lecture 4 : comets origin and interrelations · lecture 4 : comets origin and interrelations...

LECTURE 4 : COMETS

ORIGIN AND INTERRELATIONS

∗ Comets: residual planetesimals of the planet formation.∗ Rocky and icy bodies: the snowline.∗ Accretion of the giant planets and scattering of the residual material: Formation of theOort cloud and the trans-neptunian belt.∗ Galactic environment in which the solar system formed.∗ The search for a planet X.∗ How pristine are comets?.∗ Collisions of comets and asteroids with the Earth.∗ The problem of the terrestrial water.∗ Comets and the origin and development of life on Earth.

Ciclo de Cursos Especiais - Lecture 4 1

Star formation in giant molecular clouds

Typical physical parameters in giant molecular clouds:Temperature : T ' 10 KMass : 105 - 106 M�Diameter : ∼ 50 pcAverage density : ∼ 102 H2 cm−3 (up to ∼ 105−6 H2 cm−3 in dense cores)

∗ A large number of organic molecules have been detected in giant molecular clouds, ingeneral compounds rich in C, H, O, N, that can be incorporated into the planets thatformed there.


Condition to form a star

Jeans’s criterion for the collapse of a gas cloud of density n and temperature T :

Self-gravity > Thermal pressure ⇒

MJ ≈ 10T 3/2

√n

M�

In a dense region : MJ ' 1 M�


Protoplanetary discs in the Orion nebula

HST images (NASA)

Half-lifetime : ∼ 107 yr. The surrounding gas is swept by the strong UV flux of nearbyO and B stars, and/or strong stellar winds from the central star.


Collapsing nebula and formation of a protoplanetary disc: Integralview of the process


Physical properties of the protoplanetary disc

Artist concept of the protoplanetary discduring the stage of planetesimal forma-tion.

Condensation of the different materialsas a function of the heliocentric dis-tance.

Physical properties of the protoplanetary disc: Mass : 0.01 - 0.1 M�; Mass density :ρ = ρo(r/ro)

−m; Temperature : T = To(r/ro)−n.


The final stage of planet formation

“Snowline”: between r ∼ 2− 5 au


The most primitive material is the less differenciated in elementalabundances

Example of primitive material: Carbonaceous meteorites


Different stages of planet formation: A summary

∗ At the beginning the dust particles settle in a thin equatorial disc.∗ Then they start to accrete by gentle mutual collisions (adhesion by van der Waalsforces) leading to kilometer-size planetesimals.∗ The planetesimals continue their accretion by mutual collisions until the formation ofplanets. A fraction of the residual planetesimals is scattered toward the inner planetaryregion and to the outermost part. The latter form the Oort cloud.


Residues of the primordial accretion

Brownlee particle collected in the stratosphere. It is a highly porous aggregate ofmicrometer and sub-micrometer dust particles.


Planet migration in the scenario of planetesimal scattering

∗ Planet migration by exchange of angular momentum between the protoplanets and thescattered planetesimals.

The orbital radius aN of a planet (Neptune) will experience a change ∆aN due to theexchange of angular momentum with the interacting planetesimal, which it is given by

∆aNaN

∼ −2m

MN

∆h

hN∆h : change of the specific angular momentum of the interacting planetesimals.

There are two possible results:

(a) Scattering inwards toward Jupiter’s influence zone.

(b) Ejection to interstellar space or the Oort cloud.


(a). Let us first assume that all the interacting planetesimals are ejected to interstellarspace.

A planetesimal gains an amount of specific angular momentum:

∆h = (√

2− 1)aNvN

vN = (µ/aN)1/2 : heliocentric circular velocity at Neptune’s distance.

mr : total mass of planetesimals ejected to interstellar space.

Change in the orbital radius:

∆aNaN

∼ −2(√

2− 1)mr

MN

For example, if Neptune ejected a total mass mr = 0.5MN , its orbital radius would haveshrunk to a′N = aN + ∆aN ∼ 0.6aN .


(b). All the residual planetesimals of Neptune’s accretion zone are scattered inwardtowards Jupiter’s influence zone, from where they are ejected by Jupiter’s perturbations.

The specific angular momentum by each one of the interacting planetesimals (and gainedby Neptune) is

∆h ' −[

1−(

2aJaN + aJ

)1/2]aNvN

aJ : Jupiter’s orbital radius.

In this case Neptune will increase its orbital radius by

∆aNaN

∼ +2

[1−

(2aJ

aN + aJ

)1/2]mr

MN

∗ The balance is not zero: Process (b) predominates over Process (a) in the cases ofNeptune, Uranus and Saturn, so these planets will move outwards. On the other hand,in the case of Jupiter Process (a) predominates over Process (b), so it will move inwards(Fernandez & Ip 1984, 1996).


Planet migration: A numerical model

(Fernandez & Ip 1984)


The Nice model

Orbital evolution taken form an N-body simulation with 35 M⊕ (3500 particles truncatedat 30 au). The evolutions of the semimajor axis a, minimum perihelio distance (q) andmaximum aphelion distance (Q) are considered for each planet. The vertical dotted lineindicates the time of orbit crossing of proto-Uranus and proto-Neptune induced whenJupiter and Saturn enter into the 1:2 mean motion resonance (MMR) (Tsiganis, Gomes,Morbidelli & Levison 2005).


Cont.

Simulation showing the outer planets and the planetesimal disc: a) primordial configura-tion before the time Jupiter reached the 1:2 MMR; b) scattering of planetesimals towardthe inner solar system triggered by the displacement of Neptune (dark blue) and Uranus(pale blue); c) planet configuration after the eyection of planetesimals by the planets(Tsiganis, Gomes, Morbidelli & Levison 2005).


How comets are born: collisional or primordial rubble piles?

Artistic conception of the accretion andfragmentation of comets in two scenar-ios: collisional (product of the laterevolution of the comet), or primordial(preserved from the formation time).The study of 67P/C-G shows that it haslow density, high porosity, weak strengthand contains supervolatiles that experi-enced little to no aqueous alteration.These features seem to favor a pri-mordial origin, yet at a slow rate thanTNOs whose rapid growth led to ther-mal processing and compaction by heat-ing by the short-lived 26Al radioisotope(Davidsson et al. 2016).


Formation of the Oort cloud in different galactic environments

(Fernandez & Brunini 2000)

∗ loose star cluster : 10 stars pc−3

∗ dense star cluster : 25 stars pc−3

∗ superdense star cluster : 100 stars pc−3

⇒ These simulations show that different Galactic environments are coupled with thedegree of compactness of the formed Oort cloud.


Are there distant massive planets? The search for a planet X

¿Existen companeros solares distantes masivos?

∗ Fundamentos:1) Scattering de objetos masivos por los planetas gigantes.2) Captura de algun objeto cuando (y si) el Sol formaba parte de un cumulo estelar.

∗ Un planeta como Neptuno a una distancia de 1200 UA tendrıa una magnitudaparente 24.

Curso TNOs 2010, Julio A. Fernandez 18

What are the reasons to support theexistence of distant massive planets?(1) Cosmogonic reasons.(2) The discovery of dwarf planets.(3) Anomalies in the distribution oforbital elements of some populations(comets, TNOs).


Sedna: An anomalous case

∗ Sedna with a periheliondistance q = 76 au shows thatthere are objects decoupled from theTN region moving in very eccentricorbits.

POSSIBLE ORIGIN:1) Objects of planetary size formed within the solar nebula scattered by the Jovianplanets.2) Objects captured within a star cluster in which the Sun was assumed to bee formed.


2012VP113: a new extremely distant object

There is an anomalous alignment of the argument of perihelion of extreme TNOs (q > 30au, a > 150 au) around ω ≈ 0 attributed to the perturbations of a super-Earth massbody at some hundreds au from the Sun (Trujillo & Sheppard 2014).


Other recently discovered extreme TNOs

Two other extreme objects have been recently discovered, 2013 FT28 and 2014 SR349with perihelion distances q = 43.6 and q = 48 au and semimajor axes a = 310 au anda = 288 au respectively. Their arguments of perihelion also fall within the clusteringaround ω ≈ 0 (Sheppard & Trujillo 2016).

Such an alignment of the arguments of perihelion can be maintained by a distant eccentricplanet of mass >

∼10 M⊕ whose perihelion is 180◦ away from the perihelia of these extremeobjects (Batygin & Brown 2016).


Could the resonant dynamics explain the high perihelion distances?

5 6 7 8

plan

et

90 180 270

w

100

1000

10000

a (A

U)

30

40

50

q (A

U)

30

40

50

0 500 1000 1500 2000 2500 3000 3500

i

time (Myr)

Dynamical simulation of the objectfrom the Scattered Disc 1999 DP8

(Fernandez, Gallardo & Brunini 2004).

∗ q raises due to the conjunction of a mean motion resonance with the Kozai mechanism:

θ = (1− e2o) cos2 io = (1− e21) cos2 i1

⇒ when i1 is maximum, e1 is minimum, and since 1 − e2 ' q/2a, q must also bemaximum.


Other hypoteses

∗ Decouple of Sedna caused by a massive body bound to the Sun (Gomes, Matese & Lissauer 2006).

∗ Clustering of aphelia of new comets along a great circle attributed to a gravitationally bound solar

companion (Murray 1999; Matese, Whitman & Whitmire 1999).

WARNING! SMALL SAMPLES CAN BE MISLEADING!Arguments for the presence of an undiscovered planet 33

been determined show more scatter than those of the short-period

comets associated with the planet Jupiter. One comet in Fig. 1

shows an aphelion 198 from the orbit of the hypothetical object;

there are few comets in Jupiter's family with aphelia more than

128 from Jupiter's orbit. However, comets associated with Jupiter

are likely to have undergone several refinements and changes of

orbit, whereas the cometary orbits considered here are first or

second solar approaches only. The retrograde motion of all but

two of these comets is shared by the hypothetical object.

3 D ISCUSS ION

The hypothetical planet is within the distance range where large

numbers of small planets are predicted (Stern 1991), but the

presence of a large object orbiting so far from the Sun would be

surprising, as it would be very weakly bound and is extremely

unlikely to have been an original member of the Solar system. On

the other hand, recent capture of an object into a bound orbit at

this distance, although possible, is also extremely unlikely. The

number of cometary orbits of sufficient accuracy for the present

analysis is small, only 13, but the probability of the cluster in

Fig. 2 occurring by chance is less than 0.0006 (see the appendix).

It is possible that some of these comets were not perturbed by

the unknown planet and lie within the same area by chance. Some

comets could be rejected from the analysis because they are

furthest from the supposed orbit, and this would produce higher

correlation coefficients and apparently less uncertain orbital

elements and present position. However, such rejection would

necessarily be subjective, as there is no way of distinguishing such

comets.

The scenario that the alignment is due to a recent single

approach of a perturber on a hyperbolic orbit, such as a passing

star, is not possible, because the cluster in Fig. 2 extends to nearly

2708. If we reject comet 1993a and all second-return comets, then

the arc is only about 1308 and such a hypothesis might be tenable,

but the same argument as in the previous paragraph applies: there

is no objective reason for rejecting these comets. In the past, the

possibility of a distant companion star to the Sun was discussed

(Davis, Hut & Muller 1984; Whitmire & Jackson 1984), and one

of the arguments in favour included the anisotropy in the positions

of long-period cometary orbits (Delsemme 1986). However,

because of its brightness, a much more distant and eccentric

orbit than that indicated in Fig. 3 was implied. Furthermore, such a

companion star is now considered extremely unlikely for a variety

of other reasons (Vandervoort & Sather 1993). We are therefore

left with an object smaller than a star, and at a distance that only

comets are known to reach.

The mass of the hypothetical object would presumably be large

compared with those of the known planets, in order to produce a

detectable family of comets. However, the mass cannot be too

large or it would be subject to energy-releasing nuclear reactions

(Saumon et al. 1995) that would make the object too bright to have

remained undiscovered. Assuming a diameter 10 times that of

Jupiter, and a similar albedo, gives the object a visual magnitude

fainter than 23.

An object as faint as this would be unlikely to have been picked

up by any of the past searches for distant Solar system objects

(Tombaugh 1961; Kowal 1989), because of its faintness and small

q 1999 RAS, MNRAS 309, 31±34

Figure 2. Plot of aphelion positions for all high-precision cometary orbits with aphelia between 30 000 and 50 000 au from the Sun listed in Marsden &

Williams (1994). Note the apparent non-random distribution of those between 08 and 1808 (filled circles). The curve is the best-fitting sine function to these

points, which are assumed to be comets on their first return to the inner Solar system after capture by the hypothetical distant planet.

Table 1. Comets with aphelia between 30 000 and 50 000 au (fromMarsden & Williams 1994). Columns from left to right: cometidentification; q� perihelion distance; v � argument of perihelion;V� longitude of ascending node; i� inclination; LA� longitude ofaphelion; BA� latitude of aphelion; Q� aphelion distance. All anglesare in degrees; distances are in astronomical units.

Comet q v V i LA BA Q

1925 I 1.109 36.2 319.1 100.0 131.9 235.5 50 0001946 VI 1.136 320.4 238.3 57.0 34.1 132.3 45 0001990 VI 1.569 137.8 280.0 59.4 255.2 235.3 41 0001889 I 1.815 340.5 359.0 166.4 198.0 14.5 42 0001993a 1.937 130.7 144.7 124.9 178.4 238.5 33 0001932 VI 2.314 329.7 216.1 125.0 54.6 124.4 44 0001972 VIII 2.511 167.9 358.9 138.6 6.3 19.0 41 0001983 XII 3.318 186.2 209.6 134.7 205.2 14.4 44 0001987V 3.625 329.1 194.5 124.1 33.0 125.2 34 0001955 VI 3.87 144.7 265.3 100.4 272.6 234.7 48 0001979 VI 4.687 10.1 293.1 92.2 112.7 210.1 48 0001986 XIV 5.458 17.0 268.3 132.5 76.7 212.5 43 0001975 II 6.881 193.4 22.8 112.0 17.7 112.4 34 000

0 90 180 270 360ecliptic longitude

−90

−60

−30

0

30

60

90

eclip

tic la

titud

e

Murray’s (1999) planet X based on a sample of 13

comets with aphelion distances between 30,000 and

50,000 au taken from Marsden & Williams’s (1994)

catalog.

Updated sample from Marsden &

Williams (2008).


Perturbations by a distant solar companionProducing distant detached objects 593

Fig. 4. Direct numerical integration were undertaken with all major planets anda companion with ρc = 1.5 × 10−14 M� AU−3 as perturbers. Distributions ofsemimajor axes and perihelia of particles started near Neptune after 109 yearsof evolution are plotted. Upper panel ↔ Mc = 5 × 10−5 M� , ac = 1500 AU,ec = 0, ic = 90◦; lower panel ↔ Mc = 4 × 10−4 M�, ac = 3000 AU, ec = 0,ic = 90◦ . Gray dots ↔ i < 15◦ , black dots ↔ i > 15◦ , triangles ↔ Sedna and2000 CR105. These plots can be compared to the secular analysis results givenin the bottom panel of Fig. 2.

pointing towards an explanation of the lunar heavy bombard-ment, the origin of the Trojans and the present orbital structureof the giant planets. We also considered the galactic tide in thisrun.

The set of runs for the first model used 1 year for thesteplength. For the migration model 0.5 year was used in thebeginning and 1 year after the LHB had calmed down and theplanets were close to their present orbits. All integrations wereperformed using the MERCURY package (Chambers, 1999).

3.1. Four known planets and companion

For this model (massless particles), we begin by showingexamples meant to compare with the semianalytical approachof Section 2. First we compare the distribution created bytwo different companions. Both components have circular or-bits and their semimajor axes and masses are, respectively,ac = 1500 AU, Mc = 5 × 10−5 M� and ac = 3000 AU, Mc =4×10−4 M�. These two sets of companion’s parameters corre-spond to the same strength parameter, ρc [Eq. (5)], and shouldinduce the same a–q distribution for a common companioninclination if the secular approximation is appropriate. Each nu-merical integration simulated 109 years. Fig. 4 shows the pairof distributions for ic = 90◦. The inner border of the detachedregions and the distributions of low inclination objects are quite

Fig. 5. At 109 years, the distributions of semimajor axes and perihelia of parti-cles started near Neptune. Direct numerical integration were undertaken with allmajor planets and a companion with ρc = 1.5×10−14 M� AU−3 as perturbers.Companion parameters ↔ Mc = 5 × 10−5 M�, ac = 1500 AU, ec = 0; incli-nations as indicated in each panel. Gray dots ↔ i < 15◦ , black dots ↔ i > 15◦ ,triangles ↔ Sedna and 2000 CR105. These plots can be compared to the secularanalysis results given in Fig. 2.

similar, suggesting that the secular effects as developed in Sec-tion 2 play a prominent role in the establishment of the a–q

distribution of detached scattered objects. Differences with thedirect numerical integration model are of two kinds. First, thelarger, more distant companion is more effective at detachingperihelia of scattered objects with larger semimajor axes. Sec-ond, the smaller, closer companion forms a 28% more massiveinner Oort cloud at 109 years. The reason for this deserves adeeper investigation. A larger Mc raises the perihelia of scat-tered objects in a shorter timescale, but also brings them backto Neptune-crossing orbits in the same short timescale. More-over, the companion can directly scatter the objects away fromthe inner Oort cloud. There must be an ideal companion (mass,distance from the Sun, eccentricity and inclination) that willcreate the largest inner Oort cloud population at the Solar Sys-tem’s age, but this goes beyond the scope of this paper. Notealso that even for this high value of ic there is no significantKozai mechanism altering the companion’s orbit; ec only goesup to 0.05 and ic varies by only ±2◦.

For the smaller, closer, companion, integrations with ic = 0◦,45◦, 135◦, 180◦ were also undertaken. The a–q distributionscreated by this companion are shown in Fig. 5. The inclinationsequidistant from 90◦ are placed side by side so as to comparetheir similarities. In principle, by the secular theory these dis-tributions should be equivalent, which is fairly well confirmedby comparing Figs. 4 and 5 with Fig. 2.

We conclude that secular analysis fails where it is expectedto fail, i.e., when the tidal approximation is invalid, particu-larly when impulses can occur. Nonetheless, it provides a useful

Simulations for 109 yr of a sample of fictitious scattered disc objects with initial qobetween 32 and 38 au, subject to perturbations by a companion of mass Mc = 5× 10−5

M�, semimajor axis ac = 1500 au, eccentricity e = 0, and the inclination indicatedin each panel. The triangles indicate the locations of objects 2000 CR105 and Sedna(Gomes, Matese & Lissauer 2006).


Birth of the Sun in a star cluster

1

ρo: central density of the cluster (M� pc−3)Small black circles: Sedna, 2000 CR105, 2003 UB313

(Brasser, Duncan & Levison 2006)


All-sky searches of massive objects

VISIBLE

Jupiter Neptunedistance (au) / apparent (visual) magnitude 103 / 20 23

5000 / 27 30

INFRARED∗ Wide-field Infrared Survey Explorer (WISE) launched in December 2009 provided anall-sky map at 3.4, 4.6, 12 and 22 µm

Wide-field Infrared Survey Explorer Launch

PrESS K It/DECEMBEr 20 09

WISE could have detected objectssize similar to:

Jupiter at distances <∼ 2× 104 au

Saturn “ <∼ 104 au

Neptune “ <∼ 600 au

But no such objects were discovered!


Collisions of comets and asteroids with the Earth

It is a relevant topic for the origin of life on Earth and the risk of provokingmass extinctions.


For an object in an orbit with elements q, a, i, the collision probability with the Earth is(Opik 1951):

PJFC =σ2U

π sin i|Ux|where σ2 is the collision cross-section enlarge by gravitational focusing, we have

σ = πR2p

(1 +

v2escu2

)where Rp is the planet radius and vesc the escape velocity, u is the encounter velocityof the body with the planet, assuming that it moves on a circular orbit of radius ap andvelocity vp, we have

U2 = 3− 1

A− 2√

2Q(1−Q/2A) cos i

where the variables are in relative units: U = u/vp, A = a/ap and Q = q/ap.


The radial component Ux is given by

U2x = 2− 1

A−A(1− e2)

By introducing appropriate values for the populations of JFCs and NEAs in Earth-crossingorbits with diameters > 1 km (∼ 20 and 650 respectively), we can compute the averagecollision probability of a NEA and a JFC with the Earth, we obtain

pJFC = 2.6× 10−8 yr−1

pNEA = 1.5× 10−9 yr−1

Namely, one collision of a JFC every ∼ 1.9× 107 yr, and one collision of a NEA every∼ 6.7× 105 yr (objects with diameters > 1 km).


Frequency of collisions

Impact rate (Number of objects with D > 1 km per 100 Myr)

Object Impact velocity (km s−1) Impact rateLPCs 56 0.67JFCs 18 2.6HTCs 40 0.23

Dormant comets 18 1.0-7.8Comet showers 56 <

∼ 70ECAs 18 150

Ratio of the Asteroid/Comet impact rate for different sizes

Diameter: D > 0.2 km D > 1 km D > 5 km D > 10 km D > 15 kmA/C: 40 6.7 2.0 0.19 ∼ 0


Contribution of comet material to the terrestrial planets during thelast formation stages

∗ The Earth formed in a region near the Sun where the high temperature only permitted the condensation

of the most refractory materials (silicates, Fe, Ni). Then, how and from where did the water and other

volatiles rich in H, C, N, O, necessary for life, reach the Earth?

Cometary matter trapped by the Earth(∗)

Cometary matter (g) Time (years) Reference

2.0× 1014−18 2.0× 109 Oro (1961)

1.0× 1025−26 Late accretion Whipple (1976)

3.5× 1021 Late accretion Sill & Wilkening (1978)

7.0× 1023 4.5× 109 Chang (1979)

2.0× 1022 4.5× 109 Pollack & Yung (1980)

1.0× 1023 2.0× 109 Oro et al. (1980)

1.0× 1024−25 1.0× 109 Delsemme (1984, 1991)

6.0× 1024−25 1.0× 109 Ip & Fernandez (1988)

1.0× 1023−26 4.5× 109 Chyba et al. (1990)

3.0× 1024−25 some 108 Fernandez & Ip (1997)

4.5× 1024−25 some 107 Brunini & Fernandez (1999)

(*) the values cited before 1997 were taken from Oro & Lazcano (1997)


Besides water, comets could have implanted on the Earth a largevariety of complex organic molecules


The origin of the terrestrial water: Does it come from comets?

The problem is that the D/H ratio in the water from comets is a factor of about twolarger than that found on the Earth’s oceans! −→ Part of the terrestrial water must havecome from material formed in the outer asteroid belt.

Fig. 3. D/H ratios in different objects of the solar system. Data are from (1, 2, 5–7, 26–28) and references therein. Diamonds represent data obtained by in-situ mass spectrometry measurements, and circles refer to data obtained by astronomical methods.

/ sciencemag.org/content/early/recent / 11 December 2014 / Page 6 / 10.1126/science.1261952

In order to be depleted in deuterium (with respect to comets), the H2O ice must have sublimated. The

gaseous H2O molecules have the capacity to transfer their deuterium to the hydrogen molecules of the

protoplanetary disc through the reaction:

HDO + H2 ⇀↽ H2O + HD


Some meteorites (carbonaceous chondrites) seem to have the rightD/H and 15N/14N isotopic ratio

Marty (2012)


THANK YOU FOR YOUR ATTENTION!


lecture 4 : comets origin and interrelations · lecture 4 : comets origin and interrelations...

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