Aims. We investigate the influence of three basic factors on water production rate as a function of heliocentric distance: nucleus shape, the spin axis orientation, and the distribution of activity on a comet’s surface.
Methods. We used a basic water sublimation model driven by solar insolation to derive total production rates for different nuclei shapes and spin axis orientations using the orbital parameters of 67P/Churyumov-Gerasimenko. We used known shape models derived from prior missions to the Jupiter Family and short period comets. The slopes of production rates versus heliocentric distance were calculated for the different model setups.
Results. The standard (homogeneous) outgassing model confirms the well-known result regarding the heliocentric dependence of water production rate that remains invariant for different nuclei shapes as long as the rotation axis is perpendicular to the orbital plane. When the rotation axis is not perpendicular, the nucleus shape becomes a critically important factor in determining the water production curves as the illuminated cross section of the nucleus changes with heliocentric distance. Shape and obliquity can produce changes in the illuminated cross section of up to 50% over an orbit. In addition, different spin axis orientations for a given shape can dramatically alter the pre- and post-perihelion production curves, as do assumptions about the activity distribution on the surface. If, however, the illuminated cross section of the nucleus is invariant, then the dependence on the above parameters is weak, as demonstrated here with the 67P/Churyumov-Gerasimenko shape. The comets Hartley 2 and Wild 2 are shown to yield significantly different production curve shapes for the same orbit and orientation as 67P/CG, varying by as much as a factor of three as a result of only changing the nucleus shape. Finally, we show that varying just three basic parameters, shape, spin axis orientation, and active spots distribution on the surface can lead to arbitrary deviations from the expected inverse square law dependence of water production rates near 1 au.
Conclusions. With the results obtained, we cannot avoid the conclusion that, without prior knowledge of basic parameters (shape, spin axis orientation, activity locations), it is difficult to reveal the nature of cometary outgassing from the heliocentric water production rates. Similarly, the inter-comparison of water production curves of two such comets may not be meaningful.
Interpretation of heliocentric water production rates of comets
