\documentstyle{article} \textwidth= 14truecm \textheight= 22truecm \hoffset = -1.5truecm \voffset = -2truecm \parindent 0mm \pagestyle{empty} \begin{document} {\bf Abstract} \medskip The physical and dynamical evolution of Jupiter family comets are analysed separately and then combined into a model of the long-term coupled evolution. Dynamically, Jupiter family comets are distinguished by their short periods ($< 20$ years) and by a motion governed by frequent encounters with the planet. These encounters could temporarily transfer a comet into a satellite-like orbit around Jupiter. These ideas lead us to formulate an observational strategy to search for comets encountering Jupiter. A first campaign allowed us to put upper limits on the size of the Jupiter family population. Described is a model for the evolution of a porous cometary nucleus, originally composed of dust, amorphous water ice and trapped CO gas in the ice matrix. The model is applied to the study of the long term physical evolution of Jupiter family comets. After a few revolutions in a Jupiter family orbit the crystallization of the amorphous ice in the cometary interior settles to a slow rate and total crystallization of the nucleus is predicted to occur in a time scale at least as long as their expected lifetime in the family. These ideas are then gathered together to develop a model of the coupled dynamical and physical evolution. Comets can be in two different states: active and inactive or dormant (i.e., comets with a surface totally covered by a dust mantle). The total time the observable comets stay in the Jupiter family is of the order of $10^4$ yr; only during $~ 1/5$ of this time are the comets active, while the rest of the time they are in the dormant state. The results presented in this thesis emphasize the important interrelation between the processes that govern the evolution of Jupiter family comets and the necessity to treat them as a joint process. \vfill\eject {\bf Introduction} \medskip In the past, comets aroused admiration and fear. Admiration because of their beauty in the night sky. Fear because of their unpredictable apparition and behaviour. After several hundred years of cometary research, ordinary people and scientists still share the same feelings. Planetary researchers ``admire'' comets because of the clues they hide about the origin of the solar system. But they also are ``afraid'' of these objects because of the vast research tools that are necessary to use in order to understand their behaviour. Comets are such complex systems that scientists working in fields as far apart as thermochemistry and hamiltonian mechanics are looking to them. To enumerate a few fields related to the modelling of cometary evolution, we mention: plasma physics, hydrodynamics in rarefied media, diffusion processes in porous media, thermochemistry at low and ambient temperatures, collisional and break-up processes, hamiltonian and non-hamiltonian mechanics. Regarding the observational and experimental approach to understand these systems, astronomers make use of several research tools like: visual and UV spectrophotometry, radio astronomy at mm and cm wavelength, radar, wide- and narrow-field imaging, photography, {\sl in situ} measurements of physical and chemical characteristics, laboratory studies of cometary-like materials, astrometry and orbit determinations, numerical integration algorithms, etc. Other possible extensions to the list of research fields related to comets are e.g. the ecological and geophysical consequences of catastrophic events like the impact of comets onto the Earth or the interaction with the Earth's atmosphere. One could figure out that it is impossible for a single person or research group to deal with all these problems, so the tendency has been to split the cometary research into small sub-fields and try to solve the different problems independently. An obvious drawback of such a strategy is the fact that one tends to disregard the interrelation between different processes. We must never forget that we are aiming to understand the evolution of a comet as an entity. In that entity there are not closed ``rooms'' for the different processes, it is a ``house'' with a lot of connecting ``doorways''. An aim of this thesis is to stand at the center of the ``house'' (the problem of cometary evolution) and look into a few ``rooms'' (processes) and their connecting ``doorways'' (their interrelations). The first problem to face is that not all the comets are similar from the evolutionary perspective. Comets are classified in two groups with respect to their orbital periods ($P$): long-period comets ($P > 200$ years) and short-period ones ($P < 200$ years). The former group is believed to correspond to comets that come directly from the Oort cloud or that have made a few passages close to the Sun since their origin. The short-period comets are further classified in two groups: the intermediate or ``Halley-type'' comets ($20 < P < 200$ years) and the Jupiter family comets ($P< 20$ years), hereafter referred to as JF comets. The processes governing the physical evolution of every comet while it is close to the Sun could possibly be fitted into a single picture, the competing action between processes like: sublimation, recondensation, phase transition, dust mantling and the hydrodynamics of escaping gases. On the other hand, the time-scale for physical evolution of long-period comets is much longer, and there are other processes that matter when the objects dwell in the Oort cloud, e.g. radiogenic heating, cosmic ray bombardment and heating by passing stars or supernovae. Regarding the dynamics, the evolution shows more remarkable differences between the groups. Long-period comets are gravitationally affected by molecular clouds, passing stars, galactic tides; and when they come close to the Sun by very fast encounters, especially with the outer planets, and the jetting effect due to the escaping gases (the non-gravitational forces). The two short-period groups can hardly be analysed with the same dynamical tools. The differences are already stated in their names: the dynamics of JF comets is mainly governed by frequent encounters with Jupiter and the evolution is typically chaotic on a short time scale. Halley-type comets have more sporadic, generally distant, encounters with Jupiter (if they have at all) for long periods of time and the influence of the outer planets is manifested in their secular perturbations. Due to the precession of the nodes they could become planet node-crossers and the dynamics could then resemble more the Jupiter family type. The differences between the two short-period groups lead to a refinement of the definition of the JF that will be discussed later. We decided to concentrate our research efforts on a single and consistent group of comets, analysing their evolution with a wide perspective: both the dynamical (Papers I and II) and physical aspects of them (Paper V). The dynamical studies led us to formulate a search strategy for JF comets that makes use of the peculiarities of the motion of these objects (Paper III). Although the first search carried out in March-April 1992 was unsuccessful (i.e., we could not discover any new comet), the negative result enables us to set limits to the size of this population (Paper IV). Finally, we try to make use of the knowledge acquired in the previous studies, in a simulation of the combined physical and dynamical evolution of JF comets (Paper VI), where we estimate the lifetimes and the steady state distribution over perihelion distance. \bigskip {\bf Paper I} \medskip As mentioned above, close encounters with Jupiter play an important role in the cometary evolution since they govern the dynamical replenishment of the short-period comet population, sending comets from the outer to the inner solar system and vice versa. A kind of encounter that deserves special attention is the case of temporary satellite captures (TSC's), when the comet is gravitationally bound to Jupiter for a certain period. TSC's are of interest as possible routes by which stable captures might occur, e.g. in the presence of a dissipative medium. Most of the comets that experience TSC's have a distinctive property: large-$q$, low-eccentricity orbits near the 3/2 resonance with Jupiter ("quasi-Hilda type" motion; see Kres\'ak 1979). Until recently three members of this group had been recognized. On Jan. 2, 1989, a new member was discovered: comet P/Helin-Roman-Crockett (hereafter: HRC). We have performed numerical integrations of the motion of comet HRC to analyse the short- and long-term evolution of its orbit and to discuss the similarities with the evolutions of other quasi-Hilda type comets and the possible interpretations of these similarities. Although there are some uncertainties due to the chaotic nature of the evolution, with the latest orbit available we found that comet HRC remained gravitationally bound to Jupiter for 11.53 years (Dec. 1973 to July 1985) and it performed two revolutions in the prograde sense around the planet during that interval, with a minimum distance to Jupiter of 0.018 AU. Regarding the long-term evolution, we conclude that comet HRC shares the behaviour of the other quasi-Hilda type comets in that it repeatedly switches between the regions just outside and just inside Jupiter's orbit. The region near the 3/2 and 4/3 resonances seems preferred for the interior sojourns. A very deep and long-lasting encounter was found around 2075 AD, with a beautiful flower-like trajectory in the jovicentric frame (Fig. 1). In view of the great similarities between the orbit of HRC and another quasi-Hilda type comet (P/Gehrels 3), we looked for an explanation. Both comets left their TSC's nearly one jovian revolution apart when the comets were near the Lagrangian point $L_2$ interior to Jupiter and the planet was close to perihelion, so that the comets entered a heliocentric motion with a nearly transverse velocity smaller than the circular velocity, i.e., near the aphelion point. A similar pattern is observed in the other two cases of recent TSC phenomena. By a simple calculation we explained the similarities of the apsidal lines, semimajor axes and eccentricities of such comets. Tentative physical, observational or dynamical explanations of these similarities are discussed in the paper and a yet unexplored feature of TSC dynamics is favoured as the most plausible explanation. \bigskip {\bf Paper II} \medskip In Paper I we see that there are still several unexplained aspects of the orbital evolution of JF comets that deserve further inspection. We thus decided to carry out a numerical integration of the orbital evolution of all the observed JF comets to create a data base that could be used to analyse the characteristics of this sample of objects. Due to inherent errors of numerical methods and to the chaotic behaviour of the majority of JF orbits, it is not possible to draw definitive conclusions about the particular evolution of any one object, but we can use these integrations to extract statistical information on a sample of objects that resembles the evolution of the observed population. The integrations presented in Paper II correspond to a time span of 2000 years centered at the present. 143 JF comets were included, i.e., all the observed JF comets up to 1990. A clear concentration of comets towards smaller perihelion distances at present compared to the distribution in the past and future was observed. This effect had been seen before and explained (Fern\'andez 1985) as an observational bias because comets tend to be discovered when they get low-$q$ orbits. Similar minima were found for the semimajor axis ($a$), the eccentricity ($e$) and, surprisingly, the inclination ($i$). Histograms of the distribution of comets over perihelion distance ($q$) showed that the present distribution, peaked around 1-2 AU, diffuses already within a few hundred years, and we get a much flatter distribution over the 1-5 AU range. Based on a shorter integration data set (Carusi {\sl et al.} 1985), Fern\'andez (1985) found a past-future asymmetry in the cometary $q$-distribution (i.e., a larger number of comets with greater $q$ in the past than in the future). Although this asymmetry was observed in our data set for large-$q$ comets, it was not present for comets with $q<1.5$ AU at a 1-$sigma$ confidence level (see Fig. 2). Assuming a steady-state population, he explained the asymmetry as the consequence of physical loss, and estimated the active lifetime as 1000 revolutions for comets with $q<1.5$ AU. From our negative finding and the fact that Fern\'andez's sampling times in the future coincide with local minima of the curve, we conclude that the previous value could only be used as a lower limit to the active lifetime. Then, the independent estimate presented by Kres\'ak (1981) based on the statistics of comets lost and disappeared seems to low. Our data, unfortunately, does not allow to set any further limits. The analysis of the discovery circumstances of JF comets and their evolution shortly before discovery shows that we are reaching completeness of the sample of objects with $q<1.5$ AU, because: i) except for the latest 20 yr, the discovery rate of comets with $q < 1. 5$ AU has been decreasing since the end of the last century, and the latest discoveries mostly correspond to comets with $q$ close to the upper limit; ii) the fraction of comets that have jumped to lower $q$ prior to discovery at present is twice that at the end of last century. We thus conclude that we are reaching completeness of the population of ``stable'' orbits in the $q<1.5$ AU range and approaching a state where we are left to discover only comets that have just entered the region. The distribution of number of encounters with time shows a clear peak starting in the present century and extending for a few centuries to come. To explain this feature two possible alternatives were considered: the shift of the $q$-distribution to lower values at present would produce an increase in the number of encounters due to a shorter orbital period for low-$q$ comets, but the effect seems not to be large enough. As a second alternative, a combination of a physical and observational selection effect was proposed -- the encounters are associated with jumps in $q$ and perhaps partial or total blow off of the dust mantles. Consequently, a brightening of the comet would increase its discovery chances. In view of the dynamical differences between members of the JF (e.g., a few comets have no close encounter with Jupiter for the whole span of our integrations), we decided to further constrain the definition of the JF by using some more dynamical information. In this respect, the Tisserand parameter $T$ , a quasi-constant in the Sun-Jupiter-comet system, seems to be appropiate, since the $T$-distribution of the observed population shows a concentration of values $< 3$ and this is largely mantained during the integrations. For the rest of the thesis we consider a comet to be a member of the JF if its period is $<$ 20 yr and if it has $2 < T < 3$. \bigskip {\bf Papers III and IV} \medskip In Paper I we showed that comets could be temporarily bound to Jupiter for a period of several years. Meanwhile, in Paper II we proved that many new comets have been discovered just after an encounter with Jupiter; and we stressed the importance of close encounters with Jupiter in understanding both the dynamical and physical evolution of JF comets. A natural consequence of these reasonings is to ask ourselves ``why don't we look for comets during close encounters with Jupiter when they are in such an interesting dynamical phase rather than wait to find them afterwards?''. In Paper III we estimate the feasibility of this proposal and develop a search strategy to distinguish comets during an encounter from other moving objects in the field. From the numerical integration data base presented in Paper II we computed the space distribution of JF comets in a rotating-pulsating frame, with the instantaneous distance Jupiter-Sun as unit distance and the instantaneous jovian angular velocity as the velocity of rotation. The density distribution shows a clear peak at Jupiter's position, meaning that comets spend a considerable time close to the planet, as compared to any other place in the inner Solar System. Although in the ten times longer integrations presented in Paper IV the peak around Jupiter gets less pronounced, the number density in Jupiter's neighbourhood is still higher than at any other place in the inner Solar System (see Fig. 3). The low relative encounter velocity of JF comets leads to a clear separation in velocity space between comets undergoing an encounter and asteroids that are in the same region of the sky. If the observations are made close to Jupiter opposition and one tracks the telescope on the planet, asteroids and stars will show up as long trails (but in opposite directions), while comets encountering Jupiter will show much shorter trails. We then have a very straightforward method to pinpoint comets during a close encounter. A first search for comets encountering Jupiter was conducted in March-April 1992 with the European Southern Observatory 1m Schmidt telescope and the results are presented in Paper IV. We covered a field of 16 deg. 2 by 16 deg. 2 around Jupiter down to a limiting V--magnitude for stationary objects of 21.4, corresponding to a limiting absolute V--magnitude of 13 for slowly moving objects. No object down to this limiting magnitude was found. From an extended version of the integrations data set described in Paper II we estimated the probability of finding a given comet at any time within a certain distance of Jupiter (named the neighbouring probability). It was shown that for comets with $q > 1.5$ AU (the supposed vast majority of the JF population) the probability is almost independent of the perihelion distance of the objects (see Fig. 4), which removes an important source of uncertainty from the final estimate of the size of the Jupiter family. Using the results from this modelling together with the negative results of the search, we applied Poisson statistics to set an upper limit to the number of objects in the Jupiter family. Within the Jupiter family we distinguish two classes of objects: the active comets and the inactive or ``dormant'' ones (i.e., comets with a surface totally covered by a dust mantle). To interpret the results we analysed two alternative cases: i) all comets are inactive at $~$ 5 AU from the Sun; and ii) there is a contribution of coma in the magnitude estimates for at least a certain fraction of comets. In the first alternative, and assuming that dormant comets are dynamically similar to the observed sample of JF comets from which the neighbouring probabilities are extracted (see Paper VI for a justification of this statement), we were able to set upper limits to the combined population of active plus dormant comets, since these objects would be indistinguishable at $~$ 5 AU. We concluded that the total number of Jupiter family comets both in the active and dormant phase brighter than absolute nuclear magnitude 13 is less than 210 -- a limit obviously holding for the individual populations too. This estimate can be transformed into an estimate of the total size of the JF population if a power law magnitude distribution with an index $s$ is assumed. For absolute nuclear magnitudes brighter than $H_N^B=18$ in the blue region (corresponding to a nuclear radius of 1.3 km for an albedo of 0.03), the upper limits for the combined and individual populations of active and dormant JF comets are 3900, 10000 and 27000 for $s=$ 0.3, 0.4 and 0.5, respectively. To test the possibility of coma contamination in the observed magnitudes of comets at $~$ 5 AU we looked into the scanty available data on observations of active JF comets at large heliocentric distances. We found that roughly half of the comets appear nuclear at distances $<=$ 4 AU and the other half are brightened by typically 1.5 magnitudes due to comae. Correcting for this fact, the upper limits to the number of active JF comets brighter than nuclear magnitude 13 become 110, 80 and 60 for $s=$ 0.3, 0.4 and 0.5, respectively. For absolute nuclear magnitudes brighter than $H_N^B=18$, the upper limits to the population of active JF comets are 2000, 4000 and 8000 for the three indices, respectively. Under the assumption of inactivity of comets at $~$ 5 AU, the upper limits derived from our search are still too high when we compare with previous estimates of the population size of the active members of the JF. However, under this assumption the limits also correspond to the combined population of dormant plus active comets; in that respect the results are much more relevant since very little is known about the total population of the JF. Under the assumption of an important contribution of active comets to the population of objects encountering Jupiter, the upper limits set by our search are comparable to previous estimates. The big advantage of our estimate relies on the fact that the number of comets encountering Jupiter is not dependent on the particular shape of the distribution of $q$. Therefore, in order to estimate the total size of the JF population we do not have to make use of an uncertain $q$-distribution as the other estimates did, nevertheless we do also make use of an ill-defined nuclear magnitude distribution. The search strategy described in Paper III, and first applied in Paper IV, can be repeated at every Jupiter opposition. Since the duration of encounters is on the order of a year and the almost constant number of Jupiter vicinity visitors must be continuously replenished by new comets, new searches would improve the statistics and either reduce the upper limits or estimate the size of the JF population when comets would be found. \bigskip {\bf Paper V} \medskip Although the prevailing ideas about the physical characteristics of cometary nuclei are still based on the ``dirty snow ball'' model presented by Whipple in 1950, major advances have been made, such that, e.g., people start to talk about a ``snowy dust ball'' as the new cometary nuclei paradigm. But not only has dust became a major component; our knowledge of the ``snow'' characteristics has also gone through an important evolution. We now believe that the original water ice in the cometary nuclei was in the amorphous phase, and due to different heating processes it crystallizes with a consequent release of large amounts of latent heat. The nuclei are supposed to have porous structure with very low density where gases could flow up and down in the interior. These ideas have led to a new area of cometary research: modelling of the thermochemical evolution of cometary nuclei, where hydrodynamics in porous media plays a crucial role. Several papers have been published on this subject (see Rickman 1991 and Paper V for an account of them); however, numerical modelling of the cometary nuclear processes over long periods of time and exploration of the unconstrained ranges of inaccurately known yet influential parameters still has not advanced very far. New experimental results related to the physical characteristics of the material components and new ideas about several aspects of the modelling encouraged us to make a new attempt to analyse the physical evolution of JF cometary nuclei over time scales comparable to their lifetime. The new model is described in Paper V where we present results concerning the evolution of JF comets and make comparisons with previous models. Our model of the cometary material includes a porous solid matrix and vapour filling the pores. As basic constituents of the solid matrix we consider three omnipresent species: a ``dust'' component, made up of non-volatile substances; a water ice component, that exhibits two phases: amorphous and crystalline; and H$_2$O vapour. We do not consider any ``dust mantle'' in the sense of a surface layer of finite thickness devoid of ice. In addition to the above, we include one substance more volatile than H$_2$O, CO, which may occur in three different forms. First, the amorphous ice holds a certain relative amount of the volatile as ``trapped gas''; secondly, upon crystallization, this is released into the pores as vapour; and thirdly, at low enough temperature, the vapour condenses into an additional ice component of the solid matrix. We improved on the earlier models by accounting for the state of near saturation attained by the vapour inside the nucleus, by including a separate treatment of an unsaturated surface layer from where most of the escaping water flux comes and by explicitly including the erosional velocity of the surface. As far as physical parameters are concerned, our basic improvements on earlier models were: 1) the allowance for an important or even dominant non-volatile component of the solid matrix; 2) the representation of this matrix as an aggregate of micron-sized core-mantle grains; 3) the adoption of a very low thermal conductivity of the amorphous ice mantles, based on recent experimental results where it was found a decrease by several orders of magnitude of the thermal conductivity of amorphous ice with respect to the standard value used in all earlier models; and 4) the existence of CO trapped gas in the amorphous ice with a correct account of the energetics of gas release and the allowance for condensation of CO ice below the crystallization front. We first made comparisons of the results coming from our modelling with earlier studies (e.g. Espinasse {\sl et al.} 1991, Prialnik 1992). To make the comparisons meaningful we had to taylor our comparison models to fit the parameters chosen by the other authors as closely as possible. The differences were important and they could be understood in the framework of the improvements described above. We defined a ``standard'' nuclear model with the best guesses of the many unknown or poorly known parameters, and we ran it for 500 years in a typical JF orbit ($q=1.5$ AU, $Q=6$ AU), a time comparable to $~$ 10 % of the duration of a dynamical visit to the observable JF (Lindgren 1992) or their expected active lifetime (Paper VI). The long-term evolution of the model is illustrated by Fig. 5. The CO bursts (associated with crystallization spurts, not clearly visible on the scale of this plot) are notorious in the first revolutions, but then, they gradually evolve from the sharp spikes to a much more subdued appearance. The CO ice always starts a few meters below the crystallization front, and this creates a very unstable region where trapped CO gas is being released, then diffuses in- and outwards, recondenses and sublimates again during quiescent periods of crystallization. The upper plot corresponds to the H$_2$0 flux (full-drawn curve) and CO flux (dotted curve). In the lower plot we find, from top to bottom: total radius of the nucleus, radius where the amorphous ice is half the original value (dotted curve), radius of the uppest CO layer, radius of the lowest CO layer. The lower $x$-axes in both plots are expressed in years, while the upper ones in number of revolutions starting at aphelion. A set of variant models were run to explore the consequences of some of our assumptions. Variations of the following parameters were considered: dust to ice ratio, porosity and amorphous ice conductivity. We note the broad similarity between our standard and variant models, although some differences in the {\sl a priori} expected direction are observed. The ``standard'' model was also run in a capture scenario, where the comets first stay for 20 revolutions in a high-$q$ orbit ($q=$ 3.5 and 5.5 AU) and then are captured into an orbit with $q=1.5$ AU. The rate of CO outgassing exceeds the perihelion H$_2$O outgassing rate by two orders of magnitude in the former case and five orders in the latter. Nevertheless, one has to be cautious to interpret this as a CO-driven activity for large-$q$ comets, since a more favourable insolation geometry at perihelion would lead to a much higher H$_2$O flux compared to the average insolation assumed in our model. Upon capture, we could have the crystallization zone several hundred meters below the surface and the evolutionary pattern in the new orbit looks very similar to that of the standard model at a similar stage. We conclude that the comet basically behaves in accordance with the burial depth of the crystallization zone for any given set of physical parameters, independent of which previous orbital evolution has led to this state. Concluding on the behaviour of Jupiter family comets from the present results, we find that within the framework of our assumption of an initially CO-rich amorphous ice and an important dust component, the complete crystallization of a sizeable nucleus with an initial radius of several km should take $~ 10^4$ years. This means that Jupiter family comets with our assumed properties should still retain their CO, although in most cases buried deep below the nuclear surface. \bigskip {\bf Paper VI} \medskip After analysing several aspects of the dynamical (Papers I and II) and physical (Paper V) evolution of JF comets, it is clear that these two processes are closely related. Both have important consequences in the interpretation of the observational material and, even, in the definition of a search strategy for new members of the JF (Papers III and IV). It is then wise to consider the evolution as a unique process and combine the information gathered in the previous studies into a simulation of the physico-dynamical evolution of this population of objects. In Paper VI, we describe a method to simulate the coupled process based on the analysis of the observed sample of JF comets. The work is a continuation of a previous attempt (Rickman {\sl et al.} 1992), where the dynamical modelling was done with an stochastic approach. In this paper, we developed a more realistic dynamical modelling, by numerically integrating all the observed Jupiter family comets and 3 variant orbits until they leave the family. The sets of variant orbits were created from the observed orbits by keeping the action variables ($a$, $e$ and $i$) and exchanging the angular elements ($omega, Omega$ and $M$) between the objects. This represents an attempt to increase the number of simulated objects while keeping the dynamical characteristics of the observed population of comets. Regarding the physical modelling, the nucleus is taken to be a homogeneous sphere, whose surface is partly fresh and outgassing, and partly covered by dust. The processes governing the physical evolution are described as: {$bullet$} during the time a comet smoothly changes its $q$ its previously mantled areas remain unaffected, but the fresh area gradually becomes mantled; {$bullet$} when a jump occurs into an orbit with a lower $q$, some of the previously formed mantles are removed and the corresponding area returns to the fresh (i.e., `active') state; {$bullet$} an upward jump in $q$ has no effect on previously formed mantles. In addition, outgassing from the active surface leads to mass loss that could shrink the mass to zero, we then refer to a meteoroidal end state, since then the comet would be physically dispersed into a meteor stream. If dust mantling proceeds to a stage where only a tiny fraction of the surface is active, the comet becomes dormant, but it could possibly be reactivated by a downward jump in $q$ and a consequent dust mantle blow off. If the comet is active, however, this does not immediately imply that it would be detectable as an active object. We estimate the chances of detection of a comet by computing the total magnitude at perihelion from the water production rate (an output from our modelling) and then comparing it with the empirical detection limiting magnitude set by the present observational techniques. Physical parameters like the dust mantling rate and the gas fluxes were taken from models of these phenomena that appear in the literature. A wide range of possible models for the blow-off fraction in a downward jump were tested, although no significant differences were observed. The combined physico-dynamical evolution of almost five hundred objects were computed for three different initial radii: $R_o=1.5$, 3 and 5 km. The simulations started with the comet outside the JF and a completely free-sublimating surface and proceed until the object was either dynamically ejected from the family or dispersed into a meteor stream (only relevant for small comets). The total time span in the Jupiter family (named a visit), is shown to be on the order of 13000 yr for our modelled population. The comets spend only $~ 1/5$ of the time in the active state, while the rest of the time is spent in the dormant phase. The active lifetime is anticorrelated with the radius, since the dust mantling rate is higher for bigger comets. The time until the comet ends its activity is slightly longer than half the total lifetime (the latter is, typically, the time it takes to reach the overall minimum perihelion distance). The comets thus tend to be active while still decreasing their $q$, but rapidly become dormant after reaching the overall minima. A steady state picture of the population was created by randomly picking the physical and dynamical characteristics for each object at any point of their evolution and constructing the distribution of the desired parameter using the whole sample of objects. In Fig. 6 we present the $q$-distribution of the number of objects for the three initial radii: 1.5, 3 and 5 km and a combined population using a mass power law distribution with index 0.7. From top to bottom, the curves correspond to total number of comets (both active and dormant), number of active comets and number of detectable ones. The overall shape of the total number of comets is approximately the same for the three radius and reflects the particular dynamical evolution of our modelled sample and the bias towards small-$q$ orbits of the observed sample. However the contributions of active and detectable comets present remarkable differences. The ratio between active and total numbers is larger for the smallest radius and the difference is most pronounced for low-$q$ orbits. For $q >= 1.5$ AU most of the active comets are not detectable with the present techniques. The combined population pretty much resembles the 1.5 km case. The fraction of active area was shown to be quite low (typically less than 10 %, except for small comets in low-$q$ orbits), in accordance with the scanty observational measurements of this parameter. An analysis of the distribution of total absolute magnitudes showed that it largely echoes the size distribution of the observed population, but the effect of the spread in the fraction of active area has a non-negligible influence on the combined magnitude distribution involving different radii. The estimates of the mass power law index from the observed total magnitude distribution that appear in the literature thus have to be taken with caution, especially if a very narrow range of mass index is given. Finally, the results presented in this paper show the importance of a proper account of the dynamical evolution, since the steady state distribution presented in our previous paper (Rickman {\sl et al.} 1992) was largely altered with the present more realistic model. The method described here is still subject to several improvements, especially the possibility to allow for the tendency of comets to revisit the Jupiter family several times before being finally ejected; and the consideration of other physical phenomena like splitting and the brightening due to high CO fluxes at large heliocentric distances (see Paper V). \bigskip {\bf Future Work} \medskip There are several directions where the work presented in this thesis could (and will) be continued. The cometary search programme described in Papers III and IV is now under its second campaign and a better estimate of the size of the JF will be obtained. The fast development of the observing techniques (e.g., use of large-field CCDs) could give an important impulse to our search strategy. Regarding the dynamical evolution, a future task would be to further extend the integrations of observed orbits until they are finally ejected from the Solar System or send them back to an hypothetical transneptunian source region. The comets then would make several visits into the JF, and hopefully, the bias towards low $q$ would disappear. The thermochemistry model described in Paper V can be applied to different scenarios, e.g. the long-term evolution due to radiogenic heating, or combined with models of the formation of a dust mantle to properly simulate the evolution of a JF comet. A full 3-dimensional code would be desired to account for the irregular cometary shape and the influences of topography on the insolation. Some of the observational predictions presented in Paper V (e.g., high CO flux at large heliocentric distance) could lead us to formulate observing programmes to test this hypothesis and learn more about the trigger mechanisms for the sometimes erratic activity of JF comets (e.g. ultraviolet spectroscopy of recently captured comets). All this information could then be included into an increasingly complex model of the coupled physical and dynamical evolution on the lines described in Paper VI. \bigskip {\bf References} \medskip Carusi,A., Kres\'ak,\v L., Perozzi,E., Valsecchi,G.B., 1985, {\sl Long-Term Evolution of Short-Period Comets}, Adam Hilger,Bristol,UK Espinasse S., Klinger J., Ritz C., Schmitt B., 1991, ``Modelling of the thermal behaviour and of the chemical differentaition of cometary nuclei'',{\sl Icarus} {\bf 92}, 350 Fern\'andez,J.A., 1985, ``Dynamical capture and physical decay of short-period comets'', {\sl Icarus} {\bf 64}, 308 Kres\'ak, \v L., 1979, ``Dynamical interrelations among comets and asteroids'', in {\sl Asteroids,} T. Gehrels (ed.), Univ. of Arizona press., p. 289 Kres\'ak, \v L., 1981, ``The lifetimes and disappearance of comets'',{\sl Bull. Astron. Inst. Czechosl.} {\bf 32},321 Lindgren, M., 1992, ``Dynamical timescales in the Jupiter family'', in {\sl Asteroids, Comets, Meteors 1991}, A. Harris, E. Bowell (eds.), Lunar Planet. Inst., Houston, p. 371 Prialnik D., 1992, ``Crystallization, sublimation, and gas release in the interior of a porous comet nucleus'', {\sl ApJ} {\bf 388}, 196 Rickman, H., 1991, ``The thermal history and structure of cometary nuclei'', in {\sl Comets in the Post-Halley Era}, R.L. Newburn Jr., M. Neugebauer, J. Rahe (eds.), Kluwer Acad. Publ., p. 733 Rickman, H., Bailey, M.E., Hahn, G., Tancredi, G., 1992, ``Monte Carlo simulations of Jupiter family evolution'', in {\sl Proc. of the International Workshop on Periodic Comets}, J.A. Fern\'andez and H. Rickman (eds.), Universidad de la Rep\'ublica, Montevideo, Uruguay, p. 55 \vfill\eject {\bf Fig. 1.--} Trajectory of comet P/Helin-Roman-Crockett during the encounter with Jupiter around 2075. The planet is at the origin, and a rotating frame has been used in which the Sun is always on the negative $x$-axis. Arrows indicate the direction of motion. \smallskip {\bf Fig. 2.-- a)} Number of comets with $q$ less than certain limits as a function of time. {\bf b)} Enhancement of Fig 4a for $q<1.5$ AU. The connected dots were obtained with the same sample time as F85. c) Average number of comets with $q<1.5$ AU using a bin width of 250 yr. \smallskip {\bf Fig. 3 --} Grey-scale picture of the positional distribution of observed short-period comets at any time in a rotating-pulsating frame with Jupiter fixed (Sun at (0,0) and Jupiter at (1,0)). A grey-scale in arbitrary relative units is shown to the right of the plot for illustration. \smallskip {\bf Fig. 4 --} The neighboring probability ($p$) as a function of $q$ for encounters with $D < 0.5$ AU (lower curve), 1 AU (upper curve) and 1.5 AU (upper curve). \smallskip {\bf Fig. 5.--} The standard model evolution over 500 yr of the water and CO flux, and the interior structure of the nucleus. The upper plot corresponds to the H$_2$O flux (full-drawn curve) and CO flux (dotted curve). In the lower plot we find, from top to bottom: total radius of the nucleus, radius where the amorphous ice is half the original value (dotted curve), radius of the outer border of the CO ice layer, radius of the inner border of the CO ice layer. The lower $x$-axes in both plots are expressed in years, while the upper ones in number of revolutions starting at aphelion. \smallskip {\bf Fig. 6.--} The steady state distrbutions of comets with $q$ for the three radii and for the combined population with a mass index $s=0.7$. From top to bottom, the curves correspond to total number of comets (both active and dormant), number of active comets and number of detectable ones. The full lines are the mean values of the distributions and the dotted lines show the $+-3 sigma$ errors. \end{document}