The problem of too a high mass of Oort Cloud in its …lal.univ-lille1.fr/talks-oortws2011/LN.pdflower actual ﬂux of new comets and, consequently, a lower OC population L. Neslušan

The problem of too a high mass of Oort Cloudin its cosmogony

L. Neslušan

Astronomical Institute, Slovak Academy of Sciences, 05960 Tatranská Lomnica, Slovakia;E-mail: [email protected]

Workshop on the formation and dynamics of the Oort CloudLille, France

L. Neslušan (Astron. Inst. S.A.S.) High-mass problem in Oort-Cloud cosmogony 1 / 22

Introduction

In this contribution:

on an occurence of the „high-mass problem”

on new circumstances which could help us to solve the problemwithin the current main-stream concept

about unification of cometary cosmogony with the cosmogony ofTN structures and cosmogony of giant planets


Introduction

the current main-stream theory: the nuclei formed in the outerregion of once existing PPD and were ejected into the largeheliocentric distances by giant planets (Uranus & Neptune)

the main problem of this concept: too a high total mass of the OCestimated

→ too a large amount of solids in the PPD

→ too a high angular momentum of OC and

→ too a high orbital energy of comets with respect to that ofejecting planets


High-mass problem

recent simulations of the OC formation have yielded a lowefficiency of the ejection process to the OC:

◮ Duncan et al. (1987): ∼5% in outer OC at 4.5Gyr◮ Dones et al. (2004): 1.7% to 2.5% in outer OC at 4Gyr◮ Dybczynski et al. (2008; 2009), Leto et al. (2008): ∼0.3% at 2Gyr◮ Kaib & Quinn (2008): 1.0−1.5%

the low efficiency requires a large original mass in solids in thePPD; 3−6 times exceeding the mass according to the concept ofMMSN (Dones et al., 2004)


Recently revealed facts

there are several new discoveries/facts which should be taken intoaccount in course to correct the old, main-stream theory or at afurther development of the new theory by Levison et al. (2010)

a brief summary of news...



Hughes (1981) found a break in the size distribution of cometnuclei at absolute magnitude Hb ≈ 6.5, which he explained as aconsequence of the observational selection

however, Francis (2005) analysed the data gained within theLINEAR program and, as a result, suggested that the break is real

→ the number of comets with decreasing size does increase as1.07H−Hb , i.e. much more slowly than believed before (2.2H−Hb )

Francis also derived about 5 times lower flux of LP comets withH < 10.9 than Everhart (1967); the Everhart’s flux has often beenused to estimate the OC population



Another argument for a lower OC population: a higher discoveryefficiency of dynamically new comets in comparison with the oldcomets (Neslušan, 2007).The OC population uses to be estimated in the following way:

estimated number of OC comets == (actual (seen+unseen) flux of new comets through the ZV)//(amount of OC comets predicted to appear in the ZV during agiven period)

actual flux of new comets == (observed/discovered flux of new comets) ×× (correction factor for the observational incompleteness, 1/η)



or,

nall =ncat

ηnew=

1ηall

ncat + lcat

ncat +(ηnew/ηold)lcatncat ,

in the old estimates ηall = (ncat + lcat)/(nall + lall) was used

it was, therefore, assumed that ηnew = ηold = ηall

the efficiency of the discovery of new comets is higher than that ofold comets: ηnew > ηold (also ηnew > ηall ); or, rather, ηnew ≫ ηold

(ηnew ≫ ηall)

the lower correction factor (higher discovery efficiency) implies alower actual flux of new comets and, consequently, a lower OCpopulation



The fact that ηnew ≫ ηold can be documented...

0

0.2

0.4

0.6

0.8

1

0 0.005 0.01 0.015 0.02 0.025 0.03re

lati

ve

num

ber

of

com

ets

reciprocal semi-major axis [1/AU]

(Wiegert & Tremaine, 1999) (Marsden & Williams, 2003)



possibility of alternative explanation of the deficit in the1/a-distribution: comets can disrupt or completely extinct and,thus, there are actually less old comets to discover

this possibility can be invalidated comparing the q-distribution ofall long-period comets and new comets

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

rela

tive

num

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of c

omet

s

q [AU]



the selection effects are also well seen comparing theq-distribution of all LP comets and those discovered withinLINEAR

0

20

40

60

80

100

0 1 2 3 4 5 6

num

ber

of c

omet

s

q [AU]

it was estimated: ηnew ∼ 101ηold

this estimate implies the outer-OC population to be few times of1010 bodies



a gradual improvement of the observational technique leads to acertain elimination of the selection effects, which is reflected in atrend in the ratio of known new and old comets, ncat/lcat , whichwould scarcely exist in the case of disruption/extinction:

◮ Oort, 1950: ncat/lcat = 0.58◮ Festou et al., 1993: ncat/lcat = 0.5◮ Neslušan, 2007 (CCO, 2003): ncat/lcat = 0.41 (0.21 according to

the Dybczynski’s criterion)

from LINEAR discoveries (1/a < 10−4 AU; Dybczynski):◮ q < 3AU: ncat/lcat ∼ 0.2; ∼0.04◮ q > 3AU: ncat/lcat ∼ 1.2; ∼0.4


Recently revealed factsif the disruption or complete extinction was the cause of thedisappearance of old comets in their orbital 1/a-distribution, thenthe reduction of the OC population would also be theconsequencethe effect of disruption/extinction actually removes comets fromthis category of objects, therefore there is less undiscoveredobjects and, thus, larger ηold (and larger ηall at the same time)in this case, it would be necessary largely to increase ηall ; if thedisruption/extinction was the dominant effect, then ηall > 0.5for example, if ηall ∼ 0.05 and nall = ncat/ηall ∼ ncat/0.05 for theexplanation due to fading, then nall (nall < ncat/0.5) would be lowerabout the factor of less than ∼10 for the disruption/extinctionconsequently, the OC population would have to be reduced by thecorresponding factorthe reduction is necessary due to else reason than in the case offading domination, but is necessary



Kaib & Quinn (2009) found a largely unexplored pathway ofcomets from the inner OC to the ZV through the Jupiter-Saturnbarrier

it seems that a significant, possibly a prevailing part of newcomets can come from the inner OC

this would allow to consider a less populated outer OC to explainthe observed new-comet flux



Królikowska & Dybczynski (2010) incorporated non-gravitationalforces into the determination process of new-comet orbits thatresulted in a large change of amount of new comets separatedfrom the cataloque of all LP comets

in the sample of 26 comets with precise original orbits having1/aorig. < 10−4 AU−1, only 5 or 6 comets did not appear in the ZVin their previous perihelion passage

→ the Jupiter-Saturn barrier does not appear to be so effectivedynamical barrier that it must be typically overcome within a singleorbital revolution

the population of outer OC can, consequently, be reduced by thefactor equal to the number of repeated perihelion passages ofcomets with 1/aorig. < 10−4 AU−1, in fact


New hints − scattered-disk contribution

Is the total mass of the OC actually as high as was estimated?

In the following, several issues, that should be taken into account at acreation of an improved comet-formation scenario, are outlined.

NEW SOURCE REGIONS of comets regarded as dynamically new:

the study by Królikowska & Dybczynski (2010) indicates thepossibility that the old comets were regarded, in the past, as new(=repeated passages of OC comets through the ZV)

the result by Kaib & Quinn (2009) indicates that a lot of newcomets can originate in the inner OC

as well, many comet-sized bodies today situated in the SD mayevolve to an orbit of OC comet for a limited period (according thestudies of the origin of Jupiter-family comets)


New hints − tide from a dark matterin more precise quantitative calculations, the galactic-tideperturbation should be completed including the term describing anaction of dark matterthe force is evident from the Galactic-rotation curve


New hints − tide from a dark matter

linear increase of mass: M(r) = const .× r

consequently, the x-component of tidal acceleration:

ax = (A−B)(3A+B)x

should be modified to:

ax = (A−B)(3A+B)x +GMo

R3o

x ,

where Mo = 9.0×1010 M⊙ (vcirc. = (220±20)kms−1) andRo = (8.0±0.5)kpc (Binney & Tremaine, 2008, p. 18) for the currentposition of the Sun in the Galaxy


New hints − tide from a dark matter

if we consider ρGM = 0.10M⊙/pc3, then the amplitude ratio of thedominant z-term and dark-matter x-term equals4πGρGM/(GMo/R3

o) = 7.1

for A = (14.8±0.8)kms−1 kpc−1 andB =−(12.4±0.6)kms−1 kpc−1 (Binney & Tremaine, 2008, p. 18),the ratio of known centrifugal x-term and new, dark-matter x-termis 1.15

new term is important at the assumption that the Sun migratednearer to the Galactic center; new term (for M(r) = const .× r ) isGMo/(Ror2); its magnitude is, e.g., 16 times larger in r = 2kpc


New hints − comet formation within a unified theory

the recent models of the OC formation assumed the jovian planetson their current orbits

however, the comet formation cannot be fully clarified until it is notdescribed within a unified theory of the formation of all giantplanets, TNOs, and OC

according to the Nice model (Tsiganis et al., 2005) of giant-planetformation, the orbits of planets were initially in a more compactconfiguration; later, after the occurrence of an instability, Uranusand Neptune penetrated into an outer disk of small bodiesnew studies are needed to be done on:

◮ possible pre-instability stage of the OC formation◮ post-instability stage of the OC formation when migrating Uranus

and Neptune eroded the outer belt of small objects and, likely,ejected a plenty of these bodies to the OC


Conclusions

The old theory of the OC formation, in the PPD, can perhaps beimproved by (except of other):

considering the broken distribution law of comet sizes and largelydifferent discovery efficiency of the new and old comets → itwould reduce the estimate of the OC population

considering some to-outer-OC alternative source regions of „new”comets (like the inner OC, SD, or, possibly, JFC end state) → itwould also reduce the OC population

unification of the concept of OC formation with the concepts ofboth the formation of TNO reservoirs and giant planets (Nicemodel) − an enhanced effectivity of the OC formation couldappear as a consequence


Conclusions

If the high-mass problem as well as another still problematic detailswithin the concept of the OC formation in the PPD cannot be removedtaking the new, above-mentioned, circumstances into accout, then analternative OC theory will be needed.

* * *


REFERENCES

Binney J., Tremaine S.: 2008, "Galactic Dynamics", 2-nd ed.,Princeton Univ. Press, Princeton and Oxford.

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Dones L., Weissman P.R., Levison H.F., Duncan M.J.: 2004, in:Comets II, eds. M. C. Festou, H. U. Keller, and H. A. Weaver, Univ.Arizona, Arizona, p. 153.

Dybczynski P.A., Leto G., Jakubík M., Paulech T., Neslušan L.:2008, A&A 487, 345-355.

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Everhart E.: 1967, Astron. J. 72, 1002.L. Neslušan (Astron. Inst. S.A.S.) High-mass problem in Oort-Cloud cosmogony 22 / 22

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Królikowska M., Dybczynski P.A.: 2010, Mon. Not. R. Astron. Soc.404, 1886-1902.

Leto G., Jakubík M., Paulech T., Neslušan L., Dybczynski P.A.:2008, Mon. Not. R. Astron. Soc. 391, 1350-1358.

Levison H.F., Duncan M.J., Brasser R., Kaufmann D.E.: 2010,Science 329, 187-190.


Marsden B.G., Williams G.V.: 2003, Catalogue of Cometary Orbits2003, 15-th ed., Smithsonian Astrophys. Obs., Cambridge.

Neslušan L.: 2007, A&A 461, 741-750.

Oort J.H.: 1950, Bull. Astron. Insts. Netherlands 11, 91.

Tsiganis K., Gomes R., Morbidelli A., Levison H.F.: 2005, Nature435, 459-461.

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Documents

The problem of too a high mass of Oort Cloud in its …lal.univ-lille1.fr/talks-oortws2011/LN.pdflower actual ﬂux of new comets and, consequently, a lower OC population L. Neslušan