P Rousselot
email: rousselot@obs-besancon.fr

A C Levasseur-Regourd

K Muinonen
email: muinonen@cc.helsinki.fi

J.-M Petit

POLARIMETRIC AND PHOTOMETRIC PHASE EFFECTS OBSERVED ON TRANSNEPTUNIAN OBJECT (29981) 1999 TD 10 *

Keywords: transneptunian objects, polarimetry, photometry, (29981)

The Kuiper-Belt Object (29981) 1999 TD 10 , classified as a Scattered-Disk Object, has been observed at three different phase angles with the ESO 8.2-m VLT and FORS 1 instrument in polarimetric mode in November and December 2003. These observations have been used to compute the Stokes parameter q, which represents the linear polarization degree. We have also used the previously published photometric observations to improve the Rband phase function. The main conclusions are as follows: (i) a negative linear polarization degree decreasing with phase angle α up to, at least, α = 3 • , (ii) q = -1.2% for α = 3 • , (iii) a possible color effect between the R and V band, the polarization degree being more negative in R. The R-band polarimetric observations can be explained by the coherentbackscattering mechanism and fitted by a two-component Rayleigh-scatterer model for a spherical small body. The rotation period of 15.382±0.001 hrs published by Mueller et al. (2004) and Choi et al. (2003) is confirmed. The R-band phase curve provides H=8.35±0.02 and G=-0.25±0.022 parameters with the IAU H-G formalism.

Introduction

Kuiper Belt Objects (KBOs), whose existence was confirmed observationally in 1992 (Jewitt and Luu, 1993), represent an important clue to understand the formation and early evolution of the outer solar system. The relatively large number of known KBOs (1082 officially reported, when Centaurs are included, as of January 2006) provides more and more efficient tests for the different models of formation of the Kuiper Belt (e.g. Levison and Morbidelli, 2003).

The main problem encountered by astronomers to study the physical properties of KBOs comes from the faintness of these objects. Most of the observational work published so far was focused on color indices (see e.g. Doressoundiram et al., 2002;Hainaut and Delsanti, 2002). Quiet a few results about rotational lightcurves (see e.g. [START_REF] Ortiz | [END_REF] and (noisy) visible and near-infrared spectra have also been published (see e.g. Brown, 2000a;Lazzarin et al., 2003;[START_REF] Fornasier | Astron[END_REF]. This paper presents observational results based on a different approach to study the physical properties. Our observations are focused on the linear polarization degree of the solar light scattered by the target. It has been known for a long time that the solar light scattered by planetary surfaces presents a polarization, varying with the phase angle α (angle Sun-targetobserver) [START_REF] Lyot | Recherche sur la polarisation de la lumière des planètes et de quelques substances terrestres[END_REF][START_REF] Levasseur-Regourd | Polarimetry of dust in the solar system: remote observations, in-situ measurements and experimental simulations[END_REF]. This effect has been studied for asteroids (see e.g. Belskaya et al., 2005) and cometary dust (see e.g. [START_REF] Levasseur-Regourd | [END_REF] and constitutes a useful tool to improve our knowledge of the surface properties of KBOs. This work presents also a reanalysis of previously published photometric of the target.

So far only two studies dedicated to polarimetric observations of KBOs / Centaurs have been published (Boehnhardt et al., 2004;Bagnulo et al., 2006). The observations published in these two papers have been obtained on Ixion and Quaoar and the Centaur Chiron. These three objects have revealed negative polarisation surges, with very different slopes, the steepest one being obtained for Ixion. This paper presents observational data obtained on another KBO, (29981) 1999 TD 10 . It is a Scattered Disk Object (SDO) discovered on October 3, 1999 by Spacewatch. It is one of the brightest KBOs known and, due to its large eccentricity (see Table 1), currently one of the nearest KBOs to the Sun.

Different papers dedicated to observational studies of 1999 TD 10 have already been published, including three detailed studies, a first one focused on visible lightcurve and phase function curve (Rousselot et al., 2003), a second one to the rotation period and a claimed cometary activity (Choi et al., 2003) and a third one to the visible lightcurve and to near-infrared photometry [START_REF] Lyot | Recherche sur la polarisation de la lumière des planètes et de quelques substances terrestres[END_REF]. Other papers and meeting presentations have also provided information on its color indices (Delsanti et al., 2001;[START_REF] Lederer | Asteroids, Comets, Meteor meeting[END_REF], its lightcurve (Consolmagno et al., 2000;[START_REF] Ortiz | Asteroids, Comets, Meteor meeting[END_REF] or its infrared spectrum (Brown 2000b).

Observational data are described in the next section. Section 3 presents our data analysis, both for the polarimetry and the photometry. The results are discussed in section 4.

The KBO (29981) The detector is a thinned and coated Tektronix CCD chip of 2048×2048 pixels, with a pixel size of 24 µm and a field of view 6.8×6.8 arcmin (0.2 arcsec/pixel, standard resolution). During our observations FORS 1 was functionning in imaging and polarimetric mode. This mode uses Wollaston prism as a beam splitting analyzer and one superachromatic λ/2 phase retarder plate, allowing the measurement of the linear polarization.

The target was observed at four different position angles of the retarder plate (0, 22.5, 45, and 67.5 • ) through V and R broadband filters. The observing circumstances are presented in Table 2. The number of series is the amount of times where the above-mentionned observing cycles of the retarder plate are performed.

The data pre-processing has been performed with the MIDAS package.

The BIAS has been computed by averaging about ten different raw bias images, after rejection of the minimum and maximum values for each pixel.

The flat fields have been obtained by computing and normalizing the median of a set of twilight flat fields in imaging mode, without the retarder plate and the Wollaston prism. Different images of Highly Polarized Stan-dard Stars were also obtained during the different observing runs. We used these images to compute the degree of linear polarisation of these stars and to check the results with the one provided by the ESO documentation (http://www.eso.org/instruments/fors/inst/pola.html).

Analysis

Polarimetry

Ordinary and extraordinary beams of the target were processed in a similar way following standard procedures of aperture photometry. The target fluxes were obtained with an aperture radius of 2.5 times the FWHM, and the sky background was determined using a 2 arcsec width annulus with internal radius of 5 arcsec.

For each series of exposures the following Stokes parameters were computed:

Q/I = 0.5 f o -f e f o + f e α =0 • - f o -f e f o + f e α =45 • U/I = 0.5 f o -f e f o + f e α =22.5 • - f o -f e f o + f e α =67.5 •
where α is the position angle of the retarder plate, and f o and f e are, respectively, photon counts of the ordinary and extraordinary lightbeams.

Because these parameters correspond to the exposure frame, with a y-axis oriented along the South-North direction, it has been necessary to transform them to a reference frame related to the scattering plane on the target. This plane is defined by the Sun-Target-Earth triangle. Calling θ the angle between the direction 1999 TD 10 -North Pole and the direction Sun-1999 TD 10 , increased of 90 • (in order to have a y-axis perpendicular to that plane), the transformation formulae can be written:

q = cos(2θ)(Q/I) + sin(2θ)(U/I) u = -sin(2θ)(Q/I) + cos(2θ)(U/I)
Because of their definition q and u values can be either positive or negative.

The absolute polarization value p has also been computed. This parameter is always positive and is defined by :

p = (Q/I) 2 + (U/I) 2
or by :

p = q 2 + u 2
The q, u and p parameters have been computed for each night by averaging the results obtained for different combinations of the retarder plates.

These combinations correspond to a shift of one image between two successive series. For example if the images are labelled chronologically 1 2 3 4 5 6

Photometry

As already mentionned 1999 TD 10 had been observed before this work, with photometric measurements published by Mueller et al. ( 2004) and Rousselot et al. (2003). It is possible to combine these data to improve the phase function of this target.

Mueller et al. present an accurate double-peaked lightcurve of 1999 TD 10 with a period of 15.382±0.001 hr (their Fig. 7). This curve is based on R-band photometric data obtained by them and by Rousselot et al. (2003). With these results it is also possible to derive a new phase curve, more accurate than the one published by Rousselot et al.

We applied the method described by Rousselot et al. (2003Rousselot et al. ( , 2005) ) ). The main difference between our method and that of these authors is that we solve explicitly for the phase effect at the same time as for the lightcurve, while Mueller et al. used an assumed phase function to first correct their magnitude estimates for the phase effect, and then solved for the lightcurve (they did not computed, consequently, the phase function). The best period is 15hr22mn57s±3s, or 15.3825±0.001 hr, in perfect agreement with the values published by Mueller et al. and Choi et al. (2003). The corresponding lightcurve is given in Fig. 2.

Using these period and lightcurve, we have derived the phase curve presented in Fig. 3. We fitted this curve using both the H-G formalism and the linear fit as used by, e.g, Schaefer & Rabinowitz (2002) and Sheppard & Jewitt (2002). The H-G formalism gives a very good fit for H=8.35±0.02

and G=-0.25±0.022 (curved dashed line in upper part of Fig. 3). The linear fit (dash-dotted straight line on the same figure) is definitly less satisfactory.

The best fit corresponds to: m 0 = 8.45 and β = 0.12 (linear dash-dotted line in upper part of Fig. 3). It should be pointed out that the negative G value provided by this calculation is indicative of the difficulties of the H-G system to describe KBO opposition effect (see Rousselot et al. 2005 for a more detailed discussion on this topic).

Discussion

We explain the polarimetric and photometric phase curves of 1999 TD 10 through extensive numerical simulations of coherent backscattering by Rayleigh scatterers (Muinonen 2004;Muinonen et al. 2002b). Based on the V-band albedo obtained with Spitzer observations (Stansberry et al., 2005) and the (V-R) color of 1999 TD 10 (Rousselot et al. 2003), we used for the simulations geometric R-band albedos in the 0.06-0.12 range.

The observations have been tentatively interpreted through existing coherent backscattering computations for altogether 360 spherical media of Rayleigh scatterers. The computations entailed 18 different single-scattering albedos ω = 0.05, 0.10, . . . , 0.90 and 20 different dimensionless mean free 10, 20, 30, . . . , 100, 120, 140, . . . , 200, 250, 300, . . . , 400, 500 (k and λ are the wave number and wavelength).

paths k = 2π /λ =
For a fixed geometric albedo, the one-component Rayleigh-scattering model parameterized by the single pair of single-scattering albedo and mean free path results in polarizations that are larger than the observed polarizations.

For 1999 TD 10 , we confirmed the poorness of the fits by comparing the polarimetric observations against all 360 one-component media of Rayleigh scatterers.

As in Boehnhardt et al.(2004) for Ixion, we then examined a two-component Besides the polarization fits, approximate brightness fits (lower part of Fig. 3) were obtained by varying the absolute magnitude H R , residual enhancement factor ζ R , angular peak width d R , and slope parameter k R for a linear-exponential phase dependence multiplying the coherent backscattering contribution (Muinonen et al. 2002a). In the present context, the enhancement factor thus represents a residual enhancement due to, e.g., mutual shadowing among regolith structures large compared to the wavelength.

Conclusion

This work presents the first polarimetric observations of 1999 TD 10 . These observations have revealed: (i) a negative linear polarization degree which decreases with the phase angle α up to, at least, α = 3 • , (ii) q = -1.2% for α = 3 • , (iii) a possible color effect between the R and V band, the polarization degree being more negative in R.

The R-band polarimetric observations can be explained by the coherentbackscattering mechanism and fitted by a two-component Rayleigh-scatterer model for a spherical small body. For a realistic example geometric albedo of p R = 0.085, 95% of the small-body surface area would be covered by a medium of single-scattering albedo ω = 0.30 and dimensionless mean free path k = 250 whereas, for the remaining 5% of the surface, the numbers would be 0.90 and 10.

We also present a re-analysis of the already published photometric data of 1999 TD 10 , permitting an improvement of the R-band phase function.

The rotation period of 15.382±0.001 hrs published by [START_REF] Lyot | Recherche sur la polarisation de la lumière des planètes et de quelques substances terrestres[END_REF] and Choi et al. (2003) is confirmed. The R-band phase curve provides H=8.35±0.11 and G=-0.25±0.022 parameters with the IAU H-G formalism.

The polarimetric results are only a first step for this object, since more observational data and more thorough coherent-backscattering modeling for 1999 TD 10 would be necessary to put more constraints on its surface properties. Such a work is beyond the scope of the present study. 2003) (solid circles) in R-band, using a best fit period of 15.3825 hr. The magnitudes have been corrected for a heliocentric and geocentric distance of 1 AU and for the phase effect shown in Fig. 3, using phase angle 0.35 o as a reference. The dashed line represents the best fit for these data using the previous period.

  1999 TD 10 was observed with the 8.2 m Very Large Telescope (VLT) Unit Telescope 1 (called Antu), at the Cerro Paranal Observatory (Chile), managed by the European Southern Observatory (ESO). During the period November -December 2003, three different observing runs were conducted in service mode. The observations were performed with a focal reducer and low dispersion spectrograph called FOcal Reducer/low dispersion Spectrograph 1 (FORS 1).

7

  and 8(1 and 5 corresponding to α = 0 • , 2 and 6 to α = 22.5 • , 3 and 7 to α = 45 • and 4 and 8 to α = 67.5 • ), then the above mentioned parameters are computed by using firstly the images 1 2 3 4, secondly the images 2 3 4 5, thirdly the images 3 4 5 6 etc... For the first observing night, two different sets of series have been used (with 12 different images the first series goes from 1 2 3 4 to 5 6 7 8 and the second one from 6 7 8 9 to 9 10 11 12 ), providing two different measurements for the same night. The calculation of the standard deviations is based on the different data obtained for each series of combination of retarder plates. This method provided good results for most of the data. A close examination of the resulting values lead, nevertheless, to the suppression of a few images that obviously produced wrong values when taken into account (for example the images obtained on November 29 with a highly polarized sky background).To enhance the accuracy of the results for the last series of images (obtained during the last two nights), corresponding to very similar phase angle values, we have combined the polarimetric parameters obtained for the December 19 th and 20 th (the series of images used for these computations being not mixed with each other).The results obtained are presented in Table3. We have computed, for each parameter, the standard deviation values (σ). Two different sets of results appear. The first one corresponds to a simple average of the different values obtained, when using the different possible combination of images (see above). The second one provides the results obtained with a σ-clipping algorithm. This algorithm rejects the values that deviate more than 1.5 times the standard deviation σ from the median. The remaining values are then averaged. In both cases the corresponding standard deviation is given. Because the calculation of this standard deviation is based on data not completely independent of each other (because only one image out of four is changed at each time), the values given in the Table3are probably slightly underestimated. For most cases the results are identical, indicating a small dispersion in the results. Fig.1presents Stokes parameters q and u, respectively without and with the σ-clipping algorithm, as a function of the phase angle.

  Rayleigh-scattering model consisting of dark and bright scatterers. There are five parameters in such a model: two single-scattering albedos and two mean free paths, and the weight factor w d for the dark component (the weight factor of the bright component being w b = 1 -w d ). Fixing the geometric albedo fixes the weight factor, reducing the number of free parameters to four. After a systematic study of physically realistic combinations of the two kinds of scatterers, satisfactory fits were obtained for the polarization across the entire range of possible geometric albedos of p R ∈ [0.06, 0.12]. Among the solutions for 1999 TD 10 , there are ones that, qualitatively, resemble those obtained for Ixion by Boehnhardt et al. (2004), eventhough the polarimetric phase curves differ substantially. We can fit the 1999 TD 10 observations by a two-component model where the dark component shows a mean free path substantially longer than the wavelength and where the bright component shows a short mean free path. Example model parameters with the corresponding rms value of the fit are given in Table 4 with the actual fits depicted in Fig. 4. Note that the fits are by no means unambiguous. They rather demonstrate the capability of the two-component model to explain the observations.

Figure 1 :

 1 Figure captions:

Figure 2 :

 2 Figure 2: Lightcurve plot of the combined data set of Mueller et al. (2004) (solid triangles) and Rousselot et al. (2003) (solid circles) in R-band, using a best fit period of 15.3825 hr. The magnitudes have been corrected for a heliocentric and geocentric distance of 1 AU and for the phase effect shown in Fig.3, using phase angle 0.35 o as a reference. The dashed line represents the best fit for these data using the previous period.

Figure 3 :

 3 Figure 3: Phase function curve derived from the data published by Rousselot et al. 2003 (crosses) and Mueller et al. 2004 (circles). Upper Fig.: the dashed line shows the best fit function in the H-G formalism, while the dash-dotted line represents the best linear fit to the data. Lower Fig.: the dashed line shows the best fit function model of coherent backscattering and shadowing.

Figure 4 :

 4 Figure 4: The R-band polarization as explained by a model of coherent backscattering and shadowing. The values used are the ones with the sigmaclipping algorithm. See the text for more details.

  Figure 2:

Table 1 :

 1 Orbital characteristics of 1999 TD 10 .

	a (AU) e	q (AU) Q (AU) i
	95.1	0.87 12.28	178.0	6.0 •

Table 2 :

 2 Observing circumstances for 1999 TD 10 (R: Heliocentric distance (AU); ∆: Geocentric distance (AU); α: phase angle). For the sky CLR means and PHO mean photometric sky.

	UT Date	Start/end (UT) ∆	R	α	Filter(exp. time) Number Sky
						of series
	2003 Nov. 12 00:08/01:28	13.01 13.98 0.77 • R(305s)	3	CLR
	2003 Nov. 29 00:52/02:28	13.15 14.02 1.93 • R(225s)/V(335s) 2	CLR
	2003 Nov. 30 04:54/06:29	13.16 14.02 2.00 • R(225s)/V(335s) 2	PHO
	2003 Dec. 19 00:54/03:32	13.40 14.06 3.05 • R(225s)/V(335s) 3	CLR
	2003 Dec. 20 03:38/05:07	13.42 14.06 3.10 • R(500s)/V(700s) 1	CLR

Table 3 :

 3 Polarimetric parameters computed with the observational data. N is the number of series of images used to compute the average value given in the Table.The origin of the rotational phase has arbitrarily been chosen as equal to zero for the first observation. It is based on the rotation period published by[START_REF] Lyot | Recherche sur la polarisation de la lumière des planètes et de quelques substances terrestres[END_REF].

Based on observations obtained at the Cerro Paranal observatory of the European Southern Observatory (ESO)

Filter

Phase angle q/σq(%) u/σu(%) p/σp(%) N Rotational Phase R 0.77


Keywords: Centaurs, trans-neptunian objects, photometry, (60558) 2000 EC 98

We present photometric observations of Centaur (60558) 2000 EC 98 and trans-neptunian object (55637) 2002 UX 25 at different phase angles and with different filters (mainly R but also V and B for some data). Results for 2000 EC 98 are: (i) a rotation period of 26.802±0.042 hours if a double-peaked lightcurve is assumed, (ii) a lightcurve amplitude of 0.24±0.06 for the R band, (iii) a phase curve with H=9.03±0.01 and G=-0.39±0.08 (R filter) and H=9.55±0.04 and G=-0.50±0.35 (V filter) or a slope of 0.17±0.02 mag.deg -1 (R filter) and 0.22±0.06 (V filter), (iv) the color indices B-V=0.76±0.15 and V-R=0.51±0.09 (for α=0.1-0.5 • ) and 0.55±0.08 (for α=1.4-1.5 • ). The rotation period is amongst the longest ever measured for Centaurs and TNOs.

We also show that our photometry was not contaminated by any cometary activity down to magnitude ≃27/arcsec 2 .

For 2002 UX 25 the results are: (i) a rotation period of 14.382±0.001 hours or 16.782±0.003 hours (if a double-peaked lightcurve is assumed) (ii) a lightcurve amplitude of 0.21±0.06 for the R band (and the 16.782 hours period), (iii) a phase curve with H=3.32±0.01 and G=+0.16±0.18 or a slope of 0.13±0.01 mag.deg -1 (R filter), (iv) the color indices B-V=1.12±0.26 and V-R=0.61±0.12. The phase curve reveals also a possible very narrow and bright opposition surge.

Because such a narrow surge appears only for one point it needs to be confirmed.

Introduction

Kuiper Belt Objects (KBOs), whose existence was confirmed observationally in 1992 [START_REF] Jewitt | Discovery of the candidate Kuiper belt object 1992 QB 1[END_REF], represent important clue for the formation and early evolution of the outer solar system. Nowadays, thanks to an important effort deployed in the search of new objects, a relatively large number of KBOs are officially repertoried (about 940 different objects, when Centaurs are included, as of July 2004). Such a sample has already permited to develop different dynamical models designed to explain the formation of the Kuiper belt (e.g. [START_REF] Levison | The formation of the Kuiper belt by the outward transport of bodies during Neptune's migration[END_REF].

The study of the physical properties of KBOs is more complicated, because of the faintness of these objects. So far such studies have been focused mainly on the color indices, leading to some trends in the different categories of KBOs identified by the dynamicists (e.g. [START_REF] Doressoundiram | The color distribution in the Edgeworth-Kuiper belt[END_REF][START_REF] Hainaut | Colors of minor bodies in the outer solar system[END_REF]. Some spectral studies, in the visible or near-infrared range, have also been conducted. Due to the very poor signalto-noise ratio of these spectra such studies have produced, so far, limited results [START_REF] Brown | Near-infrared spectroscopy of Centaurs and irregular satellites[END_REF][START_REF] Lazzarin | ESO large programme on physical studies of transneptunian objects and centaurs: visible spectroscopy[END_REF][START_REF] Fornasier | Water ice on the surface of the large TNO[END_REF]. This paper presents observational results based on a different approach of the physical properties of KBOs. This approach consists in studying how the reflected light varies with the phase angle α (i.e. the angle Sun-KBO-Earth). Such an approach has already been used for many solid planetary surfaces, e.g. the moon, asteroids, Saturn's ring or giant planets satellites.

For these planetary bodies the opposition surge is a common phenomenon.

This phenomenon is a non-linear increase in the average surface brightness as the phase angle decreases to zero. Two causes of the opposition effect are usually considered: (1) shadowhiding and (2) interference-enhancement, often called coherent-backscatter. Some general regolith property-dependent characteristics of each mechanism are understood, and several papers are devoted to discuss the relative contribution of both mechanism [START_REF] Drossart | Optics on a fractal surface and the photometry of the regoliths[END_REF][START_REF] Helfenstein | The lunar opposition effect: a test of alternative models[END_REF][START_REF] Helfenstein | Galileo observations of Europa's opposition effect[END_REF][START_REF] Hapke | The opposition effect of the moon: coherent backscatter and shadow hiding[END_REF][START_REF] Nelson | The opposition effect in simulated planetary regoliths. Reflectance and circular polarization ratio change at small phase angle[END_REF][START_REF] Belskaya | Opposition effect of asteroids[END_REF][START_REF] Shkuratov | The opposition effect and the quasi-fractal structure of regolith: I[END_REF][START_REF] Poulet | A study of Saturn's ring phase curves from HST observations[END_REF].

For "typical" KBOs, located at about 40 AU from the Sun, the maximum possible value of α is about 1.5 • . For Centaurs, expected to have very similar physical properties to KBOs, but located closer the Sun, α can reach up to typically 6 • (for a heliocentric distance of 10 AU). Compared to the properties of the opposition surges observed for asteroids, for example, which have typically a Half Width at Half Maximum of a few degrees [START_REF] Belskaya | Opposition effect of asteroids[END_REF], such phase angle ranges can seem to be too limited to really permit an accurate physical modeling. Nevertheless the properties of the opposition surge appearing in the KBOs are not necessarily similar to the one usually observed for the asteroids. [START_REF] Belskaya | Opposition effect of Kuiper belt objects: preliminary estimations[END_REF] has pointed out the possibility of a very narrow (i.e. less than a few tenth of a degree) opposition surge.

The observations presented in this paper have been obtained on one Centaur -( 60558 [START_REF] Marsden | Eight TNOs and Centaurs[END_REF]. 2002 UX 25 is a Trans-Neptunian object (TNO) classified as a "classical" and discovered on October 30, 2002 by the same telescope [START_REF] Descour | UX 25[END_REF]. Table 1 presents the orbital characteristics of both objects. Because of its large inclination, superior to 4.5 • , 2002 UX 25 can be classified also as a "hot" classical object. Since it has been possible to identify this object on images obtained well before its discovery [START_REF] Stoss | colleagues[END_REF] its orbital elements are very accurate.

We conducted a photometric study of both objects. The main objective was to derive an observational phase function for these targets. This objective has been partially reached. Interesting results have been obtained but complementary data would be also useful to confirm the trends we have detected. This study also includes a search for cometary activity for 2000 EC 98 .

In the next section the observational data are described for both targets.

Section 3 presents the different aspects of our analysis of these data, and in section 4 the results are discussed and compared with similar works already published.

2 Observations and data reduction The observations conducted with the NTT had for main objective to search for a cometary coma. Different Centaurs were observed during this observing run, including 2000 EC 98 , and both nights were dark and photometric. We used the direct imaging camera Superb-Seeing Imager (SUSI 2), equiped with two 2048×4096 CCDs, and with a field of view of 5.5'×5.5'.

Given the very small plate scale of the instrument (0.0805" pixel -1 ) and the seeing (varying from about 0.9 to 1.3") we used the 2×2 binned mode.

In order to avoid any trailing due to the proper motion of the object the exposure time was limited to 205 s, corresponding to a motion of 0.3". Most of the images were obtained with a Bessel R filter, with some others with B and V filters, allowing an accurate determination of the magnitude of the reference stars.

The images were bias-subtracted using an averaged 2-D bias image. The resulting images were flat-fielded for instrumental sensitivity pattern removal using a combination of dome and sky flats (science frames). Using standard star images, we computed the photometric coefficients (zero points, extinction coefficients and color terms) using the IRAF package. 22 images obtained during the first night and 32 obtained during the second night, all in R filter, were used for the coma search. For the photometry only the 22 images of the first night were used. We have chosen not to use the data obtained during the second night for the photometric processing, mainly because of the lack of bright possible reference star appearing in the field of view (the final stability of the photometric reduction could not be checked properly).

The observations of the second observing run were performed at the Danish 1.54-m telescope. Four half-nights (second part) were allocated to this program. The observations were performed with the Danish Faint Object Spectrograph and Camera (DFOSC), a focal reducer instrument, equipped with a backside illuminated CCD chip 2048×4096 15 µm pixels. As the optics of DFOSC cannot utilise the whole area of the CCD, the readout area was only 2148×2102 pixels, which includes 50 pixel pre-and post-overscan regions in the X-direction and 22 masked pixels in the Y-direction. The CCD scale was 0.39" pixel -1 and the field of view 13.7'×13.7'. Exposures were taken using Bessel BVR filters with typical sequences like RVRB.

Data processing followed the previous lines, just adding the use of the overscan region, and using twilight sky images only for the flat fielding. Here again we could compute the photometric coefficients.

Observations at the 3.6-m telescope used the ESO Faint Object Spectroraph and Camera (EFOSC2) in imaging mode. This instrument is equipped with a 2048×2048 15 µm pixel CCD chip. The scale is 0.157" pixel -1 (0.314" pixel -1 for our observations because we used the 2×2 binning mode) and the field of view 5.4'×5.4'. Exposures were taken using Bessel BVR filters with typical sequences like RVRB and exposure times varying from 150 to 180 s (R and V filters) and 240 s for the B filter. The data processing was similar to the one for DFOSC images.

2002 UX 25

This TNO was observed with a 2-m telescope located at the Pik Terskol observatory, managed by the International Center for Astronomical Medical and Ecological Research (ICAMER, Kiyv, Ukraine and Terskol, Russia). This observatory is located in the russian Caucasus at an altitude of 3120 m and the telescope is a 2-m Ritchey Chretien-Coude telescope. The obser-vations were performed with a focal reducer instrument equipped with a 512×512 20 µm pixel CCD chip. The scale is 1.0" pixel -1 and the field of view 8.5'×8.5'. Exposures were taken mainly with R filter and also with B and V filters.

The target was observed during two observing runs. A first one in October 2003 -when the TNO was at opposition -and a second one in December (first half part of the nights). Table 3 gives the observing circumstances. Some standard stars were observed during both runs and the fields of the second observing run were observed during the first one, in order to check the absolute consistancy of the photometric reduction.

The data processing was similar to the one DFOSC and EFOSC2 images.

Since the observing nights in October were not all photometric, the photometric coefficients were computed using the coefficients obtained during the first two nights of the December run. The consistancy of these coefficients was checked using the standard stars observed during the nights October 19 and October 22, when the sky was photometric. Because all the reference stars (see below) were observed during these two nights it was possible to compute their absolute magnitude.

Analysis

Search for cometary activity on 2000 EC 98

Thanks to the data collected with the NTT we have performed a search for a cometary activity on the Centaur 2000 EC 98 . We first created some special MIDAS scripts in order to extract all the subimages where 2000 EC 98 was clearly visible, as well as similar subimages for a bright star appearing in the same frames. All the subimages extracted were coadded, allowing an accurate determination of the surface brightness profile, both for the reference star and the Centaur. The brightness profiles were obtained by using a small C code, designed to average the pixel intensities for a given radial distance.

Lightcurve

The photometric reduction of these observations was based on a two-step process. The first step consisted in determining the absolute magnitudes of a few bright stars, called "reference stars" appearing in the same frames and with similar color indices as the one of the targets (V-R≃0.5). This determination was based on images obtained when the sky was photometric.

The second step consisted in performing relative photometry with the different reference stars observed. This relative photometry was performed by aperture-photometry and using an aperture with a radius equal to about 1.3-1.5 times the FWHM of the PSF. In some cases, for 2000 EC 98 we have averaged the magnitudes obtained with two successive images, in order to improve their accuracy. Tables 4 to 9 present all the reduced magnitudes derived from our observations, with the uncertainty given at a one sigma level.

The data were further corrected to obtain the absolute magnitude for a heliocentric and geocentric distance of 1 AU. A second correction was added to the time of the measure to account for the light-time variations due to the changing geocentric distances. Data obtained on April 10, 2003, andOctober 15, 2003, were The lightcurve is derived from these corrected data, modelling the light variations of the objects as a Fourier expansion plus a phase effect [START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF]Harris et al., 1989):

H(α, t) = H(α) + m l=1 A l sin 2Πl P (t -t 0 ) + B l cos 2Πl P (t -t 0 ) (1)
The Fourier expansion gives the rotational lightcurve of the object. The phase term H(α) is fixed for any data with a similar phase angle. In [START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF], the grouping occured for each magnitude measured in a given night.

Here we have extended the grouping to all observations performed with a phase angle in a small range.

For The long period is the double of the short one, to within the error bars, and shows a double peak, while the short period shows only a single peak.

The best fit for the long period is reached for a degree of expansion of 2, and yields a bias-corrected χ 2 of 0.833. For the short period, a degree of expansion of 1 gives a similar value for the bias-corrected χ 2 . According to the hypothesis that the lightcurve is due to the rotation of an elongated body, we will consider only the double peak curve with a period of 26.802 ±0.042 hours. The V filter lightcurve was obtained using the same period and degree of expansion as for the R filter. The peak-to-peak amplitude of the smoothed lightcurve is 0.24 ± 0.06 in R filter. For the V filter we found 0.36 ± 0.09, nevertheless this amplitude is less accurate, because of the lack of data for certain part of the lightcurve. Only R and V filter data are shown as the quality of the B filter data did not allow us to fit equation (1).

2002 UX 25

From Table 7 and Fig. ??, one can see that the rotational lightcurve has a very small amplitude. This makes the determination of the rotational period quite difficult. This also means that the 2002 UX 25 is rather spherical, at least in its current projection on the sky, and that is does not have any important surface feature.

We searched for a good period shorter than a day and found three possible values with similar bias-corrected χ 2 . The periods are 16.782±0.003 hours, with degree of expansion 3, 14.382±0.001 hours, with degree 8 and 7.1908±0.0004 hours, with degree 6. All three periods seem perfectly compatible with the data.

Also, all these lightcurves show multiple peaks superimposed on a single (for the shortest period) or double (for the 2 longest periods) non-symmetrical oscillation. The smoothest fit is shown in Fig. ?? for period 16.782 hours.

The peak-to-peak amplitude of the smoothed lightcurve is 0.21 ± 0.06. Given the very small number of data in V and B filters, it was not possible to fit them with equation (1). It is important to note that we do not claim that this is the correct period, but we use it for display purpose only. As it will be seen below, the actual period do not change the phase curve, which is what we are interested in the end. Similarly to 2000 EC 98 , we tend to favor the lightcurves with double peak.

Improving the determination of the period would require a set of high signal to noise data points, which can be obtained only with a large aperture telescope, such as a 4-m class telescope with good seeing. The error bars on the parameters are derived analytically from the fit.

We checked that they are consistent with those obtain with a Monte Carlo method that generates 1000 fake lightcurves and fit them again [START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF]. The good agreement between these two methods leads us to believe our initial estimate of the errors on the measured magnitudes is correct.

2002 UX 25

Precise determination of the period is made difficult by the small peak-topeak amplitude of the signal, which in the same time makes the determination of the phase effect less sensitive to the determination of the period. It turns out that the phase functions derived for each of the three previous periods are compatible with each other. From the phase function curves we derived the standard H and G parameters of Bowell's et al. (1989) formalism (Table 10). The same data were also used to compute the color index V-R for two different phase angle ranges (Table 11). The V-R color index does not present any significant change with the phase angle inside the uncertainties. If a color effect exist for the phase function curve it is too small to be detected with our data. Since we didn't get the phase curve for the B filter, the B-V color index presented in Table 11 was computed directly from the photometric measurements given in Table 5 and 6 using successive measurements in V and B filters.

The absolute H R magnitude allows to estimate the diameter of 2000 EC 98 using Russell's equation [START_REF] Russell | On the albedo of the planets and their satellites[END_REF]:

D = 2 2.24 × 10 16 × 10 0.4(Rs-H R ) p R , ( 2
)
where D is the diameter of the object (in km), R s is the Sun's R magnitude, H R is the object's absolute magnitude in the R band (given in Table 10) and p R the geometric albedo in the R band. With R s = -27.26 [START_REF] Allen | Astrophysical quantities[END_REF]) and a red albedo in between 0.04 (the canonical value of cometary nuclei) and 0.10 (the largest one ever measured so far [START_REF] Altenhoff | Size estimates of some optically bright KBOs[END_REF],

Chiron excepted, which is known to have a cometary activity) this leads to a diameter of ∼ 50-80 km. Such a diameter classifies 2000 EC 98 as a "normal size" Centaur.

Assuming the brightness change is due to an elongated shape, we can compute a lower limit for the axis ratio a/b, where a and b are the semiaxes such as a ≥ b (the rotation axis being supposed perpendicular to the line of sight). If ∆m R is the lightcurve amplitude we have:

a/b ≥ 10 0.4∆m R (3)
Using ∆m R = 0.24 we obtain a/b ≥ 1.25 : 1. This is not the only possible interpretation, and the difference in amplitude between the R and V filters hints towards a lightcurve due to a change in apparent albedo as the object rotates. This possibility is further enhanced by the quasi symmetry between the two parts of the rotational lightcurve in Fig. ??. In such a case, the single-peaked lightcurve would be more realistic and the rotational period would be 13.401 hours.

2002 UX 25

Contrary to the case of 2000 EC 98 we could derive the standard H and G parameters for 2002 UX 25 only in the R band (Table 10). We computed the color indices with the few measurements acquired in all 3 filters at roughly the same time. This is not the best way to compute these quantities, but the only available to us in this case. The resulting uncertainties are somewhat larger than for 2000 EC 98 (Table 11).

The Here we have only one lightcurve in R filter. And the lightcurve is all but symmetrical. The brightness variation is most probably due to a surface feature. We can nevertheless put an upper limit to the potential elongation of the object. Using ∆m R = 0.21 we obtain a/b ≥ 1.21 : 1.

Comparison with other works

This work provides, for two different objects, four differents types of informations: (i) the color indices (and the absolute magnitudes), (ii) the ligthcurve amplitude, (iii) the rotation period and (iv) the phase curve. It is interesting to compare these results to the other works already published, especially for the phase curve, for which very few data are available yet.

The color indices presented in Table 11 can be compared to the other ones published for similar objects (e.g. [START_REF] Peixinho | ESO large program on Centaurs and TNOs: visible colors -final results[END_REF]. 2002 UX 25 corresponds to a typical classical object, but appears among the reddest "hot classical" objects. The Centaurs measured so far fall into two sub-groups.

2000 EC 98 belongs to the sub-group with lowest V-R and B-V color indices.

Our value of V-R for 2000 EC 98 is similar to the one published by [START_REF] Bauer | [END_REF] (0.47±0.06).

The lightcurve amplitudes can also be compared to the statistics already available. Both 2000 EC 98 and 2002 UX 25 , with a R lightcurve amplitude of 0.24 and 0.21, appear to have a relatively large but not exceptionnal lightcurve amplitude, when compared to other similar objects (Ortiz et al., 2003a). presents a more common rotation period, in between the one of Quaoar and Varuna, that have comparable size. Both objects have a rotation period well above the critical 3.3 hours corresponding to a spherical body with a density of 1 g.cm -3 [START_REF] Romanishin | Rotation rates of Kuiper-belt objects from their light curves[END_REF]. Table 10 shows that the G parameter for 2000 EC 98 is negative for both R and V bands. The one for 2002 UX 25 is either positive or very close to zero. A negative G would be surprising for an asteroid, since this formalism was originally designed to describe all type of surfaces with 0 ≤G≤1 (the negative values are not formally excluded, however). The G=0 value was designed to describe the darkest surfaces of the asteroids and the G=1 value the brightest ones. A small, or negative value would be an indication of a very low albedo surface, as it is already generally assumed for KBOs.

Four different works have been published that present phase function of

TNOs and/or Centaurs with the H-G formalism [START_REF] Bauer | Observations of the Centaur 1999 UG 5 : evidence for a unique outer Solar System surface[END_REF][START_REF] Sheppard | Time-resolved photometry of Kuiper belt objects: rotations, shapes, and phase functions[END_REF][START_REF] Bauer | Physical survey of 24 Centaurs with visible photometry[END_REF][START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF] [START_REF] Bauer | Physical survey of 24 Centaurs with visible photometry[END_REF]. For these objects the G factors published are below the median value for asteroids (0.08 to 0.17).

Note however that the results of the H-G formalism have to be taken with care for such phase curves, because of the very limited phase angle range covered by the observations (and, sometimes, the very limited number of data available; some G parameters published by [START_REF] Sheppard | Time-resolved photometry of Kuiper belt objects: rotations, shapes, and phase functions[END_REF] are based on only two points on the phase curve). The fact that only Centaurs present, so far, positive G values may be correlated to the larger phase angle range covered. The main conclusion based on the H-G formalism is probably the poor capability of this formalism to describe the phase function for low albedo surfaces, such as the one of Centaurs or TNOs.

This issue was already pointed out by other authors (see e.g. [START_REF] Belskaya | Opposition effect of asteroids[END_REF].

The other way to compare our results with other authors is to assume a linear increase of the magnitude m R with phase angle α such that m R = m 0 +βα. Such a formula is a very crude approximation of the phase function.

Nevertheless, when the phase angle coverage is very limited, it can provide a quick way to look at the importance of the opposition surge. For 2000 EC 98 our phase curve leads to m 0 = 9.10 ± 0.03 and β = 0.17 ± 0.02 (R filter) and m 0 = 9.59 ± 0.05 and β = 0.22 ± 0.06 (V filter), and for 2002 UX 25 similar calculations lead to m 0 = 3.34 ± 0.01 and β = 0.13 ± 0.01 (R filter).

Our β values are in good agreement with the one already published. The mean value published by [START_REF] Sheppard | Time-resolved photometry of Kuiper belt objects: rotations, shapes, and phase functions[END_REF], based on 7 different objects, is 0.15 mag.deg -1 . The other values published so far (Shaefer and Rabinowitz, 2002;[START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF][START_REF] Belskaya | Opposition effect of Kuiper belt objects: preliminary estimations[END_REF] vary from 0.084 to 0.145 mag.deg -1 . Our β values do not present a special difference with the other ones already published.

While an artefact on our data cannot be excluded, 2002 UX 25 exhibits an unsual narrow photometric opposition effect at phase angles smaller than 0.1 deg (Fig. ??). Opposition effect appearing at phase angles less than 0.1-0.2 deg has also been detected for some Centaurs and KBOs [START_REF] Belskaya | Opposition effect of Kuiper belt objects: preliminary estimations[END_REF]. Amongst atmosphereless planetary satellites, only Rhea, Europa, and Ariel have similar opposition effect [START_REF] Domingue | Europa's phase curve: Implications for surface structure[END_REF][START_REF] Williams | [END_REF]. This could be the result of the shadow-hiding effect due to the porosity of the surface [START_REF] Hapke | Bidirectional reflectance spectroscopy. 4. The extinction coefficient and the opposition effect[END_REF][START_REF] Hillier | Shadow-hiding opposition surge for a two-layer surface[END_REF] and/or of a second effect called coherent backscattering which depends primarly on the grain size and the albedo of the regolith particles [START_REF] Muinonen | Electromagnetic scattering by two interacting dipoles[END_REF]Mishchenko andDlugach, 1992, 1993;[START_REF] Shkuratov | Opposition effect from Clementine data and mechanisms of backscatter[END_REF][START_REF] Poulet | A study of Saturn's ring phase curves from HST observations[END_REF]. Assuming the shadow-hiding as the possible explanation, the surface of 2002 UX 25 has to be extremely porous with values of the porosity certainly larger than 95%. If coherent bacscattering mainly contributes to the unusual photometric behavior, then the assumed low-albedo particles of regolith have to be very small to allow the effect of multiple scattering to be responsible of the coherent backscattering. Precise modelings would better quantify the respective contribution of these two effects, but complementary observations at very small phase angles, are necessary to give a firm conclusion on this problem. If a very narrow opposition surge is confirmed it would be an exciting discovery for the KBOs.

Conclusion

The data presented in this paper provide more photometric informations on one Centaur -2000 EC 98 -and one TNO, 2002 UX 25 . The main results concern their rotation period which is 26.802±0.042 hours for the Centaur (one of the longest one ever measured for Centaurs and TNOs) and 14.382±0.001 hours or 16.782±0.003 hours for 2002 UX 25 (assuming a double peak rotational lightcurve). Note that for 2002 UX 25 , the period value could not be firmly established due to the small lightcurve amplitude, and the real period could be different from those quoted here. Our NTT observations also allowed us to search for cometary activity on 2000 EC 98 down to magnitude≃27/arcsec 2 , with negative results.

The phase curve derived from our data are similar to the one already published for similar objects, except for a possible very narrow opposition surge in 2002 UX 25 that needs to be confirmed. For this target complementary observations are welcome, especially at very small phase angles, both to improve the period determination and the phase curve. Given the bright absolute magnitude of 2002 UX 25 and, consequently, its probable large diameter (between 720 to 1140 km, depending of its albedo) some direct determination of its albedo and diameter, with radio observations, would probably be possible and certainly very useful. As already mentioned in [START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF], the H and G formalism of [START_REF] Bowell | Application of photometric models to asteroids[END_REF] may not be well suited for KBOs.

The other parameters presented in this paper, i.e. the color indices and lightcurve amplitudes of both objects, do not differ significantly to the similar parameters published for other TNO or Centaurs. MJD represents the Modified Julian Date -52000 and is given for mid-frames. Some data are the result of the average of two successive measurements, in order to improve their accuracy.

Table 5: Photometric data of 2000 EC 98 used for this work, for the V filter. MJD represents the Modified Julian Date -52000 and is given for mid-frames. Some data are the result of the average of two successive measurements, in order to improve their accuracy. Table 6: Photometric data of 2000 EC 98 used for this work, for the B filter. MJD represents the Modified Julian Date -52000 and is given for mid-frames. Some data are the result of the average of two successive measurements, in order to improve their accuracy.

  ) 2000 EC 98 -and one KBO -(55637) 2002 UX 25 -referred to hereafter as 2000 EC 98 and 2002 UX 25 . 2000 EC 98 is a Centaur which was discovered on March 3, 2000 at Kitt Peak observatory by Spacewatch

  2.1 2000 EC 98 This Centaur was observed during three different observing runs at La Silla Observatory (Chile), managed by the European Southern Observatory (ESO). Three different telescopes were used: the New Technology Telescope (NTT, a 3.5-m telescope) in April 2001, the Danish 1.54-m telescope in March 2002 and the 3.6-m telescope in April 2003.

  It has been possible to co-add a total of 54 different images for 2000 EC 98 , obtained on April 26 and 27, 2001, corresponding to a total integration time of 3.075 hours. Fig. ?? presents the radial profile obtained. The profile of a reference star is superimposed and adjusted in maximum intensity, in order to permit a better examination of the Centaur profile. The examination of Fig. ?? shows that 2000 EC 98 does not present any sign of cometary activity down to magnitude ≃ 27/arcsec 2 .

  used as a reference for 2000 EC 98 (∆ = 13.552 AU) and for 2002 UX 25 (∆ = 41.553 AU) respectively. Figs. ?? and ?? graphically present these corrected data, respectively for 2000 EC 98 and 2002 UX 25 .

Fig. ? ?

 ? Fig. ?? shows the actual data, shifted in time according to this period, and shifted in magnitude to account for the phase effect. The dashed and dashed-dotted lines represent the best fit lightcurve following equation (1).

3. 3

 3 Phase function 3.3.1 2000 EC 98 As described in section 3.2, we modelled the phase curve H(α) with a stepwise function with constant value over each group of phase angles. Hence the fitted function depended linearly on the Fourier coefficients and the p = 4 (or 3 for the V filter) values of H(α). The best fit values of those parameters were all obtained at once. Values of H(α) for R and V filters are presented in Fig. ?? for the double peak long period lightcurve of Fig. ??.

  Fig. ?? shows this function for the same 16.782 hours period as in Fig. ??. The most important character of this function is the potentially very narrow opposition effect that can be seen below 0.1 • phase angle. This would warrant more observations at low phase angle (α < 0.1 • ) and intermediate phase angle (0.5 • < α < 0.7 • ).

  The phase curves of 2000 EC 98 and 2002 UX 25 can be compared to the ones already published using either the standard H-G scattering parametrization or the slope of a linear approximation of the brightness decrease. As pointed out by[START_REF] Rousselot | Photometry of the Kuiper-Belt object 1999 TD 10 at different phase angles[END_REF] neither of these comparison is really significant. The H-G formalism is not really relevant for TNOs and Centaurs because it was established for asteroids which have obviously very different surfaces and a phase function known for a much broader range of phase angle values. The comparison of linear slopes is also irrelevant because the phase curve is not linear. Unfortunatly, because these two parameterizations are the only one published so far they are still the easiest ones to use for a general comparison.

Figure 1 :

 1 Figure captions:

Figure 2 :

 2 Figure 2: Corrected magnitudes of 2000 EC 98 in the 3 filters, R (filled circles), V (triangles) and B (diamonds) for the eight different nights of observations available. The time is given in Modified Julian Date -52000 and is light-time corrected for ∆ = 1 A.U..

Figure 3 :

 3 Figure 3: Corrected magnitudes of 2002 UX 25 in the 3 filters, R (filled circles), V (triangles) and B (diamonds) for the nine different nights of observations available. The time is given in Modified Julian Date -52000 and is light-time corrected for ∆ = 1 A.U..

Figure 4 :

 4 Figure 4: Corrected magnitudes of 2000 EC 98 (dots with error bars) for R (filled circles) and V (triangles) filters. The time axis has been folded to display a double-peaked lightcurve with a 26.802 hours period. The magnitudes have been shifted according to the phase effect (see Fig. ??) to all fit on the same curve. The lines are drawn with equation (1) and the best fit parameters for the given period and expansion orders given in the text.

Figure 5 :

 5 Figure 5: Corrected magnitudes of 2002 UX 25 (dots with error bars) for R filter . The time axis has been folded to display a lightcurve with period 16.782 hours. The magnitudes have been shifted according to the phase effect (see Fig. ??) to all fit on the same curve. The line is drawn with equation (1) and the best fit parameters for the given period and expansion orders given in the text.

Figure 6 :

 6 Figure 6: Mean magnitudes of 2000 EC 98 (see equation (1)) for the R (filled circles) and V (triangles) filters obtained with the double-peaked lightcurve with period 26.802 hours (see Fig. ??). The phase curves are compared to their H-G scattering parametrization.

Figure 7 :

 7 Figure 7: Mean magnitudes of 2002 UX 25 (see equation (1)) for the R filter obtained with the 16.782 hours period lightcurve. The phase curve is compared to its H-G scattering parametrization.

Table 2

 2

	gives the observing circum-

  2000 EC 98 , we had 4 different values of the phase angle: 0.145 for

	To determine the rotational lightcurve, we used only the R filter data for
	each object. B and V filter data were not numerous enough to represent any
	improvement. Using them would have increased the number of degrees of
	freedom.
	As explained in Rousselot et al. (2003), we determined all our model
	parameters at once (period, phase terms H(α) and Fourier expansion coeffi-
	cients) using a χ 2 minimization technic (Press et al., 1992).
	3.2.1 2000 EC 98
	March 18 and 19, 2002, 0.485 for March 23 and 24, 2002, 1.42 for April 10,
	11 and 12, 2002, and 2.81 for April 26, 2001.
	For 2002 UX 25 , we had 4 different values of the phase angle: 0.02 for
	October 19, 2003, 0.045 for October 16 and 20, 2003, 0.10 for October 14
	and 22, 2003, and 1.22 for December 21, 22, 23 and 24, 2003.

On Fig.

?

?, one clearly sees a magnitude variation during the observations, with a period substantially larger than our longest continuous observation, i.e. longer than 8 hours. So we searched for a good period in the range 500 to 2000 minutes. This yielded two possible periods: 13.401 ±0.033 hours or 26.802 ±0.042 hours.

  absolute H R magnitude of 2002 UX 25 is among the brightest known for a KBO. As of July 2004 only about 10 KBOs or Centaurs, out of more than 940 known objects, have such a low (or lower) H R magnitude. With

a red albedo comprised between 0.04 and 0.10 it leads to a diameter equal of ∼ 720-1140 km (see equation 2 above). 2002 UX 25 is, then, among the biggest KBOs known so far.

Table 12

 12

presents an overview of all the Centaurs and TNOs for which a rotation period has been published, including our results. 2000 EC 98 has one of the longest period ever measured for a Centaur or TNO. There are only two other objects (1997 CV 29 and 1999 UG 5 ) that have possibly a rotation period as long as this Centaur (if a double-peaked lightcurve is assumed and taking into account the longest possible period for the first object). 2002 UX 25

Table 1 :

 1 Orbital characteristics of 2000 EC 98 and 2002 UX 25 .

	Object	a (AU) e		q (AU) Q (AU) i
	2000 EC 98 10.759 0.455 5.86	15.65	4.3 •
	2002 UX 25 42.600 0.144 36.46	48.73	19.5 •
	Table 2: Observing circumstances for 2000 EC 98 (R: Heliocentric distance
	(AU); ∆: Geocentric distance (AU); α: phase angle).
	UT Date	R	∆	α	Telescope

Table 4 :

 4 Photometric data of 2000 EC 98 used for this work, for the R filter.

Table 8 :

 8 Photometric data of 2002 UX 25 used for this work, for the V filter. MJD represents the Modified Julian Date -52000 and is given for mid-frames.

	UT Date	MJD	Mag.
	2003 Oct. 14	926.8712	20.204± 0.085
	2003 Oct. 22	934.8509	20.336± 0.069
	2003 Oct. 22	934.9979	20.322± 0.107
	2003 Dec. 21	994.8283	20.206± 0.041
	2003 Dec. 22	995.8343	20.200± 0.054
	2003 Dec. 22	995.8423	20.274± 0.059

Table 9 :

 9 Photometric data of 2002 UX 25 used for this work, for the B filter. MJD represents the Modified Julian Date -52000 and is given for mid-frames.

	UT Date	MJD	Mag.
	2003 Oct. 22	934.8672	21.141± 0.102
	2003 Dec. 21	994.8471	21.640± 0.159
	2003 Dec. 21	994.8547	21.276± 0.138
	2003 Dec. 22	995.8606	21.582± 0.198

Table 10 :

 10 H-G scattering parametrization obtained from the phase curve

	Object	V	R
	2000 EC 98 H 9.55 ± 0.04	9.03 ± 0.01
	G -0.50 ± 0.35 -0.39 ± 0.08
	2002 UX 25 H		3.32 ± 0.01
	G		+0.16 ± 0.18

Table 11 :

 11 Color indices of 2000 EC 98 and 2002 UX 25 .

	Object	B-V	V-R
	2000 EC 98 0.76±0.15 0.51 ± 0.09 (α = 0.1 -0.5 • )
			0.55 ± 0.08 (α = 1.4 -1.5 • )
	2002 UX 25 1.12 ± 0.26	0.61 ± 0.12

Table 12 :

 12 Centaurs and TNOs with known lightcurve period. DP) or 16.782 (DP) This work a. For the TNOs "S" is for scattered-disk object. b. SP: Single-peaked lightcurve assumed. DP: double-peaked lightcurve assumed.

	Object	Class a	H (mag.) P(hr) b	Refs
	(2060) 1977 UB (Chiron)	Centaur	6.5	5.917813± 0.000007 (DP)	1
	(5145) 1992 AD (Pholus)	Centaur	7.0	9.9825± 0.004 (DP)	2
				9.9768±0.001 (DP)	3
	(15789) 1993 SC	TNO	6.9	≃7.7 (SP)	4
	(15820) 1994 TB	TNO	7.1	6.0 or 7.0 (DP)	5
	(19255) 1994 VK 8	TNO	7.0	7.8, 8.6, 9.4 or 10.4 (DP)	5
	(8405) 1995 GO (Asbolus)	Centaur	9.0	8.9351±0.0003 (DP)	6
	(32929) 1995 QY 9	TNO	7.5	≃7.0 (DP)	5
	(19308) 1996 TO 66	TNO	4.5	6.25±0.03 (SP)	7,8
	1997 CV 29	TNO	7.4	8.0, 11.2 or 15.8 (SP)	9
	(33128) 1998 BU 48	Centaur	7.2	9.8 or 12.6 (DP)	10
	(52872) 1998 SG 35 (Okyrhoe) Centaur	11.3	16.6 (DP)	11
	(26308) 1998 SM 165	TNO	5.8	7.966 (DP)	12
	(40314) 1999 KR 16	TNO	5.8	11.858 or 11.680 (DP)	10
	(31824) 1999 UG 5 (Elatus)	Centaur	10.1	13.41±0.04 (SP)	13
	(29981) 1999 TD 10	TNO (S) 8.8	15.42±0.04 (DP)	14
				15.382±0.002 (DP)	15
				15.382±0.001 (DP)	16
	(38628) 2000 EB 173 (Huya)	TNO (?) 4.7	6.68, 6.75 or 6.82 (SP)	14
	(60558) 2000 EC 98	Centaur	9.5	26.80±0.04 (DP)	This work
	(54598) 2000 QC 243 (Bienor)	Centaur	7.6	9.14 (DP)	17
	(47932) 2000 GN 171	TNO	6.0	8.329±0.005	10
	(20000) 2000 WR 106 (Varuna) TNO (?) 3.7	6.3442±0.0002 (DP)	18
				3.1718±0.0001 (SP)	14
	(32532) 2001 PT 13 (Thereus)	Centaur	9.0	4.1546±0.0001 (SP)	14
	(42355) 2002 CR 46	TNO (S) 7.2	3.66 or 4.35 (SP)	14
	(83982) 2002 GO 9	Centaur	9.1	6.97 or 9.67 (SP)	14
	(50000) 2002 LM 60 (Quaoar)	TNO	2.6	17.6788±0.0004 (DP)	19
	(73480) 2002 PN 34	TNO (S) 8.2	4.23 or 5.11 (SP)	14
	(55636) 2002 TX 300	TNO	3.3	7.89±0.03 (SP)	20
	(55637) 2002 UX 25	TNO	3.6	14.382 (

Acknowledgements

The authors are grateful to both the National Academy of Science of Ukraine and the Russian Academy of Science, co-funders of ICAMER, for allowing them access to the Pik Terskol observatory.