ABSTRACT

Title of Dissertation PHYSICAL PROPERTIES OF COMETARY NUCLEI

Yanga Rolando Fernandez Do ctor of Philosophy

Dissertation directed by Professor Michael F AHearn

Department of Astronomy

I present results on the physical and thermal prop erties of six cometary nuclei

This is a signicant increase in the numb er of nuclei for which physical information

is available I have used imaging of the thermal continuum at midinfrared and radio

wavelengths and of the scattered solar continuum at optical wavelengths to study

the eective radius reectivity rotation state and temp erature of these ob jects

Traditionally the nucleus has b een dicult to observe owing to an obscuring coma

or extreme faintness I have taken advantage of new midinfrared array detectors to

observe more than were p ossible b efore I have also codevelop ed a technique

to separate the coma and nucleus from a image I develop ed a simple mo del

of the thermal b ehavior of a cometary nucleus to help interpret the thermal ux

measurements the mo del is an extension to the Standard Thermal Mo del for aster

oids We have enough nuclei now to see the rst demarcations of the cometary

region on an alb edodiameter plot I make a comparison of the cometary nuclei

with outer Solar System small b o dies and near All of the cometary

nuclei studied in this thesis are dark with geometric alb edos b elow and have

eective diameters of around to km except for comet HaleBopp C O

which is in the next order of higher I give an extensive discussion of

the nuclear characteristics of comets HaleBopp and PEncke the two comets for

which I have large datasets

PHYSICAL PROPERTIES OF COMETARY NUCLEI

by

Yanga Rolando Fernandez

Dissertation submitted to the Faculty of the Graduate Scho ol of the

University of Maryland College Park in partial fulllment

of the requirements for the of

Do ctor of Philosophy

Advisory Committee

Professor Michael F AHearn Chair

Do ctor Alan P Boss

Professor Paul D Feldman

Do ctor Lucy A McFadden

Professor Virginia Trimble

Professor Richard J Walker

c

Copyright by

Yanga Rolando Fernandez

PREFACE

Sections of this thesis have already b een published in scientic p eerreviewed jour

nals and conference pro ceedings A discussion of comet Hyakutake app eared in

Planetary and Space Science in volume pages A treatment of

comet Encke is currently under review by Icarus An overview of comets Temp el

Tuttle Wild and Utsunomiya will app ear in the up coming b o ok Cometary Nuclei

in Space and Time edited by M F AHearn and published by the Astronomical So

ciety of the Pacic which is based on the IAU collo quium held in Nanjing China

in May of A pap er on comet HaleBopp app eared in Icarus in July vol

ume pages A discussion of the imagepro cessing technique that I call

the comatting metho d app ears in a pap er rstauthored by my coinvestigator

Dr C M Lisse published in Icarus in July volume pages ii

DEDICATION

To the two constants of my Universe Mom and Dad iii

ACKNOWLEDGEMENTS

This thesis is formally credited to one p erson but it is not completed without the

assistance of many other p eople of course Mike AHearn has guided me through the

bulk of my graduate career and to him I owe many thanks not only for mentoring

me through the scientic asp ects of my apprenticeship but through the so ciologi

cal and p olitical ones as well The rst scientic talk I heard him give was at the

Donn Symp osium in Charlottesville VA in Novemb er of Until then I had

b een waing ab out deciding on a concentration for my thesis but after hearing him

sp eak ab out his database pap er and seeing his enthusiasm ab out these new break

throughs that nally revealed themselves after studying seven dozen comets I

really started to understand some of the excitement and allure of studying these

buggers So thank you so much Mike for all your help

Casey Lisse has b een my other close collab orator in this scientic journey I am

grateful for his quick mind innite patience with my questions and wacky humor

And of course who can forget the Red Pen I will always lo ok fondly back on these

very scientically pro ductive years with him

I also owe a deep debt of thanks to Dennis Wellnitz who is such an exp ert on

things mechanical and electronic The smashing success of the HaleBopp o ccul

tation adventure in a trashdump in upstate Utah would not have happ ened iv

without his exp ertise and quick thinking at the critical moments Yet again I think

how fortunate I am to have entered Mikes Comet Group just when all these terric

p eople were there to help me out

I am very grateful to Lucy McFadden for allowing me to start work on an

pro ject in and nally allowing me to realize that I really did like planetary

science much more than studying clusters of galaxies And she has continued to b e

a great teacher through my graduate career Thanks Lucy

Lastly on the scientic front I have to thank b oth NASA and NSF for there

consistent nancial supp ort throughout these last years the telescop e allo cation

committees and stas of IRTF KPNO CTIO ESO VLA Lowell Observatory and

MKO for there helpful service and p ositive attitude Mike Ressler Bill Homann

and Ulli Kau for granting us p ermission to play with their instruments Without

all of these p eople I would not have b een so successful in gaining the necessary data

to complete this thesis Among other things Ive learned you can have o o dles of fun

with only oxygen in your lungs formtting foam is a go dsend theres nothing

like jicama and asparagus salad to help you gure out how to drive a stickshift

Now planetary science has b een go o d to me if I had not b een studying comets

I would not have b een able to travel all over the world and exp erience more of our

planet than I had imagined It makes you realize how much of Earths culture and

nature is still left to explore Twentyeight trips in grad scho ol and I have only

scratched the surface from strolling along Victoria Harb or among the bright lights

of Hong Kong to bathing in a giant waterfall in Waipio Valley on the Big Island to

b eing the highest human for miles around at the tip of Mt Lassen to watching the v

rainb ows app ear and reapp ear on a misty summers in Sto ckholm I could go

on for a while Unfortunately now I have no choice but to submit to this wanderlust

Ive picked up and sp end the rest of my life traveling the no oks and crannies of our

planet

One rep ercussion of all this scamp ering around has b een to instill in me a great

sense of appreciation for how lucky I am Though the physical distance b etween me

and that subsistence farmer in central Chile that family selling trinkets in Nogales

and those p o or homeless blokes near Constitution Avenue may b e small what an

incredibly fortunate p erson I am to b e able to go to my warm house my wellsup

plied gro cery my steadily paying job We are all just a few small but critical events

away from any of these predicaments

And now for the other imp ortant p eople of my time here Thanks to Arunav

Kartik and Laura I wouldnt have b een able to nish this tome without all of their

supp ort and understanding through this crabby and grumpy time esp ecially near

the end Mes amis your friendships mean more to me than you imagine The mid

to late s would have b een quite a bit more dicult to slog through without

you all Lets all nd enough inner p eace and gumption to make the XXIst century

b etter than the XXth AK Thank you for keeping my head on straight KS Thank

you for keeping me honest LW Thank you for giving me selfcondence

Continuing with the imp ortant p eople thanks Don for among other things

bringing ice cream and going sledding thanks Leslie for among other things playing

racquetball and nding my bike thanks Amy for among other things going to see

ob eat movies with me thanks Doug for among other things making me stay loyal vi

to the Padres thanks Steve for among other things having practical knowledge

in a institute full of geeks thanks Pete for among other things endlessly quoting

The Simp ons thanks Alison for among other things endlessly quoting Star

Wars

Where would we b e without the department sta shielding us from the three

to ed sloth that is the university administration To John T Mary Ann and Maggie

thanks for your protection Where would I b e if I hadnt babysat the PDS machine

during SL impact week To Anne thanks for that job years ago and for your

humor in the meantime

Where would I b e if I were not able to go to Giant at oclo ck in the morning

and buy PopTarts What a country

Finally thanks to

 Carl Sagan for writing Cosmos

 Halleys Comet for b eing visible right when I was so impressionable may

I see you again when Im ninety

 Voyager for sending back very co ol pictures of Uranus and Neptune vii

TABLE OF CONTENTS

List of Tables xi

List of Figures xii

Cometary Nuclei Their History and Imp ortance

A Brief Rundown

The Role in the Solar System

Motivation

A Description of Chapters

Data Acquisition and Pro cessing

Obtaining Optical Data

Obtaining Infrared Data

Obtaining Radio Data

The Ideal Dataset

Pro cessing the Data Coma Removal

Data Interpretation

Philosophy of Thermal Mo deling

The Energy of a Nucleus

The Augmented Thermal Mo del

Rotation of the Nucleus viii

The Nucleus of Comet HaleBopp

Background

Occultation Measurements

Thermal Emission and Scattered Light Imaging

Summary of HaleBopp Results

The Nucleus of Comet Encke

Background

Observations and Reduction

Analysis

Discussion

Previous Work

Summary of Encke Results

The Nucleus of Comet Hyakutake C B

Background

Thermal Measurements

Optical Measurements

Summary of Hyakutake Results

The Nucleus of Comet Temp elTuttle

Background

Thermal Measurements

Optical Measurements

Summary of Temp elTuttle Results

The Nuclei of Comets Wild and Utsunomiya ix

Background

Utsunomiya

PWild

Summary of This Chapter

Conclusions and The Future

Comets and Their Disguised Relations

Comparing Radii and Alb edos of Cometary Nuclei

Alb edo and Orbital Parameters

A Motivator for the Future

Future Data Rates

References x

LIST OF TABLES

Characteristics of Comet HaleBopp Occultation

Observations of Occultation by Comet HaleBopp

Parameters of the Mo del of Nuclear and Comatic Structure

Constraints on Parameters to Occultation Mo del

Observations of Comet HaleBopp

Observations of Comet Encke

Flux of Comet Encke

Estimated Nuclear or m Magnitudes for Enckes Nucleus

2

Sizes and Alb edos of Cometary Nuclei xi

LIST OF FIGURES

Current Canonical Cometary Nucleus

Main Belt Asteroids Radius Distribution Function

Schematic of MidInfrared Observing

Schematic of Temp erature Map for Slow and FastRotators

Lo cations of Observers for Occultation by HaleBopp

Comparison of Occulter Cometary and Occultee Stellar Sp ectra

of Occultation by HaleBopp Team

Light Curve of Occultation by HaleBopp Team

Schematic of Occultation and Light Curve

ad Example Mo del Fits to Occultation Light Curve

eh Example Mo del Fits to Occultation Light Curve

PreOccultation Image of Comet and Star

ComaFitting Metho d Applied to Optical Image of HaleBopp

ComaFitting Metho d Applied to Optical Image of HaleBopp

ComaFitting Metho d Applied to Optical Image of HaleBopp

ComaFitting Metho d Applied to Optical Image of HaleBopp

ComaFitting Metho d Applied to MidInfrared Image of HaleBopp

Rotation Sequence of Comet HaleBopp xii

LIST OF FIGURES contd

CLEAN Contour Map of Comet HaleBopp Microwave Continuum

Radio Continuum Sp ectrum HaleBopp Nucleus Mar

Temp erature Map of HaleBopp Mar

Comet Encke at Microns a and Angstroms b

Radial Proles of Comet Encke in MidIR a and Optical b

Light Curve of Comet Encke Phased by hr

StringLength Metho d Determination of Enckes Rotation Perio d

Optical Phase Behavior of Comet Enckes Nucleus

ISOPHOT Sp ectrophotometry of Encke Dust Coma Plus Nucleus

2

Plots of Encke Dust Temp erature and Nucleus Size



Comet Hyakutake in a wide Field of View

CLEAN Contour Map of C B

Size and Temp erature of C B Nucleus

ComaFitting Metho d Applied to Optical Image of Hyakutake

Rotation Sequence of Comet Hyakutake

Light Curve of Comet Hyakutakes Photo center

MidInfrared Images of Comet Temp elTuttle

MidInfrared Sp ectrophotometry of Comet Temp elTuttles Nucleus xiii

LIST OF FIGURES contd

ComaFitting Metho d Applied to Optical Image of Temp elTuttle

Optical Phase Behavior of Comet Temp elTuttles Nucleus

MidInfrared Images of Comets Utsunomiya and Wild

ComaFitting Metho d Applied to Comet Utsunomiya

ComaFitting Metho d Applied to Comet PWild

Size and Alb edo of Cometary Nuclei and CometLike Asteroids

Alb edoOrbit Connection of Cometary Nuclei and

CometLike Asteroids Perihelion

Alb edoOrbit Connection of Cometary Nuclei and

CometLike Asteroids Tisserand Invariant

Current Size Distribution of Known Cometary Nuclei

and CometLike Asteroids xiv

Chapter

Cometary Nuclei

Their History and Imp ortance

A Brief Rundown

Most studies of the comet phenomenon fo cus on the coma and tail of the ob ject

usually the most obvious parts that one sees However this thesis presents a study

of the nuclei of several comets which are in general much harder to observe While

much work has b een done to understand the nuclei indirectly by studying the gas

and dust around them I have tried to directly prob e their physical and thermal

prop erties It is only in the last two decades that this has b een observationally and

computationally p ossible the recorded history of the study of comets extends back

a few millenia but for the vast ma jority of that time the very existence of a cohesive

b o dy in the middle of the coma never mind its prop erties was not known

Though Seneca seems to have had the correct idea in the st century AD for

much of history a comet seen in the sky by the ancients was not even recognized as an

astronomical phenomenon until the th century when Tycho Brahe set an upp er

limit on the comets that put it far from Earth previously comets were

b elieved to b e atmospheric phenomena The comets basic place in the planetary

system moving on parab olae or on ellipses typically crossing the orbits of several

ma jor planets was of course noted by Halley using Newtons thennew universal

gravitation idea through his accurate timing and astrometric prediction of the

return of the comet now b earing his name Aside from most notably work by

Bessel investigations into the physical nature of comets as opp osed to just orbital

or astrometric studies b egan in earnest only in the late th century with detailed

studies of morphology and apparent luminosity and the advent of photography and

then sp ectroscopy

The study of a comets nucleus sp ecically was fraught with uncertainty As

Bobrovniko wrote in reference to comet PHalleys app earance around

the term nucleus has no precise signicance Sometimes the nucleus was

p erfectly starlike without any measurable diameter Sometimes it lo oked like a

small planetary disc Sometimes there was nothing that could b e interpreted as a

nucleus It is questionable whether most observations of the diameter of the nucleus

refer to the real nucleus A pap er by VorontsovVelyaminov gives no less

than seven separate op erational denitions of the nucleus The rampant confusion

of nuclear nomenclature is indicative of the lack of understanding of exactly what is

at the heart of a comet That is not to say that we are fully enlightened now but

in hindsight we can see fundamental misconceptions

The dominant mo del for the comets nucleus for ab out a full century from the

mids to the mids was the sandbank mo del whose tenets were most re

cently championed by Lyttleton The main motivations for p ostulating

the nucleus as an unb ound agglomeration of meteoritic solids and not a monolithic

mo del were a a cometary coma contracts as the comet approaches the b

meteor streams are coincident with cometary orbits c nuclei tend to uctuate in

apparent size and brightness sometimes even disapp earing and d comets are of

ten as much as an arcminute away from predicted ephemeris p ositions even for well

determined orbits The obvious choice to make at least back then was to assume

that there is no one central b o dy in the photo center of the comet but rather just

a cloud of dust grains and that what one observes as the nucleus is just the place

where the optical depth or the concentration of particles is higher The complicated

patterns that emerge in the nearnuclear coma of some of the more active comets

made it attractive to assume that there is just an amorphous cloud of dust grains

deep inside the coma For example the head of comet PHalley during its appari

tion in Bobrovniko showed many centers of brightness with tendrils

and sheets of coma p ointing in multiple directions The mass of the comet would

b e spread out over much of the coma not just in the photo center but all of the

particles in the comet are on indep endent orbits of all more or less the same p erio d

there is no gravitational binding but also they are not tidally disrupted as they

pass close to a planet or the Sun

The literature is full of measurements of the size of the nucleus that range

from a few tens to a few thousand kilometers eg Chamb ers p Vo

rontsovVelyaminov Lyttleton pp Frequently observers would

measure the angular size of whatever resolved disk was at the center of the comet if

any A few published rep orts give values within the same order of magnitude of the

mo dern values ie a few kilometers but the ma jority are similar to the case eg

of a sp ecic comet mentioned by Richter with a diameter lower limit that

is times bigger than the currently accepted value Of course there was also the

problem of a thentotally unknown alb edo and thenundetermined phase eect that

complicated matters The observation of comets transiting the solar disk Finlay

and Elkin Bobrovniko placed upp er limits on the diameter of roughly

to km but in the context of the sandbank mo del this was taken to conrm

the idea that there were several smaller b o dies at the heart of the comet rather than

one single b o dy pro ducing the coma and tail phenomena

This then was the heart of the problem for the sandbank mo del the actual

diameters of cometary nuclei and here I do mean the central monolithic b o dy

are much smaller than was commonly thought a century ago As I will show in later

chapters most comets seem to b e on the order of just a few kilometers in radius

This is not to say that comets do not have multiple sources for the dust and gas we

see for of course there are a couple dozen cometary nuclei that have b een known

to split into pieces some for not obvious reasons Sekanina However

usually the pieces evap orate away or cease activity in short order so that at any

given moment a comets nucleus is usually just a singular ob ject with a radius on

the order of to km This should not b elittle the work of the th and early

th centuries I merely p oint out that in hindsight many conclusions were based on

incorrect precepts Indeed the main problematical situation in observing cometary

nuclei still remains when the comet is close by the nucleus is shrouded in the

coma but when it is far away and the coma is not so strong the nucleus is faint

and dicult to measure The recent journals contain many estimates of the size of

cometary nuclei but the error bars are usually large and if they are not then many

times they probably should b e

The late s and early s saw the publication of signicant pap ers on

several cometary phenomena the nucleus Whipple the plasma tails Bier

mann the reservoir of longp erio d comets Oort and the source of the

Jupiterfamily comets Edgeworth Kuip er For my immediate purp oses

here Whipples work is the most signicant The nucleus is a single b o dy a con

glomerate of ices combined in a conglomerate with meteoric materials to use

the original wording with ices subliming o due to insolation Quantitative studies

of the sheer magnitude of gas mass in cometary comae and tails at the time indi

cated that a huge reservoir of ice was needed in the comet far more than could

b e supplied by the grains in a sandbank even if the grains did adsorb volatiles on

their passage through space The ejection of material would over time leave an

insulating mantle on the nucleus surface and also measurably push the nucleus in

a reaction force This latter p oint made Whipples mo del sup erior to the sandbank

mo del in that b oth acceleration and deceleration could b e explained by the sense

of rotation of the central b o dy The sandbank mo del used solar radiation pressure

and collisions within the bank to explain acceleration but not deceleration The

idea of a single b o dy for the nucleus was not totally new in eg Wurm

mentions it in the context of the formation of the gas coma

Whipple was the rst to make an extensive analysis of the rotation states of

many cometary nuclei he has given a summary and historical and contex

tual review However his metho d for determining rotation p erio ds based on the

timing of features moving through the coma app ears frequently to give misleading

results Whipple himself states that his metho d either gives exactly the right answer

or something totally sp ecious The photo electric measurement of the brightness of

a comets photo center as a function of time was rst done only in The de

termination of a cometary rotation state is a dicult problem a go o d review of

the pitfalls is given by Belton and it has not b een done satisfactorily even

for the nucleus of comet PHalley a comet visited by several spacecraft I will

elab orate on the metho dology of rotation p erio d determination later

In the mid to lates a series of groundbased exp eriments were p erformed

that gave us size and reectivity information on cometary nuclei for the rst time

Much of my work elab orates on the same principle ie combining the information

from the thermal radiation and reected light of a nucleus The advent of sensitive

germaniumgallium b olometers to detect to m radiation made this metho d

p ossible I will describ e the metho d fully in Chapter The work gave our rst

indication that cometary nuclei are some of the blackest ob jects in the solar system

with geometric alb edos of just a few p ercent Previously the consensus was to

assume a much higher value something comparable to the icy satellites of the outer

Solar System

The study of cometary nuclei received a b o ost in with the data taken by

the otilla of spacecraft that ew by comet PHalley most esp ecially by Giotto

For the rst time ever a resolved image of a nucleus was pro duced and I show

a representation in Fig taken from a review article by Keller which

is the combination of several highresolution images The ybys conrmed many

of our basic suspicions Halleys nucleus is a cohesive b o dy and not a sandbank

its visual geometric alb edo is very low a few p ercent it is approximately prolate

and elongated by ab out there are regions on the surface that are more active

than their neighb ors are these regions pro duce jets similar to what is seen in the

groundbased images an active region is active apparently only on the sunlit side

not on the night side but a go o d fraction of the gas and dust do es not come from

these active regions While the study of Comet PHalley revolutionized cometary

science it of course left many questions still unanswered Most obviously it would

b e wise to obtain similarly detailed closeup data of other nuclei Fortunately this

will probably happ en in the next decade there are several spacecraft missions with

cometary targets scheduled to y in the coming years and we hop e not all of them

will suer from the budget axe or system failure The near future will bring exciting

scientic knowledge to us ab out these denizens of our Solar System

This short history should make it clear how dicult observations of the nucleus

can b e In general if the comet is close to Earth it is also close enough to the

Sun to b e outgassing and the light from the gas and dust coma comp etes with and

often swamps the light from the nucleus On the other hand if the comet is far

from the Sun where it is not outgassing and we have an easier view of the nucleus

the comet is also far from Earth and the nucleus is dicult to observe due to

its faintness Furthermore once the comet is several AU away it b ecomes extremely

dicult to tell the dierence b etween a little bit of comatic ux and no comatic ux

since there is no set distance known a priori at which one can declare the comatic

activity negligible This Catch problem exists in b oth the infrared and optical

regimes In the radio there is some hop e b ecause there are not enough grains in

the coma to pro duce enough radiation to comp ete with the nucleus However at

these wavelengths the PSF b eam in this case is so large as to make spatial

dierentiation of the coma and nucleus very dicult it is even harder to tell how

much ux is comatic and how much is nuclear Interferometric observations can b e

used to improve the spatial resolution as I will show in Chapter but then one

needs a large nucleus since the wavelengths are so far down on the RayleighJeans

side of the Planck function The fact that our knowledge of cometary nuclei was

almost nonexistent all the way up into the mids dramatically indicates the

diculties in approaching the study of these ob jects

The Role in the Solar System

Origins

In the midth century Kant sp eculated that the nonastrological and non

Figure Current canonical cometary nucleus This is a pro cessed image of the

nucleus of comet PHalley taken by the Giotto spacecraft in March Keller

This image represents our current view of the typical cometary nucleus

anthropic reason for the comets existence was tied to the origin of the Solar System

To this day among the largest unanswered questions in comet science are What

exactly was the role of the comets in the Solar Systems formation and How

is the currentlyobserved group of comets related to the original p opulation The

comets are some of the b est prob es we have for studying Solar System origins since

they are some of the least pro cessed observable ob jects

The story apparently b egins b efore the Solar System was b orn Recent studies

of the bright comets Hyakutake and HaleBopp have indicated an interstellar origin

for the ices based on the isotopic ratios Meier et al a b and unusual

hydro carb on abundances Mumma et al The ices were in the solar nebula as

the gas giants were forming and the comets are remnants from the accretion pro cess

that created the gas giants There is much debate ab out the exact metho d of gas

giant formation gravitational stability Boss or core accretion Pollack et

al but lowsp eed collisions of grains undoubtedly played some role in the

agglomeration of the cometesimals The existence of the ice implies that the comets

we see to day formed in the AU range and b eyond since closer to the Sun they

would not have retained the volatile comp onent

Currently there are four ma jor ideas for the structure of the nucleus as a result

of the formation pro cess Whipples icy conglomerate mo del is the original

Variations on that idea have b een created by Donn who created a fractalized

y aggregate by Weissman who created a primordial of a

cometesimal collection with low tensile strength and by Gomb osi and Houpis

who p ostulated a collection of closelypacked b oulders held together with icy glue

This is by no means exhaustive and extensive reviews of the mo dels of the bulk

structure of cometary nuclei have b een written by eg Donn The main

variations among the mo dels are the density of packing of the cometesimals from

which they formed and the makeup of the icero ck matrix of which they are made

There are apparently testable predictions for the mo dels based on how they suer

collisions and the physics and hydro dynamics of the gas and dust ejection Work

on split comets Sekanina seems to indicate a very low tensile strength

for the b o dies but in general dierentiating b etween the mo dels may have to wait

until we have many very close observations of several nuclei by spacecraft Notable

among the future missions is Deep Impact which will re a missile at a comet and

simulate a meteorite impact and thus allow us to observe crater formation on the

surface

The current domicile of a comet within the Solar System dep ends strongly on

its birthplace Gyr ago According to numerical simulations comets b orn near

Jupiter and Saturn predominantly found themselves either crashing into the Sun or

b eing ejected from the Solar System entirely due to the strong gravitational inuence

of the two largest gas giants A small p ercentage collided with the terrestrial planets

ie Jupiter and Saturn provided the imp etus for some of the heavy b ombardment

suered by Earth in its early history It should b e noted that even to day it is thought

that a typical shortp erio d comet with a year p erio d and aphelion passing less

than AU from Jupiters orbit can exp ect to survive less than a million years

b efore b eing strongly p erturb ed into the Sun out of the Solar System or into a

nearEarth asteroidlike orbit Wetherill

Then there are the comets b orn near Uranus and Neptune The lower mass of

these gas giants compared to Jupiter and Saturn prohibited them from completely

ejecting the comets into interstellar space However they were apparently very

go o d at p opulating the Weissman Once a comet had b een ung

outward by Uranus or Neptune it would sp end several thousand years barely held

by the Suns gravity and sub ject to signicant p erturbations by passing stars giant

molecular clouds and the Galactic tides One net eect was to raise the p erihelia

and aphelia distances of these comets and hence keep them out of the inner Solar

3

System Weissman the residents of the Oort Cloud live b etween ab out 

5

AU and  AU from the Sun However the p erturbative sources also tend to

destroy the Oort Cloud over time sending the comets into interstellar space The

existence of an Inner Oort Cloud has b een invoked to resupply the outer cloud since

apparently few outer cloud memb ers could survive Gyr at the edge of the Suns

gravity Duncan et al have done numerical calculations to show that an

inner cloud would b e p opulated by ejected memb ers of the UranusNeptune region

and could help to preserve the outer clouds p opulation

Lastly I will mention the Kuip er Belt originally lled with comets that were

b orn b eyond Neptune With no large planet to shepherd them the planetesimals

remained planetesimals Many of the Kuip er Belt ob jects discovered in the past

seven years reside in a resonance with Neptune as do es that keep them

safely orbiting over Gyr timescales However Fernandez no relation was one

of the rst to numerically explore the idea that the shortp erio d comets originally

came from this region and recently Levison and Duncan have p erformed

extensive numerical calculations to mo del the currently observed orbital spread of

Jupiter family comets by integrating the orbits of particles in the Kuip er Belt

Classication

I will give here a brief description of the relation b etween cometary dynamics

and nomenclature Historically a comet has either a shortp erio d SP or a long

p erio d LP the dividing line b eing at years An LP comet can either b e new

or old in the Oort sense dep ending on whether or not it is passing for the rst

time through the inner Solar System An SP comet can either b e a memb er of

the Jupiter family JF or Halley family HF JF comets originally come from the

Kuip er b elt HF ones came from the Oort Cloud Both JF and HF comets have

b een p erturb ed by the gas giants into orbits that keep them mostly in the inner

Solar System The usual distinguishing characteristics b etween JF SP and HF SP

comets are the inclination and p erio d In my opinion one can make a case for the

existence of an Encke family of SP comets EF for comets in orbits similar to

the ma jority of nearEarth asteroids NEAs Levison has come up with

a similar categorization but currently this family is p opulated by only known

memb ers Recent observations have found comets residing in the Main Asteroid

Belt Marsden b Lien but these ob jects represent exceptional cases and

are probably caused by colliding asteroids rather than indep endent outgassing so

it is likely that this is not a separate dynamical class of comets

With the publication of a pap er by AHearn et al detailing molecular

gas sp ecies abundances in seven dozen comets we may have entered the era of com

etary taxonomy based on comp ositional dierences instead of just dynamics Such

categorizations are just starting to b e found and understo o d but continuing surveys

of cometary comae and improved remote sensing techniques may allow us to obtain

more accurate determinations of the comp ositional dierences from comet to comet

Evolution

The cometary nuclei have not b een quiet since their formation Numerical con

siderations indicate that comets from anywhere from b oth the Oort Cloud and

Kuip er Belt have undergone some collisional events in the intervening eons Stern

Stern Farinella and Davis an imp ortant question is how many

The observed size and rotation distribution that we measure from the p opulation

of nuclei that has managed to p enetrate the inner Solar System will likely not b e

the same as the original distribution with which the nuclei were b orn However

we would b e able to tell if the nuclei are as collisionally relaxed as the main b elt

asteroids are or if they have not quite reached that stage yet

There are other eects that have altered the comets even those that were in the

deep freeze of the Oort Cloud Cosmic rays have b ombarded the nuclei and aected

the top layer of cometary material although presumably this is blown o on the rst

passage of a comet near the Sun Passing stars and nearby sup ernovae briey warm

the nuclei from their usual K temp erature and hence motivate some chemical

reactions in the ice Some calculations Stern and Shull indicate that at least

once during the previous Gyr have the Oort Cloud nuclei warmed up to K

due to passing stellar or sup ernova radiation which could initiate sublimation of the

more volatile icy comp onents and induce some otherwiseinert chemical reactions

The shortp erio d comet p opulation of course is more evolved than their long

p erio d new in the Oort sense counterparts The aging pro cess is thought to

manifest itself among other ways in the chemical dierentiation of the topmost

layers of the nucleus and the creation and thickening of a mantle Meech

The physical destruction of the comet also contributes eg via splitting or the

blowing o of relatively large fractions of the comets mass during outbursts These

phenomena could aect any observed size distribution and would tend to smear out

the small end of the distribution However currently there is a much more worrisome

problem to overcome namely the small numb er of ob jects ab out which we have a

detailed physical understanding Also the evolution of cometary nuclei is a mostly

theoretical pursuit at the moment b ecause we have not b een able to observe the

decay of a nucleus through multiple passages The most obvious candidate for such

a study Enckes comet has selshly guarded its nuclear secrets until recently

see Chapter and we will have to wait a few more years b efore the eect can b e

observed on that ob ject There may b e some indication that small comets simply

do not exist in great numb ers in the inner Solar System Rickman and that

nuclei disintegrate rapidly once they get b elow some threshhold size However the

observational bias is strong and until we are more condent of sampling most of the

shortp erio d comets we should hold o on any conclusions Future cometdetection

searches or asteroidsearches adapted for comets could help improve the statistics by

at least removing the sky coverage bias that currently prevents us from discovering

many long p erio d ob jects

Motivation

We need detailed studies of more than just a few cometary nuclei if we are ever

to place the nuclei in the correct context of Solar System formation and evolution

Our current knowledge of the nuclei is rather limited so learning basic physical

characteristics such as size shap e reectivity rotation state and thermal b ehavior

represents a ma jor step Spacecraft will b e busy during the next few years studying

a few nuclei in detail but I hop e that we can more rapidly build up a reliable

database of information with groundbased observations

As an indicator of how imp ortant thermal studies of nuclei are as opp osed to just

using optical data I show the cumulative size distribution function of the Main Belt

asteroids in Fig I have used the database of Bowell lo cated on the World Wide

Web at httpasteroidlowelledu to create this graph One can estimate a

radius based on just the optical magnitude by assuming a geometric alb edo in this

case for the asterisks in the graph and for these mainb elt asteroids

2:5

that gives roughly a R size distribution I have considered only the high end

of the distribution where the sampling is at least reasonably complete However if

one lo oks at the actual radii of the ob jects measured via the thermal radiation for

ab out mainb elt asteroids with the IRAS satellite one gets a much dierent

3:5

distribution of R in the more complete end This eect do es not dep end on

the value of the assumed alb edo since changing it would merely slide the p osition

of the asterisks left or right Moreover the slop e is shallower for the b ettersampled

optical case whereas if this alb edo eect were a manifestation of our incomplete

knowledge of the mainb elt one would exp ect a steep er slop e since there would b e

more smaller asteroids known I do not want to argue the actual value of these

slop es my p oint is simply that they are very dierent and that a similar pitfall

could very well o ccur for the cometary nuclei Optical data alone cannot necessarily

guarantee the validity of size distribution information

The fruition of such an endeavour is guaranteed as evidenced by the previous

lyunknown conclusions from the work of AHearn et al I make no claims

that an understanding of the Solar System origins can b e teased out of my study of

a halfdozen ob jects but the revolution in infrared astronomy currently happ ening

will make it technically and observationally feasible to continue studying the small

b o dies of the Solar System and eventually reach the holy grail of comet science

answers to such questions as How do comets t into the birth and evolution of the

Solar System How many times have they collided with each other What accounts

for the dierences in the reectivity the dusttogas ratios the active regions and

the emitted grains Is there any correlation with dynamical age How do the

comets contribute to the interplanetary medium and the dust p opulation of the

Solar System How do es their app earance reect the alterations they have suered

Do es their comp osition reect an interstellar origin for the volatiles

A Description of Chapters

I will rst describ e the metho ds used to study the nuclei and then individually

discuss each nucleus Sp ecically in Chapter I will discuss my reduction metho ds

for this study Chapter will have a description of my interpretation metho ds this

Figure Main Belt asteroids radius distribution function The asterisks repre

sent the distribution using an assumed alb edo and so give a naive radius when

combined with the known absolute visual magnitude The diamonds represent the

IRASderived radii and so they have the alb edo ambiguity removed Note that

the slop es of the two distributions in the large particle wellsampled end are quite

dierent

chapter will explain how I have taken advantage of the new generation of sensitive

midinfrared detector arrays to overcome the problems of nucleus observation that

I mentioned in Section In Chapters through I will discuss the nuclei of

comets HaleBopp Encke Hyakutake and Temp elTuttle resp ectively I will add

some information ab out two other comets with smaller datasets in Chapter

Finally in Chapter I will combine the results of the previous chapters and make

comparisons with other ob jects of the Solar System and try to place these results

within the framework of Solar System formation and evolution

Chapter

Data Acquisition and Reduction

The vast ma jority of the data for this thesis are in the form of continuum imaging

That is true for all wavelength regimes optical infrared and radio The remaining

small fraction of data consists of midinfrared photometry with no spatial resolu

tion

Obtaining Optical Data

In the optical a chargecoupled device CCD was used in combination with ei

ther broadband or narrowband lters For most comets in order to get a sucient

signaltonoise ratio in a short amount of time the  A lters were necessary

We typically used the Cousins R and I lters Bessel discusses the sp ec

tral resp onses of these lters Bessel and Zomb eck p discuss the

photometric zero p oints

For the bright comets Hyakutake and HaleBopp narrowband  A comet

lters could b e employed The narrow widths can isolate p ortions of the sp ectrum

that are relatively gasfree to just sample the scattered solar continuum There

are currently two sets of narrowband lters in existence one from the International

Halley Watch AHearn Osb orn et al the other recently develop ed

sp ecically for HaleBopp with improvements in the wavelength ranges to remove

contamination to the continuum lters by unwanted gaseous emission Farnham et

al Fortunately it turns out that most of the strong gas emission o ccurs

in the bluer end of the optical sp ectrum making R and I bands fairly free of gas

emission lines

The basic pro cedure for obtaining calibration data for the CCD is as follows

Images of the blank twilight sky or if not p ossible of a blank space inside the

telescop es dome were used to remove pixeltopixel variations in the CCD resp onse

ie to atten it with a at eld Sets of zeroexp osure frames were taken at

least twice during a night to measure the bias count level of the CCD All CCDs used

in this study had a low enough dark current to make it unnecessary to p erform that

calibration pro cedure To measure the photometry and account for the extinction

of the atmosphere standard stars were observed during the night at various zenith

distances

I note that some of the optical imaging has come via the Hubble Space Tele

scop e The Space Telescop e Science Institute of course has a detailed set of cali

bration and reduction pro cedures that they incorp orate into the HST data so the

scientist frequently obtains sciencequality images with very little further pro cessing

necessary The only pro cessing I p ersonally have done to HST data that I use in

this dissertation is to remove cosmic rayaected bad pixels

Obtaining Infrared Data

Of the infrared data I have used for this dissertation all sets measure the thermal

emission from the comets and reside in what is lo osely called the midinfrared

wavelength regime from ab out to m Thus my use of the word infrared

or IR should b e taken to refer to this wavelength range Strictly sp eaking the

infrared part of the electromagnetic sp ectrum includes to m ux that in

comets is usually dominated by scattered sunlight For my purp oses it is imp ortant

to b e only measuring the thermal emission not the scattered in the infrared

Recent advances in infrared detector technology have made it p ossible to create

array detectors thus bringing highspatial resolution imaging to these wavelengths

This is a critical asp ect to this dissertation as will b e seen since it allows us to

separate the comatic and nuclear contributions to the ux

At this wavelength range ro om temp erature ob jects near the detector eg the

telescop e the sky itself provide the vast ma jority of the counts the astronomical

source is usually only a small or excess on top of all that terrestrial

ux Thus chopping and no dding are employed to remove all of that The

former involves the secondary mirror of the telescop e oscillating back and forth

usually to times p er second so that the detector sees alternately the eld of

view with the comet and a eld of view some distance away I often used a throw

oset of to arcseconds The dierence of the two elds leaves the comet

although the subtraction is not p erfect b ecause the skys apparent brightness is not

necessarily the same in the two frames To correct this one no ds the telescop e o

the source by some distance again I used to arcseconds and do es the

same pro cedure as b efore with chopping and subtracting If the no d is not to o far

then the dierence of the two dierence frames will remove all of the fo cus problems

and sky variations and retain just the comet In summary one obtains four frames

rst one on the source then one o the source after chopping the secondary then

another one o the source after no dding the telescop e and nally yet another one

o the source after chopping the secondary with the telescop e still at the no dded

p osition The workable image is rst minus second minus third minus fourth

that is the result of a double dierence A caveat here is that for the bright comets

the no d and chop frames cannot b e so close to the comets photo center that one

accidentally incorp orates coma in the three osource p ositions since then some of

the coma signal would b e subtracted o A schematic of this choppingandno dding

idea is shown in Fig

In practice one obtains several rst and several second frames combining

them via the average or the median to get a more accurate rst and second

frame Then the no d o ccurs and the same thing happ ens for the third and

fourth frames This is done since no dding takes several seconds but chopping is

relatively quick at a rate of a few hertz To clarify my nomenclature an image

of a comet is built up from averaging or medianing several frames together from

the p ositions and then taking the double dierence Commonly we used to

frames at each of the four p ositions b efore creating an image

Figure Schematic of MidInfrared Observing Here is the basic idea for the ideal

metho d of observing in the midIR One uses four frames and their double dierence

to actually get an image of the comet Note that the three osource frames do not

cover any of the comets coma

To account for atmospheric absorption and obtain a photometric calibration one

observes standard stars At this wavelength range the b ehavior of the atmosphere

is not necessarily as straightforward as in the optical so to b e safe it is wise to

pay attention to the humidity and see if the magnitudes of the standard stars as a

function of airmass are not following a straight line

The attening of the array can b e done by a variety of metho ds One metho d

is to observe a star multiple times at various lo cations on the array calculate the

relative photometry and then interp olate for the rest of the array One drawback

is just that the uncertainty in interp olation Moreover you a priori have to know

that the pixeltopixel variations in the array are smo oth enough to b e well sampled

by this shotgun technique Another subtlety is that one must b e sure to observe

the star over a large enough region on the array to include all of the observations of

the comet ie it is dicult to extrap olate the at eld so any images of the comet

near the edge of the array have much larger errors asso ciated with their ux

An alternate metho d is to stare at a blank sky and then at the inside of the

telescop e dome and take the dierence of the two images The sky is a fairly uniform

emitter but when lo oking at the blank sky one is really seeing the contribution

from the hot telescop e as well not just atmospheric emission and indeed that can

dominate the signal The telescop es dome on the other hand is brighter than the

telescop e and swamps the detector that is in a sense one sees more ux in the mid

infrared with the dome shutter closed than when it is op en Subtracting the blank

sky image from the dome image eectively takes away the telescop es contribution

and the observer is left with a at eld for the IR array Of course one do es this

multiple times say ten times to build up go o d statistics

Obtaining Radio Data

In this wavelength regime again I have only lo oked at a small fraction of the full

part of the electromagnetic sp ectrum classied as the radio part My radio data

covers the X band ie a wavelength of cm and has a bandwidth of MHz

This wavelength was chosen mainly for two reasons a I desired to detect as little

of the coma as p ossible and the longer the wavelength the fewer dust grains there

are and b the sensitivity of the centimeterwave receivers is near its maximum

Only comets Hyakutake and HaleBopp were observed at this wavelength b oth

at NRAOs interferometer Very Large Array VLA At least of the available

telescop es were used at all times The observations were all done almost totally

automatically A VLA user typically writes an observing program with a syntax

applicable to the telescop e control computer and submits it the observatory do es

the rest and the user later picks up the data via Internet or magnetic recording

material For the Hyakutake observations a colleague was dispatched to oversee

the exp eriment during HaleBopps apparition everything was done remotely

For ux calibration one observes a calibration source in this case a quasar

near the comet at the b eginning and end of each observing day or track in the

parlance of the radio astronomer Since these were interferometric observations it is

necessary to monitor the phase stability of the telescop es this is done by observing



a bright  Jy source near  the target roughly every minutes or so

The reduction uses the Astronomical Image Pro cessing System AIPS software

package sp ecically designed for this interferometric data The pro cedure is outlined

in The AIPS Co okb o ok National Radio Astronomy Observatory The basic

idea is to ag the bad visibility data p oints compare with the ux calibrator then

do the inverse fourier transform to obtain an image Deconvolution can then b e

employed using the CLEAN algorithm Hogb om although in this case there

was not much dierence since in one case the comet was not detected and in the

other case the comet was a p oint source

The Ideal Dataset

It is worthwhile to clearly sp ell out exactly how the ideal observing campaign

would pro ceed for the study of the nucleus Of course reality often prevents one

from p erforming this but here are my observational goals during an exp eriment

Two observing runs would b e scheduled simultaneously one at an optical tele

scop e and one at an IR telescop e Obviously colleagues assistance is vital Each

run would last at least four nights This length of time and the simultaneity allows

us to follow the rotational variations in the comets brightness in b oth wavelength

regimes At b oth telescop es we would obtain continuum images at two or three

wavelengths cycling through them continuously We would use another lter every

so often to have b etter sp ectrophotometric wavelength coverage The images would

contain coma and we would see the coma out to several PSF FWHMs away from the

photo center Of course the data would b e photometric since we are after absolute

brightnesses

We cho ose the targets that are observed during our telescop e time by two meth

o ds First we nd which shortp erio d comets are within roughly AU of Earth

of course we try to cho ose a time for the observing run when we would maximize

the numb er of p ossible targets It was our exp erience that the typical comet that is

farther than ab out AU from Earth is exceedingly dicult to observe so much so

that one cannot usually even nd the comet on the instrument monitor HaleBopp

of course was an exception to this

The second criterion for cho osing targets is more up to random chance Oc

casionally a longp erio d comet that was discovered after the telescop es prop osal

deadline will b e visible in the infrared sky at the time of the scheduled run This is

usually the only way to observe longp erio d comets by fortuitous accident Hale

Bopp again was a notable exception If a longp erio d comet is available and all else

is equal that new comet will take observational precedence during the run over the

shortp erio d ob jects

Pro cessing the Data Coma Removal

A cometary image usually includes ux from the coma To understand the

nucleus requires accounting for this contribution and deleting it For this thesis

this was a severe problem for comets Hyakutake and HaleBopp and a less severe

but still appreciable problem for the other comets One way to deal with the coma is

to mo del its shap e in the skirt and extrap olate back to the photo center to calculate

its contribution in those few central pixels since that is where the nucleus is We

dubb ed this metho d the comatting metho d Dr C M Lisse and I codevelop ed

the computer program that uses it although we are not the rst Lamy and Toth

Lamy et al a and Jorda et al have done similar exp eriments

although they have concentrated on HST optical and low spatial resolution ISO IR

data

To use the comatting metho d the PSF is required It is desirable to have as

high a signaltonoise PSF as p ossible so usually a bright ux standard star is used

Not only should the total integrated signaltonoise b e high but in each pixel near

the center as well It is b est also if the PSFs wings are apparent Naturally of course

the PSF should b e wellsampled spatially since that will make it easier to nd the

lo cation of the p ointsource nucleus within in the image Unfortunately high spatial

resolution and high signaltonoise p er pixel are comp eting desires but usually one

has no choice ab out the spatial resolution since it just dep ends on the instrument

and telescop e that is b eing used It is also desirable to image the star close to the

time at which the comet image was obtained so that eects that change the seeing

like thermal exure of the instrument temp erature changes of the telescop e and

evolving sky conditions are not signicant

In addition the cometary image itself should b e of high signaltonoise again

p er pixel not just integrated Mo deling the comas shap e is easier if there is decent

signal in many pixels away from the photo center I dene decent and many

b elow However this only holds up to a p oint b ecause at a high cometo centric

distance a comas surface brightness is less likely to b e correlated with its b ehavior

close to the nucleus This distance is dierent from comettocomet so there is no

set rule ab out how far the coma should b e imaged The dust grains in the coma

could b e fading or they could b e feeling signicant radiation pressure b efore they

reach the edge of the images eld of view making it much more dicult to mo del

their b ehavior Related to this it is always preferable to obtain images with ux

that mostly comes from the comets continuum If the ux is heavily contaminated

by emission from the gas sp ecies in the coma it again hugely complicates the eort

to mo del the comas structure since the shap e of the gas coma is a much more

complicated function

A rule of thumb that has b een employed at the telescop e is that one should try

to see the coma out to at least a few and probably several FWHMs This guarantees

that there is no ux from the nucleus b eing spread into the part of the coma that

is b eing mo deled and of course with more coma available it is more mo delable

Frequently however nature do es not follow the rules of thumb and the images

that are acquired at the telescop e show just a hint of coma As said ab ove strong

coma was detected in HaleBopp and Hyakutake at b oth optical and midinfrared

wavelengths while a fairly weak coma existed for Encke and Temp elTuttle even in

the optical Moreover there is no clearly detectable coma at all in the midinfrared

images of the other comets

The actual pro cedure for mo deling the comas shap e is straightforward Assum

ing the coma is strongly present rst a lo cation for the nucleus within or near the

brightest pixel is assumed and the image is unwrapp ed ab out this p oint that is

mapp ed onto the r plane This is done using a cubic convolution interp olation

metho d Then a certain numb er of azimuths usually are chosen and the

n

surface brightness of the coma in each azimuth is t according to A  PSF

ie the convolution of a p ower law with the PSF and A and n are obtained This

is where it is critical that at each azimuth the coma b ehaves like a single p ower

law and not say the sum of two p ower laws Each azimuth can have a dierent

p ower law but each must b e characterizable by a single A and n Presently our

computer co de nds the value of A and n by trial and error since it is not so easy to

analytically derive the b estt values when there is a convolution integral involved

The tted region extends from a cometo centric distance or FWHMs away from

the photo center out until the signaltonoise is to o small to b e useful If there are

obvious kinks in the surface brightness prole at the azimuth the tting region is

shortened to not include that

There is a subtlety here in the way the surface brightness is t The PSF

is usually not azimuthally symmetric so it cannot b e unwrapp ed to get a radial

prole That would make the convolution easy since it would basically only require

a convolution in one dimension r the radial dimension but it is rare that the PSF

actually is circular Instead it is necessary to make a separate mo del coma image

from the trial values of A and n we assume for the moment that every azimuth in

the coma has those values of A and n that are currently b eing tried and we make

a coma map out of those parameters in the xy plane convolve that with the PSF

unwrap this image and then see how well it ts to what the coma actually lo oks

like

Strictly sp eaking this is not the correct way since adjacent azimuths contrib

ute to each other up on convolution and our metho d do es not account for this To

do this rigorously would require tting hundreds of parameters simultaneously by

trialanderror a computationally intensive prosp ect Hence this simplication was

intro duced It do es not create a signicant error as long as the tting is done far

enough away from the photo center so that the surface brightness is not changing

rapidly ie at least FWHM away from the photo center

Once A and n are found for every azimuth that is all one needs to recreate an

image of the comets coma The mo del coma is subtracted from the image and the

residual is compared to the PSF The only slight complication is the pixelization of

the photo center since in those pixels one must do an integral of an expression in

p olar co ordinates over a Cartesian area

The whole pro cess is iterated several times by assuming the nucleus lo cation

in a grid of lo cations within and near the brightest pixel of the image Of all these

trials the residual that is most like the PSF and leaves as little ux as p ossible in

the skirt is chosen to b e the correct one and that lo cation is declared to b e where

the nucleus is One can then move on to the photometry

I will make a nal note concerning images of comets that only p ossess a weak

dust coma ie a coma that do es not extend more than a few pixels away from the

photo center In this case the same algorithm describ ed ab ove is used except there

is no tting of the exp onent n to each azimuth The lack of data simply just do es

not justify such an extensive parametrization Instead I let n for all azimuths

and t a value for A that is applicable for every azimuth As will b e seen in later

chapters this approximation works well for the low signal images

Chapter

Data Interpretation

In this chapter I will discuss the interpretation metho ds that are common to

most of the data used in this thesis Descriptions of sp ecialized analyses eg of

a technique that is applicable to only one of the comets will b e discussed in the

relevant cometsp ecic chapters

Philosophy of Thermal Mo deling

The energy available to a cometary nucleus comes from the Sun Internal heating by

eg radioactive decay is not an imp ortant factor owing to the small size of the ob ject

The insolation absorb ed by a surface element of the nucleus either is reradiated is

passed along to adjacent elements or helps to sublimate ice Currently the numerical

value of imp ortant factors that heavily inuence the nucleus thermal b ehavior are

unknown though we hop e to achieve some understanding with the cornucopia of

spacecraft visits in the coming decade Detailed mo dels of a cometary nucleus make

estimates of such quantities as the thermal conductivity the p orosity the heat

capacity the surface roughness the shap e the eective radius the comp osition

the structure of the icero ck matrix the emissivity and the rotation state to try

to match the observed ux Only rarely are any of these quantities actually known

for a given nucleus a priori the mo deler must simplify the situation to make the

problem tractable

The advent of more sensitive IR instrumentation has led to the acquisition of

b etter datasets and I have attempted to apply some thermal mo deling that go es

b eyond the standard simple metho ds to some of the datasets in this study There

are mo dels created by others that are more complex but in my opinion the direct

application of a very complicated mo del to a real nucleus ab out which we know very

little detail may not really help one understand the basic prop erties of the nucleus

any b etter than a relatively simple mo del can

Previous work on understanding the thermal b ehavior of nuclei has mostly ex

ploited the two p opular thermal mo dels for asteroids the standard thermal mo del

STM also known as the slowrotator mo del SRM and the rapidrotator mo del

RRM also known as the isothermal latitude mo del ILM and the fastrotator

mo del FRM As the names imply the STM assumes the asteroid is rotating slow

ly compared to the timescale for the thermal wave to p enetrate one thermal skin

depth into the nucleus and the RRM assumes it is rotating much faster than that

For example for ob jects AU from the Sun a slow rotator would have a rotation

p erio d of roughly whereas a fast rotator would spin in roughly hours

Both mo dels assume the ob ject is spherical The temp erature map of a sphere that

follows the STM lo oks like a bullseye centered on the subsolar p oint the hottest

p oint on the ob ject with the temp erature decreasing as the lo cal solar zenith angle

increases The night side is at absolute zero For an ob ject following the RRM the

temp erature at any p oint only dep ends on the distance from the subsolar p oints

latitude not the longitude This is the origin of the isothermal latitude name I

have displayed in Fig a schematic based on a similar gure made by Leb ofsky

and Sp encer their Fig showing typical temp erature maps for the two

mo dels

The STM uses a measured ux and assumes values for the b olometric IR emissiv

ity the optical geometric alb edo the IR phase function the optical phase integral

and the roughness of the surface emb o died in a factor diminishing or enhancing

the overall observed ux With these quantities one nds the eective radius The

RRM uses the measured ux and requires values for the b olometric IR emissivity

the optical geometric alb edo the optical phase integral and the rotation axis di

rection to nd the eective radius As an aside if one assumes a p ole orientation

p ointing toward the Sun then the RRM and the STM yield the same temp erature

map

For this asteroidal mo del to b e applicable to a cometary nucleus one has to b e

sure that a the nucleus is a slowrotator b it is not very active or rather not

much of the solar input energy is going to sublimating gas instead of heating up the

ro ck and c the coma is not providing a secondary source of energy via backwarm

ing which is only a problem for very active comets like HaleBopp It is not really

necessary that the cometary nucleus b e spherical which is advantageous since many

are not Meech but the output of the STM is then the eective radius not

the radius itself There is a complication with this since the radiometric eective

radius do es not have to b e the same as the geometric eective radius supp ose the

nucleus were cigar shap ed with the long axis p ointing toward the Sun An observer

would measure a relatively small thermal ux and derive a small eective radius

since most of the cigar would not b e signicantly warmed by the Sun Fortunately

observing the thermal ux over the course of a rotation p erio d and if p ossible at sev

eral p oints in the orbit can assuage most fears ab out this pathological case skewing

the radiometricallyderived size The uncertainties from other asp ects of the mo del

eg the infrared phase eect and the b eaming eect describ ed b elow usually

make the uncertainty in the resulting radius estimate large enough so that it engulfs

some of this systematic error anyway Moreover the uncertainty from extracting the

nuclear signal from a comaladen image increases the error estimate

The Energy of a Nucleus

The STM and RRM mo del mark the extremes many ob jects lie in b etween For

cometary nuclei historically the STM has b een used b ecause it has b een assumed

that the thermal inertia of nuclei are small ie the nuclei are slowrotators

The value of is known only for the Mo on and a few other satellites and Sp encer

et al p oint out that the value for an asteroid or cometary nucleus could

Figure Schematic of contour temp erature map for a slow and b fastrota

tors For each spherical ob ject the grayshaded area is unlit by the Sun In a

the subsolar p oint and lo cation of highest temp erature is at the dot leftofcenter

the temp erature decreases toward the terminator in every direction In b I have

assumed that the rotation axis is p erp endicular to the ob jects orbit plane so the

subsolar latitutde is at the equator The temp erature is a maximum there and falls

o toward the p oles Note that the contours extend b eyond the terminator This

gure is based on Figure of Leb ofsky and Sp encer

b e lower since most of these ob jects are farther from the Sun so the heat capacity

could b e lower at the co oler temp eratures Moreover at the lower temp eratures

the radiative heat transp ort that is so imp ortant in the lunar regolith and which

b o osts the eective conductivity is not necessary On the other hand the thermal

inertia could b e higher since the small b o dies of the Solar System presumably have

less regolith they simply cannot gravitationally retain it and the bare ro ck is a

more eective conductor Harris et al have claimed that thermal IR data

on some NEAs incorp orating some of mo deling done by Sp encer seem to

indicate a higher thermal inertia than previously supp osed

I have made an attempt to handle the intermediate case b etween the STM

and RRM with a mo del that is one or two steps farther in complexity Further

augmentation b eyond what I describ e here should wait until more elab orate datasets

have b een collected As it is I will only apply the mo del to the HaleBopp data

since certain imp ortant physical prop erties of the other comets in this thesis most

notably the spin axis direction are unknown First I will describ e the basic STM

and then the enhancements that I have supplied A go o d discussion of the STM is

given by Leb ofsky and Sp encer

The energy balance on a facet on the nucleus is

Energy Absorb ed Energy Emitted

where for a facet at some latitude and longitude on a spherical nucleus

the lhs is

Z

F

2

Energy Absorb ed A R cos z d cos dd

2

r

and the rhs is

Z

2

Energy Emitted B T R d cos dd

where F is the solar sp ecic luminosity r is the comets helio centric distance

A is the Bond alb edo and is equal to pq the pro duct of the geometric alb edo and

the phase integral R is the nucleus radius z is the zenith angle of the Sun as seen

from the facet B is the Planck function is the emissivity which is near unity and

T is the temp erature Since the STM was designed for asteroids usually A and

are taken to b e indep endent of p osition although currently there is no indication of

any large alb edo sp ots on cometary nuclei either In addition it is assumed that A

is indep endent of wavelength in the optical where most of the Suns energy is and

is indep endent of wavelength in the midIR where most of its thermal output is

This simplies the equations to

L

2 2 4

R A cos z R T

2

r

where L is the solar luminosity and is the StefanBoltzmann constant The

result is a temp erature that dep ends on the onefourth p ower of the lo cal solar zen

ith angle with no dep endence on R only T the subsolar p oints temp erature

SS

is needed to describ e the temp erature map By plugging in the temp erature map

into Eq accounting for the observing geometry one can nd the value of R

satisfying what the observer measures with the photometry

There are two added features to the STM that complicate this picture First

there is an arbitrary constant multiplied to the rhs Eq a b eaming factor

to account for the fact that the asteroid is actually not a p erfect sphere but has

surface roughness For example if at the subsolar p oint on the asteroid there were a

crater the thermal ux coming out of the asteroid would b e higher since the surface

of the asteroid in the crater would b e hotter from backwarming by the walls The

value of seems to b e approximately unity with a known range for a few asteroids

and satellites of to Sp encer et al Harris The problem is

is not known a priori so there is some ambiguity akin to the alb edo problem with

optical data However it is much less signicant since the p ossible range of only

covers ab out a factor of and moreover with ux measurements at multiple midIR

wavelengths it is in principle p ossible to constrain the value Harris et al

The other added feature to the STM is the phase eect Since we hardly ever



observe an ob ject at phase angle of zero and often is when observing

nearby comets and NEAs one needs to know the phase b ehaviour One p opular

mo del is to have the phase eect in magnitudes prop ortional to itself Matson

Leb ofsky et al The known range for the prop ortionality constant is

to magdegree Another metho d is to just integrate the amount of light

1

one sees on the Earthfacing hemisphere This is akin to using a cos phase

2

law in the optical regime except that in the midIR each dierential of area on the

4

surface is weighted by T There is some evidence Harris that this latter

metho d describ es the phase b ehavior of asteroids b etter than the older metho d at

least for the large asteroids

The optical data enter the analysis for the determination of the alb edo A in Eq

2

since the optical ux from a spherical ob ject is prop ortional to pR The phase

integral q connecting A and p is roughly known from the optical phase b ehavior

which has b een studied quite a bit more than its IR counterpart The result is that

the problem essentially b ecomes a system of two equations with two unknowns R

and p This is the basic metho d b ehind the work of Campins et al Millis

et al and AHearn et al when they made the rst groundbased

measurements of nuclear alb edos in the mids

The Augmented Thermal Mo del

For the augmentation of the mo del I have used two basic equations the con

servation of energy equation and the onedimensional heat transp ort equation the

simple parab olic partial dierential equation Energy conservation is treated with

the input b eing insolation and the outputs b eing reradiation volatile vap orization

and conduction into the subsurface layers I have not attempted to treat lateral

heat transp ort

Energy conservations dictates

Z Z

dM dT L

4

LT A T d cos d

2

dz dt

r

where is the thermal conductivity LT is the latent heat of vap orization and

dM dt is the gas mass loss rate Except for comets such as Hyakutake which had

an extremely active nucleus the contribution of the third term in that equation will

usually b e only on the few p ercent level For this reason I have simplied the mo del

by having the gas emanate uniformly over the nucleus surface

The heat equation is

2

T T

2

t c

z

where is the bulk density and c is the heat capacity The simultaneous solution

of these equations is the basis of my augmented thermal mo del The solution is a

temp erature map from which the exp ected ux is calculated for a given radius size

The continuum b etween STM and RRM is sampled simply by altering the thermal

p

c inertia

Sp encer et al have done much work on the thermophysical b ehavior

b etween the STM and the RRM They formulated the constant the thermophys

ical parameter to indicate when the STM the RRM or something in b etween is

applicable dened as

p

3

c T

SS

where is just divided by the rotation p erio d It is basically a comparison of

the rotation time scale and the timescale for the thermal wave to p enetrate one skin

depth where the skin depth l is given by

l

c

If then STM is applicable whereas if the RRM is the one to use

For example if a cometary nucleus at AU from the Sun has a lunar thermal inertia

1 2 12

J K m s and spins on its axis in hours then since the

subsolar p oint will have T K This places it in the slowrotator regime but

SS

since is of the same order as unity we would not exp ect the STM to p erfectly

describ e the ob jects thermal b ehavior

Another asp ect of my augmented mo del is the ability to handle ellipsoidal nuclei

This intro duces yet more parameters into the mo del since not only are the axial

ratios of the nucleus required but also the rotation state since the ux observed

at Earth will now dep end on the subearth latitude and longitude Note that the

usual observations of nuclei that measure the varying cross section reveal only the

pro jected axial ratio not the actual ones unless the data can b e combined with

measurements at other p oints in the comets orbit I will show an example of this

in Chapter Brown has studied the eects of ellipticity on the output of

the STM and shown that slight asphericity do es not make much dierence in the

use of the STM but as with the cigarshap ed nucleus example that I previously

mentioned serious systematic problems can exist if the ob jects are signicantly

elongated

Since the augmented mo del explicitly calculates the temp erature at several lay

ers within the nucleus the mo del is able to handle my radio data which the STM is

unable to do Our microwave observations do not sample the surface temp erature

but rather the temp erature several skin depths b elow the surface The subsurface

layer that is sampled could b e a few wavelengths deep for relatively ro cky material

or a few tens of wavelengths deep for icier material de Pater et al Regard

less of the exact depth it is clear that the microwave data show a lower temp erature

than at the surface Here we see a case where the uncertain nuclear p orosity com

p osition and conductivity have a very direct eect on the interpretation of data

Rotation of the Nucleus

The rotation of cometary nuclei has b een studied for the past few decades as

mentioned in Chapter However for only a handful of nuclei are there arguably

welldetermined rotation p erio ds A thorough review has b een written by Belton

and Meech has added more information from the s It is likely

that some cometary nuclei are in complex rotation complicating ones derivation

of the rotation state via observations and it is telling that there is still uncertainty

in the rotation state of PHalleys nucleus one of the most deeply studied comets

in all history In this section I will give a brief description of the easy metho ds to

determine a p erio dicity in the rotation state of the nucleus but there is the caveat

that it is not the only p erio dicity

There are two main metho ds I employ for determining p erio dicity one based on

the morphology of the nearnuclear coma the other based on the photometry of the

comets photo center I did not use the zerodate metho d used by Whipple

b ecause the other two metho ds are more reliable as Whipple himself has stated

The rst metho d used for Comet Hyakutake and HaleBopp requires taking

images over a long enough time baseline to b e able to match up when a particular

feature in the dust coma eg a jet or an envelop e returns to the same orientation

The time b etween these witnessed events is an integer multiple of the rotation p erio d

There are pitfalls to this metho d there is a basic assumption that an active area on

the nucleus that pro duces the coma feature when it is rst seen will stay active long

enough for the observer to witness it later Moreover even if it do es stay active it

may not b e easy to tell when that particular feature is back in view eg one could

b e fo oled if there is another similarlo oking jet in the coma Implicit in the use of this

metho d is that the comet itself do es not change signicantly during the observing

interval For example determining the p erio dicity could b ecome problematical if

during the observing interval the comet go es into outburst or splits

The second metho d which was also used on comet Hyakutake and on comet

Encke involves measuring the photometry over a long enough continuous time in

terval to watch the variation in brightness In principle one could do this with the

p ostpro cessed images where the coma has b een removed leaving just the light of

the nucleus but this has not b een p ossible for any of the comets in this study This

metho d measures the variation due to the changing cross section of the nucleus

plus whatever variation is due to the coma Fortunately for the two comets it was

not dicult to tell which comp onent was b oth dominating the ux value and the

variation The data set for this metho d is a light curve a timeseries of the ux

The extraction of a p erio d from these data is a nontrivial problem For the

rst metho d at the most basic level one matches images by eye although for go o d

temp oral sampling crosscorrelation metho ds may b e p ossible When employing the

second metho d common simple algorithms that are used in the cometary science

community as well as other elds of astronomy eg variable star research are

describ ed by Stellingwerf and Dworetsky these involve trialanderror

of many p otential p erio ds minimizing the length of a string that connects the time

series photometry in a phased light curve plot An advantage is that the algorithm

is p erfectly able to deal with data sampled at a nonp erio dic rate and also it is

not b eholden to any assumed shap e of the light curve sinusoidal or otherwise A

related metho d is to just take the Fourier transform ie get a p ower sp ectrum

of the timeseries and nd the most imp ortant frequency Since the mathematical

pro cess of transforming can intro duce extra noise into the data this metho d works

b est when there are many p oints to the light curve

One signicant problem with the morphological and photometric metho ds is that

an observer usually do es not have p erfect temp oral coverage of the entire rotational

phase An observing night often just do es not last long enough to watch a nucleus

cycle through one complete rotation Stringing observations together over several

nights helps alleviate this problem but it is hardly ever completely eradicated

there are usually aliases to the b est choice of p erio dicity P that one nds for the

3 1

particular observing run aliases with values like P or P ie small wholenumb er

2 2

ratios multiplying P In general the longer the baseline over which one observes

the b etter one can constrain the p erio d

Chapter

The Nucleus of Comet HaleBopp

Background

Comet HaleBopp discovered in July of likely was the most watched

comet in all of history A pro digious pro ducer of dust and gas and a marginally

advantageous orbital geometry combined to provide quite a show for several months

in early However all of that gas and dust made it exceedingly dicult to

measure the nucleus the continuum of the comet was dominated by the dust grains

in the optical and midIR regimes Two unusual techniques help ed to partially side

step this problem the observation of an o ccultation of a star by the comet and

the measurement of the microwave continuum The latter has b een discussed briefly

in Chapter The former I will describ e in detail here with text heavily b orrowed

from a pap er I wrote Fernandez et al

Occultation Measurements

Intro duction

Since the length scales of the nuclei and inner comae of comets are so small

stellar o ccultations hold great promise for probing these deep regions at the heart

of the comet see eg Comb es et al For a comet that is AU away the

km length scale subtends less than or less than half the width of a pixel

on the Planetary Camera of HSTs WFPC Unfortunately there are only a few

published rep orts of observed o ccultations by comets and the rep orted chords have

not come particularly close to the nuclei The extinction of the star has b een found

to b e a few p ercent at a distance of several hundred kilometers from the nucleus for

comets of various activity levels and dusttogas ratios eg Larson and AHearn

and Lecacheux et al One comet has b een the target of an o ccultation

observation with an impact parameter so small that the star was o cculted by the

nucleus itself not just the coma P Chiron Bus et al Of course

the very low activity large nucleus and regular orbit of this ob ject mark this as a

sp ecial case

Though most previous data on cometary o ccultations were obtained at p erma

nent observatories with a sucient numb er of p ortable telescop e systems spaced

across a territory over which an o ccultation is predicted to o ccur as we have done

here one can in principle obtain a size and shap e estimate of the nucleus indep en

dent of the alb edo ambiguity found in optical photometry and an estimate of the

opacity structure of the coma to learn ab out the dynamics and scattering prop erties

of the dust

It is worthwhile to emphasize the dierences b etween observing comet o ccul

tations and the much more common asteroid counterparts While an asteroid is a

p oint source lo cated near the center of brightness and usually on a welldened

path making the prediction uncertainty just a few shadow widths a cometary

nucleus is often swamp ed by coma emission of an uncertain morphology making

it hard to decide exactly where the nucleus is within the comet images bright

est pixel This is esp ecially true for HaleBopp the dustiest comet on record

Moreover nongravitational forces push the comet away from the ephemeris p osition

although fortunately this is probably not a problem for HaleBopp There are

even p otentially signicant errors in the ephemeris itself since it is usually derived

from astrometry of the comets brightest sp ot not the nucleus lo cation Lastly the

typical comet nucleus is only a few kilometers wide The result is to make observ

ing cometary o ccultations more logistically dicult than observing their asteroid

counterparts

Here I rep ort the observation of the dimming of star PPM due to its

o ccultation by Comet HaleBopp C O The star is also known as SAO

BD and GSC Barring a terrestrial explanation the

stars light was completely or nearly completely blo cked along part of one o cculta

tion chord implying that a line of sight through an optically thick p ortion of the

inner coma or through the nucleus itself was observed On two other chords no

signicant diminution of light was observed If our interpretation is correct this is

the closest to the nucleus a typical comet has ever b een sampled via a stellar o ccul

tation I will give results from analyses of the data from this unique observation in

the following sections

Observations

The circumstances of the Octob er UT event are given in Table

The o ccultation path uncertain to s in time and km in distance passed

through the western United States so on after sunset on Oct Six p ortable teams

were arrayed across the region and one p ermanent facility was used a map is shown

in Fig with the lo cation of the teams as crossedsquares Table lists the

lo cation equipment and data obtained by the seven teams Each mobile team

through had two memb ers I was part of Team Originally the teams were to

spread out from central Nevada northward to maximize the chance that at least one

team would record a signicant optical depth through the coma clouds

covering Washington Oregon Idaho and western Montana during the event dic

tated where each p ortable team p ositioned itself Sucient signal during the event

was obtained only by Teams and Team recorded a feature that app ears

to b e the event itself through passing cirrus clouds while observing at the town

dump of Snowville Utah Team has at b est a marginal light curve feature at the

appropriate time and Team did not detect the event

Table Characteristics of Comet HaleBopp Occultation

The Star PPM

ab

Magnitude m

V

b c

MK Sp ectral Typ e Luminosity Class KV

b h m s

J Right Ascension

b

J Declination

The Comet C O HaleBopp

Magnitude in arcsec wide circular ap erture m

R

Helio centric Distance AU

Geo centric Distance AU

Distance Scale at Comet km arcsec

Solar Elongation

Phase

Prop er Motion and PA arcsechr

Equivalent Linear Sp eed kms

d

The Observing Lo cale

Time of midevent Oct UT s

Sp eed of Nuclear Shadow kms

Elevation and Azimuth of Comet

a Smithsonian Astrophysical Observatory

b Roser and Bastian

c Measured by Jerey Hall of Lowell Obs private communication

d Sp ecically lo cation of Team see Table at the time of event

Table Observations of Occultation by Comet HaleBopp

y

Team Lo cation System Summary of Results

CCD PMT

p

N W Heavy clouds during event

p

N W Heavy clouds during event

p

N W Heavy clouds during event

p

N W Heavy clouds during event

p

N W Thin clouds but detection of event

p

N W Clear marginal detection

p

N W Clear but not detection

y

Teams through used Celestron C in m telescop es Team

used the Lowell Observatory in m NURO telescop e Teams with CCD

used a chargecoupled device Teams with PMT used a photomultiplier tub e with

eective wavelength near A

The three solid lines in Fig trace out two km wide swaths which show

the last preevent prediction of the o ccultation track The true track was only

as wide as HaleBopps nucleus with pro jection eects and the swaths do not

represent the systematic error in the determination of the tracks lo cation which

were closer to km These swaths were used to aid in cho osing lo cations

for the p ortable teams

The preevent ephemeris Solution by D K Yeomans of Jet Propulsion Lab

oratory predicted an o ccultation path shown by the longdashed lines in Fig

Astrometric corrections to this path using images of the comet taken with the U

S Naval Observatory Flagsta Station USNOFS m telescop e moved the pre

dicted track to the shortdashed lines in Fig The comatting technique that I

describ e in Chapter was employed to nd the source of the coma ie the nucleus

within an image of the comets center of brightness moving the track to the solid

lines in Fig The corrections gave a net shift to the prediction of Yeomans

ephemeris of ab out km northwest Our apparent detection of the nucleus

o ccurred closer to the original prediction than the corrected one indicating we had

underestimated the prediction errors and that our corrections did not reduce the

error only delimit it As we will show with all the uncertainties of event prediction

as mentioned in Section the detection of the o ccultation km away

from the b est guess is p erfectly reasonable

Weather and equipment problems prevented Team from observing the comet

and the star separately to determine their relative brightnesses in the photometer

passband Using the known sp ectral characteristics of b oth ob jects combined with

broad and narrowband imaging taken near the day of the event we estimate the

star to b e times as bright as the sum of the comet sky ux and detector

noise The metho d is describ ed here

The bandpass of Team s system is shown in Fig all that is needed is the

ratio C of star ux to the sum of uxes from comet sky and detector noise within

this band and within the arcmin wide ap erture that was used Starting with CCD

observations of the comet and star taken with the USNOFS m telescop e on

and Oct We know the relative brightnesses to in their passband

the sp ectral shap e of which is also shown in Fig Monet et al To switch

to Team s band now requires knowing the sp ectra of the comet and the star

Fig shows the sp ectrum of a typical KV star Kharitonov et al Silva

and Cornell Jacoby et al and of the Sun Neckel and Labs Labs et

al The comets sp ectrum is the same as the solar sp ectrum plus uorescence

emission lines and any reddening of the dust Using CCD imaging taken on

Oct UT with the Lowell Observatory m Hall telescop e and narrowband

International Halley Watch lters as describ ed by Vanysek we found the

dust to b e at most only mag redder than the Sun Moreover we found

that CN and C emission the dominant sp ecies in Team s sp ectral range would

contribute only ab out of the ux Hence the solar sp ectrum in Fig is

actually a go o d representation of the comets sp ectrum In Oct the comet had

almost constant morphology and magnitude so there is little error in using images

taken days after the o ccultation

Thus we can calculate the relative star and comet brightnesses to within a few

Figure next page Lo cations of observers for o ccultation by HaleBopp

Here is a map of the western United States showing the lo cations of the participating

teams crossedsquares and the o ccultation track predictions The longdashed

lines show the original ephemeris prediction shortdashed lines show intermediate

solution including astrometric corrections solid lines show last prediction including

corrections from deriving the nucleus p osition within the comets photo center The

three lines mark out a km wide swath which was used for planning purp oses

the nucleus shadow is much narrower

p ercent The only caveat is that the systematic error may b e higher if our star is

not a typical KV star Our remaining task is to account for sky and detector noise

contributions The latter we measured to b e negligible compared to that of the sky

and the comet From practice observations in conditions roughly as dark as for the

observation of the o ccultation itself we found the sky to b e ab out of the

comets brightness thus the factor from the sp ectral analysis should b e divided by

The combination of all information yields C

Data

The light curve from Team is shown in Fig The data span ab out

minutes top graph the minutes centered on the time of deep est o ccultation

at UT s are shown in the lower panel The photometer integrations

were ms long and the ap erture was circular and one arcminute wide

The light curve is characterized by a long several minute gradual changes

in the count rate due to passing clouds eg the general trend from to

b precipitous drops in ux due to the comet and star which were near

ly sup erimp osed b eing near the edge of the ap erture immediately followed by even

more rapid few second rises as the target is restored to the center of the eld of

view eg at and c small drops in ux due to the comet and star

moving a bit ocenter in the ap erture followed by a quick restoration as the tar

get is recentered eg at and imp ortantly at

and d the o ccultation event itself near The distinct morpho

logical dierences b etween these four typ es give us condence that we have observed

the o ccultation event The o ccultation caused a fairly symmetric valley in the light

curve of ab out one minute in length shorter than the time scale for the eects of

passing clouds but longer than the time scale for a drop and rise in ux due to the

p osition of the target in the ap erture

Cases b and c ab ove were caused by the telescop e not exactly tracking at

the prop er motion rate of the comet The times of these corrections are marked

with arrows in Fig The correction at the one b efore it and the two

after were all minor and b elong to case c Since most of the comets ux was in

its coma a slight oset of the target did not cause a signicant decrease in ux the

more obvious manifestations of these corrections are the small noise spikes from the

telescop e drives electrical interference

The drop in count rate at the time of deep est o ccultation is ab out which

is consistent with the star b eing totally blo cked from view since it was times

the brightness of the other contributors to the ux Moreover

it o ccurs close to the predicted time of for the lo cation of Team The

dip could not b e due to a jet contrail since the light curve would resemble a prole

through a uniform density gas cylinder which would have a shallower slop e through

the middle of the event unlike what has b een recorded While we cannot unambigu

ously rule out that an unusual cloud passed in front of the comet the circumstantial

evidence do es imply an observation of the o ccultation

There is a dip in the light curve at approximately UT which may b e

interpreted as morphologically distinct from the eects of b oth clouds and tracking

errors and so could b e construed to b e the o ccultation event it is the only other

Figure next page Comparison of o cculter cometary and o ccultee stellar

sp ectra The dashed lines give the bandpass of the observing system at the USNO

m telescop e and of the C and photometer system used by Team for the

o ccultation A comparison of the sp ectra solid lines of a KV star and a solar

typ e star which in this case approximates the sp ectrum of the comet was used to

transform the relative brightnesses of the comet and star from the USNO system to

the Team system

Figure next page Light curve of o ccultation by HaleBopp Team This

light curve shows the o ccultation event a feature that is morphologically distinct

from all others The top plot covers all minutes of the light curve b ottom plot

shows minutes centered on the o ccultation feature The integration time for each

data p oint was ms Arrows indicate tracking corrections see text for details

The tracking correction near the center of the o ccultation was not signicant The

asterisks indicate the lo cations where the largescale eect of the cirrus clouds was

sampled and the thick line is a spline t to those p oints This t was used by our

mo del to grossly account for the nonphotometric conditions

feature in the light curve aside from the one at UT that could have b een

caused by the o ccultation An event this early would however imply a rather large

error of thousands of kilometers While it is p ossible to mo del the circumstances of

the event in the manner describ ed in the next section to repro duce the curve the

ts are less robust than those for the feature Accounting for the eects of

extinction by the clouds makes the feature quite skew which reduces the ability of

our mo del to adequately t it

In sum due to the unique shap e of the feature at our ability to mo del

it well its closeness to the predicted time and its depth we b elieve that it is likely

due to the o ccultation event and not due to tracking errors or clouds

The light curve recorded by Team is shown in the top of Fig observed

from a p osition km farther along the shadow track from Team and km

p erp endicular to it This light curve was obtained in a cloudless sky so all variations

are due to tracking errors gain changes and manifestations of the o ccultation At

the time one would exp ect the comets shadow to pass over Team based on Team

s results marked on the gure there is a drop in ux of a few p ercent lower

panel of Fig That features shap e is similar to other tracking error corrections

in the light curve so it is not clear if this is the o ccultation However it do es allow

us to limit the opacity of the coma km from Team s chord at

Analysis

Mo del and Assumptions

Our mo del for the light curve assumes the optical depth is prop ortional to

the inverse of the cometo centric distance raised to a constant p ower n The

steadystate forcefree radiallyowing dust coma would have n As the comet

passes b etween Earth and the star the attenuation of starlight will dep end on time

A schematic of the scenario is given in Fig Ignoring clouds for the moment

we express each p oint in the light curve S t as a constant term S the comets

ux plus sky ux and detector noise plus a term representing the stars ux times

t

the attenuation factor e Let C b e the ratio of the stars

t

unattenuated ux to S Then S t S C e If the comets nucleus itself

passes b etween the star and Earth the ux during that interval will just b e S If

the star disapp ears b ehind the nucleus at time t and reapp ears at time t then

o

i

the light curve can b e represented by

t

i

S C e if t t

i

S t

S if t t t and

o

i

t

o

S C e if t t

o

Since we do not assume a priori that the two sides of the coma that are sampled

by the inb ound and outb ound sections of the o ccultation are the same we have a

threepiece function We can however remove the nuclear chord in the mo del simply

Figure next page Light curve of o ccultation by HaleBopp Team This

light curve has the exp ected time of the o ccultation marked based on the time of

deep est o ccultation recorded by Team The Top panel shows the whole curve

lower panel shows a closeup of the most relevant section Ordinate units are arbi

trary There is a slight dip in the count rate at the appropriate time but it is not

distinguishable from other comparablyshap ed features

by setting t t The subscript i denotes a quantity related to the ingress o to

o

i

the egress

Evaluating as a function of time requires knowing The distance from the

q

center of the nucleus at a given time t is just b v t t where b is the

m

impact parameter v is the sp eed of the comet across the sky and t is the time of

m

mido ccultation Since the center of the assumed spherical nucleus do es not have

to b e the co ordinate origin for we include an extra term l that describ es the

oset parallel to the stars direction of motion of the co ordinate origin from the

q

nuclear center Thus t b v t t l and the optical depth is given

m

by

n

i

i

q

t a

i

b v t t l

m

i

n

o

o

q

b t

o

v t t l b

m

o

where is the length scale of the opacity Since we allow the time t to b e t

m

by the mo del we have overparameterized the lateral shift in the co ordinate origin

the b est parameter to quote really is l l l ie the separation of the two

o

i

co ordinate origins In later discussion we will mention the nuclear radius R which

is just

s s

R b b l v t t

n o

i

ie the square ro ot of the quadratureaddition of the impact parameter and half

the length of the chord through the nucleus A listing of all quantities is given in

Table

Note that the impact parameter b was not used as a measure of the oset from

the co ordinate origin in the p erp endicular direction The co ordinate origin always

lies on the horizontal line in Fig that runs through the center of the nucleus

There is no evidence that our assumption is justied but it do es make the mo deling

tractable and allowed us to constrain prop erties of the nucleus

In addition to this theoretical mo del we accounted for the largescale extinction

in the light curve due to clouds near the time of the event by multiplying our mo del

by an empirical function On Fig the asterisks in the light curve indicate where

it was sampled to estimate the clouds eect The thick line is a spline t through

those p oints and represents the empirical function We sampled the clouds eect

outside the region to which we applied our mo del The observation site of Team

was dark and mo onless so the clouds would only cause extinction of the starlight

not increase the sky brightness

We have made some assumptions to simplify the tting The spherical nucleus

assumption immediately implies that t t t t Also note that our mo del

o m m

i

coma Fig is not p erfectly circular n and can b e dierent b etween the two

hemispheres but within one hemisphere they cannot vary We have not included in

our tting the data near the time of the tracking correction seconds centered at

UT and two brief noise spikes seconds starting at UT

Figure Schematic of o ccultation scenario and light curve The top plot shows

a generic light curve based on the stars passage b ehind the coma and nucleus of

the comet The arrow in the drawing indicates the stars motion Times of the

b eginning and end of nuclear chord are marked t and t resp ectively as is mid

o

i

o ccultation t note the abrupt jump in the ux at time t as the star passes

m

i

b ehind the nucleus The lo cations of a coma opacity of and are marked All

variables are dened in Table

Table Parameters of the Mo del of

Nuclear and Comatic Structure

Symb ol Description

Fit Variables

S count rate from cometskydark current

t t b eginning and ending times of o ccultation by nucleus

o

i

t time of midevent

m

l length of the nuclear chord of the o ccultation

n

b impact parameter

n n exp onent of the p owerlaw prole of the opacity

o

i

length scale of the opacity

o

i

distance of cometo centric co ordinate

l l

o

i

origin from center of nucleus

Variables Derived from Fit

opacity

o

i

R nuclear radius

Known Constants

C ratio of count rate from star to S

v sp eed of comet across sky kms

Subscripts

subscript i o variable p ertains to ingress and egress of o ccultation

seconds starting at UT see Fig Lastly we have assumed that

the radius of the nucleus is no bigger than km Analysis of highresolution mid

infrared microwave and optical imaging of the comet have constrained the nuclear

size to b e smaller than this value Altenho et al Weaver and Lamy

and a later section of this Chapter so our assumption allows for a large error in

these works In terms of our tting this means we will not consider mo dels that

require a combination of b and l such that R km

n

Further assumptions were made ab out the physical environment of the coma

First we assumed that n could b e no larger than Hydro dynamic mo dels of

the coma Divine imply that a steep ening of the dust density prole to the

equivalent of yielding a surface brightness and opacity prop ortional to

can o ccur within a few nuclear radii of the nucleus Others eg Gomb osi et al

Marconi and Mendis have also used dustyhydro dynamic

mo dels to calculate dust velo cities andor numb er densities as a function of come

to centric distance and their results do show some steep ening of the dust prole

within a few nuclear radii of the surface From these works we conjecture that the

tenable limit to n in this phenomenon is to though the higher values have

less theoretical supp ort Again we allow for a large error in these previous works

Our second assumption is that l can not b e so large as to extend o the near edge

of the nucleus itself In other words we did not allow the case where and

the divergence of the opacity could b e encountered by the star

Results of Mo del Fitting

Since there are so many data p oints in this case the statistic is useful only

as a coarse indicator of go o d and bad ts eg a t that go es through all of the

p oints but is to o shallow to cover the light curves minimum could have a reduced

of just which would still b e b eyond the condence level for the

R

o dd degrees of freedom The b est way to ascrib e a go o d t is by eye with

b eing a rough guide There are three morphological characteristics that must b e

satised for a t to b e considered go o d a it must b e suciently deep to cover

the valley at UT determined by n b and to some extent by t t

o

i

b it must follow the shap e of the valleys walls from to and from

to UT determined by n and l and c it must lie on the

median value of the wings from to and from to

UT determined by and n We say median b ecause we do not attempt to t the

small jumps in ux that o ccur in the wings these may b e due to clouds or to real

opacity features in the comets coma A given mo del was detuned with the various

parameters until the t could no longer b e considered marginally go o d

The results of the tting are summarized in Table We have explored pa

rameter space using b and km and higher values but

it turned out that they never suciently t the light curve and n

and Entries in the table give values or ranges for the quantities

and l that yield go o d or marginally go o d ts as dened ab ove In the

o n

i

Comments column the presence or absence of m indicates a marginally go o d

or go o d t All ts listed in the table have with most around

R

or With only one chord through the comet showing unambiguous

extinction the valid parameter space oered by our mo del is large Moreover the

unfortunate lo cation of the tracking correction so close to the valley of the light

curve thus removing those data p oints allows an even wider valid space

Figure displays representative ts to our light curve It is not meant to b e

as exhaustive as Table is but graphically shows the large variation in parameter

values that still allows adequate tting The rst four plots have forced l

the last four allow it to vary The value of b is written within each plot The abrupt

jumps in the ux predicted by some mo dels are due to the star passing b ehind the

nucleus note the jump at time t in the schematic light curve of Fig Sp ecial

i

note should b e taken of one mo del in Fig a using n n it cannot t the

o

i

curve Also Fig d shows a mo del with b km such a high impact parameter

allows only a marginal t to the curve The value of is in all but the one

R

obviously incorrect mo del where it is

We mention some other notable results from the mo deling

Our mo deled constraints on b limit the nucleus radius R via Eq to

km Restricting ourselves to the b est not marginal ts and to n then

R km

For completeness we mo deled the case where b and l even though

n

clearly this is an unphysical scenario Fortunately it was never the case that the

light curve was signicantly b etter t with l than with l

n n

The distance from the co ordinate origin to the p oint in the coma is given

by For some mo dels in Table R so the maximum coma opacity is less

than unity The t to the light curve for these mo dels requires the nuclear chord to

pass through the baddata gaps On the other hand with a small R the maximum

opacity can b e as high as Note that the noise in the light curve prevents us from

condently distinguishing b etween and or

For clarity we have not put in the allowable ranges of for each mo del in

Table Typically changing by km still yields a go o d or marginally go o d t

The acceptable ts to the light curve require n to b e at least though the

ts are slightly b etter as n increases Further if n in one hemisphere then

n in the other This steepness to the coma is opp osite the sense found in

Giotto images of comet Halleys inner coma where n as R due to lo calized

sources of dust on the surface Thomas and Keller Reitsema et al

We p ostulate that the steepness in HaleBopps coma is due to azimuthal structure

where we have assumed none andor to the passage of the stars path through the

acceleration region of the dust Clearly our mo del is simplistic but the lack of data

do es not justify using a more complex formulation

One p ower law can satisfy the constraints of the light curves measured by b oth

Team and Team if in general n A letter c in the Comments column

of Table indicate which mo dels are consistent with b oth curves Furthermore

if we force the coma to b e consistent it would then b e imp ossible for the nuclear

shadow to have passed b etween the two teams Ie if Teams and were on

opp osite sides of the nucleus the parameters describing the two sides of the coma

sampled by the two teams would have to b e dierent which is b eyond the scop e of

our mo deling An alternate explanation is that the coma merely do es not have the

spherical or hemispherical symmetry that is assumed

Figure ad Example mo del ts to o ccultation light curve Shown here are ex

ample go o d mo del ts using various combinations of parameters overlaid on the

Team light curve This is not an exhaustive p ortrayal of the entire valid parameter

space but only demonstrates how well the curve can b e t All mo dels presented

here assume there was no nuclear chord Each plot has the impact parameter b

written within its b orders The rst plots assume l l l Each plot

o

i

shows or mo dels with varying n and n written as n n n Plot a shows

o o

i i

clearly that n n do es not t the curve plot d shows an example of an

o

i

impact parameter higher than km that marginally ts the curve The blank

section near minutes past UT caused by a tracking correction allows for

great latitude in the kind of mo dels that can t the data

For most mo dels we nd km l km though for b km

the range is only a few kilometers Moreover having the co ordinate origin of b oth

hemispheres on the ingress side of the nucleus is slightly favored by a decrease

in Note that in comet Halley the origin was found to b e near the center of the

R

nucleus Thomas and Keller

Figure eh Example mo del ts to o ccultation light curve Here is the same

scenario as for ad except the plots allow l and each mo del mentions

the value used

Table Constraints on Parameters to Occultation Mo del

b n n e l range R range Comm

o o n

i i

a a b c d e f

km km km km km

m

m

m c

m

c

m

m

m

m c

m

c

c

m c

m c

Table Continued

b n n e l range R range Comm

o o n

i i

a a b c d e f

km km km km km

m c

m c

m

m

m

m

m c

m

m

m

c

m c

m c

m

Table Continued

b n n e l range R range Comm

o o n

i i

a a b c d e f

km km km km km

m c

m

m c

m c

m

m

c

m

c

m c

c

m c

m c

m

m c

c

Table Continued

b n n e l range R range Comm

o o n

i i

a a b c d e f

km km km km km

m c

m c

m c

m c

m c

m c

m c

m c

c

m c

m c

c

c

m c

c

m c

c

c

m c

m c

Table Continued

b n n e l range R range Comm

o o n

i i

a a b c d e f

km km km km km

m c

m c

c

m c

m c

c

m c

c

c

m c

m c

m c

c

c

m c

m c

Table Notes

a

Error from tting is km

b

Cometo centric distance at which coma opacity is Error from tting

is km Two values are given one for each hemisphere

c

Mean value of e within km of nuclear surface Error from

tting is ab out

d

Range of lengths of nuclear chord that yields an adequate t Error from

tting is km

e

Range of p ossible nuclear radii based on the range of l and b

n

f

Comments Letters meanings m marginally go o d t c t is consistent

with opacity measured by Team

Discussion

Nucleus

As mentioned we assumed that the nucleus has R km but our tting

further constrains this numb er to km by making two reasonable assumptions

Only marginally go o d ts are found for mo dels with R much bigger than this up

to km ie almost up to the assumed maximum For mo dels that yield R

km or even km for that matter the ts are not even marginally go o d

Millimeter wave measurements by Altenho et al and our centimeter

wave measurements as will b e seen later in this Chapter agree with this o ccult

ationderived limit However I emphasize that this o ccultation analysis assumes a

spherical nucleus

Astrometry

Our apparent detection of the o ccultation implies the nucleus was

km on a p erp endicular from the last prediction of the nuclear track Mid

event o ccurred ab out s b efore the predicted time for the lo cation of Team

corresp onding to km along the track Considering the errors involved with the

prediction this is not an unacceptably large oset as we now explain

Figure a shows an image of the comet and star taken one b efore the

event from the USNO Flagsta Station m telescop e Figure b showing

an expanded view of the central pixels of the comet is marked with the middle

of the brightest pixel M the lo cation of the centroid of brightness C and

the estimated p osition of the nucleus using our comatting technique L

pixel The pixel size for the images in Fig is arcsec km at the

comet Our astrometry of the comets oset from the ephemeris p osition using

nights of USNO images as mentioned in xI I was uncertain to arcsec

km ie almost one pixel Combined with the uncertainty from the comatting

technique this gives an error of ab out km So it is quite reasonable to

exp ect the nuclear shadow to have passed over a team several hundred kilometers

from the predicted center line

Our constraint on the lo cation of the nucleus is reasonably consistent with

calculations for the orbit of HaleBopp Donald Yeomans private communication

However it should b e noted that we are estimating the error with resp ect to the

measured p osition of the comet from the astrometry not from the ephemeris Had

we used a dierent ephemeris say one that was thought to b e more accurate the

only dierence would have b een to change the osets measured via the astrometry

of the USNO images We would have arrived at the same prediction and the same

observing strategy Hence a p ostfacto ephemeris which might b e used to try to pin

down exactly how far Team was from the nucleus shadow would not make much

dierence In essence our astrometry provided a truer prediction of the comets

p osition than any ephemeris would have Astrometric measurements from p ost

event imaging would have help ed but these data were not taken

Inner Coma Alb edo of Dust Grains

Figure Preo ccultation image of comet and star In a an image of b oth comet

HaleBopp C and PPM S is shown taken less than one hour b efore

the o ccultation The scale is arcsec p er pixel corresp onding to km of linear

distance at the comet our entire o ccultation event marked in Fig covers ab out

onehalf of a pixel Line segments indicate the most prominent jets in the comets

coma and show that on ingress the star was traveling along a jets edge In b

I show an expanded view of the central pixels of the comet The middle of the

brightest pixel M centroid of brightness C inferred p osition from comatting

technique of Lisse et al b L

Since we have measured the opacity of the coma we can calculate the alb edo of

the dust in the inner coma by using measured values of Af a quantity intro duced

o

by AHearn et al where A is the alb edo f is the lling factor and is the

o

size at the comet of the ap erture used It is obtained via

F r

comet

Af

o

F AU

o

where r is the helio centric distance of the comet is the geo centric distance F

is the solar ux at Earth and F is the comets ux measured in the ap erture

comet

The lling factor is the ap ertureaverage of e Here the alb edo is prop erly

the value of the scattering function relative to a conservative isotropic scatterer as

outlined by Hanner et al and equal to G in that work

We analyzed HST WFPC images of the comet obtained twelve days b efore and

twelve days after the o ccultation event provided by H A Weaver of Johns Hopkins

Univ and Af was measured down to a cometo centric distance of km ab out

o

arcsec A steadystate forcefree radiallyowing dust coma would have an

ap ertureindep endent value of Af but since HaleBopps coma was not like this

o

we extrap olated Af down to km for comparison with our o ccultation results

o

Since the phase angle of the observations was only we removed the phase angle

eect by using

where is the phase co ecient of magdegree a value roughly consistent

across several comets Meech and Jewitt and is the phase angle at the time

of the observation We estimate that Af was ab out km on

o

Sep and km on Oct Time variability of the comets ux in

the HST images leads to the large error estimates Taking Af

o

km on Oct km and the ap ertureaverage of e to b e ab out

o

we nd A to b e formal error This leads to an

equivalent geometric alb edo p of A I use the value of

to follow the notation of Hanner et al This value is rather low eg

Divine et al collate information from various workers to obtain an average

p of and a p ossible explanation similar to that given by Larson and

AHearn is that a photon is doublyscattered by the dust in the inner coma

It is not unreasonable to exp ect such a scenario in the opticallythick p ortion of the

coma If every photon were doublyscattered A would b e the square ro ot of

the value given ab ove formal error and p That the

calculated alb edo is acceptable provides one selfconsistent check that our mo del

results and sp ecically the high opacity of the coma make sense

Inner Coma Plausiblity of Findings

Our mo deling implies that the column density of dust in the inner coma follows a

p ower law of with an index steep er than This steepness is not evident in large

scale imaging of the comet The path of the stars ingress followed the edge of one

of HaleBopps jets short line segments in Fig a that had a surface brightness

prop ortional to during egress the path did not follow a jet and the coma

surface brightness was prop ortional to However one can t just the wings

of our o ccultation light curve ie b etween and km from mido ccultation

and match the proles from the largescale imaging It is only in the central region

within km of the nucleus where these proles fail and the density of dust must

b e a steep function of Unfortunately the small scale of these prop erties of the

coma are b eyond the reach of other Earthbased observations even HST Planetary

Camera imaging would have covered a full km p er pixel

It is p ossible that we observed the acceleration region of the dust and that it may

have extended km from the nucleus steep ening the dust prole Gomb osi et

al in their review of inner coma dynamics state that their mo deling shows

dust still accelerating toward terminal velo city several nuclear radii away from the

nucleus alb eit in a mo del coma with a lower dusttogas ratio and lower r than

HaleBopps A larger could extend the comas acceleration region but the larger

r lower insolation lower dust sp eed may counter that eect

A detailed dusty gasdynamic mo del of HaleBopps coma is b eyond the scop e of

this pap er but using estimates of the dust sp eed v we can show the steep opacity

prole is roughly compatible with the mo dels of Gomb osi et al We note that

azimuthal variations in the dust density not only the acceleration of the dust can

contribute to the measured shap e of the dust prole but a mo del of such variations

would b e dicult to constrain owing to a lack of data Thus we show here only a

gross justication of a steep opacity prole The prole is prop ortional to

or so which makes v since surface brightness is prop ortional to v

Let us take the nucleus radius to b e km we cannot exp ect the dep endence

of v to hold all the way to the surface so we will estimate v at kilometers ab ove

it say km Assuming the dust is accelerated out to km v will b e

ab out times smaller

Now the terminal velo city v of the dust grains at the time of the o ccultation

t

was ab out kms This is based on a v at p erihelion r AU b eing ab out

t

kms Schleicher et al a and b v r which is a relation similar

t

to that used for the sp eed of the gas in the coma Biver et al Therefore at

km v kms kms Figure a of Gomb osi et al

shows their mo del giving a micron wide dust grain a sp eed of ab out kms

at ab out nuclear radii ab ove the surface equivalent in this case to km

Since there are dierences b etween HaleBopps environment and that used in the

mo del of Gomb osi et al and further their calculated v do es not strictly

follow this match b etween v is somewhat coincidental but it is clear that v is

roughly comparable to mo del calculations

We noted the high optical depth implied by our mo deling Canonically comae

must b e optically thin so that sunlight can reach the nucleus to drive the sublimation

of gas leading to the pro duction of the dust in a selfregulating manner However

an optically thick inner coma could b e a secondary source for energy via scattering

of sunlight and thermal reradiation esp ecially if the dust has b een sup erheated as

seems to b e the case for HaleBopp Lisse et al a This problem has b een

analyzed by others who have found by various analytic and numerical simulation

metho ds that the energy dep osited to the nucleus is a weak function of comatic

optical depth even up to reradiation almost comp ensates or in some anal

yses overcomp ensates for the decrease in sunlight see eg Salo Hellmich

An imp ortant check is whether a high makes sense We argue that it do es as

follows Af derived ab ove is km at km At the time of

o o

the Giotto yby of comet PHalley Schleicher et al b rep ort that Halleys

Af km and Keller et al calculate from Giotto imaging that

o

the p eak opacity of the dust coma a few kilometers ab ove the surface of the nucleus

was ab out So HaleBopps Af from xIVc was at least times larger

o

than Halleys during the yby With the two comets dust grains having roughly

the same alb edo it is clear that it would b e not b e dicult for HaleBopp to have

had a p eak around unity Furthermore it is likely that HaleBopps near nucleus

Af was even higher for the following reason Our mo deling shows the dust

o

opacity prole to b e prop ortional to or so making

o

Af

o

o

This is not strictly true at the higher optical depths since f is not allowed

but it do es imply that Af is higher than the km as one travels in from

o

km so that it is probably more than three times larger than Halleys when

measured near the nucleus surface

Summary of Occultation Results

We rep ort constraints on the nuclear and comatic prop erties of Comet Hale

Bopp as implied by our observations of an o ccultation of a ninthmagnitude star

Except for the sp ecial case of Comet Chiron this would b e the rst time such an

event with so small an impact parameter has b een observed Our observations were

marred by thin clouds and a lack of adequate corrob orating data only one chord

through a suciently thick p ortion of the coma was apparently measured but

there are many pieces of circumstantial evidence to show that we indeed observed

the o ccultation Moreover we know of no other observations of the comet that

can refute our conclusions Our data nearest the nucleus were collected ab out

km from the latest prediction but this is not unreasonable since such a distance is

comparable to the astrometric error in determining the nucleus lo cation within a

nitelypixelized image dominated by comatic ux

By mo deling the shap e of our light curve with a simple coma and spherical

nucleus mo del and assuming that our observation recorded the o ccultation we nd

the following

Assuming the p owerlaw opacity prole of the coma with exp onent n is as

shallow as or shallower than the impact parameter b is km but the b est ts

o ccur when b km Our o ccultation observation has sampled the nearnuclear

inner coma which has only rarely b een observed b efore in any comet

If n the nucleus is spherical and the co ordinate origin is constrained

as depicted in Fig then the nuclear radius R must b e smaller than ab out

km Relaxing the constraints on n yields an upp er limit of km

The inner coma of HaleBopp is probably optically thick even at nearly

AU from the Sun Regardless of the values for the other parameters go o d ts to the

data can only b e found if the opacity within the rst few tens of km of the center

not the surface of the nucleus was at least unity For some applicable mo dels R

is bigger than this distance in which case the maximum coma opacity is less than

one but never much less

We nd that the alb edo A of the dust while it is within km of

the nucleus center is formal error The equivalent geometric alb edo

p is formal error This assumes that all photons within this region

are doublyscattered Without this caveat the calculated alb edo is lower than the

typical value p compared to from Divine et al

The dust opacity prole is probably steep er than the canonical p ower

n

law b eing most likely prop ortional to with n Marginal ts can b e

found for n for one hemisphere The other hemisphere is in that case quite

steep n This o ccurs p ossibly within or km of the nuclear center

but denitely within km This chord through the coma may have sampled the

acceleration region of the dust andor azimuthal variations in the inner coma so

our mo del which describ es the comas density as two hemispheres each having a

single p owerlaw function of cometo centric distance would b e to o simplistic

The steepness of the prole in the deep est coma do es not match that of the

jet structure seen in largescale images although the resolution of all groundbased

imaging fails to directly sample the kilometer scales we are measuring via the

o ccultation The characteristic n for the wings of the o ccultation light curve could

follow the same value as for the largescale images and the pro cesses mentioned in

Item ab ove may only b e imp ortant within the rst km of the coma

Thermal Emission and Scattered Light Imaging

Observations

Table lists the nono ccultation data taken on comet HaleBopp in the opti

cal midIR and radio regimes Helio centric distance r geo centric distance

and phase angle are given along with our measurement of the ux from the

nucleus of the comet In all observations except for the microwave where the comet

app eared as a p oint source pro cessing using the comatting metho d from Chapter

was required to separate the comatic from the nuclear ux One notices that

unfortunately the image pro cessing was inconclusive for many of the datasets The

brightness of the nucleus is stated using either its Cousins R magnitude or its ux

in Janskys One Jansky is Wm srHz Images from Apr near p er

ihelion were to o choked with coma to detect the nucleus these data were used

however to infer the nucleus rotation p erio d The comets coma during late Nov

emb er and Decemb er and July was not structured enough to allow an

analysis with our metho d these entries are italicized in the table

Analysis

Infrared and Optical Data

We p erformed the comatting analysis on our infrared and optical data sets

and we show some of the results in Figs optical and

Table Observations of Comet HaleBopp

No Date UT System Wavelength

Oct HST WFPC A

May HST WFPC A

Jun HST WFPC A

Oct HST WFPC A

Oct Nov ESO m TIMMI m

Nov Dec ESO m TIMMI m

Jan NASAIRTF MIRAC m

Mar VLA cm

MIRLIN

Apr NASAIRTF m

MIRAC

Jul ESO m TIMMI m

Table Continued

a b

No r AU AU deg Nuclear ux CF Rot

R Y N

C

R Y N

C

R Y N

C

R Y N

C

Jy Y N

NA N N

NA N N

c

Jy NA N

NA N Y

NA N N

a

CF Coma tting Are the data go o d enough to use the

comatting technique Chapter

b

Rot Rotation Was the rotation p erio d deriveable from the data

c

Image is a p ointsource no coma seen

infrared Each gure shows the analysis of one typical image from each of the

ve observing runs where the analysis was applicable The upp er left panel in each

gure shows the original image the upp er right shows the mo del the lower left

shows the residual and the lower right compares the residuals prole with that of

a PSF All images have used logarithmic scaling The residual plot in each gure

follows the prole of the PSF reasonably well

For the four optical datasets we nd a consistent value for the nuclear cross

section even though the inner coma of HaleBopp is thought to b e optically thick

as explained in Section It is p ossible that all three measurements show

actually the cross section of the opticallythick p ortion of the coma rather than of the

nucleus Optical images from Oct oer the b est chance to detect the nucleus

without much intervening nearnuclear coma The interpretation of the optical and

midIR measurements of the nucleus will b e explained b elow

Infrared images taken near p erihelion were useful in constraining the rotation

p erio d of the nucleus Indeed it was the only p ortion of the datasets that indicated

this since photometric determinations of the rotation were imp ossible Morpho

logical changes in the coma during the p erio d of UT Apr to Apr were

analyzed and it was found that the rep eatability of the structure had a mean p eri

o dicity of P hr over that time p erio d The sequence of images

is shown in Fig The rotational phase is written in each image of the sequence

I have a ninehour sequence of images from Apr and a vehour sequence from

Apr which have b een combined to pro duce the image sequence this is the MIR

LIN sequence lab elled on the gure The two days limited the p ossible p erio ds to

P and P Subsequent imaging on Apr the MIRAC image on the gure

was matched with the rst two days to remove the p erio d ambiguity The caveats

to attaching a rotation p erio d of the nucleus to the variability of coma morphology

have b een explained in Chapter

Figure next page Comatting metho d applied to optical image of Hale

Bopp The extraction of the nucleus from HST WFPC image of the comet taken

on Oct is displayed Upp er left panel is the original image upp er right

is the mo del created by the comatting metho d lower left is the residual and

lower right shows a plot comparing the prole of the residual and the PSF the two

match each other very well indicating we have removed the skirt of the coma The

intensity scale in the images is logarithmic

Figure page Comatting metho d applied to optical image of Hale

Bopp Same as Fig except for May

Figure page Comatting metho d applied to optical image of Hale

Bopp Same as Fig except for Jun

Figure page Comatting metho d applied to optical image of Hale

Bopp Same as Fig except for Oct

Figure page Comatting metho d applied to midinfrared image of

HaleBopp Same as Fig except for Oct and taken with ESO m

telescop e and TIMMI midinfrared camera

Figure next page Rotation sequence of comet HaleBopp Sequence of

IRTF  images of the comet indicating its rotation p erio d taken during to

Apr Two days of MIRLIN images were phased together to create the image

sequence The rotational phase of the image is noted in white in each frame Ab out

a week later we obtained MIRAC images and were able to match the phase with

the earlier sequence as shown The p erio d is  hr

Secondary Nuclei

We have examined the HST images for evidence of any secondary nuclei as was

suggested by Sekanina b We deconvolved the residual images left after our

application of the comatting metho d We used the same p ointspread function

as Sekanina used and also a theoretical one that we found to closely mimic the

structure of observed stars The two PSFs dier a bit in shap e but are not to o

dissimilar when pixelized to the WFPC PC resolution We found no clear indication

of a second nucleus we were able to obtain satisfactory ts to our residual maps

using just one p ointsource A second p ointsource would of course improve our ts

but not signicantly Moreover we do not nd the need to intro duce a secondary

nucleus as strong ab out onefth the brightness of the primary as mentioned by

Sekanina b Undoubtably this is due to the dierent metho ds used to mo del

the emission from the coma Sekanina uses an analytic function with just a few

parameters to match the comas brightness whereas we are tting the structure at

every azimuth for a total of a few hundred parameters It is also p ossible that the

secondary nuclei that Sekanina claims are actually jet features in the nearnuclear

coma

Microwave

We detected the thermal continuum from the comets nucleus at the level

after a hr integration at VLA The image is a p oint source and the most im

p ortant section of our CLEAN map is shown in Fig The detection at VLA

of HaleBopps thermal continuum was the rst such detection by that observatory

after only upp erlimits were found for ve other comets Snyder et al de

Pater et al Schenewerk et al Hoban and Baum and Chapter

of this thesis It is arguably the rst detection ever of the thermal continuum

radiation from a cometary nucleus in the centimeterregime similar observations of

comets West C XX XX n Hobbs et al and Kohoutek

C XX XX f Hobbs et al imaged their comae and

singledish observations of comet IRASArakiAlco ck Altenho et al while

yielding uxes consistent with a nucleus had b eam sizes that were large enough to

arguably include ux from the coma esp ecially since a skirt of decimetersized grains

was detected by the radar exp eriments of Goldstein et al and Harmon et

al Our VLA measurements had a synthesized HPBW of only arcsecond

and moreover a reduction of the data excluding the very long antenna baselines of

VLA which deemphasizes any smo oth underlying comp onent to the emission ie

a coma still yielded a p oint source Hence we conclude that thermal emission

from centimetertodecimeter sized grains in HaleBopps coma is negligible in com

parison to the emission from the nucleus itself At the very least this is the rst

interferometric detection of the microwave continuum from a nucleus

There have b een other interferometric observations of the radio continuum in

the millimeter regime and they to o were taken near p erihelion so we can construct

a radio sp ectrum of the HaleBopp nucleus one of the rst such sp ectra in existence

This is shown in Fig We used the uxes rep orted by Altenho et al

using the IRAM Plateau de Bure interferometer and Blake et al using the

Owens Valley interferometer and scaled them to account for the small dierences in

2

geo centric distance in the comet The sp ectrum follows the RayleighJeans law

quite well tting the p oints to a line implies the emissivity could not have any more

01

than a overall dep endence Alternatively the deviation from the Rayleigh

Jeans law could b e due to the dierent depths and hence dierent temp eratures

at which the millimeterwave and centimeterwave observations sample

Discussion

Mo del of Microwave Emission

Use of the augmented thermal mo del I describ ed in Chapter is justied with

comet HaleBopp since we have an idea of the rotation state and photometry at

multiple wavelengths The extra trick however is that the microwave data do es not

sample the nucleus surface but several radiative skin depths deep and the ux

that the augmented mo del predicts for the centimeter wavelengths dep ends on how

steep the temp erature gradient is within the nucleus The wavelength is cm

exactly how far down from the surface the continuum is emitted is a matter of some

debate it could b e a few wavelengths roughly one decimeter if the material is

mostly ro ck or it could b e signicantly larger roughly half a meter or more if a

substantial ice comp onent is present de Pater et al Since the cometary ice

is not exp ected to b e found in patches around the surface but rather in a mixture

with the ro ck I will cho ose the former scenario to constrain the mo deling

Another matter that one must take into account is the eect of the coma on the

total energy put into the nucleus The contribution of direct sunlight is decreased

due to the optically thick coma but this is somewhat comp ensated by the thermal

emission of the dust and to a lesser extent by the scattering of the visualband

sunlight o the dust grains Salo has already made detailed calculations of

the energy available to a nucleus surrounded by a coma of a given optical depth with

grains of a given singlescattering alb edo and HenyeyGreenstein asymmetry factor

Henyey and Greenstein I will use his results here For small micron

and b elow dust grains of which HaleBopp was a pro digious pro ducer Lisse et

al a Williams et al forward scattering is exp ected to b e imp ortant

and Salo calculates that in that case the reradiative comp onent to the total

p ower onto the nucleus would b e ab out to of the total p ower on a bare

nucleus This is for opacities of unity and greater In other words in the limit

of an innitely thick coma the nucleus would receive to of the energy

it otherwise would without that coma For the opacities of HaleBopps coma

describ ed in section there would b e the e reduced direct sunlight comp onent

also or to of the unextincted sunlight to bring the total to ab out to

of the original available energy I do not want to overstate the accuracy of this

calculation other workers have done similar computational exp eriments and have

found dierent answers dep ending on the mo del assumptions eg Marconi and

Mendis Hellmich However the consensus seems to have the nucleus

losing little net available energy despite having a coma with 

Figure CLEAN contour map of comet HaleBopp microwave continuum This

the image obtained with the VLA b etween and March of the nucleus

microwave continuum The CLEAN algorithm has b een applied Contours are

and The dark circle at lower left represents the synthesized b eam

HPBW ab out arcsec wide

Thus the augmented mo del was mo died to allow an additional of the solar

1

ux on top of the extincted  e direct contribution The rotation p erio d of

hr was used and the comets rotation axis was directed toward a cometo centric

 

longitude of and latitude of a direction close to what has b een

derived by several groups Licandro et al Jorda et al The shap e

of the nucleus is totally unknown but due to its apparently large size it may b e

tempting to think of it as spherical This is complete guesswork since plenty of

comparablysized asteroids are elongated To reduce the numb er of parameters I

have arbitrarily set one axial ratio to and the other to

To mo del the microwave ux I allowed the thermal inertia and eective radius to

vary leaving the opacity at unity The problem was then to just nd a combination

of eective radius and emitting layer depth that pro duced the observed microwave

ux The trend is for the emitting layer to b e deep er as b oth the eective radius and

thermal inertia increase a higher thermal inertia means there is less of a temp erature

gradient in the nucleus and a higher eective radius simply means there is more

surface area and the ob ject is more luminous

For a lunarlike thermal inertia and an eective radius of km I nd that

my augmented mo del repro duces the observed ux if the microwave continuum were

emitted from a layer cm deep This is toward the high end of the plausible depths

it is wavelengths For comparison the thermal inertia for Phaethon a

likely dormant comet is ab out times the lunar value Harris et al and

the emitting layer on HaleBopp would b e ab out cm deep probably to o far

However if the radius were in this case only ab out km then the emitting layer

would b e only cm

For a thermal inertia more like that of the Main Belt asteroids roughly onefth

the lunar value Sp encer et al the depth of the emitting layer is only cm

for a radius of km and so the radius can b e very large km or more if we allow

the emitting layer to b e as deep as cm Based on my o ccultation results such a

radius is to o large since the impact parameter of that observation was so small so

one could conclude that HaleBopps nucleus has lunarlike or Phaethonlike thermal

inertia and the radius is in the to km range

Figure a shows the temp erature map derived from the augmented thermal

mo del using the lunarlike thermal inertia The axes are longitude and latitude

Since the nucleus is aspherical the longitude and latitude system are based on

the sphere that inscrib es the ellipsoid ie a sphere with a radius equal to the

smallest semima jor axis of the ellipsoid The undulations in the contours give some

indication of where the elongation of the nucleus lies Also note that near p erihelion

the currently accepted p ole p osition p ointed almost directly at the Sun causing

the almost STMlike contours The at temp erature on the night side is due to

the isotropic comas contribution to the impinging p ower Figure b shows

the temp erature map of the surface the dierence is ab out K in just a few

decimeters

Of course near p erihelion the nucleus orientation with resp ect to the Sun was

changing most rapidly Dep ending on the inertia this aects the mo del temp erature

map esp ecially since a large fraction of the Sunfacing hemisphere of the nucleus

near p erihelion is almost totally in darkness for most of HaleBopps orbit That

Figure Radio continuum sp ectrum HaleBopp nucleus This broadband sp ec

trum has b een created by combining my VLA results with OVRO and IRAM PdB

data The p oints follow a RayleighJeans law quite well dashed line What little

deviation there is could b e due to wavelength dep endence of the emissivity or the

thermal gradient of the nucleus sampled by the dierent wavelengths

hemisphere turns toward the Sun just a few months b efore p erihelion and turns

away again a few months after For this reason I ran my augmented thermal mo del

over to rotations to remove any transient eects from the choice of initial

conditions

Mo del of MidIR Emission

The next step is to check the low conductivity and the eective radius with

the infrared photometry from Octob erNovemb er Of course the comas con

ditions are dierent but we will take the opacity to b e approximately unity again

Unfortunately the mo del predicts ab out Jy less than half the Jy we found from

Fig In fact the radiation of thermal continuum from the dust would have to

deliver ab out of the energy received by a bare nucleus not the we have

used based on the work of Salo Under the formalism I have used here the

dust grains cannot b e ecient enough to backwarm the nucleus surface to the requi

site temp erature Now the grains of the coma were apparently indeed sup erheated

Williams et al Lisse et al a but this likely could not provide the extra

energy needed since the emissivity of the grains is to o low these grains are smaller

than the wavelength of the continuum emission sp ectrums maximum

Comet HaleBopp was ab out AU from Earth at the time of these midIR

observations and so one pixel of the detector covered more than km Though it

is a testament to the incredible infrared brightness of this comet this pixel scale is

much larger than the usual case where we concentrate on comets that are less than

AU away This means that the comatonucleus brightness ratio within the central

pixels is in general higher since each of those pixels can pick up such a huge area of

comatic ux Thus it is not completely surprising that the comatting technique

is unable to cleanly separate the coma and the nucleus This extra p ointsource

emission that the technique found in Fig may b e related to the opacity of the

coma near the nucleus

Implications of Optical Measurements

The optical magnitudes of the nucleus in Table can b e used with ab ove

derived range of the radius to nd the alb edo As stated I will use the Octob er

value since that dataset is probably the least contaminated with an optically

thick coma Also note that the phase angle is small so there is little added error

from the uncertain optical phase b ehavior A caveat to this analysis is that dierent

workers have derived dierent brightnesses for the emb edded p oint source within

these very same HST images Weaver et al Weaver and Lamy Sekanina

using dierent indep endent programs to account for the coma This is almost

certainly due to two factors the pixel scale covers a large linear distance at the comet

compared to the size of the nucleus and the dust coma morphology in the inner

coma is more complicated than what we naively see in the images Small subpixel

features in the coma will adversely aect ones ability to photometrically extract

the nucleus esp ecially when the comet is very active and nearly AU away

Yet another p otential problem that adds to the error in the nuclear ux estimate

is the unknown rotational context of the HST images since we may b e viewing

dierent cross sections at dierent times

Figure Temp erature map of HaleBopp Mar This gure shows the

temp erature map of comet HaleBopps nucleus for Mar during the time of

our VLA microwave observations The map was created from my augmented thermal

mo del The top panel shows the temp erature skin depths into the nucleus the

b ottom shows the surface temp erature The temp erature drops by roughly K

in just a few decimeters

For an eective radius of  km and an HST R magnitude of 

C

on Oct the geometric alb edo is  Including the relatively dimmer

nucleus found by Weaver et al and Weaver and Lamy and the

relatively brighter nucleus found by Sekanina the geometric alb edo is within



Summary of HaleBopp Results

The combination of the o ccultation observations and the mo deling of the thermal

data provides the following conclusions ab out HaleBopps nucleus

 If the thermal inertia to HaleBopps nucleus is lunarlike or Phaethonlike

and if the emitting layer sampled by the VLA observations is less than cm then

the eective radius of HaleBopps nucleus is  km In general the higher the

thermal inertia the smaller the radius must b e in the range given This range is

also consistent with the upp er limit derived from the o ccultation results which set

a limit of km on the radius

 These inertias and radii cannot repro duce the  Jy of ux that was

measured at microns in Octob er and Novemb er so presumably the large

geo centric distance prevented our comatting metho d from reliably extracting the

nucleus This is b ecause there were to o many kilometers at the comet p er pixel and

hence to o much coma

 The o ccultation mo deling assumed a spherical nucleus so if the real nucleus

deviates from this then it is conceivable that the eective radius is larger than

km but that the section sampled during the o ccultation has lo cally a smaller radius

or that the nearnuclear dust coma has an unusual morphology that would fo ol us

into thinking that the nucleus radius is smaller than it is In that case the thermal

inertia could conceivably b e lower than the lunar value Moreover then it is easier

to repro duce the thermal IR measurement from later since with a larger radius

the nucleus has a higher luminosity

 The optical HST data have b een analyzed by many p eople in an attempt

to extract the nuclear ux Based solely on my results the geometric alb edo is

 but by including the eorts of others on the same dataset the visual

geometric alb edo is 

 Using the morphological changes in the midIR data I constrain the rotation

rate to b e hr  hr Strictly sp eaking this is the average rate b etween

and April

Lastly I mention the very signicant nding of an optically thick inner coma

from the o ccultation observation This was the rst time a dust coma with such a

high opacity had b een found

Chapter

The Nucleus of Comet Encke

Background

Comet PEncke has b een observed by mankind since Of the roughly

known p erio dic comets that have not b een lost only four others have an observa

tional baseline as long The comet was discovered indep endently four times once

each on four dierent apparitions b efore J F Encke published an orbit connecting

them all and successfully predicting the next apparition The orbital p erio d is

years the shortest known and so at rst glance one would think that it would b e

the comet we know the most ab out In some asp ects this is true eg Whipple

and Sekanina and Sekanina ab have a detailed mo del of the nucleus

rotation but the comet furtively guarded the basic prop erties of its nucleus until

the apparition when it made its closest recorded passage to Earth ever We

set up a multiwavelength observing campaign to take advantage of this opp ortunity

I have describ ed much of this exp eriment elsewhere Fernandez et al c and

repro duce much of the text

Observations and Reduction

The three datasets used in this study are describ ed in Table along with

helio centric distances geo centric distances and phase angles The measured uxes

are given in Table Images from the Europ ean Southern Observatory ESO

m telescop e were taken with the TIMMI instrument Kau et al at

wavelengths b etween and m The images have pixels and cover

Each pixel width covered to km at the comet during the observing run The

plate scale was measured using the known relative p ositions of Cen A and B

Perryman et al The p ointspread functions PSF full width at half

maximum FWHM varied from to arcsec Chopping of the secondary mirror

northward and no dding of the telescop e westward with typical throws of arcsec

were employed An array at eld was created by measuring the relative photometry

of a bright star at dierent lo cations on the array and then interp olating a surface

with a minimum of curvature We observed the comet at three wavelengths but only

at m was the comet bright enough to let us build a wellsampled time

series of data Absolute ux calibration was done using Cen A and interp olating in

wavelength information given by van der Bliek et al its m magnitude

is and the zero p oint is at Jy Color corrections were at most a

few p ercent Relative ux calibration was done using SAO HD

V Nor Kazarovets et al a star that was a short angular distance from the

comet and thus useful for measuring the atmospheric eects and the comets light

curve Its optical variability is mag with sp oradic mag jumps every

few years Perryman There was no indication of variability in the midIR

data that exceeded photometric uncertainty

The Infrared Space Observatory ISO data taken with the ISOPHOT instru

ment Lemke et al used a arcsec wide circular ap erture at wavelengths

b etween and m The data were reduced using the PIA software version

Gabriel et al Corrections to the measured uxes were made to account

for the nonlinearities in the detector the diraction of light b eyond the ap erture

and the color of the ux standard visavis the comet these corrections were at most

The Hubble Space Telescop e HST images were taken with the CCD on the

Space Telescop e Imaging Sp ectrograph STIS Wo o dgate et al as acquisition

images for a separate sp ectroscopic program A Awide red lter was used

We used the sciencequality output of the pip eline pro cessing of the data Each pixel

covers or km at the comet The high prop er motion of the comet

p er second left all stars as trails we estimate that the PSF FWHM

based on archival HST images taken with the same instrument detector and lter

within a few weeks of our observations

Analysis

ESO Photometry

Figure a shows the median of ESO TIMMI images of the comet with

a linear intensity scale Each image was weighted by the total signal The total

Table Observations of Comet Encke

Date Wavelength

No UT System m

Jul HST STIS

Jul ISO ISOPHOT

Jul ESO m TIMMI

r

No AU AU

Table Flux of Comet Encke

Wavelength Filter Filter Ap erture Flux

a

m Name Width m Radius Jy

b

ESO

N

NN

SiC

ISO

p UM P

P p UM

UM P

P p UM

P UM

UM P

P UM

UM P

HST

c

XLP

Table Notes

a

Width at halfmaximum eciency for ESO Kau and HST

Space Telescop e Science Institute For ISO the width of the

equivalent rectangular lter that has a height of the mean eciency of the

real lter Klaas et al Laureijs et al

b

Fluxes refer to the comets brightness at a geo centric distance of

AU and in the middle of the amplitude due to rotation

c

Flux is valid for ie Cousins R band We transformed

the instrumental ux to this band The equivalent magnitude is

eective onsource integration time is min Figure a compares this median

comets and Cen As enclosed ux as a function of photo centric distance The

star is a proxy for the PSF taken during the course of the comet images The

graph shows that a higher fraction of the comets ux resides in the wings compared

to the PSF and hence the comet is an extended source although the extent may

b e an artifact of imprecise adding of the images The amount of coma in the image

is calculated in Section

Figure shows our time series of the comets ux over four nights The ux

and error bar of each p oint are calculated from three ux measurements spaced

closely in time The time axis is mo dulo hr to show the p erio dicity in the

data explained in Section The ordinate is helio centric magnitude m at a

h

wavelength of m which is related to the observed apparent magnitude m by

 

m m log

h

AU

where is the geo centric distance This accounts for the changes in brightness due

to the rapidly varying during the observing run The m ux of the comet

referred to the geo centric distance on Jul UT AU and midway

b etween the minimum and maximum ux of the rotational variation was

Jy

ISO Photometry

The high spatial resolution of the ESO image has resolved out most of the

comatic ux but it is clear from Table that Comet Encke had a dust coma

the ux measured with ISOPHOT in the m range is much higher than that

measured with TIMMI Using the ap erture size and ux we can

ISO

estimate the amount of coma in the ESO image Fig a as follows Let F

ESO

b e the ux measured from the comet via our groundbased imaging Jy

The ap erture radius is Let F b e the ux measured by ISO within

ESO ISO

its ap erture The wavelengths sampled by ESO and ISO do not exactly match

but interp olating with a cubic spline we nd that ISO saw Jy at m

The rotational phase at the time of the ISO observations falls near a time of mid

brightness in the nucleus rotation though this is a small eect since the comas

ux dominates

The ux measured at ESO is valid for helio centric distance r AU

AU and phase angle while the ux measured by ISO is valid for

r AU and To compare we must correct for the

geometry and ap ertures First we assume that the surface brightness of the coma

n

is prop ortional to where is the cometo centric distance so that the comatic

n

ux is prop ortional to and that the ux within an ap erture of radius of

n

is prop ortional to A m ISOCAM image of the comet taken in early July

Reach et al shows a coma with mean n Second we assume that

the comatic and nuclear uxes are prop ortional to

 

p

hc r

exp

k T

Figure Comet Encke at microns a and Angstroms b Here images

of Comet PEncke with linear intensity scale are displayed Image a was taken

with the TIMMI camera at ESO m telescop e on UT Jul and image

b was taken with the STIS instrument ab oard HST on Jul North east

and the solar directions are marked Pixel scales are and resp ectively

Wavelengths of observation are m and A resp ectively The ESO image

is the weighted median of individual frames and the total integration time was

minutes The HST image exp osure time was s

where h is Plancks constant c is the sp eed of light k is Boltzmanns constant and

p p

T is K AU for the coma and K AU for the nucleus This is just the

representation for a spheres and a hemispheres resp ectively temp erature Since

the two r are not very far apart this gross approximation will suce Third we

assume that the nuclear ux is prop ortional to and where is

magdegree further discussed in Section Fourth we assume no phase

dep endence over the phase angles for the thermal emission of the dust

With these assumptions we calculate that ISO would have seen a coma that

was G times brighter than what ESO saw with the same ap erture and a

C

nucleus that was G times brighter The ap erture correction is A

N

Let F and F b e the ux of the coma and nucleus resp ectively as seen by ESO

C N

F F F Then F F G A F G Solving we nd F

ESO C N ISO C C N N N

Jy F Jy and thus only twelve p ercent of the ux seen by ESO is

C

due to coma

HST Photometry

Due to guidestar acquisition problems only two images of the comet were ac

quired with STIS Figure b shows the higher signaltonoise image of the two

with a linear intensity scale The integration time is only ve seconds which pre

vents us from seeing much of the extended structure In addition the high spatial

resolution has resolved out most of the coma Figure b compares the comets and

PSFs enclosed ux as a function of photo centric distance The graph shows that a

higher fraction of the comets ux resides in the wings compared to the PSF so the

comet is an extended source Also plotted is the prole of a mo del comet with a

p oint source nucleus plus a PSFconvolved coma that mimics the real comet

Ab out to of the ux is due to the nucleus so in our analysis b elow we have

assumed that the nucleus magnitude is log mag fainter than the

total magnitude Fortunately the derivation of the absolute zerophase magnitude

in Section is insensitive to the exact HST magnitude within a few tenths

Discussion

Perio dicity of Flux

We determined the aforementioned hr p erio dicity in our ESO data using

the stringlength metho d outlined by Dworetsky mentioned in Chapter

The string length trials are shown in Fig Also marked in the gure are the

p ossible p erio ds quoted by Jewitt and Meech JM hereafter and Luu and

Jewitt LJ hereafter using optical measurements near aphelion there is

go o d agreement among the three datasets A hr or hr p erio d gives a single

p eaked light curve but hr hr and the higher p erio ds either

imply two p eaks or leave enough unsampled ro om in the phase plot to allow for a

second p eak and valley One exp ects a doublep eaked curve for a rotating nucleus as

it shows dierent cross sections to the observer The hr p erio d is the only one

that gives temp oral coverage of most of the rotational phase and shows two p eaks

The errors attached to the rotation p erio ds are derived from a visual insp ection

of the phased light curve plot Perio ds near the lo cal minima in Fig are

Figure Radial proles of Comet Encke in midIR a and optical b Here I

compare the cumulative ux proles of Comet Encke and the p ointspread function

Squares are for the comet diamonds are for the PSF and triangles are for the mo del

a This is the prole from the TIMMI image in Fig a An image of Cen A

is used as a PSF proxy and the prole is scaled to the rightmost comet p oint b

This is a prole from the STIS image in Fig b A bright star imaged near in time

with the same instrument setup is used as a PSF proxy and the prole is scaled to

the rightmost comet p oint The mo del is a p ointsource plus a PSFconvolved

coma the coma contributes to of the total ux

acceptable only if the overlapping data in the phased light curve do not have widely

disparate magnitudes This denes the range of p ossible p erio ds and thus the errors

are not normally distributed

LJ remark that hr is the most likely syno dic p erio d of the

nucleus rotation so our measurement is consistent with this The correction from

our measured syno dic p erio d to the sidereal p erio d is small since the asp ect angle of

the comet as seen by Earth changed by only ab out p er rotation p erio d b etween

UT Jul and UT Jul At most the correction is

much smaller than the fractional error

Shap e and Precession of the Nucleus

By insp ection of Fig the p eaktop eak amplitude ptpa is

mag though it may b e higher since we have not sampled all turnover p oints This

ptpa is similar b oth to that found for other comets Meech and to that

measured for Encke by JM and LJ in the optical regime This variability is

likely due to the changing cross section and not the alb edo The emissivity would

have to b e near or much to o low to explain this midIR variability with

alb edo sp ots since the midIR ux is prop ortional to the emissivity

Assuming that the results of JM and LJ and our ESO results are all free

of coma contamination we can constrain the nucleus shap e and rotation state

The four data p oints for this exercise are the dierent ptpa JM measured the

ptpa mag on Sep and mag on Oct LJ measured

mag on Sep and we measured mag on Jul

Sekanina a found a rotation axis direction that did not change much from

to but this direction cannot account for the four ptpa a drifting

axis is required We created a simple mo del where the angular momentum vector

initially at the lo cation found by Sekanina a is pushed by a torque from

the outgassing regions on the surface The nucleus would b e a triaxial ellipsoid

in principal axis rotation ab out the shortest axis To make the problem tractable

we restricted this precession of the vector to a constant rate in a circle The

mo del thus has ve parameters the latitude and longitude of the precession axis

the p erio d of the precession P and the two axial ratios ac and bc of the nucleus

p

where c represents the short one The ptpa m is related to the shap e by

 

ac tan l

m log

bc tan l

where l is the subEarth latitude on the comets surface

With no degrees of freedom we could nd which parameter values were p ossible

but not their likeliho o d We found that a any precession axis direction greater

than from the angular momentum vector was allowable b P must b e

p

years c ac must b e and d bc ac Furthermore

the limit of P is smaller for smaller values of bc This short precession p erio d and

p

high elongation are necessary to reconcile the ptpa lower limits in and

with the ptpa that was smaller in

Comparing with a review by Meech Enckes long axial ratio is toward

the high end of known values with four nuclei having a ratio of or larger Only

Figure Light curve of Comet Encke phased by hr This is a fourday light

curve of comet Encke where the time co ordinate is mo dulo hr The ordinate

shows helio centric magnitude in the m lter The p erio dicity is derived from

Fig Zero phase corresp onds to Jul UT

PSchwassmannWachmann has a ratio as large as However many of these

are pro jected ratios so it is unclear how Encke precisely compares to these other

b o dies A recent study of comet PBorrellys nucleus yielded a depro jected axial

ratio of Lamy et al b

According to Sekaninas analysis ab the comets angular momentum vec

tor was precessing at a continuously decreasing rate averaging yr until around

after which it was mostly constant up to A mass ejection event or the

activation of new vents may have o ccurred in the mids to start the nucleus pre

cessing again Although Samarasinha and Belton showed that the nucleus

ratio of precession to rotation p erio d could evolve to a constant value that assumes

a consistent pattern of outgassing orbit after orbit which may not b e the case for

Encke Samarasinha and Belton and Samarasinha also mention that

the nucleus will spin up and eventually orient itself with the p ole p ointing at the

orbital longitude at which maximum outgassing o ccurs Usually this is just the

Suns cometo centric longitude at the comets p erihelion The uncertainties here

are to o great to address this the CONTOUR visit in will hop efully help our

understanding of Enckes rotation state

The contribution of the coma to the rotational mo dulation is imp ortant to con

sider If coma was present in JMs and LJs photometry but not rotationally

mo dulated then the lower limits to the ptpa are even higher and the limits on P

p

ac and bc would b e more extreme If however the coma was mo dulated by eg an

active patch or small jet swinging in and out of view then the comets light curve

would show the addition of two oscillating curves a twop eak curve from the nu

cleus and a onep eak curve from the coma and the nuclear ptpa could b e smaller

than the total ptpa We argue here though that the comatic contribution to the

amplitude is probably negligible First the bright aphelion outburst witnessed by

Barker et al showed no extended emission but completely obliterated any

mo dulation of the ux over the course of the night Hence we supp ose that the

comas ux in the outburst was not tied to its natal active area Second LJ show

no dierence b etween the amplitudes and shap es of their light curves two p eaks

unlike what one would exp ect if there were a strong singlyp eaked comainduced

underlying curve

Our own light curve Fig may b e asymmetric b etween the two p eaks but

the photometric uncertainties are to o large to b e sure A lower ptpa than

the one used ab ove would slightly mitigate the axial ratio and precession p erio d

limits but the optical data of JM and LJ are the more restrictive constraints

Optical Phase Behavior

We combined our HST nuclear magnitude with measurements from previous

apparitions to estimate the phase b ehavior of the nucleus and derive the absolute

magnitude m We used three phase laws the linear law

m m

where is a constant the IAUadopted H G formalism for asteroids Lumme et

Figure Stringlength metho d determination of Enckes rotation p erio d This is

a diagram to nd p erio dcity based on the metho d of Dworetsky Four days

worth of data were used to nd the rotation p erio d Minima indicate the most likely

rotation p erio ds but some are more favorable than others text gives details The

dashed and dashdotted lines indicate p erio ds that have b een p ostulated by LJ

and JM

al Swings

 

tan tan

m H log Ge Ge

where H m and the original LummeBowell law Lumme and Bowell

m m log F

tan

F Qe Q sin cos

where Q is the fraction of multiplyscattered light

Figure shows a plot of m for the Encke nucleus as measured by seve

ral observers the data with notes are listed in Table An observer had to rep ort

either the nuclear magnitude or the m magnitude to have hisher datum in

cluded in this plot The ordinate m is the observed magnitude minus the

geometric factor log r Symb ols indicate some information ab out each datum

written in the legend The data from LJ JM Barker et al Garradd

Spinrad as rep orted by LJ and us were taken with linearresp onse de

tectors the other p oints are photographic Our data and those of Garradd do

not have much coma contamination despite b eing taken at low r Of the historical

data only JM LJ and Barker et al have information on the rotation

of the nucleus hence all the other p oints have an uncertainty of at least mag

ie half the approximate ptpa Only Barker et al and LJ were able to

measure enough of the light curve to factor out the rotational mo dulation in the

former case there was no mo dulation detected JM were twice able to nd the

turnover p oint at the bright end of the rotational variation but not at the dim end

so we have used magnitudes for Fig that we estimate probably lie close to the

average brightness and we have assigned sensible error bars Sp ecically for one

p oint we plotted a magnitude mag fainter than their extremum with errors of

mag for the other p oint we plotted a magnitude mag fainter than their

extremum with errors of mag

We assigned a photometric error of mag to photographic data This par

tially comes from the fact that Ro emer and Lloyd photographed the comet

only minutes after van Biesbro eck did on Oct and yet they dier

in their magnitude estimates by mag Combined with the mag of uncertainty

due to rotation the total error is ab out mag We assigned an error of mag

to the data from linearresp onse detectors when no other estimate was available

Thus the rotational uncertainty dominates and the total uncertainty is ab out

mag

We converted all data in Table to Cousins R magnitude R the band of our

C

HST magnitude b efore plotting in Fig To do this we assumed the following

solar colors a B R Allen b B m Allen c

pg

J J J

V m Allen d V R Allen e R R

pv

J J J J C

Fernie and f R R For some p oints noted in Table

C

M oul d

we have assumed that the photographic data were taken on blue plates so that m

pg

is the applicable quantity Ro emer for example explicitly states that this is

the case

Figure next page Optical phase b ehavior of comet Enckes nucleus By

collecting historical data I plot comet Enckes nuclear magnitude as a function of

phase angle Ordinate is in Cousins R magnitude oset by logr to account for

diering observing geometries A linear phase law the LummeBowell Lumme and

Bowell phase law and the IAUstyle asteroid phase law Lumme et al

Swings are plotted Despite the uncertain interpretation of some rep orted

magnitudes there is steep phase darkening more drastic than that of other cometary

nuclei and C typ e asteroids shown OtNo Oct e Sep Jl Jul Jl Jul Jl Jul Jl Jul Jl Jul Jl Jul e Sep u Jul u Jul Jl Jul No v v UT T Date be able Medium Photo CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD CCD IDS siae Ncer r or Nuclear Estimated a Band m R R R R R V V V V V V V pg M M M M J J J J J J J C b e orted Rep Mag j i  m A 2 r antdsfrEnc for Magnitudes U c A U Crxn Color d m k e Nucleus es h Coma N N N Y F F F F F F F F f Wt g Ref

k Ot Oct u Aug c Oct Ag Aug Ag Aug Ag Aug Ag Aug Ag Aug Ag Aug Sp Sep No c Oct e Sep v UT Date Medium Photo Photo Photo Photo Photo Photo D D D D IDS IDS IDS AP AP AP AP a Band m m m m m m R R R V V V V pg pg pg pg pg M M M J J J J pg b e orted Rep Mag T bec able  A r U c ontinue A U d Crxn Color d m e Coma N N N N N Y Y Y Y f Wt g Ref

k Ag Aug Dc Dec Ot Oct Ot Oct Sp Sep Ma Ma e Sep Ag Aug No Sp Sep Sep Sp Sep y y v UT Date Medium Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo a Band m m m m m m m m m m m m m pg pg pg pg pg pg pv pg pg pg pg pg pg b e orted Rep Mag T bec able  A r U c ontinue A U d Crxn Color d m e Coma N N N Y N Y N Y Y N N f Wt g Ref

k Ag Aug Ag Aug Dc Dec Ot Oct Ot Oct Ot Oct Jn Jan Sp Sep Sp Sep Sp Sep Sp Sep No a Jan v UT Date Medium Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo Photo a Band m m m m m m m m m m m m m pg pg pg pg pg pg pg pg pg pg pg pg pg b e orted Rep Mag T bec able  A r U c ontinue A U d Crxn Color d m e Coma Y Y N N Y N N Y N N N F F f Wt g Ref

k Ag Aug c a b D e d g f Jl Jul Jul e Sep Aphelion seik niaeweeteueo bluesensitiv a of use the where indicate Asterisks m C hreculddevice Chargecoupled CCD T Relativ niae rsneo nobserv an of presence Indicates Pdigital AP r ocon to erm UT Date e e re Mag orted Rep w r eigh v r rmrpotdmgiueto magnitude orted rep from ert raphotometer area Medium ftepoin p the of t Photo Photo Photo Photo A P U a erihelion Band m m m m sdwe tigtepaela phase the tting when used t pg pg pg pg b o log dcoma ed ht htgahcplates photographic Photo e orted Rep Mag r r ClrCrxn Color T y Y A bec able U  R s y F es C band e A lt w plate r U c ontinue sbtfain but es A w sassumed as U d D mg dissector image IDS Crxn Color Nn no N t d m e unkno Coma Y Y Y Y scanner f wn Wt g Ref

k Llo R mr e re b orted rep emer Ro R mr e re b orted rep emer Ro i k h hoadSc and Shao j b R mr e re b orted rep emer Ro antd smgfain mag is Magnitude ase a Marsden y antd smgfain mag is Magnitude References de a oaccoun to mag Added d yd R mr emer Ro ard Garradd h w rz artz Helin ase Marsden y ase Marsden y ase n oee b emer Ro and Marsden y o coma for t e hnatos e re brigh orted rep authors than ter e hnatos e re brigh orted rep authors than ter tal et pna priv Spinrad v hsw This nBeboec Biesbro an Bark R mr e re b orted rep emer Ro Sa Shao ork T bec able LJ k er t comm ate tal et R mr e re b orted rep emer Ro ontinue extrem t R mr e re b orted rep emer Ro extrem t JM nct e re nJM in orted rep n o unicati d GloeadKlat n Kilmarti and Gilmore ase Marsden y um um isn e re b orted rep Gibson ase n oee a emer Ro and Marsden y ase Marsden y R mrand emer Ro ho e orted rep Shao

ase b Marsden y

Ideally all the p oints would tightly follow a curve but clearly some choice has

to b e made ab out which data are worth tting since the coma contamination is

obvious for some p oints eg the ten photographic p oints at low r b etween

For such p oints the observers likely measured the comets central condensation

inner coma rather than the nucleus itself With other p oints the exact amount of

contamination is unclear it may b e none or half a magnitudes worth An indication

of how much coma contamination there is might b e determined by lo oking at the

intrinsically faintest data at a given but in this case that is not so helpful b ecause

that usually turns out to b e a photographic p oint and the error bars are to o large

Hence it is nontrivial to incorp orate all the data into a t to the phase law Moreover

the problem is most contentious at low phase angle ie right at the lo cation where

we need the b est data to determine the The data p oint due to

LJ is very well determined mag and so normally would provide a very

go o d constraint however if there were a tiny amount of coma contamination that

would compromise its usefulness in the tting

A further complication is that the plotted error bars are not normally distrib

uted so any t statistic must b e carefully interpreted A sinusoidallyvarying ux

sp ends more time at the extrema than at the average value so the measured value

is likely to b e far from the average brightness

Our solution is to t the phase laws through the selection of p oints marked in

Table and enclosed in circles in Fig We use all of the lineardetector data

and the fainter photographic p oints For a given p oint we assigned it double weight

if it was an intrinsically fainter p oint relative to its immediate neighb ors in phase

angle The results are provided in Fig The rms oset is ab out mag for

all three ts The IAU law fails at the higher phase angle but the other two laws

are adequate Considering the uncertainties we take the absolute magnitude to b e

mag

The slop e of the phase law is quite steep at magdegree making Enckes

nucleus one of the most phasedarkened ob jects in the Solar System It is p ossible

that shap e eects are anomalously depressing the brightness at high phase angle

and fo oling us but the smo oth linear b ehavior of our HST p oint and the Garradd

p oints argue against this Cometary nuclei Jewitt and Meech Chapter

of this thesis and Ctyp e asteroids Lumme and Bowell to which the

nuclei are commonly thought to b e evolutionarily linked typically have only ab out

magdegree of phase eect as drawn in Fig Further study of the phase

b ehavior of nearEarth asteroids NEAs and cometary nuclei over a large range of

is clearly desirable

The unphysical and negative value of Q the fraction of multiply scattered light

and the steep slop e b oth imply that the surface of Encke is very rough Lumme and

Bowell mention this phenomenon in reference to Hidalgo a cometary

candidate also with Q Sp ecically the depthtodiameter ratio of features on

the surface is apparently larger than for their average asteroid and Q is actually

close to zero This makes sense since the reectivity of the nucleus is so low so very

few measured photons would have b een multiply scattered

It is interesting to note that the aphelion data from and

all apparently have signicant coma though none were spatially resolved by

the observers The Barker et al data prove that aphelion outbursts exist

and it is imp ortant to justify the inability to spatially resolve the coma which we

assume is mostly dust Some measurements had fairly large seeing disks which

could p otentially hide the coma but JM and LJ with seeing sp ecically

used diering ap ertures to detect comatic ux but did not nd any Thus any

existing dust would have to b e slowmoving andor have a surface brightness steep er

than the usual dep endence on cometo centric distance We know that large tens to

thousands of microns grains are emitted by Encke from IRAS trail and ISO tail

and trail observations Sykes and Walker Reach et al Lisse et al

and such particles move slowly with resp ect to the nucleus since radiation pressure

is inecient Thus it is not unreasonable to exp ect that the outbursts originate as

large dust grains traveling at ms ie just b elow escap e velo city and eventually

falling back on to the surface At aphelion the largest dust grain that can b e lifted

v

g

o the nucleus has a radius of just m Z s cm where v

g

ms

is the sp eed of the gas and Z is the vap orization rate based on an equation given

by Keller

Nucleus Size and Geometric Alb edo

Now we can apply the thermal mo del to the data First let us assume

and T K which will b e justied b elow If J K m s ie

ss

ab out the lunar value Winter and Saari then dened in Chapter

and Enckes nucleus is a mo derately slowrotator Harris et al estimate

J K m s on the surface of Phaethon which is presumably

an owing to its parentage of the Geminid meteor stream if applicable

to Enckes nucleus placing it on the b order b etween slow and fast rotator

Thus the STM will work reasonably well but not p erfectly represent Enckes thermal

b ehavior Since the orientation of the nucleus spin axis app ears to have changed

since the Sekanina a analysis it would b e dicult to constrain any of the

other parameters in the augmented thermal mo del even though we have derived

some information ab out the shap e Thus we will apply the STM and compare the

results with the RRM to get some sense of the mo deldep endent error

Some parameters of the STM were assumed to b e as follows infrared phase

co ecient to magdegree emissivity optical phase integral q

i

which can b e derived from the phase analysis of a previous section b eaming

parameter to For the RRM we assume the limiting case of the rotation

axis p erp endicular to the SunEarthComet plane

In Section we found the nucleus ux to b e Jy for this ux

the STM provides us with an eective radius R of km and a subsolar

N

temp erature T in midJuly of K This justies our use of K in the

SS

calculation ab ove The errors are derived from a Monte Carlo simulation

letting and all uniformly

i

distributed and using the normallydistributed ux estimate By similarly applying

the simplied RRM we nd R km and T K These

N SS

may b e interpreted as the upp er and lower limits resp ectively to these quantities

since they would b e physical only if we were grossly underestimating the thermal

inertia of cometary nuclei It is clear however that if the thermal inertia is more

Phaethonlike than Mo onlike then R is probably a few tenths of a kilometer larger

N

than that given by the STM

From our discussion in Section we estimate the optical cross section at zero

phase angle to b e equivalent to a magnitude of The relation b etween the

optical cross section and the comets magnitude is

m m

km pR

N

based on an equation given by Jewitt where p is the geometric R band alb e

do and m is the solar apparent R band magnitude of We calculate from

this that p

Consistency with ISO Data

Our broadband sp ectrophotometry obtained by ISO is shown in Fig The

dusts contribution to these data is more fully discussed in a related pap er by Lisse

et al Presently we will only show that our other results are consistent with

this dataset

Our simple mo del of the sp ectrum uses the sum of two comp onent sp ectra one

for the dust and one for the nucleus Reach et al have shown that there is a

signicant p opulation of large radius m grains in Enckes coma so we have

mo deled the thermal emission of the dust in the to m wavelength range

as a greyb o dy with temp erature as a free parameter and emissivity indep endent

of wavelength Such a null dep endence can explain midIR observations of large

dust grains from other comets Lisse et al We are unconcerned with the

actual values of the dusts emissivity and optical depth we scale our mo del to yield

the b est t for particular values of the parameters ISOPHOTs m ux has a

signicant scattered sunlight comp onent in addition to the thermal emission and so

is not used to constrain our mo del b eyond b eing an upp er limit to the thermal ux

We mo deled the sp ectrum of the nucleus using the STM cho osing to b e either

or to b e either or magdegree and to b e The

i

parameter R could b e any value Thus our mo del has four imp ortant parameters

N

temp erature of the dust T R An example mo del and the excellent t to

i

D N

the sp ectrophotometry are shown in Fig

With this metho dology the results of the tting can b e displayed as a contour

plot of the reduced tstatistic as a function of T and R The six plots

D N

in Fig show this for each value of and Owing to the low numb er of

i

sp ectrum p oints visavis the mo del parameters it is imp ossible to constrain the

four parameters but the ISOPHOT sp ectrum is consistent with our groundbased

derivation of R whose b oundaries are noted by the shaded rectangles across

N

the range of previouslyfound values for and In particular cannot b e con

i

strained from Fig since the ESO constraint on R never strays far from

N

even when It is satisfying that the derived dust temp eratures are sensible

an isothermal black b o dy at Enckes distance from the Sun would have T

D

K

Previous Work

Figure ISOPHOT sp ectrophotometry of Encke dust coma plus nucleus The

symb ols show a broadband midinfrared sp ectrum of the nucleus and dust of comet

Encke taken by ISOPHOT Also plotted is a sample mo del solid line that ts the

sp ectrum with degrees of freedom R km T K

N D

magdegree Dashed line is a mo del sp ectrum of the nucleus generated

i

by the STM dashdotted line is a Planck sp ectrum of the dust

Thermal infrared measurements in the past have b een made by Ney

Campins and Gehrz et al to estimate the size of the nucleus All

used singleelement b olometers so no spatial information was obtained The present

study is an improvement b ecause of our higher sensitivity and spatial resolution

Ney

On Apr Ney measured a ux of and Jy at wavelengths

of and m resp ectively converting from the rep orted magnitudes His

rep orted upp er limit to Enckes R of to km is derived from an assumed

N

correlation b etween nuclear size and comatic thermal infrared b ehavior observations

of Comet Bradeld b III C C and an assumed value for the

nuclear alb edo that is now known to b e to o high Instead if we apply the STM to

his Encke thermal uxes and use the assumptions we outlined in Section we

nd an upp er limit to the nuclear radius of approximately km which is ab ove

our calculated value

Campins

Seven observations at m are rep orted during the apparition two

during the apparition and the uxes vary from to Jy By using his

intrinsically faintest data p oint and applying the STM he estimates an eective

radius of km at rotational minimum and km at rotational maximum

These are the midIR measurements with formerly the least amount of coma con

tamination but our calculated eective radius is smaller

Gehrz et al

Near and midIR measurements are rep orted on four dates during the

apparition and two dates during the apparition with uxes ranging from

to Jy Using their intrinsically faintest data p oint and assuming an isothermal

nucleus not the STM they derive an upp er limit to R of km Applying the

N

STM to their rep orted uxes gives an upp er limit of to km dep ending on the

mo dels parameter values which is ab ove our calculated value

Kamoun et al

From the radar echo es at cm these workers found a radar cross section

of km in the circular p olarization sense orthogonal to that of the trans

mitted pulse If Encke is like other comets where the radars reection is mostly

sp ecular Harmon et al then this is roughly the total radar cross section also

Further using the bandwidth of the returned pulse they found an eective radius

R of km although with more mo dern values of the rotation p erio d LJ

N

and spin axis direction Sekanina a R would b e km Our measurement

N

of R is within this range

N

With our eective radius in hand further rudimentary interpretation of the rad

ar results are p ossible The geometric alb edo at cm p which is just

Figure plots of Encke dust temp erature and nucleus size Here are contour

plots of showing that the simple mo del describ ed in the text dust black b o dy

sp ectrum plus nucleus STM sp ectrum adequately ts the ISO sp ectrum and is

consistent with the groundbased results Shaded rectangles indicate the range

of nuclear radii implied by our ESO data Contour levels are

and Each panel represents one value of and one value

i

of leaving the other two parameters of the mo del dust temp erature and nuclear

radius to b e plotted

the radar cross section divided by R is a value comparable to

N

the one at optical wavelengths and to that found for other comets Harmon et al

Campb ell et al Following the argument and assumptions made by

Harmon et al in their treatment of Comet IRASArakiAlco ck C H

the dielectric constant of the Encke nucleus surface layer is corresp onding

to not surprisingly a mixture of dust and snow

Summary of Encke Results

We have discussed the prop erties of the nucleus of Comet PEncke as derived

from data obtained during its close approach to Earth in July The CONTOUR

spacecraft is scheduled to encounter comet Encke in and this information can

aid in the mission planning and design We measured the thermal continuum of

the comet in the to m range with the TIMMI instrument at the ESO m

telescop e and in the to m range with the ISOPHOT photometer on the

ISO spacecraft We also used the STIS CCD ab oard HST to measure the optical

A scattered continuum of the comet We nd the following

Assuming the nucleus thermal b ehavior can b e describ ed using the Stan

dard Thermal Mo del STM Leb ofsky and Sp encer the eective nuclear radius

is km km and the subsolar temp erature at a distance of AU from the

Sun is K The eective radius is smaller than the upp er limits found by

other researchers using thermal continuum observations Ney Campins

and Gehrz et al and within the range found via the radar exp eriment in

Kamoun et al The applicability of the STM could b e questioned since

the thermal inertia is unknown but the eective radius is probably at most only a

few tenths of a kilometer larger than the value given ab ove

Using our HST data and other datasets JM LJ Garradd along

with various photographic data from previous apparitions we nd the optical phase

law of Enckes nucleus out to can b e well t with a LummeBowell phase

law Lumme and Bowell with absolute R band magnitude and

C

Q The equivalent linear slop e is magdegree which is one of the

steep est slop es known for any small b o dy of the Solar System The negative value

of Q and the steep slop e imply that the nucleus surface is rougher than the typical

asteroid used to create the LummeBowell law The absolute magnitude yields a

visual geometric alb edo for the nucleus of Use of this absolute magnitude

do es mean that bright mag but spatiallyunresolved outbursts were observed

at several separate aphelia AU by many observers

The nucleus rotation p erio d is likely hr hr but our data cannot

rule out some harmonics of this value as they also show or imply a doublep eaked

light curve ie as if we had observed a rotating nucleus Optical measurements

give hr LJ so our data are consistent with this value

We measured a p eaktop eak amplitude ptpa of the light curve of

mag though it may b e larger since we could not sample the entire rotational

phase With a mo del that assumes the nucleus is a triaxial ellipsoid with an angular

momentum vector a initially p ointing in the direction found by Sekanina a

and b precessing in a circle due to a torque from the outgassing vents on the

surface we combined our dataset and the ptpa rep orted by JM and LJ to

nd that the precession p erio d is less than years one axial ratio ac is at least

and the other one bc satises bc ac The precession

circles axis must b e at least from the angular momentum vector We surmise

that a signicant mass ejection event could have o ccurred in the mids to start

the angular momentum vector moving again since according to Sekanina a

on average it was in the same place for much of the th century

The nucleus radius is toward the low end of known radii of nuclei while

the axial ratio is toward the high end Meech The alb edo is comparable

to Halleys and not unlike the other few comets for which it has b een measured

Chapter Among known nearEarth asteroid prop erties the radius is in the

middle and the alb edo is on the low end However the samples of comets and

NEAs b oth suer from incompleteness and observational bias

Under the STM formalism we can constrain neither the b eaming parameter

nor the infrared phase co ecient other than to say Enckes thermal b ehavior

i

is consistent with the values found for these parameters from asteroids and icy

satellites Future studies of comet Enckes nucleus should try to employ a wide

range of phase angles and a wider range of wavelengths to b etter understand its

thermal phase b ehavior and improve the interpretation of radiometry

Chapter

The Nucleus of Comet Hyakutake C B

Background

Six months after the discovery of HaleBopp a Japanese amateur astronomer

discovered his second longp erio d comet in a sevenweek p erio d an th magnitude

smudge Nakamura and Nakano Four days later it was realized that this

comet would make a very close approach to Earth in late March and probably b e an

easy nakedeye ob ject Marsden The rest of the story is well known comet

Hyakutake blazed through the Northern Hemisphere sky at a visual magnitude of

ab out and sp orted a tail extending many tens of degrees The photograph in Fig

shows how the comet lo oked to my camera on Mar the eld of view

is ab out degrees wide In contrast to HaleBopp later on Hyakutake ashed in

and out of our skies in a week The short lead time necessitated a scramble for

requesting access to telescop es fortunately many observatory directors recognized

the sp ecial signicance of this comet the closest one to Earth since and the

brightest one since for which comet scientists were exceedingly grateful

Thermal Measurements

A track of observations was done at the Very Large Array VLA two days

after the March th close approach of the comet I have describ ed that exp eriment

elsewhere Fernandez et al a and I repro duce much of the text here Our

infrared thermal data were obtained around the time of the comets close approach

and have b een describ ed in detail by Lisse et al b Since most of the work in

that wavelength regime for this comet was done by Lisse I will give space to those

results only as they relate to my data

Details of Observations

Our VLA observations consisted of one twelvehour track from UT to

UT on March The ux calibrator was C QSO J ux of

ab out Jy and our phase calibrator was C a radio galaxy having a ux

of ab out Jy Perley and Taylor Individual integrations were ten seconds

long the total amount of time sp ent integrating on the comet was ab out ten hours

Phase stability during the track was go o d

During the observation the comet itself was b etween and AU from



Earth and AU from the Sun and the phase angle was b etween and



The ephemeris that was used at the time of the observation was provided by

D K Yeomans private communication but owing to the proximity of the comet

had formal p ositional uncertainties of arcsec in right ascension and arcsec in



Figure Comet Hyakutake in a wide eld of view This is a photograph of

the comet taken by me near the time of closest approach on Mar The eld

of view on the long dimension is ab out degrees the tail is clearly visible over

most of that arc

declination The prop er motion of the comet ranged from to arcsec

p er integrationtime and decreased by ab out arcsec p er integrationtime p er

hour

The VLA telescop es can only track the linear prop er motion of a source But

due to the rapid motion of the comet we had to take into account the second order

1

motion We up dated the linear tracking rates every to minutes so that the array

2

was always p ointed within one synthesized b eam arcsec of the most accurate

formal p osition of the comet available at the time

Data Reduction and Correction

The standard data reduction yielded no signicant signal from the comet One

problem we considered was that due to the p ositional uncertainty of the comet

the signal might have b een smeared during the course of our observation A more

accurate ephemeris of the comet pro duced by D K Yeomans a few weeks after

p erigee revealed that our tracking rates were not signicantly in error o by 

arcsec p er integration time but the center of p ointing was indeed oset from the

true p osition of the comet by up to arcsec at times during our observing run

It should b e p ointed out here that the halfp ower bandwidth HPBW of the VLA

telescop es at our observing frequency is arcmin and primary b eam attenuation

is negligible for these osets In essence the amplitude and phase of the complex

integration data p oints were correct but the pro jected baselines or uv spacings

of the telescop es were slightly oset b ecause of the dierence in the observed and

actual p osition of the comet We recalculated the correct uv spacings for each

baseline for every tensecond integration and inserted these corrected spacings into

the dataset After the correction we obtained a more robust map

This problem is imp ortant to consider for any interferometric observation of

a fastmoving ob ject b ecause of the inherent uncertainty in the ephemeris and in

the way the data are taken at the observatory To stress this latter p oint it was

imp ortant that in order to correctly reduce our data we understand intimately

where the telescop es p oint at a given time and what information p ertaining to that

are stored as data In this case the data were not correct and we were forced

to alter them by hand Since the VLA or any radio interferometric array typically

do es not p erform observations of this sort we emphasize the sp ecial requirements

of the data analyst in this situation A description of some of the problems with

interferometric observations of close fast ob jects is given by de Pater et al

Our CLEAN map with and contours is shown in Fig Since we had

directly manipulated the data via the corrections we would exp ect the signature

from the comet to app ear in the middle of the map The synthesized b eam

arcsec wide is shown in the lower left The eld of view in this map is arcmin

by arcmin slightly smaller than the HPBW of the telescop es primary b eam

With such a synthesizedb eam size the nucleus would have app eared as a p oint

source The rms noise in our map is Jyb eam

There app ear to b e some linear structures or streaks running generally north

east to southwest in the map These may b e extended background sources passing

through the eld of view as the array tracked the comet or indicative of a few

Figure CLEAN contour map of C B This is acutally the CLEAN contour

map of the eld of view containing the comet since we did not detect the ob ject at

the level We used the VLA on Mar to generate this image and the

synthesized b eam is the black dot at lower left

anomalous visibilitydata p oints It is imp ortant to stress however that the struc

tures app ear only on the and level and as such are not statistically signicant

A histogram of pixel values is welldescrib ed by a Gaussian of Jy and shows

no excess of pixels or from the mean In addition the structures have a low

2:5

intensity Integrating over the roughly  synthesizedb eams that they cover

the ux density is ab out to mJy Had the hyp othetical structures b een tracked

they would have covered around to synthesized b eams based on the thickness

of the streak This implies their surface brightness was only  to Jyb eam

Implications for the Nucleus

Our measurement of the rms ux in the synthesized b eam from the comet

allows us to place a upp er limit on the thermal microwave continuum ux of

Jy at cm Of the six interferometric observations of a comets microwave con

tinuum ve including Hyakutake are upp er limits Our HaleBopp observations

Chapter resulted in the only detection Our Hyakutake upp er limit is smaller

than the other four comet Austin C M g VI was observed at

cm Snyder et al with an upp er limit of Jy comet IRASArakiAlco ck

C H d VI I was observed at and cm de Pater et al

with upp er limits of and Jy resp ectively comet Crommelin P n

IV was observed at cm Schenewerk et al with an upp er limit of

Jy and comet Halley P U i I I I was observed at cm

Hoban and Baum with an upp er limit of Jy

As mentioned in Chapter it is not obvious which thermal mo del is the most

applicable The rotation p erio d is ab out hr see next section which would

put the thermophysical parameter close to unity for lunarlike thermal inertia

However since the microwave data sample colder subsurface layers the ILM or

even an isothermal mo del is probably more applicable Also the high activity of the

nucleus approximately of the surface is active Lisse et al b probably

helps to keep the insolation energy from p enetrating deep b elow the surface since

much of it is b eing used to sublimate ice Since we do not have information on the

shap e of the nucleus and since there do es not yet seem to b e a comprehensive mo del

of the nucleus rotation state we will simplify matters by calculating an upp er limit

to the nucleus radius by assuming the subsurface layer that we have sampled is

isothermal

To obtain an estimate of the nuclear size we use

2

k T R

S

 

2 2

where S is the measured ux density from the nucleus  Jy is the wave



length cm is the geo centric distance averaging AU during the ob

servation k is the Boltzmann constant T is the nuclear temp erature is the



emissivity at cm and R is the nucleus eective radius

Radar measurements of cometary nuclei have indicated that the microwave

alb edo is quite low a few p ercent Campb ell et al Thus the emissivity

of the nuclei is probably around assuming that the emissivity is close to one

minus the alb edo For comparison the emissivity of NEAs is roughly as high to

Goldstein et al The temp erature is more problematical but based on

our eorts for HaleBopp in Chapter a temp erature of K for the sampled

layer in Hyakutakes nucleus is not unreasonable The extreme limits to the tem

p erature range from ab out or K for a very conductive nucleus down to

roughly K roughly the temp erature of formation in the Kuip er Belt Rickman

We have combined all of this information into Fig Eective radius is plotted

vs temp erature with the solid curves representing four p ossible emissivities The

dotted line marks the temp erature of an isothermal blackb o dy at the helio centric

distance and the dashed line marks the approximate sublimation temp erature for

water ice For the true emissivity and observed temp erature of the nucleus the

radius could lie anywhere to the left of the appropriate p oint For and

T K the upp er limit to the radius is km This is consistent with our

result obtained from the thermalIR imaging Lisse et al b  km as

well as the radar results by Harmon et al  km Our estimate of

the radius is not very sensitive to the temp erature when T  to K but it

b ecomes km for the K limit

The Xray Connection

Our observations were simultaneous with many of the ROSAT observations of

Hyakutake that o ccurred a few days after p erigee Lisse et al Since non

thermal radio emission is frequently coincident with Xray emission from other as

trophysical sources we were motivated to place an upp er limit on the microwave

emission from the lo cation of the Xrays in Hyakutakes coma the VLA eld of view

overlaps a p ortion of the Xray emitting region rep orted by Lisse et al The

0

center of brightness of the Xray emission with resp ect to the nucleus is ab out

0

1

north and east of the nuclear p osition on March UT whereas our map

2

0

extends only from the nucleus If we approximate the size of the Xray emitting

0 0

region as a by oval with the short axis on the Suncomet line then the overlap

b etween the VLA eld of view and the Xray emitting region is a wedge that con

tains ab out of the total Xray ux and ab out of the total VLA eld of view

Assuming the microwave ux from the coma follows the same spatial distribution as

the Xray ux we calculate that the upp er limit to the microwave ux from the

Xray emitting region is mJy This value is more than a factor of two lower than

that rep orted by Minter and Langston using the samesize Xray emitting

region of the coma This result indicates that the mechanism resp onsible for the

pro duction of Xrays is not able to pro duce much microwave radiation Lisse et al

15

found an Xray luminosity of  ergs from the coma as measured by

the ROSAT HRI which is sensitive to to keV photons Assuming a p ower

law sp ectrum where the intensity is prop ortional to where is the frequency

and is the sp ectral index and using the largest p ossible eective bandpass

keV and our microwave upp er limit we nd that must b e less ie atter than

fairly at Some of the mechanisms p ostulated by Lisse et al to ex

plain the Xray emission eg magnetic eldline reconnection and magnetospheric

Figure Size and temp erature of C B nucleus Here the lo ci of p oints

on the temp eratureradius parameter plane that can satisfy the upp er limit to the

microwave ux are displayed The dierent curves represent dierent microwave

emissivities

disruption would necessarily pro duce some microwave radiation but these theo

ries are not yet develop ed enough to provide a prediction of the microwave ux to

compare with our results However the derived atness of the sp ectrum do es rule

out synchrotron emission which typically has a sp ectral index of to as the

source of the Xrays as would b e exp ected from the typically low strength of the

interplanetary magnetic eld

Optical Measurements

I have describ ed much of this information in a pap er rstauthored by my col

league Lisse et al b and I repro duce much of the text here

ComatoNucleus Contrast in the Images

The optical data are four nights worth of imaging during to March

at the KPNO m telescop e The sky during three of the nights was photometric

or nearly photometric I used a by pixel CCD with a eld of view of over

arcmin so I have go o d maps of the inner coma immediately b efore the large

outburst of activity that coincided with the widelyrep orted fragmentation of the

nucleus Lecacheux et al Weaver The wavelengths I will concentrate

on here are at A and A the wavelengths of the narrowband continuum in

00

the International Halley Watch lter set The image scale was p er pixel side

During the run the comet was to AU from Earth to AU from

 

the Sun and to in phase angle Typical FWHM of the seeing disk during

00

the photometric and partially photometric time averaged

Considering the size of the nucleus the gas and dust output of the comet was

extremely pro digious Whereas most comets have up to just of their nuclear

surface area active Hyakutake seems to b e more in the vicinity of p ossibly

Lisse et al b This high fraction is strong evidence for an icy grain

halo contributing to the output of water the total surface area of cometary solids

2

available to release gas is not just the R of the nucleus but all of the icy grains

as well Moreover the radar exp eriment Harmon et al clearly shows that

some of the echo p ower came from grains moving a few meters p er second near the

nucleus

The rep ercussion of this phenomenon is that our optical images of the comet do

not have sucient spatial resolution to photometrically extract the nucleus Our

comatting technique fails to nd a central p ointsource the coma is swamping all

of the nuclear ux Not only is this a problem in our KPNO data where the pixels

00

subtend on a side but also in HST WFPC data where the pixels subtend

00

only on a side or just km at the comet during closest approach Weaver

et al

Shown in Fig is an example of the comatting technique applied to one

of our KPNO images The gure is taken from Lisse et al b and is their

Fig There is clearly a p ointsource residual but it is far to o bright to b e just

reected light from the nucleus unless as we mention in the pap er the nucleus

has an absurd geometric alb edo of ab out It only takes a small amount of dark

absorbing material mixed with the ice to reduce the alb edo b elow this value

Figure Comatting metho d applied to optical image of Hyakutake Here I

show the results of this image pro cessing technique for Hyakutake The upp er left

panel is the original image the upp er right panel is the mo del the lower left panel is

the dierence and the lower right panel compares the proles of the residual and the

PSF The residual is p ointlike but far to o bright to b e just scattered light from the

nucleus Apparently there was a halo of sublimating icy grains around the nucleus

contributing to the optical ux and the grains were to o close to b e accounted for

in our image pro cessing technique

Rotation Perio d

One physical prop erty that we had more success on is the rotation p erio d Two

dierent metho ds were used b oth the photometric and the morphological metho ds

describ ed in Chapter

Figure shows a sequence of narrowband continuum images of the comet over

a p erio d of several hours The overall trend of the comas brightness a recipro cal

dep endence on the cometo centric distance has b een removed to bring out

some of the detail in the coma Thus it is easier to see when a feature in the

coma returns to the same azimuth after one rotation p erio d The p erio d can b e

clearly measured as approximately hours with the caveats mentioned regarding

this metho d in Chapter

A tighter constraint on the p erio d is derived from the photometric data Figure

shows the photometry of the comet nucleus and coma over nights The top

panel is the absolute ux the b ottom panel has the linear trend removed from the

data and an arbitrary sine wave plotted through the p oints The data have b een

scaled in the lower panel to simplify the plotting of this sine wave The asterisks give

the Aux and the crosses give the Aux The circular ap erture used for this

photometry was km wide at the comet The p erio d is quite easily distinguished

as  hr just by varying the frequency of the sine wave While this analysis

cannot rule out a hr p erio d which would yield a classic doublep eaked curve

the coincidence of this p erio d with the morphological evidence in Fig indicates

that hr and not hr is the more tenable choice The morphological changes

and the p erio dicity are consistent with that found for Hyakutake by Schleicher et

al c

Summary of Hyakutake Results

The thermal microwave data places a constraint on the nucleus eective radius

of ab out km This is consistent with the radar results Harmon et al and

the midIR imaging results Lisse et al b Unfortunately the comet was to o

active to let us use the comatting metho d on the optical data to derive the nucleus

optical cross section this problem even existed for the extreme high resolution HST

images Weaver et al Our only constraint is the geometric alb edo of the

nucleus is less than

The rotation p erio d however was extractable from the optical data and com

bining the photometric and morphological metho ds I nd a p erio d of  hr

The variation in ux within a km wide ap erture was very drastic and mostly

due to coma features sweeping in and out of view not the variation of the nucleus

cross section The advantage to this is that the p erio d determination b ecame fairly

easy The quoted rotation p erio d has also b een widely discovered indep endently

eg Schleicher et al c The rotation p erio d is toward the low end of known

p erio ds implying that the comet do es not have much tensile strength Lisse et al

b

Figure Rotation sequence of comet Hyakutake This is a sequence of pro

cessed optical images of the comet showing the jets sweeping in and out of view over

the course of a rotation p erio d From this it is p ossible to constrain the rotation

p erio d to ab out hours The last panels right side of b ottom row show an

original unpro cessed image and the prole of the comets photo center resp ectively

In the other thirteen panels the general trend of the coma has b een removed

to help bring out the jet features

Figure Photometry light curve of comet Hyakutakes photo center The top

panel shows the absolutely calibrated light curve of the comet at two optical wave

lengths over the course of several days Data from two continuum narrowband

lters A and A were used In the b ottom panel a linear trend has b een

removed so we can place a sinusoid on top of the light curve to derive a p erio d of

ab out hr  hr

Chapter

The Nucleus of Comet Temp elTuttle

Background

Comet PTemp elTuttle currently is the thirdlongest known p erio dic comet

Chinese records indicate it was observed in Octob er only PSwiftTuttle and

PHalley have b een observed longer than that The more tactile claim to fame

however is the comets parentage of the Leonid meteor stream The Novemb er

asso ciated with it b ecomes a veritable storm for a few lucky lo cations

on Earth roughly every years that is around the time of p erihelion of this

year p erio d comet In addition to all the other reasons for studying nuclei mo dels

of the meteor stream grain p opulation dep end on the parameters of the nucleus and

the dust pro duction rate

I have describ ed much of this work elsewhere Fernandez et al a and will

repro duce some of the text here

Thermal Measurements

We observed this comet on Jan at NASAIRTF with the MIRLIN

midIR imager and on to Jan with a CCD on the UH m telescop e

on Mauna Kea The comets helio centric distance r was to AU the

geo centric distance was to AU and the phase angle was b etween

 

and

Our midIR dataset is shown in Fig in logarithmic intensity scale each

frame shows a separate lter and the lters wavelength and bandpass of the are

written in white in m There are two images of the comet and two negatives

in each frame b ecause our chop and no d throws were smaller than the eld of

view of the instrument An M band m observation is not shown since only

upp er limits could b e had from that wavelength There is some coma visible in the

images and we p erformed the comatting metho d to extract the nucleus At each

wavelength ab out to of the ux is due to coma We p erformed photometry

on the residuals and the result is shown as a broadband sp ectrum in Fig The

S N is low but we nd a consistent ux of ab out Jy in the micron range This

is one of the few midIR broadband sp ectra of a cometary nucleus in existence cf

eg Hanner et al

Figure Midinfrared images of comet Temp elTuttle The two p ositive and two

negative comets in each image are caused by the chop and no d throws b eing smaller

than the eld of view of the detector The wavelength and bandpass are written in

each frame

The current b est estimate of the rotation p erio d is ab out hr Jorda et al

rep orted by Green For a lunarlike thermal inertia the nucleus of Temp el

Tuttle is reasonably mo deled with the STM and plotted on the sp ectrum in Fig

are mo del sp ectra based on the STM The usual plausible input parameters

mentioned in previous chapters yield an eective radius of  km a

subsolar temp erature T of to K and a brightness temp erature T of

SS B

ab out to K

Figure Midinfrared sp ectrophotometry of comet Temp elTuttles nucleus The

mo del sp ectra drawn through the data are based on the STM and varying all of the

STMs parameters indicate that the eective nuclear radius is  km The

plotted example mo dels assume a b eaming parameter of an emissivity of

an infrared phase co ecient ranging b etween and magdegree and an

eective radius ranging b etween and km UL indicates the upp er

limit to the ux at that wavelength

Optical Measurements

A typical R band optical image and its analysis pro ducts are shown in Fig

in logarithmic intensity scale The left panel is an original reduced image the

middle panel is the mo del of the coma from the comatting metho d and the right

panel is the residual from the subtraction of the two Clearly go o d removal of the

coma was apparently achieved as can b e seen from a comparison of the PSF the

residuals prole and the original comet prole plot in Fig The residual

is a p ointsource and we ascrib e its ux as reected light from the nucleus The

photometry of the residual has magnitude R  This magnitude do es

C

not have rotational context but the uncertainty from removing the coma ameliorates

this somewhat An indep endent analysis of this optical dataset has not revealed

any clear rotational signature in the comets photo center J M Bauer private

communication so the nucleus may happ en to b e not very elongated

We now characterize the optical phase eect of the nucleus by combining our

data with the magnitudes rep orted by Lamy and Hainaut et al in

Fig The asterisk is from this work the triangle is from Lamy the rhombuses

are photometric p oints from Hainaut et al and the crosses are p ossibly photometric

p oints from Hainaut et al A straight line gives a satisfactory t with

magdeg a not atypical value for nuclei Jewitt and Meech We have also t

the data according to the panasteroidal phase law of Lumme and Bowell

as we did in Chapter with comet Encke Though the two mo dels yield equally

go o d ts we prefer the latter since it has a physical basis The parameter Q

which attempts to account for multiple scattering of light on the surface is around

implying that here just as with comet Encke the surface of the cometary

nucleus is rougher than for the typical asteroid The zerophase absolute magnitude

is  note the mag dierence in absolute magnitudes b etween the two

mo dels

Using this phaselaw and the absolute magnitude our derived radius implies that

the geometric alb edo p is  higher than the canonical value but not out

of the range Assuming the formalism for would have yielded p 

Summary of Temp elTuttle Results

Our observations of Temp elTuttle resulted in several unique data pro ducts

First we have one of the few midIR sp ectra of a cometary nucleus in existence

This allowed us to derive the radius  km based on the STM although

the low S N do es not allow us to derive b eaming parameters Harris et al

Second we have constrained the optical phase law although the rotational con

text of all the optical data is unknown With that caveat the phase law is equivalent

to a linear co ecient of magdegree or in the Lumme and Bowell for

malism Q implying a surface rougher than the typical asteroid The

alb edo of the nucleus based on our determination of the absolute magnitude is



Figure Comatting metho d applied to optical image of Temp elTuttle On

the left is an R band image of comet Temp elTuttle in the middle is a mo del of the

coma from the comatting metho d and on the right is the dierence b etween the

two The plot compares the residuals prole with the PSF and the original comet

prole it is clear that we have found a p oint source nucleus after subtracting the

coma

Figure Optical phase b ehavior of comet Temp elTuttles nucleus The data

include the measurement in this Chapter and other magnitudes culled from the

literature The straight line ts well but since a physicallybased phase law Lumme

and Bowell do es also we use the latter to derive the absolute magnitude

Chapter

The Nuclei of Comets Wild and Utsunomiya

Background

These are the two comets for which I have the least amount of data so I will

discuss b oth in one chapter Much of the text I have already presented elsewhere

Fernandez et al a

PWild is the target of the Stardust mission which is currently en route If

successful the spacecraft will collect grains from the comets dust coma by trapping

them with an aerogel and return them to Earth An interesting factoid ab out the

comet itself is that it was p erturb ed into its present orbit only in when it

passed less than Jovianradii within Ganymedes orbit from the gas giants

cloud tops Before that the comet lived almost totally in the outer planetary region

with a p erihelion slightly within Jupiters orbit and aphelion around Uranus orbit

and b eyond Thus among the shortp erio d p opulation this is likely one of the least

pro cessed ob jects having sp ent so little time within AU of the Sun

Comet Utsunomiya T was discovered at th magnitude by an amateur

This comet is old in the Oort sense having an original semima jor axis of AU

Marsden and Williams It is one of many runofthemill long p erio d comets

that we must eventually sample in great numb ers

Utsunomiya

On Nov we imaged Utsunomiya at NASAIRTF with the MIRAC



infrared camera At the time r AU AU and

The comet had a ux of  Jy at m and is shown in Fig a as the

median of images It was slightly extended apparently not a p ointsource In

Fig I show a mo del coma which when subtracted from the image leaves hardly

any p ointsource remaining ab out of the ux However this do es not mean the

dust coma dominated the signal since the centroiding and adding of the images

together was tricky due to the low S N p er pixel It is entirely p ossible that the

dust coma is spurious b ecause of incorrect registering of the image centroids

Strictly sp eaking we can only calculate an upp er limit to the eective radius

Assuming all of the ux is nuclear I assign the usual ranges for the parameters of

the STM and nd an eective radius R  km T to K and

N SS

T to K To our knowledge this is the only infrared data on this comet and

B

Figure Midinfrared images of comets Utsunomiya and Wild On the left a

is an image of comet Utsunomiya at a wavelength of m and on the right b

is comet PWild at m The comets are extended sources but it is unclear

whether this is due to real dust comae or just a consequence of the tricky registering

of multiple images of a faint comet

the only estimate of its nuclear size Unfortunately we have access to neither nuclear

magnitudes of this comet nor deep images so we cannot yet estimate p Also the

rotation p erio d is unknown so there is no rotational context for this measurement

If the nucleus were a rapid rotator and if the rotation axis were p erp endicular to

the SuncometEarth plane at the time of observation the eective radius would b e

higher ab out  km

PWild

On Jan we imaged Wild at NASAIRTF with the MIRAC infrared



camera A the time r AU AU and

The comet had a ux of  Jy at m and is shown in Fig b as the

median of images It to o was slightly extended apparently not a p ointsource

however the S N p er pixel was even lower than for Utsunomiya In Fig I show a

mo del coma which when subtracted from the image leaves hardly any p ointsource

remaining less than of the ux I am less condent of the reality of the dust

coma for this comet than for Utsunomiya

Hence again we can only calculate an upp er limit to the eective radius Assum

ing all of the ux is nuclear and again assuming the usual range of parameters for

the STM I nd R  km T to K and T to K

N SS B

We were unable to acquire any rotational information so we cannot tell how much

variation there is in the cross section However Meech and Newburn rep ort

that time series of optical ux while the comet was at high helio centric distances do

not show much rotational signature at all ie there is a go o d chance that the comet

is close to spherical So the lack of rotational context for our midIR measurement

may not b e a problem

Meech and Newburn have also derived the nucleus optical cross section

 km With our derived value of R we calculate p to b e pR

N

N

 formal error lower than the canonical value An overestimation

of the nuclear IR ux due to coma contamination might explain the low alb edo

However there are comets with comparably low values see Chapter

If the nucleus were a rapid rotator it would have to b e close to spherical and the

radius based on my midIR data would b e ab out  km Moreover the alb edo

would then b e even lower than quoted ab ove

Summary of This Chapter

Comets Utsunomiya and PWild were briey imaged in the midIR from the

Infared Telescop e Facility in Hawaii The former comet has a maximum eective

radius of  km if the STM is valid or ab out km if it is instead a rapid

rotator No companion optical data are available and the rotation state is unknown

The latter comet is the target of a spacecraft and thus is a more p opular ob ject

for study Our midIR data imply a radius of  km if the STM is valid

Optical data Meech and Newburn imply that the nucleus is either spherical

or has a very long on order of days rotation p erio d The alb edo is apparently

very low ab out but it is p ossible that there is some coma contamination in the

thermal data

Figure Comatting metho d applied to comet Utsunomiya Here I show the

results of the comatting metho d after application to comet Utsunomiyas midIR

image Virtually all of the ux can b e mo deled as comatic since there is very little

ux left in the dierence image but since the individual images of the comet were

dicult to centroid prop erly this may b e just an error in pixel registering

Figure Comatting metho d applied to comet PWild Here I show the results

of the comatting metho d after application to the midIR image of comet PWild

Virtually all of the ux can b e mo deled as comatic since there is very little

ux left in the dierence image but since the individual images of the comet were

dicult to centroid prop erly this may b e just an error in pixel registering

Chapter

Conclusions and The Future

In this chapter I will sp ecify some conclusions that can b e drawn by combin

ing the results presented in this thesis with earlier studies of cometary nuclei Of

course my work has not made the sample of nuclei complete and a few dozen more

ob jects with welldetermined physical prop erties would b e helpful b efore any anal

ysis b ecomes statistically defensible However it is interesting to collate the current

information and see what trends may b e app earing and what observational biases

are dominating the study of comets

Comets and Their Disguised Relations

Figure shows a plot of the eective diameters and geometric alb edos for

several cometary nuclei including the ones I have discussed in this thesis Also

plotted are nuclei studied by others and several NEAs and Centaurs The data are

listed in Table with the information from this thesis having an arrow in the

Ref column Not all data in Table are plotted on Fig Here are some

caveats ab out this table

 Most of the entries are from rep orts of a nuclear size measurement made using

thermal infrared techniques In a few cases radar or optical observations that have

spatiallyresolved images of the ob ject were used Observations in those wavelength

regimes that just have cross sectionintegrated photometry were not used

 The vast ma jority of the radii and alb edos were derived using the Standard

Thermal Mo del A few used the Rapid Rotator Mo del and one was even derived

from the Isothermal Mo del I have not made an attempt to reanalyze these data

I simply have quoted the values and errors that the authors themselves state even

though there are very clearly cases where the error bars are underestimated Consid

ering the uncertainties in some of the parameters that go into the thermal mo dels

such as the b eaming factor and the phase b ehavior Chapter the systematic

error of the absolute ux calibration ab out Tokunaga Rieke et al

and the exp erience of the several comets presented in this thesis it seems that some

of the diameters error bars could b e closer to and the alb edos error bars clos

er to This is esp ecially true where the thermal data is of low S N and this

do es not even include any systematic error with using an idealized mo del Excep

tions to this include but are not limited to Comet Halley and Asteroid Eros

which have b een optically imaged with subkm spatial resolution Asteroid

Toutatis which has b een the sub ject of multiple extensive radar exp eriments and

Comet IRASArakiAlco ck which passed so close to Earth and resulted in a mul

tiwavelength data cache so large that it was probably only a matter of time b efore

someone collated everything into a coherent picture Sekanina c

Figure The sizes and alb edos of active cometary nuclei some nearEarth aster

oids and Centaurs The cometary region is now starting to ll out thanks to

many thermal studies done since the mids

 One notices that some cometary diameters have no attendant alb edos Iron

ically it is often the case that reliable optical cross sections do not exist for the

comets that have b een observed in the midIR In the future more co ordination

b etween observations in the multiple wavelength regimes is needed In Chapter I

discussed some of the problems of nucleus observation that contribute to this lack

of optical cross sections

 The Rotation column shows many more entries with N than with Y

ie for most of the listed ob jects the rotational context is unknown This has

not b een reected in the error bars of the diameters and alb edos so the true error

bars are even higher for many ob jects For some ob jects this is not a problem

b ecause the observations to ok so long that the rotational variation has probably

b een averaged out and so is incorp orated into the error estimate already For

example the multiple midIR exp osures of Hyakutake cover several hours of time

and hence a large fraction of the rotation p erio d

 Note that the Cometary Nuclei in the title is in quotation marks I have

included many asteroids in the table some fraction of which are extinct comets I

will now discuss this p oint in more detail

The Tisserand parameter T is a constant of motion in a restricted threeb o dy

J

problem Considering the Sun Jupiter and a small b o dy as the three memb ers of

a system as long as the b o dy is not having a close encounter with Jupiter at the

time of the observation the value of T is constant In practice the value uctuates

J

by a few p ercent due to p erturbations by other planets The denition is Danby

p

v

u

2

u

e a

J

t

T cos i

J

a a a

J

where a is the semima jor axis of Jupiter AU a is the ob jects semima jor axis

J

e is the ob jects eccentricity and i is the ob jects Tisserand

himself recognized in the late th century that this constant of motion could b e

used to identify two comets observed far apart in time as the same ob ject if the

comet had had a close encounter with Jupiter in the interval and thus had its orbital

elements drastically changed

The value of the parameter indicates the strength of the dynamical coupling of

the ob jects orbit to Jupiter Most asteroids have T while the shortp erio d

J

comets mostly have T ie T is the b oundary b etween the coupling

J J

almost all shortp erio d comets are dynamically coupled to Jupiter while most

asteroids are not An indication of this can b e seen in the q column in Table

ap

for ob jects with T the aphelion is close to Jupiter

J

Of course the T b order is not p erfect There are asteroids that have T

J J

these are usually NEAs with a suciently large aphelion distance and there are

comets that have T the socalled Encke Family Levison which so

J

far only has two known memb ers b oth of which are in Table These are comets

in more classic NEA orbits ie the aphelion distance is never high enough to bring

them close to Jupiter

The explanation for the asteroids in cometary orbits follows from the supp osed

typical life cycle of a shortp erio d Jupiter Family comet After b eing p erturb ed

out of the Kuip er Belt and into the outer planetary region the nucleus is at the

mercy of the gas giants Approximately thirty p ercent of these comets that leave

the Kuip er Belt b ecome part of the Jupiter Family Levison and Duncan the

rest are either ejected or sent farther out in the Solar System Centaurs are thought

to b e Kuip er Belt ob jects currently in transition since their dynamical lifetimes is

6

roughly only year Dones et al

Once an ob ject is in the Jupiter Family its dynamical lifetime there is ab out

5

years Wetherill afterwhich the comet collides with a planet or the Sun

or is sent into a classic NEA orbit decoupled from Jupiter Of course during those

5

years the comet is outgassing since it passes close enough to the Sun but the

4

store of volatile material in the comet will only last ab out years either the

comet will disintegrate by then or the mantled surface will b e to o thick choking

o the available ice Levison and Duncan Hence on average a comet will

b ecome dormant while still coupled to Jupiter Observationally one would discover

an asteroid in a cometlike orbit T a few of which are noted in Table

J

However it is p ossible that a comet will b e quickly sent into an NEA orbit and

decoupled from Jupiter b efore all available ice is gone and we will see active comets

in NEA T orbits which we do see most famously as comet Encke The

J

existence of this comet and comet WilsonHarrington guarantee that despite the

fact that the Main Belt can p otentially provide a large fraction of the kilometer

size and larger NEAs Rabinowitz some fraction of the NEAs must b e dead

cometary nuclei The trick which we have not yet solved is to nd some diagnostic

that indicates which of the NEAs are cometary and which are asteroidal McFadden

Future studies of NEAs and nuclei may shed light on this problem

In Table I have made an arbitrary separation at T to mark which

J

asteroids might dynamically have a higher probability of b eing dead comets How

ever there are two intriguing asteroids that have high T and yet could very well

J

b e cometary Asteroid Phaethon is the parent to the Geminid meteor stream

Whipple which is strong evidence for a cometary origin despite the fact that

its aphelion distance is almost full AU smaller than the next smallest cometary

one Encke Asteroid Oljato was observed to have a transient blue excess

by McFadden et al which they argued was caused by a cometary outburst

One problem with Oljato is its high alb edo much higher than all of the known com

etary nuclei Nevertheless I have separated these ob jects from the other high T

J

crowd to emphasize that these ob jects have additional extenuating circumstances

Immediately one notices that there are some very black asteroids in b oth the

lowT and highT sections In my opinion these ob jects are the prime candidates

J J

for b eing extinct nuclei and further study is needed to nd out if there is any

distinguishing characteristic observable from Earth that separates them from the

other Main Beltderived NEAs

Furthermore there are many asteroids such as Hidalgo Damo cles

and BC that have low T and resp ectively but that simply

J

have not yet had their thermal ux measured Presumably when that happ ens

they will take their place alongside the other lowalb edo ob jects P P PT P PT PdArrest PEnc PHalley ject Ob icb iZ nner niZi PGiacobi PSwiftT alyF Halley Enc uie F Jupiter IRAS m el emp m elT emp k k F e e amily amily ml Comets amily isnHrington WilsonHarri tle uttl tle uttl Comets Comets T be able ie n l dso Cmtr Nuclei Cometary of edos Alb and Sizes Diameter  km         +0 1 4 5 l edo Alb      d d d  +0 0 4 6 T J A q U ap a Rotation NA N N N N Y N N N Y b Ref c

N Y N Y Y N N Y Y Y Fig In PHrl y PHartle PArendRigaux PSc i d PWil PSc eji PNeujmin C PKop ject Ob C C C otsneOdLongP Old Oortsense uie F Jupiter h haumasse H SuganoSaigusaF J HaleBopp O Hy B w s annW ma ass amily IRAS akutak AaiAc c ArakiAlco oescon Comets e ac mn hmann rodComets d erio j k uji k td a w a Diameter  km          T becon able l edo Alb      d d    td T e e e e J A q U e e e e ap a Rotation N Y Y N N N N Y N N N b Ref 1 1 c

9

N Y Y N Y Y Y Y N nFig In Y Y Betulia Gan P C ject Ob Qezlo tl Quetzalcoa Pholus C Cen otsneOdLongP Old Oortsense Eswt Lo with NEAs otsneNwLongP New Oortsense taurs LINEAR U Utsunomiy T CU ymed Chiron w 26 T J a rodCmt con Comets d erio rodComets d erio Diameter km         T becon able None l edo Alb td    d d  +6  3 T td e e J A q U e e ap a Rotation N N N N N N N N b Ref c

N N nFig In N N Y N N N V Golevk D DnQuixote Don Jason T T Phaethon V Oljato Seneca ject Ob Eswt High with NEAs Eswt Lo with NEAs A outatis A A A a w T T J J con u Exten but Diameter km td            aigCircumstances uating T l edo Alb becon able            T J td A q U ap a Rotation N Y N N N N Y N N N N b Ref c f

Y N Y Y N Y Y Y Y N Y nFig In Cr erus Cerb An T Sisyph An A ollo Ap T Geographos Iv Icarus Alinda Eros ject Ob Eswt High with NEAs zal ca o p ezcatli oro ar tinous teros us T J Diameter km             T l edo Alb becon able             T J td A q U ap a Rotation NA N N N N N N N N N N N b Ref c f g

N N N N N N N N N N N nFig In N XB Am Kh V Seleucus RaShalom Nefertiti Eger A ject Ob Beltro Eswt High with NEAs erenia ten ufu un v ata T J Diameter con km             td l edo Alb T becon able             T J td A q U ap a Rotation N N N N N N N N N N N N b h Ref c

N N N N N N N N nFig In N Y N N CA EE BW WF ject Ob v ma errors b a ariation a h bjc oainbenexplicitly een b rotation jects ob the Has bjc peindistance aphelion jects Ob Eswt High with NEAs olrea oob to as large so e b y oeta nsm ae h in the cases some in that Note w sobtained as T J Diameter con km it hspoin p this viate     td l edo Alb T     becon able tegration t lo sometimes Also tak T nin en J ie rteerrbr themselv bars error the or times oaccoun to td A q U ap a ata co partial Rotation nteqoe v quoted the in t N N Y N b i v erage Ref fterotational the of c g alues Y N N N nFig In

es Campins Campins risakadBro and Cruikshank V c F CmisadSc and Campins Murc Jones and Cruikshank Hdo n sr Ostro and Hudson Green Mottola References ern eeder andez hie tal et tal et tal et tal et tal et tal et 1 tal et hsThesis This hleic npreparation in Harris n wn Lbofsky Leb AHearn T e her Harmon Da dso edesco Bell Keller vies tal et il s Milli T Morrison becon able F tal et tal et tal et tal et tal et Sek tal et omenk tal et V nn c anina Pra o tal et v eeder apns Campin JwitadKls Kalas and itt Jew a td L ofsky b Le T Srmecanic Sar tal et Jorda v c e tal et Lisse dsoan rde Gradie nd a edesco tal et Hanner Le ofsky eb L tal et tal et tal et tal et Hanner tal et b tal et tal et tal et

i h kno the using g f d e calculate to able Explicitly T nulseabeomen edo alb Unpublished eeec nygiv only Reference Explicitly eeec nygiv only Reference J and q ap men men r o elypractical really not are naslt magnitude absolute wn in htteev these that tions in htteev these that tions h l edo alb the es srduabeocluae sn h kno the using calculated edo alb radius es ais oreliable no radius indi hsrfrnewtoterrbrrdu calculated radius bars error without reference this in tioned le r o h ligh the for are alues le r o h ligh the for are alues quan T becon able tities pia rs etonmeasuremen n sectio cross optical o on rodcomets d erio ngp lo for td tcurv tcurv e e midbrigh maxim bouemagnitude absolute n w um tness t y

teit obe b to exists et

Comparing Radii and Alb edos of Cometary Nuclei

We turn our attention to Fig a comparison of the alb edos and diameters

The addition of several p oints to that graph with this thesis and by other workers

in the last few years has started to ll out the cometary region on the graph In

the gure I have only used ob jects from Table that have b oth a known diameter

and an alb edo or at least claimed limits There are two p oints that I want to make

ab out the plot

 Clearly there is some overlap b etween the NEAs and the cometary nuclei

The nuclei all have a geometric alb edo p less than and several asteroids reside

in this region as well including some with high T The overlap can b e used to

J

estimate the fraction of NEAs that are cometary nuclei If we use p as the

b oundary seven of the forty asteroids are on the cometary side Since not

all of those seven need b e dead comets this could b e interpreted as an upp er limit

However there is an observational bias to discovering bright shiny asteroids over

dark ones and hence thermal studies of NEAs will preferentially measure more of

the high alb edo ob jects simply b ecause we know more of them This eect means

that we may b e underestimating the fraction of cometary NEAs there are more

dark carb onaceous C and Dtyp e NEAs out there waiting to b e discovered

Of course if one discovers asteroids through their thermal emission the bias

ows the other way since then a lower alb edo ob ject would b e easier to see all else

b eing equal However currently the vast ma jority of NEAs are discovered optically

Numerical integrations have b een done showing that the NEA p opulations

source can b e the Main Belt via three main mechanisms Greenb erg and Nolan

Migliorini et al the resonance with Jupiter the resonance

6

with Saturn and p erturbations by Mars However the existence of active comets in

NEA orbits implies a nonnegligible fraction of old cometary nuclei are there and

this ought to b e taken into account when attempting to mo del the NEA taxonomic

distribution A more complete database of the taxonomic typ es of NEAs would in

itself b e valuable if for example there are more C and Dtyp e NEAs ie those with

low alb edo than one would exp ect from the Main Belt delivery mechanisms which

predominately op erate on the inner Main Belt where there are a higher fraction of

Styp e ob jects Gradie et al Recent estimates of the cometary contribu

tion to the NEA p opulation have b een low even approaching zero eg Rabinowitz

although others eg Wetherill have suggested fractions higher than

the value I give ab ove

 There is no apparent constraint on the size of the nuclei there are ob jects

o ccupying every size scale from subkilometer to hundreds of kilometers It is worth

while to note that there are several more comets that are not listed in Table that

probably have sizes in the subkilometer range and a few unlisted Kuip er Belt ob

jects are probably larger than the plotted Centaurs No thermal studies have b een

done of these ob jects so the alb edos are unknown this is only based on optical

studies and the range of p ossible alb edos For example comet PHondaMrkos

Pa jdusakova has a diameter of less than km even if the alb edo is as low as

Lamy et al On the other extreme Kuip er Belt ob ject TO is at least

66

km wide using its absolute magnitude Marsden and p  The only

asteroids larger than this size are Pallas and Vesta

The KBOs and many of the ob jects in Fig have a common origin and

the question of the distribution of these original ob jects or their collisional frag

ments will require many more hours at the telescop e to build up a statistically

signicant sample However it is gratifying that we have sampled almost three orders

of magnitude of cometary sizes There seems to b e no doubt as to the existence of

small comets and interpreting that p opulation in a size distribution of nuclei will

likely shed light on the aging and active lifetime of these b o dies

Alb edo and Orbital Parameters

AHearn et al after analyzing the molecular abundances and dust pro

duction rates in the comae of ab out seven dozen comets found a correlation b etween

a comets dusttogas mass ratio and its p erihelion distance They concluded that

this was due to the eect of the solar heating cycle on the mantle of the nucleus

the mantle is presumably thicker for smaller p erihelia making it harder for grains

to b e entrained in the escaping gas leading to a lower dusttogas ratio In Fig

I have plotted the cometary alb edos versus p erihelion distance but there do es not

yet seem to b e any clear trend Thus while there is some thermal pro cessing of the

surface layers of a comet this do es not app ear to inuence the alb edo This may

argue against the existence of nearsurface ice on cometary nuclei since in that case

one might exp ect the ob jects with larger p erihelia eg the Centaurs to b e more

reective This would corrob orate the ndings from simultaneous IR and optical ob

servations of nuclei that indicate cross section and not emissivity or alb edo cause

the brightness variations eg AHearn et al The cometary ice app ears to

b e in a matrix with the ro ck in a p orous subsurface layer However adding several

more ob jects to Fig would strengthen or refute this conclusion

Figure compares the alb edo and the Tisserand invariant The dashed line

marks the nominal traditional separation b etween asteroids and comets There

is no apparent trend with this parameter either reiterating that the alb edos are

seemingly not tied to the orbital characteristics of the ob jects at least with the

sample we currently have Had the aging of a comet aected the alb edo one might

have exp ected that a comparison of Halley Family with longp erio d comets and

Centaurs with shortp erio d comets would have shown dierent clustering No such

trend is evident with the current sample

A Motivator for the Future

In Fig I have shown a current estimate of the size distribution of cometary

nuclei In this case I have dened cometary nuclei very lib erally including many of

the asteroids that I mentioned in the previous subsection The ob jects that were

used to make this graph are noted in Table note that I have not included the

three Centaurs Also plotted are three p ossible size distribution p ower laws

The value of the p ower law exp onent in a system of colliding particles that have

some selfgravity has b een the target of various numerical mo dels over the years

25

Davis et al nd that the cumulative p ower law go es as D for ob jects

smaller than km wide and attens out for larger ob jects A cometary distribution

Figure A comparison of the alb edos of cometary nuclei and related ob jects to

their p erihelion distance No trend is apparent although AHearn et al nd

that the Sun thermally pro cesses the mantle and aects the size distribution of the

dust entrained with the gas This aect do es not seem to manifest itself in alb edo

however

that approaches this would indicate a high frequency of collisions among the comets

conversely a dierent size distribution shap e would contradict this idea Clearly the

1

current distribution is nowhere near this p ower law b eing more prop ortional to D

but the sampling is of course not complete and it remains to b e seen how this law

will change in the coming years as more thermal studies are done of comets and

NEAs

Connected to this issue are the separate size distributions of the Oort Cloud

comets to days Halley Family and long p erio d ob jects and the Kuip er Belt com

ets to days current KB residents and the Jupiter Family ob jects The collision

histories of the two sets of ob jects dier Stern Stern and presumably

once a large numb er of cometary nuclei are sampled the evidence will b e there

In an ideal situation we could sample many longp erio d comets that are new in

the Oort sense and see what the current distribution of sizes is to day in the Oort

Cloud Information on the rotational state of these b o dies would also determine just

how pristine the ob jects are are they rotating faster or slower than the current

inner Solar System p opulation Since splittings and nongravitational forces act on

the active comets and aect the rotation rate in addition to any rep ercussions of

the comets most recent collision it would b e interesting to see what the relatively

pristine OC comets were originally like One ought to note that there are precisely

zero Oortsense new longp erio d comets listed in Table This is mainly b ecause

there are simply fewer new Oort Cloud comets discovered compared to old ones

The cometary connection with the asteroids needs to b e solidied with more

observational data There seems to have b een a deceleration in the numb er of

thermal studies of NEAs in the past decade one hop es that this trend will b e

reversed since there are ab out NEAs currently known with new discoveries

b eing made at an increasing rate due to the fecundity of asteroid search programs

Even optical information to obtain a complete census of the representation of the

taxonomic classes among the NEAs would b e useful since that can b e correlated

with the taxonomic gradient in the other source region the Main Belt

Another more direct approach is to lo ok for faint gas emission around near

Earth asteroids Comet WilsonHarrington is the most successful example of this

phenomenon the comet was discovered in then rediscovered in its asteroidal

incarnation in and the two apparitions were linked in Bowell and Ski

rep orted by Marsden I discussed the cometary nature of the data in

a separate work Fernandez et al A deep search for any OH signature

around several NEAs would provide strong direct and mo dern evidence for the

evolutionary connection b etween the asteroids and comets

Future Data Rates

The future of thermal observations of comets is bright SIRTF will b e available in

a few years to give us unprecedented sensitivity in the thermal regime In principle

since the lifetime of the satellite is exp ected to b e three to ve years a systematic

survey of all of the Jupiter Family comets could b e done Furthermore the size

distribution of the Kuip er Belt ob jects could b e measured since the sensitivity will

nally allow us to measure the trickle of blackb o dy radiation coming from those

ob jects This is all contingent on the allo cation of sucient observing time

Figure The Tisserand invariant is compared to the alb edos An aging aect

might have manifested itself in alb edo dierences b etween longp erio d and Halley

family comets and Jupiter family and Centaurs but no such trend is yet in evidence

It should b e clear from this thesis that the advent of large arrays of and

m detectors was critical for the success of this work and that the continued

increase in size and sensitivity will make it easier to sample more comets from the

ground in the coming years Based on our exp erience one detailed study of a short

p erio d comet and quick lo oks at two other comets short or longp erio d can b e

done p er midIR observing run An obvious b enet of having frequent observing

runs for scheduled shortp erio d comets is the increased probability of b eing at a

telescop e when a newly discovered longp erio d comet unknown at the time of the

telescop es prop osal deadline is available There are approximately shortp erio d

comets worthy of intense study p er year and if a few fortuitous comets are also

observable then optimistically we could have some physical information ab out a

dozen cometary nuclei every two to three years or so The observing eciency

is even b etter for NEAs since there are more of them By the time the

spacecraft encounters comet PWirtanen in we may start to have a handle

on the ensemble prop erties of the nuclei

Figure The current size distribution of cometary nuclei and related ob jects

that may b e nuclei This is not to claim that the sample of ob jects is complete on

any size scale The eventual slop e of the real distribution function will give clues to

the collisional history of the cometary p opulation

REFERENCES

 AHearn M F Photometry and p olarimetry network In The Comet Hal ley Archive

Summary Volume Z Sekanina and L Fry Eds pp

Jet Propulsion Lab oratory Pasadena

 AHearn M F H Campins D G Schleicher and R L Millis The nucleus of comet

PTemp el Astroph J

 AHearn M F R L Millis D G Schleicher D J Osip and P V Birch The ensemble

prop erties of comets Results from narrow band photometry of comets Icarus

 AHearn M F D G Schleicher P D Feldman R L Millis and D T Thompson Comet

Bowell b A J

 Allen C W Astrophysical Quantities d ed Athlone Press London

 Altenho W J and colleagues Co ordinated radio continuum observations of comets

Hyakutake and HaleBopp from to GHz Astron Astrophys

 Altenho W J W K Batrla W K Huchtmeier J Schmidt P Stump and M Walmsley

Radio observations of comet d Astron Astrophys LL

 Barker E S A L Co chran and P M Rybski Observations of faint comets at McDonald

Observatory In Modern Observational Techniques for Comets J Brandt J M

Greenb erg B Donn and J Rahe Eds pp NASA Jet Propulsion Lab oratory

Pasadena

 Bell J F B R Hawke and R H Brown Comp osition and size of Ap ollo asteroid

KB Icarus

 Belton M J S Characterization of the rotation of cometary nuclei In Comets in the

PostHal ley Era R L Newburn Jr M Neugebauer and J Rahe Eds pp

Kluwer Academic Publishers Boston

 Bessel M S UBVRI photometry I I the Cousins VRI system its temp erature and absolute

ux calibration and relevance for twodimensional photometry Publ Astron Soc Pacic

 Bessel M S UBVRI passbands Publ Astron Soc Pacic

 Biermann L Kometschwerfe und solare Korpuskularstrahlung Z Astrophys

 Biver N and colleagues Long term evolution of the outgassing of comet HaleBopp from

radio observations Earth Moon Plan accepted

 Bobrovniko N T Halleys comet in its apparition of Publ of Lick Obs

 Boss A P Evolution of the solar nebula IV Giant gaseous protoplanet formation

Astrophys J

 Brown R H Ellipsoidal geometry in asteroid thermal mo dels the standard radiometric

mo del Icarus

 Bus S J and colleagues Stellar o ccultation by Chiron Icarus

 Campb ell D B J K Harmon and I I Shapiro Radar observations of comet Halley

Astrophys J

 Campins H The anomalous dust pro duction in p erio dic comet Encke Icarus

 Campins H M F AHearn and L A McFadden The bare nucleus of comet Neujmin

Astroph J

 Campins H D J Osip G H Rieke and M J Rieke Estimates of the radius and alb edo

of cometasteroid transition ob ject WilsonHarrington based on infrared observations

Plan Sp Sci

 Campins H and D G Schleicher Comet dArrest a small and rapidly rotating nucleus

abstract Bul l Amer Astron Soc

 Campins H C M Telesco D J Osip G H Rieke M J Rieke and B Schulz The color

temp erature of Chiron A warm and small nucleus Astron J

 Chamb ers G F The Story of the Comets Clarendon Press London 164

 Comb es M J Lecacheux Th Encrenaz B Sicardy Y Zeau and D Malaise On stellar

o ccultations by comets Icarus

 Cruikshank D P and R H Brown The nucleus of comet PSchwassmannWachmann Icarus

 Cruikshank D P and T J Jones The diameter and alb edo of asteroid AA Icarus

 Danby J M A Fundamentals of Celestial Mechanics The MacMillian Co New York

 Davies J J Sp encer M Sykes D Tholen and S Green Pholus Intl Astron

Union Circ

 Davis D R C R Chapman S J Weidenschilling and R Greenb erg Collision history of

asteroids evidence from Vesta and the Hirayama families Icarus

 de Pater I P Palmer D L Mitchell S J Ostro D K Yeomans and L E Snyder Radar

ap erture synthesis observations of asteroids Icarus

 de Pater I C M Wade H L F Houpis and P Palmer The nondetection of contin

uum radiation from comet IRASArakiAlco ck d at to cm wavelengths and its

implication on the icygrain halo theory Icarus

 Divine N Numerical mo dels for Halley dust environments In The Comet Hal ley Dust

Gas Environment B Battrick and E Swallow Eds pp Europ ean Space Agency

Scientic and Technical Publications Branch No ordwijk The Netherlands

 Divine N and colleagues The Comet Halley dust and gas environment Sp Sci Rev

 Dones L H F Levison and M Duncan On the dynamical lifetimes of planetcrossing

ob jects In Completing the Inventory of the Solar System T W Rettig J M Hahn Eds

pp Astronomical So ciety of the Pacic San Francisco

 Donn B D The formation and structure of uy cometary nuclei from random accumula

tion of grains Astron Astrophys

 Donn B The accumulation and structure of comets In Comets in the PostHal ley Era

R L Newburn Jr M Neugebauer and J Rahe Eds pp Kluwer Academic

Publishers Boston

 Duncan M T Quinn and S Tremaine The formation and extent of the solar system comet

cloud Astron J

 Dworetsky M M A p erio dnding metho d for sparse randomly spaced observations or

How long is a piece of string Mon Not Royal Astron Soc

 Edgeworth K E The origin and evolution of the Solar System Mon Not Royal Astron

Soc

 Farinella P and D R Davis Shortp erio d comets primordial b o dies or collisional frag

ments Science

 Farnham T L D G Schleicher and M F AHearn The HB narrowband comet lters

standard stars and calibrations Icarus submitted

 Fernandez J A On the existence of a comet b elt b eyond Neptune Mon Not Roy

Astron Soc

 Fernandez Y R and colleagues a Survey of the physical prop erties of cometary nuclei

Recent progress In Cometary Nuclei in Space and Time ASP Conference Series M F

AHearn Ed accepted Astronomical So ciety of the Pacic San Francisco

 Fernandez Y R and colleagues b The inner coma and nucleus of comet HaleBopp

results from a stellar o ccultation Icarus

 Fernandez Y R C M Lisse H U Kau S B Peschke H A Weaver M F AHearn P L

Lamy T A Livengo o d and T Kostiuk c Physical prop erties of the nucleus of comet

PEncke Icarus submitted

 Fernandez Y R A Kundu C M Lisse and M F AHearn a X Band VLA observations of

comet Hyakutake C B and implications for nuclear prop erties Planetary Space

Science

 Fernandez Y R L A McFadden C M Lisse E F Helin and A B Chamb erlin b Analysis

of POSS images of cometasteroid transition ob ject P W WilsonHarrington 165

Icarus

 Fernie J D Relationships b etween the Johnson and KronCousins VRI photometric systems

Publ Astron Soc Pacic

 Finlay W H and W L Elkin Mon Not Roy Astron Soc

 Fomenkova M N B Jones R Pina R Puetter J Sarmecanic R Gehrz and T Jones

Midinfrared observations of the nucleus and dust of comet PSwiftTuttle Astron J

 Gabriel C J AcostaPulido I Heinrichsen H Morris and W M Tai The ISOPHOT

interactive analysis PIA a calibration and scientic analysis to ol In Astronomical Data

Analysis Software and Systems VI ASP Conference Series Vol G Hunt and H E

Payne Eds pp Astronomical So ciety of the Pacic San Francisco

 Garradd G J Comet PEncke Intl Astron Union Circ

 Gehrz R D E P Ney J Piscitelli E Rosenthal and A T Tokunaga Infrared photometry

and sp ectroscopy of comet PEncke Icarus

 Gilmore A C and P M Kilmartin Perio dic comet Encke Intl Astron Union Circ

 Goldstein R M R F Jurgens and Z Sekanina A radar study of comet IRASArakiAlco ck

d Astron J

 Gomb osi T I T E Cravens and A F Nagy Timedep endent dusty gasdynamical ow

near cometary nuclei Astrophys J

 Gomb osi T I and H L F Houpis An icyglue mo del of cometary nuclei Nature

 Gomb osi T I A F Nagy and T E Cravens Dust and neutral gas mo deling of the inner

atmosphere of comets Rev Geophys

 Gomb osi T I K Szego B E Grib ov R Z Sagdeev V D Shapiro V I Shevchenko and T E

Cravens Gas dynamic calculations of dust terminal velo cities with realistic dust size

distributions In Cometary Exploration T I Gomb osi Ed vol pp Central

Research Institute for Physics Hungarian Academy of Sciences Budap est

 Gradie J C C R Chapman and E F Tedesco Distribution of taxonomic classes and the

comp ositional structure of the asteroid b elt In Asteroids II R P Binzel T Gehrels M

S Matthews Eds pp Univ of Arizona Press Tucson

 Green D W E Comet PTemp elTuttle Intl Astron Union Circ

 Green S F A J Meadows and J K Davies Infrared observations of the extinct cometary

candidate TB Mon Not Roy Astron Soc pp

 Greenb erg R and M C Nolan Delivery of asteroids and meteorites to the inner Solar

System In Asteroids II R P Binzel T Gehrels M S Matthews Eds pp

Univ of Arizona Press Tucson

 Hainaut O R K J Meech H Bo ehnhardt and R M West Early recovery of comet

PTemp elTuttle Astron Astrophys

 Hanner M S D K Aitken R Knacke S McCorkle P F Ro che A T Tokunaga Infrared

sp ectrophotometry of comet IRASArakiAlco ck d A bare nucleus revealed Icarus

 Hanner M S R H Giese K Weiss and R Zerull On the denition of alb edo and

application to irregular particles Astron Astrophys

 Hanner M S D K Lynch R W Russell J A Hackwell R Kellogg D Blaney Mid

infrared sp ectra of comets PBorrelly PFaye and PSchaumasse Icarus

 Hanner M S R L Newburn H Spinrad and G J Veeder Comet SuganoSaigusaFujikawa

V a small puzzling comet Astron J

 Harmon J K and colleagues Radar detection of the nucleus and coma of comet

Hyakutake C B Science

 Harmon J K D B Campb ell A A Hine I I Shapiro and B G Marsden Radar

observations of comet IRASArakiAlco ck Astrophys J

 Harris A W A thermal mo del for nearEarth asteroids Icarus

 Harris A W J K Davies and S F Green Thermal infrared sp ectrophotometry of the

nearEarth asteroids RaShalom and EE Icarus 166

 Helin E E Ney and B Hateld Perio dic comet Encke Intl Astron Union Circ

 Hellmich R The inuence of the radiation transfer in cometary dust halos on the pro duction

rates of gas and dust Astron Astrophys

 Henyey L G and J L Greenstein Diuse radiation in the galaxy Astrophys J

 Hoban S and S Baum A VLA search for cm continuum radiation from comet Halley

Icarus

 Hobbs R W J C Brandt S P Maran W J Webster Jr and K S Krishna Swamy

Microwave continuum radiation from comet Kohoutek f emission from the icygrain

halo Astrophys J

 Hobbs R W S P Maran and J C Brandt Microwave continuum radiation from comet

West n Astrophys J

 Hogb om J A Ap erture synthesis with a nonregular distribution of interferometer baselines

Astron Astrophys Supp

 Hudson R S and S J Ostro Shap e and nonprincipal axis spin state of asteroid

Toutatis Science

 Jacoby G H D A Hunter and C A Christian A library of stellar sp ectra Astrophys J

Suppl Ser

 Jewitt D Cometary photometry In Comets in the PostHal ley Era R L Newburn Jr

M Neugebauer and J Rahe Eds pp Kluwer Academic Publishers Boston

 Jewitt D and P Kalas Thermal observations of Centaur CU Astroph J

26

LL

 Jewitt D and K Meech JM CCD photometry of comet PEncke Astron J

 Jewitt D C and K J Meech Optical prop erties of cometary nuclei and a preliminary

comparison with asteroids Astroph J

 Jorda L et al The rotation p erio d of comet HaleBopp from observations of the dust jets

at Pic du Midi Observatory Earth Moon Planets accepted

 Jorda L P L Lamy I Toth and M F AHearn Prop erties of the nucleus of shortp erio d

comets from ISO observations abstract In Abstracts Asteroids Comets Meteors Cornel l

University July p Cornell University Ithaca NY

 Kamoun P G D B Campb ell S J Ostro G H Pettengill and I I Shapiro Comet

Encke radar detection of nucleus Science

 Kau H U TIMMI lter wheel conguration World Wide Web URL

httpwwwesoorglasil la Te le sc ope s ca tt im mi

timmifiltershtml February

 Kau H U R Jouan P O Lagage P Masse P Mestreau and A Tarrius TIMMI ESOs

new m camerasp ectrometer Infrared Phys Technol

 Kazarovets A V N N Samus O V Durlevich M S Frolov S V Antipin N N Kireeva and

E N Pastukhova The th sp ecial namelist of variable stars Info Bul l on Var

Stars

 Keller H U The nucleus In Physics and Chemistry of Comets W F Huebner Ed pp

SpringerVerlag Berlin

 Keller H U and colleagues First Halley multicolour camera imaging results from Giotto

Nature

 Keller H U and colleagues Comet PHalleys nucleus and its activity Astron

Astrophys

 Kharitonov A V V M Tereshchenko and L N Knyazeva Spectrophotometric catalogue

of stars Izdatelstvo Nauka Kazakhskoi SSR AlmaAta Kazakh SSR

 Klaas U H Kruger I Heinrichson A Heske and R Laureijs ISOPHOT observers manual

World Wide Web URL

httpisowwwestecesa nl ma nu al si so phtomhtml

May

 Kuip er G P Origin of the solar system In Astrophysics A Topical Symposium J A

Hynek Ed pp McGrawHill New York 167

 Labs D H Neckel P C Simon and G Thuiller Ultarviolet solar irradiance measurement

from to nm during Spacelab mission Sol Phys

 Lamy P Comet PTemp elTuttle Intl Astron Union Circ

 Lamy P L and I Toth Direct detection of a cometary nucleus with the Hubble Space

Telescop e Astron Astrophys LL

 Lamy P L I Toth M F AHearn H A Weaver The nucleus of comet PHondaMrkos

Pa jdusakova abstract Bul l Amer Astron Soc

 Lamy P L I Toth L Jorda H A Weaver and M AHearn a The nucleus and inner coma

of comet PWirtanen Astron Astrophys LL

 Lamy P L I Toth H A Weaver b Hubble Space Telescop e observations of the nucleus and

inner coma of comet P Y Borrelly Astron Astrophys

 Larson S M and M F AHearn Comet Bowell b measurement of the optical

thickness of the coma and particle alb edo from a stellar o ccultation Icarus

 Laureijs R J U Klaas P J Richards and B Schulz ISOPHOT data users manual World

Wide Web URL

httpisowwwestecesa nl ma nu al sp ht idum

Octob er

 Leb ofsky L A M J Leb ofsky and G H Rieke Radiometry and surface prop erties of

Ap ollo Amor and Aten asteroids Astron J

 Leb ofsky L A and J R Sp encer Radiometry and thermal mo deling of asteroids In

Asteroids II R P Binzel T Gehrels M S Matthews Eds pp Univ of

Arizona Press Tucson

 Leb ofsky L A M V Sykes E F Tedesco G J Veeder D L Matson R H Brown J C Gradie

M A Feierb erg R J Rudy A rened standard thermal mo del for asteroids based

on observations of Ceres and Pallas Icarus

 Leb ofsky L A G J Veeder M J Leb ofsky and D L Matson Visual and radiometric

photometry of Betulia Icarus

 Leb ofsky L A G J Veeder G H Rieke M J Leb ofsky D L Matson C Kowal C G Wynn

Williams and E E Becklin The alb edo and diameter of Ap ollo Icarus

 Lecacheux J L Jorda A Enzian J Klinger F Colas E Frappa and P Laques Comet

C B Hyakutake Intl Astron Union Circ

 Lecacheux J W Thuillot Th Encrenaz P Laques D Rouan and R Despiau Stellar

o ccultations by two comets IRASArakiAlco ck d and PIRAS j Icarus

 Lemke D and colleagues ISOPHOT capabilities and p erformance Astron Astroph

LL

 Levison H Comet taxonomy In Completing the Inventory of the Solar System T Rettig

and J M Hahn Eds pp Astronomical So ciety of the Pacic San Frsncisco

 Levison H F and M J Duncan From the Kuip er Belt to Jupiter family comets the spatial

distribution of ecliptic comets Icarus

 Licandro J et al The spin axis of comet O HaleBopp Earth Moon Planets

accepted

 Lien D J Asteroid debris trails evidence for recent collisions in the asteroid b elt abstract

Bul l Amer Astron Soc

 Lisse C M and colleagues Discovery of Xray and EUV emission from comet Hyakutake

C B Science

 Lisse C M and colleagues a Infrared observations of the dust emitted by comet Hale

Bopp Earth Moon Plan accepted

 Lisse C M M F AHearn Y R Fernandez E Grun H U Kau T Kostiuk D J Lien T A

Livengo o d D J Osip and S B Peschke ISOPHOT measurements of dust emitted

from p erio dic comets PIRAS and PEncke Icarus submitted

 Lisse C M M F AHearn M G Hauser T Kelsall D J Lien S H Moseley W T Reach and

R F Silverb erg Infrared observations of comets by COBE Astroph J 168

 Lisse C M Y R Fernandez A Kundu M F AHearn A Dayal L K

Deutsch G G Fazio J L Hora and W F Homann b The nucleus of comet

C B Hyakutake Icarus

 Lumme K and E Bowell Radiative transfer in the surfaces of atmosphereless b o dies I I

Interpretation of phase curves Astron J

 Lumme K E Bowell and A W Harris An empirical phase relation for atmosphereless

b o dies abstract Bul l Amer Astron Soc

 Luu J and D Jewitt LJ The nucleus of comet PEncke Icarus

 Lyttleton R A The Comets and Their Origin University Press Cambridge

 Lyttleton R A Intro duction In The Nature of Comets N B Richter A Beer trans

pp xviixxxviii Methuen Co Ltd London

 Marconi M L and D A Mendis The atmosphere of a dirtyclathrate cometary nucleus a

twophase multiuid mo del Astrophys J

 Marconi M L and D A Mendis The eects of the diuse radiation elds due to multiple

scattering and thermal reradiation by dust on the dynamics and thermo dynamics of a dusty

cometary atmosphere Astrophys J

 Marsden B G Comets in Quart J Roy Astron Soc

 Marsden B G Comets in Quart J Roy Astron Soc

 Marsden B G Comets in Quart J Roy Astron Soc

 Marsden B G Comets in Quart J Roy Astron Soc

 Marsden B G a Comets in Quart J Roy Astron Soc

 Marsden B G b Comets in Quart J Roy Astron Soc

 Marsden B G VA Comet WilsonHarrington I I I Intl Astron Union

Circ

 Marsden B G a Comet C B Hyakutake Intl Astron Union Circ

 Marsden B G b Come P N ElsePizarro Intl Astron Union Circ

 Marsden B G TO Minor Plan Elec Circ M

66

 Marsden B G and E Ro emer a Comets in Quart J Roy Astron Soc

 Marsden B G and E Ro emer b Comets in Quart J Roy Astron Soc

 Marsden B G and G V Williams Catalogue of Cometary Orbits th ed International

Astronomical Union Cambridge Mass

 Matson D L PhD Thesis California Institute of Technology

 McFadden L A The cometasteroid transition recent telescopic observations In Asteroids

Comets Meteors A Milani M Di Martino A Cellino Eds pp Kluwer

Academic Publ Dordrecht

 McFadden L A A L Co chran E S Braker D P Cruikshank and W K Hartmann The

enigmatic ob ject Oljato Is it an asteroid or an evolved comet J Geophys Res

 Meech K J Physical aging in comets In Comets in the PostHal ley Era R L Newburn

Jr M Neugebauer and J Rahe Eds pp Kluwer Academic Publishers Boston

 Meech K J Physical prop erties of comets In Asteroids Comets Meteors Proceedings

of the th COSPAR Col loquium AC LevasseurRegourd and M Fulchignoni Eds in

press PergamonElsevier Oxford

 Meech K J and D C Jewitt Observations of comet PHalley at minimum phase angle

Astron Astrophys

 Meech K J and R L Newburn Comet PWild inn preparation

 Meier R T C Owen D C Jewitt H E Matthews M Senay N Biver D Bo ckeleeMorvan

J Crovisier and D Gautier a Deuterium in comet C O HaleBopp detection

of DCN Science

 Meier R TC Owen H E Matthews D CJewitt D Bo ckeleeMorvan N Biver J Crovisier

and D Gautier b A determination of the HDOH O ratio in comet C O Hale

2

Bopp Science

 Migliorini F P Michel A Morbidelli D Nesvorny and V Zappala Origin of Earthcrossing

asteroids a quantitative simulation Science 169

 Millis R L M F AHearn and H Campins An investigation of the nucleus and coma of

comet PArendRigaux Astroph J

 Minter A H and G Langston and GHz continuum observations of comet

Hyakutake C B Astrophys J Lett

 Monet D G C C Dahn F J Vrba H C Harris J R Pier C B Luginbuhl and H D Ables

US Naval Observatory CCD of faint stars I Program description and

rst results Astron J

 Morrison D J C Gradie and G H Rieke Radiometric diameter and alb edo of the

remarkable asteroid AA Nature

 Mottola S and colleagues Physical mo del of nearEarth asteroid Golevka

JX from optical and infrared observations Astron J

 Mumma M J M A DiSanti N Dello Russo M Fomenkova K MageeSauer C D Kaminski

and D X Xie Detection of abundant ethane and methane along with carb on monoxide

and water in Comet C B Hyakutake evidence for interstellar origin Science

 Murchie S and colleagues Imaging results from NEARs yby of Eros abstract In

Abstracts Asteroids Comets Meteors Cornel l University July p Cornell

University Ithaca NY

 Nakamura T and S Nakano Comet B Intl Astron Union Circ

 National Radio Astronomy Observatory The The AIPS Cookbook version APR

NRAO Charlottesville Virginia

 Neckel H and D Labs The solar radiation b etween and A Sol Phys

 Ney E P Multiband photometry of comets Kohoutek Bennett Bradeld and Encke

Icarus

 Oort J H The structure of the cloud of comets surrounding the Solar System and a

hyp othesis concerning its origin Bul l Astron Inst Neth

 Osb orn W H M F AHearn U Carsenty R L Millis D G Schleicher P V Birch H

Moreno and A GutierrezMoreno Standard stars for photometry of comets Icarus

 Perley R A and G B Taylor The VLA calibrator manual National Radio Astronomy

Observatory So corro New Mexico

 Perryman M A C The Hipparcos and Tycho Catalogues Astrometric and Photometric

Star Catalogues Derived from the ESA Hipparcos Space Astrometry Mission ESA Publica

tions Division No ordwijk Netherlands

 Perryman M A C and colleagues The Hipparcos catalogue Astron Astroph

LL

 Pollack JB O Hubickyj P Bo denheimer J J Lissauer M Po dolak and Y Greenzweig

Formation of the giant planets by concurrent accretion of solids and gas Icarus

 Pravec P M Wolf L Sarounova A W Harris and J K Davies Spin vector shap e and

size of the BW Icarus

3

 Qi C G A Blake D O Muhleman and M A Gurwell Interferometric imaging of comet

HaleBopp with the Owens Valley Millimeter Array abstract Bul l Amer Astron Soc

 Rabinowitz D L Are mainb elt asteroids a sucient source for the earthapproaching

asteroids Icarus

 Reach W T M V Sykes D Lien and J K Davies The dust trail of comet Encke In

preparation

 Reitsema H J W A Delamere A R Williams D C Boice W F Huebner and F L Whipple

Dust distribution in the inner coma of comet Halley comparison with mo dels Icarus

 Richter N B The Nature of Comets English rev ed A Beer trans Methuen Co

Ltd London 170

 Rickman H The thermal history and structure of cometary nuclei In Comets in the Post

Hal ley Era R L Newburn Jr M Neugebauer and J Rahe Eds pp Kluwer

Academic Publishers Boston

 Rickman H To app ear in Cometary Nuclei in Space and Time M F AHearn Ed

Astronomical So ciety of the Pacic San Francisco

 Rieke G H M J Leb ofsky and F J Low An absolute photometric system at and

microns Astron J bf

 Ro emer E Observations of comets and minor planets Astron J

 Ro emer E and R E Lloyd Observations of comets minor planets and satellites Astron

J

 Roser S and U Bastian PPM Star Catalogue Astronomisches RechenInstitut Heidelb erg

and Sp ektrum Akademischer Verlag Heidelb erg

 Salo H Monte Carlo mo deling of the net eects of coma scattering and thermal reradiation

on the energy input to cometary nucleus sic Icarus

 Samarasinha N H Preferred orientations for the rotational angular momentum vector of

p erio dic comets abstract Bul l Amer Astron Soc

 Samarasinha N H and M J S Belton Longterm evolution of rotational stress and

nongravitational eects for Halleylike cometary nuclei Icarus

 Sarmecanic J M Fomenkova B Jones and T Lavezzi Constraints on the nucleus and

dust prop erties from midinfrared imaging of comet Hyakutake Astrophys J Lett

LL

 Schenewerk M S P Palmer L E Snyder and I de Pater VLA limits for comets Austin

VI and PCrommelin n evidence for a diuse OH halo Astron J

 Schleicher D G T L Farnham B R Smith E A Blount E Nielsen and S M Lederer a

Nucleus prop erties of comet HaleBopp O based on narrowband imaging abstract

Bul l Amer Astron Soc

 Schleicher D G R L Millis and P V Birch b Narrowband photometry of comet PHalley

Variation with helio centric distance season and solar phase angle Icarus

 Schleicher D G R L Millis D J Osip and S M Lederer c Activity and the rotation

p erio d of comet Hyakutake B Icarus

 Sekanina Z Split comets In Comets L L Wilkening Ed pp University of

Arizona Press Tucson

 Sekanina Z a Outgassing asymmetry of p erio dic comet Encke I Apparitions

Astron J

 Sekanina Z b Outgassing asymmetry of p erio dic comet Encke I I Apparitions

and a study of the nucleus evolution Astron J

 Sekanina Z c Nucleus of comet IRASArakiAlco ck VI I Astron J

 Sekanina Z The problem of split comets revisited Astron Astrophys LL

 Sekanina Z A determination of the nuclear size of comet HaleBopp C O Earth

Moon Plan accepted

 Shao CY Perio dic comet Encke Intl Astron Union Circ

 Shao CY and G Schwartz Perio dic comet Encke Intl Astron Union Circ

 Silva D R and M E Cornell A new library of optical sp ectra Astrophys J Suppl Ser

 Smithsonian Astrophysical Observatory Smithsonian Astrophysical Observatory Star Catalog

Smithsonian Institution Washington

 Snyder L E P Palmer and C M Wade An upp er limit to the microwave continuum

radiation from comet Austin g Astrophys J Lett

 Space Telescop e Science Institute Imaging Spectrograph instrument handbook

World Wide Web URL

httpwwwstscieducgi b in st is ca t doc um ent s sub ca t ihb

June

 Sp encer J R A roughsurface thermophysical mo del for airless planets Icarus 171

 Sp encer J R L A Leb ofsky and M V Sykes Systematic biases in radiometric diameter

determinations Icarus

 Stellingwerf R F Perio d determination using phase disp ersion minimization Astrophys

J

 Stern S A Collisions in the Oort Cloud Icarus

 Stern S A Collisional time scales in the Kuip er Disk and their implications Astron J

 Stern S A and J M Shull The inuence of sup ernovae and passing stars on comets in the

Oort cloud Nature

 Swings JP Transactions of the International Astronomical Union Volume XIXB Pro

ceedings of the Nineteenth General Assembly Reidel Publishing Co Dordrecht

 Sykes M V and R G Walker Cometary dust trails I Survey Icarus

 Tedesco E F The IRAS minor planet survey Technical Rep ort PLTR Phillips

Lab oratory Hanscom Air Force Base MA

 Tedesco E F and J Gradie Discovery of M class ob jects among the nearEarth asteroid

p opulation Astron J

 Thomas N and H U Keller Comet PHalleys nearnucleus jet activity In Symposium on

the Diversity and Similarity of Comets E J Rolfe and B Battrick Eds pp Eu

rop ean Space Agency Publications Divi

sion No ordwijk The Netherlands

 Thomas N and H U Keller Interpretation of the inner coma observa

tions of comet PHalley by the Halley Multicolour Camera Ann Geophys

 Tokunaga A A reevaluation of the micron magnitude system Astron J

 van Biesbro eck G Comet observations Astron J

 van der Bliek N S J Manfroid and P Bouchet Infrared ap erture photometry at ESO

and its future use Astron Astroph Supp

 Vanysek V Photometric system for the International Halley Watch In Asteroids Comets

Meteors CI Lagerkvist and H Rickman Eds pp Astronomiska Observatoriet

Uppsala Sweden

 Veeder G J M S Hanner D L Matson E F Tedesco L A Leb ofsky and A T Tokunaga

Radiometry of nearearth asteroids Astron J

 Veeder G J C Kowal and D L Matson The Earthcrossing asteroid TB In

Lunar and Planetary Science XV Abstracts of Papers Submitted to the Fifteenth Lunar and

Planetary Science Conference pp Lunar and Planetary Institute Houston TX

 VorontsovVelyaminov B Structure and mass of cometary nuclei Astrophys J

 Weaver H A Comet C B Hyakutake Intl Astron Union Circ

 Weaver H A P D Feldman M F AHearn C Arpigny J C Brandt M C Festou M Haken

J B McPhate S A Stern and G P Tozzi The activity and size of the nucleus of

comet HaleBopp C O Science

 Weaver H A P D Feldman M F AHearn C Arpigny J C Brandt and C E Randall

An HST sp ectroscopic and imaging investigation of comet Hyakutake C B

abstract Bul l Amer Astron Soc

 Weaver H A and P L Lamy Estimating the size of HaleBopps nucleus Earth Moon

Plan accepted

 Weissman P R Are cometary nuclei primordial rubble piles Nature

 Weissman P R Dynamical history of the Oort Cloud In Comets in the PostHal ley Era

R L Newburn Jr M Neugebauer and J Rahe Eds pp Kluwer Academic

Publishers Boston

 Wetherill G W Where do the Ap ollo ob jects come from Icarus

 Wetherill G W End pro ducts of cometary evolution Cometary origin of earthcrossing

b o dies of asteroidal app earance In Comets in the PostHal ley Era Newburn R L M

Neugebauer J Rahe eds Kluwer Academic Publishers Dordrecht pp 172

 Whipple F L A comet mo del I The acceleration of comet Encke Astrophys J

 Whipple F L The rotation of cometary nuclei In Comets L L Wilkening Ed pp

University of Arizona Press Tucson

 Whipple F L TB and the Geminid meteors Intl Astron Union Circ

 Whipple F L and S Zekanina Comet Encke precession of the spin axis nongravitational

motion and sublimation Astron J

 Williams D M C G Mason R D Gehrz T J Jones C E Wo o dward D E Harker M

S Hanner D H Wo o den F C Witteb orn and H M Butner Measurement of

submicron grains in the coma of comet HaleBopp C during February

UT Astrophys J LL

 Winter D F and J M Saari A particulate thermophysical mo del of the lunar soil

Astrophys J

 Wo o dgate B E and collegaues The Space Telescop e Imaging Sp ectrograph design Publ

Astron Soc Pacic

 Wurm K On the interpretation of the sp ectra of comets and their forms Astrophys J

 Zomb eck M V Handbook of Space Astronomy and Astrophysics nd ed University Press

Cambridge 173