Context

Comets spend most of their lifetimes in the cold outer solar system and are therefore believed to be largely unchanged since the era of planetary formation (e.g., Mumma et al. 1993; Dones et al. 2004). This makes them ideal tools for studying the early conditions of the solar system as well as properties of the protoplanetary disk. Furthermore, their physical properties must be explained by any unified theory of the evolution of the solar system, and thus they are valuable for testing such theories. For a complete understanding of comets, one requires knowledge of the orbital path, rotational period, and activity, as these properties are all closely linked.

led the analysis of two different comments, both of which had a prime focus on using time-series data in order to determine the rotation (and change in rotation of the comets) .

Finding the period

In order to derive the period of the brightness variation and thus the rotation period of the comet nuclei, we superimposed all of the lightcurves from different nights with the data phased to “trial” periods and the zero phases set at perihelion. This was possible as, for both comets, the geometry of the systems did not change considerably throughout their apparitions. By adjusting the trial periods with a slider in Python, we could easily scan through potential rotation periods in real time and make rapid “better-or-worse” comparisons. While iterating through the different periods, we looked for alignment of the peaks and troughs of the lightcurves in order to determine the optimal period as well as the period for which the data were first clearly out of phase. An example of this is shown in Figure to the right for one of the comets, where the data are phased to 13.44 hr, 13.45 hr, and 13.46 hr. From this plot, one can clearly see that 13.45 hr is in phase while 13.44 hr is too short and 13.46 hr is too long.

A further search for periodicity was carried out using phase dispersion minimization (PDM; Stellingwerf 1978) and Lomb– Scargle (L–S; Lomb 1976; Scargle 1982) algorithms in Python. The former is a popular method often used to analyze non- sinusoidal lightcurves that have poor time coverage as it does not require uniformly sampled data. The method phases the data according to an assumed period before dividing the data into a series of bins. The individual variances of each bin are combined and compared to the overall variance of the data set. This process is carried out for a range of trial periods. For a true period, this ratio will yield a small value θ, and the phase dispersion minimization plot will reach a local minimum.