Free Access
Issue
A&A
Volume 569, September 2014
Article Number L2
Number of page(s) 5
Section Letters
DOI https://doi.org/10.1051/0004-6361/201424590
Published online 12 September 2014

© ESO, 2014

1. Introduction

Following the Rosetta wake-up after hibernation and subsequent recommissioning of the scientific payload, which occurred in March 2014, the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS), the main imaging system onboard the European Space Agency (ESA) spacecraft, started performing periodic photometric observations of the target comet 67P/Churyumov-Gerasimenko (67P) from a range of about 5 million km. The goal of these approach observations is threefold: 1) to support the navigation of the spacecraft through optical imaging; 2) to perform early characterization of the comet to determine its rotational state; and 3) to monitor the onset of cometary activity. The last two points, besides their own scientific interest, provide valuable input for the planning of the mission operations at the comet. Comet 67P was selected as a Rosetta target only after a delay in the Ariane launcher program made it impossible for the mission to reach its originally scheduled target, comet 46P/Wirtanen. At that time, however, and only two orbital revolutions around the Sun before the scheduled Rosetta encounter, important physical properties of 67P, as its rotation state, were still unknown. Early work by Lamy et al. (2006) based on Hubble Space Telescope (HST) observations, provided a first determination of the rotation state of the comet, indicating a simple rotation and a period in the range 12.0 h to 12.8 h. The authors also performed photometric inversion of the HST light curve, which resulted in a non convex, and admittedly non unique, shape model. Further light curve observations were performed by Lowry et al. (2006) and by Tubiana et al. (2008, 2011). Lowry et al. (2012) used all the observational base available at that time and derived a best spin-state solution with Psid = 12.76137 ± 0.00006 h and ecliptic coordinates of the pole λ = 78° ± 10°; β = + 58° ± 10°, along with a convex shape model.

2. Observations and data reduction

The results presented in this paper are based on observations performed with the OSIRIS instrument (Keller et al. 2007) in 2014 in the period Mar. 23 to Jun. 24 (see Table 1 in the Online Material for the observational circumstances). OSIRIS consists of a suite of two cameras, the Narrow Angle Camera (NAC) and the Wide Angle Camera (WAC). They both use a 2048 × 2048 pixel CCD camera coupled to a reflective telescope: an f/8 telescope with a 2.2° × 2.2° field of view (FOV) for the NAC and an f/5.6, 11.3° × 12.1° FOV telescope for the WAC. The images used for this study were acquired with the NAC filter 22 (center band 649.2 nm, FWHM 84.5 nm) and WAC filter 12 (center band 629.8 nm, FWHM 156.8 nm). Typical exposure times ranged from 10 s to 12 min, selected to achieve the maximum posible signal-to-noise ratio (S/N) at the different ranges from the comet and still avoid saturation. High S/N was necessary for imaging the faint coma and for the detection of possible subtle deviations from strict periodicity in the light curves. Depending on whether the images were acquired for navigation purposes or for light curve studies, the data were either relayed as full frames to Earth or as small subframes centered around the target, as a measure for limiting data volume. We preprocessed the raw frames through the standard OSIRIS data reduction pipeline and measured the comet fluxes with the AstPhot synthetic aperture photometry tool (Mottola et al. 1995). We then reduced the raw fluxes to the standard observation geometry at 1 AU from the observer and from the Sun, and then converted them to the Kron-Cousins R band by using OSIRIS standard calibration fields. No correction for changing phase angle was applied. The typical relative photometric error of the measurements is about 0.01 mag (1σ), while the systematic absolute photometric calibration error is estimated to be of the order of 0.03 mag. During the observation period, the nucleus was still unresolved on both cameras, and the comet experienced episodes of intermittent activity (Tubiana et al., in prep.), which resulted in the presence of a clearly visible coma in some of the acquisition sessions. In order to minimize the coma contribution to the measured nuclear magnitude, we selected a small circular synthetic aperture with a radius of 4 pixels. At the distance of the comet this aperture size corresponded to a projected radius of 50 km for the single WAC observation, while it ranged from 272 km to 15 km for the NAC observations. We made no attempt to model and subtract the coma contribution to the light curves, as we estimated it to be smaller than the relative photometric error of the measurements. To determine the rotation period, we analyzed the OSIRIS photometric time series with the Fourier analysis procedure described in Harris et al. (1989). In this method, a light curve is approximated with a Fourier polynomial of the desired order. For each trial rotation period within a given range, a linear equation system is constructed, which is then least-squares fitted to the data to retrieve the best-fit Fourier coefficients and the magnitude offset for each individual night. A solution is achieved if a global minimum of the residuals in the chi-squared sense is found. The resulting composite light curve is shown in Fig. 1. The best-fit period is 12.4053 ± 0.0007 h, with an amplitude of 0.542 ± 0.005 mag. Although this period strictly represents a synodic period, the direction of the phase angle bisector (PAB, see Harris et al. 1984 for a definition) changed only by about during the three months spanned by the OSIRIS observations. For this reason, the measured comet’s synodic period is very close to the sidereal period.

3. Rotation state

The composite in Fig. 1 shows that the 67P light curves nicely overlap at the level of the photometric noise. No multiple periodicities are detected, which demonstrates that the comet is presently in (or very close to) a relaxed rotation state. Soon after the first few OSIRIS light curves were acquired, it became apparent that the measured rotation period significantly differed from the best solution from Lowry et al. (2012). Unfortunately, the HST observations of 2003 by Lamy et al. (2006), given their short time baseline, are compatible with either period, and do not allow us to discriminate between them. A possible solution with a period of about 12.4 h was found by Lowry et al. (2012) during their initial period scan (cf. their Fig. 2). This solution, however, was disregarded by the authors as unreliable, as it caused some of the light curves to appear in counterphase in the composite.

thumbnail Fig. 1

Composite light curve from the OSIRIS observations. The nuclear magnitudes are reduced to the standard observation geometry at 1 AU. The magnitude scale refers to the phase angle at the time of the first NAC observations. The following observations have been accordingly shifted in magnitude. Data points beyond rotational phase 1.0 are repeated for clarity. T0 is corrected for light-travel time. The dates refer to the midtime of the respective observation.

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thumbnail Fig. 2

Normalized χ2 map showing the goodness of the fit to the light curves as a function of the ecliptic coordinates of the pole. The contour lines show the +5%, +7.5%, and +10% levels from the minimum χ2.

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thumbnail Fig. 3

HST, ground-based and OSIRIS NAC selected light curves of 67P (from top left to bottom right) along with synthetic curves obtained with the shape model corresponding to Solution 1 (solid line). See Table 1 for observational details.

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As a first step for the determination of the spin state of 67P, we searched for a global period-pole-shape solution by using the convex shape inversion scheme (Kaasalainen et al. 2001; Kaasalainen & Torppa 2001) on the complete data set available (see Table 1). We found solutions around a period of 12.4 h, which produced satisfactory fits to the light curves in terms of χ2 and general light curve shapes. However, the family of convex shape models corresponding to those solutions all consisted of a pure rotation around the long axis of the body. Pure long-axis mode (LAM) rotation corresponds to the maximum allowable energetic state for a given angular momentum of the body. Therefore, we consider it unlikely that 67P can presently occupy this energy state exactly. Other (nonpure) LAM states have been observed (or proposed) for several comets and asteroids as 1P/Halley and (4179) Toutatis. They represent excited rotation states that are always associated with precession of the instantaneous spin vector of the body (see, e.g., Samarasinha & A’Hearn 1991). Such complex rotation, however, would necessarily cause a typical signature in the light curves, which was definitely not present in the OSIRIS observations.

Given that no viable single solution was found that could satisfy all of the available photometric observations, we considered the possibility that the rotation period of 67P could have evolved with time, subjected to a sublimation-induced torque. This choice was encouraged by the fact that both modeling and observations are providing increasing evidence that a spin period may change during a single orbital step. The last perihelion passage of 67P occurred on Feb. 28, 2009, and the previous passage occurred on Sep. 18, 2002. Therefore, all pre-Rosetta observations were obtained in the time interval between the past two perihelion passages, while the OSIRIS observations were performed after the 2009 perihelion. We therefore made the working hypothesis that the spin rate of 67P changed during some period around the perihelion of 2009 (due to cometary activity), while staying constant during the two time intervals covered by the ground-based and Rosetta observations. We consequently modified the convex inversion procedure to allow for two independent rotation periods, one before and one after the 2009 perihelion passage. The second period was kept fixed at the value found through the OSIRIS data, which provided a very solid constraint, while the first period was left free as an optimization parameter.

Figure 2 represents a plot of the normalized χ2 of the fit as a function of the ecliptic coordinates of the pole. Two regions with significantly lower residuals than the background are clearly identifiable in the plot and are labeled as Solution 1 and Solution 2. These regions are centered around J2000 ecliptic coordinates (λ = 65°; β = + 59°) and (λ = 275°; β = + 50°), respectively, and are both characterized by the same set of sidereal periods (P1 = 12.76129 ± 0.00005; P2 = 12.4043 ± 0.0007). Because the loci of the solutions have an irregular shape, simple errors on the coordinates do not represent well the accuracy of the pole location. Having this limitation in mind, we estimate the uncertainty in the orientation of the spin axis to be on the order of ± 15° for each ecliptic coordinate, and refer the reader to Fig. 2 for a more realistic representation. The two solutions, however, are not independent, and are a manifestation of the ambiguity theorem as formulated by Kaasalainen & Lamberg (2006). This theorem states that if the viewing and illumination geometry (i.e., the Sun and observer vectors) lie on the same plane for all observations (usually the ecliptic), and if (λ, β) constitutes a solution that satisfies the light curves, then also (λ + 180°, β) represents a solution for a model shape that is a mirror along the z-axis of the shape model for the original solution. Since 67P has a small orbital inclination, indeed the viewing geometry was close to (but not exactly on) the ecliptic plane for all the observations, which resulted in the observed ambiguity. This small deviation from the ecliptic geometry causes the two conjugate solutions not to be spaced by exactly 180° in ecliptic longitude. Our Solution 1 is compatible with the less favorite prograde solution by Lamy et al. (2007) and with the most likely solution by Lowry et al. (2012).

Figure 3 shows the model fits to selected light curves corresponding to the Solution 1. The model provides an excellent fit to the observations both in terms of phasing of the light curve features and in terms of amplitude. Solution 2 results in a similarly good fit. Figure 4 shows the corresponding convex shape model in three orthogonal views. It must be emphasized that the obtained shape represents the best “photometric” shape. Kaasalainen & Torppa (2001) have demonstrated that their inversion scheme converges to the real shape of the object if the object is globally convex. If the object, on the other hand, contains major concavities, the inversion procedure converges to the convex hull of the body, which is the shape that a non-convex body would have if it was “shrink-wrapped”. The occurrence of several large planar facets on our shape model is therefore a hint that major concavities might be present at those locations.

thumbnail Fig. 4

Three orthogonal views of the convex shape model corresponding to Solution 1.

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4. Discussion and conclusions

With axial ratios of a/b = 1.21 and b/c = 1.05, the derived shape is less elongated than the shape found by Lowry et al. (2012), with the uncertainty being largest on the z-axis dimension beacuse of the view near the ecliptic plane for all data sets. The presence of large flat faces (or depressions) on the surface is seen in both models.

The change in rotation rate, with the period shortening by around 21 min over the course of the 2009 perihelion passage, is within the expected range for comets. Gutiérrez et al. (2005), for example, estimated for 67P a possible change of period between orbits could be up to one hour. Four previous determinations of period changes in short period comets have been made, with magnitudes between 16 seconds per orbit for the low activity comet 10P/Tempel 2 (Knight et al. 2012) and 2 h for the hyperactive 103P/Hartley 2 (Belton et al. 2013). The other measurements were for 2P/Encke (4 min – Mueller et al. 2008) and 9P/Tempel 1 (14 min – Belton et al. 2011; Chesley et al. 2013). It is not surprising that the change for 67P is similar to that for 9P, a comet of similar size and activity level, although with a considerably longer rotation period (41 h). Samarasinha & Mueller (2013) compared the four comets with observed spin-rate changes and their activity level, and found that an approximately constant factor (within a factor of two) links them and allows the change of rotation rate to be predicted based on the size, period, and orbit of the comet, and that the changes should be independent of the active fraction of the surface area. The measurement for 67P is two to three times larger than this analysis predicted (Samarasinha, priv. comm.).

A more detailed analysis of how and when the period changed is beyond the scope of this short letter, and will include further constraints from ground-based observation. As the comet’s activity is largely similar from orbit to orbit (Snodgrass et al. 2013), and 9P was seen to have a similar change in period each perihelion (Belton et al. 2011), we can expect that the comet’s period will decrease by a further 20 min during the coming perihelion passage. With the high precision on ΔP possible by landmark tracking from OSIRIS images, a change of this magnitude will be easy to detect, and furthermore the rate of change as the comet approaches the Sun will be determined, giving us information on the moment of inertia and torques due to outgassing at different times.

Note: resolved images of 67P from OSIRIS have subsequently found a highly irregular shape, and a rotation pole consistent with Solution 1. Details on the shape from resolved images, and a comparison with the convex hull solution presented here, will be presented at a later date.

Acknowledgments

OSIRIS was built by a consortium of the Max-Planck-Institut für Sonnensystemforschung, in Göttingen, Germany, CISAS-University of Padova, Italy, the Laboratoire d’Astrophysique de Marseille, France, the Instituto de Astrofísica de Andalucia, CSIC, Granada, Spain, the Research and Scientific Support Department of the European Space Agency, Noordwijk, The Netherlands, the Instituto Nacional de Técnica Aeroespacial, Madrid, Spain, the Universidad Politćhnica de Madrid, Spain, the Department of Physics and Astronomy of Uppsala University, Sweden, and the Institut für Datentechnik und Kommunikationsnetze der Technischen Universität Braunschweig, Germany. The support of the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), Sweden (SNSB), and the ESA Technical Directorate is gratefully acknowledged. C.S. received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 268421. This research made use of JPL’s online ephemeris generator HORIZONS.

References

Online material

Table 1

Observational circumstances.

All Tables

Table 1

Observational circumstances.

All Figures

thumbnail Fig. 1

Composite light curve from the OSIRIS observations. The nuclear magnitudes are reduced to the standard observation geometry at 1 AU. The magnitude scale refers to the phase angle at the time of the first NAC observations. The following observations have been accordingly shifted in magnitude. Data points beyond rotational phase 1.0 are repeated for clarity. T0 is corrected for light-travel time. The dates refer to the midtime of the respective observation.

Open with DEXTER
In the text
thumbnail Fig. 2

Normalized χ2 map showing the goodness of the fit to the light curves as a function of the ecliptic coordinates of the pole. The contour lines show the +5%, +7.5%, and +10% levels from the minimum χ2.

Open with DEXTER
In the text
thumbnail Fig. 3

HST, ground-based and OSIRIS NAC selected light curves of 67P (from top left to bottom right) along with synthetic curves obtained with the shape model corresponding to Solution 1 (solid line). See Table 1 for observational details.

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In the text
thumbnail Fig. 4

Three orthogonal views of the convex shape model corresponding to Solution 1.

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In the text

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