Experimental Phase Function and Degree of Linear Polarization of Cometary Dust Analogs

MNRAS 000, 000–000 (2018) Preprint 12 February 2019 Compiled using MNRAS LATEX style ﬁle v3.0

Experimental phase function and degree of linear polarization of cometary dust analogs

E. Frattin,1,2? O. Mu˜noz,3,4 F. Moreno,3 J. Nava,5 J. Escobar-Cerezo,6 J. C. Gomez Martin,3 D. Guirado,3 A. Cellino,7 P. Coll,8 F. Raulin,8 I. Bertini,1 G. Cremonese,2 M. Lazzarin,1 G. Naletto, 9,10,11 F. La Forgia 1. 1 University of Padova, Department of Physics and Astronomy ”G. Galilei”, Vicolo dell’Osservatorio 3, 35122 Padova, Italy 2 INAF, Astronomical Observatory of Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy 3 Instituto de Astrof´ısica de Andaluc´ıa, CSIC, Glorieta de la Astronomia s/n, E-18008 Granada, Spain 4 Advanced Optical Imaging Group, School of Physics, University College Dublin, Dublin, Ireland 5 University of Padova, Department of Geosciences, Via G.Gradenigo 6, 35131 Padova, Italy 6 Department of Physics, University of Helsinki, Finland 7 INAF-Astrophysical Observatory of Torino, strada Osservatorio 20, Pino Torinese (TO) 8 Laboratoire Inter-Universitaire des Systemes Atmospheriques, Universites Paris 12-Paris 7, CNRS 9 University of Padova, Department of Physics and Astronomy ”G. Galilei”, Via Marzolo 8, 35131 Padova, Italy 10 University of Padova, Center of Studies and Activities for Space (CISAS) ”G. Colombo”, Via Venezia 15, 35131 Padova, Italy 11 CNR-IFN UOS Padova LUXOR, Via Trasea 7, 35131 Padova, Italy

Accepted 2018 December 22. Received 2018 December 20; in original form 2018 July 19.

ABSTRACT We present experimental phase function and degree of linear polarization curves for seven samples of cometary dust analogues namely: ground pieces of Allende, DaG521, FRO95002 and FRO99040 meteorites, Mg-rich olivine and pyroxene, and a sample of organic tholins. The experimental curves have been obtained at the IAA Cosmic Dust Laboratory at a wavelength of 520 nm covering a phase angle range from 3◦ to 175◦. We also provide values of the backscattering enhancement (BCE) for our cometary analogue samples. The final goal of this work is to compare our experimental curves with observational data of comets and asteroids to better constrain the nature of cometary and asteroidal dust grains. All measured phase functions present the typical behavior for µm-sized cosmic dust grains. Direct comparison with data provided by the OSIRIS/Rosetta camera for comet 67P Churyumov-Gerasimenko reveals significant differences and supports the idea of a coma dominated by big chunks, larger than one micrometer. The polarization curves are qualitatively similar to ground-based observations of comets and asteroids. The position of the inversion polarization angle seems to be dependent on the composition of the grains. We find opposite dependence of the maximum of the polarization curve for grains sizes in the Rayleigh-resonance and geometric optics domains, respectively. Key words: meteorites – comets – scattering arXiv:1901.05975v2 [astro-ph.EP] 11 Feb 2019

1 INTRODUCTION orbiting around the Sun as a product of the disintegration of comets and asteroidal collisional cascading (the Zodiacal Dust is a fundamental constituent of planetary systems in Cloud), as well as in the rings of the giant planets. In all their stages of development. For example, the origin addition, dust is present in the regolith surfaces of planets, of planetary systems involves a phase of aggregation of asteroids and comets, and in dense atmospheres (e.g. Venus, submicron-sized dust grains by streaming instability into the Earth, Mars, Titan) in the form of aerosol. Because protoplanetary disks (Johansen and Youdin 2007; Blum of the ubiquity of dust and its involvement in countless et al. 2014; Blum and Wurm 2008). In our mature Solar physical phenomena, from atmospheric radiative transfer System, dust can be found in the interplanetary medium to cometary activity through the tracing of Solar System primitive materials, it is important to study its nature and properties. ? E-mail: [email protected]

Comets are the most appropriate targets to study the early dust features corresponding to specific observables (Liu Solar System, since they are among the most pristine ob- et al. 2015; Zubko 2015; Escobar-Cerezo et al. 2017). jects orbiting the Sun. Because of their low-velocity, gentle All these different approaches (observations, laboratory accretion process, some of their most primitive constituents experiments and theoretical simulations) provide essential (the grains) have remained intact, i.e. as they were when the contributions to the investigation of the behavior of dust comets formed (Fulle et al. 2016). During their passage at particles as radiation scatterers. perihelion, these objects release refractory materials driven by the sublimation of trapped ices, generating a bright dust In this work we present experimental phase function coma dominated by µm-sized particles composed of silicate and degree of linear polarization curves as functions of the minerals and organics. Comets unveil the composition of observational phase angle of a selected set of cometary the primordial material from which they accreted, namely dust analogs: four meteoritic samples, two minerals (Mg- material located in the outer regions of the Solar System, rich olivine and pyroxene), and a sample of organic par- and put some constraints to the processes involved in its ticles (tholins). Light scattering measurement have been origin. The flyby missions that first revealed the nature of performed at the Cosmic Dust Laboratory (CODULAB) cometary dust with in-situ measurements were the Giotto (Muñoz et al. 2011) at the Instituto de Astrof´ısica de An- (Reinhard 1986) and Vega (Sagdeev et al. 1986) missions to daluc´ıa (IAA), spanning a phase angle range from 3◦ to 175◦ 1P/Halley in 1986. The ’Halley Armada’ was followed up at a wavelength of 520 nm. We combine the new measure- by the Deep Space 1 mission to comet 19P/Borrelly in 2001 ments presented in this work with the scattering matrices (Soderblom et al. 2002). A major breakthrough came with at 442 nm and 633 nm of a sample of the Allende mete- the Stardust mission flyby of comet 81P/Wild in 2004 (Hörz orite and of size-segregated Mg-rich olivine samples that et al. 2006), and subsequent return to Earth of samples of have been previously presented by Muñoz et al.(2000). Fi- dust collected directly from the coma of the comet. Later, nally, we compare the experimental data with observations missions to comet 9P/Temple in 2005 (Deep Impact) 2005 of asteroids and cometary dust envelops, with special em- (A’Hearn et al. 2005) and to comet 103P/Hartley in 2010 phasis on the observations of 67P by Rosetta, in order to (EPOXI) (A’Hearn et al. 2011) provided new insights of put constraints on the nature of cometary dust. these two objects. More recently, the Rosetta mission has been able, for the first time, to follow the trajectory of the cometary nucleus and observe its evolution during 2 LIGHT SCATTERING THEORY its trajectory before and after perihelion. The coma of comet 67P/Churyumov-Gerasimenko (hereafter 67P) was A beam of quasi-monochromatic light is physically defined observed during two entire years (2014-2016) from the very by the Stokes vector I = {I, Q, U, V}, where I is proportional inside, reaching distances of few km from the nucleus. The to the total flux of the light beam and Q is related to the astonishing images obtained by the OSIRIS instrument on linear polarization of the light beam, representing the dif- board the spacecraft have shed new light into the properties ference between the two components of the flux along the of cometary dust (Sierks et al. 2015) . There is now evidence x-axis and the y-axis. U is defined by the difference of the that 67P formed by gentle accretion of pebbles smaller than two components of the flux along the directions rotated by 1 cm at velocities of the order of 1 m/s (Fulle and Blum 45◦ from the x and y axis. V is related to the circular po- 2017). Moreover, photometric analysis of the overall coma larization, defined as the difference between the left-handed and single grains reveal that the majority of the material and the right-handed polarized components of the flux. has similar spectral properties to those of nucleus surface The interaction between a light beam and a cloud of par- (Frattin et al. 2017), which enables using the dust coma as ticles results in scattering of the incident light. The Stokes a proxy indicator of nucleus properties. vector of the scattered beam Isc is related to the one of The sunlight incident on a cometary dust envelope is the incident beam Iin by the so-called scattering matrix F, partly absorbed and partly scattered by the particle cloud. through the following expression: Spacecraft and ground based observations of scattered light show characteristics strictly dependent on the nature Isc F11 F12 F13 F14 Iin © ª λ2 © ª © ª and physical properties (composition, size distribution, Qsc® F21 F22 F23 F24® Qin® ® = ® ®, (1) shape, roughness, etc) of the material composing the coma. Usc ® 4π2D2 F31 F32 F33 F34® Uin® V F F F F V Since each material has characteristic scattering signatures, « sc ¬ « 41 42 43 44¬ « in ¬ scattering theory can be used to interpret observations where λ is the wavelength of the incident beam and D is the and retrieve from them some of the properties of the distance of the detector from the particles. The 16 dimen- dust. Experimental data of the angular distribution of sionless elements of the matrix depend on physical charac- the scattered intensity and degree of linear polarization of teristics of the particles such as their number, shape, dimen- clouds of cosmic dust analogs assist in the interpretation of sion (through the size parameter x = 2πr/λ) and refractive in-situ and remote sensing observations. Since these quan- index, as well as on geometrical parameters such as their tities are intimately related to the nature of the particles, orientation in the space and scattering direction. laboratory data are used as a reference for comparison When the particles are randomly oriented all scattering and interpretation, allowing a correct analysis of the planes are equivalent. Therefore, the scattering direction is observational data (Muñoz et al. 2000; Volten et al. 2006; fully described by the scattering angle, θ, defined by the Muñoz et al. 2017). Modeling of the interaction between angle between the directions of propagation of the incident electromagnetic radiation and particles in turn, supports and scattered beams. To facilitate direct comparison with the experiments, helping to discriminate unambiguously astronomical observations of comets and asteroids we use

MNRAS 000, 000–000 (2018) Scattering of cometary dust analogs 3

Figure 1. Size distribution of samples of Allende meteorite, Figure 2. Size distribution of two different samples of DaG521, Forsterite and Enstatite. FRO95002 and FRO99040. the phase angle, α = 180◦ − θ, throughout the text. Further- steps of 5◦ within the 10◦ −20◦ and 40◦ −175◦ ranges, and in more, when the particles present mirror symmetries, and are steps of 1◦ within the 3◦−10◦ and 25◦−40◦ ranges. Sinusoidal randomly oriented, the scattering matrix has 6 parameters electro-optic modulation combined with lock-in detection al- (van de Hulst 1957): lows determining all elements of the scattering matrix from eight different configurations of the optical components (eq. F F 0 0 11 12 1) and the assumption of reciprocity of the sample (see fur- ©F F 0 0 ª F = 12 22 ® (2) ther details in Muñoz et al.(2010)). In order to keep the 0 0 F F ® 33 34® scattered intensity within the linearity range of the detec- 0 0 −F F « 34 44¬ tor, a wheel of neutral density filters is placed between the laser head and the polarizer, which allows adapting the beam intensity to the scattering behavior of the aerosol sample at each particular angle. A second photomultiplier placed at 3 EXPERIMENTAL APPARATUS a fixed angle, the monitor, corrects for fluctuations in the The CODULAB facility is dedicated to measuring the el- aerosol beam. For each position of the detector, 1000 mea- ements of the scattering matrix (eq.1 and2) as a func- surements are conducted in about 2 seconds. The final value tion of the scattering angle of clouds of randomly oriented at each phase angle is obtained from the average of such cosmic dust analogs. This is achieved by means of a gonio- measurements, with an associated error given by the stan- nephelometer that has been described in detail previously dard deviation. Three measurement runs are carried out for by Muñoz et al.(2010). In the experiments carried out for each optical configuration in order to achieve further noise this work we employed an Argon-Krypton laser tuned to reduction. Due to the limited amount of material, we did 520 nm as our light source. The laser beam passes through not measure the complete scattering matrix but only the el- a polarizer and an electro-optic modulator before encounter- ements F11 and F12. For unpolarized incident light the F11 is ing a jet stream of randomly oriented particles produced by proportional to the scattered flux. The measured values of an aerosol generator (Muñoz et al. 2011). The powder under the F11 are arbitrarily normalized so that they are equal to ◦ analysis is contained in a cylindrical reservoir, and is pushed 1 at α = 150 . The F11 normalized in this way is called the by a piston in a controlled manner towards a rotating brush, phase function. The −F12/F11 ratio (where the value of F11 which disperses the particles into a flow of air which carries is not normalized) is equal to the degree of linear polariza- them trough a nozzle to the scattering volume. The parti- tion, P, for unpolarized incident light, expressed in terms of cle density in the scattering volume, which is controlled by Stokes parameters as P = −Qsc/Isc. the speed of the piston, must be high enough to produce a detectable scattering signal, but low enough to avoid multiple scattering. In this way it better approximates the low 4 MATERIALS density cometary coma. The scattered light passes through optional optics before being detected by a photomultiplier, We have selected four Carbonaceous Chondrites (CCs), the detector, which is mounted on a 1 m ring rail centered at two silicate minerals and one organic powder as sources the aerosol jet. In the measurements presented in this paper of cometary dust analogs. Bulk samples of the meteorites we have covered the phase angle range from 3◦ to 175◦ in DaG521, FRO95002 and FRO99040 were provided by the

MNRAS 000, 000–000 (2018) 4 E. Frattin et al.

(a) (b)

(e) (f)

Museo dell’Antartide Felice Ippolito, Siena especially for describe the bulk properties of these materials, the meth- this work. Batches of particulate tholins were synthesized ods employed to obtain particulate samples suitable for our at the Laboratoire Inter-Universitaire des Systemes Atmo- light scattering experiments, and the physical properties of spheriques (LISA), Paris. The Allende, olivine, and pyroxene the particles (optical constants, size distribution and mor- samples belong to the IAA-CODULAB collection and have phology). been used in a previous work (Mu˜noz et al. 2000). Below we

MNRAS 000, 000–000 (2018) Scattering of cometary dust analogs 5

(g) (h)

(i) (j)

(k) (l)

Figure 3. FESEM micro-photographs of enstatite (plates a and b), forsterite (plate c), Allende (plate d), DaG521 (plates e and f), FRO95002 (plates g and h), FRO99040 (plates i and j) and tholins (plates k and l).

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CO CV Allende DaG521 and Allende The meteorites DaG521 (Dar al Gani 521, found in Lybia in 1997 (Grossman 1999)) and Si 15.8 16.0 16.0 Allende (fallen near Parral, Chihuahua, Mexico, in 1969) Ti 0.08 0.15 0.10 are classified as CV3. CVs chondrites are characterized by large mm-sized chondrules, large refractory inclusions and Al 1.58 2.19 1.79 abundant matrix (40 %vol). They are divided into oxidized Cr 0.36 0.35 0.37 CVOX and reduced CVRED subgroups based on abundances of metal, magnetite and Ni content (McSween 1977). The Fe 24.3 23.1 23.9 main component of CV matrices is Fe-rich olivine (fayalite Mn 0.18 0.15 0.15 Fa∼30-60 and in some cases Fa>90), but there are substan- tial differences among the subgroups due to different late Mg 14.4 14.4 15.0 stage metasomatism and aqueous alteration (Krot et al. Ca 1.62 2.5 1.89 1995, 1998). Other mineral constituents are Ca-Fe-pyroxene, andradite, Fe-Ni sulfides and magnetite. Some chemical and K 0.05 0.03 0.03 textural features of the CV chondrites evidence a phase in S 1.94 1.63 1.77 which the parent body experienced temperatures <300◦C (Krot et al. 1998). P 0.11 0.13 0.10 DaG521 is the only meteorite of our set with reddish colour, Na 0.35 0.35 0.33 probably due to iron oxide generated by weathering in the Lybian desert. Ni 1.31 1.11 1.23 Allende is classified as CVOX. This group displays Calcium- O 37.9 37.9 37.2 Aluminum-rich Inclusions (CAIs) and ameboid olivine refractory elements and this suggests they have been formed at high temperature during the early stages of Solar Sys- Table 1. Mean composition of CV and CO chondrites and of tem formation. A recent discovery of a class of asteroids the Allende meteorite in %wt, taken from the meteorite database (the so-called Barbarians) seems to have a composition un- METDB (Nittler et al. 2004). usually enriched in CAI minerals, like spinel (Cellino et al. 2014). Allende differs from other CVOX meteorites in its lower matrix-chondrule ratio and in having chondrules with more opaque minerals (Brearley and Jones 1998).

4.1 Bulk materials description FRO95002 and FRO99040 These two meteorites were found in Antarctica, in the region of the Frontier Moun- 4.1.1 Meteorites tain in 1995 and 1999, respectively. Both belong to the CO3 Carbonaceous Chondrites meteorites are among the oldest class, which presents similar characteristic of CV3 regarding and most primitive materials in the Solar System. Age chondrules and matrix abundance, but differ in the chon- determination techniques indicate that they formed around drule dimensions, which in the CO3 case are µm-sized. The 4.5 Gyr ago (Chen and Wasserburg 1981; Mahnes et al. CO chondrites are all of petrologic type 3, showing slightly 1987). Since they are very old, these rocks suffered different different metamorphic stages, ranging from 3.0 to 3.7 (Mc- primary processes, which record pre-accretionary histories Sween 1977). CO chondrites usually have low Fe composi- in the solar nebula, and secondary processes like aqueous tions with olivine with Fa<1 (Brearley and Jones 1998). Also alteration, thermal metamorphism and shock metamor- Fe-pyroxenes are rare, only a few pyroxenes with Fs∼10 are phism (Brearley and Jones 1998). reported (Brearley and Jones 1998). CCs are divided in several classes based on composition: CI, CH, CO, CV, CK, CR. Most of them are fragments of 4.1.2 Minerals primitive asteroids. They come from the NEO population, which includes about 10% of extinct comets, in addition to The first hint of the presence of silicates in the cometary former asteroids (DeMeo and Binzel 2008). dust dates back to the observation of the emission feature The bulk composition of the Carbonaceous Ivuna (CI) group at 10 µm in comet Bennett and its consequent labora- of chondrites is very close to the composition of the solar tory modeling (Maas et al. 1970). The measurements of photosphere. Furthermore, interstellar grains that predate 1P/Halley mineralogical composition revealed Mg-rich the Solar System formation are found in the matrix of these olivine (forsterite) and pyroxene (enstatite) as dominant primitive chondrites (Brearley and Jones 1998). CCs are compounds from in-situ mass spectra of particles provided characterized by chondrule sizes ranging from 1 mm in the by Giotto and Vega Spacecraft (Schulze et al. 1997). CV group down to around 0.15 mm and 0.02 mm in the CO Crystalline forsterite and enstatite have been detected also and CH groups, respectively. The CV and CO chondrites on comet Hale-Bopp (Crovisier et al. 1997) and 9P/Tempel have the highest abundances of refractory inclusions, while from space-based infrared spectra (Lisse et al. 2007) and on CR and, above all, CH chondrites have the highest content 81P/Wild2 from direct measurement of particles collected of metals (Brearley and Jones 1998; Weisberg et al. 2006). by Stardust mission (Zolensky et al. 2006). These silicates In Tab.1 we report the mean composition of CO and CV are predicted by thermodynamic models to condense in chondrites and of the Allende meteorite (Nittler et al. 2004). a hot gas at 1200-1400 K, while the reaction with Fe occurs only at lower temperature. Thus, the preponderance

MNRAS 000, 000–000 (2018) Scattering of cometary dust analogs 7 of Mg-rich silicates in cometary dust can be explained Sample Refractive Index Appearance by direct condensation in the inner primordial nebula DaG521 1.65 + i10−3 reddish (Hanner and Bradley 2004). The olivine and pyroxene samples used in this work have respectively the composition FRO99040 1.65 + i10−3 dark grey Mg1.85Fe0.14SiO4 and Mg0.85Fe0.08Si0.99O3, and are FRO95002 1.65 + i10−3 dark grey therefore close to the Mg-rich endmembers, i.e. forsterite and enstatite. Thus, in the following we will refer to the Allende 1.65 + i10−3 dark grey olivine and pyroxene samples as forsterite and enstatite. Forsterite . i −5 white The forsterite sample is the one identiﬁed as ’Olivine S’ in 1 62 + 10 Mu˜noz et al.(2000). Enstatite 1.58 + i10−5 white

Tholins 1.35 + i2.3 · 10−2 dark

4.1.3 Organics Table 2. Refractive index of each sample and their relative appearance. Tholins are organic compounds generated by irradiation (solar UV, high energy particles, electrons) of mixtures of com- FRO95002M with diameters, d, in the range 53 µm < d < mon compounds of carbon, oxygen and nitrogen, e.g. CO2, 71 µm. The fractions of DaG521M and FRO99040M that CH4 and HCN (Sagan and Khare 1979). They are thought to be present on the surfaces and/or in the atmospheres of passed through the 53 µm sieve were subsequently sieved several Solar System bodies. For example, they are likely through a 45 µm sieve producing subsamples DaG521S and responsible for the reddish color of many objects such as FRO99040S (45 µm < d < 53 µm). Not enough material of Pluto (Gladstone 2016) and Ceres (Combe et al. 2017), and FRO99040M was left to produce a further sample. A similar are believed to be responsible for Titan’s atmospheric haze sieving procedure was used to produce the olivine samples (Brasséet al. 2015). described by Muñoz et al.(2000). Analysis of 1P/Halley dust mass spectra indicated for the As far as the organic sample is concerned, after their first time the existence of CHON particles in comets (Kissel synthesis, the tholins were kept in gas proof vials un- and Krueger 1987). The complex nature and variety of order dry N2 atmosphere, to avoid their chemical evolution. ganics in cometary dust was revealed by analysis of sam- Just before measurements with CODULAB the tholins were ples returned from 81P/Wild, obtained by Stardust (Clemett first homogenized with a mortar to break the agglomerates et al. 2010; Sandford et al. 2006; Matrajt et al. 2008). and sieved to obtain an homogeneous powder. Then, these More recently, the in situ analysis of 67P coma dust by tholins were introduced into the cylindrical stainless steel COSIMA/Rosetta mass spectrometer has confirmed the tank of the aerosol generator. presence of abundant high-molecular weight organic matter, nearly 50% in mass (Bardyn et al. 2017; Fray et al. 2017). Thus, the abundance of CHON compounds in cometary dust 5 RESULTS AND DISCUSSION suggests that tholins are likely to form in this environment as 5.1 Sample characterization well. Tholins have been previously used in laboratory studies as cometary dust simulants, often mixed with other compo- 5.1.1 Refractive index nents, typically silicates and ices (Poch et al. 2016a,b; Jost The refractive index of a medium is defined as: et al. 2017). √ The tholins sample used in this work was synthesized us- m = c µ = n + ik (3) ing the PLASMA experimental setup described previously by Brasséet al.(2017). It allows the production and sam- where is the electric permittivity, µ is the magnetic permeability and c the speed of light in vacuum. The pling of tholins from N2-CH4 electron irradiation in a glove box without contamination by the air of the laboratory. The optical constants n and k represent, respectively, the phase velocity of the wave in the medium and the absorption elemental composition of these tholins has been determined coefficient of the material. (Brassé 2014). They are carbon rich (C/N = 2.2 to 2.4) with a C/H of 0.7 to 0.8. Several grams of tholins were prepared Estimates of the refractive indices of our samples to perform the CODULAB measurements. are compiled in Table2. The refractive indices of forsterite and enstatite (Dorschner et al.(1995)) have been obtained from the Jena-St. Petersburg Database of Optical Constants (http://www.astro.uni- 4.2 Sample preparation jena.de/Laboratory/Database/jpdoc/index.html). The In order to obtain particulate samples with different size refractive index of tholins at 532 nm has been reported distributions within the typical size range of cosmic dust by Hasenkopf et al.(2010); for a detailed analysis of the particles, the DaG521, FRO95002 and FRO99040 samples tholins optical properties see Brasséet al.(2015). were milled and dry-sieved at the Department of Geoscience The refractive indexes of the Allende, DaG521, FRO99040, of the University of Padua. After milling, the three sam- and FRO95002 meteorite samples are unknown. Therefore, ples were first size-segregated using a 71 µm sieve. The we have assumed estimates based on literature values of fraction of sample that passed through the sieve was subse- the main constituents. The imaginary part of the refractive quently sieved using a 53 µm sieve. This procedure generated index of the terrestrial samples is significantly smaller three subsamples designated as DaG521M, FRO99040M and than that of the meteorites and tholins, which indicates

MNRAS 000, 000–000 (2018) 8 E. Frattin et al.

inversion angle of polarization of asteroid (234) Barbara as a consequence of the imaginary refractive index, in turn a consequence of the presence of nano-iron phase particles.

5.1.2 Size distribution The size distributions of our samples have been estimated using a low angle laser light scattering (LALLS) particle sizer (Malvern Mastersizer 2000, Rawle(1993)). The LALLS method relies on the measurement of the phase function of samples dispersed in a carrier fluid at 633 nm within a range of low scattering angles (0.02◦-30◦). The volume distribution of equivalent spherical particles that best reproduces the observed phase function is obtained by inverting a light scattering model based on Mie theory, which requires know- ing the complex refractive index of the samples (eq.3). Since the refractive indexes of our meteorite samples are unknown, we have carried out a sensitivity study of the impact on the retrieved size distributions of varying n and k within wide ranges. In these sensitivity tests we have used as reference value the estimated refractive index for the Allende mete- Figure 4. Phase functions of all samples at 520 nm. The inset orite (m = 1.65, k = i0.001)(Muñoz et al. 2000). First, the shows a zoom-in of the backscattering region. imaginary part of the refractive index, k, was fixed to the reference value (k = 0.001). The value of real part, n, was then varied between 1.5 and 1.7 in steps of 0.05. Second, the real part was fixed to the reference value (n = 1.65), and the imaginary part, k, was varied from 10−5 to 10−1 in factor of 10 steps. Artifacts are found in the retrieved size distributions in the small size range (r < 1 µm) when low values of the real part (n = 1.5; n = 1.55) or extreme values of the imaginary part (k = 10−5; k = 10−2; k = 10−1) are assumed. Therefore, we consider the reference value n = 1.65 + i0.001 as a reasonable estimate of the refractive index of our meteorite samples. In spite of the sieving procedure described in Section 4.2, the meteorite samples show broad size distributions with volume equivalent radii ranging from 0.3 µm to ∼ 100 µm. Figs.1 and 2 show the S(logr) size distributions of the samples. Here, S(logr) is the projected-surface-area for a volume equivalent sphere with radius r. Size distributions are commonly characterized by the effective radius ref f and effective variance vef f as defined by Hansen and Travis(1974). These parameters have a straightforward interpretation for mono-modal distributions, while for multi-modal distributions, the ref f and vef f are only first order indicators of the particles size. For example, the DaG521M and FRO99040M samples show Figure 5. Polarization curve of all samples at 520 nm. The inset bi-modal size distributions with secondary peaks at ∼ 30 µm shows a zoom-in of the inversion angle region. and ∼ 20 µm, respectively. Due to the limited amount of the tholins sample, we could not measure its size distribution. Based on the SEM images a smaller absorbance of these materials, consistent with (Figs.3k and3l) we can estimate a broad size distribution their light colour. By contrast, the meteorite powders are with sizes ranging from sub-micron up to hundred of mi- darker as a result of the higher bulk Fe content and organic crons. components. It should be kept in mind that the refractive index generally depends on the wavelength of the incident light. While the 5.1.3 Morphology Mg-rich forsterite and enstatite present a flat wavelength dependence in the visible, the Fe content of the meteorite Fig.3 shows Field Emission Scanning Electron Microscope samples is expected to produce an effect on the refractive (FESEM) images of our samples. It can be seen that in all index at different visible wavelengths. This fact has been cases the particles present a wide variety of irregular shapes. recently taken into account by Devogèle et al.(2018) Figs.3a -3d show that the enstatite, forsterite and Allende to interpret the observed wavelength dependence of the meteorite particles present sharp edges and relatively clean

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Figure 6. Measured degree of linear polarization curves for Allende meteorite (circles), forsterite (triangles), and enstatite (stars) at three diﬀerent wavelengths 442 nm (left panel), 520 nm (center panel), and 633 nm (right panel).

Sample re f f (µm) ve f f Pmin(%) αmin(deg) α0(deg) Pmax (%) αmax (deg) h(%/deg)

DaG521S 3.58 1.96 −3.3 ± 0.7 15 ± 5 32 ± 1 11.3 ± 0.91 80 ± 5 0.24

DaG521M 8.69 2.43 −4.9 ± 1.6 20 ± 5 34 ± 1 12.6 ± 1.4 75 ± 5 0.31

FRO95002M 3.92 2.72 −3.9 ± 0.1 20 ± 5 35 ± 1 10.0 ± 0.3 85 ± 5 0.20

FRO99040S 3.68 1.72 −3.3 ± 0.3 20 ± 5 33 ± 1 10.1 ± 0.3 80 ± 5 0.21

FRO99040M 5.90 3.10 −3.5 ± 0.6 20 ± 5 34 ± 1 10.7 ± 0.1 90 ± 5 0.19

Forsterite 3.06 1.04 −3.1 ± 0.3 15 ± 5 30 ± 1 9.9 ± 0.2 75 ± 5 0.22

Enstatite 3.70 3.13 −2.1 ± 0.3 15 ± 5 26 ± 1 11.3 ± 0.2 85 ± 5 0.19

Allende 2.44 3.42 −3.3 ± 0.3 22 ± 1 36 ± 1 7.5 ± 0.2 85 ± 5 0.15

Tholins -- −6.7 ± 1.5 15 ± 5 35 ± 1 19.1 ± 3.3 90 ± 5 0.35

Table 3. Polarimetric parameters of the samples. re f f and ve f f are the eﬀective radius and eﬀective variance. Pmin is the minimum of polarization and αmin the relative phase angle. Pmax is the maximum of polarization at phase angle αmax and α0 is the inversion angle. h(%/deg) is the slope of the polarization curves computed between αmax and α0. Tholins measurements were taken in the red domain, at λ = 632nm.

flat surfaces compared with the other samples. The DaG521, very elongated particles of the order of 10 µm with layered FRO95002 and FRO99040 particles (Figs.3e -3j) present substructure and sub-µm surface roughness (Figs.3k -3l). more rounded shapes with rough surfaces covered by a layer of small particles. These morphological differences could be partially caused by the powder preparation method. The 5.2 Measurements dry-sieving procedure could not remove small particles that remained stuck on the surface of the large particles by elec- In this section we present the measured phase functions trostatic forces. By contrast, the enstatite, forsterite and F11(α) (Fig.4) and degree of linear polarization for unpolar- Allende meteorite samples underwent wet-sieving, which re- ized incident light P(α) = −F12(α)/F11(α) (Fig.5) for all sam- moved a large fraction of the finest particles from the original ples studied in this work. The measurements were performed sample. For this reason the grain surfaces appear generally at a wavelength of 520 nm covering the phase angle range ◦ ◦ smoother than for the other samples. Tholins show pecu- from 3 to 175 . As mentioned, the measured phase func- ◦ liar structures due to the synthesis process that produced tions are normalized to unity at α = 150 . The experimental phase function and polarization curves are freely available in the Amsterdam-Granada Light Scattering Database

MNRAS 000, 000–000 (2018) 10 E. Frattin et al.

(www.iaa.es/scattering) under request of citation of this paper and Muñoz et al.(2012). The light scattering behavior of the samples considered in this work is qualitatively similar to that of other types of irregular mineral dust investigated in the laboratory (see Muñoz et al.(2012) and references therein). The measured phase functions show a strong peak at large phase angles, a plateau with almost no structure at intermediate angles and a moderate increase at small phase angles. Fig.4 does not reveal large differences between samples. The measured P curves display the typical bell-shape with a small negative branch starting at an inversion angle, α0 and reaching a minimum at αmin (Fig.5). The wide ◦ ◦ positive branch has a maximum Pmax at αmax = 75 − 90 . These polarization curves are also similar to those observed by remote sensing for a variety of Solar System objects such as comets and asteroids. In contrast to the phase functions, the polarization curves of our samples do show significant variability. Table3 summarizes the main parameters of the degree of linear polarization curve in the region of minimum polarization (Pmin, αmin), inversion angle (α0), and maximum polarization (Pmax, αmax). Figure 7. Measured degree of linear polarization curves for the Among our samples, tholins show the highest maximum DaG521S (blue symbols) and DaG521M (magenta symbols) samples at 520 nm. values of linear polarization (Pmax = 19%) and the deepest negative branch (Pmin = −6.7%). Note that the empirical relationship known as Umov’s effect indicates an inverse relationship between the maximum value of polarization and enhancing the intensity. The linear polarization reflects this the geometric albedo (Zubko et al. 2011), and tholins are effect as well, inverting the plane of wave polarization and indeed the darkest material considered in this study. How- favoring the parallel component of electromagnetic wave to ever, for a cloud of irregular particles in single scattering be scattered, rather than the perpendicular one. The role conditions the interrelation between Pmax and the geometric of coherent backscattering in the development of a negative albedo is dependent on the size distribution of the particle polarization branch and a backscattering enhancement in cloud (Zubko et al. 2017, 2018). Thus, the Allende meteorite the phase function has been discussed by Muinonen et al. sample, which has the smallest effective radii, also presents (2012) using the exact method known as the superposition the lowest maximum of the degree of linear polarization in T-Matrix (Mackowski and Mishchenko 1996). spite of its dark color. Interestingly, the polarization curve of the Allende sample has a distinct feature compared to the The origin of the negative branch of clouds of particles pure silicate samples, showing a shoulder near α = 150◦ at in single scattering conditions and corresponding particu- all wavelengths (see Fig.6). The measured values of α0 range late surfaces has also been investigated in several laboratory from 26◦ for enstatite to 36◦ for the Allende sample. We do studies (e.g. Shkuratov et al.(2006, 2007); Escobar-Cerezo not find a clear relation between size distribution and posi- et al.(2018)). In a recent work, Escobar-Cerezo et al.(2018) tion of the inversion angle. By contrast, for the range of sizes compare the scattering behavior of two samples of the same of our samples, the location of the inversion angle seems to lunar simulant with different size distributions. The effect be dependent on the composition. Terrestrial materials con- of removing particles smaller than ∼ 1 µm from the pristine sisting of pure non-absorbing minerals show lower inversion sample on the polarization curve is noticeable. The maxi- angles than the meteorites and tholins, which present iron mum of the linear polarization increases by a factor of 1.5. and organic material in different proportions. Apparently the small particle fraction of the pristine sample A fully satisfactory explanation of the negative branch was limiting the maximum of the degree of linear polar- of the linear polarization curve is still missing. Numerous ization. Further, the negative polarization branch (absolute Solar System objects such as cometary comae or asteroids values) is decreased from 2.4% to 0.8% after removing par- and satellites, which are covered by a thick regolith layer, ticles smaller than 1 µm. This result seem to indicate that show this feature. Even quite small asteroids, for which sub-micron scale features might be responsible for the neg- we might assume that the surface regolith layer is thinner, ative branch of the degree of linear polarization. generally exhibit the same general polarimetric behaviour In summary, it is quite difficult to disentangle all the ef- as larger asteroids. fects responsible for the polarization curve shape, we can In principle, each powdered material should produce only highlight some empiric relations, but it is essential to negative values of polarization at low phase angles, when further investigate the subject. In sections 5.3 and 5.4 the coherent backscattering by small particles is considered. differences observed in the phase function and degree of lin- This physical effect results from the interference of wavelets ear polarization are discussed in terms of different physical scattered by the particulate medium. At zero phase angle properties (size, color, shape), in order to investigate their the wavelets are in phase and they combined positively influence on the scattering behavior of the samples.

MNRAS 000, 000–000 (2018) Scattering of cometary dust analogs 11

( ) syn( ◦) syn( ◦) Sample re f f µm ve f f xe f f F11 0 F11 30 BSE (520 nm) DaG521S 3.58 1.96 43.3 0.384 0.191 2.01

DaG521M 8.69 2.43 105.0 0.419 0.214 1.96

FRO95002M 3.92 2.72 47.4 0.390 0.201 1.94

FRO99040S 3.68 1.72 44.5 0.612 0.270 2.27

FRO99040M 5.90 3.10 71.3 0.427 0.203 2.10

Forsterite 3.06 1.04 37.0 0.384 0.197 1.95

Enstatite 3.70 3.13 44.7 0.369 0.188 1.96

Allende 2.44 3.42 29.5 0.519 0.266 1.95

Table 4. Parameters related to the backscattering enhancement computed for the samples at diﬀerent wavelengths. BSE= ◦ ◦ F11(0 )/F11(30 ).

moderate aspect ratios is mainly dependent on the size and refractive indices of the particles, but not on their shapes (Liu et al. 2003). Between 175◦ and 180◦, we produce Mie calculations for projected-surface-area equivalent spheres. For the Mie computations we use the measured size distribution of the corresponding sample and the value of the refractive indices presented in Tab.2. For the backward direction, we first generate a value for the phase function at 0◦ by a quadratic function generated by least squares with the measured data points from 3◦ to 30◦. Then all values between 3◦ and 30◦ are produced by a cubic splines interpolation con- sidering an additional condition that must be fulfilled in all cases: the first derivative of the phase function at 0◦ must be zero (Hovenier and Guirado 2014). At this stage, both the forward peak (175◦ −180◦) and the rest of the phase function (0◦ − 175◦) are defined, but they are normalized in a different way: the forward peak belongs to a function normalized according to eq.4 and the normalization of the rest of the function is arbitrary. The function defined by the measured (3◦ −175◦) plus the extrapolated (0◦ −3◦) data points is then vertically shifted until the computed Fsyn(175◦) matches the ◦ 11 measured F11(175 ). The normalization condition (eq.4) is Figure 8. Measured degree of linear polarization curves for the then checked. If it is not satisfied within a 0.1% accuracy, the FRO99040S (blue symbols) and FRO99040M (magenta symbols) value of the measurement at 175◦ is increased or decreased at 520 nm. (within the experimental error bars) until the normalization condition is fulfilled. The backscattering enhancement for all 5.3 Backscattering enhancement our samples lays in the range [1.94-2.27] (see Table4). In order to give an estimation of the trend of the phase function in the backward region for all studied samples, we 5.4 The effect of size and color on polarization compute the backscattering enhancement (BSE), defined as The degree of linear polarization of the DaG521S and the ratio of measured phase function values at α = 0◦ and α = DaG521M, and the FRO99040S and FRO99040M samples 30◦ (Bertini et al. 2007). Since our laboratory measurements are plotted in Figs.7 and8, respectively. Since each figure do not cover the whole phase angle range we extrapolated refers to the same material, the differences observed are only a synthetic phase function, Fsyn, from our measurements 11 attributable to the different size distributions of the S and that range from 3◦ to 175◦. The synthetic phase function M samples. The salient feature of this comparison is an in- is defined in the full angle range from 0◦ to 180◦ and is crease of the maximum polarization with size. In fact, it can normalized according to: be seen in Fig.2 that the size distributions of the samples with a higher Pmax (DaG521M and FRO99040M) present a 1 ¹ π dαsinαFsyn(α) = 1. (4) secondary maximum at larger sizes. Thus, the contribution 2 11 0 of particles with large size parameters (xef f = 2πref f /λ) is The extrapolation of the measured phase function in most likely responsible for the measured increase in Pmax. the forward direction is based on the assumption that the The direct relationship between Pmax and ref f (or xef f ) forward scattering peak for randomly oriented particles with apparent in Figs.7 and8 suggests an inverse relationship

MNRAS 000, 000–000 (2018) 12 E. Frattin et al. between Pmax and wavelength, since the size parameter is agreement with the simulations of Zubko et al.(2009, 2015), inversely proportional to wavelength. which demonstrate that the negative polarization parameters strongly depend not only on size parameter but also on The polarization curves for the forsterite sample at the material absorption properties. three different wavelengths (442 nm, 520 nm, and 633 nm) are plotted in Fig.9. The measurements at 442 nm and 633 5.5 Comparison with asteroids and comets nm have been published previously (Muñoz et al. 2000). It can be seen that Pmax increases as the size parameter of the Ground-based observations of the intensity of light scattered particles decreases (λ increases for a fixed ref f ). In this case by cometary dust grains are usually limited to certain obser- the differences in the measured degree of linear polarization vational geometries. Moreover, time variations of the bright- are also likely related to the size parameter of the grains, ness of the coma as observed from Earth do not only depend since the refractive index of forsterite presents a flat depen- on the phase angle but also on changes of the dust produc- dence on wavelength in the studied region. tion rate as the comet moves in its orbit around the Sun The apparent contradiction between Figs.7 and8 on one (see e.g. Kolokolova et al.(2004)). The OSIRIS camera on side and Fig.9 on the other can be explained by the broad board the Rosetta spacecraft revealed the behavior of comet size range of our samples. The scattering properties of dust 67P/Churyumov-Gerasimenko phase functions from inside grains are described by three regimes: Rayleigh, resonance the coma (Bertini et al. 2017). They were obtained in a and geometric optics. When particles are smaller than the short time period (about 2.5 h) covering an unprecedented ◦ ◦ wavelength (Rayleigh regime), Pmax tends to decrease as broad phase angle range (from ∼ 10 to ∼ 155 ). The mea- the size parameter increases. In that case, Pmax increases sured phase functions show a peculiar u-shape with a mini- with wavelength if the refractive index is constant, i.e. mum at a phase angle around 100◦. That phase function is Pmax ∝ 1/x ∝ λ. By contrast, in the geometric optics regime not reproduced by any of the µm-sized randomly oriented (xef f λ), Pmax tends to increase as the size parameter be- particles studied in this work or previously presented in comes larger, i.e. Pmax ∝ x ∝ 1/λ. These trends are well illus- the Amsterdam-Granada Light Scattering Database (Muñoz trated by computed polarization data for Gaussian random et al. 2012). However, laboratory measurements of the phase shapes from the Rayleigh to the geometric optics regimes function of mm-sized particles (Muñoz et al. 2017) show a reported by Liu et al.(2015). As shown in Fig.2, the contri- distinct behavior compared to µm-sized particle clouds, with bution of grains in the geometric optics domain for samples a minimum placed at much larger phase angles more in line DaG521M and FRO95002M is relatively large. Therefore, with the 67P phase curve. Further, recent analysis of the the Pmax tends to increase as xef f increases (Figures7 and OSIRIS phase functions at low phase angles provides a range 8). The majority of the grains in the forsterite sample belong of BSE values broader [1.7-3.6] (Bertini et al. 2018) than that to the Rayleigh and resonance (xef f ≈ λ) domains where the based on ground-based observations [1.7-2.7] (Ishiguro et al. dependence of Pmax with size is nearly opposite, i.e. it in- 2013). As shown in Table4, the BSE values obtained for creases as xef f decreases (Fig.9). our µm-sized cometary dust analogues are within the range The degree of linear polarization curves for the Allende obtained from ground-based observations. The highest BSE meteorite sample at three wavelengths (442 nm, 520 nm, value obtained from the OSIRIS data (3.6) seem to be pro- and 633 nm) are plotted in Fig. 10. As shown In Fig.1, the duced by a cloud of decimetric chunks orbiting 67P nucleus Allende sample mainly consists of particles in the Rayleigh at distances smaller than 100 km (Bertini et al. 2018). All in and resonance regimes. In this case there is no clear trend of all our experimental data suggest that 67P phase function Pmax with wavelength. The higher Fe content of the Allende is not dominated by randomly-oriented µm-sized particles meteorite compared to forsterite indicates a higher imag- in line with the conclusions of multi-instrument analysis on inary part of the refractive index at shorter wavelengths, board Rosetta (Guettler submitted). implying a higher reflectance at red wavelengths. According Polarization is a powerful tool to investigate the nature to the Umov effect, the larger reflectance, the lower the max- of particles populating cometary comae and asteroidal re- imum of the degree of linear polarization. Thus, the increase goliths. The value of the minimum of the degree of linear of Pmax with wavelength seems to be balanced by a lower polarization together with the slope of polarization curve is albedo at shorter wavelengths. Therefore, the maximum of generally used to determine the albedo of asteroids. More- the degree of linear polarization is dependent not only on the over, polarimetric criteria are used to classify and refine the size of the grains but also on their refractive index. A study asteroid taxonomy (Belskaya et al. 2017). A caveat to direct of tholins generated in plasma with different size distribu- comparisons between observations and laboratory results is tions by Hadamcik et al.(2009) is in line with our results, that the assumption of single scattering is no longer valid showing that in Rayleigh regime Pmax decreases when the for such bodies, since they are covered by a layer of regolith. particle size increases, while in optical regime Pmax increases Single scattering is considered to be more adequate to ex- with the particle size. plain the behaviour of low-albedo objects, for which multiple It is worth noting that in the case of the forsterite sample scattering is less important. As a result of multiple scatter- (Fig.9), the inversion angle α0 does not change with wave- ing the minimum polarization value approaches zero, and length. However, some wavelength dependence of the nega- the inversion angle α0 decreases. Further, the positive po- tive branch minimum can be distinguished at 633 nm. In the larization maximum decreases by multiple scattering effects case of the Allende sample, both the minimum of the neg- and therefore its slope (Shkuratov et al. 2004, 2006, 2007). ative branch and the inversion angle vary with wavelength. We refer to Kolokolova et al.(2015) (chapters 5 and 8) for The apparent dependence of the negative branch parame- recent reviews on photometric and polarimetric laboratory ters on composition (i.e. refractive index) seems to be in measurements of particulate surfaces and individual parti-

MNRAS 000, 000–000 (2018) Scattering of cometary dust analogs 13

◦ ◦ ◦ Comet λ (nm) Pmin(%) αmin( ) α0( ) Pmax (%) αmax ( ) h (%/deg)

High Pmax 515 −1.5 ± 0.5 9 ± 2 22.2 ± 0.5 26 ± 2 103 ± 10 0.22 ± 0.02 670 −1.5 ± 0.5 11 ± 2 22.6 ± 0.5 28 ± 3 95 ± 10 0.25 ± 0.03

Low Pmax 515 −1.7 ± 0.5 6 ± 3 19.0 ± 0.5 10 ± 3 80 ± 10 0.20 ± 0.02 670 −1.9 ± 0.5 6 ± 3 20.5 ± 0.5 18 ± 3 95 ± 10 0.22 ± 0.02

67P red −1.7 ± 0.1 12 ± 3 22 ± 2 -- 0.35 ± 0.02*

Table 5. Polarimetric parameters of two classes of comets from Levasseur-Regourd et al.(1996). Values for 67P correspond to post- perihelion period and are taken from Hadamcik et al.(2016). *The h value for 67P is the slope at the inversion angle, since no value for Pmax are available. cles. Taking into account the mentioned multiple scattering effects, we can still retrieve information on the physical properties that determines the observed polarimetric features of asteroidal regolith particles by direct comparison with our experimental data. For instance, in the case of (the still few) Near-Earth Asteroids (NEA) observed so far, the maximum of positive polarization can reach, for low-albedo objects like (3200) Phaethon and (101955) Bennu, much higher values of linear polarization (up to 40%), well above the limits reached by the samples analyzed in this work. The covered interval of angles did not include αmax but the observed data indicate ◦ that Pmax could occur around 130 . Taking into account the decrease of Pmax due to multiple scattering effects on the regolith layer, we can expect an even larger Pmax for the single particles forming the regolith. According to previous experimental (Escobar-Cerezo et al. 2018) and computational (Liu et al. 2015) results, a high value of Pmax shifted toward large phase angles, suggests a surface covered by particles significantly larger than those studied in this work. Further, spectropolarimetric data of asteroids show that the gradient of linear polarization for increasing wavelength depends on the taxonomic class and upon the phase angle. In the positive polarization branch, the Figure 9. Measured degree of linear polarization curves for the polarization tends to decrease for increasing wavelength forsterite sample at three different wavelengths. for S-class objects (moderate albedo). Similar dependence of Pmax with λ has been found for single particles that present a significantly higher imaginary part of the refrac- have a very fine surface regolith. This is also in agreement tive index, k, at short (488 nm) than at large (647 nm) with some estimate of a low thermal inertia for (21) Lute- wavelengths (Dabrowska et al. 2015). Low-albedo objects tia, which has also a large inversion angle, not much smaller do just the opposite as is the case of dust samples with than that of Barbarians (Cellino et al. 2016). Only S-class a flat (Figures9) or moderate dependence of k with the NEAs objects have P values (7% and 10%) compatible wavelength (10). Note also that, for any given object of any max with our measurements. As opposite, there are no asteroids class, the polarimetric gradient changes sign if the object reaching negative polarization deeper than -2,-3 %. is observed in the negative or in the positive polarization The condition of single scattering holds for cometary branch (Bagnulo et al. 2015) as is the case of the forsterite comae. Observational data show the existence of two classes and Allende samples studied in this work (Figures9 and 10). of comets, based on the degree of linear polarization (Levasseur-Regourd et al. 1996; Shestopalov and Golubeva On the other hand, the angle of inversion of polariza- 2017). The high polarization comets, which are considered tion of asteroids is usually around 20◦. A few objects exhibit dust-rich, and the low polarization comets, which have a an inversion angle at lower phase angles (15◦ − 17◦). Only a higher gas component (Table5). The measurements of the few rare objects, the so-called Barbarians, show high values samples presented in this work seems to be of the order of inversion angles, up to 28◦ (Cellino et al. 2006; Devogèle of the low polarization group. Generally, cometary comae et al. 2018). As shown in Section 5.2, for the size range of behave qualitatively in a similar manner to our analog par- the samples presented in this work, the position of the in- ticle clouds: they show a negative polarization branch at version angle depends on sample composition. This is also small phase angles, and a bell-shaped curve at side and found by Devogèle et al.(2018) in their analysis of Barbarian backscattering angles, with a maximum of polarization at a ◦ asteroids. Other observed polarimetric evidence (Pmin ver- phase angle near 90 . However, the exact parameters defin- sus inversion angle plot) suggests that these objects should ing the cometary polarization phase curve (see Table5 for

MNRAS 000, 000–000 (2018) 14 E. Frattin et al.

particle sizes belonging to Rayleigh-resonance (xef f ≈ λ) and geometric optic (xef f λ) regimes. When particles are smaller or of the order of the wavelength (Rayleigh- resonance regimes), Pmax decreases with size whereas in the geometric optics regime Pmax tend to increase with size. • For the range of sizes of our samples, the minimum of the negative polarization branch seems to be dependent on both size and composition of the grains whereas the inversion angle value, α0, depends on the refractive index. • The measured degree of linear polarization curves are qualitatively similar to those obtained from ground-based observations of cometary comae. This is in line with the ﬁnd- ing that the main scatterers in the coma are larger than the wavelength of the incident light, where the surface features of the particles are of the order of the incident wavelength.

ACKNOWLEDGEMENT The authors are grateful with the Museo dell’Antartide Fe- lice Ippolito, Siena for providing the meteorite samples re- quired, with the Department of Geoscience of the University of Padua for providing the laboratory facilities necessary to Figure 10. Measured degree of linear polarization curves for the produce the samples. We are indebted to Roc´ıo Márquez Allende sample at three different wavelengths. from the Scientific Instrumentation center of the University of Granada for providing the SEM images and with Maurizio Gemelli from the Department of Earth Science of the Uni- comet 67P in particular), are different from our laboratory versity of Pisa. This work has been supported by the Plan measurements. The 67P polarization phase curve might be Nacional de Astronom´ıa y Astrof´ısica contract AYA2015- shaped by particles larger than the wavelength, but with 67152-R. wavelength-scale surface features that could produce a polarization roughly similar that of a cloud of isolated scatterers. Moreover, the h slope observed for 67P seems to indicate that it belongs to the family of ”high polarization” comets REFERENCES (Rosenbush et al. 2017). This might be in agreement with the A’Hearn, M. F., Belton, M. J. S., Delamere, W. A., Feaga, L. M., depletion of small particles (<1 µm) observed with Rosetta. Hampton, D., Kissel, J., Klaasen, K. P., McFadden, L. A., Our laboratory data support the interpretation of the Meech, K. J., Melosh, H. J., Schultz, P. H., Sunshine, J. M., decreasing polarization outward the nucleus of 67P, accord- Thomas, P. C., Veverka, J., Wellnitz, D. D., Yeomans, D. K., ing to which this results from larger particles near the nu- Besse, S., Bodewits, D., Bowling, T. J., Carcich, B. T., Collins, cleus and smaller particles moving away from it (Rosenbush S. M., Farnham, T. L., Groussin, O., Hermalyn, B., Kelley, et al. 2017). In order to enable a more consistent compari- M. S., Kelley, M. S., Li, J.-Y., Lindler, D. J., Lisse, C. M., son between astronomical observations and laboratory data, McLaughlin, S. A., Merlin, F., Protopapa, S., Richardson, future studies need to consider more appropriate mixtures J. E. and Williams, J. L. (2011), ‘EPOXI at Comet Hartley of components such as silicates, organics and ices, with im- 2’, Science 332, 1396. A’Hearn, M. F., Belton, M. J. S., Delamere, W. A., Kissel, J., proved control on other characteristics such as size, shape Klaasen, K. P., McFadden, L. A., Meech, K. J., Melosh, H. J., and surface roughness. Schultz, P. H., Sunshine, J. M., Thomas, P. C., Veverka, J., Yeomans, D. K., Baca, M. W., Busko, I., Crockett, C. J., Collins, S. M., Desnoyer, M., Eberhardy, C. A., Ernst, C. M., Farnham, T. L., Feaga, L., Groussin, O., Hampton, D., Ipatov, 6 CONCLUSIONS S. I., Li, J.-Y., Lindler, D., Lisse, C. M., Mastrodemos, N., Our results are summarized as follows: Owen, W. M., Richardson, J. E., Wellnitz, D. D. and White, R. L. (2005), ‘Deep Impact: Excavating Comet Tempel 1’, • All measured phase functions present the typical behav- Science 310, 258–264. ior of µm-sized irregular compact dust particles in random Bagnulo, S., Cellino, A. and Sterzik, M. F. (2015), ‘Linear spec- orientation. They show strong peaks at large phase angles, tropolarimetry: a new diagnostic tool for the classification and almost no structure at side phase angles and soft increase at characterization of asteroids’, MNRAS 446, L11–L15. small phase angles. Bardyn, A., Baklouti, D., Cottin, H., Fray, N., Briois, C., Pa- quette, J., Stenzel, O., Engrand, C., Fischer, H., Hornung, • The measured values of backscattering enhancement K., Isnard, R., Langevin, Y., Lehto, H., Le Roy, L., Ligier, (BSE) of our samples are within the range obtained from N., Merouane, S., Modica, P., Orthous-Daunay, F.-R., Rynö, ground-based observations of cometary comae. According to J., Schulz, R., Silén, J., Thirkell, L., Varmuza, K., Za- our experimental data small BSE values seem to indicate a prudin, B., Kissel, J. and Hilchenbach, M. (2017), ‘Carbon- coma population of µm-sized grains. rich dust in comet 67P/Churyumov-Gerasimenko measured • The dependence of Pmax with size is opposite for by COSIMA/Rosetta’, MNRAS 469, S712–S722.

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