Photometric behaviour of
67P/Churyumov–Gerasimenko and analysis of its
pre-perihelion diurnal variations

A. Longobardo, E. Palomba, F. Capaccioni, M. Ciarniello, F. Tosi, S. Mottola, L.V. Moroz, G. Filacchione, A. Raponi, E. Quirico, et al.

► To cite this version:

A. Longobardo, E. Palomba, F. Capaccioni, M. Ciarniello, F. Tosi, et al., Photometric behaviour of 67P/Churyumov–Gerasimenko and analysis of its pre-perihelion diurnal variations. Monthly Notices of the Royal Astronomical Society, 2017, 469 (Suppl_2), pp.S346-S356. 10.1093/mnras/stx1803 obspm-02190704

HAL Id: obspm-02190704

https://hal-obspm.ccsd.cnrs.fr/obspm-02190704v1

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# Photometric behaviour of 67P/Churyumov–Gerasimenko and analysis of its pre-perihelion diurnal variations

A. Longobardo,<fnref n="1" />* E. Palomba,<fnref n="1" />,<fnref n="2" /> F. Capaccioni,<fnref n="1" /> M. Ciarniello,<fnref n="1" /> F. Tosi,<fnref n="1" /> S. Mottola,<fnref n="3" /> L.V. Moroz,<fnref n="3" />,<fnref n="4" /> G. Filacchione,<fnref n="1" /> A. Raponi,<fnref n="1" /> E. Quirico,<fnref n="5" /> A. Zinzi,<fnref n="2" />,<fnref n="6" />

M. T. Capria,<fnref n="1" />,<fnref n="2" /> D. Bockelee-Morvan,<fnref n="7" /> S. Erard,<fnref n="7" /> C. Leyrat,<fnref n="7" /> G. Rinaldi<fnref n="1" /> and F. Dirri<fnref n="1" />

Accepted 2017 July 14. Received 2017 July 13; in original form 2017 April 14

## ABSTRACT

Spectral parameters measured by the Rosetta/VIRTIS imaging spectrometer on the nucleus of comet 67P/Churyumov–Gerasimenko were studied as a function of incidence, emission and phase angles. A statistical analysis was undertaken for a number of spectral parameters: reflectance at seven wavelengths (0.55, 0.75, 1.2, 1.7, 2.0, 2.8 and 4.0 µm), the depth and centre of the 3.2 µm organics band, and the visible and infrared slopes. Different photometric behaviours were assessed over the entire comet surface, on the four different comet macro-regions (head, neck, body and bottom) and for different local solar times. Phase functions are on average both spatially and temporally constant, indicating an overall homogeneity of optical properties. Comparison between phase functions of 67P/Churyumov–Gerasimenko and of other comets explored by space missions indicates a variation of phase curve steepness among comets, larger than expected for objects having similar albedo. This can be ascribed to different surface roughness, in turn due to different levels of surface erosion. Band depth appears to be independent of phase angle, which may help in constraining the surface composition. However, its band centre slightly moves to longer wavelengths with increasing incidence angle, possibly due to exposure of low amounts of water ice due to a weak cometary activity at increasing temperatures. Water ice abundance is also the main driver of the photometric behaviour of the visible and infrared slope, since larger water ice abundance causes a slope decrease and a phase reddening increase in the neck region and during the nighttime.

**Key words:** comets: general – comets: individual: Comets: Churyumov–Gerasimenko.

## 1 INTRODUCTION

The ESA Rosetta mission has been orbiting around comet 67P/Churyumov–Gerasimenko from 2014 August until 2016 September, escorting it during its orbital motion.

The comet nucleus consists of two lobes (Sierks et al. 2015), on which four main regions have been identified, i.e. head, body, bottom and neck (connecting the two lobes). The VIRTIS imaging

spectrometer (Coradini et al. 2007) revealed that the average albedo is very low, i.e. 0.062 ± 0.002, and shows small variations across the surface (Ciarniello et al. 2015). Typical spectra profiles are characterized by two distinct slopes in the visible range (0.5–0.8 µm) and the near-infrared range (1–2 µm) and by a broad absorption band centred at about 3.2 µm (Capaccioni et al. 2015). These features are compatible with a widespread occurrence of a dark, spectrally featureless material, e.g. iron sulphides (Capaccioni et al. 2015), and organic materials, responsible for the 3.2-µm band (Capaccioni et al. 2015; Filacchione et al. 2016) and whose carriers may be a carboxylic group (COOH), ammonium (NH₄), aromatic organics

<footnote n="1">¹INAF-IAPS, via Fosso del Cavaliere 100, I-00133 Rome, Italy</footnote>

<footnote n="2">²ASI-ASDC, via del Politecnico snc, I-00133 Rome, Italy</footnote>

<footnote n="3">³Institute for Planetary Research, Deutsches Zentrum für Luft- und Raumfahrt (DLR), D-12489 Berlin, Germany</footnote>

<footnote n="4">⁴Institute of Earth and Environmental Science, University of Postdam, Postdam, Germany, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam, Germany</footnote>

<footnote n="5">⁵Université Grenoble Alpes, CNRS, IPAG, F-38041 Grenoble, France</footnote>

<footnote n="6">⁶INAF-OAR, Via Frascati 33, I-00078, Monte Porzio Catone (RM), Italy</footnote>

<footnote n="7">⁷LESIA, Observatoire de Paris/CNRS/Université Pierre et Marie Curie/Université Paris-Diderot, F-92195 Meudon, France</footnote>

<footnote>* E-mail: andrea.longobardo@iaps.inaf.it</footnote>
(CH₂/CH₃) or OH (Quirico et al. 2016). This absorption band may occasionally shift to shorter wavelengths and deepen when observed along with water ice (De Sanctis et al. 2015a; Filacchione et al. 2016). However, the surface is mostly de-hydrated and water ice is observed as a result of a diurnal cycle of water in the neck macro-region (De Sanctis et al. 2015a), consisting in a percolation of water vapour from sub-surface layers during the daytime, its successive trapping in surface layers during nighttime and its sublimation during early morning, or in localized patches (Filacchione et al. 2015), corresponding to exposed subsurface regions, whose spectra show clear absorption bands at 1.5 and 2 µm. The occurrence of water ice is also highlighted by a decrease in both visible and infrared slopes (Filacchione et al. 2016). Regardless of its nature, transient exposures of water ice evidence that 67P Churyumov–Gerasimenko is subject to evolutionary processes and cometary activity, transforming its upper surface. This behaviour has been confirmed by the observation of seasonal variations of spectral properties of the surface (Ciarniello et al. 2016), by the temporal evolution of ice patches (Raponi et al. 2016), as well as by the first detection of seasonal exposure of carbon dioxide ice (Filacchione et al. 2017), a typical sub-surface volatile. Even though the comet nucleus is spectrally quite homogeneous, the most active and hence morphologically smoother areas, such as Hapi, located in the neck macro-region, show distinct behaviour, i.e. slightly higher albedo (Ciarniello et al. 2015; Fornasier et al. 2015;), lower spectral slope and deeper 3.2-µm band.

The application of a photometric correction to VIRTIS (Visual InfraRed and Thermal Imaging Spectrometer) data is fundamental to remove illumination and viewing biases from the spectra and hence to correctly associate spectral variations to changes in composition or physical properties of the surface. The Hapke photometric model has been already applied on VIRTIS data (Ciarniello et al. 2015), allowing the first albedo maps of the comet and a study of phase reddening to be obtained.

In this work, we apply a different approach to photometric correction, based on a statistical analysis of the VIRTIS data set (Longobardo et al. 2012). This semi-empirical approach, already applied on different bodies, such as Vesta (Longobardo et al. 2014; Palomba et al. 2014), Lutetia (Longobardo et al. 2016) and Ceres (Longobardo et al., in preparation), is fully complementary to a Hapke photometric correction, in several respects: (a) it emphasizes variations of photometric properties across the surface, which may be related to different physical and/or optical properties, and focus on particular regions and on particular time periods (e.g. day or night); (b) it allows comparing disc-resolved phase functions with those of other minor bodies to highlight the nature of their difference (e.g. taxonomy, composition, grain size, roughness, albedo; Longobardo et al. 2016); and (c) it can be used to study the photometric behaviour of spectral indices other than reflectance (e.g. band depths, band centres, spectral slopes), which is related to surface composition and/or abundance and/or thermal properties of an absorption carrier (Longobardo et al. 2014), as well as phase reddening.

Our study has been performed on pre-perihelion data, corresponding to a low cometary activity, in order to perform a statistical analysis on a 'stable' body. This approach was necessary to avoid misinterpretation due to the emergence of a substantial cometary activity. Because photometric properties of a surface are retrieved on the basis of observations obtained at different illumination/viewing angles and at different points in time, a robust analysis can be achieved only starting from the assumption that the surface composition is not significantly altered by cometary activity.

Section 2 describes data used from this study, from which we extracted the spectral parameters described in Section 3. The method used to analyse the photometric behaviour of these parameters is shown in Section 4, whereas Sections 5 and 6 are devoted to results and their interpretation, respectively. Finally, conclusions are given in Section 7.

## 2 DATA

VIRTIS is an imaging spectrometer (Coradini et al. 2007) composed of two optical heads, VIRTIS-H, aimed at high spectral resolution observations, and VIRTIS-M, aimed at surface mapping. While VIRTIS-H covers only the wavelength range between 2 and 5 µm with a spectral resolution of about 3 nm. VIRTIS-M works in the 0.2–5.1-µm spectral range, covered by a visible (0.2–1 µm) channel and an infrared (1–5.1 µm) channel, respectively. The spectral sampling of these two channels is 1.8 and 9.7 nm, respectively.

In our analysis, we consider only VIRTIS-M data, which provide a much broader coverage of the comet's nucleus, thanks to its imaging capabilities. In particular, we focus on Pre-Landing data, specifically Medium Term Planning (MTP) observation phases from MTP006 to MTP009. These observations have been acquired from 2014 August to September, from a spacecraft altitude between 10 and 100 km, corresponding to a spatial resolution between 2.5 and 25 m/pixels (Filacchione et al. 2016), and under a phase angle between 12.5° and 100°. They cover mostly the northern and equatorial regions of the comet.

Following the procedure described by Filacchione et al. (2016), geometry parameters, such as incidence, emission and phase angles as well as true or effective local solar time (TLST), i.e. calculated with respect to individual facets (derived from shape model; Preusker et al. 2015). We note that, due to the irregular shape of the comet and its spin axis orientation (Presuker et al. 2015), our data set includes night observations with non-null reflected signal and which can hence be used for our analysis.

The work has been performed on *I/F* calibrated spectra, where thermal emission was removed by adopting the procedure described by Raponi (2014).

About 5.8 million visible spectra and 4.9 million infrared spectra of the comet nucleus have been acquired during the above period. After the selection of the best disc function (see sub-section 4.1.1), we excluded all of the observations acquired at incidence and emission angles larger than 70°, reducing the considered data sets to 4.2 million and 3.7 million spectra, respectively. In addition, for the study of photometric behaviour of 3.2-µm band (sub-sections 4.2 and 4.3), we excluded also those spectra whose 3.2-µm band depth was smaller than 0.04, since this value is comparable with spectral oscillations observed in this spectral region due to instrumental noise, therefore reducing the infrared data set to 3 million spectra.

## 3 TOOLS

In order to study variations of the photometric behaviour in the entire range sampled by VIRTIS, we obtained phase functions at seven different wavelengths, two in the visible channel, i.e. 0.55 and 0.75 µm, and five in the infrared channel, i.e. 1.2, 1.7, 2.0, 2.8 and 4.0 µm. Albedo values at 0.55 µm and VIRTIS-based albedo maps were obtained previously by Capaccioni et al. (2015) and Ciarniello et al. (2015). The redundancy offered by the application of a different method to retrieve albedo allows for strengthening of the obtained results. Most of phase functions of other minor bodies have been obtained at, or close to, a wavelength of 0.75 µm (e.g.
Longobardo et al. 2016), and hence the study at this wavelength is useful for a comparative analysis. The analysis at 1.2, 1.7 and 2.0 µm enables monitoring the reflectance behaviour at wavelengths included in the spectral infrared slope between 1.0 and 2.0 µm (e.g. Capaccioni et al. 2015). However, the photometric behaviour of the latter is studied also independently (see later in the text). The spectral pixels at 2.8 and 4.0 µm correspond to the shoulders of the 3.2 µm band. In order to maximize the signal-to-noise ratio, the reflectance at each wavelength has been calculated as average on the four VIRTIS spectral pixels closer to that wavelength (e.g. Palomba et al. 2015). This procedure has been applied to all of the I/F values used for the retrieval of the spectral descriptors defined below.

The 3.2-µm absorption band has been defined as follows: (i) left shoulder is defined by a fourth-order polynomial fit between 2.5 and 3.0 µm; (ii) reflectance trough is defined by a third-order polynomial fit between 3.0 and 3.55 µm; and (iii) right shoulder by a fourth-order polynomial fit between 3.55 and 3.9 µm. The band continuum is a linear fit between left and right shoulder maxima, whereas the band centre corresponds to the reflectance minimum after the continuum removal. Finally, band depth is calculated as $1 - R_c/R_{con}$, where $R_c$ and $R_{con}$ are the measured reflectance and the calculated continuum reflectance at the band centre (Clark & Roush, 1984).

Visible and infrared slopes are defined as $(R_{λ2} - R_{λ1})/R_{λ1}(λ2 - λ1)$, where $λ1$ is 0.55 µm in the visible case and 1.1 µm in the infrared case (we selected 1.1 µm instead of 1.0 µm in order to have a wavelength range completely included in the VIRTIS-M infrared channel) and $λ2$ corresponds to 0.75 and 2.0 µm, in the visible and infrared slope definition, respectively.

In our work, we did not consider water ice absorption bands at 1.5 and 2.0 µm, which are rarely observed (Filacchione et al. 2016; Raponi et al. 2016), and hence are not suitable for a statistical analysis.

# 4 METHOD

The retrieval of phase functions by means of the semi-empirical approach previously adopted for Vesta (Longobardo et al. 2014) is based on a definition of reflectance families, since the phase function shape can be related to the reflectance level (e.g. in the case of Vesta, bright regions showed flatter phase functions than darker ones). This definition is in turn based on a statistical analysis of data, i.e. a reflectance family is given by $xx$ per cent of brightest pixels in each phase angle 1° bin, where $xx$ varies between 10 (brightest regions) and 90 (darkest regions), with a step of 10.

However, if the body shows a small reflectance variation across the surface, the phase functions corresponding to the different reflectance families tend to coincide. This was the case of Lutetia (Longobardo et al. 2016), and it is also the case of 67P/Churyumov-Gerasimenko, as revealed by a preliminary analysis. Therefore, we did not adopt the definition of reflectance families and calculated a single phase function for each performed analysis. Even though the albedo is almost constant on 67P/Churyumov-Gerasimenko, the phase function might still be affected by parameters as location, physical properties and local solar time. Therefore the photometric behaviour of the spectral descriptors introduced in Section 3 has been studied for:

* the whole data set (i.e. 67P/Churyumov-Gerasimenko spatial and temporal average)

* each 67P/Churyumov-Gerasimenko region, i.e. head, body, neck and bottom

* four different local time intervals, i.e. 0–6, 6–12, 12–18 and 18–24.

## 4.1 Reflectance

VIRTIS calibrated spectra are expressed in units of calibrated radiance factor $I/F$. In this paper, we will use the terms ‘reflectance’ and ‘radiance factor’ as synonyms, and will label it either as $I/F$ or $R$.

Following a commonly used definition (e.g. Schroder et al. 2013), we consider the radiance factor as the product of two terms, which correspond to the topography (disc function) and to phase (phase function) contribution, i.e.:

$$R = D(i, e, \varphi) F(\varphi) \quad (1)$$

where $D(i, e, \varphi)$ and $F(\varphi)$ are the disc function and the phase function (including albedo), respectively. The process to photometrically correct the reflectance, i.e. to obtain $R$ at a standard observation geometry (i.e. $i = e = \varphi = 0°$ or $i = 30°$, $e = 0°$; $\varphi = 30°$), is divided in two consecutive steps:

1. Selection of the disc function, among those commonly used in literature, which best removes the influence of incidence and emission angles from the reflectance and computation of the equigonal albedo $R/D$ (sub-section 4.1.1). This step has been applied to the entire data set.

2. Retrieval of the phase function that best fits the trend of equigonal albedo as a function of phase angle (sub-section 4.1.2). This step has been applied to: (a) the entire data set, (b) each comet macro-region and (c) each TLST interval.

### 4.1.1 Disk function

The equigonal albedo has been calculated for three different disc functions, i.e. the Lambert disc function

$$D(i) = \cos i,$$

the Lommel-Seeliger disc function

$$D(i, e) = \frac{2 \cos i}{\cos i + \cos e}$$

and the Akimov disc function (Shkuratov et al. 1999)

$$D(\beta, \gamma, \varphi) = \cos \frac{\varphi}{2} \cos \left[ \frac{\pi}{\pi - \varphi} \left( \gamma - \frac{\varphi}{2} \right) \right] \frac{\varphi / \pi - \varphi}{\cos \gamma}$$

where $\gamma = \arctan \frac{\cos i - \cos e \cos \varphi}{\cos e \sin \varphi}$ is the photometric longitude and $\beta = \arccos \frac{\cos e}{\cos \gamma}$ is the photometric latitude.

For each of these functions, the equigonal albedo $R/D$ has been calculated over the whole data set. In order to verify if the disc function properly removes the topography influence, incidence and emission angles were divided in bins of 1°, and the median equigonal albedo value for each bin has been calculated. A disc function is considered good as long as the equigonal albedo is independent of incidence and emission angles.

### 4.1.2 Phase function

Once retrieved the equigonal albedo at the seven wavelength considered in this study, phase bins were defined (1° width) and the median equigonal albedo value for each bin was calculated.
The phase function has been defined as the second-order polynomial fitting these values, i.e.

$$R/D = a + b\varphi + c\varphi^2, \qquad (2)$$

where a is related to geometric albedo (since it is the equigonal albedo at 0° phase) but is not the geometric albedo, because our data set does not include phase angles lower than 12.5° and hence we cannot model the opposition effect.

These polynomial fits have been applied to: (a) the entire data set, (b) each comet macro-region and (c) each LST interval.

The albedo at 0° phase (not coinciding with the geometric albedo calculated by Ciarniello et al. 2015) has been calculated as:

$$A_N = R/D - b\varphi - c\varphi^2,$$

and mapped on the 67P/Churyumov-Gerasimenko shape model.

### 4.1.3 Photometric parameters

The comparison of disc-resolved phase functions of 67P/Churyumov-Gerasimenko and of other minor bodies has been performed by defining two parameters describing and characterizing these functions (henceforth 'photometric parameters').

According to Longobardo et al. (2016), the two most suitable parameters to describe disc-resolved photometric functions are the reflectance (I/F) at 0.75 µm retrieved at 30° phase (R30) and the steepness of the phase function between 20° and 60° phase angles, henceforth Phase Curve Slope (PCS), defined as 1-R60/R20, where R60 and R20 are the reflectances (I/F) at 60° and 20° phase angles, respectively.

Photometric parameters of asteroids visited by space missions have been calculated by Longobardo et al. (2016). Concerning disc-resolved functions of comets, we extracted R30 and PCS from the phase functions obtained in the following works:

* Li et al. (2007a) for 19P/Borrelly (Deep Space 1 mission), obtained at 0.66 µm

* Li et al. (2007b) for 9P/Tempel 1 (Deep Impact), obtained at 0.67 µm

* Li et al. (2009) for 81P/Wild 2 (Stardust), obtained at 0.70 µm

* Li et al. (2013a) for 103P/Hartley 2 (EPOXI), obtained at 0.62 µm.

These phase functions were calculated in a narrow wavelength range (i.e. between 0.62 and 0.75 µm), hence we can assume that photometric parameters do not vary in this spectral range.

Li et al. (2013b) also studied the photometric behaviour of 9P/Tempel 1 using Stardust-NExT data (at 0.70 µm), obtaining results similar to Li et al. (2007b). Because we verified that the variation of photometric parameters between the two phase functions of 9P/Tempel 1 is too small to affect our interpretation, in the following we consider only the results obtained by Li et al. (2007b).

The available phase functions of comets model the behaviour of I/F and not of R/D, as a function of the phase angle. Therefore, in order to have a reliable comparison, we re-calculated the phase functions of 67P/Churyumov-Gerasimenko by applying the procedure described in sub-section 4.1.2 on the radiance factors, instead of equigonal albedo. In this case, each phase angle interval contains also information on incidence and emission angles. In order to make the comparison between comet independent of i and e, the following procedure was adopted:

a. R20, R30 and R60 were calculated on the phase function I/F vs φ phase functions modelled for comet 67P/Churyumov-

Gerasimenko. Uncertainty on these values was estimated as the difference between modelled and calculated values; these uncertainties were propagated to obtain the error on PCS.

b. For phase bins corresponding at 20°, 30° and 60°, the average values of incidence and emission were calculated: they are $i_{20} = 60°$ and $e_{20} = 44°$ at 20° phase, $i_{30} = 51°$ and $e_{30} = 43°$ at 30° phase and $i_{60} = 57°$ and $e_{60} = 41°$ at 60° phase. These three couples of values ($i_\varphi, e_\varphi$) at different phase angles φ are not identical, but are very similar (i.e. difference not larger than 9° for i and 3° for e). Since reflectance is mainly affected by phase angle rather than incidence and emission (e.g. Longobardo et al. 2016), we could consider negligible the influence of variation of $i_\varphi$ and $e_\varphi$.

c. R20, R30, R60 and hence PCS were calculated on the phase functions of other comets, using the photometric models and parameters reported in literature. In the retrieval of reflectance at a given phase angle φ, we imposed $i = i_\varphi$ and $e = e_\varphi$, i.e. the three couples of values obtained at step b.

In addition, in order to study a possible spectral variation of photometric properties of 67P/Churyumov-Gerasimenko, photometric parameters were calculated not only at 0.75 µm, but at all of the seven wavelengths considered in this study.

### 4.2 3.2-µm band depth

According to our assumptions, the disc function is a factor multiplying the reflectance (Eq. (1)) and independent of wavelength, therefore it does not affect the band depth, which is essentially a reflectance ratio.

In order to study the photometric behaviour of band depth, we skipped step 1 described at the beginning of section 4.1 and applied step 2 in order to study this band depth as a function of the phase angle.

The validity of our assumptions was verified a posteriori by studying the band depth as a function of incidence of emission, too, in order to take into account possible changes of the disc function at wavelengths inside absorption bands, which could introduce residual trends with i and e (e.g. Longobardo et al. 2014).

To study all these behaviours, the median band depth value was calculated in incidence, emission and phase bins properly defined (all having 1° width). The procedure was applied to the entire data set, to each comet macro-region and TLST interval.

### 4.3 3.2-um band centre

The band centre characterizes composition of absorbing species, hence in principle it should be independent of observation geometry. However, in some cases a slight band centre shift with increasing incidence angle can be observed (e.g. Longobardo et al. 2014), because incidence angle is related to temperature, and a temperature change might affect the frequency of vibration producing the absorption. Moreover, in the case of 67P/Churyumov-Gerasimenko, a temperature variation can also change the relative abundances of the two main carriers of this band, i.e. organics and water ice (De Sanctis et al. 2015a), which in principle may result in a band centre shift.

Therefore we studied the band centre behaviour as a function of the incidence angle and temperature, by calculating their mean value in properly defined incidence/temperature bins (1° and 1 K width, respectively). Temperatures have been calculated by means of a Bayesian approach, Surface temperature maps were obtained by VIRTIS and results are given by Tosi et al. (in preparation).
<figure><img src="image_3.png" /><figcaption>**Figure 1.** *I/F* (original data, labelled as Orig) and *R/D* (Lambert, Lommel-Seeliger and Akimov-corrected values, labelled as Lam, LS and Aki, respectively) at 1.2 µm as a function of incidence and emission angles. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Albedo at 0° phase at 1.2 µm obtained from equigonal albedo calculated by means of Lambert (Lam), Lommel-Seeliger (LS) and Akimov (Aki), respectively. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.</figcaption></figure>

This study has been performed on the entire data set, because by substantially reducing the number of observations the coverage in temperature narrows accordingly, to such an extent that it prevents the characterization of any trend. However, we studied in detail some specific regions that offer a temperature range broad enough to confirm the general trend observed for the entire data set.

## 4.4 Infrared and visible slopes

After we demonstrated that our disc function effectively removes the effect of incidence and emission angles at all of the seven wavelengths considered in this study (sub-section 5.1.1), infrared and visible slopes do not depend on these two angles.

Hence we limit ourselves to studying their behaviour as a function of the phase angle, by adopting the same procedure for band depth (sub-section 4.2), for the entire data set, for the four macro-regions and for the four LST intervals considered. The obtained results were compared with those obtained by Ciarniello et al. (2015) by adopting the Hapke method.

# 5 RESULTS

## 5.1 Reflectance

### 5.1.1 Disc function

Here we show the results obtained at 1.2 µm, but the same applies to all the wavelengths considered in this study.

The equigonal albedo, calculated for the three different disc functions, as a function of incidence and emission angles is shown in Fig. 1, compared with the average trend of *I/F* (not topography-corrected).

We can see that none of the disc functions completely removes the *I/F* trends (black line – original data) with incidence and emission angle. The residual trends at large *i* and *e* correspond to large phase angle values.

Therefore, we calculated the phase function (sub-section 4.1.2) for all the three cases and used these phase functions to retrieve albedo at 0° phase. Finally, the trend of albedo at 0° phase with incidence and emission angles was studied, selecting the disc function that gives an albedo independent of both incidence and emission angles. Fig. 2 shows that this occurs for the Akimov disc function,
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Phase functions obtained at 0.75 µm for the 67P/Churyumov-Gerasimenko average (A) and for the four macro-regions (body B, bottom T, head H, neck N) of the nucleus. Phase angle is expressed in degrees. The phase functions corresponding to average and to the head are overimposed. The behaviour at all the other wavelengths is identical. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.</figcaption></figure>

since in the Lommel-Seeliger case a residual trend with incidence and emission angles is still present, whereas the Lambert disc function overcorrects the reflectance, introducing increasing trends with *i* and *e*.

Therefore in the following we will show only results obtained by applying the Akimov disc function.

However, even in the Akimov case, the albedo independence of incidence is observed only up to 70°. Therefore, in the subsequent analysis we excluded all the spectra taken at *i* > 70°. In order to be conservative, observations taken at emission angles larger than 70° were also excluded.

### 5.1.2 Phase functions, albedo map and photometric parameters

Parameters of polynomial fits obtained for all the wavelengths, macro-regions and LST intervals are included in the Supplementary Material. The fit is always good, with a coefficient of determination (i.e. the squared correlation coefficient) $R^2$ comprised between 0.97 and 0.99.

For each wavelength, the *a*, *b* and *c* parameters of relation (2) do not display strong variations across the comet's macro-regions (Fig. 3) and LST intervals (Fig. 4): fit parameters are always equal within two times the error, except the *c* parameter at infrared wavelengths that varies within three times the error. However, the different phase functions calculated for each wavelength led to corrected reflectance values (at 0° or 30° phase angle) that are equal within errors, therefore in the following we assume the unique phase function, corresponding to the average of 67P/Churyumov-Gerasimenko, at each wavelength, independent of location and TLST.

The reflectance map obtained before and after the photometric correction is shown in Fig. 5. We can observe that extreme values corresponding to unfavourable illumination conditions are removed in the photometrically corrected maps; moreover, the reflectance distribution is in good agreement with Ciarniello et al. (2015), which applied a different method for photometric correction.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Phase functions obtained at 0.75 µm for four different LST intervals: 0–6 (night), 6–12 (morning), 12–18 (afternoon) and 18–24 (evening). From top to bottom, the four curves correspond to morning, afternoon, evening and night, respectively. Phase angle is expressed in degrees. The behaviour at all the other wavelengths is identical. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Distribution of the reflectance at 1.2 µm on the shape model of comet 67P/Churyumov-Gerasimenko before (top) and after (bottom) the photometric correction. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.</figcaption></figure>
<table><caption>**Table 1.** Photometric parameters of 67P/Churyumov–Gerasimenko at different wavelengths $\lambda$. The uncertainty in R30 is 0.001 up to 1.2 $\mu$m and 0.002 from 1.7 $\mu$m. The absolute error on PCS is 5%.</caption><thead><tr><th>λ (μm)</th><th>0.55</th><th>0.75</th><th>1.2</th><th>1.7</th><th>2.0</th><th>2.8</th><th>4.0</th></tr></thead><tbody><tr><th>R30</th><td>0.013</td><td>0.017</td><td>0.031</td><td>0.035</td><td>0.036</td><td>0.041</td><td>0.041</td></tr><tr><th>PCS</th><td>61%</td><td>60%</td><td>61%</td><td>60%</td><td>60%</td><td>57%</td><td>55%</td></tr></tbody></table>

<table><caption>**Table 2.** R30 and PCS for 67P/Churyumov–Gerasimenko and for other comets explored by space missions.</caption><thead><tr><th>Comet (λ)<br>(reference)</th><th>19P/Borrelly<br>(0.66) Li et al.<br>(2007)</th><th>103P/Hartley2<br>(0.62) Li et al.<br>(2013a)</th><th>9P/Tempel1<br>(0.67) Li et al.<br>(2007)</th><th>81P/Wild2<br>(0.7) Li et al.<br>(2009)</th><th>67P/CG (0.75)<br>This work</th></tr></thead><tbody><tr><th>R30</th><td>0.018</td><td>0.013</td><td>0.015</td><td>0.014</td><td>0.017</td></tr><tr><th>PCS</th><td>65%</td><td>67%</td><td>71%</td><td>78%</td><td>60%</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** PCS as a function of R30 for 67P/Churyumov–Gerasimenko (gray square), other comets (black squares), C-type asteroids Mathilde (diamond), S-type asteroids Gaspra, Eros and Annefrank (crosses), V-type Vesta (three asterisks, corresponding to bright, intermediate and dark terrains, respectively, where carbonaceous chondrites content increases from bright to dark terrains), E-type Steins (white square), X-type Lutetia (triangle). Details about location of asteroids in this scatter plot are given by Longobardo et al. (2016). The curve (blue, in the web version of the paper) indicates the general trend of asteroids in this scatter plot.</figcaption></figure>

Finally, we extracted the photometric parameters at all the wavelengths considered in this study to monitor spectral variations of the photometric behaviour (Table 1). PCS is constant up to 2 $\mu$m (60–61 per cent), and then it decreases down to 55 per cent, even though this decrease is contained within errors. However, the uncertainty on PCS could be overestimated, because it is essentially given by the relative error on R60 (much larger than the relative error on R20), which is in turn a ratio of low values (R60 is the reflectance of a dark body observed at a large phase angle; see Figs 1 and 2). For this reason, we will discuss the PCS trends even when it is contained within errors.

### 5.1.3 Comparison with other minor bodies

Photometric parameters of comets are shown in Table 2, whereas the scatterplot of PCS as a function of R30, including also asteroids explored by space missions, is shown in Fig. 6.

In the PCS-R30 scatterplot, asteroids identify a well-defined trend, with PCS decreasing with increasing R30, mostly due to the role of multiple scattering, which has the double effect of increasing reflectance and flatten phase functions. The location of intermediate and dark terrains of Vesta could be justified by their composition, made of a mixture of Vesta bright material and carbonaceous

chondrites, i.e. the components of C-type asteroids, whereas Lutetia is an anomaly, probably related to its different taxonomy (Longobardo et al. 2016). Asteroid 243 Ida is not considered in our analysis because it was observed at a very different space resolution and this may influence PCS (Longobardo et al. 2016).

Comet 81P/Wild2 is photometrically very similar to asteroid 253 Mathilde. On the contrary, the other comets, although showing a R30 very similar to Mathilde and Wild2, show much flatter phase functions, with 67P/Churyumov–Gerasimenko having the lowest PCS.

## 5.2 3.2-$\mu$m band depth

All of the fits performed on band depth as a function of incidence angle and phase angle provide a coefficient of determination $R^2$ lower than 0.2, indicating that there is no substantial correlation. In two cases, $R^2$ values larger than 0.80 in band depth as a function of emission angle (found for the body and for the 12–18 TLST interval). However, this trend indicates a band depth increase of 0.01 from 20° to 70° emission. We do not consider this increase physically reliable, since we estimated that spectral artefacts may produce relative minima with a ‘depth’ up to 0.04 (Section 2). Therefore, we will not discuss this behaviour in the following sections.

## 5.3 3.2-$\mu$m band centre

A clear trend of the wavelength of the band centre as a function of incidence angle is observed (Fig. 7). However, this corresponds to a very slight shift, between 1 and 2 times the VIRTIS spectral sampling.

We applied a more detailed analysis to interpret this very small variation as caused by temperature. The relation between band centre and temperature was therefore studied even for specific regions of interest, providing sufficiently broad temperature range. This allows one to rule out even little differences in composition among different regions. In most of these regions, a shift in the band centre towards shorter wavelengths is indeed observed (Fig. 8).

## 5.4 Slopes

Both visible and infrared slopes show a linear trend as a function of phase angle, i.e. $S = a + b\varphi$, being S the slope and $\varphi$ the phase angle. The a and b parameters are obtained by least squares method and represent the average slope and the phase redening, respectively. Their values, calculated for the average of
<figure><img src="image_9.png" /><figcaption>**Figure 7.** 3.2-μm band centre as a function of incidence angle (calculated on the entire pre-landing data set).</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** 3.2-μm band centre as a function of temperature for the Babi region (latitude 0–45°N, longitude 70–90°E). Each point is the median in the correspondent temperature bin of width 2.5°K. Only temperature bins with at least 300 observations were considered.</figcaption></figure>

<table><caption>**Table 3.** Parameters of the relation $S_{\text{VIS}} = a + b\varphi$ of the visible slope as a function of phase angle and the corresponding $R^2$ value. Values obtained by Ciarniello et al. (2015) are also given for comparison.</caption><thead><tr><th>Region/LT</th><th>a (·10<sup>-1</sup>)</th><th>b (·10<sup>-4</sup>)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>Ciarniello et al. (2015)</td><td>1.6</td><td>7</td><td>—</td></tr><tr><td>Average</td><td>1.55 ± 0.04</td><td>5.4 ± 0.6</td><td>0.66</td></tr><tr><td>Body</td><td>1.58 ± 0.03</td><td>4.9 ± 0.5</td><td>0.73</td></tr><tr><td>Bottom</td><td>1.69 ± 0.04</td><td>5.8 ± 0.8</td><td>0.74</td></tr><tr><td>Head</td><td>1.50 ± 0.05</td><td>6.8 ± 1.0</td><td>0.61</td></tr><tr><td>Neck</td><td>1.34 ± 0.04</td><td>7.1 ± 0.6</td><td>0.79</td></tr><tr><td>0–6</td><td>1.39 ± 0.03</td><td>7.4 ± 0.6</td><td>0.87</td></tr><tr><td>6–12</td><td>1.57 ± 0.05</td><td>5.0 ± 1.0</td><td>0.45</td></tr><tr><td>12–18</td><td>1.56 ± 0.03</td><td>5.1 ± 0.6</td><td>0.65</td></tr><tr><td>18–24</td><td>1.455 ± 0.018</td><td>6.1 ± 0.3</td><td>0.93</td></tr></tbody></table>

67P/Churyumov-Gerasimenko, the four macro-regions and the four LST slots, are shown in Tables 3 and 4, respectively, compared with those obtained by Ciarniello et al. (2015) by means of the Hapke method.

The linear fits describing the infrared slope (Table 4) are very good ($R^2$ values being generally larger than 0.90). The average slope $a$ and the phase reddening $b$ are spatially and temporally constant

<table><caption>**Table 4.** Parameters of the relation $S_{\text{IR}} = a + b\varphi$ of the infrared slope as a function of phase angle and the corresponding $R^2$ value. Values obtained by Ciarniello et al. (2015) are also given for comparison.</caption><thead><tr><th>Region/LT</th><th>a (·10<sup>-1</sup>)</th><th>b (·10<sup>-4</sup>)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>Ciarniello et al. (2015)</td><td>0.23</td><td>1.8</td><td>—</td></tr><tr><td>Average</td><td>0.199 ± 0.003</td><td>1.48 ± 0.05</td><td>0.96</td></tr><tr><td>Body</td><td>0.196 ± 0.002</td><td>1.56 ± 0.04</td><td>0.98</td></tr><tr><td>Bottom</td><td>0.210 ± 0.005</td><td>1.25 ± 0.11</td><td>0.87</td></tr><tr><td>Head</td><td>0.202 ± 0.004</td><td>1.42 ± 0.08</td><td>0.91</td></tr><tr><td>Neck</td><td>0.188 ± 0.003</td><td>1.61 ± 0.05</td><td>0.96</td></tr><tr><td>0–6</td><td>0.187 ± 0.003</td><td>1.68 ± 0.05</td><td>0.98</td></tr><tr><td>6–12</td><td>0.200 ± 0.004</td><td>1.45 ± 0.07</td><td>0.92</td></tr><tr><td>12–18</td><td>0.201 ± 0.004</td><td>1.40 ± 0.08</td><td>0.91</td></tr><tr><td>18–24</td><td>0.194 ± 0.003</td><td>1.57 ± 0.06</td><td>0.96</td></tr></tbody></table>

within the errors. The only exceptions are the slope at the neck and the average slope in the ‘nighttime’ (i.e. 0–6 and 18–14 LST intervals), where $a$ is lower and $b$ is larger. The slight difference with values obtained by Ciarniello et al. (2015) is due to the different definition of the slope (which in their case starts at 1.0 μm instead of 1.1 μm).

In the case of the visible slope (Table 3), errors are larger and $R^2$ is lower (only in one case is larger than 0.90). This is probably due to the narrow interval where the slope is defined (0.55–0.75 μm). However, the general behaviour is the same as the infrared slope, i.e. average slope and phase reddening spatially and temporally constant (within errors), with $a$ smaller and $b$ larger in the neck regions and in the LST intervals corresponding to nighttime. Even in this case, the slight disagreement with the $a$ and $b$ parameters obtained by Ciarniello et al. (2015) is ascribed to the different slope definition (0.55–0.80 μm instead of 0.55–0.75 μm).

# 6 DISCUSSION

## 6.1 Reflectance and photometric parameters

The phase functions obtained at each wavelength for different macro-regions and local times coincide within estimated errors. This finding suggests with a reflectance homogeneity across the comet surface, in both spatial and temporal terms.

In order to interpret the slight PCS decrease at increasing wavelength, we studied the role of single scattering at different wavelengths. In particular, we put in relation the average reflectance of 67P/Churyumov-Gerasimenko spectrum with the single scattering albedo (by Ciarniello et al. 2015) at all the wavelengths considered in this work, except 4.0 μm, for which the single scattering albedo is not available. The relation is shown in Fig. 9.

I/F and $w$ are linearly related. At 2.8 μm, the I/F deviation from the linear fit exceeds 0.09, which is the error on the I/F values extrapolated from the linear fit. This indicates that the role of single scattering is larger at shorter wavelengths than at longer ones, even if single scattering is the dominant mechanism in the entire spectral range (as observed for minor bodies even much brighter than 67P/Churyumov-Gerasimenko; e.g. Li et al. 2013c).

The reasons for the observed behaviours could be two. On one side, it could be due to an increasing role of multiple scattering at longer wavelengths, which would justify both the observed phase reddening (Hapke et al. 2012) and the PCS decrease at 2.8 μm. On the other side, it could be due to a change of the particle phase function (Schroder et al. 2014): in fact, an increased transparency of particles at longer wavelengths would decrease the single scattering albedo, cause the phase reddening (Schroder et al. 2014) and flatten
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Top. *I/F* of the average 67P/Churyumov–Gerasimenko spectrum as a function of single scattering albedo *w* for different wavelengths (expressed in microns for each plotted point). The error on the average *I/F* is calculated as standard deviation of the mean and is contained within the point size. The straight line models the *I/F* vs *w* behaviour. Bottom. Deviation of *I/F* from linear fit in Fig. 9a. The deviation at 2.8 µm exceeds the error on the linear fit, which is 0.09.</figcaption></figure>

the phase function. In both cases, we could expect that the deviation
from the linear trend in Fig. 9 is even larger at 4.0 µm.

**6.2 Comparative analysis of photometric parameters**

According to the *PCS* behaviour as a function of *R30* observed for asteroids (Fig. 6), we should expect that comets would be photo-metrically similar to C-type asteroids, due to their low albedo. On the contrary, Wild2 is the only comet having *PCS* comparable with Mathilde. Tempel1 also shows *PCS* larger than 70 per cent. *PCS* still decreases for Hartley2 and Borrelly and for 67P/Churyumov-Gerasimenko is similar to S-type asteroids.

The *PCS* difference among comets cannot be associated to their *R30*, which is very similar, and however a relation between *R30* and *PCS* is not observed, contrarily to asteroids.

Therefore, a difference in physical properties could explain the
different photometric behaviour of comets. In rough terrains, radi-
ation is more absorbed at large incidence, and hence phase, angle
with respect to smooth terrains, and this can result in a steeper
phase function (Hapke 1981). We investigate here the relation be-
tween comets' roughness and *PCS*. Here and in the following, we
mean for 'roughness' the roughness at VIRTIS spatial resolution,
i.e. from meters to tens of meters scale. We will refer to studies on
the other comets based on images taken at similar spatial resolution.

Basilevski and Keller (2006), based on their analysis of comets'
images, concluded that the role of smooth terrains increased in
the sequence Wild2 → Tempel1 → Borrelly, and this is related
to an increasing importance of sublimation-induced degradation
of the surface due to repeated passages close to the Sun. This
sequence reflects the *PCS* trend, decreasing from the roughest
(Wild2) to the smoothest (Borrelly) surface. The recent study by
Ip et al. (2016), taking in consideration even the Rosetta/OSIRIS
camera images, inferred that Wild2 and Tempel1 are less eroded
than 67P/Churyumov-Gerasimenko, Hartley2 and Borrelly. Again,
this is reflected on *PCS* values, larger for the two less eroded (i.e.
rougher) comets and lower for the three smoother ones.

This seems to suggest a link between surface roughness and
photometric properties. In order to support this conclusion, we cal-
culated phase functions of different regions of 67P/Churyumov-
Gerasimenko, characterized by a different level of roughness. In
particular, we considered two 'rough' regions, i.e. Anuket and

Ash, morphologically classified as Strongly Consolidated and Non
Consolidated Dust, respectively (El-Maarary et al. 2015; Thomas
et al. 2015), and two 'smooth' regions, i.e. Hapi and Imhotep,
both classified as Non Consolidated Smooth (El-Maarary et al.
2015; Thomas et al. 2015). Again, we found that phase func-
tions of Anuket and Ash are characterized by a *PCS* larger
than the 67P/Churyumov-Gerasimenko average (60 per cent), i.e.
67 per cent and 64 per cent, respectively, whereas *PCS* of Hapi
and Imhotep (two regions more eroded by cometary activity; Filac-
chione et al. 2016) is lower than the 67P/Churyumov-Gerasimenko
average, being 58 per cent and 55 per cent, respectively. The relation
between surface roughness and photometry on 67P/Churyumov-
Gerasimenko is moreover supported by photometric analyses on
OSIRIS camera data (Hasselmann et al. 2017).

This suggests that photometry of comets is affected by surface
roughness, in turn related to erosion induced by cometary activity. In
other words, a low eroded comet would be photometrically similar
to C-type asteroids, and its phase function steepness would decrease
in time as a consequence of cometary activity.

However, we could not discard other explanations for the ob-
served behaviour. Variation of a single scattering phase function
among comets could result in the observed trend of PCS. Re-
golith/dust grain size can affect the phase function shape (Hapke
1981), too, but lack of this information for some comets does not
allow evaluating their role in photometric behaviour.

6.3 3.2-µm band depth

On 67P/Churyumov–Gerasimenko, band depth is completely in-
dependent of observation geometry, contrarily to absorption bands
due to end members identified, e.g. on Vesta (Longobardo et al.
2014) and Ceres (Longobardo et al., in preparation), which instead
increase at the increasing phase angle. Two reasons can be at the ba-
sis of this behaviour: (a) the high abundance of fine-grained opaque
component(s) suppresses not only the band itself, but also its depen-
dence on the viewing geometry, and (b) different phase reddening,
driving the band depth behaviour with phase.

Since phase reddening depends also on optical properties of sur-
face components and their respective abundances, if hypothesis (b)
is valid, laboratory acquisition of spectra at different phase angles of
the candidate 3.2 µm band carriers and of mixtures between these
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Infrared slope as a function of temperature for the Babi region (latitude 0–45°N, longitude 70–90°E). Each point is the median in the correspondent temperature bin of width 2.5°K. Only temperature bins with at least 300 observations have been considered.</figcaption></figure>

candidates and opaques may help characterize the organics on the comet surface.

## 6.4 3.2-µm band centre

The shift of band centre towards shorter wavelength with increasing temperature may be due to: (a) spectral artefacts, due to residuals or overcorrection of the removal of thermal contribute; (b) temperature-induced shifts of the positions of fundamental vibrational absorption bands in the spectra of refractory species contributing to the complex 3.2-µm feature; and (c) exposure of water ice due to a weak cometary activity even during pre-perihelion and/or sublimation of other possible volatile and/or semi-volatile contributing to the 3.2-µm band.

The 4.0-µm reflectance, which is strongly affected by the removal of the thermal emission, is temperature-independent, hence we can safely discard hypothesis (a).

Although electronic absorption bands in many rock-forming minerals are known to show significant temperature-induced wavelength shifts (e.g. Moroz et al. 2000; Hinrichs and Lucey, 2002), vibrational absorption bands that can contribute to the 3.2-µm feature are likely to become narrower with decreasing temperature (e.g. Schroeder et al. 1962; Gaffey et al. 1993) without significant shifts in the positions of band centres. For example, analysis of 0.5–5-µm reflectance spectra of a kerite fine powder acquired at 80, 173 and 293 K (Moroz et al. 2004) demonstrates that the detected shifts of the band centre positions of fundamental C-H absorption bands (3.2–3.6 µm) and near-IR overtone and combination bands (2.2–2.5 µm) do not exceed 1–1.5 nm (0.001–0.0015 µm) per 100 K. Such temperature-induced effects are negligible compared to those shown in Fig. 8 and suggest that the observed wavelength shifts are not attributable to temperature-induced spectral modification of refractory organic materials contributing to the complex 3.2-µm feature. However, we cannot exclude the temperature-induced effects associated with volatile and semi-volatile components possibly contributing to the band.

In order to support hypothesis (c), we studied the behaviour with temperature of other spectral descriptors, related to water ice abundance, in the regions where the band centre shifts with increasing temperature. Infrared slope also shows a decrease with tempera-

ture (in Fig. 10, the case of Babi), which would also argue for an exposure of water ice.

Comparison between the infrared slope and band centre trends with radiative transfer models (Raponi et al. 2016; Ciarniello et al. 2016) indicates that the observed decrease of both parameters corresponds to very small variation of water ice abundance, i.e. less than 0.1 per cent.

The exposure of water ice would be therefore a possible explanation of band depth shift, even if this is not a definitive conclusion, due to the very low amount of ice that would be needed to match the observations.

## 6.5 Slopes and phase reddening

The exceptions to spatial and temporal constancy of infrared and visible slopes, i.e. their lower values in the neck macro-region and during nighttime, are compatible with a larger amount of water ice. This result is in agreement with previous work, since the neck is the region with the highest abundance of water ice (e.g. Capaccioni et al. 2015; Filacchione et al. 2016), and water ice is trapped at the surface during the night due to the diurnal cycle of water (De Sanctis et al. 2015b).

In these cases, also a larger phase reddening is observed. Also this effect is ascribable to water ice, which increases reflectance, decreases spectral slope and flattens phase curve (due to the increasing multiple scattering). This means that the influence of water ice is larger on $R_{\lambda1}$ than on $R_{\lambda2}$ (remembering that $\lambda1 < \lambda2$) and results in a larger phase dependence of the $R_{\lambda2}/R_{\lambda1}$ ratio (which is essentially the spectral slope).

## 7 CONCLUSIONS

The average photometric behaviour of main spectral descriptors of 67P/Churyumov–Gerasimenko spectra, i.e. reflectance at seven distinct wavelengths, 3.2 µm band depth and band centre, visible and infrared slope, was studied. This behaviour was studied across the nucleus also as a function of TLST.

Before 67P/Churyumov–Gerasimenko pre-perihelion, optical properties are spatially and temporally constant across the comet surface, even if phase function is steeper on rougher terrains of the comet. Roughness could be the main reason for different phase function steepness of comets previously explored by space missions, with rougher comets (Wild2 and Tempel1) being photometrically similar to C-type asteroids and showing steeper phase functions than smoother ones (Hartley2, Borrelly and 67P/Churyumov–Gerasimenko). This suggests that photometric behaviour could be an indicator of surface erosion, due to cometary activity.

The band depth of organics is independent of observation geometry, and in particular of the phase angle, and this might help constraining the surface composition. The slight band centre shift observed with increasing temperature may be caused by exposure of small amounts of water ice (>0.1 per cent), due to a weak cometary activity at heliocentric distances >3 AU.

Finally, visible and infrared slope and phase reddening are mainly driven by water ice abundance, with larger water ice contents producing a slope decrease and a phase reddening increase.

## ACKNOWLEDGEMENTS

The authors would like to thank ASI – Italy, CNES – France, DLR – Germany and NASA-USA for supporting this research. VIRTIS
was built by a consortium formed by Italy, France and Germany, under the scientific responsibility of the Istituto di Astrofisica e Planetologia Spaziali of INAF, Italy, which guides also the scientific operations. The consortium includes also the Laboratoire d'études spatiales et d'instrumentation en astrophysique of the Observatoire de Paris, France, and the Institut für Planetenforschung of DLR, Germany. The authors thank the Rosetta Science Ground Segment and the Rosetta Mission Operations Centre for their continuous support. LVM acknowledges the DFG grant MO 3007/1-1.

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## SUPPORTING INFORMATION

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**ANNEX:** Phase functions of 67P/Churyumov–Gerasimenko at different wavelengths.

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