5 Results

   

Table 3: Absolute magnitude and colors for all objects, obtained from the photometric measurements presented in Table 2. For objects measured during both runs, we present one value per run, in order to highlight any instrinsic change.

Object	(1)	(2)	M(1,1) $\pm~\sigma$	RN [km]	${\cal S} \pm\sigma$	B-V $\pm~\sigma$	V-R $\pm~\sigma$	R-I $\pm~\sigma$
1993 SB	Plut	2b	8.07 $\pm$ 0.08	65.5 $\pm$ 2.4	13.31 $\pm$ 3.78	0.76 $\pm$ 0.10	0.48 $\pm$ 0.07	0.53 $\pm$ 0.08
1994 TB	Plut	1b	7.32 $\pm$ 0.05	92.5 $\pm$ 2.5	44.89 $\pm$ 3.26	1.10 $\pm$ 0.07	0.78 $\pm$ 0.06	0.72 $\pm$ 0.08
		2b	7.59 $\pm$ 0.09	81.8 $\pm$ 3.6	28.12 $\pm$ 4.73	1.04 $\pm$ 0.12	0.60 $\pm$ 0.08	0.70 $\pm$ 0.12
1995 SM55	QB1	1b	4.39 $\pm$ 0.02	356.9 $\pm$ 4.4	0.27 $\pm$ 1.92	0.65 $\pm$ 0.02	0.38 $\pm$ 0.03	0.29 $\pm$ 0.04
		2a	4.32 $\pm$ 0.06	368.0 $\pm$ 10.2	-1.14 $\pm$ 3.58	0.63 $\pm$ 0.06	0.33 $\pm$ 0.06	0.35 $\pm$ 0.09
1995 TL8	Scat	2b	4.58 $\pm$ 0.06	325.8 $\pm$ 9.0	33.94 $\pm$ 3.05	1.04 $\pm$ 0.07	0.69 $\pm$ 0.05	0.64 $\pm$ 0.08
1996 RQ20	QB1	1a	6.89 $\pm$ 0.10	112.4 $\pm$ 5.7	23.16 $\pm$ 4.97	0.95 $\pm$ 0.14	0.61 $\pm$ 0.09	0.55 $\pm$ 0.12
1997 QH4	QB1	2b	7.19 $\pm$ 0.13	98.2 $\pm$ 6.4	20.81 $\pm$ 6.34	1.10 $\pm$ 0.17	0.52 $\pm$ 0.11	0.66 $\pm$ 0.16
1997 QJ4	Plut	1b	7.29 $\pm$ 0.12	93.6 $\pm$ 5.3	6.89 $\pm$ 5.63	--	0.45 $\pm$ 0.12	0.40 $\pm$ 0.10
1998 BU48	Scat	2a	7.03 $\pm$ 0.06	105.5 $\pm$ 3.0	26.98 $\pm$ 3.10	1.10 $\pm$ 0.07	0.65 $\pm$ 0.05	0.57 $\pm$ 0.08
1998 SG35	Cent	1b	10.83 $\pm$ 0.02	18.4 $\pm$ 0.2	12.11 $\pm$ 1.67	0.69 $\pm$ 0.02	0.46 $\pm$ 0.03	0.52 $\pm$ 0.04
1998 SM165	QB1	2a	5.91 $\pm$ 0.05	176.6 $\pm$ 4.7	29.72 $\pm$ 2.94	0.94 $\pm$ 0.07	0.64 $\pm$ 0.05	0.65 $\pm$ 0.07
1998 SN165	QB1	1b	5.44 $\pm$ 0.09	220.0 $\pm$ 9.9	7.83 $\pm$ 4.78	0.56 $\pm$ 0.12	0.50 $\pm$ 0.09	0.34 $\pm$ 0.11
1998 TF35	Cent	2a	8.51 $\pm$ 0.07	53.4 $\pm$ 1.8	36.67 $\pm$ 3.79	1.13 $\pm$ 0.08	0.68 $\pm$ 0.07	0.72 $\pm$ 0.09
1998 UR43	Plut	2a	7.94 $\pm$ 0.08	69.4 $\pm$ 2.7	5.73 $\pm$ 4.66	0.78 $\pm$ 0.10	0.49 $\pm$ 0.08	0.27 $\pm$ 0.12
1998 WH24	QB1	2b	4.43 $\pm$ 0.06	350.0 $\pm$ 10.5	22.61 $\pm$ 3.29	1.01 $\pm$ 0.08	0.58 $\pm$ 0.05	0.59 $\pm$ 0.08
1998 WV31	Plut	2b	7.64 $\pm$ 0.07	79.7 $\pm$ 2.7	10.20 $\pm$ 4.28	0.83 $\pm$ 0.09	0.51 $\pm$ 0.07	0.36 $\pm$ 0.11
1998 WX31	QB1	2a	6.22 $\pm$ 0.07	153.1 $\pm$ 5.6	26.20 $\pm$ 4.61	--	0.60 $\pm$ 0.08	0.64 $\pm$ 0.11
1999 CC158	Scat	2a	5.43 $\pm$ 0.07	220.7 $\pm$ 8.0	20.29 $\pm$ 3.66	0.96 $\pm$ 0.10	0.57 $\pm$ 0.06	0.55 $\pm$ 0.09
1999 CD158	QB1	2b	4.90 $\pm$ 0.07	281.4 $\pm$ 9.1	13.43 $\pm$ 3.73	0.87 $\pm$ 0.08	0.48 $\pm$ 0.06	0.54 $\pm$ 0.09
1999 CF119	Scat	2b	7.03 $\pm$ 0.08	105.6 $\pm$ 4.0	13.45 $\pm$ 4.60	--	0.56 $\pm$ 0.08	0.39 $\pm$ 0.11
1999 DE9	Scat	2b	4.88 $\pm$ 0.06	284.4 $\pm$ 8.0	20.77 $\pm$ 3.37	0.86 $\pm$ 0.07	0.58 $\pm$ 0.06	0.56 $\pm$ 0.08
1999 OX3	Scat	1a	6.97 $\pm$ 0.22	108.8 $\pm$ 11.5	--	--	--	0.47 $\pm$ 0.11
1999 RZ253	QB1	1b	5.43 $\pm$ 0.06	284.4 $\pm$ 7.8	29.96 $\pm$ 3.00	--	0.65 $\pm$ 0.06	0.65 $\pm$ 0.06
1999 TC36	Plut	1b	4.83 $\pm$ 0.03	290.5 $\pm$ 4.3	31.69 $\pm$ 1.70	1.03 $\pm$ 0.04	0.68 $\pm$ 0.03	0.63 $\pm$ 0.03
		2b	4.88 $\pm$ 0.05	285.0 $\pm$ 6.6	33.51 $\pm$ 2.64	1.03 $\pm$ 0.06	0.70 $\pm$ 0.04	0.61 $\pm$ 0.07
1999 TD10	Scat	1b	8.71 $\pm$ 0.02	48.8 $\pm$ 0.5	12.83 $\pm$ 1.50	--	0.51 $\pm$ 0.03	0.47 $\pm$ 0.03
1999 UG5	Cent	2a	10.09 $\pm$ 0.04	25.8 $\pm$ 0.6	28.82 $\pm$ 2.58	0.97 $\pm$ 0.05	0.65 $\pm$ 0.04	0.60 $\pm$ 0.07
2000 OK67	QB1	2a	6.14 $\pm$ 0.06	159.3 $\pm$ 4.9	--	--	0.52 $\pm$ 0.07	--
		2b	--	159.3 $\pm$ 4.9	--	0.73 $\pm$ 0.11	--	--
		(*)	6.14 $\pm$ 0.06	159.3 $\pm$ 4.9	15.97 $\pm$ 7.06	0.73 $\pm$ 0.11	0.52 $\pm$ 0.07	--
2000 QC243	QB1	2a	7.95 $\pm$ 0.05	69.2 $\pm$ 1.7	6.96 $\pm$ 2.72	0.72 $\pm$ 0.06	0.45 $\pm$ 0.04	0.40 $\pm$ 0.07

(1) class: QB1 = Cubewano, Plut = Plutino, Scat = Scaterred Disk Object, Cent = Centaur. (2) run (UT date): 1a = 2000 Sep. 04, 1b = 2000 Sep. 05, 2a = 2000 Nov. 29, 2b = 2000 Nov. 30 (*) = compilation of Run 2a & 2b. M11 is the absolute R magnitude. R_N is an estimation of the radius of the object (in km) given by Eq. (2). $\cal S$ is the spectral gradient in (%/100 nm) as defined in the text.

Figure 1: Color-color diagrams for the 27 objects. The meaning of the different symbols is given in the middle right panel. The reddening line (which is the locus of objects displaying a linear reflectivity spectrum) has a range of gradients $\cal S$ from -10 to 70%/100 nm; a tick mark is placed at every 10 units.

5.1 Color indexes

The resulting color indexes computed from the classical photometry measurements are shown in Table 3. For objects that have been measured at different epochs, we present one value per epoch in order to monitor any intrinsic brightness variation between the two runs. For objects which have repeated R measurements during the same night of observation, the colors are obtained from the average R.

5.2 Absolute magnitude

The absolute magnitude M(1,1) has been computed for each epoch. It is defined as:

$$% M(1,1) = R - 5 \log\,(r \Delta),$$ (1)

where R is the R magnitude, r and $\Delta$ are respectively the helio- and geocentric distances [AU] at the time of the observations. We do not take into account the phase correction $-\beta\alpha$ , where $\beta$ is the phase coefficient (cf. Meech & Jewitt 1987 and Delahodde et al. 2001 for values of phase coefficient; a typical value is $\beta=$ 0.04 mag/ $\hbox{$^\circ$ }$), and $\alpha$is the phase angle. Indeed, M(1,1) is used in this paper only for a rough estimation of the radius of the object, whose error is dominated by the albedo uncertainty.

As for color indexes, for objects with several epochs available, we present one value of the M(1,1)obtained per epoch. In this way, we can improve our interpretation of any brightening or change between two epochs.

5.3 Radius

Assuming a canonical surface albedo of p=0.04 (corresponding to that of cometary nuclei, Keller 1990), we can estimate the radius R_N[km] of each object. This value of the albedo is in agreement with thermal IR measurements obtained for TNOs by Thomas et al. (2000). R_N[km] is computed with the following formula (Russell 1916):

$$% p R_N^2 = 2.235 \times 10^{16}\times 10^{0.4(M_{\odot} - M(1,1))},$$ (2)

where $M_{\odot}$ is the R magnitude of the Sun, M(1,1) is the absolute R magnitude from Eq. (1) and p is the albedo. The values obtained are also presented in Table 3.

It is interesting to note that this radius, evaluated assuming an albedo p=0.04, can be in error by a factor of 2 or more because of the uncertainty of this albedo. This is especially true for bluish objects, whose albedo could be fairly high (in the case of a fresh ice surface, i.e. 0.1 for Chiron, Hartmann et al. 1981), or very low (in the order of 0.02 in case of highly irradiated objects; Thompson et al. 1987). Therefore, this estimation of the radius has to be taken with precaution.

  
5.4 Spectral gradient

 

 

Table 4: Solar colors used in this paper, from Hardorp (1980); Campins et al. (1985) and Allen's Astrophysical Quantities Cox (2000).

Color	Value
$(B-V)_{\odot}$	0.67
$(V-R)_{\odot}$	0.36
$(V-I)_{\odot}$	0.69

Figure 2: Reflectivity spectra. The reflectivity is normalized to 1 for the V filter; the "spectra'' have been arbitrarily shifted for clarity. For each object, the dotted line is the linear regression over the V, R, I range (excluding B), corresponding to the gradient $\cal S$ reported in this paper.

The color indexes can also be converted into relative spectral reflectivities ${\cal R}(\lambda)$, computed at the central wavelength of the broadband filters used (Jewitt & Meech 1986). We normalized these reflectivities at the central wavelength of the V filter, leading to the following equation:

$$% {\cal R}(\lambda) = 10^{-0.4[ (m(\lambda)-m(V)) - (m(\lambda)-m(V))_\odot]},$$ (3)

where m and $m_\odot$ are the magnitude of the object and of the Sun at the appropriate wavelength. In other words, the color indices are equivalent to very low resolution spectra. These spectra are presented in Fig. 2. To characterize a reflectivity spectrum, we can consider the reddening, $\cal S$ (also called the slope parameter or spectral index, cf. Hainaut & Delsanti 2001), defined as percent of reddening per 100 nm as:

$$% {\cal S}(\lambda_1,\lambda_2) = 100\times\frac{{\cal R}(\lambda_2)-{\cal R}(\lambda_1)}{(\lambda_2-\lambda_1)/1000}\cdot$$ (4)

As most objects have a linear reflectivity spectrum over the V, R, and I bands, we can compute the mean reddening, $\cal S$, by linear regression. All the values are presented in Table 3.

On each color-color plot we have represented a line which characterizes the locus of objects with a linear reflectivity spectrum, with reddening (i.e. spectral slope) ranging from -10 < $\cal S$ < 70$\%$/100 nm, to guide the eye.