Belgian amateur astronomer Tonny Vanmunster, seen here in his private observatory, detected the exoplanet TrES-1 as it transited its host star. He has also detected the transit of another exoplanet, HD 209458b. Courtesy Tonny Vanmunster, CBA Belgium Observatory.

Achieving photometric accuracy to better than 1 percent for bright stars does not require a gigantic telescope or a remote mountaintop observatory, but it does require careful attention to atmospheric scintillation (twinkling), random noise, and CCD instrumental noise. For a counting process such as detecting photons, the random noise is proportional to the square root of the number of photons collected. As a result, an astronomer must collect at least 10,000 photons to make a brightness measurement with 1 percent uncertainty. Even for small telescopes, scintillation rather than random noise usually sets the accuracy limit for the relatively bright stars with known planets.

Because many observers tend to overlook the importance of scintillation noise, Dorian Bohler coded a calculator that we include in the Tools section of our Web site that might be helpful. It allows astronomers to estimate the expected amount of scintillation noise for their particular observing conditions. Experimenting with this calculator will show the user what conditions minimize scintillation.

Editor's note: The scintillation calculator mentioned above no longer appears to be available. But here are some scintillation noise tables that might be helpful as well as the airmass and scintillation calculator available on our website. Laurent Corp has also written an application that adds the airmass to the old and new AAVSO formats. See Airmass Calculator 1.3.

Other suggestions for how to obtain accurate photometry:

• Image the star with the suspected planet along with a comparison star that has similar brightness and color. Keep both stars located on the same few pixels for at least several times the expected transit duration. Since there are relatively few bright stars, you will need a field of view that is about 1/2 degree across
• Take many CCD images of the field of interest at intervals much less than a transit duration, with the precision of each measurement being less than the expected transit depth. Think of precision as the repeatability of a given measurement.
• Try to obtain exposures long enough that brightness variations due to atmospheric scintillation are not the dominant source of error in each measurement. But at the same time, be careful not to saturate the CCD in just one or two seconds. Scintillation will limit the usefulness of these short exposures. A broadband filter or perhaps a moderate amount of defocusing will help by allowing you to make longer exposures.
• Take many well-controlled calibration frames that do not introduce additional errors. This procedure requires taking many bias, dark, and flat-field frames. The bias frames allow you to determine the added bias signal of your particular CCD so you can subtract it from your photometric measurements. The dark frames enable you to subtract random thermal noise. With the flat-field frames you can subtract any uneven illumination of each pixel in the CCD chip.
• Consider CCD limitations such as nonlinearity, the point where certain pixels become saturated and can no longer register additional photons. For example, our SBIG ST-7E camera becmes non-linear above 20,000 electrons, so we have to limit the digital counts in any single pixel to 8,000 or less. We measured the linearity of our CCD by making a graph [image in S&T article]. We strongly recommend that each observer make a similar plot for his or her particular CCD detector.