Forming Binary Near-Earth Asteroids From Tidal Disruptions

photometry was used. This required bright field stars present throughout all the observationsof the asteroid. Assuming that any fluctuations in seeing or atmospheric conditionswill affect the entire field of view similarly, the asteroid’s magnitude relative to the fieldstars was used to determine its brightness fluctuations. Most object’s periods were determinedfrom a single night of observing, so field stars from the same object from differentnights of observing were typically not compared.In some rare cases the technique of aperture correction was used. This is a commontechnique for photometry on very dim objects, where most of the object’s PSF is belowthe sky level, and field stars are used to estimate the total flux of an object (Howell 1989).Measurements were made on both the field stars and the object at a small aperture, andthe average difference between the small and large aperture for the field stars was addedto the measured small aperture magnitude for the object. Typically the large aperture usedhad a radius of 24 pixels, 7.32 arcsec, while the small aperture had a radius of 7 pixels,2.135 arcsecs.3.3.1 Phase dispersion minimizationThe method of period determination using Phase Dispersion Minimization (PDM), withinIRAF, was used to analyze the data set for each asteroid (Stellingwerf 1978). PDM binsthe data according to phase for a given test period, and calculates the variance for eachbin. The ratio of the average bin variance over the variance for the entire unbinned datadetermines the quality of the fit. This method is not optimized for any particular curveshape, or data spacing, which makes it well suited for asteroidal lightcurves. This fittingmethod also retains any secondary periods and also produces amplitude and epochinformation.When selecting a best-fit period for any given lightcurve, solutions were examinedand the best double-peaked period was selected. Often the best PDM fit was for a single-61