The Evolution of Long-Period Comets

The Evolution of LongPerio d Comets by Paul Arnold Wiegert A Thesis submitted in conformance with the requirements for the Degree of Do ctor of Philosophy Graduate Department of Astronomy University of Toronto c Copyright by Paul Arnold Wiegert ABSTRACT OF THE DISSERTATION The Evolution of LongPerio d Comets Paul Arnold Wiegert Do ctor of Philosophy in Astronomy University of Toronto Toronto Canada The observed distribution of longp erio d yr comet orbits has proved dicult to reconcile with theory Among the discrepancies is the fading problem the fraction of comets in the observed sample which are presumed to have made more than one p erihelion passage since leaving the Oort cloud is much smaller than that predicted by simple dy namical mo dels of the Solar System This may indicate that the lifetime of the longp erio d comets is signicantly shorter than exp ected from purely dynamical considerations This in turn p oints to the imp ortance of comet losses through volatile depletion We examine the evolution of longp erio d comets through a direct numerical integration a more realistic approach than the Monte Carlo metho ds previously used to study this problem Our mo del follows the individual tra jectories of thousands of comets from the Oort cloud to their nal demise The comets evolve within a mo del solar system consisting of the Sun the four giant planets and the Galactic tide and to which nongravitational forces and a solar companion ob ject or circumsolar disk may b e added We also consider the eects of the heliopause solar wind and radiation pressure and drag on the nucleus None of these inuences are capable of pro ducing a distribution of longp erio d comet orbits matching observations In particular the comets dynamical lifetimes are to o long We also investigate the eects of fading ie the reduction of comet brightness over time due to volatile loss which may lead to a shortening of comets observable lifetimes A numb er of simple fading laws are explored One in which the fraction of comets remaining observable go es like m where m is the apparition numb er provides a reasonable match with observations and may imply a dierential p owerlaw mass distribution dN M dM A twop opulation mo del in which approximately of comets live for only a short time orbits and the remainder indenitely also matches observations reasonably well and could b e explained physically by a division of the Oort cloud p opulation on the basis of their internal cohesiveness into fragile and robust ob jects ii ACKNOWLEDGEMENTS I would like to thank my sup ervisor Scott Tremaine for his help and patience my parents and Kathy for their unagging supp ort and understanding and all my fellow students at the University of Toronto Astronomy department for their friendship over the years I also gratefully acknowledge the nancial supp ort of the National Science and Engineering Council of Canada the Ontario govern ment and the University of Toronto iii Contents Intro duction The nucleus The gas coma The dust coma The tail Jets and streamers Observing longp erio d comets Research goals Observations The catalogue of cometary orbits Orbital elements uncertainties Comet families Orbital elements Semima jor axis Perihelion distance Inclination Longitude of the ascending no de Argument of p erihelion Aphelion directions Summary Dynamics The planets Energy iv The Gamblers Ruin problem Distant planetary encounters Angular momentum The loss cylinder Planet X The Galactic tidal eld The Galactic reference frame Nongravitational forces Passing stars Energy Angular momentum Comet showers Molecular clouds A massive circumsolar disk Miscellaneous p erturbations Radiation pressure and the solar wind Drag Comet lifetimes The Oort cloud Problems in longp erio d comet dynamics The fading problem The ratio of prograde to retrograde comets The clustering of aphelion directions The source of shortp erio d comets Hyp erb olic comets The present state of the eld Algorithm Comparison with observations Numerics The integration algorithm Regularisation v Error tolerances Random numb ers Chaos Time requirements Planetary encounters Initial conditions The entrance surface The ux of comets into the entrance surface The endstates of comets Mo del implementation and testing Integration tolerance The twob o dy problem The planets The Galactic tide Nongravitational forces Massive circumsolar disk Results Original elements The newly visible comets The longestlived comets Dynamically evolved longp erio d comets Element distribution parameters Evolved longp erio d comets The current Oort cloud p opulation The original Oort cloud p opulation Discovery probability function Shortp erio d comets Planetary encounter rates Nongravitational forces Two simple cases More realistic nongravitational forces vi Discovery probability function Other scenarios Massive circumsolar disk Massive solar companion Heliopause Fading Determining the fading function directly One parameter fading functions Two parameter fading functions Summary Conclusions A Celestial Mechanics A Orbital elements A Galactic elements A Keplers third law A Radius in the orbit .

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