Asteroid lightcurves from the Palomar Transient Factory survey: Rotation periods and phase functions from sparse photometry

We fit 54,296 sparsely-sampled asteroid lightcurves in the Palomar Transient Factory to a combined rotation plus phase-function model. Each lightcurve consists of 20+ observations acquired in a single opposition. Using 805 asteroids in our sample that have reference periods in the literature, we find the reliability of our fitted periods is a complicated function of the period, amplitude, apparent magnitude and other attributes. Using the 805-asteroid ground-truth sample, we train an automated classifier to estimate (along with manual inspection) the validity of the remaining 53,000 fitted periods. By this method we find 9,033 of our lightcurves (of 8,300 unique asteroids) have reliable periods. Subsequent consideration of asteroids with multiple lightcurve fits indicate 4% contamination in these reliable periods. For 3,902 lightcurves with sufficient phase-angle coverage and either a reliably-fit period or low amplitude, we examine the distribution of several phase-function parameters, none of which are bimodal though all correlate with the bond albedo and with visible-band colors. Comparing the theoretical maximal spin rate of a fluid body with our amplitude versus spin-rate distribution suggests that, if held together only by self-gravity, most asteroids are in general less dense than 2 g/cm$^3$, while C types have a lower limit of between 1 and 2 g/cm$^3$, in agreement with previous density estimates. For 5-20km diameters, S types rotate faster and have lower amplitudes than C types. If both populations share the same angular momentum, this may indicate the two types' differing ability to deform under rotational stress. Lastly, we compare our absolute magnitudes and apparent-magnitude residuals to those of the Minor Planet Center's nominal $G=0.15$, rotation-neglecting model; our phase-function plus Fourier-series fitting reduces asteroid photometric RMS scatter by a factor of 3.