the asteroid image. You can see from the example above that even the smallest vibrations can cause the image to wander around the focal plane. Inexpensive telescopes, mounts, and camera mounts sometimes lead to serious image stability problems so be careful when making equipment purchases.
We will provide a generic list of asteroid targets. The target will be near-Earth asteroids arranged in order of increasing magnitude. Because we do not know, in advance, which asteroids have long periods, we will probably do some work on short period asteroids. However, when we find a long period asteroid, I will share that information will all the astronomers participating in this project and we will, hopefully, spend some time each night observing this object.
The target list will provide known periods for those asteroids already studied and it will provide a quality measure of the period. If you wish to spend some time learning the technique of lightcurve observing, you might start with fairly bright NEOs with known periods. In this way you can verify that the period you find matches the known period. Then you can gradually move to fainter asteroids as your technique improves.
Target List Details:
- The asteroid position (RA and Dec) is for 07:30 UT on the specified day. This odd time is Lowell's local midnight.
- Position uncertainties smaller than a few arcsec mean you can easily find the asteroid. If they become large, comparable to the field-of-view of your telescope, you will likely have difficulty in finding the asteroid.
- Galactic latitude indicates the angular distance from the asteroid to the Milky Way's center line. When the asteroid is within ± 20° of the Milky Way, it is generally not possible and certainly not advisable to attempt photometry. There are so many stars that the asteroid is nearly always too near a star for the photometric analysis to be accurate.
- The Rotational Period Quality (Q) is explained fully on Brian Warner's web site. In general terms, Q=3 means the period is unambiguously known within the reported errors. Q=2 means the period is in some doubt but the reported period is reasonable. Q=1 means observers have attempted to find the period but have absolutely no confidence in any result they might have found. Q=0 is not often used but we will use it to mean that no one has seriously attempted to find the period.
The fundamental observing technique is to take images of the asteroid as fast as possible for as long as possible. Of course, we must state some stopping criteria, decide how fast is reasonable, and account for other special circumstances.
When we have no photometric data available, we want to take images as frequently as possible so that an asteroid with a very fast rotation time can have its period determined unambiguously. For example, if we take images every ten minutes and the asteroid rotates every 10.1 minutes, we will see a convincing period of about 17 hours. But if we take images of the same asteroid every one minute, we will find the correct period without a problem.
The other side of this issue is that we must take pictures of long enough duration to get a good signal-to-noise ratio. If we do not have a good signal-to-noise ratio, the magnitude measured with each image will be too noisy for us to pull the period out of the data. We generally believe that a signal to noise ratio of about 50 is enough to get a magnitude good enough to analyze.
We also need to select targets that are observable most of the night, especially when we are beginning a new target. If the target is available all night, we get sufficient coverage to immediately make an estimate of the period and then we can adjust our observing cadence appropriately. Conversely, if we can only observe for an hour or two, we have little or no idea of the period and we are forced to always assume that we must be dedicated to this object.
When do we stop taking pictures? Unless we can perform the period analysis during the night, the best procedure is to take pictures of a single target all night on the first night. Our goal is to get enough images that we can get a rough estimate of the period. Then, after we analyze the first night, we will know if the exposure is long enough and if we have full phase coverage. Other considerations are important here but we will discuss these as we get deeper into the project.
If we are working on two or three objects that have very slow rotation periods, say longer than 20 hours, we can take one picture of each object every 15 minutes or so. In this way, we can make very good use of our telescope time and we can get sufficiently dense time coverage of each object.
We stop observing when we can unambiguously find the asteroid's rotational period or we are forced to stop by circumstances. In order to unambiguously find the period we must have full phase coverage. That is, when we plot the brightness as a function of time, no data gaps can exist in the lightcurve. However, circumstances may prevent us from achieving this goal. The asteroid may become unobservable because of its position in the sky or because it grows to faint. Weather may prevent us from observing until the asteroid is gone. Equipment failure may ruin our efforts. We must remember that it is important to declare an asteroid done or unobservable and move to the next target without regret.
Data reduction for each project is unique. You may be experienced in data reduction for lightcurves and have no need of this section. However, if you are not and if you choose to use MPO Canopus for your reduction tool, we have provided a sequence of video training tutorials. Please watch them in sequence.
The most fundamental tool we will use for this project is a target list. From this list we can determine which asteroids are available and in need of observation. The target list has a variable format and instructions for using it are on the page itself.
Our focus will be on long period near-Earth asteroids but we will generally not know if they have a long period until we observe them. Then, we can all begin a campaign on that single object and complete it quickly.
We may have targets of opportunity. In such cases, they may take priority over the regularly scheduled asteroids.
I believe there is no robust algorithm that we can use to decide which targets should be assigned to which observers so we will attempt to make such assignments on the fly using email as our communication media. I will assume responsibility for this task. Each of you will have to be responsible for immediately reporting the outcome of your observing of your assigned asteroids. If you have a target of particular interest, let me know and I will attempt to assign that target to you.