A possible explanation of the light curve of comet Encke

Abstract

We have constructed a theoretical model for the brightness of comet Encke as a function of heliocentric distance, R, using conservation of solar energy, and assuming that C₂ molecules are evaporated at the same rate as water molecules. An equation relating the total number of C₂ molecules in the cometary coma, and the total visual magnitude, m_v, was used to produce a graph of m_V versus log R, as a function of surface albedo, A. For comparison with the theory, we have compiled all brightness observations of comet Encke, made during this century by reliable and persistent observers. The final magnitudes adopted for the coma were those of Beyer, obtained during the apparition of 1937, 1947, 1951, 1960 and 1970. Besides these visual observations, photoelectric measurements by Mianes were used to normalize the brightness curve. For the nuclear magnitudes, measurements by Van Biesbroeck and Roemer were selected, which behaved as R⁻². The final derived values were: for the nuclear radius, r_N = 0.80 ± 0.10 km; for the Bond albedo, A_bond = 0.77 ± 0.02; for the ratio of C₂ molecules to H₂O molecules, $$\alpha = (8.2\pm2.2)\times10^{-3}$$. In order to fit the observations to the theory, the solution for a fast rotating nucleus had to be adopted. A rotating nucleus is expected, since several recent comets have shown to be rotating. The value for the number of H₂O molecules evaporated per second, measured in 1970 by Bertaux et al. as (3.1 ± 0.9)×10²⁷ molecule s⁻¹, lies completely within the error of our theoretical prediction of (4.8 ± 2.6)×10²⁷ molecule s⁻¹, providing a check on our model. The standard deviation of one visual measurement of the total magnitude with respect to the theoretical curve, is ± 0.15 mag.