The scattered trans-Neptunian object 1998 XY95

The scattered trans-Neptunian object 1998 XY95

S. J. Collander-Brown,1P A. Fitzsimmons,1 E. Fletcher,1 M. J. Irwin2 and I. P. Williams3

1Department of Pure and Applied Physics, Queens University, Belfast BT7 1NN2Institute of Astronomy, Cambridge University, Madingley Road, Cambridge CB3 0HA3Astronomy Unit, Queen Mary and Westfield College, Mile End Road, London E1 4NS

Accepted 2001 February 16. Received 2001 February 16; in original form 2000 March 13

A B S T R A C T

On 1998 December 12 a new trans-Neptunian object, 1998 XY95, was discovered as part of a

deep search. Recent observations of this object have placed it amongst the class of objects

known as the scattered trans-Neptunian objects (TNOs). A total of 39 CCD images of 1998

XY95 were taken over two nights, and these were used to search for a light curve, but no

significant periodicity was found. An examination of the possible orbital evolution gives no

indication of how it may have arrived on its present orbit. The current best-fitting orbit is

unstable, but remains within a band of semi-major axis approximately 2 au wide. The bottom

of this band is due to 3:1 mean motion resonance with Neptune, while the reason for the top of

the band remains unclear.

Key words: methods: numerical – techniques: photometric – celestial mechanics – comets:

general.

1 I N T R O D U C T I O N

Over the last few years, the outer edge of the known Solar system

has been moving steadily outwards with ever more discoveries of

trans-Neptunian objects (TNOs). At present the outermost objects

of our Solar system are the 37 so-called scattered objects (Luu et al.

1997). These are objects with high eccentricity and often high

inclination that cannot have formed in their present orbits as part of

the accretion disc. This means that they must have been ‘scattered’

into their present orbits by some process in the past.

One such object is 1998 XY95, which was discovered on 1998

December 12 as part of a deep search (Fitzsimmons, Fletcher &

Marsden 1999). The nature of the deep search means that a large

number of images were taken, which allowed an examination of

the light curve of this object to look for rotational variation. In

addition, because of the uncertainty in the orbital history of this

class of object, we have carried out a series of long-term

integrations to examine the dynamical evolution of 1998 XY95.

2 O B S E RVAT I O N S

The observations of 1998 XY95 were carried out on the nights of

1998 December 12 and 13, using the prime-focus Wide Field

Camera on the 2.5-m Isaac Newton Telescope on La Palma. The

detector consisted of a mosaic of four EEV 4096 � 2048 CCDs,

each of which have a pixel size of 13.5mm. At the prime focus this

gives a pixel scale of 0.333 arcsec and a field size of 22:7 �

11:4 arcmin2 for each CCD. The observations were taken through a

Harris R-band filter ðl0 ¼ 590 nm, FWHM ¼ 150 nmÞ and

calibrated using standard stars in fields SA104 and SA92 from

Landolt (1992). A total of 37 10-min exposures of 1998 XY95

were taken on the night of December 12, with two additional

images taken on the next night to confirm the discovery. All of the

images were bias-subtracted and then flat-fielded using a median

sum of a series of offset images of the twilight sky.

The apparent magnitude was calculated by shifting and co-

adding 33 of the frames on the first night in order to maximize the

signal-to-noise ratio. The magnitude was then measured through a

small aperture of radius 2.0 arcsec. The aperture correction was

determined by combining the same exposures without shifting, and

then averaging 20 stars to obtain a high signal-to-noise ratio stellar

profile.

In order to search for magnitude variation in the TNOs, the

instrumental magnitude was measured for a number of field stars.

These stellar magnitudes were then used to calculate the change in

magnitude of the TNO. The stars were chosen to be as close as

possible on the image to the object in question in order to limit the

effect of any flux calibration or flat-field errors. Also, all the stars

chosen had to appear in all of the images. This is important as the

images of each object taken on the two nights were centred on

different coordinates, as a result of 1998 XY95 being close to the

edge of the CCD frame on the first night.

The method used to calculate the instrumental magnitudes for

1998 XY95 and the field stars was profile fitting. The point spread

function was calculated for each image, using the software routines

found in DAOPHOT and ALLSTAR (Stetson 1998), on at least nine

bright non-saturated stars. It is important to note that these were not

the field stars mentioned above. This point spread function wasPE-mail: [email protected]

Mon. Not. R. Astron. Soc. 325, 972–978 (2001)

q 2001 RAS

then used to calculate the instrumental magnitudes. The errors

were calculated for the object and the field stars using the readout

noise, the Poisson noise, the flat-fielding error and the interpolation

error. The average error for all of the guide stars was taken and this

was added in quadrature to the error in the instrumental magnitude

for the object itself.

Care has to be taken using the profile fitting method as the TNOs

are moving and are thus not strictly point sources. At the time of

observation, 1998 XY95 moved only 0.5 arcsec in a 10-min

observation. This was well within the seeing disc, which was

$1 arcsec FWHM for all exposures. When the point spread

function was subtracted from the image no residuals were found,

confirming the viability of this technique.

3 P H OT O M E T R I C A N A LY S I S

Table 1 gives the instrumental magnitudes of 1998 XY95 relative

to the mean of 12 field stars. The same data are shown graphically

in Fig. 1. The mean R-band magnitude was 22:44 ^ 0:07 which

corresponds to an R(1, 0) of 6.0 assuming current orbital

parameters. With an assumed albedo of 0.04 this gives a diameter

of 440 km. This means that 1998 XY95 is one of the largest TNOs.

Of the 400 TNOs in the lists produced by Marsden & Williams,

(2001) only 37 have a brighter absolute magnitude than 1998 XY95.

There is a clear degradation in the signal through the first night,

owing to the change in the seeing which goes from 1.5 arcsec

FWHM at the beginning of the night to 2.9 arcsec FWHM towards

the end of the night. At first glance there does not seem to be any

non-random variation. A better constraint on the existence of

significant variation is to use a chi-squared test, where the null-

hypothesis is that there is no non-random variation. This was done

using the following method. First the weighted mean magnitude

was estimated using inverse variance weights for each of the

observations; this gives �x ¼ 3:21 with s ¼ 1:3 � 1022. Then the

chi-squared was calculated:

x 2 ¼Xm

i¼1

ðxi 2 �xÞ2

s2i

;

where m is the number of observations, giving m 2 1 degrees of

freedom. Assuming that m is large enough and that the errors are

Gaussian, the mean of the limiting distribution is kx 2l ¼ m 2 1 and

the variance is s 2 ¼ 2ðm 2 1Þ. The result for the 39 observations

of 1998 XY95 gives a value for x 2 of 46.0, or 0.92s above the

mean. In addition, closer examination shows that a large part of this

result is due to the influence of one wayward magnitude (13.0816

UT). When this is removed the x 2 value drops to 34.9 or 0.24s

below the mean. This suggests that this point is a statistical

aberration. In either case we can say that the hypothesis that the

variation is simply random cannot be rejected.

Although we do not find evidence that there is any variation

outside that which would be expected by chance, it is still

instructive to look for periods within these data. This is because a

light curve could have an amplitude less than the standard errors in

the magnitudes, and therefore would not be revealed by the chi-

squared test. Hence we used the Lomb–Scargle method (Lomb

1976) to search for any low-level periodic light curve. Scargle

(1982) showed that this was exactly equivalent to least-squares

fitting of sine waves to the data. The routine used was that from

Press et al. (1992).

The Lomb–Scargle method applied to the data for 1998 XY95

produced the periodogram shown in Fig. 2. The frequency is in

inverse days and the power relates to the probability that the

corresponding frequency is simply random noise. It is important to

note that this is the probability that the specific frequency is due to

random noise, and does not mean that the probability that the data

Figure 1. The variation of magnitude with time of 1998 XY95. The

magnitude is relative to the mean instrumental magnitude of 12 field stars.

The x-axis gives the time in days.

2.8

2.9

3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

12.8 13 13.2 13.4 13.6 13.8 14 14.2 14.4

Rel

ativ

eR

Mag

.

Date Dec. 98

Table 1. The instrumental magnitude of1998 XY95 relative to 12 field stars.

Date (in 98 Dec. UT) rel. mag. error

12.8573 3.145 0.07712.8665 3.252 0.08312.8796 3.345 0.08212.8885 3.301 0.07612.8974 3.291 0.07012.9063 3.336 0.06412.9152 3.220 0.06412.9241 3.174 0.05612.9330 3.228 0.05112.9419 3.345 0.06712.9508 3.204 0.05212.9630 3.171 0.06412.9722 3.195 0.05712.9811 3.036 0.06412.9900 3.192 0.06912.9993 3.130 0.06113.0105 3.230 0.07213.0194 3.213 0.06213.0283 3.176 0.07513.0372 3.111 0.06913.0460 3.289 0.08013.0549 3.342 0.09513.0638 3.208 0.08513.0727 3.092 0.09013.0816 2.932 0.08313.1012 3.188 0.11513.1101 3.247 0.14113.1190 3.241 0.13213.1281 3.315 0.19713.1370 3.231 0.17013.1459 3.082 0.10913.1548 3.214 0.12513.1637 3.285 0.20613.1726 3.314 0.23813.2001 3.203 0.25313.2121 3.460 0.23313.2210 3.212 0.16913.8653 3.166 0.11514.1912 3.247 0.124

The scattered trans-Neptunian object 1998 XY95 973

q 2001 RAS, MNRAS 325, 972–978

set contains a real signal is one minus this probability. The exact

relationship between the power and probability depends on both the

number and spacing of the data (see Press et al. 1992 for details).

1998 XY95 does not show any strong periodicity. The highest

peak corresponds to a 1.31-h period which has a 83 per cent

probability of being due to random variation. To test the signifi-

cance of this periodicity a Fisher randomization test was carried

out. This involved assigning the measured magnitudes to one of the

times of observation chosen at random and then applying the

Lomb–Scargle method to this data set. This was done 99 times and

the results of these tests and the true results are shown in Fig. 3.

This figure clearly shows that the results for 1998 XY95 are well

within the bounds of random variation.

These results show that that there is no rotation curve detectable

for 1998 XY95 at the level of , 0.1 mag. It might be expected that

such a large object would be near-spherical owing to self-gravity.

Therefore our result is primarily a constraint on the hemispheri-

cally averaged albedo variation across its surface (cf. Pluto: Stern,

Buie & Trafton 1997).

4 DY N A M I C A L I N V E S T I G AT I O N

The orbit of 1998 XY95 is dynamically interesting. It appears to be

a scattered object, yet given the current orbital elements, most

notably a perihelion distance of 37.4 au, there is no obvious

mechanism for the scattering. This raises the following question:

How did 1998 XY95 become a scattered object?

In order to discuss the long-term dynamics of 1998 XY95, we

need to know not only the best-fitting orbit but also the errors on

that orbit. Bernstein & Khushalani (2000) have produced software

which will give an estimate of the errors in the orbital elements

based on the initial observations. This software was applied to the

observations listed by Parker, Offutt & Marsden (1999) and

additional observations provided by Brian Marsden (private

communication), giving a set of values for the barycentric orbital

elements and their associated 1s errors. These were then

transformed into heliocentric form and the resulting values are

listed in Table 2.

Most of the following integrations were produced using the

Swift symplectic integrator (Levison & Duncan 1994), which was

modified to allow integration backwards in time and to output the

heliocentric Cartesian coordinates. The second modification was

made in order to simplify the conversion to the barycentric frame.

The barycentric frame was used because at large distances from the

Sun the motion of the Sun causes large periodic variations in some

of the osculating orbital elements in the heliocentric frame, which

can mask smaller features in the orbital dynamics. Each integration

included the five outer planets, with the mass of the four inner

planets being included in that of the Sun.

The first integration consisted of placing 500 test particles at

random in Gaussian distributions about the best-fitting orbital

elements, with the error as the standard deviations. These 500 test

particles were then integrated for 108 yr into the past. This

integration shows that almost all of the particles in the integration

behaved in the same way. This behaviour is typified by that of the

best-fitting orbit shown which is shown in Fig. 4. Here both the

semi-major axis and the eccentricity undergo a series of kicks of

varying magnitudes at random intervals, with the perihelion

distance remaining more or less constant. All of the particles

underwent these random kicks despite the fact that none of them

came within 6 au of Neptune over the length of the integration. In

addition, almost all of the particles stayed within the initial range of

the integration. This is shown clearly in Fig. 5, which shows the

initial and final semi-major axes for all 500 test particles. Here,

although almost all the particles undergo significant changes in

semi-major axes, only two of them leave the initial range of the

integration. One obvious possible cause is the nearby 3:1 mean

motion resonance with Neptune which is located at approximately

62.5 au. However, an examination of the resonant arguments for

each of the 500 test particles showed that only one of the particles

(particle 385) was in resonance during the integration. This was

one of the particles that left the initial range.

To examine both these random changes and the apparent bounds

Figure 3. The results of a Fisher randomization for 1998 XY95. For each of

99 random redistributions of the magnitude data, the most likely frequency

and its corresponding power are marked by an asterisk. The true value for

1998 XY95 is marked by an enclosed asterisk.

Figure 2. The periodogram for 1998 XY95. The frequency is in inverse

days and the power relates to the probability that the corresponding

frequency is noise. The higher the power, the lower the probability.

Table 2. Heliocentric orbitalelements for 1998 XY95.

Best fit Error

a (au) 64.341 0.281e 0.418 0.004i (degrees) 6.7 0.001v (degrees) 88.7 0.006V (degrees) 47.3 0.4M (degrees) 337.8 0.07

Epoch 2000 January 1.

974 S. J. Collander-Brown et al.

q 2001 RAS, MNRAS 325, 972–978

of the above integrations, a number of smaller integrations were

carried out. Each of these involved placing 20 almost identical test

particles at various positions within the bounds of the above

integrations. The test particles in each integration differed only by

having their semi-major axes spread at random over a range of

10210 au or <15 m. These particles were then integrated for 108 yr

into the past. The results of these integrations are typified by the

results shown in Fig. 6. This shows the evolution of the semi-major

axes and the perihelion distance over the length of integration of a

set of particles near the bottom of the range. To aid comprehension,

Figure 4. The variations in the orbital elements with time of the best-fitting orbit of 1998 XY95 for 108 yr into the past. This figure shows the semi-major axis

(au), eccentricity, inclination, longitude of ascending node (V), argument of perihelion (v ) and perihelion distance (au). All the angles are in degrees and the

time is in years.


q 2001 RAS, MNRAS 325, 972–978

Figure 6. The changes in barycentric semi-major axis and perihelion of 20 nearly identical test particles with time. The dots show the values every 2:5 � 106 yr

and the connecting lines show the path of an individual particle.

Figure 5. The changes in barycentric semi-major axis between the initial value (crosses) and the final value (end of the vertical bar) for the 500 test particles.

The integration was over 108 yr.


q 2001 RAS, MNRAS 325, 972–978

the positions have been plotted every 2:5 � 106 yr with lines

connecting them to make the motion of each particle clear. This

figure shows that first even very similar orbits diverge very quickly:

from an initial separation an order of magnitude less than the

diameter of the object there is a distinct spread after the first

2:5 � 106 yr. Secondly, although the orbits spread rapidly they

remain bound to the same range as in the integration above. Finally,

the range of perihelion distance is more limited than the semi-

major axes, although this would be expected as any perturbation by

Neptune would be strongest at perihelion.

In order to examine the reasons for this strange behaviour, a

number of shorter integrations were carried out using a 12th-order

Runge–Kutta–Nystrom integrator written by SJC-B, based on the

algorithm of Dormand, EI-Mikkai & Prince (1987). The first of

these integrations established that the same behaviour occurs in a

system consisting only of the Sun and Neptune on a circular orbit.

This result means that, as well as removing many more

complicated possibilities such as secular resonances and high-

order mean motion resonances with the inner giant planets, it also

allows the use of much simpler and therefore faster numerical

models. It also allows the use of methods derived for the circular

restricted three-body problem. One of the most powerful of these is

the derivation of zero-velocity curves: these are a consequence of

the Jacobi integral which is a constant of motion in a frame

corotating with the two massed bodies. The zero-velocity curves

bound an area of this rotating frame that the particles cannot enter.

This can be a powerful tool in limiting the motion of particles in the

inertial frame. Assuming that Neptune is on a circular orbit then the

Jacobi constant for 1998 XY95 is 3.11, which gives the zero-

velocity curves shown in Fig. 7. These show a band around the

orbit of Neptune approximately 10 au across which in the restricted

three-body problem 1998 XY95 cannot cross. Although care has to

be taken in applying the results of such a simplified model to the

real Solar system, this result does strongly imply that 1998 XY95

cannot have been scattered directly on to its present orbit by a close

encounter with Neptune. It does remain possible that 1998 XY95

was scattered by Neptune and then its orbit was changed by the

influence of factors other than Neptune.

By using a series of very short integrations (103 yr) we were able

to follow test particles through single close encounters with

Neptune. These integrations show that the test particle undergoes

small changes in semi-major axis when it goes thorough perihelion

passage close to Neptune. The magnitude and direction of the kicks

are dependent on the encounter geometry, but they are of the order

of 0.1 au. The extreme dependence on encounter geometry explains

the rapid divergence of the test particles in the integration above.

Each of the particles is doing a random walk, with any small

difference in time of perihelion passage changing the encounter

geometry with Neptune and hence the outcome of the encounter.

This in turn will change the time of perihelion passage for the next

encounter with Neptune. The reason for the lower limit depends on

the nature of the encounters. If the test particle is ahead of Neptune

during a close encounter it is drawn into a slightly tighter orbit,

decreasing the semi-major axis. If on the other hand the test

particle is behind Neptune during an encounter then it is drawn on

to a slightly wider orbit, increasing its semi-major axis. In order to

approach the lower limit a particle has on average to experience

more encounters ahead of Neptune than behind it. However, when

the particle approaches the 3:1 mean motion resonance with

Neptune, any encounter will be followed one orbit (slightly more

than three Neptune orbits) later by another encounter. Because the

orbital period is still longer than the 3:1 resonance period, this

means that an encounter ahead of Neptune which decreases the

semi-major axis of the particle is followed by an encounter behind

Neptune which increases the semi-major axis. Thus the particle

reaches a point where it can no longer decrease its semi-major axis,

only increase it.

Unfortunately there is no similar simple mechanism for the

upper limit. It is important to note that the upper limit is in semi-

major axis only. Particles at this upper limit can have a perihelion

distance anywhere within the range shown in Fig. 6. This figure

also shows that particles at the upper limit can have encounters that

reduce their semi-major axis. Thus it is clear that there must be a

similar mechanism for the upper limit to that for the lower limit.

The integrations above show that this mechanism must be due to

Neptune alone. Another series of short integrations (,500 yr) show

that the magnitude of the change in semi-major axis during a close

encounter does not change significantly over the range within the

bounds. This suggests strongly that, like the lower boundary, it

must be somehow a function of the orbital period. Although

increasing the orbital period will reduce the number of close

encounters within any given time, this should lead to a gradual tail-

off, not a sharp cut-off, and does not explain how particles at the

upper limit can have large reductions in semi-major axis as shown

by several particles in Fig. 6. This means that the most likely

explanation is some connection between the orbital period of the

test particle and Neptune, in other words a resonance. There are,

however, no low-order resonances anywhere near the required

location. This means that the upper limit to the motion of the test

particles remains a mystery.

5 C O N C L U S I O N S

We have examined the light curve and the orbital evolution of the

TNO 1998 XY95. We have found that the light curve does not show

Figure 7. The zero-velocity curves for 1998 XY95 in a frame corotating

with the Neptune–Sun system, where Neptune is assumed to be on a

circular orbit. The black dots represent the positions of Neptune and the

Sun.


q 2001 RAS, MNRAS 325, 972–978

any signs of rotational variation to within the errors of , 0.1 mag.

This result is consistent with 1998 XY95 possessing a low albedo,

which combined with its bright absolute magnitude would imply

that it is large and thus likely to be spherical. Hence we conclude

that there is no large-scale variation in the hemispherically

averaged albedo above 10 per cent.

The examination of the orbit of 1998 XY95 has shown that it

cannot have been scattered on to its present orbit by a close

encounter with Neptune. There remain a few other possibilities,

most notably that the object was once in the 3:1 mean motion

resonance with Neptune and a overlapping secular resonance

pumped up the eccentricity before the object was kicked out into

the region above the 3:1 by a collision or a close encounter with

another large TNO. Once within this region its semi-major axis

would undergo the random changes described above, taking it

rapidly away from the edge of the resonance. These random

changes mean that it is impossible to know the past or future of this

object on even relatively short-time scales. Indeed, this object

would even defeat the statistical approaches usually used for

examining the long-term dynamics of TNOs.

AC K N OW L E D G M E N T S

The Isaac Newton Telescope is operated on the island of La Palma

by the Isaac Newton Group in the Spanish Observatorio del Roque

de los Muchachos of the Instituto de Astrofı́sica de Canarias, and

we acknowledge the assistance of their staff and the financial

assistance of PPARC. EF acknowledges financial support from

DENI. SJC-B acknowledges financial support from PPARC. We

thank Apostolis Christou for his advice on resonant arguments, and

Brian Marsden for supplying the observational data.

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This paper has been typeset from a TEX/LATEX file prepared by the author.


q 2001 RAS, MNRAS 325, 972–978

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The scattered trans-Neptunian object 1998 XY95