Chapter 10

Astronom

0 - Comets

my 9601

1

Topics to bTopics to bC t bit d• Comet orbits and reserv

• Coma and tail (10.3)• Composition (10.4)• Nucleus (10.6)( )• Comet formation: (10.7)

be coveredbe coveredi (10 2)voirs (10.2)

)

2

ComeAn icy/rocky body a few to 10-20 measurements of about 10 nucle

Resolved:Halley (Giotto 1986) 8x15km y ( )

Borrelly (Deep Space 1) 8km lonWild 2 (Stardust) 5km

Tempel 1 (Deep Impact, Stardust) 8x

Borrelly

p ( p p )

Wild 2

t nucleikm in diameter. We have size i

Halley

ng

x5 km

Tempel 1Tempel 1

2 3

ComeInferred diameters:Schwassmann-Wachmann 1: 30Schwassmann-Wachmann 1: 30Hale-Bopp: 60 kmSwift-Tuttle: 26 kmNeujmin: 20 km

Albedos:2-5%

Schwassmann-Wachmann 1 (IR)

Albedos:2 5%,darker than coal

t nuclei

0 km0 km

Hale-Bopp 4

When comets aWhen (if?) a comet’s orbit takes itbegins to vaporize and produces spherical cloud of gas near the nu104 to a few x 105 km across.

A hydrogen coma, invisible to the naked eye, stretches out to several times 107 km, composed primarilycomposed primarily of H dissociated from H20 (observed in UV)

Tail to nucleus size ratio: 10,000,000 to 1

approach the Sunt near the Sun (r <~ 3 AU), ice a tail up to 108 km long. The near-

ucleus is the coma and is typically

5

Comet orbits are typically (but not always) highly elliptical.

As a result, they only spend a small fraction of their lives as activefraction of their lives as active comets. Most of the time, they are frozen inert bodies, far from the Sun.

When inactive, comets are difficult todetect even with large telescopes.detect even with large telescopes. So the properties of these objects (including any which may remain

tl il d i th t S lpermanently exiled in the outer SolarSystem), must be deduced from theibrief active phases.p

.

Note: comet tail always points roughly away from the Sun due to solar wind

o and radiation pressure

r r

6

Active cActive c

Hyakutake (1996

West (1976)

cometscomets

6)

Hale-Bopp (1997)

7

Nucleus: a dNucleus: a d• Whipple (1950) proposed the pp ( ) p p

“dirty snowball” theory of cometary nuclei

• This theory has stood up wellThis theory has stood up well,though some argue comets armore like ‘snowy dirtballs”

• Densities of cometary nuclei a• Densities of cometary nuclei ahard to determine, but modelsindicate 0.3-0.7 g/cm3, which less than most icesless than most ices.

• Low density points to a porous“rubble-pile” model containingi ifi idsignificant void space

• Comet nuclei may be held together by “sintering” and othtogether by sintering and othrelatively weak contact forces

irty snowballirty snowball

, re

areare s is

Schematic representation of a cometarynucleus according to the rubble-pile model; individual fragments are lightly

s g

model; individual fragments are lightly bonded by thermal processing or sintering (Weissman 1986)

herher

sintering8

Nuclear surNuclear sur•

Tempel 1 90 seconds before the Deep Impact probe hit

•

One of the last images before Deep Impact

rface layersrface layersComet nuclei that do not passComet nuclei that do not pass near the Sun are expected to build up a dark, reddish, tar-like surface irradiation layer ofsurface irradiation layer of tholins, carbon chains produced by long-time irradiation of the nucleus constituents Recentnucleus constituents. Recent observations, however, indicate that some distant comet nuclei have much higher albedos (later)have much higher albedos (later)Comets that have passed by the Sun on many occasions are thought to have a dust crust anthought to have a dust crust, an accumulation of large non-volatile rocky material that builds up as the ices disappearup as the ices disappear.

9

Different dynamical fA long-period comet is one with than 200 years.

These comets have orbits which eplanetsplanets.

Perhaps moreimportantly, the orbits of these comets are quite different fromquite different from those of short-period comets, those with P

20< 20yrs.

families of cometsan orbital period (year) longer

extend beyond the orbits of the

10

ShortSmal

Inclinations near those of the planets (prograde)

Inclinations at right angles tothose of the planetsthose of the planets

In the plane of the planets, p p ,but moving in the opposite direction (retrograde)

ter periodsler orbits

Short pd comets

Long-period comets11

Q: What makes SP and LP comQ: What makes SP and LP com

A: Their origin

Short-period comets come from the Kuiper-Edgeworth belt, a ring of "leftovers" at the edge of our Solar System.

TfofopinKenneth E. Edgeworth

1880 1972Gerard P. Kuiper

1905-1973

1880-1972

mets different?mets different?

These remnants of planetary ormation orbit in the plane of theormation orbit in the plane of the planets, hence their low nclinations.

12

Long-perioLong-perioCloud, a spnuclei reac

Jan Oort

stars (arouis 4.3 ly aw

Jan Oort1900-1992

Both the Oort cloud and the KuiperBoth the Oort cloud and the Kuiperbelt are made up of planetesimalsleft over from the era of the formation of the planets.

So why are they different?So why are they different?

od comets come from the Oortod comets come from the Oortpherical cloud of frozen comet ching up to half-way to the nearest

5und 105 AU or 1.6 ly; recall α Cenway).

13

The formation ofThe formation of

Solid matter condensed out of thecloud of gas and dust (the ''solar ncloud of gas and dust (the solar nproto-Sun.

El t t th d f h tElements at the edge of what wousystem were too sparse to form pstill remains of this material.st e a s o t s ate a

Solid bodies within the planetary si t th i l tinto the growing planets.

Or were they?y

f the solar systemf the solar system

e original spinning, flattened nebula'') surrounding thenebula ) surrounding the

ld b l tuld become our planetary planets. The Kuiper Belt is what

system itself were all swept up

14

GravitationaGravitationaA number of space probes, including Vused a planet's gravity to slingshot theused a p a e s g a y o s gs o e

Many planetesimals in the early Solar happenstance undergone a similar effhappenstance, undergone a similar eff

Some of these would have crashed into planets, some would haveinto planets, some would have received only minor orbital changes. Still others would have been ejected into deep space never to returninto deep space, never to return.

A few would have been flung far but no

al Slingshotal SlingshotVoyager 1 and 2, have deliberately emselves into different orbits.e se es o d e e o b s

System would have, by fectfect.

SEGWay (UC Berkeley)

ot quite out... 15

The edge of thComets ejected into the Oort cloud eof a (or 1/a ~ 0). Th l bit lThese large orbits are only very weaperturbations by passing stars, for eperhaps 50,000 AU are stable, definp pwhich is thought to contain ~1012 ob

he Oort cloudend up on orbits with large values

kl b d d b d bakly bound and can be removed by example. Only orbits up to a of ning the edge of the Oort cloud, g gbjects > 1 km.

Comets in the Oort cloud go around the Sun in tens of millions of years, and might be expected to have returned toexpected to have returned to the inner part of the Solar System many times over its 4.5 billion year history (recall P = a1.5) but they usually don’t. Why?Why?

16

Life in the Oort cloud

Passing stars and galactic "tides" (perturbations due to the overall mas(perturbations due to the overall masdistribution of the galaxy) modify theorbits of Oort cloud comets. The effeare varied, but often result in large, quasi-random changes in perihelion

• This raising of the perihelion removsolar system preventing their returnsolar system, preventing their return

• These perturbations also scramble making the originally largely planar dspherical.

• These effects are much stronger fotransition between different dynamic

ssss

ects

q.

ves their orbit from the inner to the vicinity of the Sunto the vicinity of the Sun.

the comets' inclinations, distribution of orbits essentially

or larger a, and so there is a al regions 17

Dynamical ry

•35-50 AU: Kuiper Belt•50-2000 AU: dynamically inert region•2000-15000 AU the inner Oortcloud, affected by galactic tidescloud, affected by galactic tides•15000-100,000 AU: the outer Oort cloud (tides and stellar pert rbations)perturbations)

regionsg

18

Stellar perStellar per• Stars in the disk of the Milky Wa

d th t f th laround the center of the galaxy,other.

• The typical velocity differences ayp yneighborhood are about 20 km/

• As a result, comets in the Oort Ctimes per million yrs by the gravtimes per million yrs by the grav

• When a star of mass M* passesspeed V*, the impulse approxim

l it f biti O t Clvelocity of an orbiting Oort Clou

GM2dV

GMV *2=Δ

dV*

rturbationsrturbationsay share a common motion

b t l l ti t h but also move relative to each

among stars in the solar gs. Cloud are perturbed a few vity of passing starsvity of passing stars. s the Sun at distance d and

mation to the change in the d t id comet is

19

Stellar perStellar per• For a solar mass star passinFor a solar mass star passin

with V* = 20 km/s, the veloci• This is to be compared with

f b t 100 / i th O tof about 100 m/s in the Oort• The stars approach from ran

velocity changes are sometivelocity changes are sometinegative.

• The combined effect is a ranthe velocity perturbation suchave passed by, the originaldrastically altereddrastically altered.

rturbationsrturbationsng at 0.5 parsec (330 000 AU)ng at 0.5 parsec (330 000 AU) ity change is about 1 m/s.the Keplerian orbital velocity

t Cl dt Cloud. ndom directions, so the mes positive sometimesmes positive, sometimes

ndom walk in the magnitude of ch that, after 10,000 stars orbit of the comet has been

20

Stellar perStellar perH l d thi t k ?How long does this take? • The answer depends on w

comet residescomet resides. • At the outer edge, the attra

and passing stars have aand passing stars have a • Most of the LPCs are thou

parts of the Oort Cloud. p• Closer to the Sun, the Oor

held and may never be disi tpassing stars.

rturbationsrturbations

where in the Oort Cloud the

action to the Sun is weak big effectbig effect.

ught to fall from the outer

rt Cloud comets are tightly slodged by the gravity of

21

Comet s• A particularly close encounter

between the Sun and a starbetween the Sun and a star could produce a strong perturbation that would send a comet shower into the innercomet shower into the inner Solar System (note DV ~ 1/d). The duration is ~ one orbital time (millions of years), the frequency ( y ), q y~ 1 per 108 yr

• Most Oort cloud cometsMost Oort cloud comets currently arrive from the outer Oort cloud where perturbations are usually stronger. y g

A stellar passage within the inner Oort clouA stellar passage within the inner Oort clouthe current outer cloud) could produce an inas well as transferring comets from the inne

showers

Stars in the solar neighbourhood

ud (with a population 5 10x larger than

22

ud (with a population 5-10x larger than ncreased flux in the inner solar system, er Oort cloud to the outer one.

Return from thThe perturbations that raised the cothem to low values allowing them tothem to low values, allowing them toWhen Oort cloud comets return to thrun the gauntlet of the planets.

Being on nearly unbound orbits, theBeing on nearly unbound orbits, thesmall energy gain due to the gravityonto unbound orbits, or much moreE GM/2 h i EE = -GM/2a, so a change in E meanchange in orbit size.

The distribution of energy kicks for planets has D(|1/a|) ~ 4x10-4 AU-1 . this means a transfer to an orbit witthis means a transfer to an orbit wit

he Oort cloudomets’ perihelia eventually return o re-enter the planetary systemo re-enter the planetary system. he inner Solar System, they must

ese comets have E~0. Even aese comets have E 0. Even a y of the planets can send them

e tightly bound ones. Recall h i hi hns a change in a, which means a

comets with q inside the giant For a comet starting with E~0

th a~2500 AUth a~2500 AU

23

Dynamically new Ootime

Roughly half of dynamically new Oort cloud comets (distinguishableby their very large a upon arrival)by their very large a upon arrival) have their orbits so disturbed they are subsequently ejected from the Solar System.

The other half end up on variousThe other half end up on various smaller, more tightly bound orbits.

F t t th O t l dFew return to the Oort cloud.

ort cloud comets: one only

e

Extreme example of a perturbed dynamically new Oort cloud comet24

Oort cloud: tOort cloud: t● Since Oort cloud comets cannot be

large a values for some comets is tlarge a values for some comets is tcloud’s existence.

● Note the absence of large negativel di i i l i hb h● vel. dispersion in solar neighbourho

interstellar comets to come in with limit (which is 72km/s at Earth (q=1easily seen)easily seen)

the evidencethe evidencee imaged yet in situ, the measured he primary evidence for the Oorthe primary evidence for the Oort

e 1/a implies no interstellar cometsd i 20 30k / ld tood is 20-30km/s, so we would expect

this much energy above the parabolic 1AU), so a 20-30 km/s excess would be

Histogram of 1/a f h l i dfor the long-period comets. “Error bars” are just sqrt(N) to indicatesqrt(N) to indicate statistical noise.

25

Kuiper belt covisib

Th 109 1010 t l• The 109-1010 comet nucleon orbits outside Neptune

30 AU 50 AU– 30 AU> a > 50 AU – low e (<0.2)

low i (< 30o)– low i (< 30o)

• These orbits do not bring• These orbits do not bring How do these objects evecomets?comets?

omets: path to bilityi i th K i B lti in the Kuiper Belt are

e, typically with

them near the Sunthem near the Sun. entually become visible

26

Kuiper belt covisib

Neptune is the dominant• Neptune is the dominant player out here. Secular and mean-motion resonances can modifresonances can modify KBO orbits to ones that cross Neptune.

• A close approach with that planet will change the orbit: if a is decreased the comet is “handed down” to the inner giant planets, where it “pinballs” pbetween them, possibly eventually reaching the inner solar system, and y ,visibility as an active comet (a SP comet).

omets: path to bility

Pre-encounter Post-encounter

27

Comet classifiComet classifi• Oort cloud comets (long-period c• Jupiter-family comets

– aphelion Q ~ 5.2 AU (near Jupite– low inclinations– orbit dominated by encounters w– most originated in the Kuiper Be

• Halley-type comets– spherical distribution of inclinatio– various a’s, but usually 20yr < P– originated in the Oort cloud, orbit

• Centaurs– orbits between the giant planets– low inclinations, moderate eccen– normally do not get close enough

• notable exception: first centaur 20– origin: KBOs being handed down

lt th bit t– as a result, these orbits are unsta

ication repriseication reprisecomets)

er) (short-period comets)

with Jupiterlt (only 0.1% of OCC reach this stage)

onsP < 200yrsts changed by planet encounters

ntricitiesh to Sun to display coma/tail060 Chiron shows intermittent coman

bl ith lif ti f 106 108able with lifetimes of 106-108 years

28

Non-gravitatNon gravitat• Th

nunutheno

• ThWild 2me

• Thmocobaco

Borrelly –

–

y

–

Halley

tional forcestional forceshe sublimation of ice from the ucleus is non-isotropic As a resultucleus is non isotropic. As a result, ere is a net reaction force (called on-gravitational force)he effect is normally small, but y ,easurable for some comets.he standard Type II (or symmetricodel) empirically best-fits 3

ffi i t A A A t th NG foefficients A1, A2, A3 to the NG force ased the observed motion of the omet

A is the radial (Sun-comet)A1 is the radial (Sun-comet) component

• largest, but averages to ~zeroA3 is normal to the comet orbit plane3

• smallest, usually neglectedA2 is in comet orbit plane, but at right angles to the radius vector

• Caused by rotation of the• Caused by rotation of the nucleus/thermal lag

• Usually the one with the largest net effect29

The A parameters are typically( 1 / d )(approx. 1 cm/s per day)

The empirical determination ofshows that some comets feel ashows that some comets feel a

y of order 10-8 AU day-2

f the tangential (A2) force a fairly constant onea fairly constant one….

Yeomans 1993 30

…while others feel a force whorapidly changing. All comets ap

se magnitude and sign is ppear as individual cases

Yeomans 199331

Cometary gaCometary ga• Cometary activity (gas production)Cometary activity (gas production)

triggered by proximity to the Sun (heating)– Most comets at r > 3 AU are inert

t d i id thi di tto produce gas inside this distanc• The onset of activity near 3 AU is

of water ice on the nucleus, as thislocation at which solar heating sholocation at which solar heating shoto sublimate it in significant quanti

• Some comets produce little gas evsmaller distances (eg P/Tempel 2)smaller distances (eg P/Tempel 2)

• Some produce gas at larger distan– 2060 Chiron (between Sat. & Ura

intermittent coma (outbursts)( )– Hale-Bopp displayed a coma at r – Comae at larger r are indicators o

volatile species eg CO, CO2

as productionas production) is) is (solar

, and begin ceindicative s is the ould beginould begin tiesven at )

Hyakutake

)ncesa):

> 6 AUof more

C/2001 Q4 (NEAT) 32

BrightBright• The light received by a come

brightness as 1/r2 (r = Sun cbrightness as 1/r2 (r = Sun-cwe receive from the comet dcomet distance, often calledcomet’s apparent brightnesscomet s apparent brightnessν to vary like

• This equation is correct for inqbodies like asteroids, but cobrighter as they approach thas gas production increasesg peffective optical cross-sectio

• As a result comets typically ssharper increase in brightnesharper increase in brightnerSun decreases, typically as alarger than 2

tnesstnesset from the Sun decreases in omet distance) and the lightomet distance), and the light

decreases as 1/r∆2 (r ∆ = Earth- ∆) so we might expect a

s B at a particular wavelengths Bν at a particular wavelength

1B ∝ 2 2vBr rΔ

∝

nert

1

mets get he Sun, s their

2

1vB

r rζΔ

∝on.show a ss as r rΔss as a power

33

An example: Cp• Water production is usually trace

by OH, photo-dissociated by solaUV ( ater lines blocked b atmosUV (water lines blocked by atmos

• Note sharp drop in water production beyond 3 AU inbound

• However, Hale-Bopp showed coma at r up to 6 AU: what was tsource?

• CO (either primary or as photoproduct of CO2) was most abundant at r >3 AU

• CO production rate decreased from 3 to 1.6 AU: depletion of surface layer?

• Also note presence of CH3OH (methanol), H2S, H2CO, HCN, CSand other species. These may be

i h t d tprimary or photoproducts.• Note slope z generally > 2

C/Hale-Bopppped ar s)

Hale-Bopp is an LPC, with a period of a few x 103 yr (so not freshly arrived from OC)

s).

d

he

S e ζ=2

Biver et al 1999 (radio)34

Visual mVisual m=−= MBm vvv log5.2 vvv g

• mv is the comet’s apparent M i th t’ b l t• Mv is the comet’s absolute

basically the apparent visuafor an observer 1 AU from bofor an observer 1 AU from bo•Comets tend to be brightestperihelion (presumably due tperihelion (presumably due t•Clearly from observations oa constant, so neither is Mvv

agnitudeagnitudeΔ++ rrv log5log5.2 ζ Δv ggζ

t visual magnitudei l it dvisual magnitude

l magnitude as determined oth the Sun and the cometoth the Sun and the comett a few days after to thermal lag)to thermal lag)

of Hale-Bopp, ζ is not really

35

Visual mVisual m• New comets tend to be bright

(presumably due to relatively felements like CO and CO2) buelements like CO and CO2) buperihelion (ζ~ 2.5)

• Older comets (eg. short-pd comdistances but brighten more sh

• ζ ~4 is the “standard” value, acomet’s absolute magnitude wcomet s absolute magnitude w

agnitudeagnitudeat larger distances r ~ 5AU fresh supplies of more volatile ut do not brighten as sharply nearut do not brighten as sharply near

mets) typically are faint at large harply at perihelion (ζ~5)and the derived estimate of the with this z is called Hwith this z is called H10

36

Thermal balance( ) =−

−

RRr

eFA iSun

b24

2 41 εππτ

Assuming only solar heating, the heh t l t ( di ti l ll th

r

heat lost (radiatively as well as throtransmitted deeper into the nucleus

Ab = Bond albedo: the total radiation reflected from an object compared to the total incident

εicσcompared to the total incident

radiation from the Sun, may be complicated to computeF = solar constant at Earth (1 37

σQLoFSun = solar constant at Earth (1.37

kW/m2)r = heliocentric distance (AU)

i l d h f h

oNK

τ = optical depth of the comaR = comet radius

nδ

e of the nucleus⎟⎠⎞

⎜⎝⎛

∂∂

++zTKR

NQLT T

sir

24 4πσ

eat received must be balanced by h th l f ) ll h t

⎠⎝ ∂zN A

ugh the loss of gas) as well as heat s.

εir = infrared emissivity (~1 for most ces)σ = Stefan-Boltzmann constantσ Stefan Boltzmann constantQ = gas production rate (molecules s-1)Ls = latent heat of sublimation per mole of nuclear iceof nuclear iceNA = Avogradro’s numberKT = thermal conductivity of the

l ( ll ll)nucleus (usually small)δΤ/δΖ = thermal gradient in the nucleus

37

38

Conditions iConditions i• The terms in the thermal balance

are complicated by compositionalare complicated by compositionalquestions, asymmetries in the nuconstants that are difficulty to detetc.

• However, if one molecule dominacan get some handle on things– If sublimation is primarily CO, thep y

temperature of the nucleus T is b45 K for 0.2 < r < 10 AU

– for CO2, 85 < T < 115 K, for H2ONote: sublimation carries away a• Note: sublimation carries away a and so the nuclear temperature isfar below the equilibrium blackbodtemperature of an asteroid, for exp ,the same r.

• Sublimation is also generally not but concentrated on the sunward

it ti l f )gravitational forces)

in the comain the comaequation

ll ucleus, ermine,

To Sunates, we

e surface

To Sun

between 30-

O, 90-210Klot of heat

Halley from Giotto

To Sunlot of heat s generally dy xample, at

jet

To Sun

p ,

symmetric side (non-

nucleus2200 km

HST image of Tempel 1pre-Deep Impact

39

Gas oGas o• The gas leaves the nucleus

velocity v0velocity v0– where m is the molecular mas

t 1AU i 0 5k /• at r~1AU, v0 is ~ 0.5km/s, mvelocity of the comet

• The gas accelerates away frg yterminal velocity, its final vel

• The gas density drops as roeventually changes from hydeventually changes from hydfree molecular (collisionless

• The transition distance Rc ischance of an outward particchance of an outward-particdrops to 50%, usually 1000-

50∫∞

dQ xσ whe5.04 0

2 =∫ drvr

Q

cR

x

π

utflowutflowat the thermal expansion

31ss

h l th th

kTv23

21 2

0 =μ

much larger than the escape

rom the nucleus, reaching gocity, within ~1000km

oughly 1/r2 so the flow drodynamic (collisional) todrodynamic (collisional) to ) flow.

s defined to be where the cle having another collisioncle having another collision -5000km from nucleusere r = cometocentric distance

σx = collisional cross-section

40

Gas flow is cGas flow is cThe expanding gases at leas• The expanding gases, at leascollisionless, may interact chemomentum through collisions

• The photolysis of molecules bvelocity profile of the gas.– Photolysis products (particulary p (p

molecules can accelerate them• Complicating matters is dust

organics)g )– dust slows the gas over the firs

flow– dust may be both a source anddust may be both a source and

• source as “dust” grains may rsublimate

• sink as molecules may recondf th lfrom the nucleus

complicatedcomplicatedst until the flow becomesst until the flow becomes emically or exchange s.by solar UV may also affect the

rly H and OH) colliding with other y ) gm(non-volatile silicates and/or

st few tens of meters by impeding its

d a sink of gasd a sink of gaseally be ice grains that continue to

dense on/react with dust grains further

41

ChemicalChemical • The optical depth of the

t f th i 100except for the inner 100– result: the gas is largely

receives significant exporeceives significant expo– the mean lifetime tl of m

dissociation by sunlight

λσλ

Ft

x )(112 ∫=

rt xl

)(0

2 ∫r = heliocentric distance in AUr heliocentric distance in AUFsun(λ) is the solar flux at waveσx(λ) = photo-destruction crossλ threshold a elength for pλt = threshold wavelength for pwavelength that dissociates th

evolutionevolutione coma is generally < 1 0k0km

transparent and all the coma osure to solar radiationosure to solar radiation

molecules against photo-is

λλ dFsun )(sun )(

elength λ at 1 AUs-sectionphoto destr ction (longestphoto-destruction (longest he molecule, usually in UV)

42

Photo destructioPhoto-destructioAt 1 AU f t l• At r=1 AU, a free water mole104 s (25000-40000 km at 0

• Typically H2O photo-dissociaTypically H2O photo dissociaan average of 18 and 1 km/sexcited O, H2O+, OH+, O+ an

• OH subsequently dissociategets a 7 km/s kick

• The large kicks H receives a• The large kicks H receives athe large hydrogen coma dis

• Neutral H is then ionized eitexchange with the solar win

on and the comaon and the comal h lif ti f 5 8ecule has a lifetime of 5-8 x

0.5 km/s)ates to H and OH which gainates to H and OH, which gain s excess speed resp., though nd H+ are other optionses to O and H, where H now

are fundamental in creatingare fundamental in creating scussed earlier her by UV or charge y gd.

43

Coma proocesses

Crovisier & Encrenaz 1995 44

ModellingModelling• A knowledge of the collisional and

of various species (often not wellof various species (often not wellmolecules in the coma to be mod

• The simplest approach is the Hasisotropic outflow and a finite lifetimp

• The distribution of parent molecu

Q N = numbpRr

p

pp e

vrQ

rN /24

)( −=π

N numbr = cometRp = vp tlpvp = veloc

• If the daughter products (subscrivp, we get their distribution from

p

dpd RR

RQrN 24)( =

dd RRvr 24 −π

the comathe comad photo-destruction cross-sections known) allows the distribution of known) allows the distribution of

deledser model, which assumes smooth me for molecules.les (subscript p) is given by

ber densityber density ocentric distanceis the scale length for a given molecule pcity of molecule p

pt d) continue to move out with vd =

y p

( )pd RrRr eeR

// −− −( )pR

45

Excitation

Radiation by: rotational, vibratioffbetween different energy levels

E ample triatomic molec lesExample: triatomic molecules

Vibrational it tiexcitation

Rotational it tiexcitation

of radiation

nal and electronic transition fof gaseous molecules and atoms.

Electronic transitions

46

Allowed transitions betweenAllowed transitions between wavelength λ:

1 ()( 1 ''' 'vibelel EEE −+−∝

λλ 1 100 10λ~1 μm -100 nm ~10

UV, optical, near IR I, p ,

Hale-Bopp (7.Hale-Bopp (optical)

energy levels withenergy levels with

)() ''''rot

'rotvib EEE −+−

1μm ~1 cm

IR radio

Hale-Bopp (3mm).75 microns) 47

Mean lifetime of an excitedMean lifetime of an excited state u(pper) to drop to stat

electronic transitions:

ib ti l t itivibrational transitions:

rotational transitions:

If an electronic state is excitedfaster than others this is thin optical range

I l l llIn parent molecules usually otransitions are excited. Highedissociation of the moleculesdissociation of the molecules

energy 1energy te l(ower):

ulu A

=τ

τel ~ 10-8 s

10 3τvib ~ 10-3 s

τrot ~ 1 s

d, the transitions are much he case for radicals emitting

l i l d ib i lnly rotational and vibrational r excitation energies lead to ..

48

FluoresThe primary optical emission mecelectrons are excited by solar radtheir return to the ground statetheir return to the ground stateThe strongest lines are usually rethe first excited state and the groThe brightness of a spectral line dmolecules multiplied by the g-facmolecule which could be complicmolecule, which could be complicon the populations of the various question.F i l fl if tFor simple fluorescence, if most s(ie. the time to emit a photon << twe first compute the absorption r

)( lusunlu FB λ Blu = Einstein

p pmolecule ga

2)(

sun

lusunlua r

g = lu

scencechanism is fluorescence, where diation and they re-emit upon

esonance transitions (between und state)depends on the number of

ctor or emission rate per cated to compute as it dependscated to compute as it depends levels above the one in

i i th d t tspecies are in the ground state time between absorbed photons), rate of photons that excite the

n coefficient from l(ower) to u(pper)

p

( ) (pp )

49

FluoresFluoresOnce we have ga, we just need

= uAgg

of the downward transition to ge

i l

∑≤uj

a Agg

simple resonance:

g=gag ga

general resonance fluoresc

g < ga

Important: g and g are propoImportant: g and ga are propoflu

scencescence the branching ratio

ul

et the g-factor

jlA

cence:

ortional to the incoming solarortional to the incoming solar ux! 50

Converting to c

Once g is known, we can dete(molecules per unit area) of m(molecules per unit area) of mthrough the coma if we know tBλ in photons s-1 cm-2 and Ωs, t

c gBN = λ

g

For simple resonance, we can s

BrQ λπ 24 Δ=Note: thout of g( ll t

lgtQ = (recall t

If more dissociadissociaidea is more co

column density

ermine the column density Ncmolecules along our line of sightmolecules along our line of sight the brightness of a particular line the solid angle observed

sΩπ4

s

show gas production Q is

he heliocentric distance cancels gtl, which does not change with r t l l th f l l )tl = scale length of molecule)

excitation/de-excitation levels, ation etc have to be included theation, etc have to be included the the same, but the equations are omplex

51

Example of optic

∆v=0∆v=1 ∆v=-1

Some molecular transitions are vresolved only by very high-resolusequences

cal observationsImportant optical species:species:

CN, C3, C2, CH 2,NH3, NH2, H2O+

Solar spectrum

very close together and can be y gution spectroscopy band

52

Changing speectral featuresComet C/Hale-Bopp:

discovered: 23 July 1995 at r=7.1 AU

perihel: 1. April 1997, r=0.914 AU

period: 2380 years

inclination: 89.4°

diameter: 27-42 km

Hale-Bopp long-term observations:Hale Bopp long term observations:

• April 1996 – January 2001

• r = 4 6 – 2 9 AU 2 8 – 12 8 AUr = 4.6 – 2.9 AU, 2.8 – 12.8 AU

• Optical Spectroscopy + imaging

• European Southern Observatory• European Southern Observatory

53

Doppler effect and rad

In the optical and UV the solar flux has manysolar flux has many absorption lines shifts in wavelengths by the Doppler ff l d i ieffect can lead to variations

of the solar flux at the wavelengths that excitewavelengths that excite cometary lines by up to a factor 2 and more

Swings effect (Swings 1941)

Doppler shift of the solar spectrumopp e s o e so a spec uheliocentric velocity component othe Sun.

typical heliocentric velocity compokm/s, this corresponds to ∆λ ~ 0.7

diation excitation

m at the comet due to the a e co e due o eof the comet on its orbit around

onents: -50 km/s < vhel < +50 7 A at 400 nm 54

SwingDoppler shift of a cometary Na eDoppler-shift of a cometary Na estrong solar Na solar absorptionperihelion of comet Hale-Bopp iDoppler shift, the more solar ex

Greenstein effect (Greenstein 1958)

Doppler shift of the solar spectrum drelative to the comet nucleus (import

gs effectemission line relative to aemission line relative to a n line before and after the n 1997. The higher the citation = stronger line

Arpigny et al. 1997, A&A

ue to the motion of the ions/atoms tant e.g. for ions, H, Na) 55

Coma com• Water and its derived species

(H,OH, H20+, H3O+,O) are dominantdominant

• Carbon compounds are import(C, C2, C3, CH, CH2, CN, CO) w

b bl i i f CO HC3

a probable origin from CO2, HCCH4, H2CO (formaldehyde), CH3OH (methanol)3– CO production ~15-20% of water

CO2 ~ 3% and others lower still• N and S compounds are presep p

in small amounts• Na is regularly seen in comets,

though only Sun-grazing comethough only Sun grazing come(r <0.2AU) show other metal linsuch as Ca, K, Fe, Ni, Co, etc, presumably from vaporizing dupresumably from vaporizing duparticles

mpositionp

ant with CNCN,

r,

nt

, tsts

nes

ustust

56

Du• Dust is entrained away from

sublimate• Dust-to-gas ratio varies: 0.1• Small (submm) particles can

( 1k / ) b t l b(~1km/s) but larger ones ba(~1m/s)

• At a few nuclear radii the duAt a few nuclear radii, the du• After decoupling, the dust is

which owing to the slightly dand dust, is usually separate

• The dust tail is usually yellowthe gas tail is usually bluishthe gas tail is usually bluish

• The colour of the dust tail imcalculations of the maximumgas implies the largest dust thermal emission puts most

ustm the nucleus as the ices

to 10n reach the gas velocity

l h l itrely reach escape velocity

ust and gas decoupleust and gas decouples “blown” back into the dust taildifferent dynamics of the gas e from the gas tail (or ion tail)w-ish (reflected sunlight) with (CN C C lines)(CN, C3, C2 lines)

mplies few particles < 0.1mm; m size that could be entrained by y

particles are < 10 cm or so; dust grains at 0.1 – a few mm.57

Active cActive c

Hyakutake (1998

West (1976)

cometscomets

8)

Hale-Bopp (1997)

58

SyndSynddynesdynes• Because dust particles

released have different sizes and hence b (recall b = ratio of radiation force to solar gravity in discussion of g yP-R drag) they will follow different paths.

• Consider a comet that has• Consider a comet that has been releasing particles over a number of days. A snapshot of the positions ofsnapshot of the positions of all particles with the same b at a particular instant is called a syndynecalled a syndyne.

• The syndynes of all b combined trace out the dust tail of the comettail of the comet

59

SynchSynch• Alternatively we can ask: where a

size, that were released at a part, p• A line traced through these partic

hroneshronesare all the particles, regardless of icular time t?

cles is called a synchrone.

Dashed lines are syndynes

60

AntiAnti-

• If the Earth is near the planecurvature of the dust tail macurvature of the dust tail macomet to appear to stick forwcalled an anti-tail

tails-tails Comet Bradfield

e of the comet’s orbit, the ay allow material behind theay allow material behind the ward of it in a phenomenon

61

Dust fe• Dust emission from comets

inhomogeneities in the dust t i )striae)

• The rotation of the nucleus mof dust being ejected from ag jdetectable using polarimetry

• Rotation is very difficult to monly a few (~7) have had theonly a few ( 7) have had theby radar or from dust jets): a

unpolarized

Hale-Bopp

eaturesis often uneven, resulting in tail (dust jets, streamers,

may result in a spiral pattern a strong jet, a feature often g j ,y.

measure due to the coma, and eir spin state estimated (ofteneir spin state estimated (often a few hours to several days

polarized

62

Splitting andSplitting and• Comets are

ti tsometimes seen to break apart (about 2 dozen cases reported

f ) h ddiso far), shedding a few small pieces, other times

d iundergoing more dramatic breakups

• Splits are often first pseen as outbursts of gas and dust from the nucleus, as it usually Drnucleus, as it usually takes some time for the fragments to drift apart enough to

Dr

apart enough to become visible individually

d disruptiond disruption

rawing of comet 3P/Biela in 1846rawing of comet 3P/Biela in 1846

Comet 73P/SW3 in 1995

63

Comet C/199Comet C/199b k i t t l t• broke into at least 16 “cometesimals” as it passed theas it passed the Sun in 2000

9 S4 LINEAR9 S4 LINEAR

64

Formation: the outer rea

The volatile components of cofrom the Sun The most volatifrom the Sun. The most volati

indicates condensation t

silicate-rich planetesimals

EVMe Ma J1 AU

EVMe Ma J

H2O

156 KCondensation temperature:

aches of the Solar System

omets indicate they formed far le components N S and COle components N2, S2 and CO temperatures of 20-25 K

ice-rich planetesimals (comets)

S U N10 AU

100 AUS U N

CO

24 K

CO2

70 K

CH4

30 K

N2

17 K

Kuiper belt

slingshot to Oort cloud65

66

The End

67