Water release rates, active areas, and minimum nuclear radius derived from visual magnitudes of comets—an application to comet 46P/Wirtanen

A semi-empirical photometric method is developed to estimate water release rates from visual magnitude measurements of “normal” comets of abundance ratio C2:CN ≈ 1.46 ± 0.68 for the heliocentric distance range 2.5-0.5 AU for which the aperture of the instrument, projected on the coma, is larger than the effective scale length of C2. The method is applied to comets Austin (1982 VI), Bradfield (1979 X), Bradfield (1980 XV), Bradfield (1987 XXIX), P/Brorsen-Metcalf (1989 X), Levy (1990 XX), Liller (1988 V), and 46P/Wirtanen. The water release rates are compared with those derived from observed OH or OI (6300 Å) line fluxes. The H2O release rates estimated from visual magnitude measurements may have typical errors of about 2–4, while maximum errors may be as high as a factor of 10. The total active area (AA) on the sunlit side of the nucleus has been estimated from derived water release rates combined with theoretical estimates of H2O flux rates (molecules cm−2s−1) by vaporization theory for an assumed nuclear visual albedo pv = 0.03. The constraint AA ≤ 2π(RN)2 has been used for estimation of the lower limit of the nuclear radius of a comet. For comet 46P/Wirtanen, the variation of water release rates with heliocentric distance (r), total active area, lower limit of nuclear radius, and fractional active area are: Q(H2O) = 1.8 × 1028r−7.0±0.4mols−1, 6 ± 3 km2, 1.0 km, and 0.15, respectively.