Although the telescope beam for the Pluto observations encompasses both Pluto and Charon, we assume that only Pluto contributes to the CO emission.

There is no clear observational evidence for the presence of an atmosphere around Charon. For a similar atmospheric composition and structure, atmospheric escape per surface unit would be about five times larger at Charon than at Pluto (Trafton et al. 1988; Yelle & Elliot 1997; Trafton et al. 1997). For atmospheres buffered by volatile ices, an integration of the escape fluxes over the Solar System age suggests a typical loss of N₂ ice surface layers of 3 km for Pluto and 8 km for Charon. Therefore, in both cases, volatiles initially exposed on the surface are likely to be exhausted, but both bodies must have retained some of their original inventory. Whether an atmosphere is present now depends on resupply mechanisms. The presence of an atmosphere around Pluto and of volatile ices on its surface suggest that geological processes must operate on Pluto. Such processes, however, are less likely on Charon because of its small size, and the absence of volatile ice signatures from Charon's surface (see Cruikshank et al. 1997) suggests that Charon currently has no atmosphere. The possibility that Charon may capture some of Pluto's escaping atmosphere leads to a negligible, 10^-7 $\mu$ bar, pressure at Charon. Yet, we note that, from stellar occultation data, Elliot & Young (1991) reported a hint of a charonian bound atmosphere with low scale height, implying the presence of heavy species (Ar, etc.). The reality of the detection is however not considered likely by Trafton et al. (1997). In any event, there is currently no support for the presence of CO in an hypothetical Charon atmosphere, justifying our assumption to attribute all of the observed signal to Pluto.

Modelling of the CO emission from Pluto was performed using a standard atmospheric radiative transfer code. Indeed, as shown by Strobel et al. (1996), the CO emission occurs in local thermodynamical equilibrium conditions down to pressure levels of about 10^-5 $\mu$ bar. This is 11.7 scale heights above the 1.2 $\mu$ bar, 1250 km radius reference level indicated by the stellar occultation (Yelle & Elliot 1997). For an upper atmospheric temperature in the range 80-106 K, this corresponds to a 900-1400 km altitude above the 1250 km radius.

Because there remains considerable uncertainty about Pluto's atmospheric thermal structure, we used two different atmospheric models, both of which assume hydrostatic equilibrium. The first one is based on the thermal models of Strobel et al. (1996). These models account for solar heating in the near-infrared bands of CH₄, and cooling in the 7.6 $\mu$ m CH₄ band and in the CO rotational lines. Strobel et al. investigated the sensitivity of their calculations to the surface pressure and CH₄ abundance and vertical distribution. We specifically adopted the model with a 3 $\mu$ bar surface pressure, in which most of the CH₄ is confined to the bottom two scale heights (see their Fig. 11). This model reproduces the major features indicated by the stellar occultation data, namely a 15 Kkm^-1 temperature gradient at the surface and a $\sim$ 100 K quasi-isothermal temperature just above the $p = 2~\mu$ bar level. Yet, it implies a value of $\sim$ 1200 km for Pluto's surface radius, distinctly different from the radius indicated by the mutual event data (about 1158 km, Buie et al. 1992). For this reason, Stansberry et al. (1994) suggested that Pluto may possess a $\sim$ 40 km deep "hidden'' troposphere. They formulated a suite of models based on various tropospheric lapse rates and a Bates profile for the thermosphere. We adopted, as an alternative model, their profile with a tropospheric ${\rm d}T/{\rm d}z = -0.7$ K kms^-1 lapse rate, and a surface pressure of 24 $\mu$ bar. This profile becomes isothermal at 106 K, $\sim$ 45 km above Pluto's surface.

$\begin{figure} \par\includegraphics[width=10cm,clip]{MS1578f2.eps} \end{figure}$

Figure 2: The pressure-temperature-altitude thermal profiles adopted for the Pluto models. Solid line: "Strobel'' model. Dashed line: "Stansberry'' model. Since the two models correspond to different surface pressure and radius, the altitudes are expressed in terms of the distance from Pluto's center.

In both cases, the models were extended up to the $p = 10^{-5}~\mu$ bar level, which corresponds to 980 km and 1520 km altitudes, for the "Strobel'' and "Stansberry'' models, respectively. The two models are shown in Fig. 2 with the distance from Pluto's center as the altitude variable. We verified that the hydrodynamically escaping CO atmosphere has a negligible contribution to the CO line emission. This was done using the cometary model presented in Sect. 3.2 (see the related discussion). The only difference in the modelling with respect to Centaurs and KBOs is that collisional excitation is from CO-N₂ impacts instead of CO-CO impacts. With $v_{\exp} = 0.2$ kms^-1, T=60 K at the exobase, a N₂ escape rate of $2\times10^{27}$ mols^-1 (e.g. Krasnopolsky 1999) and CO/N₂ = 1%, the contribution of the escaping atmosphere to the CO J(2-1) line intensity is 0.05 mK MHz.

In all models, CO, which has the same mass as N₂ and is photochemically stable, was assigned a vertically uniform distribution, and the CO mixing ratio was varied from 0.01% to 10%. Pluto's brightness surface temperature was taken to be 31.5 K, in agreement with bolometric measurements in the same wavelength range (Altenhoff et al. 1988; Lellouch et al. 2000).

Line opacities were calculated using Voigt profiles, using broadening coefficients (CO by N₂) from Colmont & Monnanteuil (1986) and Semmoud-Monnanteuil & Colmont (1987). The transfer equation was integrated over all emission angles. As Pluto's atmosphere has considerable extent compared to the planet's radius, limb emission was taken into account. Because the CO lines are heavily saturated already in vertical viewing, they remain optically thick in horizontal viewing up to large altitudes. For example, in the case of the Stansberry model and for CO/N₂ = 0.1%, the $\tau = 1$ level in horizontal viewing for the CO J(2-1) line is reached at p = 2 nanobar, i.e. 450 km above Pluto's surface. This gives an additional 106 K emitting area essentially equal to Pluto's solid area. Therefore, the brightness temperature contrast in the line core is boosted from a maximum of 75 K for the vertical viewing to an actual value of $\sim$ 190 K!

Table 4: CO J(2-1) line area within $\pm$ 1 MHz from line center for different models and CO/N₂ mixing ratios.
Mixing ratio Line area [mK MHz]

Strobel model Stansberry model

10^-4 4.13 4.73

10^-3 7.59 9.02

10^-2 13.2 17.0

10^-1 18.2 27.1

**Table 4:** CO J(2-1) line area within $\pm$ 1 MHz from line center for different models and CO/N₂ mixing ratios.
Mixing ratio	Line area [mK MHz]
	Strobel model	Stansberry model
10^-4	4.13	4.73
10^-3	7.59	9.02
10^-2	13.2	17.0
10^-1	18.2	27.1

Figure 1 shows the comparison between observations and models for the CO J(2-1) line. Calculated line areas are given in Table 4. The effect of saturation is clearly evident, with the line contrast growing by only a factor of 2-3 for a CO abundance increasing by three orders of magnitude. The tentatively measured area of 18 mK MHz and the spectrum appearance is reproduced for CO/N₂ = 7%, in the case of the Strobel model, and CO/N₂ = 1.2% for the Stansberry model, but, as mentioned above, we regard these values as upper limits (note that, taking instead the 3- $\sigma$ upper limit on the line area of 11.7 mK MHz, the upper limits would be CO/N₂ < 0.6% and 0.3%, for the Strobel and Stansberry models, respectively). The higher sensitivity for the Stansberry model is due to the higher upper atmosphere temperature than in the Strobel model, which also causes it to be more extended. The possible presence of a troposphere and the exact value of the surface pressure are, in contrast, inconsequential to first order. We note that, with these values, the CO J(1-0) line shows a contrast of $\sim$ 0.003 mK for both models and an integrated area of 3.1 (respectively 2.0) mK MHz for the Strobel (respectively Stansberry) model. This is fully consistent with the upper limit for this line given in Table 1. Essentially, the 115.271 GHz line does not appear to be constraining because the filling factor of Pluto in the telescope main beam is four times smaller than at 230.538 GHz.

While our observations constrain the CO mixing ratio in Pluto's atmosphere rather than the integrated abundances, the above upper limits correspond to CO column densities of $1.2 \times 10^{20}$ molcm^-2 for the Strobel model and $8.75 \times 10^{19}$ molcm^-2 for the Stansberry model. For a "Stansberry-type'' model with a 58 $\mu$ bar surface pressure, the upper limit on the column density would be $\sim$ $2\times 10^{20}$ molcm^-2, significantly more constraining than the $(1.2{-}3.5) \times 10^{21}$ molcm^-2 values reported by Young et al. (2001). We note also that the Young et al. observations do not provide any useful constraint in the case of a "Strobel'' 3 $\mu$ bar atmosphere. Yet, our improved upper limits of (1.2-7%) remain clearly insufficient for further understanding of Pluto's thermal structure and surface-atmosphere interaction. As mentioned in the introduction, the expected atmospheric CO mixing ratio for an ideal solid solution of CO in N₂ is at least an order of magnitude less than our upper limits. As shown by Young et al. (2001), even if a "detailed balance'' model is envisaged (Trafton et al. 1998), the CO atmospheric abundance cannot exceed (0.1-0.5)%. The only situation that our upper limits can exclude is the case of isolated CO patches at temperatures similar or higher than N₂ ice, which would dictate CO/N₂ mixing ratios of 5-20% for T = 35-50 K. This situation is unlikely because CO and N₂ ices are miscible in all proportions and have only a weak difference in volatility, which must strongly inhibit a CO segregation.

3.2 Centaurs and KBOs

**Table 5:** Objects characteristics.
Designation	Name	Type	H^a	D^b[km]
1977 UB	2060 $\phantom{9}$ Chiron	Centaur	6.5	168-180
1992 AD	5145 $\phantom{9}$ Pholus	Centaur	7.0	189
1993 HA2	7066 $\phantom{9}$ Nessus	Centaur	9.6	80
1995 GO	8405 $\phantom{9}$ Asbolus	Centaur	9.0	106
1997 CU26	10199 Chariklo	Centaur	6.4	275-302
1998 SG35		Centaur	11.3	37
1994 TB	15820	KBO	7.1	254
1996 TL66	15874	SKBO	5.4	555
1996 TO66	19308	KBO	4.5	840
1996 TP66	15875	KBO	6.8	290
1998 WH24	19521	KBO	4.9	700

^a Absolute magnitude from Central Bureau for Astronomical Telegrams.
^b References for diameters: Chiron (Bus et al. 1996; Groussin et al. 2000; Campins et al. 1994;
Altenhoff & Stumpff 1995); Pholus (Davies et al. 1993); Chariklo (Jewitt & Kalas 1998; Altenhoff et al. 2001);
for other objects, they were calculated from optical photometry alone, assuming a geometrical albedo of 0.04.

CO observations of Centaurs and KBOs, and the single observation of HCN in 10199 Chariklo (Table 3), were interpreted using models developed for cometary atmospheres. These models assume freely escaping gas from the surface at constant velocity, namely a Haser density distribution:

Conservatively, we have assumed an expansion velocity $v_{\exp} = 0.4$ kms^-1 for all objects, regardless of their distance to the Sun. CO outflow velocities $\sim$ 0.4-0.5 kms^-1 have been measured in comets Hale-Bopp and 29P/Schwassmann-Wachmann 1 (P/SW1) at $r_{\rm h}> 6$ AU (Crovisier et al. 1995; Biver et al. 1999a). This value of 0.4 kms^-1 is higher, by a factor of a few (2-4 for the observed objects, assuming an albedo of 0.04), than the initial sonic gas velocity expected near the surface for freely escaping gas. This might account for the increase of the radial gas velocity during adiabatic expansion, although, for tenuous atmospheres, the small extent of the collision zone limits gas acceleration. For weakly bound atmospheres with hydrodynamically escaping gas, the sonic level is predicted to lie below the exobase (Chamberlain & Hunten 1987). Therefore, terminal outflow velocities of a fraction of kilometer per second might be also expected. This is also the case for Pluto's atmosphere. Modelling shows that its escaping atmosphere does not fit completely the hydrodynamic case. At the exobase, 1500-4000 km altitude above the surface according to Krasnopolsky (1999), the gas radial velocity is subsonic and estimated to $\sim$ 1-2 ms^-1 only (Krasnopolsky 1999; see also Trafton et al. 1997). However, due to the geometric effect (Hodges 1990), the transverse velocity due to random thermal motions at the exobase (where $T\sim60$ K; Krasnopolsky 1999) will be converted at larger distances, in the collisionless atmosphere, to a radial velocity component. Taking into account that 3- $\sigma$ upper limits on the line areas vary as the square root of the velocity window where they are computed, production rates upper limits scale proportionally to $v_{\exp}^{3/2}$ . Possibly, in most cases, the $Q_{\rm CO}$ upper limits given in Tables 3 and 6 may be somewhat too conservative.

The computation of production rates upper limits requires the modelling of the CO rotational population distribution. We used a CO excitation model developed for cometary atmospheres, which includes collisional excitation by CO-CO impacts and radiative excitation by the Sun and 3 K cosmic background radiation (Biver et al. 1999b, and references therein). This model computes CO rotational populations as function of distance to object's center. An important parameter for CO excitation in distant objects is the gas kinetic temperature. Indeed, although the radial extent of the collisional region at thermal equilibrium is small compared to that of the region sampled by the beam, fluorescence equilibrium does not apply for the relevant rotational levels because of their long radiative lifetimes. In Table 3, we present calculations performed with T=10 K and T=50 K. Kinetic temperatures $\sim$ 10 K were measured in comets P/SW1 and Hale-Bopp at $r_{\rm h}> 6$ AU (Crovisier et al. 1995; Biver et al. 1999a), in good agreement with fast adiabatic cooling (Crifo et al. 1999). We explore a temperature of 50 K, because expansion cooling can be "frozen'' out in tenuous atmospheres and we cannot exclude significant heating linked to gravity (e.g. heating by dust in case of Chiron, Boice et al. 1993, or from near-IR CH₄ bands in the extreme case of Pluto's atmosphere).

Table 3 presents 3- $\sigma$ upper limits obtained on the CO and HCN production rates. Data acquired on the same line and with the same telescope, but at different dates, have been averaged. The final 3- $\sigma$ $Q_{\rm CO}$ upper limits, obtained by combining upper limits from different lines and telescopes, are given in Table 6. These upper limits are typically $\sim$ 10²⁸ mols^-1 for Centaurs, and between 1 and $5 \times 10^{28}$ mols^-1 for the best observed KBOs. The upper limit obtained for the HCN production rate in 10199 Chariklo is strongly model dependent and is equal to $8\times10^{27}$ mols^-1 for T = 10 K, and $4\times10^{26}$ mols^-1 for T = 50 K.

**Table 6:** Centaurs and KBOs: CO production rates upper limits averaging all data and CO depletion with respect to comet Hale-Bopp.
Object	$Q_{\rm CO}^a$	minimum CO
	[10²⁸ mols^-1]	depletion^b
2060 Chiron	<0.31-0.45	38-55
5145 Pholus	<1.0-2.3	4-9
7066 Nessus	<4.6-5.6
8405 Asbolus	<1.2-1.9	4-6
10199 Chariklo	<0.51-1.1	20-43
1998 SG35	<0.77-1.8
1994 TB	<5.1-8.3
1996 TL66	<1.3-4.4	3-10
1996 TO66	<1.5-5.5	3-11
1996 TP66	<1.0-4.5	1-6
1998 WH24	<10-19

^a 3- $\sigma$ upper limits inferred with T = 50 K (lower values) and T = 10 K (larger values).
^b Minimum CO depletion with respect to comet Hale-Bopp, assuming $Q_{\rm CO} \propto r_{\rm h}^{-2}\times D^2$ ,
and using D = 40 km (Altenhoff et al. 1999) and $Q_{\rm CO}$ = 10²⁸ mols^-1 at $r_{\rm h} = 9$ AU
for comet Hale-Bopp (Biver et al. 1999c). Only depletions greater than 1 are given.

Because Chiron presents cometary-like activity, rotational lines of CO were searched for in this Centaur on several occasions. Womack & Stern (1999) announced the detection of the J(1-0) line in June 1995, using the NRAO 12-m telescope. With a pure thermal model at T = 10 K and $v_{\exp} = 0.2$ kms^-1, assuming that CO emission fills the telescope beam, they inferred a CO production rate of $(1.5 \pm 0.8) \times 10^{28}$ mols^-1. The production rate we derive from their observations using our model with $v_{\exp} = 0.4$ kms^-1 is $2.9 \times 10^{28}$ mols^-1 and $5.2 \times 10^{28}$ mols^-1, for T = 10 and 50 K, respectively. Boice et al. (1999) observed the J(1-0) line in February 1998 with the Nobeyama 45-m telescope, from which we derive $Q_{\rm CO}< 5\times 10^{28}$ mols^-1 for T=10 K. Rauer et al. (1997) observed both the J(1-0) and J(2-1) lines with the IRAM 30-m in June, September and November 1995 and used the same model as ours for their interpretation. Their 3- $\sigma$ upper limit obtained in June 1995 is consistent with the Womack and Stern's result, but the upper limit derived from the combined June 1995 to November 1995 data ( $1\times10^{28}$ mols^-1 for T = 10 K) is clearly below the Womack & Stern's value. Our derived upper limit of $\sim$ $0.3{-}0.5 \times 10^{28}$ mols^-1 for 1998-2000 (Table 6) is even more stringent, a factor of $\sim$ 10 lower than the production rate derived from Womack and Stern's marginal detection using same modelling. From optical photometry, Chiron's activity shows short-term variability and a long-term trend to be lower near perihelion (February 1996) than near the aphelion (Bus et al. 2001; Lazzaro et al. 1997). Photometric measurements obtained in March, May 1995 (Bauer et al. 1997), January 1998, May 1999 and June 2000 (Bauer, private communication) show that Chiron was fainter over the years 1998-2000 by 0.3 magnitude (in absolute magnitude units) when compared to 1995. This 0.3 magnitude variation would correspond to a CO production rate variation of 40% only, using the correlation between CO production rates and heliocentric magnitudes established from comet Hale-Bopp data (Biver 2001). Yet, the absolute V magnitudes deduced from the 1998 to 2000 observations, ( $H_{\rm v}\sim 7$ , not corrected from phase function; Bauer, private communication) indicate that Chiron was in its most quiescent state since its discovery. Therefore, we cannot exclude that Chiron was in outburst in June 1995, but, without any additional evidence for that, the low CO production rates derived for the June-September 1995 (Rauer et al. 1997) and 1998-2000 periods make the proposed detection of Womack and Stern at best tentative.

Thermal models of the interiors of Centaurs and KBOs have been developed to follow their evolution and differentiation and better understand their relationships with short-period comets (Capria et al. 2000; De Sanctis et al. 2000; De Sanctis et al. 2001). These models assume that these objects are porous bodies made of ices of different volatilities (amorphous H₂O, CO and CO₂ as main constituents) and dust. They treat the heat diffusion in the porous material, the sublimation of volatile ices, the amorphous/crystalline phase transition, the diffusion of the produced gases and their recondensation or their escape into space. The model developed by De Sanctis et al. (2001) for KBOs includes the combined effects of radiogenic and solar heating. They show that the upper layers of Kuiper Belt objects could be strongly volatile-depleted, with CO ice completely absent down to several kilometers below the surface. CO production rates are expected to be very low (less than 10²³ mols^-1 for an object of 200 km diameter; De Sanctis et al. 2000), making our upper limits meaningless in that context. However, the results of these simulations are strongly dependent upon size and model parameters, such as porosity and thermal conductivity, and more investigations of the thermal differentiation of KBOs are needed. Other simulations predict, for large objects, a runaway increase of their internal temperature due to radiogenic heating, which can squeeze out volatiles trapped in water amorphous ice and concentrate them near the surface where the temperature is lower (Haruyama et al. 1993; Prialnik & Podolak 1995). Impacts may play also an important role in redistributing materials towards the surface, or ablating CO depleted layers. Transient cometary activity around 1996 TO66 has been proposed to explain a strong change of its lightcurve between September 1997 and September 1998 (Hainaut et al. 2000).

From their study of the thermal evolution of 2060 Chiron, Capria et al. (2000) concluded that Chiron's activity, if driven by CO, can be explained only if CO is present near the surface as an ice, or as a gas trapped in the amorphous water ice. It is believed that Chiron originated from the Kuiper Belt and moved to its present orbit by gravitational perturbations. If the upper layers underwent CO-ice devolatization in the Kuiper Belt, as it follows from the model of De Sanctis et al. (2001), then Chiron's activity could be explained by the release of trapped CO during the amorphous to crystalline transition. Although there are many assumptions in their model, Capria et al. (2000) show that CO production rates strong enough to explain the dust coma, and comparable to or even larger than our upper limits, can be obtained with this mechanism. The activity could also be explained by the outgassing of CO₂ ice (Capria et al. 2000), for which no significant devolatilization is expected in the Kuiper Belt due to its relatively low volatility (De Sanctis et al. 2001). But, this would require Chiron to have moved on its present orbit recently. The model developed for Pholus predicts CO fluxes lower than for Chiron because of its more distant orbit (De Sanctis et al. 2000), which might partly explain its inactive appearance. Finally, it is interesting to note that the comparison between the Hale-Bopp CO outgassing rates measured at large distances from the Sun and the upper limits obtained for Centaurs and KBOs demonstrates that, indeed, these latter underwent significant CO-depletion since their formation, when compared to Oort cloud comets. A CO production rate varying approximately in $r_{\rm h}^{-2}$ and equal to $\sim$ 10²⁸ mols^-1 at $r_{\rm h}\sim 9$ AU was measured in comet Hale-Bopp post-perihelion (Biver et al. 1999c). If we apply a scaling law in $r_{\rm h}^{-2} \times D^2$ , then the CO production rates we infer for the corresponding (D, $r_{\rm h}$ ) of our objects are, in most cases, significantly larger than the measured upper limits (Table 6).

3 Analysis

3.1 Pluto

3.2 Centaurs and KBOs