Properties of the dust in the coma of
67P/Churyumov-Gerasimenko observed with VIRTIS-
M

G. Rinaldi, U. Fink, L. Doose, G.P. Tozzi, F. Capaccioni, G. Filacchione, D.

Bockelée-Morvan, C. Leyrat, G. Piccioni, S. Erard, et al.

<figure><img src="image_1.png" /></figure>

To cite this version:

G. Rinaldi, U. Fink, L. Doose, G.P. Tozzi, F. Capaccioni, et al. Properties of the dust in the coma of 67P/Churyumov-Gerasimenko observed with VIRTIS- M. Monthly Notices of the Royal Astronomical Society, 2016, pp.stw3197. 10.1093/mnras/stw3197. hal-02399960

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https://hal.science/hal-02399960

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# Properties of the dust in the coma of 67P/Churyumov–Gerasimenko observed with VIRTIS- M

G. Rinaldi,<fnref n="1" />* U. Fink,<fnref n="2" />* L. Doose,<fnref n="2" /> G. P. Tozzi,<fnref n="3" /> F. Capaccioni,<fnref n="1" />* G. Filacchione,<fnref n="1" /> D. Bockelée-Morvan,<fnref n="4" /> C. Leyrat,<fnref n="4" /> G. Piccioni,<fnref n="1" /> S. Erard,<fnref n="4" /> A. Bieler,<fnref n="5" /> M. Błecka,<fnref n="6" /> M. Ciarniello,<fnref n="1" /> M. Combi,<fnref n="5" /> N. Fougere,<fnref n="5" /> A. Migliorini,<fnref n="1" /> E. Palomba,<fnref n="1" /> A. Raponi<fnref n="1" /> and F. Taylor<fnref n="7" />

Accepted 2016 December 6. Received 2016 December 5; in original form 2016 July 8

## ABSTRACT

An investigation is presented of the dust scattering in the coma of 67P/Churyumov–Gerasimenko for the dates of 2015 February 28, March 15 and April 27. A comparison of the morphology of dust continuum maps at 1.1 µm and gas emission shows that for the above dates the spatial distribution of the dust is strongly correlated with H₂O but not with CO₂ emission. For April 27, the radial profile on the illuminated side of the nucleus in the inner coma agrees well with the direct simulation Monte Carlo (DSMC) calculations as the dust is accelerating and flows outwards but follows a 1/ρ distribution at distances larger than 4 km from the nucleus. The azimuthal distribution of the dust is narrower than the broader emission of the gas. Afp values are 1.13 m for 2015 February 28, 2.02 m for April 27, while local values for March 15 are 2.3–5.3 m, depending on the nucleus illumination. In the inner coma, the spectral reflectivity from 0.35 to 3.5 µm displays a red slope with a change at around 1 µm. From 0.35 to 0.8 µm, the values range from 9 to 12 ± 1 per cent per 100 nm both on the sunlit side and on the dark side. From 1 to 2.5 µm, the values are 1.7 ± 0.2 per cent per 100 nm on the sunlit side and 3 ± 1 per cent per 100 nm on the dark side. For the August 26 jet, no significant increase of the colour gradient with distance from the nucleus could be observed, nor any significant difference detected between the jet and the background coma.

**Key words:** methods: data analysis – methods: observational – techniques: imaging spectroscopy – comets: individual: 67P/Churyumov–Gerasimenko.

## 1 INTRODUCTION

The aim of this work is to study the properties of the dust and its correlation with gas in the inner coma of comet 67P/Churyumov–Gerasimenko (in the following, referred to as 67P/CG). Jupiter Family Comets have spent more than 4 billion years far from the Sun at temperatures not exceeding those of their formation, and they are thus considered to be the least processed bodies in the Solar system. Their study provides insights into the processes at work during the early phases of the formation of the Solar system and its

subsequent evolution. The Rosetta mission gave us the opportunity to analyse the properties of the dust in the immediate vicinity of the nucleus and compare it with the evolution of the gas.

During the last 30 yr, several cometary fly-by missions have provided useful input to understand the processes in the inner part of the coma of comets. Vega (Sagdeev et al. 1986) and Giotto (Reinhard 1986) observed comet 1P/Halley. Deep Space 1 performed a fly-by of 19P/Borrelly (Soderblom et al. 2002). The Deep Impact mission visited comet 9P/Tempel 1 in 2004 July (A’Hearn et al. 2005; Feaga et al. 2007), and then (renamed EPOXI) performed a fly-by of 103P/Hartley 2 (A’Hearn et al. 2011). In addition, the Star-dust mission (Brownlee et al. 2006) collected samples from comet 81P/Wild 2 and flew by Temple 1 in 2011 (Veverka et al. 2013). Despite these investigations, the physical characterization of

<footnote n="1">¹Istituto di Astrofisica e Planetologia Spaziali, Istituto Nazionale di Astrofisica, 00133, Rome, Italy</footnote>

<footnote n="2">²Lunar Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA</footnote>

<footnote n="3">³INAF – Osservatorio Astrofisico di Arcetri, 50125, Firenze, Italy</footnote>

<footnote n="4">⁴LESIA, Observatoire de Paris, LESIA/CNRS, UPMC, Université Paris-Diderot, F-92195 Meudon, France</footnote>

<footnote n="5">⁵Department of Climate and Space Sciences Engineering, University of Michigan, Ann Arbor, MI 48109, USA</footnote>

<footnote n="6">⁶Centrum Badan Kosmicznych, PAN, 00-716 Warsaw, Poland</footnote>

<footnote n="7">⁷Department of Physics, Oxford University, Oxford OX1 4BH, UK</footnote>

<footnote>* E-mail: giovanna.rinaldi@iaps.inaf.it (GR); uwefink@lpl.arizona.edu (UF); fabrizio.capaccioni@iaps.inaf.it (FC)</footnote>
cometary nuclei and the inner regions of the gas and dust environment can benefit from more temporal and spatial resolved studies. This is partially due to the very brief duration of fly-by observations (less than one full rotation of the nucleus) and the limited spatial resolution of ground-based observations.

The European Space Agency thus initiated the Rosetta corner-stone mission to rendezvous and land on the Jupiter Family Comet 67P/CG, and perform a thorough investigation of its surface and inner coma environment. The spacecraft successfully met with, and entered into an orbit around the comet. The spacecraft then monitored the evolution of its activity and travelled with the comet while it approached the Sun towards perihelion and then accompanied the comet in its orbit back out towards aphelion.

Since 2014 August, the Visible and InfraRed Thermal Imaging Spectrometer (VIRTIS) (Coradini et al. 2007) on board the Rosetta spacecraft performed continuous observations of the inner coma of the Rosetta spacecraft target 67P/CG. VIRTIS is composed of a high spectral resolution channel (VIRTIS-H) and two channels devoted to spectral mapping (VIRTIS-M), covering the spectral range of 0.22–1.04 µm (VIS) and 0.95–5.06 µm (IR), both with 432 spectral bands. This work is concerned with the analysis of the data provided by both VIS and IR channels of the VIRTIS-M instrument. Several results on the coma gas properties of 67P/CG using the VIRTIS instrument have been published so far. Bockelée-Morvan et al. (2015) analysed H₂O and CO₂ emissions detected by the VIRTIS high-resolution channel. In their work, the CO₂-to-H₂O column density ratio varies from 2 to 30 per cent, depending on the region observed. Migliorini et al. (2016) reported that the H₂O emission is mainly concentrated above two active regions, while the CO₂ distribution appears more uniform with significant emission coming both from the head and from the south latitude regions. In a comprehensive paper, Fink et al. (2016) presented an investigation of the emission intensity of CO₂ and H₂O and their distribution in the coma of 67P/CG. They find that unlike water, which has a reasonably predictable behaviour and correlates well with the solar illumination, CO₂ arises almost exclusively from the weakly illuminated southern hemisphere. These results indicate that the observed differences might be indicative of a different thermal history of the northern and southern hemispheres of 67P/CG.

In this paper, we present an analysis of the pre-perihelion VIRTIS-M hyperspectral images for the dates of 2015 February 28, March 15 and April 27, when the comet was at heliocentric distances of 2.2 to 1.76 au from the Sun, and data for a jet on August 26, three weeks after the perihelion passage. In the first section, we describe the selection and processing of the data. Since the evolution of the gas is driving the dust, in the second section, we investigated the radial and azimuthal distributions of dust and gas (H₂O and CO₂) to study any correlation among them (refer to Fink et al. 2016 for the more detailed analysis of the gas properties). Dust and gas correlation results are discussed both in terms of spatial distribution and in terms of temporal evolution. In sections that follow, we give an analysis of dust properties in terms of radial profiles (Section 4), Afρ (Section 5) and colour (Section 6). Conclusions and perspectives are provided in Section 7.

# 2 OBSERVATIONS AND DATA REDUCTION

## 2.1 Instrument description

The VIRTIS is composed of two instruments, a medium-resolution imaging spectrometer (VIRTIS-M) and a high-resolution spectrometer (VIRTIS-H).

VIRTIS-M is a long-slit Offner type spectrometer able to acquire hyperspectral images with a maximum spatial resolution of 250 µrad. It has a visible (VIS) section from 0.25 to 1 µm and an infrared (IR) section from 1.0 to 5 µm each sampled by 432 spectral channels. Coupled to VIRTIS-M is a bore-sighted higher resolution pointing echelle spectrometer, VIRTIS-H, with a numerical resolution of about 2000 and a field of view (FOV) of 500 × 1500 µrad. For a complete description of the VIRTIS instrument, see Coradini et al. (2007).

## 2.2 Data reduction and analysis method

The data used in this work have been acquired by VIRTIS-M on 2015 February 28, March 15, April 27 and August 26. A list of the observations with all the relevant information is provided in Table 1. We list the observations in the VIS and IR channels of the instrument. The VIS and IR image cubes were taken at essentially the same time, with the VIS exposure sequences starting 9.01 s after those for the IR. The second and third columns give file names according to the rules of planetary data system (PDS). To make the description of our data easier, we have assigned simple letter and number designations to these file names in the first column. The fourth column lists the image size in number of samples per line, number of scan lines and spectral bands. The fifth and sixth columns show the starting and stopping times (UT), while the following column indicates the total time of the observations. In all the acquisitions, and in the images shown, the Sun illumination is always from the top of the figure.

Also listed in the table are additional self-explanatory parameters such as the sub-solar longitude and latitude, which serve as an indicator of the orientation of the comet. Additionally, we list the distance from the surface, the phase angle and the heliocentric distance ($r_h$). The geometry information for each VIRTIS-M observation is calculated by a SPICE routine (Acton 1996) using the spacecraft's trajectory/orientation reconstructed kernels and 67P/CG SHAP5 shape model (Jorda et al. 2016).

We choose the March 15 data set because it allowed us to investigate the coma above the illuminated nucleus during a complete rotation of the comet. For this data, the FOV of the VIRTIS-M instrument is pointed at a roughly fixed location about 1 km above the illuminated surface of the comet. The data set covers 11.8 h, almost a complete rotation period of 67P/CG. The slit extends horizontally for 256 pixels (~4.5 km) and is scanned vertically for 66 lines (~1.15 km) using the scanning mirror of the instrument (Coradini et al. 2007).

We analysed a set of two image cubes obtained on February 28 at a distance from the comet of 103 km and at a heliocentric distance of 2.21 au. The spacecraft was essentially looking down on the north pole of the comet. For April 27, a set of seven image cubes was obtained at a distance from the comet of 130–140 km, giving us an FOV of about 9.0 × 7.7 km with the comet centred roughly in the centre of the FOV. The spacecraft is approximately in a terminator orbit so that one side of the comet is illuminated by the Sun and the other side is in darkness. For August 26, we analysed one image obtained at a distance from the comet of 410 km at a cometary heliocentric distance of 1.2 au, post-perihelion. In view of large distance, the spatial resolution is about 100 m pixel⁻¹ and the FOV shown is 10 × 26 km².

The analysis of the dust continuum at certain locations can be limited by in-field stray light, which results from the presence of the nucleus within the slit of instruments. Many different causes are responsible for the stray light such as light scattered by optical
<table><caption>**Table 1.** VIRTIS-M observations in both channels analysed in this work.</caption><thead><tr><th rowspan="2">Img</th><th rowspan="2">IR file name</th><th rowspan="2">VIS file name</th><th rowspan="2">Cube dimension</th><th colspan="2">Data observations</th><th rowspan="2">Duration time (s)</th><th rowspan="2">Range (km)</th><th rowspan="2">Phase angle (°)</th><th rowspan="2">Subsolar latitude (°)</th><th rowspan="2">Sub-solar Lon (°)</th><th rowspan="2">R<sub>h</sub> (AU)</th></tr><tr><th>Start time</th><th>Stop time</th></tr></thead><tbody><tr><td colspan="12" style="text-align:center; font-weight:bold;">March 15 MTP14/STP47</td></tr><tr><td>a</td><td>I1_00385045109</td><td>V1_00385045118</td><td>256 66 432</td><td>12:59:44.109</td><td>13:23:08.737</td><td>1395</td><td>70.65</td><td>43.6</td><td>7.7</td><td>135.5</td><td>2.09</td></tr><tr><td>b</td><td>I1_00385046608</td><td>V1_00385046617</td><td>256 66 432</td><td>13:24:43.076</td><td>13:48:07.715</td><td>1395</td><td>70.55</td><td>43.4</td><td>8.4</td><td>120.8</td><td>2.09</td></tr><tr><td>c</td><td>I1_00385048108</td><td>V1_00385048117</td><td>256 66 432</td><td>13:49:43.120</td><td>14:13:07.753</td><td>1395</td><td>70.46</td><td>43.3</td><td>9.0</td><td>103.4</td><td>2.09</td></tr><tr><td>d</td><td>I1_00385049609</td><td>V1_00385049618</td><td>256 66 432</td><td>14:14:44.082</td><td>14:38:08.713</td><td>1395</td><td>70.368</td><td>43.2</td><td>9.2</td><td>84.5</td><td>2.09</td></tr><tr><td>e</td><td>I1_00385051108</td><td>V1_00385051117</td><td>256 66 432</td><td>14:39:43.053</td><td>15:03:07.679</td><td>1395</td><td>70.279</td><td>43.2</td><td>8.7</td><td>66.2</td><td>2.09</td></tr><tr><td>f</td><td>I1_00385052608</td><td>V1_00385052617</td><td>256 66 432</td><td>15:04:43.063</td><td>15:28:07.700</td><td>1395</td><td>70.194</td><td>43.1</td><td>8.0</td><td>50.4</td><td>2.09</td></tr><tr><td>g</td><td>I1_00385058594</td><td>V1_00385058603</td><td>256 66 432</td><td>16:44:29.107</td><td>17:07:53.739</td><td>1395</td><td>69.887</td><td>43.1</td><td>5.9</td><td>9.0</td><td>2.09</td></tr><tr><td>h</td><td>I1_00385060454</td><td>V1_00385060463</td><td>256 66 432</td><td>17:15:29.149</td><td>17:38:53.777</td><td>1395</td><td>69.803</td><td>43.1</td><td>5.8</td><td>359.4</td><td>2.09</td></tr><tr><td>i</td><td>I1_00385062254</td><td>V1_00385062263</td><td>256 66 432</td><td>17:45:29.116</td><td>18:08:53.742</td><td>1395</td><td>69.728</td><td>43.0</td><td>6.0</td><td>350.1</td><td>2.09</td></tr><tr><td>j</td><td>I1_00385064054</td><td>V1_00385064063</td><td>256 66 432</td><td>18:15:29.068</td><td>18:38:53.767</td><td>1395</td><td>69.657</td><td>42.9</td><td>6.3</td><td>340.0</td><td>2.09</td></tr><tr><td>k</td><td>I1_00385065854</td><td>V1_00385065863</td><td>256 66 432</td><td>18:45:29.102</td><td>19:08:53.735</td><td>1395</td><td>69.591</td><td>42.7</td><td>7.0</td><td>328.2</td><td>2.09</td></tr><tr><td>l</td><td>I1_00385067654</td><td>V1_00385067663</td><td>256 66 432</td><td>19:15:29.164</td><td>19:38:53.794</td><td>1395</td><td>69.531</td><td>42.5</td><td>7.8</td><td>313.6</td><td>2.09</td></tr><tr><td>m</td><td>I1_00385069454</td><td>V1_00385069463</td><td>256 66 432</td><td>19:45:29.108</td><td>20:08:53.739</td><td>1395</td><td>69.476</td><td>42.4</td><td>8.7</td><td>295.2</td><td>2.09</td></tr><tr><td>n</td><td>I1_00385071074</td><td>V1_00385071083</td><td>256 66 432</td><td>20:12:29.162</td><td>20:35:53.791</td><td>1395</td><td>69.431</td><td>42.3</td><td>9.1</td><td>275.5</td><td>2.09</td></tr><tr><td>o</td><td>I1_00385074607</td><td>V1_00385074616</td><td>256 66 432</td><td>21:11:22.052</td><td>21:34:46.681</td><td>1395</td><td>69.347</td><td>42.3</td><td>8.1</td><td>233.7</td><td>2.09</td></tr><tr><td>p</td><td>I1_00385076286</td><td>V1_00385076295</td><td>256 66 432</td><td>21:39:21.141</td><td>22:02:45.772</td><td>1395</td><td>69.315</td><td>42.4</td><td>7.3</td><td>218.5</td><td>2.09</td></tr><tr><td>q</td><td>I1_00385077967</td><td>V1_00385077976</td><td>256 66 432</td><td>22:07:22.103</td><td>22:30:46.726</td><td>1395</td><td>69.287</td><td>42.5</td><td>6.6</td><td>206.3</td><td>2.09</td></tr><tr><td>r</td><td>I1_00385079647</td><td>V1_00385079656</td><td>256 66 432</td><td>22:35:22.124</td><td>22:58:46.773</td><td>1395</td><td>69.264</td><td>42.5</td><td>6.1</td><td>196.0</td><td>2.09</td></tr><tr><td>s</td><td>I1_00385081327</td><td>V1_00385081336</td><td>256 66 432</td><td>23:03:22.162</td><td>23:26:46.803</td><td>1395</td><td>69.245</td><td>42.5</td><td>5.9</td><td>186.9</td><td>2.09</td></tr><tr><td>t</td><td>I1_00385083007</td><td>V1_00385083016</td><td>256 66 432</td><td>23:31:22.073</td><td>23:54:46.731</td><td>1395</td><td>69.231</td><td>42.5</td><td>5.8</td><td>178.3</td><td>2.09</td></tr><tr><td>u</td><td>I1_00385084687</td><td>V1_00385084696</td><td>256 66 432</td><td>23:59:22.153</td><td>00:22:46.783</td><td>1395</td><td>69.222</td><td>42.5</td><td>6.0</td><td>169.6</td><td>2.09</td></tr><tr><td>v</td><td>I1_00385086367</td><td>V1_00385086376</td><td>256 66 432</td><td>00:27:22.089</td><td>00:50:46.724</td><td>1395</td><td>69.217</td><td>42.4</td><td>6.3</td><td>160.1</td><td>2.09</td></tr><tr><td colspan="12" style="text-align:center; font-weight:bold;">February 28 MTP013/STP45</td></tr><tr><td>1</td><td>I1_00383725469</td><td>V1_00383725481</td><td>256 255 432</td><td>06:25:55.64</td><td>07:55:15.302</td><td>5359</td><td>106.86</td><td>61.5</td><td>9.4</td><td>315.0</td><td>2.21</td></tr><tr><td>2</td><td>I1_00383731109</td><td>V1_00383731111</td><td>256 253 432</td><td>07:59:45.63</td><td>08:44:05.279</td><td>2659</td><td>105.88</td><td>61.3</td><td>11.1</td><td>266.6</td><td>2.21</td></tr><tr><td colspan="12" style="text-align:center; font-weight:bold;">April 27 MTP015/STP53</td></tr><tr><td>a</td><td>I1_00388760487</td><td>V1_00388760489</td><td>256 264 432</td><td>13:02:43.33</td><td>13:49:03.975</td><td>2778</td><td>129.79</td><td>72.9</td><td>1.9</td><td>146.5</td><td>1.76</td></tr><tr><td>b</td><td>I1_00388763546</td><td>V1_00388763549</td><td>256 264 432</td><td>13:53:41.95</td><td>14:40:03.936</td><td>2778</td><td>130.84</td><td>72.9</td><td>2.3</td><td>118.6</td><td>1.76</td></tr><tr><td>c</td><td>I1_00388766847</td><td>V1_00388766849</td><td>256 264 432</td><td>14:48:43.33</td><td>15:35:03.968</td><td>2778</td><td>131.99</td><td>72.9</td><td>2.4</td><td>78.29</td><td>1.76</td></tr><tr><td>d</td><td>I1_00388770446</td><td>V1_00388770449</td><td>256 264 432</td><td>15:48:41.96</td><td>16:35:03.933</td><td>2778</td><td>133.26</td><td>73.1</td><td>2.0</td><td>40.61</td><td>1.76</td></tr><tr><td>e</td><td>I1_00388776027</td><td>V1_00388776036</td><td>256 264 432</td><td>17:21:43.27</td><td>18:52:07.952</td><td>5416</td><td>135.72</td><td>73.7</td><td>1.5</td><td>358.75</td><td>1.76</td></tr><tr><td>f</td><td>I1_00388781546</td><td>V1_00388781556</td><td>256 264 432</td><td>18:53:41.92</td><td>20:24:07.948</td><td>5416</td><td>137.71</td><td>74.0</td><td>1.8</td><td>326.43</td><td>1.76</td></tr><tr><td>g</td><td>I1_00388787067</td><td>V1_00388787076</td><td>256 264 432</td><td>20:25:43.34</td><td>21:43:08.220</td><td>4635</td><td>139.57</td><td>74.0</td><td>2.4</td><td>273.87</td><td>1.76</td></tr><tr><td colspan="12" style="text-align:center; font-weight:bold;">August 26 MTP020/STP71</td></tr><tr><td>1</td><td>V1_00399218472</td><td></td><td>256 103 432</td><td>14:02:30.729</td><td>14:37:50.364</td><td>2119</td><td>410.43</td><td>82.3</td><td>-22.19</td><td>2.84</td><td>1.25</td></tr></tbody></table>

elements, diffuse reflection from mirror surface imperfections and ghost orders caused by the diffraction grating (Filacchione 2006). As a consequence of these optical effects, for the data of February 28 and April 27, when the instrument's slit is partially filled by the bright nucleus, a sizeable fraction of the incoming photons are spread into the adjacent coma pixels. When the slit is entirely on the coma, as for the data of March 15, there is no nucleus contribution to the stray light, which is why we concentrated on the March 15 data for much of our morphological analysis.

The spectra and images used for our analysis were reduced using the VIRTIS reduction pipeline. This includes dark subtraction, flat-fielding with correction for the odd/even differences of the column readout amplifiers, interpolation over known artefacts, flux calibration applying the instrument sensitivity function (Ammannito et al. 2006, Filacchione 2006; Filacchione et al. 2006) and additional corrections derived from in-flight data (Raponi 2014).

Additionally, the radiance spectra still contain a large number of noise spikes in single pixels or small clusters of pixels, due to bad pixels or cosmic-ray strikes. We remove these using a me-

dian filter de-spiking algorithm, which is employed only in the horizontal dimensions of the data, thus leaving the spectral data intact.

A typical radiance spectrum of the coma in the IR is shown in Fig. 1. The four vertical lines represent the regions of the order sorting filters, which were not included in the analyses. The spectrum shows a continuum due to light scattered from the dust, which follows the solar radiance fairly closely and emissions due to water vapour and CO₂ at 2.7 and 4.2 µm, respectively. None of our continuum spectra investigated show any evidence of absorption bands due to the dust particles. To obtain the emission intensity of the gas, we subtract the continuum fitted on either side of the emission bands and integrate the radiance for each band. The continuum is fitted with a second-order polynomial function to the regions of 2.2–2.5 and 2.9–3.2 µm. For the H₂O emission, the band integration is defined in the interval of 2.6–2.8 µm. For the CO₂, the continuum is fitted with a straight line in the region of 3.8–4.5 µm and the band emission is defined in the range of 4.2–4.3 µm. As a measure of the continuum intensity in the IR, we chose a narrow band
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Radiance spectrum of 2015 March 15 for cube I1_00385076286 in the IR channel, showing the H₂O emission at 2700 nm, CO₂ emission at 4200 nm and dust continuum. The grey strips indicate the positions of the order filters.</figcaption></figure>

pass of 0.10 µm in width centred on 1.10 µm. For the VIS part of the spectrum, we chose the wavelength range of 0.505–0.565 µm, which corresponds to the green filter used in both the narrow- and wide-angle cameras of the OSIRIS imaging instrument on board Rosetta. This will allow a comparison of the results obtained by the two instruments, which is part of the future work.

## 3 MORPHOLOGICAL CORRELATION BETWEEN DUST AND GAS

In this section, we present the analysis of the data taken on 2015 March 15 and on April 27 by VIRTIS-M. The data consist of 22 and 7 hyperspectral cubes, respectively (see Table 1). Each hyperspectral cube is composed of 432 monochromatic images covering the full IR range of the VIRTIS-M channel (1–5 µm).

The objective of the analysis is to identify spatial correlations between gases' (H₂O and CO₂) outflow and dust. A typical radiance spectrum of the coma in the IR range is shown in Fig. 1. The spectrum demonstrates the unique capability of the VIRTIS instrument to simultaneously measure the dust continuum (scattered solar radiation) in the range of 1–3 µm, the dust thermal emission in the range of 4–5 µm, and the fluorescence emission of water vapour and CO₂ at 2.7 and 4.2 µm, respectively. The full sequences of the March and April data sets also allow studying the evolution of the gas and dust plumes for a complete rotation period of the nucleus and above the sunlit and dark sides of the nucleus.

### 3.1 The March 15 data set

Probably the best sequence to search for correlations between dust and gas is 22 hyperspectral cubes acquired on March 15, labelled with the letters a through v (see Table 1). To analyse the spatial behaviour of the coma components, we display in Figs 2–5 the intensity maps of the dust continuum at 1.1 µm and of the H₂O and CO₂ bands. To limit the number of figures, we show only 12 representative cubes of the total 22, spanning the full cometary rotation. We did not find major deviations of this general pattern for the other cubes. In particular, the chosen cubes represent the coma above specific regions of the nucleus: body (Fig. 2), the neck and

head (Figs 3 and 4), and body again (Fig. 5u). Figs 2–5 are divided into four rows for each hyperspectral cube acquisition.

In the first row of Figs 2–5, we show the configuration of the nucleus of the comet with respect to the FOV of VIRTIS-M, at the time of the observation, indicated by the yellow box. The illumination of the nucleus is an important parameter to be correlated with the spatial distribution of dust, H₂O and CO₂. The intensity of the solar illumination is represented by the cosine of the solar incidence angle (as derived using the shape model SHAP5 v0.3), with decreasing solar illumination from red to green. The regions marked blue receive essentially no solar illumination. The effects of shadows by the head on to the body are not included in this analysis. The thick yellow line indicates the Sun direction. These images were generated using a program made available to us by A. Bieler. In the next three rows, we report, from top to bottom, the intensity distribution of the dust continuum (measured at 1.1 µm), the water vapour and CO₂ band intensities. The contour plots were drawn after applying a Gaussian smoothing of 5 × 5 pixels to remove high-frequency noise. The dust continuum unit is W⁻¹ m⁻² sr⁻¹ µm⁻¹ and the band intensity units are 10⁻⁵ W⁻¹ m⁻² sr⁻¹. The colour maps were generated by stretching the contour scale; however, the colours in the maps are adapted to each image to increase the contrast.

A cursory observation of the contour plots for the dust, H₂O and CO₂ already indicates the close correlation between dust and water and their correlation with the solar illumination of the nucleus, although their detailed distributions exhibit a rather complex pattern. This is mostly evident in acquisitions h, i, o, p, q, s and t, where CO₂ follows a completely different pattern with respect to water and dust. It is interesting to note that in all these observations the neck is illuminated by the Sun, although its illumination level varies. The water-dust correlation becomes less evident in acquisitions b, d, f and u (where the most illuminated part of the nucleus is the bottom of the body) and l, where, instead, it is the head illuminated by the Sun. In all images that follow, one should keep in mind that we are looking along a line of sight (LOS) so that the dust and gas distributions that we see may originate from sources behind the displayed orthographic profile view.

Looking in more detail at the dust and water distributions, we see that in Fig. 2, the whole bottom of the body is illuminated and the water vapour has a fairly broad distribution. However, although the pattern of the dust follows the water, it does not have such a broad distribution. In acquisition f, the water vapour shows an additional source beam coming from the neck/head on the right-hand side. Fig. 3 illustrates dust and water vapour coming from an illuminated head, body and neck. Water vapour is more distributed and show more features than the dust. In image h, the maximum intensities of water and dust are located in the centre of the frame corresponding to the position of the neck. The head, even if illuminated as in l, does not show a strong source of dust and water vapour emission. Fig. 4 shows a lit head, northern neck and body with different inclinations. The head, neck and body (long dimension of the comet) are illuminated together, and so the patterns of the dust and water vapour are very broad. When the neck is directly illuminated, the dust and water vapour peaks are located above this region (images p and q). In Fig. 5, we do not see any deviation from the previous cases; the comet is in the last rotation phases, showing the bottom part of the body again. The behaviour of the dust and H₂O pattern is the same, showing a close correlation. Each part of the nucleus, if illuminated, produces dust and water vapour. The dust behaviour in some of the maps displays a collimated structure (Combi et al. 2012), which can be assimilated to a jet-like pattern. However, its contrast ratio between the maximum value of the dust and the coma
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Spatial distribution of the dust continuum at 1.1 µm, and the H₂O and CO₂ band intensities for 2015 March 15. The image details are listed in Table 1, as identified with the italic character. The first column is for image (b), the middle column for image (d) and the last for image (f). The first row shows the configuration of the nucleus of the comet with respect to the VIRTIS-M frame (yellow rectangle). The different colours on the nucleus show the intensity of the solar illumination depicted by the cosine of the solar incident angle, with the colour red having the strongest solar illumination, yellow less and blue none illumination. The second row shows the spatial distribution of the dust continuum at 1.1 µm. The spatial distributions of the water vapour and CO₂ are shown in the third and last rows, respectively. The gas contour lines have units of 10⁻⁵ W⁻¹ m⁻² sr⁻¹.</figcaption></figure>

background is not severe. The average values of the contrast are about 3 for the head and body and about 5 for the neck. This is an additional clue to the fact that the neck region is producing more dust than the head and body.

CO₂ shows a completely different pattern from water. A detailed analysis of the CO₂ outgassing has been done in Fink et al. (2016) and will not be reported here. As shown in that paper and in the publications of Migliorini et al. (2016) and Fougere et al. (2016), CO₂ does not come from the illuminated northern hemisphere but rather from the dark but more primitive southern hemisphere. While the maximum of CO₂ in all this data set appears above the head region, we note that when we used the comet viewing program by Bieler to look down on the comet from the direction of the Sun, the CO₂ emissions along the LOS appear to originate from the terminator region separating the northern and southern hemispheres.

In Fig. 6, we show plots of the dust continuum and H₂O and CO₂ band intensities for the 22 image cubes of March 15 listed in Table 1. Each acquisition has been divided into four horizontal strips located at different distances from the nucleus surface. In each box, we calculated the average distance and the average values of the 0.55 and 1.10 µm dust continuum intensities as well as the H₂O and the CO₂ band intensities. These quantities are reported

as a function of the time of observation for two different mean distances: 1.38 km (green curves) and 1.98 km (blue curves). The distances from the nucleus surface are taken in the middle of each box. Several conclusions can be drawn from these figures.

All three components of the coma clearly show strong variations with the rotational phase of the nucleus. Water vapour and dust show a significant variation of about a factor of 3 with the rotational phase. This variation with rotational phase is a combination of the illumination pattern (proportional to the cross-sectional area) and of the nature of the illuminated region. The absolute maximum is in the neck region. As noted in the previous discussion, the activity pattern of CO₂ shows a maximum in the head area. While there is a direct correlation between the distributions of the water vapour and the dust, there is an anticorrelation with the distribution of CO₂.

This behaviour is very different from what observed at comets 9P/Tempel 1 and 103P/Hartley 2 by the *Deep Impact* mission. Feaga et al. (2007) show the dust, water vapour and CO₂ maps of the coma of 9P/Tempel 1. All volatiles appear to drag dust off the nucleus, and the dust is enhanced in areas of both H₂O and CO₂ enhancement.

In the case of 103P/Hartley 2, as shown in fig. 7 of A'Hearn et al. (2011), a strong time correlation was found between dust, CO₂, and water vapour, although, in detail, they are not in complete
<figure><img src="image_5.png" /><figcaption>**Figure 3.** The same as Fig. 2, showing the dust continuum at 1.1 µm, and the water vapour and CO₂ band intensities for a sequence of three VIRTIS-M images: h, i and l, as reported in Table 1.</figcaption></figure>

agreement. In fact Protopapa et al. (2014) found that the dust is not uniformly distributed and its ejection is driven by the CO₂ flux. This points either to a different ejection mechanism or, most probably, to different gas flux levels at different heliocentric distances.

## 3.2 The April 27 data set

On April 27, VIRTIS-M collected a set of seven hyperspectral cubes showing the full nucleus and its surrounding coma spanning 70 per cent of the full rotation period. The advantage of these observations lies in the capability of studying the coma components at all local times (above sunlit and unilluminated regions).

The results of our analysis are shown in Figs 7 and 8, where only the hyperspectral cubes *a*, *d*, *e* and *g* (Table 1 for details) are displayed as an example; the intermediate ones show the same behaviour. The maps are composite images where the comet nucleus image (taken as an average in the wavelength range between 4.05 and 4.15 µm) is superimposed on the maps of the dust continuum at 1.1 µm (left-hand panels), the water vapour (middle panels) and the CO₂ band intensities (right-hand panels). The Sun is always at the top of each image. The dust and gas intensity contour lines are in units of radiance (W⁻¹ m⁻² sr⁻¹ µm⁻¹). The presence of the nucleus in the acquisition introduces some stray light and affects the retrieval of the dust continuum profile. In the spatial regions

where this is true, the dust maps are covered by semitransparent strip overlays (see Section 2).

As for the March 15 data set, the temporal coverage allows study of the behaviour of the three components of the coma for various local times and imaged regions of the nucleus. Dust and water vapour have a reasonable and predictable behaviour correlated with the illumination conditions, and their intensity decreases moving away from the nucleus.

The anticorrelation of CO₂ with respect to water vapour is most strikingly exhibited in this data set, as demonstrated in all four acquisitions shown. The most plausible explanation of this has already been discussed in Fink et al. (2016), but it is briefly repeated here. Because of the orientation of the comet's spin axis, during these observations, it is northern summer. However, since the comet at that time is still far from the Sun, the amount of sunlight it receives is relatively weak. The surface of the northern hemisphere ice is depleted in CO₂ because not enough material is eroded to expose fresh interior layers. It is covered by a thick layer of insulating dust, and the heat never reaches the deeper interior layers rich in CO₂. When the comet comes close to the Sun, the southern summer is very intense. The strong sunlight can erode several metres of material from its surface, exposing fresh primordial layers of interior, which are rich in CO₂. Quantitative calculations of the comet erosion rates during its orbit are presented by Keller et al. (2015). Thus, during the southern winter, even a small amount of glancing sunlight will
<figure><img src="image_6.png" /><figcaption>Figure 4. The same as Fig. 2, showing the dust continuum at 1.1 µm, and the water vapour and CO₂ band intensities for a sequence of three VIRTIS-M images: o, p and q, as reported in Table 1.</figcaption></figure>

be able to evaporate CO₂ ice because it is freshly exposed on the comet's surface. In fact, observations of the southern hemisphere in the Anhur region have now revealed patches of exposed CO₂ ice on the surface (Filacchione et al. 2016).

In Fig. 9, we plot the angular distribution of the three components under study for the acquisition I1_00388760487. To perform this analysis, we display the data in polar coordinates. The origin of the polar coordinate system (x0,y0) is the centre of the nucleus, as shown in the frame. The angular distribution has been calculated at 3 km from the centre of the nucleus. The distance is calculated using the angular distance of each pixel from the centre of the nucleus and the distance of the spacecraft to the centre of the comet both given in the geometry files. According to the description of the shape model by Preuske et al. (2016), this centre is defined as the centre of mass. The illuminated equator is centred around the polar angle 270° and the dark equator around 90°. The southern hemisphere is near 170°. The dust continuum could not be calculated in the regions where nucleus stray light is present (in this case, from 170° to 220° and from 310° to 360°). The absolute maximum for dust and water vapour is located on the dayside at mid-day (270°) as expected, while the maximum for CO₂ is located at 180°, consistent with Figs 7 and 8. The dust is slightly more focused than the broader emission of the water vapour. The radiance of the continuum distribution decreases going from the terminator (around 0°) to the dark equator (90°) and increases in the illuminated part. A fraction of dust radiance and

water vapour band intensity is observed on the night side, and this can have several causes as described in Fink et al. (2016).

## 4 RADIAL PROFILES

The data of April 27 allowed us to cover the maximum radial distance from the nucleus and to study the radial distribution of the dust over distances up to about 6.5 km. Fig. 10 shows the results of the radial profile determination for image cube I1_00388787067 and for the continuum intensity integrated over the wavelength interval of 1.05–1.15 µm. The overall profile is a composite obtained in two steps: The radial profile in the sunward direction (profile with blue empty circles), going from 1.18 to 4.21 km, gives the contribution closer to the nucleus, while a diagonal profile, going from 2.73 to 6.47 km and scaled to the sunward profile in the region of overlap, provides the extension to 6.47 km from the nucleus centre. Radial profiles at different azimuth angles have different absolute intensity values (cf. Fig. 9). However, we found their radial behaviour to be quite similar. This allowed us to scale the profiles to a common value and thus cover a larger range.

The radial column dust particle density profile $n(\rho)$ is expected to follow the expression

$$n(\rho) = \frac{Q}{4\rho v(\rho)},$$
<figure><img src="image_7.png" /><figcaption>**Figure 5.** The same as Fig. 2, showing the dust continuum at 1.1 µm, and the water vapour and CO₂ band intensities for a sequence of three VIRTIS-M images: s, t and u, as reported in Table 1.</figcaption></figure>

where $\rho$ is the distance from the comet centre, $Q$ is the production rate of the number of particles of a given size and $v(\rho)$ is the particle outflow velocity. It assumes that for the distances involved, no dust particles are destroyed or created after leaving the nucleus. This dust density is related to the observed dust light intensity via the scattering properties of the particles for which a derivation is given in Fink & Rubin (2012). If there is no acceleration of the particles lifted off the surface, the observed scattered light intensity should follow a simple $1/\rho$ profile. This is the case for the night-side profile, which is the red curve in Fig. 10. This is not the case for the day-side profile, which is considerably steeper than $1/\rho$ because of the acceleration of the dust particles.

To derive information on the acceleration, we compare our measured dust intensity profiles with direct simulation Monte Carlo (DSMC) models carried out by Tenishev et al. (2011a) for the hypothetical dust evolution of comet 67P/CG. A variety of numerical results of these models are available on the web site ‘Inner Coma Environment Simulator’ (http://ices.engin.umich.edu; Combi 1996; Combi et al. 2004; Tenishev, Combi & Davidsson 2008; Tenishev, Combi & Rubin 2011b; Rubin et al. 2011). We select the model Case 1.3 with dust particles of radius 10.0 µm having a terminal velocity of 33 m s⁻¹. We integrated the DSMC particle density along the LOS from the spacecraft to infinity. This calculation is described in detail in our earlier dust scattering paper (Fink & Rinaldi 2015). To allow a comparison with the model DSMC calculations, we normalized these particle density values to agree with the radial dust

intensity profile in the range of 4–6 km. In addition, since the DSMC model calculations were carried out for a nucleus radius of 2.0 km, we shifted these by 0.45 km to bring them into accord with real distances from the nucleus centre. The result is shown as a dashed yellow line in Fig. 10.

The agreement between the shape of the DSMC calculations and our measured radial column density profile is clearly very good. It shows that the model calculation correctly takes into account the acceleration of the dust particles from the nucleus surface. Looking in more detail into the particle acceleration of particles of different sizes from the nucleus surface, as given by the DSMC model, we found that the acceleration of dust particles for sizes from 0.10 µm to 1.0 cm has almost an identical shape. Our choice of 10.0-µm particles, rather than some other particle size, in our comparison above is thus not constraining. It also unfortunately prevents us from deriving any information on the particle size distribution from a study of the column density dust intensity distribution.

## 5 THE CALCULATION AND MEASUREMENT OF $Af\rho$

For the spacecraft observations of comet 67P/CG, the radiation scattered by the dust is measured as radiance in W⁻¹ m⁻² sr⁻¹ µm⁻¹. However, it is common practice in the study of cometary dust to express the amount of light scattered by the dust using the quantity $Af\rho$. This concept was first introduced by A’Hearn et al. (1984).
<figure><img src="image_8.png" /><figcaption>Figure 6. Plots of the continuum radiance at 0.55 µm (in the VIS) and at 1.1 µm (in the IR), as well as the H₂O and CO₂ band intensities for the 22 image cubes of 2015 March 15 listed in Table 1. The emission intensities are plotted against the observation start time. Data are shown for a strip at 1.38 km (green curves) and at 1.98 km (blue curves) from the surface of the comet. The continuum intensities in the VIS and IR track each other exceedingly well and correlate well with the water band intensity, but are anticorrelated with CO₂.</figcaption></figure>

In this expression, A represents the scattering power of the dust particles. Very often this is taken to be the *Bond albedo* or the *geometric albedo*, but neither of these is correct, as the scattering is produced by small particles (Fink and Rubin 2012). In addition, the size distribution of the dust particles has to be taken into account. The term *f* is the *ratio* of the sum of the geometric cross-sections of the dust particles within an observing aperture to the projected observation area having an aperture of radius *ρ*.

The observed scattered light intensity along the LOS path through the coma observed with an instrument of a given angular FOV can be translated into a local *Afρ* using the formalism developed in Fink & Rubin (2012) and Fink & Rinaldi (2015). The expression for doing this is given below:

$$Af\rho = \frac{I_{\text{obs}}(a, \lambda) 8\pi^2 \rho}{\mathcal{F}_i(\lambda) 2\varphi} \approx \frac{I_{\text{obs}}(a, \lambda) 8\pi \rho}{\mathcal{F}_i(\lambda)}.$$

In this expression, $I_{\text{obs}}$ (W⁻¹ m⁻² sr⁻¹ µm⁻¹) is the observed scattered light intensity by the instrument, $\mathcal{F}_i(\lambda)$ is the incident solar flux and $\varphi$ is the angle between the intersection of the LOS with the coma and the impact parameter. The FOV of the instrument for the observed scattered light from the dust is taken into account

in the data reduction pipeline for $I_{\text{obs}}$, which is reduced to units of per steradian. We also note that $\mathcal{F}_i(\lambda)$ is the solar flux at the comet in W⁻¹ m⁻² µm⁻¹ and is not to be confused with F (W⁻¹ m⁻² sr⁻¹ µm⁻¹) used in Section 5 to calculate the reflectance of the dust. In our case, the LOS goes from the spacecraft to +∞, and the LOS integration gives 0.493π + 0.50π, which is sufficiently close to π so that we can approximate 2φ by π.

The *Afρ* defined above is for a specific LOS and FOV by the spacecraft instrument. For example, close to the nucleus there will be higher values on the sunlit side than on the dark side. These values can thus not be directly compared with ground-based global measurements of *Afρ*. However, a reasonable but not exact comparison is possible if we consider an annulus at 3 km from the comet centre, which essentially captures all the dust leaving the nucleus. If our annulus is at a sufficiently large distance from the nucleus, so that it is in the collision-less free flowing zone and no additional production or destruction of the dust occurs, our observations can yield a global measure of *Afρ* in the immediate vicinity of the nucleus that can be compared with ground-based observations, which typically use an aperture of 10 000 km or more. We will miss a small fraction of the total spherical dust emission by the dust particles that
<figure><img src="image_9.png" /><figcaption>**Figure 7.** The distribution of dust, water vapour and CO₂ for the selected images I1_00388760487 (a) (sequence at the top) and I1_00388770446 (d) (sequence at the bottom) acquired on 2015 April 27, showing the whole nucleus and surrounding coma. The left-hand panel shows the dust continuum intensity at 1.1 µm, the middle panel shows the band intensity maps of H₂O and the right-hand panel shows maps for CO₂. A VIRTIS-M image at 4.2 µm was inserted into the nucleus area for better visualization. The dust contour lines have units of W⁻¹ m⁻² sr⁻¹ µm⁻¹ and the band intensity of the gas has units of W⁻¹ m⁻² sr⁻¹. Semitransparent strips indicate areas of instrumental scattering light from the nucleus.</figcaption></figure>

are emitted directly towards the spacecraft within a cone of base radius ρ of ~3 km at the spacecraft distance to the comet of ~130 km or an angle 3/130 of ~1.2°.

The determination of global *Afρ* values close to the nucleus can be carried out using the data of February 28 and April 27. Since portions of the coma within the annulus cannot be used due to scattered light interference, we have interpolated the data in these regions and then calculated our average intensity values. The results of these calculations are presented in Table 2. The uncertainties in Table 2 and Fig. 11 are calculated by propagating the formal errors. For February 28, we get an average value of 1.13 ± 0.12 m, and for April 27, we get an average value of 2.02 ± 0.12 m. These values should be compared with the H₂O production rates reported in Fink et al. (2016), which for February 28 averaged 2.49 × 10²⁶ molecules s⁻¹ and for April 27 averaged 4.65 × 10²⁶ molecules s⁻¹. The CO₂ production rate, on the other hand, stayed about the same for the two dates. The average water production rate increased by a factor of 1.87, while the average dust production increased by a very similar factor of 1.79. The close conformance between the two species provides additional evidence that water vapour is the main driver of the dust in the coma.

We could find only a few pre-perihelion ground-based measurements for 67P/CG for the heliocentric distances or our observations. These are summarized in Snodgrass et al. (2013). From their table, one can see that *Afρ* values stayed essentially constant with an average value of ~0.8 m for the heliocentric distance range of 2.28 to 1.89 au. Thus, within the uncertainties of both measurement sets, these numbers agree quite well. There is a considerable gap in the

observational data between 1.89 and 1.34 au when the ground-based data jump to about 4.7 m. Our measured value of 2.02 ± 0.12 m at 1.76 au falls well into the range of these values.

In Fig. 11, we plot the local *Afρ* values in a rectangle strip of 1.38 km above the nucleus surface for all 22 image cubes of March 15. The highest values of *Afρ* are 6.0 ± 0.7 and 3.7 ± 0.5 m, which are observed when the long axis of the nucleus, including the neck area, faces the instrument LOS. The lowest values of about 2.2 m occur when the head faces our LOS.

## 6 COLOUR AND REFLECTIVITY OF THE DUST

By combining data from the VIRTIS-M VIS and IR channels, a spectral reflectivity range from about 0.3 to 5.0 µm is potentially available. In the VIS channel, however, a considerable amount of instrumental scattered light and stray light from higher orders of the IR channel, which share the convex grating mirror in the Offner spectrometer (see Filacchione 2006; Coradini et al. 2007), limits the useful range to about 400–800 µm, and even in this interval, there may be issues. We note that there is a considerable amount of colour information that can be obtained from the VIRTIS data so that the present analysis must be considered preliminary.

The dust reflectance, *R*, is a dimensionless quantity calculated by dividing the measured scattered light intensity *I* (W⁻¹ m⁻² sr⁻¹ µm⁻¹) by *F*, where π*F* is the solar incident flux (W⁻¹ m⁻² µm⁻¹) at the comet. The wavelength-dependent solar flux is taken from Kurucz (1992). The colours or slope of the reflectance of the dust were
<figure><img src="image_10.png" /><figcaption>**Figure 8.** The same as Fig. 7, showing the dust continuum at 1.1 µm, and the water vapour and CO₂ band intensities for a sequence of two VIRTIS-M images: The top row is for image cube I1_00388776027 (e) and the bottom row for image cube I1_00388787067 (g).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Angular distribution at 3 km from the nucleus centre for the dust continuum at 1.1 µm, as well as the H₂O and CO₂ band intensities for the image of April 27, as reported in Table 1. The good correlation of dust and water is clear, while the CO₂ emission is strongly anticorrelated.</figcaption></figure>

obtained for the two cubes of February 28, 22 cubes of March 15 and seven cubes of April 27 (see Table 3). Colours were obtained for both the VIS and IR channels.

The standard notation for the colours, or more accurately the mean reflectance gradient, of Solar system objects such as planets, asteroids and comets is % per 1000 Å. This can be calculated if the reflectance, R, is measured at two wavelengths λ₁ and λ₂ either using spectroscopy or using filter photometry. The mean reflectance

gradient per 100 nm, r, for a particular wavelength interval then becomes

$$r = \left( \frac{dR}{d\lambda} (\text{nm}) \right) * \frac{100}{R_{\text{mean}}}$$

The mean reflectance gradient per 100 nm can then be readily converted into % per 100 nm, equivalent to % per 1000 Å. We will use the terms mean reflectance gradient and colour in units of % per 100 nm interchangeably in this paper.

A sample reflectance spectrum from 350 to 3500 nm is shown in Fig. 12. It can be seen that in the IR region a single reflectance gradient fits the data quite well from about 1100 to 3500 nm. Instead of simply picking the reflectivity at two wavelengths in our spectral range, we decided to fit the reflectance R by the equation R = a+bλ. The fitting routine uses all wavelength bands in the wavelength interval to be analysed, thus assuring us an optimal signal-to-noise ratio (S/N) and decreasing the internal error in our colour determination by a considerable factor. The fitting routine also provides us with a statistical uncertainty in our fit.

The VIS channel roughly from 350 to 1000 nm, unlike the IR region, appears to show that a single reflectance gradient does not fit the data well. The reflectance spectra of March 15 (cf. Fig. 12) give the appearance that there is a relatively flat portion from 450 to 600 nm with a low reflectance gradient of ~1.5 per cent per 100 nm and a steeper gradient of 14 per cent per 100 nm from 600 to 750 nm. A definitive conclusion regarding the change in the colour index with wavelength, however, cannot be reached since the VIS spectrum is contaminated by the scattered light. The contamination becomes strong below about 400 nm and above 800 nm (Carlson, private communication).
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Radial profiles of dust and gas for image cube I1_00388787067 on 2015 April 27. Seven radial profiles are shown. The profile of the dust continuum is a combination of the day-side profile and a scaled diagonal profile. Also plotted are two $1/\rho$ profiles for the day and night sides and a scaled water column density profile for comparison. For the day side, the continuum intensity rises much faster close to the nucleus than the $1/\rho$, and faster than water. On the night side with much lower intensity, a $1/\rho$ profile fits quite well. A DSMC dust profile as described in the text fits the observations quite well.</figcaption></figure>

<table><caption>**Table 2.** $Af\rho$ calculated at 3 km from the comet centre for February 28 and April 27.</caption><thead><tr><th>Image cube</th><th>Average impact parameter (ρ)<br>(m)</th><th>Average intensity @ 1.1 μm<br>(W<sup>-1</sup> m<sup>-2</sup> sr<sup>-1</sup> μm<sup>-1</sup>)</th><th>Solar flux @ 1.1 μm<br>(W<sup>-1</sup> m<sup>-2</sup> μm<sup>-1</sup>)</th><th>Afρ<br>(m)</th></tr></thead><tbody><tr><td colspan="5"><strong>2015 February 28</strong></td></tr><tr><td>I1_383725469</td><td>2980</td><td>1.80E-03</td><td>123.0</td><td>1.10 ± 0.16</td></tr><tr><td>I1_383731109</td><td>2980</td><td>1.98E-03</td><td>123.0</td><td>1.16 ± 0.17</td></tr><tr><td>Average</td><td></td><td></td><td></td><td>1.13 ± 0.12</td></tr><tr><td colspan="5"><strong>2015 April 27</strong></td></tr><tr><td>I1_00388760487</td><td>3050</td><td>4.57E-03</td><td>193.7</td><td>1.59 ± 0.23</td></tr><tr><td>I1_00388760487</td><td>3050</td><td>4.69E-03</td><td>193.7</td><td>1.66 ± 0.25</td></tr><tr><td>I1_00388760487</td><td>3050</td><td>5.16E-03</td><td>193.7</td><td>1.86 ± 0.28</td></tr><tr><td>I1_00388760487</td><td>3050</td><td>5.68E-03</td><td>193.7</td><td>2.06 ± 0.31</td></tr><tr><td>I1_00388760487</td><td>3050</td><td>6.76E-03</td><td>193.7</td><td>2.45 ± 0.37</td></tr><tr><td>I1_00388760487</td><td>3050</td><td>6.27E-03</td><td>193.7</td><td>2.33 ± 0.35</td></tr><tr><td>I1_00388760487</td><td>3050</td><td>6.70E-03</td><td>193.7</td><td>2.21 ± 0.33</td></tr><tr><td>Average</td><td></td><td></td><td></td><td>2.02 ± 0.12</td></tr></tbody></table>
<figure><img src="image_13.png" /><figcaption>**Figure 11.** *Afp* values for all 22 images of 2015 March 15 compared to the viewing aspect of the nucleus. Maximum *Afp* values occur when the cross-section of the comet below is largest and the neck area is exposed to our FOV.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 12.** Spectral reflectance of the coma continuum from 350 to 3500 nm. The spectrum is an average inside a box for cube I1.00385076286 on 2015 March 15. The red part is the IR channel. The emission band of H₂O at 2700 nm is quite evident. The blue part is the VIS channel, which shows a spike at the junction of the order-sorting filter. The dashed line, between 800 and 1000 nm, corresponds to the range where the data exhibit considerable instrumental scattered light. In the IR region from about 1200 to 3500 nm, a single reflectance gradient of 1.7 per cent per nm fits of the data quite well.</figcaption></figure>

Thus, we presently prefer to determine an average gradient for the wavelength range of 450–750 nm. This range was chosen because it exhibited the minimum amount of instrumental scattered light as well as minimum stray light from higher orders of the IR portion of the spectrometer. The fitting routine used all 106 wavelength bands in that interval.

A change in colour with the source region near the nucleus or with distance from the nucleus might indicate a change in the composition of the dust or a change in the particle size distribution. We searched but could not find any meaningful changes within the uncertainties of our measurements. To illustrate this, we plot in Fig. 13 the reflectance gradient for all 22 image cubes of March 15. As can be seen in Figs 2–5, the dust in these images originates from different surface areas of the nucleus, such as the head, the bottom of the body or the area along the long axis of the comet,

<figure><img src="image_15.png" /><figcaption>**Figure 13.** Reflectance gradient (colour) for all 22 images of 2015 March 25 in the VIS (upper image) and IR channels (lower image). The green colour is for a distance of 1.38 km from the surface, and the blue colour is for a distance of 1.48 km. No significant variation of the colour with the nucleus below which exposes various dust source regions and with distance from the surface is evident.</figcaption></figure>

<table><caption>**Table 3.** Average colour on the sunlit and dark sides of the image cubes for February 28, March 15 and April 27, and average colour into the jet and in the background coma for August 26.</caption><thead><tr><th rowspan="2">Observation</th><th rowspan="2">Channel</th><th colspan="2">Colour</th></tr><tr><th>Sunlit</th><th>Dark side</th></tr></thead><tbody><tr><td rowspan="2">February 28</td><td>VIS</td><td>11.0 ± 0.5%</td><td>10.3 ± 1.2%</td></tr><tr><td>IR</td><td>1.6 ± 0.1%</td><td>3.0 ± 0.7%</td></tr><tr><td rowspan="2">March 15</td><td>VIS</td><td>9.3 ± 1%</td><td></td></tr><tr><td>IR</td><td>1.7 ± 0.2%</td><td></td></tr><tr><td rowspan="3">April 27</td><td>VIS</td><td>12.5 ± 0.5%</td><td>12.4 ± 0.6%</td></tr><tr><td>IR</td><td>1.75 ± 0.2%</td><td>2.5 ± 0.6%</td></tr><tr><td>Inside the jet</td><td></td><td>Outside the jet</td></tr><tr><td>August 26</td><td>VIS</td><td>13.9 ± 0.1%</td><td>11.8 ± 1.7%</td></tr></tbody></table>

which emphasizes the neck region. Fig. 13 shows no discernable difference in colour for these 22 images. Also plotted in Fig. 13 are the colours for two different distances from the nucleus, 1.38 km (green curves) and at 1.98 km (blue curves) from the surface of the comet.

Our measured reflectance gradients for the dates of March 15, February 28 and April 27 and a jet feature on August 26 and are summarized in Table 3. For March 15, the average gradient for all 22 images in the VIS wavelength range is 9.3 ± 1 per cent per 100 nm, and in the IR range, it is 1.7 ± 0.2 per cent per 100 nm. The uncertainties are estimated from the variation between all 22 frames and are roughly twice the standard deviation of these cubes.

As can be seen in Table 3, the reflectance gradients for the two images of February 28 and the seven images of April 27, within our estimated error, are essentially the same as for the 22 observations of March 15. For these two dates, it was possible to measure the colour in the coma on the dark side of the nucleus. For the VIS range, these colours are also consistent with the data of March 15. For the IR, they are slightly higher, but the signal was quite low so that
within our estimated errors the colours do not differ. This is also the case for our observations of the jet on August 26, where we might expect a colour difference, but again no significant difference was observed. Thus, our analysis of the reflectance gradient for the dates analysed in this paper appears to preclude any possible major changes in the dust properties that might be reflected in the dust colour such as changes in the dust composition of the particle size distribution.

It is instructive to compare our colour gradients with measure-
ments obtained on other comets. Unfortunately, these measurements
show a large amount of scatter because most of them were taken with
filter photometry, which can be perturbed by unknown cometary gas
emissions, and so we presently do not review all of these reports.
Probably, the most reliable ones are those for comet 1P/Halley by
Meech & Jewitt (1987), who reported a colour of 9 ± 2 per cent
per 100 nm for the wavelength range of 440–689 nm and those of
Hoban et al. (1989), who obtained 7 per cent per 100nm using two
continuum filters at 484 and 684 nm. The reflectance colours for
1P/Halley can also be seen in eight spectra from 520 to 1040 nm
in Fink (1994). Though no slopes were measured, a later analysis
of 23 pre-perihelion spectra yielded a fairly linear colour gradient
of 6 ± 2 per cent per 100 nm, and for 8 post-perihelion spectra,
a slope of 7 ± 2 per cent per 100 nm (Fink et al. 2016, private
communication). Jewitt & Meech (1986) computed optical colours
from near-IR photometry for nine observed comets. They found that
the reflectivity gradient decreases with wavelength from 5–18 per
cent per 100 nm at wavelengths 0.35–0.65 µm to 0–2 per cent per
0.1 nm at 1.6–2.2 µm. An interesting and extensive overview has
been done by Jewitt (2015). He find that the mean optical colours of
the dust in short-period and long-period comets are identical within
the uncertainties of measurement, as are the colours of the dust and
of the underlying nuclei. These populations show no evidence for
scattering by optically small particles or for compositional gradi-
ents, even at the largest distances from the Sun, and no evidence
for ultra-red matter. Colour gradients for 67P/CG in the range of
540–670 nm of 32 ± 6 per cent per 100 nm from space telescope
data reported by Lamy et al. (2006) appear considerably out of line.
Probably, there was a gas contamination in the pass band of the
filter used.

Figure 3 of Protopapa et al. (2014) shows the comparison between two reflectance spectra extracted inside and outside the jet emerging from the small lobe of the nucleus of 103/P Hartley 2 facing the Sun. Both spectra are red sloped from 1.2 to 2.5 µm with values of 5.10 ± 0.08 per cent per 0.1 µm and 1.41 ± 0.02 per cent per 0.1 µm.

Colours of sizable dust/debris pieces for 67P/CG have been re-
ported by Cremonese et al. (2016). From filter imaging photom-
etry making use of the OSIRIS camera, these authors measured
a slope in the wavelength range of 481–744 nm of 14 per cent
per 100 nm. These partially resolved measurements are probably
more comparable to the dust on the surface of 67P/CG since scat-
tering effects for these large debris pieces are minimal. For the
surface of 67P/CG, these authors report a value of 20 per cent per
100 nm.

7 CONCLUSION

The Rosetta mission to comet 67P/CG has given us the opportunity
to observe the regions of the coma within a few km of the surface
and to study the dynamical and physical properties of the emitted
dust. In this paper, four dates of VIRTIS-M observations have been

analysed: 2015 February 28, March 15 and April 27, when the
comet was in the pre-perihelion phase at heliocentric distances from
2.2 to 1.76 au, and August 26, in the post perihelion phase, at
1.25 au. We analysed the radial and azimuthal distributions of the
dust and gas (H₂O and CO₂) to determine any correlation between
them. We investigated radial dust profiles and compared them with
DMSC calculations. We calculated the *Afρ* of the dust from its
radiance to compare it with ground-based observations. We derived
the spectral reflectance gradient (or colour) both in the VIS and
in the IR regions. Our main dust results can be summarized as
follows:

(1) The morphology of the dust in the coma for the above dates shows a fairly complex pattern that is related to the irregular geometrical shape and illumination of the nucleus. The gas and the dust are not uniformly distributed with several jet-like features detected from different regions of the comet. The spatial dust distribution is considerably narrower than that of the gas, indicating that the dust production falls off fast when the gas production rates slow down, and that the majority of the dust is lifted and accelerated when the gas production is high.

(2) The general spatial distribution of the dust is strongly cor-
related with the presence of H₂O emission and is quite different
from the distribution of CO₂ emission. This indicates that during
our dates of observation, H₂O is the main driver of the dust. This
is not surprising since the production rate of H₂O is about a factor
of 40 higher than that of CO₂ during these dates, with production
rates for water being about (3–5) × 10²⁶ molecules s⁻¹, while for
CO₂ they are about 1.1 × 10²⁵ molecules s⁻¹ (Fink et al. 2016).

(3) The sunward radial profiles of the dust follow the DSMC models of the dust quite well, where the dust is lifted off the nucleus, accelerated by the gas in the first 4–5 km and then transitions into the free flowing collision-less zone with a 1/ρ column density profile. This indicates that the basic mechanisms of the coupling of the gas and dust in the DSMC model are valid. The night-side radial profile follows 1/ρ, most likely because the dust and gas seen on the night side are the result of dust density projection far from the nucleus into our LOS rather than direct escape close to the nucleus.

(4) Global *Afρ* values of 1.13 ± 0.12 m for February 28 and 2.02 ± 0.12 m for April 27 were calculated from the observed dust intensity in an annulus surrounding the comet in the free-flowing zone. These values compare well with global ground-based measurements of 67P/CG during its previous apparition (Snodgrass et al. 2013). Local *Afρ* values above the sunlit side of 67P/CG vary by about a factor of 2 from 2.0 ± 0.2 to 6.0 ± 0.7 m, having a maximum when the long axis, including the neck area, is illuminated by the Sun, and smaller values when the top of the head or body is illuminated and facing our FOV.

(5) The colour of the dust in the coma has a fairly steep red slope in the VIS of about 9 to 12 ± 1 per cent per 100 nm from 0.45 to 0.75 µm both on the sunlit side and on the dark side. The reflectance then transitions into a much shallower slope in the IR from 1 to 2.5 µm with values of 1.7 ± 0.2 per cent per 100 nm on the sunlit side and 3 ± 1 per cent per 100 nm on the dark side.

(6) No spectral features attributable to the dust could be detected. The colours of the dust do not show any spatial variation, nor any variation with distance from the nucleus. This indicates that the dust expelled into the coma from the nucleus is quite uniform, although it could also be that any changes in its composition or particle size distribution do not affect its colour. No change in the colour of the dust for the jet of August 26 could be observed, nor any significant difference between the jet and the background coma (Fig. 14).
<figure><img src="image_16.png" /><figcaption>**Figure 14.** Image of the jet in the VIS at 0.55 µm, as observed on 2015 August 26 (upper image), and the VIS spatial distribution of the colour calculated in the red square of the dust image. Again no significant changes in the colour of the jet are seen.</figcaption></figure>

## ACKNOWLEDGEMENTS

We thank the following institutions and agencies for support of this work: Italian Space Agency (ASI, Italy) contract number I/024/12/1, Centre National d'Études Spatiales (CNES, France), DLR (Germany), NASA (USA) Rosetta Program and Science and Technology Facilities Council (UK). The work of UF, LD and partially salary of GR was supported by NASA Rosetta Grant JPL-1270007. VIRTIS was built by a consortium, which includes Italy, France and Germany, under the scientific responsibility of the Istituto di Astrofisica e Planetologia Spaziali of INAF, Italy, which also guides the scientific operations. The VIRTIS instrument development, led by the prime contractor Leonardo-Finmeccanica (Florence, Italy), has been funded and managed by ASI, with contributions from the Observatoire de Meudon financed by CNES, and from DLR. We thank the Rosetta Science Ground Segment and the Rosetta Mission Operations Centre for their support throughout all the phases of the mission. The VIRTIS calibrated data will be available through the ESA's Planetary Science Archive Website (www.rssd.esa.int/index.php?project=PSA&page=index) and is available upon request until posted to the archive.

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This paper has been typeset from a *TEX/LATEX* file prepared by the author.