The Origin of Comets and the Oort Cloud

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Why Astronomy?! Three main strands of interest: The Origin of Comets and the 1. The broadly cosmological, ‘quasi-religious’ strand, going back thousands of years — the quest to understand our ‘Origins’, Man’s Oort Cloud place in the Universe etc.; 2. The ‘practical’ strand, i.e. the commercial, military, and economic ‘spin-oﬀ’ from astronomy, nowadays including education and the arts Comets from Ancient Times — e.g. the calendar; navigation; celestial mechanics; Earth to the Modern Era observation; image processing; the ‘inspiration of astronomy’ and its technical ‘spin-oﬀ’; 3. The strand of pure science or ‘Astrophysics’ — the project to Mark E. Bailey understand the nature, contents and interactions of all the objects in Armagh Observatory the entire Universe . . . We live in a Golden Age, where the three strands have come together http://star.arm.ac.uk/ [email protected] in a rare conjunction of activity: hence unprecendented advances in both http://climate.arm.ac.uk observations and theory, the former almost always leading the latter! STFC Summer School STFC Summer School 2010 September 10 – #1 2010 September 10 – #2

Cradle of Civilization: Eastern View Cradle of Civilization: Western View

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Ancient Greek Views: Anaximander’s Jets of Fire Table of Babylonian/Greek/Roman Theories of Comets 1. Earth as a short, squat cylinder three times as wide as long, Date Broad Type Originator Brief Description surrounded by air and floating freely at the centre of the observable c.2000 BC Celestial Babylonians Earthy bodies akin to planets Universe in an infinite space. c.2000 BC Celestial Babylonians Fiery celestial phenomena c.575BC Celestial Anaximander Jets from fiery celestial hoops 2. Sun, planets, stars are enclosed circular hoops of fire; they only c.550 BC Atmospheric Xenophanes Burning clouds become visible due to holes in their enclosing hoops, which allow the c.450 BC Celestial Anaxagoras Planetary ‘conjunctions’ on sky fiery substance to leak out and become visible. No direct evidence of c.450 BC Celestial Pythagoreans Rare sighting of a planet c.430 BC Celestial Hippocrates A kind of planet his thoughts about comets; but note the hoops of fire lie below the c.430 BC Atmospheric Pythagoreans Reflected sunlight Sun and Moon. c.430BC Celestial Diogenes Chainsofrockybodies(stars) c.400 BC Celestial Artemidorus Chains of unseen planets c.350 BC Atmospheric Aristotle Fiery atmospheric phenomena c.350 BC Atmospheric Heracleides Reflections from high clouds c.330 BC Atmospheric Metrodorus Influx of Sun into clouds c.330 BC Celestial Apollonius Celestial bodies c.300 BC Celestial Zeno Conjunctions of stars c.290 BC Celestial Strato Stars enveloped by cloud c.130 BC Atmospheric Panaetius False images of stars c.100 BC Atmospheric Böethus Violent, fiery winds c.50 AD Celestial Seneca Celestial bodies Image credit: Tony Mendes STFC Summer School STFC Summer School 2010 September 10 – #5 2010 September 10 – #6

Early Developments of Astronomy Later Developments of Astronomy 3. Horoscopic Astrology ( 400 BC to 1600 AD) Four broad phases can be identified: ≈ ≈ Based on the entirely false premise that wandering stars (‘planets’) 1. Judicial Astrology ( 3000–1000 BC) ≈ exert a distant controlling influence on human affairs. Events in sky self-evidently influence events on Earth. Provides an early example of a powerful, but ‘magical’ scientific Celestial ‘order’ transmitted to Earth by sky-gods or deities. concept, i.e. ‘action at a distance’. = a powerful ‘motive’ to observe the sky and interpret the celestial ⇒ ‘omens’. Motivates careful observations of the planets; their paths against the fixed stars; their periods of revolution etc; all linked to predictions. The sky gods are ‘announcing’ events on Earth, for example through the appearance of a bright comet or meteor, or by the fall Demonstrates growing understanding and an increasingly of a meteorite or thunderbolt hurled by the sky-god Jupiter etc. ‘scientific’ approach to observatons of the natural world; 2. Zodiacal Astrology ( 1000–400 BC) Nevertheless, the focus on unimportant chance alignments of planets ≈ and stars, planetary conjunctions etc. (e.g. ‘Star of Bethlehem’), and The slow transformation from Judicial Astrology to a growing focus on on the ‘random’ appearance of an occasional bright comet etc. an important region of the sky associated with the principal sky-gods, ultimately proves to be a cul-de-sac for science. i.e. the Zodiac. Despite this, the idea of horoscopic astrology has an enduring legacy The sky divided into sections, each with a different perceived — still believed by upwards of 25% of the population! ‘influence’ on people or events on Earth. 4. Scientific Astronomy ( 1600 AD to present) ≈ STFC Summer School STFC Summer School 2010 September 10 – #7 2010 September 10 – #8

1 Comets and Meteors as Omens or Prophecies Cradle of Civilization: Atlantic View 1. Precise astronomical observations were the key to prophecies; and the omen literature always took the form “If [astronomical observation] then [terrestrial effect].” E.g., quoted by Bjorkman (Meteoritics, 8, 91, 1973): “If ashootingstar flashes as bright as a light or as a torch from east to west and disappears on the horizon, then the army of the enemy will be slain in its onslaught” 2. Some early cometary observations are quoted by Olivier (in “Comets”, 1930). Thus, on a Bablyonian tablet dated around 1140BC and referring to a military campaign, we read: “a comet arose whose body was bright like the day, while from its luminous body a tail extended, like the sting of a scorpion.” And in Diodorus Siculus’s account of the expedition of Timoleon (344 BC): “On the departure of the expedition of Timoleon from Corinth to Sicily the gods announced his success and future greatness by an extraordinary prodigy. A burning torch appeared in the heavens for an entire night, and went before the fleet to Sicily.”

What could have led to these ideas? Seneca (c.4BC – 65AD) gives some insight. Refer- ring to the ‘diﬀerence’ between us Romans and Etruscans, he remarks, “. . . We believe that lightning is caused by clouds colliding, whereas they believe that clouds collide in order to create lightning. Since they attribute everything to the gods, they are led to believe not that events have a meaning because they have happened, but that they happen in order to express a meaning.” STFC Summer School STFC Summer School 2010 September 10 – #9 2010 September 10 – #10

Rock Art at Knockmany Chambered Tomb, Co. Tyrone View of Knockmany in Nineteenth Century

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Rock Art and Megalith in Scotland Further Examples of Rock Art in UK and Ireland

Megalithic markings on a rock from Traprain Law, Midlothian, Scotland; and the huge megalith at Beacharr, Argyle Peninsula, Scotland

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Commonly Occurring Motifs in British Rock Art Chinese/Greek/Roman Classiﬁcation of Comets

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2 Comet Images from Fifteenth to Nineteenth Century Great Comet of 1910: Drawing versus Photograph

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Comets of 1577 and 1995 Hale-Bopp (Two Prints) 17th and 19th-Century Views of Halley’s Comet

Artistic renditions of two comets drawn 400 years apart: the Great Comet of 1577, and Comet Hale-Bopp produced by S. Farrington in 1997. STFC Summer School STFC Summer School 2010 September 10 – #19 2010 September 10 – #20

Impacts Occur: 20th Century Examples Eﬀects of Impacts: Great and Small

Impacts can produce eﬀects ranging from mass-extinctions of life (e.g. K/T boundary c.65 Myr ago) to merely local damage (e.g. Sikhote-Alin meteorite, 1947). They can also lead to new mythology and superstition Left: The c.10Mt Tunguska event in Siberia on 1908 June 30 (Kulik), compared with (e.g. the erection of a totem pole at the Tunguska ground-zero to Agby, the tree-fall pattern superimposed over London (J. Tate). Right: Sikhote-Alin meteorite the Siberian god who brings ﬁre to the forest). STFC Summer School (Courtesy Russian Academy of Sciences). STFC Summer School 2010 September 10 – #21 2010 September 10 – #22

Short-Term Implications — I Short-Term Implications — II Ancient societies appear to be Ancient Greek “mysteries”: Problem of Milky Way . . . Zodiacal Light? obsessed by the sky: Anaximander:describesstarsaslikelightedjetsofgasspurtingoutofapunctured e.g. early astronomical interest in hoop of ﬁre. ‘the sky’; evidence of megalithic Aristotle:believestheMilkyWaytolieinthesublunaryzone,ahotaccumulation monuments/prehistoric ‘rock art’. of the disintegration products of many comets. Neugebauer: “. . . ancient ‘astrology’ Anaximander, Parmenides, Leucipus:the‘stars’liebelowtheSunandtheMoon. can be much better compared with weather prediction from phenomena Metrodorus and Oenopides of Chios: the Milky Way is the former path of the Sun. observed in the sky than with Anaximander and Democritus:theMilkyWayliesintheshadowoftheEarth. astrology in the modern sense of the word.” Suggests knowledge of direct link between sky and Earth. Consistent with more “activity” in the sky in the distant past. Suggests that some solar-system phenomena may change on much shorter time-scales than we normally consider possible. Image of Milky Way (A. White); Leonid meteor storm; and zodiacal light. STFC Summer School STFC Summer School 2010 September 10 – #23 2010 September 10 – #24

3 Debating Origin of Comets in Mid-17th Century Scientific Advances: Sixteenth Century and Beyond 1. Aristotelian dogma: Comets are atmospheric phenomena; the Earth is the centre of the Universe; the Moon, Sun and planets revolve around the Earth, as too do the fixed stars. The dogma persisted nearly 2000 years. 2. Renaissance: Rediscovery that comet tails always point away from the Sun (Apian et al.). Showed that comets not totally unpredictable! 3. Distance: Comet of 1577 shown to be at least 6 times farther than Moon (Tycho) — helps to undermine the Aristotelian theory. 4. Orbits: Gradual acceptance of heliocentric theory (Copernicus, Galileo) together with Kepler’s and Newton’s insights into planetary motion leads to new ideas about comets. Are they ‘solar system’ or ‘interstellar’ objects; are they ‘gravitating’; and what ‘risk’ do they pose to Earth in its orbit? 5. Halley’s Comet: Halley shows that the orbits of the comets seen in 1456, 1531, 1607 and 1682 are closely similar. Predicts the comet’s return in 1759, a prediction confirmed. Demonstrates that comets are indeed ‘gravitating’ matter, and at least one has a periodic orbit.

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New Theories for Old: Decline of Catastrophism Parallel Worlds: Comets in Literature and Poetry 18th century sees contrast between an older ‘astrological’ view, with comets as 1. Virgil “At no other time did more thunderbolts fall in portents of doom potentially disastrous for life on Earth; and a new ‘teleological’ A clear sky, nor so often did dread comets blaze.” view developed by Newton and his disciples, with emphasis on the providential characteristic of comets. Thus: Georgica, Book I. 2. Homer “Like the red star, that from his flaming hair 1. Comets supply the “most subtle and active parts of our air, upon which the life of things chiefly depends” (Pemberton 1728); and comprise a “pure, elementary fire, Shakes down diseases, pestilence, and war.” of absolute necessity for the life and being of all things” (Hill 1754). The Iliad. 2. Stars and planets are inhabited by living things, and comets — in moving from 3. Shakespeare “Comets importing change of times and states one stellar system to another — provide the means by which stars and planets can Brandish your crystal tresses in the sky,” replenish their day-to-day losses (Herschel 1790). Henry VI. In contrast, an older, ‘astrological’ view persists amongst the general public: 4. Milton “Satan stood Unterrified, and like a comet burn’d That fires the length of Ophiuchus huge in th’Artick sky, and from its horrid hair Shakes pestilence and war.” Paradise Lost.

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Comets as Portents: Presaging the Death of Kings Comets as Horror-Movies: “Monstriferus” (Pliny) 1. Shakespeare: “When beggars die, there are no comets seen; The Heavens Ambrose Paré(1510–1590), the father of French surgery: “The comet was so horrible, so themselves blaze forth the death of Princes.” Julius Caesar. frightful, and it produced such terror in the vulgar, that some died of fear and others fell sick. It appeared to be of excessive length and was the colour of blood. At the summit 2. Seneca: [after death of Demetrius, king of Syria] “. . . there appeared a comet as of it was seen the figure of a bent arm, holding in its hand a great sword, as if about to large as the Sun. Its disc was at first red, and like fire, spreading sufficient light to strike. At the end of the point there were three stars. On both sides of this comet were dissipate the darkness of night; after a little while its size diminished, its brilliancy seen a great number of axes, knives, blood-coloured swords, among which were a great weakened, and at last it entirely disappeared.” 146 BC. number of hideous human faces, with beards and bristling hair.” 3. Suetonius: [after death of Julius Caesar] “A hairy star was then seen for seven days under the Great Bear. ...It rose at about five in the evening, and was very brilliant, and was seen in all parts of the Earth. The common people supposed that the star indicated the admission of the soul of Julius Caesar into the ranks of the immortal gods.” 44 BC.

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Table of Cometary Theories from c.1600–1800 Initial Conclusions — Drawn from History Originator and Date Theory and Broad Type 1. Comets can be the most prominent objects in sky, as bright as the Tycho(c.1600) Cometsare exhalations from planets: a ‘halfway house’ be- brightest stars. Appear unpredictably,butmove like planets . . . tween the ‘celestial’ and ‘atmospheric’ theories Kepler (c.1600) Comets are interstellar objects; move on rectilinear paths and 2. Observations go back thousands of years, when comets and associated populate the ‘heavenly air’ in great numbers. Form from the meteoric phenomena were scrutinized as ‘omens’ for events on Earth. celestial fires by process akin to cloud formation Provide insights into early cosmologies and ideas about the sky. Galileo (c.1600) Last genuinely ‘atmospheric’ theory: comets are a form of reflected sunlight, akin to rainbows, parhelia etc. 3. Mankind’s puzzling ‘fear’ of comets never adequately explained. Sir William Lower and Comets are celestial objects; orbits elongated ellipses Evidence suggests ‘the sky’ may have been significantly different in Henry Percy (c.1610) proto-historic times. Anon. (c.1620) Comets are exhalations from Sun: the cindery refuse from great solar conflagrations = ancient experience of what is a quite recent discovery, namely Hevelius (c.1680) Comets are vapours that condensed in planetary atmospheres; that⇒ Earth is an ‘open’ system — in touch with its near-space celestial ejected by violent whirlwinds into parabolic orbits environment. But is such a change in our celestial environment, on Cassini (c.1680) Comets are interstellar objects: vapours ejected from stars nearly historical timescales, possible? Halley/Newton (c.1680) Comets are gravitating solar-system objects; akin to planets Buffon (c.1745) Comets akin to planets; formed as part of solar system 4. Two thousand years of ‘atmospheric’ ideas about comets finally through collision of a comet with the Sun superseded during the 1600s by the ‘celestial’ hypothesis. Subsequent Kant (c.1755) Nebular Hypothesis: comets, like planets, form by condensa- debates focus on ‘interstellar’ versus ‘solar system’ ideas. tion in protosolar nebula; comets akin to planets STFC Summer School STFC Summer School 2010 September 10 – #31 2010 September 10 – #32

4 Early ‘Planetary’ versus ‘Interstellar’ Arguments Lexell’s Comet: Complex Dynamical Evolution Increasing data set plus translations of historic (mostly Chinese) records 1. Discovered by Messier on 14/15 June 1770; soon recognized as having an meant that comets became definitely established as celestial objects; but unusually large daily motion; are they solar system or interstellar in origin? 2. Exceptionally close approach to Earth (∆E = 00146 AU) on 1st July 1770, 1. Most comets have parabolic orbits — quite different in shape and the closest approach of any comet to Earth in recent times; inclination from the planets 3. First comet to have mass estimated (<1/5000 M ); ⊕ 2. The few known ‘periodic’ orbits (e.g. Halley’s Comet) could be — 4. First comet to have elliptical orbit determined from observations of just one and were — questioned, e.g. revolution, i.e. a 3.15 AU, q 0.67 AU, P =5.6yr 0.5PJ — but comet never seen again! how far did Newton’s new law of gravity (‘action at a distance’) extend how sure can we be that two comets with similar orbital elements are 5. Later calculations show comet had an original orbit with q 2.9AUand the same comet, or — coincidentally — two separate comets? P 9.2yr. Exceptional close approach to Jupiter (∆ =0.02 AU, on 27 J 3. Return of Halley’s comet in 1759, as predicted, a significant advance March 1767) led to observed Earth-crossing orbit destined to pass just 2 Jovian radii above Jupiter (∆J =0.002 AU, on 2 July 1779), which 4. But appearance of Lexell’s comet (1770) proved the matter was not drastically changed orbit again; clear-cut 6. New orbit has perihelion near Jupiter (q 5.17AU) and semi-major axis Orbit definitely elliptical, but object previously ‘captured’ and then a 43.0AU,i.e. P 280 yr. Illustrates complexity of cometary dynamical ‘ejected’ by Jupiter evolution . STFC Summer School STFC Summer School 2010 September 10 – #33 2010 September 10 – #34

Laplace’s ‘Nebular Hypothesis’: Interstellar Comets Formation of Solar System Following Nebular Hypothesis By early nineteenth century, the 2,000-year long debate ‘atmospheric vs. celestial’ ﬁnally settled in favour of celestial theory, with comets as ‘gravitating’ bodies ... But are comets truly ‘solar system’ or ‘interstellar’ objects? Laplace’s Nebular Hypothesis (1805): Developed independently of Kant’s (1755) theory; emphasizes the regularities of solar system, e.g. the central dominance of the Sun; the planetary orbits being nearly circular and coplanar etc.

1. Provides a physical model based on Newtonian principles and collapse and contraction of initially slowly rotating promordial gas cloud:

Contraction leads to ‘spin-up’ and shedding of rings of gas from the central body’s equator — leading to formation of the observed planets Most of the mass remains at the centre — leading to the Sun

2. But comets remain an anomaly —andthereforemusthaveaseparate ‘interstellar’ origin . . .

NB: Kant (1755) had developed a diﬀerent nebular theory, but had thought that comets could be incorporated into the model. Illustration of origin of solar system according to Laplace’s Nebular STFC Summer School STFC Summer School Hypothesis, after Whipple (1964) 2010 September 10 – #35 2010 September 10 – #36

Lagrange’s ‘Planetary’ Theory for Comets Laplace (1805) versus Lagrange (1814) 1. Discovery of ﬁrst asteroids: Ceres and Pallas, by Piazzi and Olbers in 1801 1. Laplace — the French ‘Newton’ — argues that his Nebular Hypothesis and 1802 respectively explains the main regularities of solar system, but not the comets;and

Ceres originally described by Piazzi as a ‘star-like’ comet; If Sun at rest with respect to interstellar population of comets, then we Early suggestions of transient nebulosity around both objects expect to see overwhelming excess of near-parabolic orbits —as (Herschel, Schr¨oter); conﬁrmation elusive; observed; Anomalies, such as Halley’s comet, explained by appeal to ad hoc 2. The new objects (‘asteroids’) upset underlying simplicity of Laplace’s planetary ‘capture’ mechanism, illustrated by Comet Lexell. nebular hypothesis, proving there exist minor ‘planets’ in relatively high-inclination, non-circular orbits. 2. Lagrance and others focus on growing number of known ‘short-period’ comets: Olbers speculates they might be fragments of a former much larger Too many to be explained by “ad hoc” chance capture, but the planet between Mars and Jupiter — blown to pieces by internal forces, formation of comets remains unexplained on the planetary theory: or the impact of a comet . . . another ad hoc process. 3. Thus a new ‘solar system’ theory introduced, harking back to earlier Neither theory perfect: Laplace’s founded on an assumption about solar motion ‘planetary’ and catastrophic notions about comets. (later proved wrong); Lagrange’s on an assumption about the (catastrophic) origin of comets. Either way, the near-parabolic excess remains problematic (e.g. evidence 4. Lagrange (1814) posthumously publishes proposal that at least some comets for two sorts of comet?) might have such an origin. STFC Summer School STFC Summer School 2010 September 10 – #37 2010 September 10 – #38

New Discoveries c.1800–1900 AKeyObservation:TheSolarMotion 1. Rapid increase in comets with 1. Interstellar theory depended on Sun essentially at rest with respect to ‘known’ mostly parabolic orbits. assumed interstellar population; 2. Whereas in 1790 there were 78 2. Herschel (1783) previously concluded Sun was moving, but results not parabolic comets (including 7 statistically significant (e.g. Biot, Bessel); Gauss (1815) nevertheless sightings of Halley’s comet); by highlights its potential importance for comets; 1890 there were c.270, of which 3. Argelander (1837) demonstrates reality of solar motion;butbythenits 20 were definitely periodic and 43 implications for comets ‘forgotten’; Laplace’s ‘interstellar’ theory survives. definitely elliptical. 4. Carrington (1860, 1863) emphasizes that solar motion would produce more 3. Leads to growing focus on the comets coming from one direction than another (cf. abberation). But ‘periodic’ subsample: comets with cannot see any effect — and concludes solar motion is wrong! mostly low-inclination, ‘direct’ 5. Peirce 1849) and Schiaparelli (1860) put argument right way around, but orbits and greater orbital similarity not accepted: e.g. Newton (1878): “Professor Schiaparelli by introducing to asteroids than to other comets. (improperly, as I am sure he will concede) the motion of the Sun in space 4. Suggests a ‘planetary’ was led to decide against a foreign origin for comets.” solar-system source for these 6. Fabry (1893) finally overthrows Laplacian paradigm: concludes Sun short-period, low-inclination Increasing rate of comet discoveries surrounded by comoving comet cloud; hence comets are ‘Solar System’ comets. with ‘known’ orbits, 1680–1980 objects STFC Summer School STFC Summer School 2010 September 10 – #39 2010 September 10 – #40

5 Laplace Rejected: A ‘New’ Solar System Paradigm c.1900 Paths Leading to Oort Cloud c.1920–1950 1. Number of short-period comets a growing problem for ‘capture’ hypothesis. 1. New age for Earth around 1920 (billions of years rather than tens or hundreds) highlights survival problem for parabolic comets. 2. If so, then short-period comets perhaps formed — like asteroids — in a ‘planetary disruption’ event (cf. Lagrange 1814, Proctor 1870); or by The ‘Darwinian’ argument now implies we should see no comets at all! break-up of a single, large comet (Alexander 1850, Bredichin 1889) . . . And ‘capture’ theory still fails to explain number of short-period comets. In any case, short-period comets must have ‘solar system’ origin. And so too — somehow — must the comets with ‘parabolic’ orbits. 2. Still, most astronomers remain irrationally attached to ‘solar system’ model. 3. Afewdevelop alternative ‘interstellar’ theories, e.g. (1) recent ‘capture’ of 3. Laplace’s ‘interstellar’ theory therefore rejected;leadstoareturn to Kant’s comets by passage of Sun through a dense ‘interstellar cloud’ of comets ‘solar nebula’ picture. (Nolke 1909, Bobrovnikoff1929); and (2) comets formed by passage of Sun 4. Two new themes at this time: (1) if comets are ‘solar system’ in origin, then through a dense interstellar dust cloud (Lyttleton 1948). what do comets tell us about origin of solar system?; and (2) the observed 4. Opik¨ (1932) notes Darwinian argument depends on comets always being orbits are probably not those that originally prevailed. subject to decay. Theories now suggest observed orbits are example of Darwinian evolution. The first quantitative theory of stellar perturbations on long-period Parabolic excess an example of Darwinian ‘survival of the fittest’ — origi- orbits. Shows cometary perihelia evolve outwards (and inwards) under nating from an initial primordial population containing all possible orbits. stellar action; the seed for ‘Oort cloud’ picture.

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Nineteenth and Early Twentieth-Century Theories Improved Statistics c.1920–1950: LP and SP Comets Originator and Date Theory and Broad Type LPcomets (P > 200 yr): nearly isotropic;and Laplace (c.1805) Comets are interstellar objects strong ‘parabolic excess’. Lagrange/Brewster Comets are result of planetary explosion Range 1/aN (c.1810) Peirce (1849) Comets are solar system objects, originating at great helio- 0.000–0.002 177.0 centric distances 0.002–0.004 10.0 Schiaparelli (c.1860) Comets are solar system bodies, occupying a huge co-moving 0.004–0.006 8.0 swarm about the Sun 0.006–0.008 7.0 Proctor(1884) Cometsareformedinvast planetary explosions 0.008–0.010 2.5 Newcomb (c.1910) Comets originate in the collapsing protosolar nebula 0.010–0.012 6.5 Chamberlin/Crommelin Short-period comets originate in planetary explosions or ejec- 0.012–0.014 1.0 (c.1920) tion of material from Sun > 0.014 9.0 Bobrovnikoff(1929) Comets are interstellar;occurindenseinterstellarswarmsand LP comets (1850–1936) have been recently captured 1/a distribution (Van Vsekhsvyatski (c.1930– Comets originate in explosions on the outer planets or their Woerkoem 1948). Left: Near-isotropic distribution of LP cometary 1980) satellites inclinations (589 LP comets up to 1982). SP comets (P < 200 yr): Opik¨ (1932) Comets are primordial solar system bodies;LPorbitsaffected mostly low-inclination; Right: Distribution of SP comet aphelia Q correlating by stellar perturbations aphelia correlate with Nölke (1936) Comets are interstellar; recently captured via interaction with with planetary semi-major axes (121 periodic comets planets dense resisting medium up to 1982). STFC Summer School STFC Summer School 2010 September 10 – #43 2010 September 10 – #44

Progress in Calculating Planetary Perturbations Cometary 1/a-Distribution: Early Diffusion Theory 1. Observed orbits not the ‘original’ orbits. 1. Changes in x =1/a akin to random walk in E. 2. Planetary perturbations change mostly the orbital energy E per unit mass, 2. Define σE =r.m.s.∆(1/a) per revolution. i.e. lead to ∆E =∆( GM /2a) ∆(1/a). 3 − ⊙ ∝ = after N revolutions,expectx √NσE,i.e. 10 revolutions to ⇒ ≈ ≈ 3. For randomly distributed close encounters (i.e. strong perturbations), reach P < 200 yr. 3 probability of energy change ∆is ∆ − , i.e. (for encounters with Jupiter): ∝| | 3. Solve diffusion equation (ignoring decay): 2 8 MJ 1 3 2 2 φ(∆) d∆ 2 ∆ − d∆ ∂ν σE ∂ ν 1/2 3/2 3 M aJ | | = where P(a)=2π(GM )− a ⊙ ∂t 2P(x) ∂x2 ⊙ 4. Leads to concept of ‘capture probability’, p (cf. Lexell), i.e. probability to c 4. Leads to: evolve in one revolution to semi-major axis less than a: t 2 2 D 2 ν(x, t)= 1+ exp( tD/t) where tD =8√xP(x)/σ ; 4 MJ a E pc (< a) t − 3 M aJ ⊙ i.e. diffusion time-scale < 1 Myr. 5 5. = Capture probability to period P < 200 yr is < 5 10− ;emphasizes ∼ ⇒ × 5. = rapid evolution to a quasi-steady state distribution ... problem of observed number of observed short-period∼ orbits. ⇒ STFC Summer School STFC Summer School 2010 September 10 – #45 2010 September 10 – #46

Solution of Diﬀusion Equation Lyttleton’s (1948) Accretion Theory 1. A novel variant of the interstellar hypothesis; the ﬁrst to address both where comets come from and how they are formed.

2. Consider motion of Sun through a dense dust cloud of density ρdust. Collisions of dust grains on axis of symmetry dissipate energy and cause some grains to be captured — these coalesce to become proto-comets.

Solution of diffusion equation with no 3. Get inflow within a stagnation radius r0,approximatelytheaccretion radius σ distribution versus q (AU 1)for 2 1 E − decay (after Van Woerkom 1948); note RA = GM /V .ForV =5kms− , RA 35 AU. randomly distributed initial parabolic rapid evolution to ‘flat’ distribution, ⊙ 4. In a steady-state, the stream mass per unit length is µ 2πρ R2 and the orbits. Very roughly, completely contrary to observed dust A 3 1 stream velocity V is roughly the free-fall speed from R .Thus,anynew σE(q) 10− exp( q/5.2AU)AU− . 1/a-distribution (histogram). s A ≈ − comets have initial semi-major axes a < RA/2. STFC Summer School STFC Summer School ∼ 2010 September 10 – #47 2010 September 10 – #48

6 Problems with Lyttleton’s Theory Birth of a Theory: The 1950 Oort Cloud

1. Dust clouds do not exist on their own. The interstellar dust is dominated 1. Oort considers the original (by a mass fraction of at least a factor of 50) by hydrogen gas. Effects of 1/a-values of the 19 most gas must be included; this never done. accurate orbits; i.e. those with 2. The supposed proto-comets are far too small. Even if an accretion stream 4 1 mean errors < 10− AU− . could be set up, only very short segments of length d(r) < 2 µr 3/M at heliocentric distance r could successfully contract against∼ the tidal field⊙ of 2. Enables fine-grained binning of < 8 1 9 22 3 3/2 the Sun. This leads to mc 10 (10 km s− /V ) (ρdust/10− kg m− ) kg. 1/a-distribution for first time. ∼ 3. Inital orbits too short period and too anisotropic. Lyttleton argues for a long 3. More than half had ‘original’ 6 1 period of randomisation of orbits following the last accretion episode, but 1/a-values < 50 10− AU− ; × then the predicted 1/a-distribution quite wrong (diffusion theory). and none had 1/a > 750 10 6 AU 1. 4. The supposed proto-comets are on initial orbits directed towards Sun (or × − − solar-system barycentre). Unless inhomogeneities or planetary perturbations 4. Note the extreme narrowness are invoked to deflect the stream, all the initial comets will fall onto the Sun. of the sharp peak in the distribution of ‘observed’ In summary, despite strong advocacy of theory by Lyttleton for next 30 original 1/a-values. years: “The theory is disproved: an honourable fate for a good theory”!

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Comparison with Modern Data Argument for Oort Cloud — c.1950

1. Sharp spike in observed 1/a-distribution rules out interstellar capture (Van Woerkom 1948); Lyttleton’s ‘capture theory’ (1948) seriously deﬁcient . . . suggests comets have primordial solar system origin, and the observed comets are coming into inner planetary region for the ﬁrst time. 2. If comets are primordial,theremustbea‘comet store’ — the ‘home’ of the comet — somewhere beyond the zone of visibility, where comets can survive. Logically, this must contain comets in orbits of large perihelion distance. 3. Oort then addresses how to get comets from safe storage into inner solar system:

Planetary perturbations? —NO: they broaden the 1/a-distribution too much (van Woerkom). Resistance of dense interstellar medium? —NO:itisimplausible,and such a medium would primarily aﬀect the comets’ aphelion distances, again contradicting the observed 1/a-distribution. Stellar perturbations? —YES: cometary orbits extend up to halfway to the nearest star; they must be aﬀected by passing stars (cf. Opik¨ 1932).

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Argument for Oort Cloud — In Modern Terms Modern Argument (cont.) 1. ‘New’ comets are only lost if q lies within loss cone, i.e. q < 15 AU; 1. Observations = We see 1 ‘new’ comet (q < 5AU, H10 < 7) ⇒ ∼ = Oort’s reservoir must contain long-period comets of large∼ q. discovered per year. ⇒ 4 2. For long-period orbits, planets change the orbital energy,∆1/a, Semi-major axes a > 2 10 AU: near the parabolic limit; orbital periods P 3–30 Myr —× short compared to age of solar system. keeping q nearly constant; stars change the angular momentum,∆q, These ‘new’ comets strongly perturbed by Jupiter,sothat 50% keeping 1/a constant. ∼ ejected, the remainder ‘captured’. 3. In other words, stellar perturbations change q. ‘Captured’ comets return, to be ejected or lost to short-period orbits and eventual decay. ∆q per revolution is about the size of the loss cone, provided the orbit is large enough. 2. Conclude: ALL observed comets are ultimately lost; and the ‘loss = the reservoir must contain comets of very long orbital period cone’ aﬀects all orbits with q < 15 AU; and the loss timescale age (a⇒> 2 104 AU, P > 5 Myr) — just like the observations. × of solar system. ∼ Leads to Oort’s idea of a nearly spherical cloud of comets with orbits extending up to halfway to nearest star. 3. = comets are either a transient phenomenon,orthereisa ⇒ long-lived reservoir to replenish those that are lost. 4. The cloud is ‘gardened’ by external perturbations.

4. Oort adopts primordial ‘steady-state’ hypothesis. including stellar, molecular cloud and large-scale systematic eﬀects of Galactic tide.

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View of Oort Cloud Standard (1950) Model 1. Assume: (1) spherical symmetry; outer radius R 200, 000 AU; (2) 1. Like a globular star cluster, such as 0 M13. . . random velocities, ‘gardened’ by stellar perturbations; (3) hydrostatic equilibrium (cloud neither expanding nor contracting); and (4) a simple Imagine Sun at centre energy distribution, e.g. a power-law distribution of orbital energies per unit the stars become ‘comets’ mass E = GM /2a. − ⊙ the shape (like a ﬂattened rugby γ 2. If f (E) dE E − dE,thenthenumberdensityn(r) is roughly proportional ball) is about right γ 4 ∝| | to r − . the strong concentration of comets towards the centre is 3. Oort’s (1950) model has γ =5/2, corresonding to velocity space being

about right uniformly ﬁlled at r up to a value Vmax equal to the free-fall speed from R0 3/2 the overall dynamics is similar to r.Thisimpliesn(r) r − ,i.e.most of the mass near the outer edge. ∼∝ 2. Can calculate ‘families’ of Oort 4. Other models have smaller γ (e.g. γ 0), and much sharper inward density ∼ cloud models, in the same way as The ‘loss cone’ behaves just increases. The structure is much more like a dense star cluster, with a strong concentration of mass towards the centre, not a shell. for star clusters and galaxies like the loss cone around a 3. External perturbations (e.g. stars) black hole in a galactic 5. Leads to the concept of the Oort cloud Dense Inner Core, a region change cometary orbits nucleus containing most of the cometary mass, and relatively safe from external perturbations. STFC Summer School STFC Summer School 2010 September 10 – #55 2010 September 10 – #56

7 Evolution and Survival Long-Term Evolution

1. 1950 Model: quasi-steady state; comets in long-term ‘deep freeze’ of 1. Two main types of external perturber: stars and molecular clouds. Oort cloud; stars dominate the evolution; no dense inner core. Galactic tide also drives comets into inner solar system, but has little direct effect on Oort cloud’s disruption. 2. Modern view: Short timescales: t < 10 Myr:∆q dominated by Galactic tide and 2. Stars pass through and beyond the Oort cloud, causing gradual passing stars; quasi-steady∼ long-period comet flux; ∆E dominated by unbinding of cometary orbits; the ‘stellar’ half-life is stars. 9 4 t1/2, 2 10 2 10 AU/a yr. Medium timescales: 10 < t < 500 Myr: periodic new-comet flux due to ∗ × × Sun’s orbit about Galactic∼ plan;∼ rare, close stellar passages more 3. Molecular cloud pass beyond the Oort cloud, but are much more massive than stars; the ‘molecular cloud’ half-life is important in randomizing orbits; ∆E still dominated by stars. < < t 2 109 2 104 AU/a 3 yr Long timescales: 500 t 4000 Myr: rare, close molecular cloud 1/2,c × × encounters disrupt outer∼ cloud,∼ dominating ∆E there; rare, close = ‘standard Oort cloud dynamically unstable beyond a 2 104 AU stellar encounters stir up inner core. ⇒ × over age of solar system; it must be replenished from within: the Dense Inner Core. Together, these replenish transition zone between inner and outer Oort cloud and stir up orbits in Dense Inner Core.

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Variable Oort Cloud Flux Fading Problem: First Recall 1/a-distribution

1. Galactic tide dominates quasi-steady new-comet ﬂux from Oort cloud. 2. Comet ﬂux roughly proportional to mass-density, ρS(t) at Sun’s location in Galaxy (see Figure, after J. Matese et al. 1995). 3. ∆q per revolution depends on q, a, and Galactic latitude of perihelion, b,i.e.

∆q per revolution = (10π2√2 ρ/M )sin(2b) q1/2a7/2 ⊙

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Fading Problem: Where Are the ‘Dead’ Comets? Physics of External Perturbations

1. Consider a perturber of mass M passing Sun with velocity V and impact 1. Observed new-comet ﬂux: Approximately 1 comet per year brighter parameter b with respect to Sun and d with respect to a comet at than H10 = 7 (corresponds to diameter d > 5km)with q < 5AU,i.e. heliocentric distance r. with perihelion distance within Jupiter’s orbit.∼ 2. Capture probability to ‘Halley-type comet’ (HTC),i.e.capture probability to P < 200 yr: p 0.01 per new comet; the rest get c ejected. ∼ 3. Mean dynamical lifetime as a Halley-type comet: t 3 105 yr. dyn × 4. = steady-state number of HTCs, N , given by ⇒ HTC N 1 0.01 300, 000 3000. HTC × × ≈ 5. Greater than 100 times more than observed:wherearethedead 2. Then the relative velocity change of the comet with respect to the Sun is comets?! the diﬀerence of the two impulses, i.e.

Perhaps ‘dark HT asteroids’; ‘boulders’; or ‘dust’? 2GM 2GM 2GM b2 rb ∆v = dˆ bˆ = 1 bˆ ˆr (ˆr .Vˆ)Vˆ dV − bV bV d 2 − − d 2 − STFC Summer School STFC Summer School 2010 September 10 – #61 2010 September 10 – #62

Heuristic Results Mean Energy Transfer Rate 1. Mean relative velocity change in a single encounter is approximately: 1. Change in orbital energy in a single encounter:let∆v be the relative velocity change of the comet with respect to the Sun, and let v0 be √ 2GM 2 b < 7/12 a its orbital velocity, then ∆v =  bV 7/6 a/bb> 7/12 a  1 2 ∆E = v0.∆v + (∆v) 2 2. On short timescales (e.g. t <30 Myr), the closest stellar encounter expected 1/2 during a given time interval∼t has impact parameter b (2πnVt)− , Cometary orbital energies thus diﬀuse and systematically increase (i.e. min where n is the number density of perturbers. For stars this usually implies become less tightly bound) owing to external perturbations. b > a,whichleadsto ∼ 1/2 2. Approximate result for point-mass perturbers:deﬁne ∆vmax 4π(7/6) Gρat a = 12/7b ,whereb (2πnVt) 1/2 is the most probable c min min − 3 where ρ = nM ( 0.05 M pc− for stars) is the mass density of perturbers. minimum impact parameter for the perturbers of number density n, ≈ ⊙ 4 1 then the mean energy transfer rate can be shown to be approximately 3. This leads to ∆vmax 4.3(a/3 10 AU)(t/10 Myr) m s− . × 4 3/2 2 4. Finally, setting t = P(a) 5.2(a/3 10 AU) Myr, the maximum change 4πG 2M2n (a/ac ) a < ac in perihelion distance during a single× revolution can be shown to be of the ε˙(t)= V  order of 2ln(a/ac )+1 a > ac ∆q 5(a/3 104 AU)7/2(q/1AU)1/2 AU  STFC Summer School ≈ × STFC Summer School 2010 September 10 – #63 2010 September 10 – #64 

8 Oort Cloud Survival Problem Conclusions — General Points

1. For stars and t 4.5Gyr,wehave a ac .Thisimpliesε˙ const.. ∗ ≈ 1. ‘Comets’ can sometimes be the most prominent objects in sky; their 2 2. For molecular clouds and t 4.5Gyr,wehave a ac ,i.e.ε˙c a . study goes back thousands of years. ∝ 3. The net result is: 2. Comets touch on many areas of astronomy, not least solar-system 2 ε˙ =˙ε +˙εc A + Ac a science; they have had a significant impact on the Earth and on the ∗ ∗ 13 2 3 44 3 where for typical parameters A 10− m s− and Ac 10− s− . development of scientific ideas. ∗ ≈ 4. Solving the energy evolution equation for each type of perturber leads to the 3. Earth an ‘open’ system, in touch with its near-space celestial half-life due to stellar and molecular cloud perturbations, i.e. environment: a paradigm shift as significant as Copernicanism.

4 4. Solar system ‘very leaky’; interesting implications for the dust, small 1 GM 9 2 10 AU t1/2, = ⊙ 2 10 × yr bodies and planets in molecular clouds and the interstellar medium; ∗ 4.732 A a × a ∗ what about comet clouds around other stars? and 5. Modern picture of comets;abalancebetweenthehistorical 4 3 1 GM 9 2 10 AU t = ⊙ 2 10 × yr catastrophist and Newtonian uniformitarian views; comets as 1/2,c 8.190 A a3 × a c potential destroyers of life and as objects that bring the necessities of 5. Thus, due to both clouds and stars, the majority of comets with initial life (e.g. water, organics, perhaps seeds of life itself) to Earth. a > 2 104 AU will be lost. This is the Oort cloud survival problem. × STFC Summer∼ School STFC Summer School 2010 September 10 – #65 2010 September 10 – #66

Conclusions — Issues of Current Concern

1. Ancient history suggests ‘the sky’ may have been significantly different in proto-historic times (e.g. more ‘active’, more Acknowledgements interplanetary debris, brighter zodiacal light etc.); how can that be? 2. Cometary masses range up to the size of dwarf planets; what are the effects of occasional ‘giants’ on Earth? 2 3 Astronomy at Armagh Observatory is funded 3. Total mass of Oort cloud may be very large ( 10 M pc− ); implies ≈ ⊕ potentially serious difficulties for ‘standard’ primordial solar system by the Northern Ireland Department of picture? Culture, Arts and Leisure 4. ‘Fading problem’ still not understood, but effectively determines the predicted 1/a-distribution; what happens to cometary debris? 5. Meteoroid streams initially very fine-grained; leads to strong time-dependence in accretion of dust and small bodies on Earth.

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Twentieth-Century Theories: c.1940–1970 Originator and Date Theory and Broad Type Edgeworth (1938–1961) Comets are solar system objects formed by accretion in outer protoplanetary disc Lyttleton (1948) Comets are swarms of interstellar dust grains,concentrated and captured into solar system by the accretion mechanism Oort (1950) Comets originate in asteroid belt or in disruption of a former asteroidal planet;nowinavast swarm about the Sun Kuiper(1951) Comets accumulated from icy condensates in or beyond Neptune-Pluto zone of low-mass protoplanetary disc Krat(1952) Cometsformedby collisions of bodies beyond Neptune Katassef(1955) Cometsformedby disruption of a former asteroidal planet Cameron(1962) Comets formed beyond Pluto by accretion in massive, extended protoplanetary disc Donn (1963) Comets are fractal aggregates of interstellar grains Whipple(1964) Cometsformedin outer regions of protoplanetary disc,either in Uranus-Neptune-Pluto zone or a little beyond Pluto Opik¨ (1966–1978) Comets accumulated in Jupiter-Saturn region of a low-mass protoplanetary disc Safronov (1967–1978) Comets formed in Uranus-Neptune zone of a low-mass protoplanetary disc STFC Summer School 2010 September 10 – #69