Transneptunian object 2003 UB 313 as a source of comets

ISSN 0038-0946, Solar System Research, 2007, Vol. 41, No. 1, pp. 46–55. © Pleiades Publishing, Inc., 2007.Original Russian Text © A.S. Guliev, 2007, published in Astronomicheskii Vestnik, 2007, Vol. 41, No. 1, pp. 51–60.

46

INTRODUCTION

The question about the presence of large transneptu-nian bodies that inject specific comets observable fromthe Earth was raised previously (Guliev, 1986; 1987;1992). Subsequently, we developed this idea in manypapers, some of which are given in the list of referencesat the end of this paper. In these papers, the emphasiswas, on the one hand, on the distribution of intermedi-ate comet aphelia and, on the other hand, on the trendsinherent in the comet crossings in the chosen planes.Recall that when the cited papers were written, therewas no information about Kuiper Belt bodies. Amongthe largest Kuiper Belt bodies found to date, the objectoriginally designated as 2004 SB 60 corresponds mostclosely in its parameters to our original prediction(Guliev 1986; 1987; 1989). It will be discussed at theend of this paper.

The distribution of transneptunian comet apheliawas analyzed by Guliev and Dadashov (1989). Asregards the distribution of comet crossings in this con-text, it was subsequently developed and studied indetail for Pluto (Guliev and Nabiev, 2001; 2004; 2005),i.e., for a typical transneptunian large planetary body.Our analysis has shown that Pluto may well be a sup-plier of observable comets.

Recently, another large transneptunian object tenta-tively designated as 2003 UB 313 has been recorded inastronomical catalogs. According to preliminary calcu-lations, it surpasses Pluto in mass and size. The discov-ery of this object necessitates investigating the distribu-tion of orbital nodes for long-period comets (below

referred to as cometary nodes) relative to its plane ofmotion. This is the main goal of our paper.

ON THE SEARCH FOR EVIDENCEOF INTERRELATION BETWEEN COMETS

AND 2003 UB 313

An observable comet injected by a distant planetshould have the following properties. If the semimajoraxes of the planetary and cometary orbits are compara-ble, then the aphelion of the latter must be in the regionof motion of the “parent” body. Otherwise, a distantnode of the cometary orbit should be in this region. Ifthe comet has a zero orbital inclination with respect tothe plane of motion of the planet, then the latter condi-tion is optional.

One corollary concerning the comets and 2003 UB313 follows from the above considerations. If the latteris a source of comets, then the number of cometarynodes should increase near its orbit. The object 2003UB 313 moves in the plane with the parameters

(1)

at the distances

(2)

Consequently, to a first approximation, one mightexpect an increase in the number of cometary nodes inplane (1) and interval (2). Naturally, we are talkingabout the distant cometary nodes. If the expectedexcess is confirmed by the facts, then, changing condi-

Ω 35°.875; i 44°.177= =

37.8 R 97.6 AU.< <

Transneptunian Object 2003 UB 313 as a Source of Comets

A. S. Guliev

Shemakha Astrophysical Observatory, National Academy of Sciences of Azerbaijan, Shemakha, 373243 Azerbaijan

Received November 8, 2005

Abstract

—The possibility of interrelation between long-period comets and 2003 UB 313, a recently discov-ered large Kuiper Belt body, is investigated. For this purpose, 78 objects crossing the plane of motion of thisbody at distances from 37.8 to 97.6 AU have been selected from 860 long-period comets. The overpopulationof comets with this characteristic is also considered. The plane of motion of 2003 UB 313 is compared with theorbital planes of other objects in number of comet crossings in the specified distance interval or in some partsof it. A statistically significant overpopulation of elliptic and intermediate comets with the corresponding orbitalnodes has been established. Recently discovered and absolutely faint comets show the best effect in this sense.The same is also true for comets with osculating eccentricities

e

< 1. A similar result is also obtained for cometswith “original”

a

–1

> 0.010000. It is hypothesized that the 2003 UB 313 family is present among the 78 comets.Four of them have aphelion distances from 37.8 to 97.6 AU. An ellipticity is traceable in the distribution of someof the 78 distant nodes. This may be considered as a further argument for the suggested hypothesis. Generally,the body 2003 UB 313 may be assumed to play a prominent role in injecting observable comets from the tran-sneptunian region

PACS numbers: 96.30.ï‡, 96.25.Bd

DOI:

10.1134/S0038094607010054

SOLAR SYSTEM RESEARCH

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TRANSNEPTUNIAN OBJECT 2003 UB 313 AS A SOURCE OF COMETS 47

tion (2), narrower bands or regions near the orbit of thetransneptunian object 2003 UB 313 can be searchedfor. In this case, other parameters of the object shouldalso be taken into account:

(3)

Since 2003 UB 313 is a distant and massive objectcompared to Pluto, one may expect the excess ofcometary nodes near its orbit to be also more pro-nounced.

The method for testing the overpopulation ofcometary nodes applied in this paper is essentially thesame as that used for Pluto (Guliev and Nabiev, 2001).Let us briefly remind its essence as applied to our prob-lem. Initially, the number of cometary nodes (

N

) rela-tive to the reference plane (1) under condition (2) isfound. Subsequently, the parameters

Ω

and

i

are variedin a certain way; thus, various comparison planes areconsidered and the number of cometary nodes undercondition (2) is determined from them. Following thetechnique used in the cited paper, for comparison wewill use data on 67 planes chosen as follows. We varythe parameter

Ω

between

0°

and

330°

at

30°

steps andthe inclination

i

between

0°

and

90°

(a total of 6 values)in such a way that

sin

i

has equal steps. In this arrange-ment of (

Ω

,

i

) pairs, the corresponding planes will haveequidistant poles.

After the corresponding calculations, we will have67 values of the number of crossings (

N

i

) or cometarynodes from which the mean ( ) and rms deviation (

σ

)can be obtained.

If 2003 UB 313 is actually an injector of comets,then the normalized difference

in the total population of comets (below referred to asTP) or in certain cometary systems should be not onlypositive, but also statistically significant. In this case,naturally, the distance interval (2) can occasionally benarrowed and its individual parts can occasionally beconsidered. In addition, the isolation of certain cometscompared to TP can also serve as circumstantial evi-dence for the interrelation between the transneptunianobject and these comets. Therefore, this possibility willalso be investigated in our paper.

It should also be noted that we will use Student’sdistribution to determine the confidence probability ofthe difference

t

. This is legitimate for a normal distribu-tion of 67 values of the number of cometary nodes.

THE COMETARY DATA USED

In this paper, we used the cometary data collected inthe catalog by Marsden and Williams (2005). However,the Kreutz family comets, periodic comets, and inter-mediate comets whose aphelion distances do not reach37.8 AU were excluded from this data set. Thus, ourbase list covers the data for 860 comets. This base was

e 0.4416; ω 151°.311.= =

n

t n n–( )/σ=

used to compile an electronic catalog that allows thecharacteristics of this set to be instantaneously deter-mined not only relative the ecliptic, but also in anyother system.

We analyzed in detail the data for the following cat-egories of comets in terms of the formulated problem:

– all of the comets without exception from the com-piled list;

– comets with osculating eccentricities

e

< 1 (“ellip-tic” comets);

– comets with various absolute magnitudes;– intermediate comets with aphelion distances from

37.8 to 97.6 AU;– comets discovered in certain time intervals;– all of the comets with the exception of those with

a suspected dynamical link to other planets;– comets grouped by “original”

a

–1

.We calculated the heliocentric distance of the distant

cometary node using the formula

where

Here,

i

p

and

Ω

p

are the parameters to be investigated foroverpopulation of cometary nodes in the plane,

Ω

and

i

are the elements of the cometary orbit, and

L

and

B

areits longitude and latitude, respectively.

RESULTS OF COMETARY NODE CALCULATIONS

The number of cometary nodes relative to the refer-ence plane (1) under condition (2) is

n

= 78. A list ofthese comets and the corresponding values of

R

aregiven in Table 1. A comparative analysis for otherplanes shows that this number is at the level of the meanobtained from 67 comparison planes. In other words,the confidence probability (

α

) of the difference

t

islower than the required value of 0.95. To prove thelegitimacy of apply here and below Student’s distribu-tion for 67 values of

n

i

, we calculated the theoreticalfrequencies of the normal distribution (Gmurman,2000). Our comparison of these frequencies with

N

i

using the Pearson

χ

2

test revealed an insignificant devi-ation.

At the next step of our calculations, we analyzed theindividual parts of interval (2) in terms of the formu-lated problem. We established three zones with anexcess of distant cometary nodes. The first zone corre-sponds to the

R

interval 49.05–54.16 AU with 14 comet

Rq 1 e+( )

1 e 1x

1 y2–-------------⎝ ⎠

⎛ ⎞ 2

––

----------------------------------------------,=

x B ip B ip L Ωp–( );sinsincos–cossin=

y i ip i ip Ω Ωp–( ).cossinsin–coscos=

48


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GULIEV

crossings. The results of our cometary node calcula-tions for this interval are presented in Table 2.

The data of Table 2 give the following statistical pic-ture:

The second crossing-saturated zone corresponds tothe

R

interval 60.95–71.62 AU (

n

= 20). The distribu-tion

N

(

Ω

p

,

i

p

)

for this interval is given in Table 3.

We see that there are cases where the node frequen-cies exceed

n

= 20, but we are interested in the ultimatestatistical picture. It appears as follows:

n 14; n 8.44; σ 2.61; t 2.10;= = = =

α 0.99.>

n 20; n 12.79; σ 3.54; t 2.04;= = = =

α 0.99.>

Table 1.

List of 78 long-period comets and

R

values

Comet

R

Comet

R

Comet

R

C/2001 W1 37.86 C/1980 E1 49.88 C/2001 A2 64.36

C/1991 Q1 37.96 C/2004 DZ61 49.97 C/1881 W1 64.67

C/1943 W1 38.22 C/1903 M1 50.18 C/1999 K8 64.98

C/2002 P1 38.78 C/1861 J1 51.24 C/2000 CT54 65.18

C/2002 F1 38.81 C/2003 S4 51.46 C/1997 A1 66.07

C/1997 G2 39.47 C/2004 U1 51.54 C/1618 V1 66.57

C/1304 Y1 39.83 C/1989 A5 52.4 C/1884 A1 66.82

C/2003 K1 40.16 C/1822 K1 53.09 C/1940 O1 68.09

C/1968 L1 40.26 C/1992 U1 53.21 C/1888 P1 69.75

C/1925 F2 41 C/1986 E1 53.3 C/1892 F1 70.57

C/1973 N1 41.64 C/1987 Q1 53.97 C/1968 U1 71.26

C/1999 T3 42.36 C/1813 G1 54.16 C/2004 B1 71.62

C/1997 J1 43.38 C/1880 G1 55.47 C/2004 L2 73.51

C/1900 B1 44.08 C/2002 R3 56.41 C/1989 Q1 75.72

C/2004 K1 44.18 C/1892 W1 57.04 C/1582 J1 79.39

C/1853 G1 44.36 C/1930 E1 57.25 C/2001 a1 79.43

C/1860 U1 44.64 C/1790 A1 57.61 C/2003 V1 79.94

C/1973 D1 44.95 C/1948 R1 58.49 C/2003 J1 81.03

C/1538 A1 46.58 C/1997 BA6 60.95 C/1952 Q1 81.77

C/2001 O2 46.81 C/2003 L2 61.09 C/1896 C1 82.22

C/1999 J4 47.97 C/1989 X1 62.06 C/1796 F1 82.55

C/1810 Q1 48.21 C/1999 K3 62.12 C/2002 V2 86.92

C/1857 D1 48.81 C/2003 G1 62.14 C/1990 E1 89.52

C/2003 G2 49.05 C/1968 Q2 62.38 C/1981 H1 89.75

C/1857 O1 49.25 C/2005 L2 63.12 C/1956 F1-A 90.82

C/1723 T1 49.55 C/2004 X2 63.2 C/2000 OF8 94.08

Table 2.

Distribution N(Ωp, ip) in the interval 49.0−54.2 AU

Ωp,deg

ip, deg

0 9.59 19.47 30 41.81 56.44 90

0 3 7 9 9 5 8 6

30 8 10 10 5 6 8

60 9 6 12 7 8 14

90 4 11 10 8 9 13

120 9 9 7 11 6 13

150 9 16 8 8 9 10

180 11 11 7 10 9

210 9 11 10 7 9

240 8 8 5 8 5

270 4 11 6 5 7

300 8 12 11 11 11

330 3 10 6 6 10

SOLAR SYSTEM RESEARCH Vol. 41 No. 1 2007


Finally, the third, less saturated zone corresponds to theR interval 79.39–82.55 AU:

In this case, t does not reach the desirable level, but lagsbehind it only slightly.

Three types of eccentricities (elliptic, e < 1; para-bolic, e = 1; and hyperbolic, e > 1) of long-period com-ets are encountered in the cometary catalog (Marsdenand Williams, 2005). For our problem, the case of e < 1is of greatest interest. In the two remaining cases, eitherthe probability of the orbits being inaccurate is high orthe osculating orbits differ markedly from the “origi-nal” ones. Compared to the two remaining types, theelliptic comets (N = 282) give higher values of t, but astatistically significant result is obtained only in the Rinterval 60.9–69.8 AU:

When analyzing long-period comets with variousmagnitudes in terms of our problem, we have estab-lished the following. A statistically significant negativevalue of t over the whole interval (2) is characteristic of

comets with absolute magnitudes exceeding 6 2 (ourlist contains 263 such comets):

As regards fainter comets, we failed to find any sig-nificant deviations for them:

Of course, comets with unknown absolute magni-tudes were not included in our analysis. The revealedpeculiarity of absolutely bright comets arouses consid-erable interest, since usually bright and, hence,“young” comets in such situations exhibit interestingtrends. Note that studying the cometary data relative tothe plane of motion of Pluto, we (Guliev et al., 2005)recently obtained essentially the same result.

When distributing the comets in discovery epochs,we have found a very interesting trend, which isreflected in the figure. We see that if the comets aregrouped by discovery epochs (e.g., after 1900, 1925,etc.), then higher values of t will correspond to later dis-covered comets. For comparison, the results of ourcometary node calculations relative to the plane ofmotion of Saturn (2000) in the R interval 9–9.8 AU arealso presented in this figure. In this case, there is thesame trend, but it is much less clear. The advantage inthe case of calculations for Saturn is that the values of tfor any time interval are statistically significant.

Incidentally, the distant node for the same comet canbe located near the orbits of several planets. Therefore,

n 7; n 3.35; σ 2.00; t 1.83;= = = =

0.90 α 0.95.< <

n 10; n 4.03; σ 2.01; t 2.96;= = = =

α 0.99.>

m.

n 15; n 25.99; σ 4.67; t 2.00– ;= = = =

α 0.99.=

n 18; n 17.75; σ 3.90.= = =

this possibility must somehow be taken into accountwhen counting the crossings. For this purpose, we suc-cessively excluded the comets from the general list thatcorresponded to the Jovian, Saturnian, etc. zones.Every time we took Ωp and ip (2000) of the correspond-ing planet and its perihelion and aphelion distances asthe boundaries for the nodes. Our calculations showthat t actually changes for this sorting (the number ofremaining comets is N = 741); it decreases in some ofthe above intervals and increases in others. In particu-lar, the R interval 47.96–54.16 AU in this case has anexcess of crossings:

n 15; n 8.99; σ 2.99; t 2.04;= = = =

α 0.99,>

Table 3. Distribution N(Ωp, ip) in the R interval60.95−71.62 AU

Ωp,deg

ip, deg

0 9.59 19.47 30 41.81 56.44 90

0 14 17 11 15 12 14 13

30 13 9 15 14 15 11

60 6 13 12 18 14 9

90 14 14 7 11 21 11

120 11 13 7 14 11 11

150 10 11 6 7 14 12

180 15 15 11 9 15

210 16 10 8 12 11

240 10 15 14 18 9

270 16 17 15 9 23

300 16 12 9 22 14

330 15 16 16 9 10

20101890 1910 1930 1950 1970 1990T, years

00.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0t

Distribution of parameter t for comets in discovery epochsafter year T (the squares and diamonds correspond to 2003UB 313 and Saturn, respectively).

50


GULIEV

while in the R interval 79.38–82.22 AU,

At the same time, the value of t = 1.6 in the R interval60.9–69.8 AU is positive, but it is below the admissiblelimit.

Subsequently, we studied the data for intermediatecomets in terms of the formulated problem. For thispurpose, we selected objects with aphelia in the R inter-val 37.8–97.6 AU (N = 28) from the general list. Thefollowing result was obtained from them in the interval40.2 < R < 51.5 AU:

Curiously enough, three of these objects (C/2003 K1,C/2003 S4, and C/2004 DZ61) were discovered after2000, while the fourth object (C/1857 O1) was discov-ered much earlier.

When intermediate comets are analyzed in terms ofour problem, the following should be kept in mind. Anobject that has escaped from the sphere of action of theplanet 2003 UB 313 and that has the minimum value ofQ can have a distant node outside interval (2). The min-imum perihelion latitude relative to plane (1) can be anadditional criterion as to whether this object belongs tothe planet’s family. Our calculations show that in thisrespect, apart from the four listed comets, the objectC/2005 O2 with the following parameters is of greatestinterest:

n 6; n 2.41; σ 1.69; t 2.13;= = = =

α 0.99.>

n 4; n 1.69; σ 1.15; t 2.01;= = = =

α 0.99.>

R 34.98 AU; B' 10.63; Q– 44.00 AU.= = =

As we have noted above, to a first approximation,our reference interval (2) covers a large belt in plane(1). However, for greater clarity in the question understudy, this belt should be replaced with a relatively nar-row band along the orbit of the transneptunian body. Inother words, a certain ellipticity resembling the elliptic-ity of the orbit of 2003 UB 313 itself should be trace-able in the distribution of nodes in the plane. Of course,we are talking about the possible statistical correlationbetween the heliocentric distances of the nodes, on theone hand, and the planet’s distances, on the other hand.In other words, to improve the statistics, we must alsotake into account parameters (3) in our calculations.

To check the ellipticity of the points, we calculated

R

for the body under study in the directions of the dis-tant nodes for 78 comets. If these comets are not relatedto the object 2003 UB 313, then we should expect thefollowing: the distribution of differences

|∆

R

|

betweenthe heliocentric distances of the object and the corre-sponding crossings in the interval 0–53.4 AU should bechaotic. If the reverse is true, then the distribution ofthis quantity should have a maximum at low values.

The distribution of

|∆

R

|

in this interval for 78 cometsis presented in Table 4. We see that it is by no meanschaotic and has extrema that qualitatively agree withour working hypothesis about the relationship of com-ets to the planetary body. For comparison, this tablegives a similar distribution for TP, which shows theopposite behavior of the distribution.

The correlation coefficient between the distances ofthe planet and the nodes for 78 comets is only 0.053.However, if the objects are arranged in order of increas-ing

∆

R

, then it can be easily verified by graduallyexcluding the extreme comets that there is a clear cor-relation for 70 of the objects under consideration with aconfidence probability higher than 0.95. This trenddoes not apply only to the comets C/2004 K1, C/2004DZ61, C/2003 G2, C/1986 E1, C/1973 N1, C/1853 G1,C/1980 E1, and C/2002 V2. The subsequent exclusionsshowed that, for example, the correlation coefficient forthe remaining 62, 58, 54, 29, and 16 comets is 0.37,0.53, 0.61, 0.90, and 0.98, respectively.

Another method for checking the ellipticity in thedistribution of crossings can be the substitution of otherfictitious values for the parameter

ω

of 2003 UB 313and comparison of the derived distribution of crossingswith the original picture. Let us explain this using a spe-cific example. Our calculations show that the sum of theabsolute values of

∆

R

relative to plane (1) is

(4)

For comparison, let us now vary

ω

between

0°

and

340°

at

20°

intervals and calculate

Σ|∆

R

|

for each case(Table 5).

As we see from the data of the table, the sum in allof the cases under consideration exceeds (4), whichonce again proves the presence of evidence for elliptic-ity in the distribution of cometary nodes in plane (1).

Σ ∆R 1511.=

Table 4.

Distribution of

|∆

R

|

for 78 comets and TP in the

R

interval 0–54 AU

|∆

R

|

, AU 0–9 9–18 18–27 27–36 36–45 45–54

For 78 comets 25 19 17 8 5 4

for TP 32 35 45 113 119 106

Table 5.

Dependence of the sums

|∆

R

|

on

ω

ω

, deg 0 20 40 60 80 100

Σ|∆

R

|

1737 1737 1714 1763 1823 1825

ω

, deg 120 140 160 180 200 220

Σ|∆

R

|

1735 1628 1550 1537 1550 1656

ω

, deg 240 260 280 300 320 340

Σ|∆

R

|

1606 1656 1647 1648 1680 1726


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To make sure that there is evidence of ellipticity inthe distribution of 78 cometary nodes in plane (1), weresorted to the third checking method. Retaining theorbital elements

e

,

q

,

and

ω

of 2003 UB 313, we variedthe elements

Ω

p

and

i

p

of its plane according to theabove method and, in this way, obtained a set of

R

val-ues for the cometary nodes relative to 67 “pseudoplan-etary” planes.

Their comparison with the principal plane for inter-val (2) revealed the following picture.

Σ|∆

R

|

for 63planes is considerably higher. Only for four planes is itslightly lower than that in plane (1). If

R

is limited to theinterval 55–96.7 AU, then plane (1) will lag behind inparameter

Σ|∆

R

|

. Consequently, we got another argu-ment for ellipticity in the distribution of cometarycrossing points in plane (1).

Further analysis shows that the mentioned ellipticityis particularly distinct for absolutely faint comets. In

particular, for 19 long-period comets with

H

10

> 7 4

,the correlation coefficient between

R

p

(the planet’sheliocentric distance at the corresponding longitude)and

R

n

(the node distance) is

We also performed such an analysis based on the datafor comets with known “original” values of

a

–1

from thecatalog by Marsden and Williams (2005). Our analysisrevealed 46 such comets among the 78 comets. In thiscase, a positive correlation with a confidence probabil-ity

α

> 0.95 is observed for 15 of these comets withnode distances exceeding 65 AU:

In both cases, the confidence probability of the correla-tion coefficient was determined from Student’s distri-bution.

During our subsequent analysis, we will considerone alternative point of view that arose during thedebate over our previous paper (Guliev and Nabiev,2001). Recall that the cited paper is very similar in goaland technique to this paper; the difference lies only inthe object under study. We are talking about the depen-dence of the table cells

N

(

Ω

p

,

i

p

) from which the meanand variance are calculated. To be more precise, thedata for the same comet to some degree affect the vari-ous cells, thereby making them interdependent. Tomake the data of this table independent, we resorted tothe successive exclusions of crossings from our analy-sis. For example, if n1 comets cross the plane with ip = 0°and Ωp = 0° in the R interval 37.8–97.6 AU, then theywill be excluded from the subsequent analysis and thenumber of crossings is replaced with their frequency,i.e., h = N1/860. For the next plane with ip = 9.59° andΩp = 0° , the crossing frequencies for (860 – N1) cometsetc. are analyzed in a similar way. Thus, the exclusioncycle of the already used cometary data covers 66 cellsof the corresponding table. The crossing frequencies in

m.

K Rp Rn,( ) 0.47; α 0.95>( ).=

K Rp Rn,( ) 0.64.=

the cells then prove to be completely independent. Thecalculations performed according to this scenarioyielded t = 1.54. However, according to the data after1950 (Table 6), this parameter is considerably higherand more significant:

where h is the crossing frequency for the referenceplane and is the mean frequency for 67 planes. Theparameters h and t after 1950 increased by almost 30and 90%, respectively, and their further increase withtime can be confidently predicted.

Finally, let us analyze the comets grouped by “orig-inal” a–1 from the catalog (Marsden and Williams,2005) in terms of the formulated problem. For this pur-pose, let us divide the entire set of a–1 values into 4groups: more than 10000 units (1 unit = (AU)–1), from1000 to 10000 units, less than 1000 units, and negativea–1. Table 7 gives statistical characteristics of the nodesfor each individual group.

As we see from the table, the first group of comets(objects with minimum orbital sizes) in the R interval49.9–68.1 AU yields the best result. The confidenceprobability of the parameter t for the second group (inthe extended R interval 37.9–81.8 AU) is also higherthan 0.95, which is not the case for the third group (thefifth row). In this group, the value of t does not exceed 1.60even in the densest part of the crossings (49.8–66.1 AU).

h 0.120; h 0.039; σ 0.028;= = =

t 2.95; α 0.999,>=

h

Table 6. Frequency distribution of cometary nodes for67 planes

Ωp, deg

ip, deg

0 9.59 19.47 30 41.81 56.44 90

0 0.05 0.11 0.09 0.12 0.04 0.11 0.04

30 0.03 0.04 0.03 0.06 0.08 0.05

60 0.03 0.03 0.02 0.05 0.03 0.07

90 0.04 0.03 0.02 0.03 0.03 0.14

120 0.03 0.03 0.02 0.02 0 0.06

150 0.04 0.04 0.02 0.03 0.04 0.1

180 0.04 0.02 0.03 0 0.04

210 0.04 0.02 0.04 0.06 0.02

240 0.03 0.04 0.03 0.03 0.02

270 0.03 0.01 0.02 0.03 0.04

300 0 0.02 0.02 0.08 0.06

330 0.01 0.01 0.03 0.01 0.04

52


GULIEV

The fourth row of the table gives the combined picturefor the first two groups. Here, t is 2.35 and its confi-dence probability is higher than 0.99. The results of ourcalculations for “hyperbolic” comets are presented inthe sixth row. Thus, comets with highly eccentric orbits(there are also “new” comets among them) are noteffective enough in terms of our problem, while cometswith hyperbolic eccentricities yield a negative result.

DISTINCTIVE FEATURES OF THE SELECTED GROUP OF COMETS

When comparing the selected group with the totalpopulation of comets, we have found the following dis-tinctive characteristics.

(1) Magnitudes. As we have already found, the num-ber of absolutely bright objects in the selected group of78 comets is relatively small. This is the first distinctivefeature of the group. Table 8 gives the distribution ofparameter H10 for 48 of the selected comets (n1) and604 of the total population (n2). Of course, in the caseunder consideration, our analysis covers only cometswith known H10.

A more detailed comparison shows that the fraction

of comets with absolute magnitudes up to 6 3 is 31%in the selected group and 41% in the total population.

(2) Pattern of dependence H10(q). There is aninverse relation between these quantities in the totalpopulation, which is the result of observational selec-tion. This is particularly true for comets with q > 1 AU.Indeed, as our calculations show, the regression equa-tion for comets with q from 1 to 3 AU is

(the number of comets is n = 209 and the residual vari-ance is 11817). For the selected comets with similar q,it has the empirical form

(the number of comets is n = 20 and the residual vari-ance is 120). This sharp difference of the selected com-ets may not suggest that they are physically isolated,but together with some of the dependences concerningphysical parameters, it arouses considerable interest.

(3) Perihelion distances. Analysis shows that theselected group of 78 comets differs from TP in q distri-bution. To test the significance of the difference, weresorted to the Wilcoxon test (Gmurman, 2000). Thevalues of q for these comets are distributed in the range0.1447–6.812 AU. We divided this range into 7 inter-vals of equal length and counted the numbers of perihe-lia for the comets of the selected group and TP in eachof them. After the standard procedure, the observedvalue of the Wilcoxon distribution turned out to belower than the critical one at a 0.05 significance level.This implies that the two distributions N(q) disagree.TP of 860 comets has

= 1.592 (at σ = 1.565),

while the selected group has

= 2.225 (at σ = 1.593).

m.

H10 q( ) 7.71 0.32q–≈

H10 q( ) 5.64 1.04q+≈

q

q

Table 7. Statistical characteristics of cometary groups with various a–1

Interval a–1, 1 unit = (AU)–1 N R, AU n σ t

>10000 unit 44 49.9–68.1 5 1.57 1.00 3.43

From 1000 to 10000 unit 122 37.9–81.8 17 9.71 3.68 1.98

>1000 unit (combined picture) 166 37.9–53.3 13 7.16 2.34 2.35

From 0 to 1000 units 250 49.8–66.1 1.60

<0 32 37.8–97.6 1 2.87 1.49 –1.25

n

Table 8. Comparison of the absolute magnitudes for twogroups of comets

H10, mag. n1 n2 H10, mag. N1 N2

to 4 2 58 from 7 to 8 12 77

from 4 to 5 8 69 from 8 to 9 6 67

from 5 to 6 5 98 more than 9 7 130

from 6 to 7 8 105



This difference also means that the number N = 78could be even larger, but it is limited by observationalselection.

(4) Perihelion longitudes. Based on the optimalinterval for 78 values and according to the Sturges rule,having chosen an interval with a length close to

so as to cover the entire interval 0°–360°, we con-structed the distribution of perihelion longitudes for thecomets of the selected group and TP. These are reflectedin Table 9.

After the corresponding normalization of N1, apply-ing the Pearson χ2 test (Gmurman, 2000) showed a sig-

nificant excess of (39.8) above (11.1) at a0.05 significance level. In practice, this implies that theselected group has its own pattern of L distributioncompared to TP.

(5) Longitudes of distant nodes. When investigatingthe distant nodes, we decided to pass to a new systemwhere plane (1) would replace the ecliptic and the

∆L 360°/ 1 3.322 78log+( ) 49.4°,≈=

χobs2 χtheor

2

ascending node of the corresponding celestial circlewould be the reference point. After the correspondingcalculations, we were able to construct Table 10 tocompare the two categories of comets.

However, in contrast to the previous case, a simplecomparison gives nothing here. The point is that TP hasa roughly uniform distribution, while the selectedgroup is characterized only by a deficit of nodes insome intervals. Applying the χ2 and Wilcoxon testsshowed no proper agreement in distribution of distantnodes between the two classes of comets. A noticeabledeficit of nodes is observed near the perihelion of theplanet. For example, only 9 nodes correspond to theinterval 93°–182°.

(6) Inclinations of cometary orbits. The distributionof orbital inclinations for the total population of cometsand the selected group is given in Table 11. Here, n1 andn2 are the numbers of inclinations in individual inter-vals and n3 is the effective number of inclinations cal-culated through the corresponding coefficient forapplying the χ2 test (Gmurman, 2000).

It can be easily verified that the observed χ2 value(25.19) exceeds its critical value (9.5) at a 0.05 signifi-cance level. This implies that the distributions of incli-nations for the two classes of comets differ. The differ-ence is related to a deficit and excess of orbital inclina-tions for the selected group of comets in the second andsixth intervals, respectively.

(7) Comet number dynamics. Above, we pointed outthat the parameter t increases with time. It is also inter-esting to trace the pattern of change in the weight ofcomets with R in interval (2) in TP.

Based on the data of Table 12, we can predict thatthe number of such comets and their weight in the totalpopulation will steadily increase in the comingdecades. It should also be noted that only 20 cometswith aphelion distances from 30 to 100 AU were knownbefore 1980. Their number has doubled over theelapsed period and 13 such comets have been discov-ered only after 2000. The increase in their number iswell ahead of the increase in the number of long-periodcomets as a whole. Therefore, it is believed that interest

Table 9. L distribution for two types of comets

L, deg 0–51.4 51.4–102.9 102.9–154.3 154.3–205.7 205.7–257.1 257.1–308.6 308.6–360

N1 12 16 11 7 14 13 5

N2 110 135 123 98 134 181 79

Table 10. Ω' distribution for two types of comets

Ω', deg 0–51.4 51.4–102.9 102.9–154.3 154.3–205.7 205.7–257.1 257.1–308.6 308.6–360

N1 14 11 4 13 12 17 7

N2 142 120 83 122 115 142 136

Table 11. Distribution of orbital inclination i for comets ofTP and the selected group

i, deg 0–30 30–60 60–90 90–120 120–150 150–180

n1 6 10 18 21 15 8

n2 62 153 188 215 179 63

n3 66.14 110.26 198.46 231.54 165.38 88.21

Table 12. Percentage change in the number of comets fromthe selected group with time

1900 1925 1950 1975 2000 2005

6.9 6.5 6.5 6.4 7 9

54


GULIEV

in the transneptunian zone in the context of cometarycosmogony zone will increase in future.

DISCUSSION OF RESULTS AND PREDICTIONS

Our calculations and their results show that thehypothesis about the interrelation between some of theobservable long-period and intermediate comets andthe object 2003 UB 313 has weighty arguments. Wecannot unequivocally assert that the number of suchobjects is 78 of the 860 comets, or 9% of the total pop-ulation. However, their number is probably so large thatthey make the selected group isolated in many parame-ters (in magnitude, inclination, directions of the distantnodes and perihelia, perihelion distances, etc.). Theobjects whose distant nodes lie in the immediate vicin-ity of the orbit of 2003 UB 313 are the most likely can-didates for this role. Below, we give a list of eightobjects whose node distances lie within ±1.5 AU of theheliocentric distances of the planet at the correspondinglongitudes: C/1861 J1 (0.05 AU), C/1968 U1(0.76 AU), C/1981 H1 (0.74 AU), C/1989 L2 (1.07AU), C/1999 T3 (1.49 AU), C/2001 A2 (1.22 AU), andC/2005 L2 (1.07 AU). In addition, the comets witheither low inclinations or the highest inclinations (i.e.,about 180°) with respect to plane (1) should also bekept in mind. The parameter R for them can lie outsideinterval (2). The following comets in our list arouseinterest in this sense: C/1368 E1 (175.1°), C/1847 C1(9.8°), C/1905 W1 (172.6°), C/1949 K1 (173.5°),

C/1968 U1 (175.3°), C/1983 O1 (175.4°), and C/1999U4 (8.2°).

A transneptunian planet even with the mass of Plutoat distances of ~90 AU can have a sphere of influencecomparable to that of Jupiter. It can actively interactwith closely passing Kuiper Belt bodies and directsome of them to the visibility zone. Direct collisionswith these bodies are not ruled out either. After suchcollisions, the ejection fragments can exist as observ-able comets.

In conclusion, we present (Table 13) the results ofour calculations to test some of our previous results(Guliev, 1987; 1989; 1992; 1999) on comet crossings.Recall that the amount of cometary data has increasedfrom 24% to 45% since the publication of the citedpapers. As a result of this increase (the accuracy of thedata also increased), the “random” effects that wefound from cometary nodes could completely or par-tially disappear. To make the parameters , σ, and tmore reliable, we decided to increase the number ofplanes from 67 to 229.

In three cases, the values of t are fairly high. In thesecond zone, it slightly lags behind the critical value oft = 1.96 (at a 0.05 significance level). Generally, it maybe assumed that the increase in the amount of data notonly retained, but also increased the reliability of theprevious conclusions regarding the identified zones.The first among these zones arouses particular interestbecause of its proximity and high t. Recall in this con-nection that a relatively large Kuiper Belt body, 2004SB 60, was recently discovered in this zone. Table 14gives data for comparison of its parameters with ourpredictions (Guliev, 1987; 1989).

While noting a similarity between the data, we donot rule out the possibility of discovering an even moremassive planetary body in this zone in future.

ACKNOWLEDGMENTS

I wish to thank R.A. Guliev for help with the calcu-lations. I am also grateful to B. Marsden, who kindlyprovided the cometary catalog (2005).

REFERENCES

Gmurman, V.E., Teoriya veroyatnostei i matematicheskayastatistika (Theory of Probability and Mathematical Sta-tistics), Moscow: Vysshaya Shkola, 2000.

Guliev, A.S., On the Hypothetical Planet of the Solar System,Astron. Tsirk., 1986, no. 1430, pp. 6–8.

Guliev, A.S., A Possible Existence of an Unknown Planet inthe Neptune–Pluto Region, Kinematika Fiz. NebesnykhTel, 1987, vol. 3, no. 2, pp. 28–33.

Guliev, A.S., On Periodic Comet Bradfield 2, Komet. Tsirku-lyar, 1989, no. 406, pp. 4–5.

Guliev, A.S. and Dadashov, A.S., Transplutonian CometaryFamilies, Astron. Vestn., 1989, vol. 23, no. 1, pp. 88–95.

n

Table 13. Results of our analysis of cometary nodes in indi-vidual zones

Stat. charac-teristic

ip, deg; Ωp, deg; R, AU

25.6; 285.6;30.1–37.7

29.6; 272.7;50.7–55.7

30.5; 341;99.6–117.5

85.84; 272.6;250.2–401.96

n 41 13 17 32

24.69 8.50 10.70 17.20

σ 4.92 2.63 3.06 5.49

t 3.31 1.71 2.06 2.70

n

Table 14. Comparison of the data for the transneptunian ob-ject 2004 SB60 and the predicted planetary body

Transneptu-nian object a e ω Ω i

Pl X 36.9 AU 0.11 287° 285°.6 25°.6

2004 SB60 41.89 AU 0.11 308° 280° 23°.9

Deviation 11% 0% 6% 2% 2%



Guliev, A.S., The Possible Existence of Two TransplutonianPlanets, Pis’ma Astron. Zh., 1992, vol. 18, no. 23,pp. 182–188 [Astron. Lett. (Engl. Transl.), vol. 18,no. 23, p. 75].

Guliev, A.S., Results of Investigations of Nodal Distances ofLong-Period Comets, Kinematika Fiz. Nebesnykh Tel,1999, vol. 15, no. 1, pp. 85–92.

Guliev, A.S. and Nabiev, Sh.A., Pluto and Comets. 1. Is Therea Group of Comets Associated with Pluto, KinematikaFiz. Nebesnykh Tel, 2003, vol. 18, no. 6, pp. 525–531[Kinematics Phys. Celest. Bodies (Engl. Transl.), 2003,vol. 18, part 6, pp. 370−374].

Guliev, A.S. and Nabiev, Sh.A., Pluto and Comets. 2. Somepeculiarities of a cometary group probably associated

with Pluto, Kinematika Fiz. Nebesnykh Tel, 2004, vol. 20,no. 3, pp. 283–288 [Kinematics Phys. Celest. Bodies(Engl. Transl.), 2004, vol. 20, no. 3, pp. 205–208].

Guliev, A.S. and Nabiev, Sh.A., Pluto and Comets. 3. Possi-ble relationship mechanisms, Kinematika Fiz. NebesnykhTel, 2005, vol. 21, no. 1, pp. 53–59. [Kinematics Phys.Celest. Bodies (Engl. Transl.), 2005, vol. 21, no. 1,pp. 40−44].

Guliev, A.S., Abbasov, Dzh.G., and Kakhramanov, G.M., OnAbsolutely Weak Long-Period Comets, Tsirk. ShAO,2005, no. 109, pp. 54–58.

Marsden, B.G. and Williams, G.V., Catalogue of CometaryOrbits, 16th ed., Cambridge: SAO, Solar, Stellar & Plan-etary Science Division, 2005.

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Transneptunian object 2003 UB 313 as a source of comets