F Acero
email: facero@in2p3.fr

Y Gallant

J Ballet

M Renaud

R Terrier

A new nearby pulsar wind nebula overlapping the RX J0852.0-4622 supernova remnant

Keywords: ISM, supernova remnants -pulsars, general -X-rays, individuals, RX J0852.0-4622

Context. Energetic pulsars can be embedded in a nebula of relativistic leptons that is powered by the dissipation of the rotational energy of the pulsar. The object PSR J0855-4644 is an energetic and fast-spinning pulsar ( Ė = 1.1 × 10 36 erg s -1 , P = 65 ms) discovered near the southeast rim of the supernova remnant (SNR) RX J0852.0-4622 (aka Vela Jr) by the Parkes multibeam survey. The position of the pulsar is in spatial coincidence with an enhancement in X-rays and TeV γ-rays, which could be due to its putative pulsar wind nebula (PWN). Aims. The purpose of this study is to search for diffuse non-thermal X-ray emission around PSR J0855-4644 to test for the presence of a PWN and to estimate the distance to the pulsar.

Methods. An X-ray observation was carried out with the XMM-Newton satellite to constrain the properties of the pulsar and its nebula. The absorption column density derived in X-rays from the pulsar and from different regions of the SNR rim was compared with the absorption derived from the atomic (HI) and molecular ( 12 CO) gas distribution along the corresponding lines of sight to estimate the distance to the pulsar and to the SNR. Results. The observation has revealed the X-ray counterpart of the pulsar together with surrounding extended emission, thus confirming the existence of a PWN. The comparison of column densities provided an upper limit to the distance to the pulsar PSR J0855-4644 and the SNR RX J0852.0-4622 (d ≤ 900 pc). Although both objects are at compatible distances, we rule out that the pulsar and the SNR are associated. With this revised distance, PSR J0855-4644 is the second most energetic pulsar, after the Vela pulsar, within a radius of 1 kpc and could therefore contribute to the local cosmic-ray e -/e + spectrum.

Introduction

The Vela region (approximately centered on ℓ = 265 • , b = -1 • ) is host of several remnants of stellar explosions including the eponymous supernova remnant (SNR). The Vela remnant is among the brightest and most extended X-ray sources in the sky and is also the closest SNR currently detected (the distance to the remnant's pulsar has been measured to be 290 pc; Dodson et al. 2003). With its large angular size (8 • in diameter) the object is overlapping several remnants such as the Puppis A SNR and RX J0852.0-4622. In the X-ray spectral domain, this complex region is dominated by the Vela and Puppis remnants in soft X-rays and the RX J0852.0-4622 SNR (aka Vela Jr) becomes apparent only above 1 keV (Aschenbach 1998).

The Parkes multibeam radio survey discovered a pulsar, PSR J0855-4644, lying on the southeast rim of the RX J0852.0-4622 SNR (Kramer et al. 2003). This young and energetic pulsar (characteristic age τ c = 140 kyrs, Ė = 1.1 × 10 36 erg s -1 and P = 65 ms) is in spatial coincidence with an enhancement in the X-and γ-ray maps (presented in Aschenbach et al. 1999;Aharonian et al. 2007, respectively), which could be the signature of its pulsar wind nebula (PWN). Based on the radio dispersion measure of the pulsar (DM = 239 cm -3 pc; Kramer et al. 2003) combined with the NE2001 model of Galactic electron distribution from Cordes & Lazio (2002), the distance to the pulsar is estimated to be 4 kpc. However, estimating the distance with this method in this specific region of the sky can be erroneous (see Mitra & Ramachandran 2001) due to the structured and nearby emission of the Gum nebula, a 35 • large nebula located at ∼500 pc. The electron density inside the Gum nebula can strongly vary from 0.1 to 100 cm -3 (Reynolds 1976;Wallerstein et al. 1980;Dubner et al. 1992;Reynoso & Dubner 1997) and therefore so can the DM of a pulsar lying in the background of the nebula. This complex region is modeled as a simple sphere (the Gum nebula) of homogenous density in the NE2001 model.

To better constrain the distance to the pulsar and search for a potential X-ray nebula, an XMM-Newton observation was carried out, whose results are presented in this article. In Sect. 2,we present a detailed morphological and spectral analysis of the pulsar and its nebula. A discussion of the distance to the PSR and to the SNR RX J0852.0-4622 is presented in Sect. 3. To conclude, a summary of the proposed scenario, the potential relation between PSR J0855-4644 and the RX J0852.0-4622 SNR and the expected TeV emission from the PWN is presented in Sect. 4.

X-ray observations

The SNR RX J0852.0-4622 was first discovered in X-rays by the ROSAT satellite in a high-energy image (E > 1.3keV has revealed the energy-dependent morphology of this complex region. Due to its large angular size (nearly 1 • in radius), the SNR has only been partly observed by the new generation of X-ray telescopes and, so far, no mosaics that cover the whole remnant at high angular resolution is available. Most observations have been focused on the intriguing bright and thin filaments that emit synchrotron emission in the northwest of the remnant (see e.g. Bamba et al. 2005).

The XMM-Newton observation presented in this study is centered on the pulsar and also unveils the previously unobserved southeastern shell of the RX J0852.0-4622 SNR. Several other XMM-Newton observations in the northwest and in the south of the SNR were used in this study to compare the spectral properties of the SNR along the shell.

Data analysis

The region of the pulsar was observed with XMM-Newton for 55 ks using the Full Frame mode of the three EPIC instruments. After flare screening, the remaining exposure time is 40 ks and 29 ks for the MOS and PN cameras, respectively. For the image generation, the instrumental background was derived from a compilation of blank sky observations (Carter & Read 2007) renormalized in the 10-12 keV energy band. The background-subtracted and vignetting-corrected images in a low (0.5-0.8 keV) and high-energy band (1.2-6 keV) are presented in Fig. 1. These images clearly show two very different facets of the Vela region. While the low-energy image is dominated by the large scale structure of thermal emission from the Vela SNR, the high-energy band reveals a faint rim of the RX J0852.0-4622 SNR and the X-ray counterpart of the pulsar. Interestingly, diffuse emission is also seen surrounding the pulsar. The spectral properties of the pulsar and the diffuse emission are presented in the following sections.

The thermal emission from the Vela SNR is extremely bright at low-energy (E < 1 keV) and therefore the statistics gathered with the PN camera is very high. We have encountered a calibration problem with the spectral response of the PN camera, particularly visible in the oxygen lines. This is a known problem for the XMM-Newton team, and following their recommendation, an offset in energy in the PN spectral response function (rmf ) was introduced via the gain function in Xspec. See Appendix A for more details. All spectra were fitted using MOS1+2 and PN, although for graphical purposes, only the MOS1+2 spectra are shown along with the best-fit obtained with the three instruments.

Morphology of the nebula

To further investigate the morphology of this diffuse emission, a radial profile (shown in Fig. 2, middle), centered on the position of the pulsar, was extracted in the high-energy band (1.2-6 keV). The profile was then fitted with a combination of a point-like component (using the XMM-Newton point spread function (PSF) from the calibration files), an extended component (a Gaussian profile), and a constant that represent the pulsar, the nebula, and the background. The best-fit Gaussian width deconvolved from the PSF of the extended component is 45 ′′ ± 1.5 ′′ (unless otherwise noted, all error bars are given at a 90% confidence level) and the diffuse emission around the pulsar is detected up to ∼150 ′′ . The large-scale emission is fairly symmetric and no indications of a trail or of a bow-shock structure (reminiscent of a fast-moving pulsar) are observed.

Interestingly, at smaller scale the inner part of the nebula (r < 60 ′′ ) seems to show some azimuthal variation. To test the significance of these variations, an azimuthal profile was extracted from an annulus region (R1 = 15 ′′ < r < R2 = 60 ′′ ,see Fig. 2 North is up and east to the left. The region is annotated with the annulus regions of radii R1, R2, and R3 (15 ′′ ,6 0 ′′ , and 150 ′′ ) used in the morphological and spectral analysis. A contour at the level of 2.5 × 10 -5 ph/cm2 /s/arcmin 2 i so v e r l a i di nr e dt oo u tline the morphology of the inner nebula. Middle:r a d i a lp r o fi l eo ft h e PWN in the high-energy band (1.2-6 keV) extracted from a region centered on the pulsar. The best-fit two-components model (point-like + diffuse) is overlaid. Bottom: azimuthal profile extracted from the annulus region R1-R2 (15 ′′ < r < 60 ′′ ) illustrated in the top panel in the high-energy band. Position angle 0 • corresponds to the west and 90 • to the north. Two significant enhancements over the mean value (dashed line) are seen at ∼50 • and ∼230 • . The fact that these knots of emission are separated by 180 • is suggestive of a jet morphology. distribution presented in Fig. 2 (bottom) is not compatible with a flat profile and exhibits features, 180 • apart, at 50 • and 230 • that are suggestive of jet-like structures as observed in many other young pulsars (see [START_REF] Kargaltsev | 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More[END_REF]. However, the limited spatial resolution of XMM-Newton hampers a study of the immediate environment of the pulsar. To confirm the presence of jets in the nebula and to search for a torus, high spatial resolution observations with the Chandra X-ray satellite would be needed.

Spectral analysis of the nebula

To extract the spectral properties of the nebula, the instrumental and astrophysical backgrounds have to be modeled carefully in this complicated region of the sky. The instrumental-and particle-induced background were derived from a compilation of observations with the filter wheel in closed position1 and renormalized in the 10-12 keV energy band over the whole field of view. The spectral data were fitted using Cash statistics and the goodness-of-fit was assessed trough Monte Carlo simulations using the goodness command in Xspec (v12.5). This command returns the fraction of simulated spectra whose fit statistics value is lower than the one obtained on the real data, which is equivalent to 1-p-value 2 . If the model is a good representation of the data, a p-value around 0.5 is expected. If the p-value is close to 0, the model is clearly a poor representation of the data. The Tuebingen-Boulder ISM absorption model (tbabs) was used for all absorbed components together with the abundances of Wilms et al. (2000).

The astrophysical background in this region is particularly complex, as illustrated in Fig. 1. The low-energy part of the spectrum is dominated by the thermal emission from the Vela SNR and from the Local Bubble, while in the high-energy band nonthermal emission from RX J0852.0-4622 (the contribution from the SNR's rim at the PWN's position is not negligible; see Sect. 2.7) and the cosmic X-ray background (CXB) are present.

To model this background a spectrum from a region (dashed circle in Fig. 1, right) located at the same distance from the shock front of the RX J0852.0-4622 SNR (to have similar spectral properties) was obtained.

The spectrum from this background region is well fitted by a two-component model (p-value = 0.24). The first component is an absorbed variable abundances astrophysical plasma emission code (VAPEC) model that represents the thermal contribution from Vela. The X-ray absorption column N H of this component is poorly constrained with XMM-Newton's energy range (0.4-10 keV) and was therefore fixed to 5 × 10 20 cm -2 , the typical value derived by Aschenbach et al. (1995) using data from the ROSAT satellite, whose energy range extends to lower energies (0.1-2.4 keV). The best-fit parameters for this thermal component are the following: kT = 0.14 keV, oxygen abundance = 0.453 , and a normalization of 7.1 × 10 -3 cm -5 .T h e second component is an absorbed power-law model representing the contributions from RX J0852.0-4622 and the CXB. Adding another component to separately represent the CXB, with spectral parameters fixed from De Luca & Molendi (2004), did not improve the quality of the fit. The best-fit parameters give N H = (0.45 ± 0.10) × 10 22 cm -2 , Γ=1.90 ± 0.04, and norm = (2.70 ± 0.11) × 10 -4 keV -1 cm -2 s -1 at 1 keV.

The best-fit model obtained from the background spectrum was then used as a fixed template model in the spectrum of the nebula (annulus: R1 = 15 ′′ < r < R3 = 150 ′′ )w h e r et h e Bottom: X-ray spectrum of PSR J0855-4644 extracted from a 15 ′′ radius region. The astrophysical background (dashed lines) is composed of Vela's thermal emission at low energies while the contribution of the nebula and of RX J0852.0-4622 at higher energies is not negligible. For graphical purposes only the MOS1 and MOS2 data are shown although the PN data were also used in the fitting process.

normalization was set to the ratio of geometrical areas for the non-thermal emission and was let free to vary for the thermal emission because the emission from the Vela SNR is seen to slightly vary in the low-energy map shown in Fig. 1. All other parameters (kT , power-law absorption column, and spectral index) for the background model were kept fixed. To represent the emission from the nebula, an absorbed power-law model was added to the previously derived background model. The spectrum from the nebula is well modeled (see Fig. 3,top) with the sum of the background + power-law model (p-value = 0.14), thus confirming the non-thermal nature of the nebula's X-ray emission.

Spectral analysis of PSR J0855-4644

To derive the X-ray properties of the pulsar, and in particular the column density along the line of sight to discuss its distance, we extracted a spectrum in a 15 ′′ radius region centered on the pulsar. For this region, the astrophysical background is composed of Vela and the Local Bubble at low energies and of the sum of the contributions from the nebula (which is not negligible based on the radial profile modeling in Fig. 2), RX J0852.0-4622 and the CXB.

The astrophysical background model was obtained from the best-fit model of the spectrum extracted in the PWN region (15 ′′ < r < 150 ′′ ). The non-thermal component of the template was renormalized using the nebula's geometrical model shown in Fig. 2 (middle) while the thermal component was renormalized using the geometrical ratio of the areas (i.e., thermal emission is assumed to be homogeneous at the scale of the PWN).

The spectrum of the pulsar (presented in Fig. 3, bottom) is well described (p-value = 0.46) at low energies by the fixed template (absorbed VAPEC model) and at high energies with two absorbed power-laws, one representing the astrophysical background and one for the non-thermal emission of the pulsar. The spectral parameters of the pulsar best-fit model are listed in Table 1. A black body model has also been tested to model the X-ray emission of the pulsar, but resulted in a poor fit to the data (p-value = 4 × 10 -3 ).

The derivation of the N H from the pulsar is sensitive to the normalization of the thermal component, dominating at low energies. To estimate the accuracy to which we can fix the normalization of the thermal model, we calculated the ratio of brightnesses in the pulsar region over the PWN region in the 0.4-0.6 keV energy band. The resulting ratio is 1.13 ± 0.08, confirming that the assumption of homogeneous thermal emission at the scale of the PWN is reasonable. When the normalization of the thermal component in the pulsar spectral model is increased by a factor 1.13, the best-fit value of N H increases to 0.71 +0.13 -0.11 ×10 22 cm -2 , within statistical errors of the value quoted in Table 1. This test provides an estimate of the systematic error associated with the normalization of the thermal emission at low energies.

Electron cooling in the nebula

To test for a possible spectral cooling in the nebula, a spectrum was derived in the inner (15 ′′ < r < 60 ′′ ) and outer part of the nebula (60 ′′ < r < 150 ′′ ). For both regions, the astrophysical background was fixed to the best-fit model obtained from the whole PWN in Sect. 2.3. To limit the degeneracy between the absorption column and the photon index, the N H of non-thermal emission from the nebula was fixed to the value derived from the pulsar.

The best-fit parameters of the inner and outer region of the nebula are presented in Table 1. A significant steepening of the spectral index toward the external region of the nebula is observed (from 1.70 +0.07 -0.06 to 2.01 +0.04 -0.04 ). This is consistent with the scenario of a population of electrons cooling as they are advected away from the pulsar.

In connection with the spectral parameter evolution in the inner nebula, the background model for the pulsar was revisited. The inner region of the nebula, instead of the whole nebula, was tested as the template background model for the pulsar. The best-fit parameters of the pulsar with this new background model are N H = 0.59 +0.14 -0.13 × 10 22 cm -2 and Index = 1.20 +0.08 -0.11 . When rescaling the normalization of the thermal component by the same 1.13 factor (as tested in the previous section), the N H value slightly increases to 0.67 +0.15 -0.13 × 10 22 cm -2 and Index = 1.23 +0.10 -0.11 . Those parameters are compatible with those presented in Table 1, and in the following discussion only the best-fit parameters from the pulsar presented in the table are used. 1 and4. Only the parameters from the non-thermal components are listed in this table while the parameters of the thermal component are fairly constant from one region to another (kT = 0.14-0.17 keV and the N H was fixed to 5 × 10 20 cm -2 for all the regions). The unabsorbed non-thermal fluxes of the PWN, PSR and SNR's rim are given in the 2-10 keV energy range and the N H in units of 10 22 cm -2 . The area of the extraction region and the annulus radii for the PSR/PWN analysis are also given. The error bars are given at 90% confidence level.

Spectral analysis of the SNR rim

To discuss the relative distances of the SNR and of the PWN, we carried out a spectral analysis of different regions of the RX J0852.0-4622 SNR. In the same pointing where the PWN is observed, we extracted a spectrum from the rim in the region labeled SE rim in Fig. 1. The region does not fully encompass the rim to avoid the bright structure of thermal emission from Vela that would hamper a proper determination of the absorption column. As in the previous sections, an astrophysical background model (absorbed VAPEC + absorbed power-law) was fitted to a region outside the SNR represented by the dashed box in Fig. 1. The total spectral model for the SNR rim is the sum of the previously estimated background model plus an absorbed power-law representing the synchrotron emission from the SNR. The parameters of the background model were fixed in the analysis of the rim except the normalization of the thermal emission. The best-fit parameters of the non-thermal emission from the rim are listed in Table 1. The same procedure was then applied to other regions of the SNR where X-ray observations were available, namely the northwest and the south of the SNR. The 1.2-6 keV image of those regions together with the spectral extraction regions and background regions are shown in Fig. 4. The eastern rim of the SNR has also been observed by XMM-Newton but the observation has been, unfortunately, strongly affected by solar flares and only 5 ks out of 36 ks of observation are usable. As a consequence, no reliable spectral information could be derived from the diffuse and faint emission from the SNR in this region.

The resulting best-fit parameters of the spectral analysis from three different regions of the SNR are listed in Table 1.

Radial profiles of the SNR rim

To estimate the non-thermal contribution of RX J0852.0-4622 at the PWN position, a radial profile was extracted from a region of the same width and direction as the region labeled SE rim in Fig. 1 (right panel) but with a different length. The resulting profile, shown in Fig. 5 (top), demonstrates that the emission of RX J0852.0-4622 is not negligible at the reported distance of the PWN behind the shock front and its implementation in the astrophysical background modeling, in Sect. 2.3, is justified.

To measure the scale width of this filament, the profile was fitted with an exponentially decreasing model of the form e -|r 0 -r|/w d ,w h e r ed denotes the downstream side of the shock (same geometrical model as in Bamba et al. 2005,w h e r et h e northwest rim of the SNR is studied). The best-fit model is overlaid in Fig. 5 (top) and the best-fit parameter is w d = 6.85 ± 0.55 arcmin. For comparison, the radial profile of the northwestern region is shown in Fig. 5 (bottom). The latter profile was obtained from a region of the same direction as the white region shown in Fig. 4 (top). The same geometrical model was used and the best-fit parameter is w d = 1.61 ± 0.05 arcmin. We note that the downstream of the rim in this region is nearly four times thinner than in the southeast region. The implication of those different widths on the value of the magnetic field that can be derived is discussed in more detail in Sect. 4.5.

Distance estimate

The method for tackling the problem of the distance to the pulsar is based on the existence of a strong contrast of integrated 12 CO between the eastern and the western parts of the SNR, as sho wninFig. 7 (left). This contrast is due to the Vela molecular ridge (VMR) cloud C (see Murphy & May 1991, for cloud nomenclature), lying at a distance of 700 ± 200 pc. One of the method to derive this distance is an infrared photometric study of the star-forming regions in the VMR (see Liseau et al. 1992, and references therein). Other independent methods, discussed in Murphy & May (1991), give a similar distance. This cloud is the main contributor of 12 CO emission along the line of sight, as seen in Fig. 6 (bottom panel), and is located at a radial velocity in the local standard of rest of V LSR ∼ 5k ms -1 .I ft h e SNR RX J0852.0-4622 lies behind the VMR, the observed gradient in 12 CO should also be visible in the measurement of the X-ray absorption column.

To investigate this correlation, absorption column density maps (presented in Fig. 7) were calculated using HI data from the Parkes Galactic all-sky survey (McClure-Griffiths et al. 2009;Kalberla et al. 2010)and 12 CO data from the Dame et al. (2001) survey. To fully enclose the gas material lying between the observer and the back of the VMR, the data were integrated on radial velocities from -10 km s -1 to 15 km s -1 .D u e to the intrinsic velocity dispersion of the 12 CO emission line, A7, page 5 of 10 it is unfortunately not possible to estimate the column density between the observer and the foreground of the VMR. The COto-H 2 mass conversion factor and the HI brightness temperature to N H used to produce the maps are 1.8 × 10 20 cm -2 K -1 km s -1 (Dame et al. 2001)a n d1 .82 × 10 18 cm -2 K -1 km s -1 (Dickey & Lockman 1990). The same conversion factors were used to compute the cumulative absorption column at the pulsar's position shown in Fig. 6 (top panel). From this curve, we estimate that, along the line of sight of the pulsar, the N H between the observer and the back of the VMR is 0.97 × 10 22 cm -2 , while the total N H along the line of sight is 1.65 × 10 22 cm -2 .

Using the previously generated maps, a comparison plot was built (see Fig. 8)w he r et heN H derived from the gas maps and integrated up to the VMR is plotted against the best-fit values of the X-ray absorption for several positions in the sky. No correlation is observed in this plot indicating that the SNR is lying in the foreground of the VMR. In addition we note that the N H toward the pulsar (0.64 +0.13 -0.11 × 10 22 cm -2 ) is slightly lower than the column toward the SNR rim in the same region A7, page 6 of 10 (0.88 +0.08 -0.06 × 10 22 cm -2 ), suggesting that the pulsar is closer to, or at the same distance as the SNR RX J0852.0-4622.

An additional test to determine whether the pulsar is in the foreground or background of the VMR is to look for the ratio of neutral hydrogen (related to the X-ray absorption column N H ) to free electrons (given by the pulsar radio dispersion measure DM). As discussed in Gaensler et al. (2004), this ratio has been observed to be high for pulsars that are known to lie behind dense molecular material (e.g. N H /DM = 85 (40) for PSR J1747-2958 and PSR 1757-24), whereas the typical value for other pulsars is on the order of 5-10. The value we derive for PSR J0855-4644 is 8 ± 1.5, which suggests that the pulsar is not located behind dense material.

We therefore conclude that both the SNR and the pulsar are lying in the foreground of the VMR, i.e., at a distance d ≤ 900 pc. This distance constraint to the RX J0852.0-4622 SNR is compatible with a recent estimate based on the measurement of the proper motion of the shock in X-rays in the northwestern part of the rim by Katsuda et al. (2008), who derived d ∼ 750 pc. Concerning the pulsar, a closer distance (than the 4 kpc derived from the radio DM measurements) confirms a suggestion made by [START_REF] Redman | [END_REF], who derived a distance of ∼750 pc.

Discussion

Proposed scenario

In the previous sections, we have shown that RX J0852.0-4622 and PSR J0855-4644 are lying in the foreground or at the interface of the VMR. The SNR and the pulsar are therefore thought to be nearby (d ≤ 900 pc), but surprisingly, the absorption columns derived from the X-ray analysis show high values ranging from 0.64 to 0.88 × 10 22 cm -2 . This is intriguing because the N H toward the Vela SNR, whose distance is known precisely4 to be d = 287 +19 -17 pc (Dodson et al. 2003), is much lower at ∼10 20 cm -2 .

To understand this apparent discrepancy, we investigated the spatial distribution and the density of the local gas toward the Vela region. We note that due to the intrinsic velocity dispersion of the VMR emission both in HI and in 12 CO (see Fig. 6, bottom) and the proximity of the object, it is not possible to separate the emission from the VMR from the foreground emission. However, the density of the nearby gas (the Local Bubble) can be probed by other methods such as the study of the absorption line features of NaI and CaII toward stars with known distances (see Lallement et al. 2003;Welsh et al. 2010). These studies revealed interstellar tunnels of low density connecting the Local Bubble to other surroundings cavities. One of these tunnels is in the line of sight of the Vela region at ℓ ∼ 265 • , extending at least to 250 pc (Welsh et al. 2010). This tunnel could explain the low value of the N H measured in X-rays in the direction of the Vela SNR. Using the N H measured toward the Vela SNR (10 20 cm -2 ), the mean density in this line of sight is on the order of 0.1 cm -3 .

After the Local Bubble, the line of sight encounters the Gum nebula, a large-scale structure centered at ℓ = 262 • , b = -3 • and located at a distance of ∼500 pc for a physical radius of ∼150 pc and an angular radius of 17 • . Over a distance of 200 or 600 pc (distance between the Vela SNR at 287 pc and the VMR at 700 ± 200 pc), the required densities must be on the order of 9 to3cm -3 respectively to reach the N H value measured in X-rays of ∼0.6 × 10 22 cm -2 toward PSR J0855-4644. When integrating the HI spectrum between the Earth and the background of the VMR (-10 km s -1 to 15 km s -1 ), the HI alone contributes to 0.3 × 10 22 cm -2 in the line of sight toward the pulsar, corresponding to a mean density of 2-5 cm -3 over a distance of 600 and 200 pc. In addition, the HI emission is homogeneously spatially distributed around the RX J0852.0-4622 SNR region and is not correlated with the VMR, as shown in the HI map shown in Fig. 7 (middle panel), thus contributing to all the lines of sight used in the X-ray analysis, which is consistent with the relatively high N H values measured across the SNR. The aforementioned densities are compatible with the density of ∼7cm -3 measured in the inner region of the Gum nebula (the thick HI shell discussed in Dubner et al. 1992;Reynoso & Dubner 1997), which is spatially overlapping our region of interest. H α observations the nebula by Reynolds (1976) provided similar values for the densities (1 to 5 cm -3 ). One possible origins of the Gum nebula is that the supershell is produced by the combination of stellar winds and repeated SN explosions (McCray & Kafatos 1987;Reynoso & Dubner 1997), which makes it a plausible location for PSR J0855-4644 and RX J0852.0-4622.

Finally, changing the electron density of the Gum nebula in the NE2001 model from 0.5 cm -3 (the currently implemented uniform value for the Gum nebula) to 1 cm -3 is sufficient to reconcile a DM of 239 cm -3 pc with a distance to the pulsar of 900 pc. This does not seem unreasonable with regard to the possible variation of density in the Gum nebula.

In summary, the line of sight toward the pulsar first encounters a tunnel of low-density gas (∼0.1 cm -3 )u pt ot h eV e l a SNR, then enters the Gum nebula thick HI shell with densities of about 1-5 cm -3 . This succession of low-and high-density environment can explain the low N H toward the Vela SNR and the high N H toward the RX J0852.0-4622 SNR and the pulsar. While the HI alone contributes to 0.3 × 10 22 cm -2 , additional molecular material in the line of sight could contribute to the measured X-ray absorption either in the foreground of the VMR5 or from the external regions of the VMR if the pulsar and SNR are lying at the interface of the molecular cloud.

4.2. Is pulsar associated with the RX J0852.0-4622 SNR?

Although the pulsar and the SNR may be at similar distances, an association is unlikely due to the characteristic age of the pulsar (τ c = 140 kyrs) being much larger than the SNR age (t SNR ∼ 4000 yrs). Assuming that τ c c o u l db ev e r yd i fferent from the real age, the required pulsar's kick velocity to explain its current position would be ∼3000 km s -1 to travel 12 pc from the SNR center (1 • at 750 pc) for an SNR age of 4000 years. This value is much higher than observed in other pulsars (Hobbs et al. 2005). Moreover, for such a high shock speed a bow-shock or a tail structure should appear in the PWN, which is not the case. In addition, a candidate neutron star CXOU J085201.4-461753 (see e.g. Kargaltsev et al. 2002) lies near the geometrical center of the SNR RX J0852.0-4622, which appears as a more simple scenario.

TeV emission from the PWN

With the new distance derived in this study, the ratio Ė/d 2 for PSR J0855-4644 reaches a value ≥10 36 erg s -1 /kpc 2 (for d ≤ 900 pc and Ė = 1.1 × 10 36 ergs). According to the TeV γ-ray PWN population study presented by Carrigan et al. (2008), ahigh Ė/d 2 pulsar like this should be detectable by Cherenkov telescopes in γ-rays. The region of the RX J0852.0-4622 SNR has been extensively studied by the H.E.S.S. experiment and an excess of TeV γ-rays is observed at the position of the pulsar (see Fig. 3 in Paz Arribas et al. 2012). However, as the pulsar is in spatial coincidence with the SNR shell, it is not possible, given the spatial resolution of the H.E.S.S. telescopes, to disentangle the contribution from the SNR shell from the contribution of the PWN. In addition, the azimuthal profile of the γ-ray emission along the SNR shell does not reveal any significant emission increase with regards to the surrounding SNR shell emission at the position of the pulsar [START_REF] Paz Arribas | Proc. 32nd ICRC[END_REF].

Pulsar contribution to observed e -/e + CRs

This new distance estimate of the pulsar strongly differs from the distance estimated with the radio dispersion measure (d = 4 kpc) and therefore implies that PSR J0855-4644 is an energetic and nearby pulsar. After the Vela pulsar, it is the most energetic pulsar within 1 kpc and could therefore contribute to the spectrum of cosmic-rays e -/e + received at Earth (see Delahaye et al. 2010, for the contribution of nearby pulsars). Obtaining a good knowledge of the nearby pulsar population is a necessary step to understand the rise in positron fraction with increasing energy measured by the PAMELA experiment (Adriani et al. 2009) and confirmed by the Fermi space telescope (Ackermann et al. 2012).

As the pulsar is rather old (τ c = 140 kyrs) and because no traces of the host SNR have been observed, one can reasonably assume that the CR accelerated in the PWN have had t i m et oe s c a p et h eS N R .T h ed i ffusion timescale of these escaping CRs to reach the Earth scales as t prop (E) ≈ d 2 /D(E) where D(E) is the diffusion coefficient with a typical value of ∼3 × 10 28 (E/1GeV) δ cm 2 /s with a large uncertainty on the energy dependence δ = 0.3-0.6( s e eStrong et al. 2007,forareview of CR propagation in the Galaxy). Therefore, t prop (E) ≈ 100 kyrs (d/100 pc) 2 (E/1G e V ) -0.5 . For a typical value of δ = 0.5, neither PSR J0855-4644 nor the Vela pulsar (τ c = 11 kyrs) are thought to contribute to the observed flux of e -/e + at 10 GeV because the diffusion timescale is 1500 and 280 kyrs (for d = 750 and 290 pc). By equating t prop = τ c and for δ = 0.5, the energy of the particles that could have diffused up to Earth is 1 TeV and 6 TeV for PSR J0855-4644 and the Vela pulsar.

The previous estimates assume that the particles start to diffuse at the birth of the SNR and do not take into account the time for the particles accelerated in the PWN to break through the SNR shell. This escape effect could be not negligible in the case of the Vela pulsar (see Hinton et al. 2011, for a study of the diffu s i v ee s c a p ee ffect on the particle spectrum) due to the relative young age of the system (τ c = 11 kyrs).

Comparison of the width of the SNR rims

In the XMM-Newton observation of the southeast region of the RX J0852.0-4622 SNR, a faint rim of non-thermal emission was detected (see Fig. 1, right). In Sect. 2.7, the downstream thickness of the rim was measured with an exponentially decreasing model. We observed that the filament in the southeast is nearly four times thicker (w d = 6.85 ± 0.55 arcmin) than the bright and thin (w d = 1.61±0.05 arcmin) filament observed in the northwest oftheSNRshowninFig.4.

Assuming that the thickness of the rim is limited by the synchrotron losses, while the electrons are advected away from the shock, one can derive a lower limit to the value of the downstream magnetic field B d . To derive this value, we adapted Eq. ( 9) from Parizot et al. (2006) to keep track of the observed photon energy E ph and obtained the following relation:

B d ≥ 37 µG × V 2/3 sh,3 × (θ obs,arcmin × d kpc ) -2/3 × E -1/3 ph, keV , (1)
where V sh,3 is the shock speed in units of 1000 km s -1 , θ obs,arcmin is the observed width of the rim at half maximum in units of arc minutes (θ obs = w d × log(2)) and E ph is the average emitted photon energy in keV. For a distance to the RX J0852.0-4622 SNR of 750 pc (see Katsuda et al. 2008, and Sect. 3 of this article for a more detailed discussion of the SNR distance), a shock speed of 3000 km s -1 (Katsuda et al. 2008) and a mean photon energy of ∼2.5 keV, the downstream magnetic field value is 24 µG and 63 µG for the southeast and for the northwest rim. We note that in the northwest region, an X-ray proper motion of the shock ( θsh = V sh /d) has been measured6 by Katsuda et al. (2008). As the ratio of V sh /d can be replaced by θsh in Eq. ( 1), the Fig. 8. Comparison plot of the absorption column density values derived from the atomic and molecular gas and from the X-rays using XMM-Newton observations. The X-ray columns derived toward the rims of the RX J0852.0-4622 SNR, PSR J0855-4644 and the PWN are represented by black circles, a blue square, and a green square. The errors on the X-ray N H are 1σ error bars. The label over each point corresponds to regions where the values were measured as defined in Fig. 7. estimate of the magnetic field, at least in the northwest, is in fact independent of the hypothesis on the shock speed and distance.

The magnetic field downstream of the shock is therefore significantly different in these two regions. This emphasizes that the magnetic field derived from a one-zone modeling of the SED of the whole SNR (giving an average value of the magnetic field) is not directly comparable to the magnetic field derived from a filament in a specific region of the SNR.

Conclusions

The search for the X-ray counterpart of PSR J0855-4644 using XMM-Newton led to the following conclusions:

1. A point-like X-ray counterpart has been discovered in spatial coincidence with the position of the radio pulsar and a surrounding extended emission of non-thermal origin was found. The nebula has a maximum extent of about 150 ′′ and the azimuthal profile has revealed two knots of emission (with angular separation of ∼180 • ), suggesting possible jets around the pulsar. High spatial resolution observations with Chandra might reveal the fine structure of the nebula. 2. A faint rim of non-thermal emission representing the southeastern part of the RX J0852.0-4622 SNR was detected. The filament in this region is thicker than the bright and thin X-ray filaments observed in the northwest of the SNR.

Assuming that the thickness of the rim is dominated by the synchrotron losses, the downstream magnetic field is 24 µG and 63 µG respectively for the southeast and for the northwest rim. These significantly different values might indicate different acceleration and/or environmental conditions at the shock around the SNR. 3. By comparing the X-ray column density on the pulsar and on different regions of the SNR with the gas map (using 12 CO and HI emission as tracers), we concluded that both the RX J0852.0-4622 SNR and PSR J0855-4644 are in the foreground or at the interface of the Vela Molecular Ridge, resulting in an upper limit of d ≤ 900 pc. Although the pulsar and the SNR may be at similar distances, they are not likely to be associated. 4. The new estimate of the pulsar distance completes our knowledge of the nearby pulsar population. If the distance of the pulsar is confirmed for instance through radio parallax measurements, PSR J0855-4644 would be the second most energetic pulsar (after the Vela pulsar) within 1 kpc and may contribute to the observed e -/e + spectrum.

Fig. 1 .

 1 Fig. 1. XMM-Newton background-subtracted flux images combining MOS and PN cameras in units of ph/cm 2 /s/arcmin 2 . Left:lo w-en er g yb an d image (0.5-0.8 keV) adaptively smoothed to a signal-to-noise ratio of 10 using the task asmooth provided in the XMM-Newton software SAS. The position of PSR J0855-4644 is shown with a red circle. Right: image in the high-energy band (1.2-6 keV) smoothed with a Gaussian width of 7 ′′ . The dashed red line shows approximately the SNR shell RX J0852.0-4622. In solid line we show the spectral extraction regions used to study the rim of RX J0852.0-4622 and the PWN whereas the dashed line regions are used to estimate the spectrum of the astrophysical background.

Fig. 2 .

 2 Fig.2. Top: zoom on the PWN region in the 1.2-6 keV image shown inFig. 1 (right). North is up and east to the left. The region is annotated with the annulus regions of radii R1, R2, and R3 (15 ′′ ,6 0 ′′ , and 150 ′′ ) used in the morphological and spectral analysis. A contour at the level of 2.5 × 10 -5 ph/cm 2 /s/arcmin 2 i so v e r l a i di nr e dt oo u tline the morphology of the inner nebula. Middle:r a d i a lp r o fi l eo ft h e PWN in the high-energy band (1.2-6 keV) extracted from a region centered on the pulsar. The best-fit two-components model (point-like + diffuse) is overlaid. Bottom: azimuthal profile extracted from the annulus region R1-R2 (15 ′′ < r < 60 ′′ ) illustrated in the top panel in the high-energy band. Position angle 0 • corresponds to the west and 90 • to the north. Two significant enhancements over the mean value (dashed line) are seen at ∼50 • and ∼230 • . The fact that these knots of emission are separated by 180 • is suggestive of a jet morphology.

Fig. 3 .

 3 Fig.3. Top: X-ray spectrum of the nebula extracted from a 15-150 ′′ annulus region shown in Fig.1. The astrophysical background components (dominated by thermal emission from Vela + non-thermal emission from RX J0852.0-4622) are depicted by dashed lines while the non-thermal emission of the nebula is illustrated by the solid line. Bottom: X-ray spectrum of PSR J0855-4644 extracted from a 15 ′′ radius region. The astrophysical background (dashed lines) is composed of Vela's thermal emission at low energies while the contribution of the nebula and of RX J0852.0-4622 at higher energies is not negligible. For graphical purposes only the MOS1 and MOS2 data are shown although the PN data were also used in the fitting process.

Fig. 4 .

 4 Fig. 4. XMM-Newton background-subtracted flux images (combining MOS and PN cameras) of the northwest (top) and south (bottom) pointings of RX J0852.0-4622 in the 1.2-6 keV energy band. As in Fig. 1, the solid lines illustrate the regions of spectral extraction, whereas the dashed lines represent the regions used to estimate the astrophysical background. The images were adaptively smoothed to reach a S/N of 10, the color scale is in square root and the units are ph/cm 2 /s/arcmin 2 .

Fig. 5 .

 5 Fig. 5. Radial profiles obtained in the rims of the RX J0852.0-4622 SNR in the southeast (top) and the northwest (bottom) along the spectral extraction regions shown in Figs. 1, 4. In the southeast, the distance of the PWN from the front shock is represented by the dashed lines. The best-fit exponentially decreasing model in the downstream side of the shock is illustrated with the solid lines.

Fig. 6 .

 6 Fig.6. Top: cumulative absorption column density (dot-dashed line) together with the 12 CO and HI contributions as a function of the radial velocity integrated on a 0.1 • box region centered on the pulsar. Bottom: corresponding 12 CO and HI spectra at the position of the pulsar. The Vela molecular ridge, centered at V LSR ∼ 5k ms -1 ,i st h em a i n 12 CO structure along the pulsar's line of sight.

Fig. 7 .

 7 Fig. 7. Maps of the absorption column density, derived from the molecular gas (left panel), the atomic gas (middle panel), and the sum of the two previous components (right panel) when integrating over radial velocities from -10 km s -1 to 15 km s -1 (see Sect. 3 for details). This specific velocity range provides an estimate of the absorption column for a source located just behind the Vela molecular ridge. The position of PSR J0855-4644 is shown with a black cross and the XMM-Newton pointings used in this study are represented by the white circles in the right panel. The white contours are taken from a ROSAT high-energy image (E > 1.3 keV) and reveal the SNR RX J0852.0-4622.

  Fig. A.1. Top: X-ray spectrum of the nebula extracted from a 15-150 ′′ annulus region shown in Fig. 2 focused on the thermal emission with MOS1, MOS2 and PN spectra represented in black, red, and green. The same spectral model as in Fig. is overlaid. Bottom: same spectra as in the top panel but with the PN response matrix modified by the gain response model implemented in Xspec.

Table 1 .

 1 Best-fit parameters obtained on the nebula, the pulsar, and different parts of the rim of the RX J0852.0-4622 SNR.Notes.For each spectrum, a two-components (absorbed VAPEC + absorbed power-law, see Sect. 2.3 for details) astrophysical background model was estimated from the background regions shown in Figs.

			Power-law best-fit parameters	Region area Annulus radii
		N H	index	flux (10 -12 ergs/cm 2 s -1 )a r c m i n 2	arcsec
	Pulsar & PWN
	PSR J0855-4644 0.64 +0.13 -0.11 PWN 0.76 +0.06 -0.05 Inner PWN 0.64 Outer PWN 0.64	1.24 +0.09 -0.10 2.03 +0.06 -0.04 1.70 +0.07 -0.06 2.01 +0.04 -0.04	0.26 +0.03 -0.05 0.88 +0.04 -0.08 0.39 +0.02 -0.06 0.55 +0.03 -0.06	0.2 19.4 2.9 16.5	0-15 15-150 15-60 60-150
	SNR
	Southeast rim South rim Northwest rim	0.88 +0.08 -0.06 0.85 +0.05 -0.05 0.68 +0.04 -0.05	2.32 +0.09 -0.08 2.66 +0.05 -0.07 2.53 +0.05 -0.04	1.83 +0.08 -0.09 2.88 +0.09 -0.08 4.10 +0.11 -0.13	25.7 42.1 15.2

http://xmm2.esac.esa.int/external/xmm_sw_cal/ background/filter_closed/

The p-value is the probability of obtaining a fit statistic higher than the observed value.

The abundance of neon was also let to free to vary as a test, but was found to be compatible with the solar abundance and was therefore fixed to the solar value in the model.

The distance to the Vela pulsar was measured by parallax.

This material can unfortunately not be separated from the VMR in the 12 CO spectrum.

The value of V sh and d used in the previous calculation were derived from the aforementioned proper motion measurements.

Acknowledgements. F.A. would like to thank Isabelle Grenier for discussions on the nearby interstellar medium and David Smith for useful discussion on the NE2001 Galactic electron distribution model. The help from Konrad Dennerl is also greatly appreciated to solve the calibration, problems with the XMM-Newton PN camera.

Appendix A: Calibration issues with the PN camera

The thermal emission from the Vela SNR is extremely bright at low energies (E < 1 keV), an energy range where the PN camera is more sensitive than the MOS. With this statistics we are limited by our knowledge of the camera calibration. Here we have observed a deficiency in the low-energy calibration of the spectral response of the PN camera. This effect is most visible around 0.6 keV in Fig. A.1, where the oxygen lines cannot be reproduced by the APEC thermal model. This is a known calibration problem 7 that is being investigated by the XMM-Newton PN calibration team. There are no 7 More information on this calibration issue can be found here: http://www2.le.ac.uk/departments/physics/research/ src/Missions/xmm-newton/technical/cal-meetings# madrid-0310 A7, page 9 of 10 A&A 551, A7 (2013) known similar calibration problems for the MOS instruments. Following their recommendation, we allowed for an empirical shift in energy in the PN response file using the gain response model implemented in Xspec. The fitted energy shift is on the order of 15 eV. Similar best-fit parameters where obtained when fitting independently the MOS and response-corrected PN spectra. This confirms that the correction of the response matrix does not alter the physical parameters that we derive from the spectrum. In the spectral analysis of the article we have therefore used the MOS1, MOS2, and response-corrected PN spectra.


R Tajeddine
email: tajeddine@imcce.fr

N J Cooper

V Lainey

S Charnoz

C D Murray

Astrometric reduction of Cassini ISS images of the Saturnian satellites Mimas and Enceladus

Keywords: astrometry -planets and satellites, individual, Mimas -planets and satellites, individual, Enceladusmethods, observational

Aims. We provide astrometric observations of two of Saturn's main satellites, Mimas and Enceladus, using high resolution Cassini ISS Narrow Angle Camera images. Methods. We developed a simplified astrometric reduction model for Cassini ISS images as an alternative to the one proposed by the Jet Propulsion Labratory (JPL). The particular advantage of the new model is that it is easily invertible, with only marginal loss in accuracy. We also describe our new limb detection and fitting technique.

Results. We provide a total of 1790 Cassini-centred astrometric observations of Mimas and Enceladus, in right ascension (α) and declination (δ) in the International Celestial Reference Frame (ICRF). Mean residuals compared to JPL ephemerides SAT317 and SAT351 of about one kilometre for Mimas and few hundreds of metres for Enceladus were obtained, in α cos δ and δ, with a standard deviation of a few kilometres for both satellites. A frequency analysis of the residuals revealed some periodic variability in the right ascension for Mimas. An additional analysis of Mimas' mean longitude suggests that some short-period terms are missing in the TASS orbital model.

Introduction

Over the past few decades spacecraft imaging has increasingly entered the field of astrometry and images from spacecraft missions are now routinely used to measure the astrometric positions of planetary satellites in order to study their orbital motion. For instance, Jacobson (1991) reduced observations of the Neptunian satellites, Triton and Nereid, from Voyager 2 optical images. Jacobson (1992) also reduced observations of the major Uranian satellites using images taken by the same spacecraft, while astrometry of the Martian satellites, Phobos and Deimos, has been performed using images from the Mars Express spacecraft (Willner 2008). Hubble Space telescope (HST) observations of the satellites of Saturn have been also been reduced astrometrically by [START_REF] Eichhorn | Astrometry of star positions[END_REF], and Cooper et al. (2006) reduced Cassini Imaging Science Subsystem (ISS) observations of the inner Jovian satellites, Amalthea and Thebe. All these examples have demonstrated the high accuracy that can be obtained from the astrometric reduction of spacecraft images compared to ground-based imaging, and spacecraft astrometry has now proven its importance in obtaining accurate planetary satellite ephemerides.

In this paper we describe the astrometric reduction of Cassini ISS narrow angle camera (NAC) observations of two of Saturn's main satellites, Mimas and Enceladus, two satellites whose dynamical and physical evolution are now considered to be of Full Table 4 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/551/A129 crucial importance in understanding the evolution of the Saturn system as a whole. In the case of Enceladus, geysers were discovered by the Cassini spacecraft in the south polar region (Porco et al. 2006) revealing the existence of liquid water beneath the surface, while an orbital acceleration has been reported by Lainey et al. (2012) for Mimas, which could have important consequences for the dynamical evolution of Saturn's rings (Noyelles et al. 2012).

The Cassini spacecraft commenced its prime mission in 2004, following Saturn-orbit-insertion in July of that year. Up until February 2011, the Cassini ISS NAC had produced approximately 9000 high resolution optical images of the Saturnian satellites Mimas and Enceladus. Of these we have found 1790 to be suitable for astrometry. For the remainder, astrometric reduction has not been possible either because suitable background stars necessary for astrometric reduction were not detectable, or the satellite was covering the entire field-of-view, or Saturn was observed in the background (we describe these issues in more detail in the sections that follow). In Sect. 2 we introduce our new astrometric reduction model, based on an approach more generally used for ground-based observations, and compare it to the Cassini ISS model proposed by [START_REF]Cassini ISS Geometric Calibration of[END_REF]. In the same section, we describe our satellite limb-measuring technique, inspired by Mallama et al. (2004), and our method for fitting an elliptical model of the satellite's shape to the measured limb. We also evaluate the importance of image distortion in limb-fitting. Astrometric observations and statistical analyses are given in Sect. 3, while further discussion and conclusions follow in the final section Article published by EDP Sciences A129, page 1 of 11

Astrometry

Astrometric calibration of a given image involves firstly correcting the camera's orientation and pointing direction, based on the position of background reference stars. In this section we describe our new model to convert a position given in right ascension and declination coordinates (in radians) to sample and line coordinates (in pixels) in a Cassini NAC image.

The images used in this work were downloaded from the Planetary Data System (PDS) website1 . After photometric calibration using the CISSCAL software package (West et al. 2010), the right ascension and declination (α c , δ c ) of the optical axis of the NAC for each image was determined at the time of observation, using the mid-times extracted from the image headers and the appropriate SPICE kernels available within the SPICE library2 (Acton 1996). Given the camera orientation and its fieldof-view, we then used the UCAC2 star catalogue (Zacharias et al. 2004) to locate reference stars within the field-of-view. This catalogue provides star positions in terms of their right ascension and declination (α * , δ * ) in the International Celestial Reference Frame (ICRF).

Astrometric model

Our astrometric reduction algorithm proceeds as follows: a star's coordinates (α * , δ * ) are first corrected for proper motion, aberration, and relativistic effects, and the observer's location translated from solar system barycentric coordinates to the Cassini spacecraft frame (Kaplan et al. 1989). A gnomonic projection is then used to convert the corrected star coordinates from the celestial sphere (with a field of view of ≈0.35 • × 0.35 • ) to coordinates (X, Y) in the tangential plane of the camera's CCD, using Eqs. (1) and (2) (see also [START_REF] Eichhorn | Astrometry of star positions[END_REF] for further details). After a further conversion from radians to arcsec, we then finally convert to sample and line (s, l) in pixels, using Eq. (3) below:

X = cos δ * sin(α * -α c ) sin δ * sin δ c + cos δ * cos δ c cos(α * -α c ) (1) Y = sin δ * cos δ c -cos δ * sin δ c cos(α * -α c ) sin δ * sin δ c + cos δ * cos δ c cos(α * -α c ) (2)
s l = -1/ρ s 0 0 1/ρ l cos(θ) -sin(θ) sin(θ) cos(θ) X Y + s 0 l 0 • (3)
In Eq. (3), ρ s and ρ l are the scale factors for sample and line, respectively, measured in arcsec/pixel. Note that at this stage, we introduce two scale factors, thus assuming a rectangular pixel shape.

Since the algorithm has been coded following the conventions used in the IDL programming language, the origin of the sample and line coordinate system is at the centre of the bottom left pixel, with sample increasing to the right and line increasing upward, when the image is displayed in its line-reversed orientation. The spacecraft's "north" is aligned with its +X axis in the increasing line direction and its "east" is aligned with the -Z axis in the decreasing sample direction, hence the "-" sign before ρ s (see Porco et al. (2004) for further details on Cassini's ISS reference frame conventions). Angle θ denotes the angle between the projection of the ICRF Z axis on the spacecraft's (XZ) plane and the spacecraft's Z axis, commonly referred to as the twist angle. Finally, s 0 and l 0 represent the necessary translations (both equal to 511.5 for 1024 × 1024 pixel images) for image centring.

For full astrometric calibration, five parameters should ideally be fitted for each image: ρ s , ρ l , α c , δ c and θ. The last three parameters vary from image to image. However the first two are properties of the camera, and hence common to each image, and can therefore be fixed in order to reduce the observational errors. We therefore calibrated the first two parameters by selecting 100 images from two series of images of star clusters (image series N1580739191 to N1580748341 and N1601334486 to N1601342286, respectively) with a mean number of 225 stars detected per image. Initially, calibration was performed assuming ρ s ρ l . The same calibration was then repeated with ρ s = ρ l (Fig. 1). In Fig. 1 we see that the value of the scale factor remains stable and image-independent. Table 1 shows the values of scale factors used in both cases. From this table we conclude that considering a square shape of pixel is a reasonable approximation and we therefore chose ρ s = ρ l = 1.2354 arcsec/pixel, reducing the number of parameters to be fitted to three. Since each star provides information for two fitted parameters, we need a minimum of two stars to correct the camera's pointing vector and twist angle. Thus, all observations that have been published in this paper contain at least two detected stars per image.

Having measured the satellite's imaged position in sample and line (s, l), it is then necessary to be able to obtain the equivalent position in (α s , δ s ). Equation ( 4) is provided for this purpose. This equation is the inversion of Eq. (3), and converts a position from (s, l) to (X, Y). Equations ( 5) and ( 6) can then be used to transform the resulting position in (X, Y) to (α s , δ s ).

X Y = -ρ s 0 0 ρ l cos(θ) -sin(θ) sin(θ) cos(θ)
ss 0 ll 0 (4)

α s = α c + arctan X cos δ c -Y sin δ c
(5)

δ s = arctan        sin δ c + Y cos δ c X 2 + (cos δ c -Y sin δ c ) 2        (6)

Owen's model

Owen ( 2003) developed a model for the astrometric reduction of Cassini ISS images, including the effects of camera distortion, in which the properties of the Cassini ISS cameras were determined empirically from images of the open star cluster M 35 (the model is also described in Cooper et al. 2006). In this model, camera distortion is treated via the following equations:

∆x ∆y = xr 2 xy x 2 yr 2 y 2 xy         2 5 6         (7)
where r 2 = x 2 + y 2 , n are camera-dependent parameters whose numerical values are given in [START_REF]Cassini ISS Geometric Calibration of[END_REF]. Thus, distortion transforms each point (x, y) on the CCD to (x+∆x, y+∆y), where ∆x and ∆y are given by the above expressions. By comparison, in our model (described earlier), distortion is not included in one explicit equation, but instead is partly absorbed during the scalefactor fitting. This accounts for the difference between the scale factor derived in this paper (≈1.2354 arcsec/pixel), and Owen's value (≈1.2357 arcsec/pixel).

To compare both models, we chose 50 images from the same series used by [START_REF]Cassini ISS Geometric Calibration of[END_REF], selected on the basis of their high star count. Star detection was performed using the IDL-based "FIND" (Stetson 1987) routine, available online from the IDL Astronomy User's Library 3 , detecting a mean number of 225 stars per image. A comparison of the mean postfit rms residuals between the two models (using ρ s = ρ l = 1.2354 arcsec/pixel) is shown in Table 2. It is noteworthy that the 3 IDL Astronomy User's Library URL: http://idlastro.gsfc. nasa.gov/ satellite resolution depends on its distance to the spacecraft. For Mimas the resolution varies from 40 km/pixel to 0.5 km/pixel, and from 35 km/pixel to 0.5 km/pixel for Enceladus. Therefore, according to the comparison in Table 2, a variation of 10 -2 pixels results in a variation in the satellite position of 5 × 10 -2 to 4 × 10 -1 kilometres for Mimas and 5 × 10 -2 to 3.5 × 10 -1 kilometres for Enceladus. Thus, the new model compares favourably with Owen's model and despite the approximations used, can still provide sufficiently accurate astrometry. On the other hand, although Owen's model is slightly more accurate, the presence of non-linear terms make the inversion of these equations in order to convert a position from (sample, line) to (α, δ)) more problematic, without compromising the observation accuracy. Thus in order to take full advantage of the accuracy obtainable with Owen's model, it is generally desirable to leave the observed positions in (sample, line) format. The benefit of the new model is that it provides the satellite's observed position in (α, δ) instead of (sample, line), which is the conventional coordinate system for published astrometric observations, without the need for an iterative inversion technique as would be required with Owen's model. Overall therefore, the new model is easy to introduce in any astrometric software, for only a small decrease in accuracy, and on this basis we have decided to proceed with our model for the astrometric reduction described in this work. Later, in Sect. 3 where we analyse the residuals, we show that the camera have been modeled well enough.

Satellite position measurement

Following correction of the camera's orientation and pointing direction, the next step is to find the centre-of-figure of the observed satellite. Since the satellites were fully-resolved in the Cassini ISS NAC images selected for this work, it was necessary to use a limb-measuring and fitting approach to find the centre-of-figure, rather than using a centroiding technique with associated phase correction.

Limb measurement

Let us consider an image of Enceladus as shown in Fig. 2. To measure one point (in sample and line) of the satellite's apparent limb, the following steps must be applied:

-First, obtain the horizontal profile of pixel intensity (DN) across the satellite (Fig. 3). -Second, compute the absolute value of the derivative of the pixel intensity curve (Fig. 4). The horizontal position of the limb corresponds to the horizontal position of the maximum of this curve. An image-dependent threshold must be added when searching for the maximum in order to avoid detecting points from the terminator. -Finally, repeat the first two steps for all lines and samples to obtain the coordinates of all detectable limb points.

Ellipse fitting

Having detected the satellite limb in the image, the next step is to fit a model of the shape of the satellite to the measured limb points. The JPL SPICE library incorporates approximate shape models for all major natural satellites in the form of triaxial ellipsoids, based on the shapes derived by Thomas et al. (2007). For a given satellite, the SPICE ellipsoid was projected on to the image, forming an ellipse which could then be fitted to the measured limb points using a least-squares technique. Such an ellipse can be parameterised in terms of five quantities: the coordinates X c and Y c , of the centre of the ellipse, the semi-major and semi-minor axes and the angle of orientation of the ellipse φ. However, given that the semi-major and the semi-minor axes are properties of the full ellipsoid, these parameters are known in advance, and hence only the remaining three parameters need to be fitted to the measured limb in order to determine the centre of the ellipse i.e. the centre-of-figure of the satellite.

To evaluate the effects of camera distortion on the satellite centre measurements, limb-fitting was performed twice on 100 randomly-selected images of Mimas and Enceladus (with random resolutions): once with the distortion correction (Eq. ( 7)) and once without. Table 3 shows the difference in sample and line (in pixels) of the measured satellite's centre of figure. We conclude from these results that the camera distortion correction does not significantly affect the measurement of the satellite's position.

Observations and analysis

Using the astrometric and limb-fitting techniques described in the previous section, we reduced 870 out of about 2500 available NAC images of Mimas and 920 out of about 5500 of available NAC images of Enceladus. The complete set of reduced observations is available at the CDS. Table 4 shows a small sample of these observations. The variables in this table are described as follows: Image name, Date and exposure mid-time of the image (UTC), Satellite name, Right ascension and Declination of the satellite (in the ICRF), observation uncertainties in Right ascension and Declination, Right ascension and Declination of the camera's pointing vector and the twist angle of the pointing vector (θ in Eq. ( 3)), Sample and Line (in pixels) of the observed satellite in the image, and finally the number of detected stars in the image. All the angle variables are given in degrees. Figure 5 shows a small sample of the Mimas and Enceladus astrometric observations. We separately provide the pixel coordinates of the satellite centre and the camera pointing information in terms of the right ascension, declination (α c , δ c ) and twist angle θ in order to give the user the option as to whether to adopt this paper's satellite measurement or pointing method, or their own. They could, for example, use our pointing correction and their own preferred centre-of-figure finding technique, or vice versa.

Analysis of results

Observation residuals relative to JPL ephemerides SAT317 and SAT351 are shown in Figs. 6789, for Mimas and Enceladus respectively, where the residuals in α cos δ and δ have been converted to kilometres. Table 6 lists the corresponding mean and standard deviation values for these residuals (also in kilometres). In Figs. 10 and 11 we show the differences |O-C| SAT317 -|O-C| SAT351 for Mimas and Enceladus, respectively. If this difference is positive then SAT317 has a larger residual than SAT351, and vice versa. The mean value of this difference is given in Table 5. From these figures and from Tables 5 and6 we cannot conclude definitively which of these Mimas ephemerides is better. Nevertheless, we notice that the ephemeris for Enceladus has been updated to a new version, SAT351. The SAT317 ephemeris used Cassini data until August 2009 while the ephemeris SAT351 used data until the end of 2011. Comparing to the observations published in this paper, 39 and 127 astrometric observations of Mimas and Enceladus, respectively, were added since August 2009.

From Table 7, where we show the percentage of residuals lower than their estimated observation uncertainties, we note that these have been better-estimated for Enceladus than for Mimas (we would expect about 66.7% of the observations to have (O-C) < 1σ). Two possibilities could explain this: since the surface of Mimas is more heavily-cratered than Enceladus, the limb-fitting is likely to be less accurate for Mimas and thus the corresponding uncertainty in the limb-fitting for Mimas could be an underestimate. On the other hand, the precision of the ephemeris for Enceladus is higher than for Mimas. In fact, the results from Table 7 agree with those in Table 6, with both tables confirming that the ephemeris precision is lower for Mimas than for Enceladus.

Cassini imaging has provided some particularly wellresolved images of the Saturnian satellites, allowing very accurate astrometric positions to be obtained. A high number of stars combined with high satellite resolution inevitably leads to better astrometric accuracy, however such an optimal combination is seldom achieved. Figures 12 and13 show the variation of the number of stars versus the observed satellite's size (in pixels) in a 1024 × 1024 pixel image for all the observations of Mimas and Enceladus, respectively. From these figures we see how the number of stars decreases as the satellite's resolution increases. This is expected since the stars tend to be hidden behind the image of the satellite in the higher resolution images, so that their detection probability is correspondingly lower. Thus, the observational uncertainty decreases with the increase in the number of detected stars in the image, as shown in Figs. 14 and15 for Mimas and Enceladus, respectively. We also notice other effects in these figures and note that the error in the detections of the stars is only one of the three main sources of error, along with the error in the spacecraft's position error and the satellite's centreof-figure measurement error. We discuss these sources of error in more detail later in this section. Since the ellipse fitting was performed using only the visible limb of the satellite, we studied the behaviour of the residuals as a function of phase angle. Figure 16 shows position residuals in kilometres for Mimas and Enceladus compared to the SAT351 ephemeris, in a frame in which the X-axis is oriented in the sun direction. Table 8 shows the corresponding mean residuals and standard deviations for both satellites in this 8 that the observed positions for both satellites are shifted towards the sun, compared to their computed positions. However, the shifts and the standard deviations are more significant for Mimas than for Enceladus. Although Mimas' ephemeris is less precise than Enceladus', the surface of Mimas is also more heavily cratered than Enceladus' and therefore the phase effect could be more important for Mimas. Another possible explanation is that the dimensions of Mimas could be larger than those based on the shape model given in Thomas et al. (2007). This could also lead to such a shift. In Fig. 17, we show the twist angle correction (in degrees) as a function of the number of stars used in its computation. It is clear from this figure that the twist angle correction converges to a precise value as the number of stars increases. This is to be expected since a higher number of stars is needed to obtain a more precise value of the correction. We used a total of 294 images from the same star cluster image series (from N1580739191 to N1637129711) to calibrate this parameter while setting the scale factor to ρ = 1.2354 arcsec/pixel. These images have been taken over a period of time of about 1.8 years. We obtained a mean twist angle correction value of about -9.6 × 10 -2 degrees with a standard deviation of 5.1 × 10 -3 degrees. Here we have used the spacecraft frame defined in the JPL SPICE-system as "Cassini_SC_COORD", while Cassini's NAC frame is named "Cassini_ISS_NAC". For comparison, the angular difference between the "north" axes of these two frames, computed directly using the SPICE system, is -9.1 × 10 -2 degrees, while our value has been obtained using star measurements (independently of the SPICE library). If using the "Cassini_SC_COORD" frame, this constant correction must be added to convert the camera's twist angle to the NAC-centred frame. A useful added benefit of our empirical measurement of this quantity is that it has allowed Table 8. Mean residuals to SAT351 in kilometres represented in a frame where X is in the sun direction. Notes. The first line gives the residuals for Mimas, the second for Enceladus and the last for both satellites.

O-C X (km) O-C Y (km) σ (O-C) X (km) σ (O-C) Y (km
us to determine the error in the camera's twist angle: we obtain about 5.1 × 10 -3 degrees. Finally, in Figs. 18 and 19 we show the residuals in sample and line, respectively, for Mimas and Enceladus versus each satellite's location in a given image. We see from these plots that for the majority of images, the satellite was located around the centre of the field-of-view, which is to be expected, since in most cases the satellites in question were specifically targeted. However, the lack of systematic trends in these plots provides assurance that the camera has been sufficiently well-modelled.

Sources of error

Each observation has three main sources of errors: 1) the pointing correction σ α p and σ δ p , 2) finding the centre-of-figure of the satellite σ c and 3) the spacecraft position σ sp . 1) As described previously, the pointing correction is derived by comparing the imaged positions of background stars with their equivalent positions obtained from a reference star catalogue (the UCAC2 catalogue in this work). Potential sources of error for the pointing correction are therefore the technique used to detect the stars in the image, and inherent errors in the star catalogue itself. Star detection was performed using the "FIND" method (Stetson 1987), which searches for Gaussian signals in the image with user-defined full width at half maximum (FWHM, for the Cassini NAC, we used FWHM = 1.3 pixels). It is noteworthy that the "FIND" routine does not do a full weighted least-squares fit. Instead, it provides approximate image centres, which are themselves intended as starting estimates for a future full non-linear least squares profile fit. On their own, the centroids provided by FIND are probably precise to 1/3 to 1/4 of a pixel. To achieve a precision of order FWHM/(S/N), a proper pointspread function would need to be provided for each image, followed by a full least-squares solution (Peter Stetson, private comm). Hence, the star detection method could be modified in this way in the future, in order to measure star positions with better precision. Also, since this routine does not provide an uncertainty for each measured star position and until a full least-squares method is adopted, we decided to set the star detection uncertainty to σ extraction = FWHM/2.355.

Errors in the reference star coordinates (σ α * , σ δ * ) are provided in the UCAC2 catalogue. Finally, the error in α and δ due to the pointing solution is a function not only of the number of stars in the field but also of their location and of the location of the satellite. The effect of an error in the camera's twist angle is generally lower near the image centre and increases towards the corners of the image. 2) Each point on the detected limb has a measurement error of 0.5 pixels, while the errors in a given satellite's 3-D shape are provided in Thomas et al. (2007). Hence, these latter form the principle sources of error for the determination of the centre-of-figure of the satellite, σ Xcen and σ Ycen .

3) The uncertainty in the spacecraft's position is estimated to about 100 metres, which causes an additional source of error on the observed position of the satellite.

The method used to estimate observational uncertainty is described in Appendix A.

Frequency analysis

The residuals between the observed positions and those derived from JPL ephemerides SAT317 and SAT351 for both Mimas and Enceladus were subject to further analysis. A frequency analysis of the Mimas residuals in α cos δ given in Fig. 6 shows a periodic signal of ≈1.8 km with a period of 0.9443 days. In Figs. 20, 21, we also show the residuals for Mimas (in α cos δ) relative to SAT317 and SAT351 respectively, versus Mimas' mean anomaly. From this figure we see a periodic bias in α cos δ compared to the respective ephemerides. However, we have not detected any periodic variations in the residuals shown in Figs. 789.

To investigate a possible origin for the detected periodic signal described above, we also performed a frequency analyse of the variation with time of Mimas' mean longitude derived from the JPL ephemeris, SAT351. Based on this analysis, we detected a short-term variation, with a period of 0.9449 days and amplitude of 33 km. Similar values were obtained using the NOE-6-12 ephemeris (Lainey et al. 2012) and the TASS1.7 orbital model (Duriez &Vienne 1997 andVienne &Duriez 1995). However, the difference between the measured period in the residuals and the period detected in these models is about 6×10 -4 days, which could be within the uncertainties of the frequency analysis. This periodic bias in the Mimas observations must be attributable to errors in the initial conditions of the integration (including the masses of Saturn and of the satellites) or to unmodeled perturbations, perhaps from very small satellites, the rings, or higherorder harmonics in Saturn's gravity field.

In both the SAT351 and NOE-6-12 ephemerides we also found two additional periods in mean longitude of 1.0016 days and 0.9424 days, with amplitudes of 255 km and 13 km, respectively, that do not appear in the TASS model (see Table 9). The period of 0.9424 days is the orbital period of Mimas, while the period of the resulting "beat frequency" between the 0.9424 and 1.0016 days signals is 15.94 days, which is the orbital period of Titan. suggesting that some terms could be missing in this model, including Titan's effect on Mimas' orbit. This is consistent with Peng et al. (2008) who found a significant periodic signal in their Mimas (O-C) residuals compared to the TASS1.7 ephemeris, based on ground-based astrometric observations.

Conclusion

In this paper, we provided 1790 astrometric observations of two of the main saturnian satellites, Mimas and Enceladus, using Cassini ISS images. We developed an alternative model to that of [START_REF]Cassini ISS Geometric Calibration of[END_REF] and shown that our model can also provide accurate satellite astrometry while at the same time (unlike then Owen model) being easily invertible. We used images of star clusters to calibrate the scale factor in our model that converts from arcseconds to pixels, obtaining a value of ρ = 1.2354 arcsec/pixel. We conclude that a square pixel shape is a reasonable approximation for the purposes of satellite astrometry using the Cassini ISS NAC. Finally, to determine the satellite's centr-offigure, methods for limb measurement and ellipse fitting were developed. We showed also that distortion does not significantly affect the satellite's measured position.

Using the methods described in this paper, we were able to reduce 870 out of about 2500 available NAC images of Mimas and 920 out of about 5500 of available NAC images of Enceladus. Comparing the observed-minus-computed residuals relative to the JPL ephemerides SAT317 and SAT351, we conclude that neither ephemeris provides significantly better results than the other for Mimas, while for Enceladus, the residuals for SAT351 are smaller than those relative to SAT317. We also found that the precision of Enceladus for both ephemerides is better than that of Mimas. An analysis of our computed twist-angle corrections showed that this correction can be set to a fixed value, so that solving for this parameter image-by-image can be avoided in future Cassini astrometric reduction.

A frequency analysis of the observed-minus-computed residuals showed a periodic variation for Mimas' residuals in α cos δ of 0.9443 days with an amplitude of ≈1.8 km. A further frequency analysis of the mean longitude derived from the TASS, SAT351 and NOE ephemerides leads us to conclude that this period may correspond to one of the known short period terms of 0.9449 days in these orbital models. We also found that two particular short-period effects were absent in the TASS analysis when compared to SAT351 and NOE-6-12, suggesting that the terms corresponding to these frequencies may be missing in the TASS orbital model.

Finally, we conclude that, with an observational accuracy of a few kilometres, Cassini's NAC high resolution imaging has proven its worth and importance for astrometric reduction and orbital modelling.

Fig. 1 .

 1 Fig. 1. Derived scale factors (considering a square pixel shape) versus image sequence number. The dashed line is the mean value of 1.2354 arcsec/pixel.

  ρ s ρ l σ(ρ s ) σ(ρ l ) rms (arcsec/pixel) (arcsec/pixel) (arcsec/pixel) (arcsec/pixel) (pixels) ρ s ρ l 1

Fig. 3 .

 3 Fig. 3. Pixel intensity (DN) profile of the chosen area in Fig. 2.

Fig. 4 .

 4 Fig. 4. Absolute value of the derivative of the Pixel intensity curve in Fig. 3. The maximum represents one point of the limb.

  ∆ s ∆ l σ ∆s σ ∆l (pixels) (pixels) (pixels) (pixels) With minus without distortion correction -0.011 -0.022 0.032 0.033 O-C (without distortion correction) 0.184 0.712 1.020 0.869 O-C (with distortion correction) 0.196 0.735 1.018 0.878 Notes. "With distortion" means that the distortion effect was included in limb measurement, "Without distortion" means that no distortion effect added on limb measurement. The first line shows a comparison between satellite positions when adding this effect and removing it. The last two lines show the comparison between the observed positions (with and without adding the distortion to limb measurement) to SAT317 ephemeris predictions.

Fig. 5 .

 5 Fig. 5. Examples of Mimas (middle) and Enceladus (top and bottom) images used in this study. Images names: N1484519176, N1487264883, N1501627117, N1514074586, N1569849851 and N1669795989, respectively. Expected positions of UCAC2 stars are superimposed on the images.

Fig. 6 .

 6 Fig. 6. Residuals for observed positions of Mimas relative to JPL predictions in α cos δ converted to kilometres. Crosses show residuals relative to SAT317 and triangles residuals relative to SAT351.

Fig. 7 .

 7 Fig. 7. Residuals for observed positions of Mimas relative to JPL predictions in δ converted to kilometres. Crosses show residuals relative to SAT317 and triangles residuals relative to SAT351.

Fig. 8 .

 8 Fig. 8. Residuals for observed positions of Enceladus relative to JPL predictions in α cos δ converted to kilometres. Crosses show residuals relative to SAT317 and triangles residuals relative to SAT351.

Fig. 9 .

 9 Fig. 9. Residuals for observed positions of Enceladus relative to JPL predictions in δ converted to kilometres. Crosses show residuals relative to SAT317 and triangles residuals relative to SAT351.

Fig. 10 .

 10 Fig. 10. Difference between residuals for Mimas compared to SAT317 and those compared to SAT351 |O-C| SAT317 -|O-C| SAT351 , with diamonds showing residual differences for α cos δ and stars for δ.

Fig. 11 .

 11 Fig. 11. Difference between residuals for Enceladus compared to SAT317 and those compared to SAT351 |O-C| SAT317 -|O-C| SAT351 , with diamonds showing residual differences for α cos δ and stars for δ.

Fig. 12 .

 12 Fig. 12. Plot showing how the possibility of star detections decreases with increase of Mimas size in the image. In X axis is the satellite size and in the Y axis is the number of stars.

Fig. 13 .

 13 Fig. 13. Plot showing how the possibility of star detections decreases with increase of Enceladus size in the image. In X axis is the satellite size and in the Y axis is the number of stars.

Fig. 14 .

 14 Fig. 14. Evolution of the observation uncertainty (σ = (σ α × cos δ) 2 + (σ δ ) 2 ) on the position of Mimas versus the number of detected stars per image.

Fig. 15 .

 15 Fig. 15. Evolution of the observation uncertainty (σ = (σ α × cos δ) 2 + (σ δ ) 2 ) on the position of Enceladus versus the number of detected stars per image.

Fig. 16 .

 16 Fig.16. Residuals of Mimas and Enceladus to SAT351 in kilometres represented in a frame where X is in the sun direction. "X" denotes for Mimas and "diamonds" for Enceladus.

Fig. 17 .

 17 Fig. 17. Difference between the corrected value of the twist angle by stars and the computed one by SPICE library, versus the number of stars. The dashed line is the mean value.

Fig. 18 .

 18 Fig. 18. Residuals of Mimas and Enceladus positions in sample (pixels) versus their sample location in the image.

Fig. 19 .

 19 Fig. 19. Residuals of Mimas and Enceladus positions in line (pixels) versus their line location in the image.

Fig. 20 .

 20 Fig. 20. Residuals in Mimas' observed positions relative to the JPL SAT317 ephemeris in α cos δ converted to kilometres and plotted versus Mimas' mean anomaly.

Fig. 21 .

 21 Fig. 21. Residuals in Mimas' observed positions relative to the JPL SAT351 ephemeris in α cos δ converted to kilometres and plotted versus Mimas' mean anomaly.

Table 1 .

 1 Values of scale factors in arcsec/pixel for rectangular pixels (ρ s ρ l ) and square pixels (ρ s = ρ l ), respectively.

Table 2 .

 2 Comparison of rms residuals (pixel) between this paper's model and Owen's model for 50 images, with a mean number of stars per image = 225. Image of Enceladus and a line showing the area where the pixel intensity is being studied.

		rms (pixels) σ rms (pixels)
	Present model	0.32	0.027
	Owen's model	0.30	0.017

Table 3 .

 3 Effects of camera distortion on the satellite's measured limb (made on 100 images of Mimas and Enceladus).

Table 4 .

 4 Sample of the results given by the astrometric reduction. .687 × 10 -4 0.662 × 10 -4 29.905985 6.76131991.115937 281.28 729.98 11 N1481705814 2004 Dec. 14 08:31:05.670 MIMAS 107.870401 -3.690718 0.379 × 10 -4 0.359 × 10 -4 107.870317 -3.733118 353.939497 498.21 634.34 29 N1484517118 2005 Jan. 15 21:25:51.308 MIMAS 175.477709 0.093303 0.129 × 10 -3 0.207 × 10 -3 175.489457 0.092305 15.269756 545.29 505.29 3 N1521712680 2006 Mar. 22 09:27:52.503 MIMAS 288.745684 1.988585 0.274 × 10 -4 0.283 × 10 -4 288.783017 2.008344 5.899863 613.73 443.05 51 N1575313583 2007 Dec. 02 18:30:33.311 MIMAS 243.610960 -4.158628 0.901 × 10 -4 0.886 × 10 -4 243.619856 -4.155943 282.100264 524.57 535.14 6 N1595040885 2008 Jul. 18 02:16:36.158 MIMAS 141.777941 -11.025407 0.686 × 10 -4 0.687 × 10 -4 141.781475 -11.021131 45.630431 509.66 495.56 8 N1634636975 2009 Oct. 19 09:06:44.682 MIMAS 272.365301 3.554427 0.416 × 10 -4 0.392 × 10 -4 272.359718 3.536634 273.882329 458.67 498.81 24 N1648319659 2010 Mar. 26 17:49:50.716 MIMAS 275.565618 3.248451 0.515 × 10 -4 0.496 × 10 -4 275.582245 3.292250 275.343224 643.08 547.78 15 N1675518282 2011 Feb. 04 12:57:06.091 MIMAS 261.632816 4.465046 0.803 × 10 -4 0.875 × 10 -4 261.636276 4.462652 243.369096 500.76 517.36 6 N1466514680 2004 Jun.21 12:47:10.340 ENCELADUS 38.588063 10.206353 0.117 × 10 -3 0.111 × 10 -3 38.574930 10.205660 0.137024 473.84 513.61 3 N1484577892 2005 Jan. 16 14:18:44.852 ENCELADUS 318.438532 1.777562 0.689 × 10 -4 0.670 × 10 -4 318.433691 1.730987 6.287934 512.35 647.95 10 N1525360749 2006 May 03 14:48:39.541 ENCELADUS 318.048782 -1.138369 0.790 × 10 -4 0.785 × 10 -4 318.060314 -1.111871 342.129492 567.17 448.32 6 N1572040488 2007 Oct. 25 21:19:21.288 ENCELADUS 133.153457 1.006058 0.114 × 10 -3 0.961 × 10 -4 133.162424 1.033192 353.446634 546.48 435.93 4 N1584025375 2008 Mar. 12 14:26:03.829 ENCELADUS 345.192303 -71.883886 0.736 × 10 -4 0.742 × 10 -4 345.246903 -71.883564 81.855844 517.56 462.39 8 N1636982497 2009 Nov. 15 12:38:29.837 ENCELADUS 293.373282 1.521043 0.608 × 10 -4 0.621 × 10 -4 293.372193 1.515141 276.126094 494.06 510.18 10 N1663946254 2010 Sep. 23 14:31:14.194 ENCELADUS 193.921811 3.487161 0.730 × 10 -4 0.738 × 10 -4 193.923545 3.490967 263.050203 521.90 517.85 7 N1675108551 2011 Jan. 30 19:08:16.839 ENCELADUS 342.949825 -3.660910 0.935 × 10 -4 0.727 × 10 -4 342.947282 -3.759135 185.366996 492.09 225.83 8

	Image name	Date	Time	Body	α	δ	σ α × cos(δ)	σ δ	α c	δ c	Twist angle Sample Line	*
			(UTC)		(degrees)	(degrees)	(degrees)	(degrees)	(degrees)	(degrees)	(degrees) (pixels) (pixels)
	N1479200258 2004 Nov. 15 08:32:05.945	MIMAS	29.979909	6.680864 0

Table 5 .

 5 Mean difference |O-C| SAT317 -|O-C| SAT351 in α cos δ and δ for Mimas and Enceladus.

	Mimas	0.09	-0.39
	Enceladus	0.17	0.26

|O-C|

SAT317 -|O-C| SAT351 α cos δ (km) δ (km)

Table 6 .

 6 Mean values of residuals with respect to the JPL SAT317 and SAT351 ephemerides in kilometres, including standard deviations.

	Mimas (SAT317)	-0.83	4.15	-1.02	2.95
	Mimas (SAT351)	-0.86	4.01	-0.91	3.39
	Enceladus (SAT317)	-0.35	3.20	0.17	2.99
	Enceladus (SAT351)	-0.25	3.00	0.04	2.78

α cos δ (km) σ α cos δ (km) δ (km) σ δ (km)

Table 7 .

 7 Percentage

	Mimas (SAT317)	47.2	63.6
	Mimas (SAT351)	48.5	53.8
	Enceladus (SAT317)	60.4	57.9
	Enceladus (SAT351)	61.0	66.6

of observations with (O-C) less than the observation uncertainty σ in α cos δ and in δ.

%(O-C) α cos δ < σ α cos δ %(O-C) δ < σ δ

Table 9 .

 9 Detected short periods from an analysis of the mean longitude of Mimas from the TASS, SAT351, and NOE-6-12 orbital models.

		Period (days) Amplitude (km)
	TASS	0.9449	32
		1.0016	255
	SAT351	0.9449	33
		0.9424	13
		1.0016	255
	NOE-6-12	0.9449	33
		0.9424	13

Planetary Data System (PDS) URL: http://pds.nasa.gov/

SPICE library's URL: http://naif.jpl.nasa.gov/naif/

Acknowledgements. The authors woud like to thank Vincent Robert and Alain Vienne for their assistance. The authors also thank the anonymous reviewer for very useful and helpful comments. This work has been funded by UPMC-EMERGENCE (contract number EME0911). This work was also supported by the Science and Technology Facilities Council (grant number ST/F007566/1) and by an International Exchange grant from the Royal Society and the CNRS.

Appendix A: Observation uncertainty estimation method

The observational uncertainties σ α cos δ and σ δ shown in Table 4 were computed using the following expressions:

(σ α cos δ) 2 = (σ α p cos δ p ) 2 + σ 2 αc + σ 2 sp (A.1)

where,

where α p and δ p are the observed satellite's coordinates, σ ρ is given in the pointing correction related to rotation and translation, respectively. These latter contain the errors in star extraction σ extraction and those provided in the UCAC2 catalogue (σ α * , σ δ * ).

The satellite centre measurement uncertainty σ αc and associated σ δc is expressed as follows:

σ Xcen and σ Ycen are the errors in sample and line from the satellite centre determination based on limb fitting. Finally, the error in the spacecraft position is,

where D is the distance (in kilometres) between the spacecraft and the observed satellite. These expressions were derived by differentiating Eq. ( 4).

Appendix B: Kernels

The following is the list of SPICE kernels used for astrometric reduction in this paper: