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Planetary and Space Science
journal h ome p age: www. e ls evier. com/locate/pss

Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy)$
Galin Borisov
a b

a,b,n

, Stefano Bagnulo b, Plamen Nikolov a, Tanyu Bonev

a

Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72, Tsarigradsko Chaussee Blvd., BG-1784 Sofia, Bulgaria Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland, UK

article info
Article history: Received 20 January 2015 Received in revised form 22 May 2015 Accepted 15 June 2015 Keywords: Comets C/2013 R1 (Lovejoy) Polarimetry Spectropolarimetry Dust Molecules

abstract
We have obtained imaging polarimetry of the comet C/2013 R1 (Lovejoy) with 2-Channel-Focal-Reducer Rozhen instrument at 2m Ritchey­ChrÈtien­CoudÈ telescope of the Bulgarian National Astronomical Observatory Rozhen in two dust continuum filters covering wavelength intervals clear from molecular emissions and centred at 4430 å in blue filter and at 6840 å in red filter. In imaging mode we measured the degree of linear polarisation 17.01 7 0.09% in the blue and 18.81 7 0.02% in the red, which is in a very good agreement with measurements of other comets at the similar phase angle. We have also obtained polarisation maps in both filters. We found a strong correlation between the spatial distribution of the polarisation and the dust colour. Spectropolarimetry of the nucleus region shows an increase of the polarisation with wavelength, and a depolarisation in the spectral regions with gas emission lines, most noticeable in C2 emission band, which shows a polarisation of 6.0 7 1.1%. & 2015 Elsevier Ltd. All rights reserved.

1. Introduction Polarimetry is sensitive to the physical properties of the dust particles: size, shape, porosity, orientation and chemical composition represented by its material complex refractive index. Polarimetric measurements give us the possibility to determine some parameters that cannot be determined through traditional intensity measurements. The first polarimetric observations of comets were made by Arago (1854), who discovered the polarised light in the Great Comet 1819 II. Later, observations of comets clarified some common characteristics of the polarised light, for example that usually the plane of polarisation is perpendicular to the scattering plane, and that there are variation of the polarisation in different parts of the comet (coma, tail). Contemporary polarimetric observations of comets began with the work of æhman (1939, 1941), who observed for the first time the continuum polarisation in comets and the polarisation of the emission lines.
Based on data collected with 2m RCC telescope at Rozhen National Astronomical Observatory. n Corresponding author at: Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72, Tsarigradsko Chaussee Blvd., BG1784 Sofia, Bulgaria. E-mail address: gborisov@astro.bas.bg (G. Borisov).

Most of the recent polarimetric observations of comets have been obtained by Kiselev and collaborators. Kiselev et al. (20 05) have also created a database with more than 260 0 measurements of linear and circular polarisation for 64 comets since 1940s. Most of the polarimetric observations of small Solar system bodies are aimed at measuring the variation of the polarisation with phase angle (which actually is 180°-scattering angle) and also its dependence on wavelength. From the theoretical side, many works have been carried out by Kolokolova and collaborators (Kolokolova et al., 1997, 20 04; Kolokolova and Jockers, 1997). The polarisation of the dust jet-like structures in the dust coma of the comet Hale­Bopp was obtained for the first time by Hadamcik et al. (1997) and was discussed later on in Hadamcik and Levasseur-Regourd (20 03). A recent review of all comets investigation can be found in the books by Mishchenko et al. (2010) and Kiselev et al. (2015). Comet C/2013 R1 (Lovejoy) was discovered by Terry Lovejoy (Thornlands, Queensland, Australia) with images acquired on 2013 September 7 and 8, using his 20-cm reflector and a CCD camera. Other polarimetric measurements of the comet C/2013 R1 (Lovejoy) are presented by Furusho et al. (2014) (imagine polarisation with the Subaru telescope) and by Rosenbush et al. (2014) (linear and circular polarimetric measurements and their modelling).

http://dx.doi.org/10.1016/j.pss.2015.06.012 0 032-0633/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: Borisov, G., et al., Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy). Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.06.012i


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G. Borisov et al. / Planetary and Space Science ( ) ­

2. Observations Comet C/2013 R1 (Lovejoy) was observed during a multi-instrument campaign with the 2 m Ritchey­ChrÈtien­CoudÈ (RCC) telescope of the Bulgarian National Astronomical Observatory (BNAO) Rozhen from 20 December 2013 until 07 January 2014. Because of thetargetbrightnesswecould achievearelatively high S /N ratio and obtain high accuracy of polarimetric measurements. C/2013 R1 (Lovejoy) was a new comet which approach to the inner Solar System for the first time and giving us an opportunity to investigate the pristine material from the era of the Solar System formation.

2.1. Instrumentation Polarimetric observations were performed with the 2-ChannelFocal-Reducer Rozhen (FoReRo2) (Jockers et al., 20 0 0) attached at the Cassegrain focus of the 2m RCC telescope. In polarimetric mode, FoReRo2 is equipped with a Wollaston prism, placed before a dichroic beam splitter, which splits the signals into two different channels, allowing us to re-construct polarimetric maps of extended objects in two spectral regions simultaneously, using narrow band filters. By replacing the filters with two grisms, we can perform spectropolarimetric measurements. An example of raw spectropolarimetric image can be seen in Fig. 1. Imaging polarimetry was obtained in two dust continuum filters covering wavelength intervals clear from molecular emission and centred at 4430 å and 6840 å, having a passband of 35 å, and 71 å and hereafter called IF443 and IF684, respectively (see Fig. 2).
Fig. 2. Continuum filters transmission curves (IF443 and IF684) overplotted on a comet spectrum. Table 1 Observing log. Date 20 21 22 23 24 29 30 31 03 08
a b

ra, AU 0.8132 0.8123 0.8118 0.8118 0.8122 0.8210 0.8240 0.8275 0.8405 0.8631

b, AU 0.8562 0.8765 0.8965 0.9161 0.9355 1.0305 1.0495 1.0675 1.1205 1.1865

c (deg) 72.2 71.1 70.1 69.1 68.1 63.0 62.0 61.0 58.1 54.6

Obs. mode HRSd HRS HRS HRS HRS ImPole NBFf H2O × SPolg NBF & H2O

December 2013 December 2013 December 2013 December 2013 December 2013 December 2013 December 2013 December 2013 January 2014 January 2014

×

2.2. Comet C/2013 R1 (Lovejoy) Imaging and spectropolarimetric data were obtained on December 29 and January 3 respectively, with FoReRo2. The geometrical conditions during the observations are shown in Table 1.

c d e f g

Heliocentric distance. Geocentric distance. Phase angle. High resolution spectroscopy. Imaging polarimetry. Gas and dust coma imaging in narrow band filters. Spectropolarimetry.

2.3. Data reduction All images were pre-processed through a standard bias subtraction and flat field correction. At the time of our observations, the polarimetric optics of FoReRo2 included a Wollaston prism but not a retarder waveplate, preventing us from adopting a beam-swapping technique to minimise instrumental effects (see, e.g., Bagnulo et al., 20 09). Previous experience showed that polarimetric observations with FoReRo2 were affected by non-negligible and non-constant instrumental polarisation. In an attempt to mitigate this problem, we decided to obtain observations at two instrument position angles, one with the principal plan of the Wollaston prism aligned to the scattering plan (i.e., the plan defined by the sun, the comet and the observer) and one perpendicular to it. By denoting with f and f the fluxes in the parallel and in the perpendicular beams, and with k and k the transmission functions in the parallel and in the perpendicular beam of the Wollaston prism respectively, the observed quantity is

^ Q 1 = I 2

= + 90 = ° k (I - Q ) - k (I + Q ) 1 k (I + Q ) - k (I - Q ) = - 2 k (I + Q ) + k (I - Q ) k (I - Q ) + k (I + Q )

f - f f + f PA

f - f - f + f PA



=

(k + k )2IQ - (k - k )2IQ (k + k )2I 2 - (k - k )2Q
2

where is the angle is the angle between the direction ObjectNorth Pole and the direction Object-Sun. If k k we obtain

^ Q Q . I I
where Q /I is the reduced Stokes parameter Q measured assuming as a reference direction that one perpendicular to the scattering plane. We did not measure U /I , assuming that for symmetric reasons it is probably zero. Of course, the images were combined together after a 90° rotation.

3. Results 3.1. Aperture polarimetry The aperture photometry with a circular aperture with a radius of 13 á 103 km on the comet was performed to measure the intensity of the two orthogonal polarised beams f and f . The

Fig. 1. Spectropolarimetric image of comet C/2013 R1 (Lovejoy).

Please cite this article as: Borisov, G., et al., Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy). Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.06.012i


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Fig. 3. Comparison of polarimetric measurement of comet C/2013 R1 (Lovejoy) and Kiselev database (Kiselev et al., 20 05) (error bars of our measurements are smaller than the symbols).

Fig. 5. Enhanced coma structure in IF684 (top panel) and colour map (bottom panel) compared with polarisation (overplayed contours). (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)

background was measured in the farthest possible place in the sunwards direction. The results for both continuum filters IF443 and IF684 are P443 = 17.01 ± 0.09% and P684 = 18.81 ± 0.02% respectively. Their comparison with the Kiselev database (Kiselev et al., 20 05) is shown in Fig. 3 and is in a good agreement with the data for the comet 1P/Halley at similar phase angles (65°). 3.2. Imaging polarimetry In order to investigate the spatial distribution of the linear polarisation of the light reflected from cometary dust we performed imaging polarimetry of the comet's coma. We construct polarisation maps by calculating the degree of linear polarisation, using the beam swapping technique, for each pixel in a pre-selected region around comet photo centre. The resultant polarimetric maps and radial profiles for the dust continuum filter IF684 are presented in the top and bottom panels of Fig. 4, respectively. Due to the low signal-to-noise ratio, the polarimetric map in IF443 does not display any remarkable structures. By contrast, the

Fig. 4. Polarisation map with a marked comet photocentre ( × ) and direction to the Sun () (top panel) and radial profiles in different directions (bottom panel) in IF684.

Please cite this article as: Borisov, G., et al., Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy). Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.06.012i


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Fig. 6. Spectropolarisation of comet C/2013 R1 (Lovejoy) and a fitted continuum polarisation.

Fig. 7. Comparison of the comet C/2013 R1 (Lovejoy) with the typical comet 1P/Halley measurements at different phase angles.

polarisation map in IF684 shows clearly a highly polarised structure apart from the nucleus. The polarisation degree in a square region 11 á 11 103 km enveloped this structure is slightly higher than that of the total jet coma, i.e., P684 = 18.83 ± 0.045% In order to investigate the nature of this structure, we first try to connect this highly polarised structure with a jet-like structure in the dust coma. Therefore we used an enhanced procedure to reveal any inhomogeneity around the nucleus caused by unsteady outflow from the nucleus. This procedure removes the average coma, modelled by fitting the radial profiles of the dust at different azimuths with a power low. Afterwards this model was subtracted and only the jet-like structure remains in the image. In the top panel of Fig. 5, such a structure is clearly visible, but it is shifted from the polarisation one, presented with overplotted contours. Next, we compared it with the distribution of the dust normalised reflectivity gradient, or the so-called reddening. That is why we construct the so-called colour map of the dust by

calculating the quantity

1 S S (1, 2 ) = , ¯ S
¯ where S = (S 2 - S 1) /2 and is usually expressed in %/1000 å, for each pixel in both dust continuum images in IF443 and IF684. The resultant colour map is presented in the bottom panel of Fig. 5. The connection between high polarisation and low reddening is clearly visible. The interpretation is that low reddening means small particles, or very dark ones, both of which give high polarisation.
3.3. Spectropolarimetry Polarisation spectrum of the comet C/2013 shown in Fig. 6. We carried out the polynomial fit to the polarisation. The result for comet 1P/Halley at angles is also presented (Kiselev et al., 20 05) and R1 (Lovejoy) is dust continuum different phase our observations

Please cite this article as: Borisov, G., et al., Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy). Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.06.012i


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We have investigated the spatial distribution of the dust in
both continuum filters. A polarisation feature in the red was found and compared with jet-like structures in the dust coma, and connected with low values in the map of the dust colour, which shows that this region is populated rather with small or very dark grains. Furusho et al. (2014) presented imaging polarisation of the comet Lovejoy with the Subaru telescope, and their results (including the detection of coma features with high polarisation values) are consistent with our results. We have obtained a spectropolarimetry of the comet and found the change of the degree of linear polarisation of the dust with wavelength. This is in a good agreement with the results obtained for comet 1P/Halley. In the C2 molecule emission band we have measured 6.0 7 1.1% degree of linear polarisation. The results deviate from the theoretical value for diatomic molecules 14.3% (Feofilov, 1961), but are in good agreement with a value measured for other comets Pmax = 7.7% (Krishna Swamy, 2010). This can be used to explain the depolarisation effect in the molecular coma.







Fig. 8. Polarisation spectrum of the C2 emission line in the coma of the comet C/2013 R1 (Lovejoy).

Acknowledgements The authors gratefully acknowledge the observing Grant support from the Institute of Astronomy and Rozhen National Astronomical Observatory, Bulgarian Academy of Sciences. G.B. and S.B. also gratefully acknowledge financial support from the COST Action MP1104 "Polarisation as a tool to study the Solar System and beyond". G.B. also gratefully acknowledges financial support from the Federation of Finnish Learned Societies and the organisers of the ACM2014. P.N. acknowledges financial support from ESF and Bulgarian Ministry of Education and Science under the Contract BG051PO0013.3.06-0047.

are very well fitted to the phase angle and wavelength trend of the comet 1/P Halley (see Fig. 7). The polarisation in molecular spectral lines is lower than that in the continuum. According to the theory of diatomic molecules it should be a constant of 1/7 (Feofilov, 1961). To estimate the polarisation of the emission lines we first subtract the continuum contribution from both spectra in the ordinary and extraordinary beams. Then, using the remaining flux from resonance fluorescence of the molecules, we calculate the degree of linear polarisation following the procedure described in Section 2.3 for each wavelength bin. The result for the main C2 molecular band is presented in Fig. 8. The average value of linear polarisation over the whole molecular band of C2 is 6.0 7 1.1%. This value is less than half that of the theoretical one, which is based on theory of anisotropic rotating oscillators. Also these values are for pure gas without the presence of other species. The theory says that polarisation of the fluorescence of diatomic molecules is reduced when foreign gases are introduced, and collisions occur, resulting in a depolarisation. Therefore we conclude that this lower value of linear polarisation in the C2 molecular band is due to collisions with other species in the comet's coma. The excitation by unidirectional natural radiation leading to linear polarisation of an emission line has a maximum polarisation value for a phase angle of 90°. The expected variation of gas polarisation with phase angle is given by the expression

References
Arago, F., 1854. Astronomie Populaire. Gide et Baudry, Paris. Bagnulo, S., Landolfi, M., Landstreet, J.D., Landi Degl'Innocenti, E., Fossati, L., Sterzik, M., 2009. Stellar Spectropolarimetry with Retarder Waveplate and Beam Splitter Devices. Publ. Astron. Soc. Pac. 121 (September), 993­1015. Feofilov, P., 1961. The Physical Basis of Polarized Emission. Consultants Bureau, New York. Furusho, R., Terai, T., Shinoda, T., Watanabe, J., 2014. C/2012 S1 (ISON), C/2013 R1 (Lovejoy), and updates of the imaging polarimetric survey. In: Muinonen, K., PenttilÄ, A., Granvik, M., Virkki, A., Fedorets, G., Wilkman, O., Kohout, T. (Eds.), Asteroids, Comets, Meteors, p. 173, July. Hadamcik, E., Levasseur-Regourd, A.C., 20 03. Dust evolution of comet C/1995 O1 (Hale­Bopp) by imaging polarimetric observations. Astron. Astrophys. 403 (May), 757­768. Hadamcik, E., Levassuer-Regourd, A.C., Renard, J.B., 1997. Ccd polarimetric imaging of comet Hale­Bopp (C/1995 O1). Earth Moon Planets 78 (July), 365­371. Jockers, K., Credner, T., Bonev, T., Kisele, V.N., Korsun, P., Kulyk, I., Rosenbush, V., Andrienko, A., Karpov, N., Sergeev, A., Tarady, V., 200 0. Exploration of the solar system with the two-channel focal reducer at the 2m-RCC telescope of Pik Terskol observatory. Kinemat. Fiz. Nebesnykh Tel Suppl. 3 (September), 13­18. Kiselev, N., Rosenbush, V., Jockers, K., Velichko, S., Kikuchi, S., 20 05. Database of comet polarimetry: analysis and some results. Earth Moon Planets 97 (December), 365­378. Kiselev, N., Rosenbush, V., Levasseur-Regourd, A.-C., Kolokolova, L., 2015. Comets. Cambridge University Press, Cambridge, UK, pp. 379­404, Chapter 22. Kolokolova, L., Hanner, M.S., Levasseur-Regourd, A.-C., Gustafson, B.å.S., 20 04. Physical Properties of Cometary Dust from Light Scattering and Thermal Emission. University of Arizona Press, Tucson, USA, pp. 577­604 (Chapter VI). Kolokolova, L., Jockers, K., 1997. Composition of cometary dust from polarization spectra. Planet. Space Sci. 45 (December), 1543­1550. Kolokolova, L., Jockers, K., Chernova, G., Kiselev, N., 1997. Properties of cometary dust from color and polarization. Icarus 126 (April), 351­361.

P ( ) =

Pmax sin2 1 + Pmax cos2

+ 2.5 From our measurements we calculate Pmax = 8. 5-1.6 % . Krishna Swamy (2010) says that the theoretical value of Pmax for the C2 and CN molecules is 7.7%, which is within our confidence interval 6.9­11.2.

4. Conclusions

We have measured the degree of linear polarisation in the
continuum filters IF443 and IF684 of the dust ejected from comet C/2013 R1 (Lovejoy), and our results (P443 = 17.01 ± 0.09% and P684 = 18.81 ± 0.02% ) are in a good agreement with measurements of the typical comet 1P/Halley.

Please cite this article as: Borisov, G., et al., Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy). Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.06.012i


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G. Borisov et al. / Planetary and Space Science ( ) ­ æhman, Y., 1941. Measurements of polarization in the spectra of comet Cunningham (1940 C) and comet Paraskevopoulos (1941 C). Stockh. Obs. Ann. 13, 11. Rosenbush, V., Ivanova, A., Kiselev, N., Afanasiev, V., Kolesnikov, S., Shakhovskoy, D., 2014. Linear and circular polarimetry of recent comets: observational results for eight comets. In: Muinonen, K., PenttilÄ, A., Granvik, M., Virkki, A., Fedorets, G., Wilkman, O., Kohout, T. (Eds.), Asteroids, Comets, Meteors, p. 450, July.

Krishna Swamy, K.S., 2010. Physics of Comets. World Scientific Publishing Co. Pte. Ltd., Singapore. Mishchenko, M.I., Rosenbush, V.K., Kiselev, N.N., Lupishko, D.F., Tishkovets, V.P., Kaydash, V.G., Belskaya, I.N., Efimov, Y.S., Shakhovskoy, N.M., 2010. Polarimetric Remote Sensing of Solar System Objects. Akademperiodyka, Kyiv. æhman, Y., 1939. On some observations made with a modified Pickering polarigraph. Mon. Not. R. Astron. Soc. 99 (June), 624.

Please cite this article as: Borisov, G., et al., Imaging polarimetry and spectropolarimetry of comet C/2013 R1 (Lovejoy). Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.06.012i