3. Model of a cometary nucleus with discrete sources of outgassing
The insolation of active regions near the perihelion varies rapidly not only due to variation of the heliocentric distance but also due to changes of the subsolar point latitude. The model of the water ice sublimation for insoled active areas, applied in this study, was formulated by Sekanina (1988). In the model the absorbed solar energy is spent on sublimation and thermal reradiation only. The emission from each active region located on the surface of rotating cometary nucleus is expressed as a product of the water sublimation rate from the unit area at a subsolar point and the dimensionless relative sublimation rate, , at the Sun's local zenith distance . A total number of N sources of outgassing has been assumed. For a small zenith distance of the Sun the relative sublimation rate varies as . Its general approximation was given by Sekanina as:
where is a third order polynomial. The angle is the critical angular distance of the Sun from the active spot, beyond which the sublimation rate is negligibly low as compared with that at the subsolar point and it depends on the . In order to employ the law of sublimation rate in orbital calculations the function has been normalized to unit heliocentric distance: , where mol/km2s. Both, function and widely used in orbital calculations function have the same form:
but differs in values of the exponents m, n, k and the scale distance , which are equal to 2.1, 3.2, 3.9 and 5.6 AU, respectively. The value of the normalizing constant was chosen to fill the equation .
Assuming that the variation in orbital position is negligible during one rotation of a cometary nucleus, the rotational-averaged orbital components of the nongravitational acceleration could be described as:
where are directional cosinus of the momentum transferred to a nucleus by the outgassing from jth source. They depend on the position of active regions and on three angles: , I, , characterizing the nuclues as it was described in Sect. 2. The location of the jth discrete center of activity is measured by a cometocentric latitude , positive to the north of the equator and negative to the south, and by an angular distance from the subsolar meridian. The angle is the critical hour angle of the Sun at which the sublimation rate from the jth active region reaches minimum or drops to zero during a diurnal cycle. It is related to by: , where the cometocentric declination of the Sun is defined by: . For zones which experience days or nights one has or , respectively. The constants are given by:
where m is the molecular mass of water, is the average outflow velocity, is the outgassing area of a jth source and M is the nucleus mass.
For orbital computations the components of the nongravitational acceleration given by Eq. (4) have been transformed into the form:
The expressions for were derived as:
Lifetime of each active region was limited by time of activation and deactivation .
The expressions (6) were incorporated directly into the equations of the comet's motion (Eq. (1)) which are solved by the recurrent power series method. For the orbit improvement, the method of Sitarski (1971, 1979a, 1979b) was applied. Parameters of the spotty-nucleus model: , , I, , and could be simultaneously determined with the orbital elements in the iterative process of the orbit improvement.
© European Southern Observatory (ESO) 2000
Online publication: December 5, 2000