1 Introduction

Transneptunian objects (TNOs) are considered among the most primordial objects accessible to Earth-based observations. They may represent the population of planetesimals left behind from the formation period of the solar system and should contain widely unmodified material from the origin of the planetary system. They are building stones that may have created the atmospheres of the gas giants and they are an important source for Jupiter family comets.

The several dynamical populations in the Transneptunian region (Gladman et al. 2008) could be the result of gravitational scattering and migration processes during the early phase of the planetary system (Morbidelli et al. 2008; Kenyon et al. 2008). The formation and evolution history of the outer planetary system may also be reflected in the physical and chemical constitution of TNOs, e.g., in sizes, albedos, and compositions. Composition information of TNOs is obtained through spectral and photometric measurements of the radiation scattered by these targets, while size and albedo estimations usually require information not only on the reflected but also emitted light of these bodies. Both approaches require the assessment of results from a larger sample of TNOs in order to synthesize population properties. Photometric and spectroscopic results of TNOs are available since two decades, however, still with insufficient coverage of the various dynamical populations and moderate to small sample sizes for statistical significance. Size and albedo estimations are even less abundant. In order to overcome this situation, a Herschel Key program (Müller et al. 2009), was initiated with the aim to determine sizes, albedo and thermal properties of about 130 TNOs and Centaurs and analyze links between physical, chemical and dynamical properties of these objects in order to further understand their formation and evolution history. It was soon realized that complementary photometric—and spectroscopic—information of the program targets is required in order to perform the analysis of the Herschel measurements and to put the results in a global context. The observations and results described below are part of the complementary ground-based support for the Herschel Key program and at the same time serve as independent information for the analysis of individual objects and population properties in the visible light.

TNOs from the target list of the Herschel Key Program ‘TNOs are Cool’ (Müller et al. 2009) were observed in order to provide photometric information on the objects in the visible wavelength range and to improve the orbit information around the time of the Herschel measurements. The TNOs’ visible photometry is used to determine the absolute magnitude of the selected targets, which can be applied together with Herschel measurements for estimations of their size and albedo. It also provides complementary physical information of the objects, e.g., their global reflectance and intrinsic surface colours (Sect. 5) and integrates in the statistical characterization of the various populations of minor bodies in the outer solar system (Sect. 6).

2 Observations

The selection criteria for the targets of the ground-based imaging observations were: (1) the TNO is in the target list of the Herschel Key Program ‘TNOs are Cool’, meaning it was already measured or was meant to be measured by the space observatory and (2) the photometric information of the target, like absolute magnitudes and/or colours and spectral information in the visible wavelength range, is missing. This way, the obtained results could also complement the MBOSS2 database (Hainaut et al. 2012) and thus be used for the characterization of photometric properties of the TNO populations. In addition, targets for which the predicted uncertainty of the ephemeris was critical for the Herschel observations received high priority for implementation. In total 36 TNOs were included in the target list of our observations of which 35 objects were actually pointed by Herschel. The remaining TNO (2001 CZ31) was included in our target list for observations since by the time of the imaging photometry it was still to be observed by Herschel, but at the end it was removed from the Herschel target list. The objects selected belong to the dynamical groups of Centaurs, Plutinos, classical disk objects (CDOs), scattered disk objects (SDOs) and detached disk objects (DDOs). The classical disk objects are furthermore distinguished in two groups, i.e. the dynamically cold ones with inclinations below 5 deg and the dynamically hot ones with inclinations above 5°. This criterion addresses a possible different formation region for both groups as suggested by dynamical models for the early planetary system (see Morbidelli et al. 2008 and references therein) as well as by the diversity of other physical properties (see Doressoundiram et al. 2008 and references therein).

The observations were performed at the La Silla-Paranal observatory operated by the European Southern Observatory ESO during October 2009 to August 2011. Two telescope-instrument combinations were used, i.e., the 2.2m MPG/ESO telescope plus the WFI instrument at La Silla and the 8.2 m VLT Unit Telescope 1 Antu plus the FORS2 instrument at Paranal. WFI is a wide field imager with a half-degree field of view with CCD pixel size of 0.238 arcsec. FORS2 is a focal reducer with a 6.8 arcmin field of view and a pixel resolution of 0.25 arcsec for the standard collimator optics used. Technical information on the telescopes and instruments are found at http://www.eso.org/sci/facilities/lasilla/telescopes/2p2.html and http://www.eso.org/sci/facilities/lasilla/instruments/wfi.html for the 2.2m + WFI and at http://www.eso.org/sci/facilities/paranal/instruments/overview.html and http://www.eso.org/sci/facilities/paranal/instruments/fors/ for the VLT UT1 + FORS2.

The 2.2m + WFI observations were done in visitor mode during observing periods of the Max-Planck Society MPG, while the VLT observations were collected in normal open-time ESO service observing mode. The imaging sequences of the TNOs used VRI or BVRI filters and repeated the R filter during sequences that lasted significantly longer than 40–60 min in order to follow possible object variability due to rotation. Typically, only a single epoch was observed per target; multiple epochs were measured in some cases if the first attempt was performed under unfavorable sky conditions. During the TNO observations telescope tracking was set to compensate for the differential motion of the targets. For calibration purposes photometric standard star fields from the ESO (for FORS2; http://www.eso.org/sci/facilities/paranal/instruments/fors/tools/FORS_Std/FORS_Std.html) or the Landolt list (for WFI; Landolt 1992) were observed and the usual bias, sky, and daytime flatfield exposures were collected. TNO and standard stars were imaged as much as possible when clear sky conditions prevailed according to the environmental monitor of the observing site. For the WFI observations a set of standard star fields covering the airmass range from 1 to 2 was imaged in order to allow for determination of the full set of photometric reduction parameters. The FORS2 standard star calibrations followed the instrument calibration plan which foresees typically only one calibration field per night and relies on the determination and stability of extinction parameters and colour transformations over longer timescales.

Table 1 provides the observing log for the TNO observations together with results for the measured filter brightness of the objects. Note that not all target TNOs were measured in all filters used at the respective telescope-instrument observations for the overall program. In general, with 2.2m + WFI TNOs were imaged through VRI-type instrument filters, while for VLT + FORS2 usually BVRI-type instrument filters were applied.

Table 1 Observing log and measured magnitudes of the TNOs and Centaurs

3 Data Processing

The data processing started with the basic reduction steps for photometry, i.e., bias subtraction, flatfield corrections, exposure time division and determination of the photometric parameters for the observing sites and telescope-instrument combination used. For the 2.2m + WFI photometric zeropoints, extinction parameters and colour transformations were obtained on a nightly basis or for an observing interval of several nights for which stable sky conditions could be assumed. Stable sky conditions were assessed via the nightly solutions and information on the sky transparency from the environmental monitor of the site. For VLT + FORS2 nightly zeropoints only were determined since usually only a single standard star field per night was taken for calibration purposes during service mode observations. Data for the sky extinction and colour transformation of the FORS2 observing periods were taken from the ESO FORS2 instrument calibration page (http://www.eso.org/observing/dfo/quality/FORS2/qc/photocoeff/photocoeff_fors.html). The mean extinction coefficients for the FORS2 filters over the observing period are: 0.21 mag/airmass for the B filter band, 0.13 mag/airmass for V, 0.09 mag/airmass for R and 0.03 mag/airmass for I with a scatter of well below 0.02 mag/airmass for B and V and about 0.01 mag/airmass for R and I filters.

The TNOs were identified in the field of view by searching for moving objects at the predicted object positions; this search was done by image blinking, and after identification the accurate astrometric position of the TNO was measured and compared with the predicted one. A list of measured object (TNOs and Centaurs) positions and exposure midpoints was reported to the IAU Minor Planet Center.

After measuring the photometry of the TNOs in relative units, the photometric magnitudes of the objects were obtained for standard Bessell filter bands VRI for the WFI observations and BVRI for the FORS2 observations. The measurement of the TNO photometry in relative units was performed on object-aligned median-averaged images by applying the aperture growth method: The relative counts of the TNO were measured in a series of apertures with increasing radius centered on the object and the mean magnitude of the TNO was determined from the average ‘saturation level’ that the object brightness reached for larger apertures well beyond the seeing limit. The same method was applied for measuring the standard stars in order to determine the photometric parameters mentioned above. The photometry used apertures without noticeable background objects included and an object free annulus centered and close to the TNO or the standard star was chosen for sky background estimation. The results of the TNO photometry are listed in Table 1.

From the filter magnitudes, when available, 2 or 3 object colours were calculated, i.e., V–R and R–I for objects observed with the 2.2m + WFI and B–V, V–R and R–I for objects observed with FORS2. When possible, the slope parameter (also known as spectral gradient, S) is calculated (a) for four individual filter combinations BV, VR, RI and BI applying the formula in Doressoundiram et al. (2008) and (b) by estimating it by linear regression of the relative spectrum represented by the BVRI filters normalized to the V filter magnitude equal to one. Before the slope calculation, intrinsic colours of the TNOs were calculated by removing the solar value for the respective filter combination. The central wavelength of the filters provided the spectral reference for the slope calculation. The slope estimation assumes a smooth and straight spectrum over the wavelength range considered and, namely, the absence of absorption and emission features. This assumption is justified—although not proven for the individual objects—since so far no strong absorptions or emissions were identified in the visible wavelength range through spectroscopy of TNOs (Barucci et al. 2008). The BV, VR, RI and BI slope values allow the comparison of the straightness of the spectral slopes over the visible wavelength range and to assess whether deviations exist in particular towards the blue and red ends of the visible spectrum. We have noted that some B filter measurements seem to be affected by relatively low signal-to-noise level such that the BV spectral slope estimations lead to discrepancies of more than 5–10 %/100 nm compared to the results from the other filters. In that case we decided not to consider the B filter for the spectral slope calculation. We have considered as final values for the spectral slope S, those measured using the method (b) described above, after comparing the latter with the values obtained from individual filter band combinations.

Absolute V and R magnitudes (HV and HR, respectively) are obtained by correcting the measured brightness for Sun and Earth distances and for an average phase function. We applied a linear phase function with slope parameter β = 0.16 ± 0.03 mag/deg for TNOs and β = 0.11 ± 0.01 mag/deg for Centaurs as proposed by Sheppard and Jewitt (2002).

The absolute magnitudes, colours, and the spectral slopes of the TNOs and Centaurs are reported in Table 2. Estimation of the result errors is done via error propagation using measurement (relative count rates for the aperture photometry) and tabulated uncertainties (for the atmospheric extinction and instrumental colours for the FORS2 photometry). Flatfield inhomogeneities are considered in the error estimation for WFI data on TNOs and standard stars, while for FORS2 only for the TNO photometry (relying on the proper treatment for the photometry uncertainty in the course of the instrument calibration plan and data quality control of ESO).

Table 2 Dynamic properties and photometric results of the observed TNOs and Centaurs

Note that not all observations of the TNO and Centaur targets of the program provided useful results from the data analysis. 2001 CZ31 and 2006 SX436 were not detected in the pointed fields, 2003 CO1 showed unrealistic colours, which may be due to variable sky conditions. It is noted that the measurements of 2002 GV31, 2005 UJ438, 2007 OR10 and 2007 RW10 are affected by blends with background objects. In general, the photometry of TNOs measured with the WFI instrument is less accurate given the lower signal-to-noise ratio of the exposures, due to the smaller aperture of the 2.2m telescope, and due the relatively unstable atmospheric conditions during the observing runs at La Silla.

4 Results

The data from the observations at ESO telescopes allowed to obtain photometric measurements of in total 33 TNOs and Centaurs, i.e., 5 Plutinos, 14 CDOs, 5 SDOs, 5 DDOs and 4 Centaurs. Of the 14 CDOs, 8 belong to the dynamically hot group and 6 to the dynamically cold population. The dynamical classification used here follows the one proposed by Gladman et al. (2008). Five objects have three filters (Bessell VRI or BRI) measured, and two TNOs have only one filter (Bessell R) observed; the rest of the sample (26 objects) has results in four filters (Bessell BVRI). In the following sections we describe the results for individual objects and consider photometric population properties for the TNOs and Centaurs. For comparison we make use of data compiled in the MBOSS2 database of minor bodies in the outer solar system as described in Hainaut et al. (2012) and available at http://www.eso.org/~ohainaut/MBOSS/ (database version for the paper of Hainaut et al. 2012). It is noted that these authors have performed a critical data evaluation of individual objects for which results are published. Thus, for comparison with our data we take the MBOSS2 results as reference in the text and tables below. The publications for the photometry of the individual objects used in MBOSS2 are listed here: 1998 SG35—Delsanti et al. (2001), Doressoundiram et al. (2001), Bauer et al. (2003), Dotto et al. (2003), Doressoundiram et al. (2007); 1999 OX3—Tegler and Romanishin (2000), Doressoundiram et al. (2001), Delsanti et al. (2001), Boehnhardt et al. (2002), Doressoundiram et al. (2002), Bauer et al. (2003), McBride et al. (2003), Peixinho et al. (2004), Doressoundiram et al. (2005, 2007), Jewitt et al. (2007), Sheppard (2010); 2002 KX14—Rabinowitz et al. (2007), DeMeo et al. (2009), Romanishin et al. (2010); 2003 FX128—Tegler et al. (2003), Jewitt et al. (2007), Benecchi et al. (2009); 2003 FY128—DeMeo et al. (2009), Sheppard (2010); 2003 GH55—Jewitt et al. (2007); 2003 OP32—Rabinowitz et al. (2008); 2004 GV9—Rabinowitz et al. (2008), DeMeo et al. (2009); 2004 SB60—Benecchi et al. (2009); 2005 RM43—Rabinowitz et al. (2008), DeMeo et al. (2009); 2005 TB190—Sheppard (2010).

4.1 Comparison of Individual TNOs in MBOSS2 Database

11 objects in our target list have entries in the MBOSS2 database, 2 more in a recent paper by Bauer et al. (2013). Both are used for comparison of the absolute brightness and the spectral gradients of the objects—see Table 3. In order to be compatible with the MBOSS2 database the result listed in Table 3 provides the ‘modified’ absolute magnitude not corrected for the phase function. From the eight objects with listed absolute magnitudes in three datasets (i.e. ours, that from MBOSS2 and from Bauer et al.) five objects (1995 SG35, 2003 FX128, 2003 GH55, 2005 TB190, 2005 UJ438) have small differences (<0.2 mag) for the modified HR such that one may speculate on a small amplitude of the rotation lightcurve. The other three objects (1999 OX3, 2002 KY14, 2003 FX128) display deviations of 0.4–0.8 mag which may indicate larger amplitudes of rotation variability and/or contributions from phase effects or activity of the objects.

Table 3 Comparison of results of our TNO and Centaur photometry with MBOSS 2 data

For the spectral gradients S our values agree—within the estimated uncertainties—with those of the MBOSS2 database and Bauer et al. (2013) for eight objects (1995 SG35, 2002 KX14, 2002 KY14, 2003 FX128, 2003 GH55, 2004 SB60, 2005 RM43, 2005 UJ438) and they are compatible (i.e., close in amplitude though outside of the formal uncertainties) for two TNOs (2003 OP32, 2005 TB190). Disagreement is found for two objects (2003 FY128 and 2004 GV9) which may indicate large-scale surface heterogeneity and deserves confirmation by new observations.

4.2 Individual Objects

In the following we provide brief comments on individual objects, grouped by dynamical types as estimated from the orbital elements and orbit integrations and applying the dynamical classification criteria as described by Gladman et al. (2008).

4.2.1 3:2 Resonance Objects (Plutinos): 2001 QG298, 2003 AZ84, 2003 FB128, 2004 EW95, 2006 HJ123 (see Tables 1, 2)

From the HR magnitudes and assuming an average albedo of 0.1 (Mommert et al. 2012, gave 0.08 ± 0.03 as average geometric albedo for a sample of 18 Plutinos), 2001 QG298, 2003 FB128, 2004 EW95 and 2006 HJ123 belong to the medium-large objects (order 200–500 km diameter) while 2003 AZ84 seems to have a larger size (order 800–900 km). The quantitative analysis of Herschel and other ground-based measurements of Plutinos (Mommert et al. 2012) provides sizes of 727 km for 2003 AZ84 and 291 and 216 km for 2004 EW95 and 2006 HJ123, respectively. It is noted that 2006 HJ123 has a relatively high albedo of 0.28, while 2003 AZ84 and 2004 EW95 show albedo of 0.11 and 0.04, respectively.

The spectral slopes of the Plutinos in our sample cover a wide range from 1 to 34 %/100 nm. Two Plutinos, 2003 AZ84 and 2004 EW95, have close to neutral intrinsic colours which may indicate the presence of ices on their surfaces. At least for 2003 AZ84 the neutral spectral gradient in the visible and the relatively high albedo is nicely compatible with the presence of water ice on its surface which is claimed by Barkume et al. (2008) based on near-IR spectroscopy of this object. 2001 OG298 and 2006 HJ123 belong to the very red Plutino objects (S above 30 %/100 nm); their sizes, albedos and spectral properties are not known.

4.2.2 Dynamically ‘Hot’ Classical Disk Objects (Hot CDOs): 2003 MW12, 2003 OP32, 2003 UZ117, 2004 GV9, 2004 SB60, 2005 RS43 (see Tables 1, 2)

With absolute magnitudes HR between 3.4 and 4.9 mag, the hot CDOs measured may fall in the size range of 500–900 km (assuming the mean albedo of 0.1 for hot CDOs; Vilenius et al. 2012, give a mean geometric albedo of 0.11 ± 0.04). Based on Herschel and ground-based measurements, Vilenius et al. (2012) and Fornasier et al. (2013) determined sizes and albedos of 680 km and 0.077 for 2004 GV9 and 901/874 km and 0.044 for 2004 SB60, respectively. The majority, i.e., 4 hot CDOs (2003 MW12, 2003 UZ117, 2004 SB60, 2005 RS43), have neutral to moderately red (0–12 %/100 nm) spectral gradients in the visible wavelength range; one hot CDO displays a slightly bluish slope (2003 OP32 with −7 %/100 nm), one seems to be very red (2004 GV9 with 46 %/100 nm)—and none of the measured CDOs falls in the intermediate to red colour range with a mean value of about 20 %/100 nm (Hainaut et al. 2012). It is noted that 2003 OP32 and 2003 UZ117 are members of the Haumea collision family; the bluish and close to neutral spectral gradients of both TNOs are very much compatible with that of the possible parent body 136108 Haumea (Jewitt et al. 2007, Rabinowitz et al. 2007) and may thus support the interpretation as collision fragments.

4.2.3 Dynamically ‘Cold’ Classical Disk Objects (Cold CDOs): 2001 QS322, 2001 QT322, 2002 GV31, 2002 KX14, 2003 FE128, 2003 GH55, 2003 UR292, 2005 EF298 (see Tables 1, 2)

From the absolute brightness range determined (3.4–7.6 mag in R) the eight dynamically cold CDOs in our observing list belong to the medium large TNOs (80–550 km for a geometric albedo of 0.15, see Vilenius et al. 2012). 2002 QT322 is the brightest (and possibly largest) cold CDO found so far. For 2002 KX14, the second brightest cold CDO in our sample, diameter and albedo estimations by Vilenius et al. (2012) gave 455 km and 0.01, respectively; 2002 GV31 seems to be a smaller TNO (<130 km diameter) though with a brighter albedo (>0.22). The spectral gradients of the 6 cold CDOs in the visible fall in the range between 22 and 29 %/100 nm, i.e., they belong to the red TNO population and are quite typical for members of the cold Classical Disk (see Hainaut et al. 2012). 2001 QT322 and 2002 GV31 displayed moderately red (9 %/100 nm) and quasi-neutral (2 %/100 nm) spectral gradients, respectively, which fall below the currently known lowest values for CDOs. It is however noted, that the measurements of 2002 GV31 might be affected by blends from a background object close to the TNO.

4.2.4 Scattered Disk Objects (SDOs): 1999 OX3, 2003 FX128, 2005 QU182, 2005 RM43, 2007 RW10 (see Tables 1, 2)

The five SDOs measured cover an absolute R brightness range from 3.4 to 6.3 mag corresponding to size of about 300–900 km when assuming the mean albedo for SDOs of 0.07 as given by Santos-Sanz et al. (2012). For two TNOs diameter and albedo were published (300 km and 0.05 for 2003 FX128 and 247 km and 0.08 for 2007 RW10; Santos-Sanz et al. 2012). The four SDOs for which spectral gradients are obtained from our photometry show no (2005 RM43), moderate (2007 RW10) and medium reddening (2003 FX128, 2005 QU182) within the range found from the measured SDO population.

4.2.5 Detached Disk Objects (DDOs): 2003 FY128, 2004 PG115, 2005 TB190, 2007 OR10, 2010 EK139 (see Tables 1, 2)

The absolute magnitudes of the measured DDOs (range is 1.5–5.5 mag in R) indicate large to medium size bodies (300–1400 km) when assuming a mean albedo of 0.17 (Santos-Sanz et al. 2012). This conclusion does not apply for 2010 EK139 since the higher geometric albedo of 0.25 results in a size of almost 1,000 km as estimated based upon Herschel observations (Pal et al. 2012). The size and albedo estimates reveal a rather wide range for diameter and albedo (460 km and 0.08 for 2003 FY128, 464 km and 0.15 for 2005 TB190, 1,280 km and 0.19 for 2007 OR10; see Santos-Sanz et al. 2012). The reddening of the DDOs is either small (4 and 9 %/100 nm for 2003 FY128 and 2004 PG115) or red (25 %/100 nm for 2005 TB190). 2007 OR10 is found with a very red spectral slope of 50 %/100 nm, although the reliability of this results is somehow jeopardized by the blend of a background object close to the TNO. It is noted that 2005 TB190 and 2007 OR10 seem to be redder than other DDOs measured so far (see Hainaut et al. 2012).

4.2.6 Centaurs: 1998 SG35, 2002 KY14, 2005 RO43, 2005 UJ438 (see Tables 1, 2)

With absolute magnitudes between 6.9 and 11.0 mag in R the Centaurs in our list are among the smaller objects (diameter of 25–200 km for an assumed geometric albedo of 0.07; Stansberry et al. 2008). With 7.4 and 6.9 mag in V and R, respectively, 2005 RO43 has the lowest absolute brightness among the Centaurs for which photometry is published. Diameter and albedo are measured for 1998 SG35 (52 km and 0.025; Stansberry et al. 2008). Two Centaurs each have moderately red (1998 SG35 and 2005 RO43) and very red (2002 KY14 and 2005 UJ438) spectral gradients S, i.e., representing the bimodal colour population put forth by Peixinho et al. (2012).

5 Population Statistics

Adding our results to those of the MBOSS2 database on TNO photometry in the visible wavelength range, we have performed a similar statistical assessment of the spectral gradients S for the different dynamical groups as described in Hainaut et al. (2012) and best illustrated in their Table 4. The assessment included the t test, the F test, and the Kolmogorov–Smirnov test of the spectral gradients distributions for Plutinos, hot and cold CDOs, SDOs, DDOs and Centaurs plus Jupiter Trojans. The key findings confirm those of Hainaut et al. (2012), i.e., the cold CDOs and the Trojans are clearly disjoint from each other and from the other TNO populations for their colour distributions. The red colour population among the CDOs was first suggested by Tegler and Romanishin (2000) and further analyzed by Doressoundiram et al. (2002), Trujillo and Brown (2002). The spectral gradient distributions of the dynamical TNO populations and of the Centaurs is shown in Fig. 1; obviously, the cold CDOs show a very wide distribution of spectral gradients peaking in the 25/30 %/100 nm bin. The bimodal gradient distribution of the Centaurs as suggested first by Peixinho et al. (2003) and Tegler et al. (2003) and reanalyzed for instance by Peixinho et al. (2012) is also noticeable in the figure, although the statistical tests performed did not address it specifically. From our statistical tests the spectral gradient distribution of the Centaurs is indistinguishable from those of the Plutinos, hot CDOs, SDOs and DDOs.

Fig. 1
figure 1

The distributions of spectral gradients for the TNO populations and Centaurs. The histogram shows the number of objects per spectral gradient bin for the dynamical populations of TNOs and for Centaurs. Abscissa bin of spectral gradient range (for instance: 5\10 means spectral gradients from 5 to 10 %/100 nm). Ordinate number of objects per spectral gradient bin

6 Concluding Remarks

Photometric measurements of 33 TNOs and Centaurs in BVRI filters are presented. The measured objects are all from the target list of the Herschel Key program ‘TNOs are cool’. They were selected for observations since visible photometry was missing either to support the immediate size and albedo estimation to be performed together with flux measurements from Herschel observations or to complement the object characterization by multi-colour data. They are thus providing valuable information and input for the analysis of Herschel data of individual objects and of the whole sample of objects measured through this program.

Indications of brightness variations are found by comparison of published results with our data for 3 objects. The suggested variations may result from non-spherical rotating objects of minimum main axes ratios between 1.2 and 2. However, no lightcurve can be compiled from the available measurements. Alternatively, parts of the variation amplitude may also be due to the phase function and/or intrinsic activity.

Rough size estimations are performed based upon the absolute R magnitudes of the objects and assumed average geometric albedo values for the respective dynamical population of the TNOs or Centaurs. These estimations fall in the size ranges known so far for the respective populations.

The statistical analysis of the spectral gradients of the measured objects added to the much larger sample of the MBOSS2 database confirmed the diversity of the spectral gradient distributions of the cold CDOs (and Trojans) from those of the other TNO and Centaur populations.

A few objects show spectral gradients at the extreme ends of the known ranges for TNOs and Centaurs. 6 objects were found to show neutral spectral gradient (S < 3 %/100 nm), i.e., 2002 GV31, 2003 AZ84, 2003 MW12, 2003 OP32, 2003 UZ117 and 2005 RM43, half of them from the population of dynamically hot CDOs. Neutral colours may indicate the presence of surface ice (suggested by spectroscopic results for 2003 AZ84). 2003 OP32 has a rather negative spectral slope (S = −7 %/100 nm) in the visible wavelength range. It is interesting to note that among the objects with neutral spectral slopes is one cold CDO (2002 GV31). Towards the very red end of the spectral slope distributions (S > 40 %/100 nm) we find three objects, i.e. 2002 KY14, 2004 GV9 and 2007 OR10. The latter object is by far the reddest DDO measured so far.