© ESO 2018

1 Introduction

Comet 2P/Encke (hereafter 2P), which is a frequently observed comet because its orbital period is short (3.3 years), has a few distinctive characteristics, including its low dust cross-section with respect to the water production rate (4.27 × 10⁻²⁷; A’Hearn et al. 1995) and high dust-to-gas mass ratio (10–30; Reach et al. 2000). These characteristics suggest that large-size grains (up to ~0.1 m) dominate in the vicinity of the comet (Sarugaku et al. 2015). It is also known that 2P is dynamicallydecoupled from Jupiter (i.e., the Tisserand parameter with respect to Jupiter is T_J = 3.025), being an archetype of Encke-type comets, and it has been proposed that a long-term residence in the inner solar system results in this unique orbital property (Levison et al. 2006).

In general, the linear polarization of cometary dust particles can be exploited to constrain physical properties, such as their size and porosity (see, e.g., Kiselev et al. 2015). However, the large portion of gas emission signals in the coma of 2P can heavily depolarize the observed linear polarization degree of the dust component (Kiselev et al. 2004; Jockers et al. 2005). In this regard, spectropolarimetry can provide more reliable information about the properties of gas and dust, free of mutual contamination. The observation technique simultaneously provides a series of information on the polarization degrees (P) of the gas (P_gas) and dust components (P_cont) and of the position angle (θ_P) with respect to the normal vector of thescattering plane (θ_r). However, only a few studies in the literature have reported spectropolarimetric results of comets (Myers & Nordsieck 1984; Kiselev et al. 2013; Borisov et al. 2015).

Here, we report a new spectropolarimetric observation of 2P at a phase angle of α = 75°.7 in its inbound orbit. From our data analysis, we derive P_gas and P_cont values at 0.50–0.97 μm. In addition, wereport P_gas of the C₂ swan band, NH₂ α band, and CN-red system (A² Π−X²Σ⁺) molecules in each branch. Based on the observational evidence, we discuss these polarimetric results in terms of the unique orbital property of 2P. We use the notations of P_X for the linear polarization degrees and P_{X, r} for the linear polarization degrees with respect to the scattering plane, where the subscript X specifies the continuum, gas, or molecular species.

2 Observations

We performed a spectropolarimetric (hereafter sppol) observation of 2P using the Hiroshima Optical and Near-Infrared Camera (HONIR) mounted on the Cassegrain focus of the 150 cm Kanata telescope at the Higashi-Hiroshima Observatory (HHO, 132°46′36′′ E, +34°22′39′′ N, 511.2 m), Japan, on UT 2017 February 21. Although we obtained optical and near-infrared data simultaneously with HONIR, we did not use the near-infrared data because 2P is not detected at this wavelength. In sppol mode, we employed a rotatable half-wave plate (HWP), a slit mask for five different fields (2.′′ 2 × 45.′′0 each), a Wollaston prism, and an optical grism (Akitaya et al. 2014). Accordingly, a single fits file consists of five pairs of sky spectra of ordinary and extraordinary light components at each HWP angle (in the sequence of 0°.0, 45°.0, 22°.5, and 67°.5 position angles to the fiducial point). The pixel and wavelength resolutions are 0.′′ 29 and R(= λ/Δλ) ~ 350, respectively (Akitaya et al. 2014).

We set the position angle of the slit parallel to the east-west direction. Initially, we positioned the nucleus on the center of the slit, but realized that the nuclear position was 8′′ off from the central slit at the last exposure because the non-sidereal tracking mode was not available for the telescope. We obtained data of a spectroscopic standard star, HR718 (B9III) (Hamuy et al. 1994), on the same night. The observed airmass of HR718 was slightly lower than that of 2P (airmass of 2.1 for HR718 and 2.7 for 2P), however, we used the standard star data for the flux calibration but not for the polarimetric calibration. We exploited the HONIR data reduction pipeline for the basic preprocessing and IRAF to extract the observed spectra. Detailed stages of P and the θ_P derivation for comets are described in Kuroda et al. (2015) and Kwon et al. (2017), and the standard sppol data reduction procedure is described in Kawabata et al. (1999). The observed polarimetric parameters were corrected for instrumental effects (i.e., for the instrumental polarization, the polarization efficiency, and for the correction angle of the HONIR sppol mode) at Stokes Q(λ) and U(λ) levels, usingroutinely checked calibration data provided by H. Akitaya (a coauthor of the paper who developed the instrument). Instrumental polarization (Figs. 12c and 13 at Akitaya et al. 2014) stably varies within ± 0.1% over the OPT filter (0.5–1.0 μm), thus we considered that its influence on our results of 2P would be negligible. For the polarization efficiency and position angle corrections, (Figs. 15a and b, respectively, in Akitaya et al. 2014), which are smoothly varying functions over the OPT filter domain, we fit the data using the least-squares methods to interpolate them in the wavelength resolution of HONIR (Δ λ ~ 0.002 μm). All polarimetric quantities discussed in the following sections are corrected for these instrumental effects.

In addition to the sppol observation, we conducted contemporaneous multi-band imaging observations with the 105 cm telescope at the Ishigakijima Astronomical Observatory (IAO), Japan, on UT 2017 February 19 and with the Okayama Astrophysical Observatory’s (OAO) 50 cm telescope on UT 2017 February 21 to monitor the dust coma morphology and brightness. We employed the MITSuME imaging system (to obtain the g′, R_C, and I_C bands simultaneously; it consists of 1024 × 1024 CCD chips with a 24.0-μm pixel pitch) at these observatories (Kotani et al. 2005). The g′, R_C, and I_C filters transmit the light at λ_c = 0.48, 0.66, and 0.80 μm with Δλ = 0.13, 0.12, and 0.16 μm, respectively, where λ_c and Δλ denote the central wavelengths of each filter and their full width at half-maximum (FWHM). We also made a spectroscopic observation using the MALLS spectrograph¹ attached to the 2 m telescope at the Nishi-Harima Astronomical Observatory (NHAO) of University of Hyogo, Japan, on UT 2017 February 19 to examine the strengths of molecular emissions with respect to the dust continuum. The observed raw data were preprocessed in a standard manner using dark (for the IAO data) and bias (for the HONIR data) and flat frames. We transformed the pixel coordinates into celestial coordinates using WCSTools (Mink 1997) and conducted flux calibration using field stars listed in the UCAC-3 catalog (Zacharias et al. 2010). We tabulate the detailed observation geometry and instrumental setup in Table 1.

3 Results

3.1 General outlines

Figure 1a shows the dust intensity map on UT 2017 February 19 taken with the IAO telescope after we subtracted the gas intensity from the observed intensity. We chose this image not only because there is no obvious change in the appearance and magnitude between the data on February 19 at IAO and February 21 at OAO, but also because the signal-to-noise ratio (S/N) of the IAO data is better than that of the OAO data. To extract dust signals from the observed signals, we used the simple manipulation of multiband images described by Ishiguro et al. (2016), assuming that I_C band has little gas contamination than g′ band. We first made the gas intensity map by subtracting the I_C-band image from the g′-band image, which in turn was subtracted from the R_C-band image, adjusting sky levels as approximately zero. The remaining intensity in R_C -band image would most likely represent the distribution of the 2P dust component. The dust cloud, which is elongated nearly normal to the antisolar direction, has 14.9 ± 0.2 mag in the R_C-band within 5.′′ 8 in radius (i.e., the physical distance of ≈4200 km from the photocenter at the comet position). Compared to the predicted apparent nucleus magnitude of 18.3 mag at the observed geometry (the phase coefficient of β = 0.06 mag deg⁻¹ and absolute magnitude of m_R (1,1,0) = 15.2 ± 0.5 mag are assumed; Fernández et al. 2000), our photometry indicates that the observed signal is largely dominated by the dust coma, with negligible amount of nucleus signal. We also note possible contamination of large dust particles in the 2P dust trail (ejected before the last perihelion passage) within the aperture we employed. However, we were unable to detect any background dust structure extending along the negative velocity vector (Fig. 1a) because the dust trail is fainter than the coma surface brightness. Although it is possible that part of the dust signals within the aperture might come from the old dust trail of 2P, we consider that most of the dust intensity comes from the fresh dust tail of 2P.

Figure 2 shows the results of the sppol observation. We do not show the spectrum taken at NHAO because there is no noticeable difference between NHAO and HHO data. It consists of a weak continuum (overlaid by the signals from coma dust) and line emissions (Fig. 2a). Assuming an optically thin coma for all species used here, the total sum of the two strongest C₂ bands (i.e., C₂(0,0) at λ = 0.51 μm and C₂ (3,4) at λ = 0.55 μm) is (3.1 ± 0.1) × 10⁻¹¹ erg cm⁻² s⁻¹. The flux of the strongest CN(1, 0) red band is (3.2 ± 0.2) × 10⁻¹² erg cm⁻² s⁻¹ μm⁻¹, and the total sum of the NH₂ bands shows a weak signal of (3.5 ± 0.4) × 10⁻¹³ erg cm⁻² s⁻¹. We note that the total flux of the above C₂ emissions at λ < 0.55 μm could be overestimated because they are blended with NH₂ α band emissions. Similarly, the fluxes of NH₂ could be slightly overestimated because of the blending with oxygen emission (O(¹D)) at λ = 0.63 μm and C₂ bands at λ = 0.54–0.62 μm.

The flux of C₂ (0,0) (Δν = 0) band (~2.0 × 10⁻¹¹ erg cm⁻² s⁻¹) allows us to conduct an order-of-magnitude estimate on the gas production rate (Q${}_{{\text{C}}_2}$; mol s⁻¹). From the parameters in Table II of A’Hearn et al. (1995), we derived the g-factor (luminosity per molecule, i.e., fluorescence efficiency), scale length, and daughter lifetime of C₂ scaled by the observing geometry (r_h = 0.54 au). To compensate for flux loss caused by a limited area of the slit we employed, we estimated the dimensionless Haser correction factor from the volume fraction of total coma contained within the circular aperture of radius 2.′′02, which covers the equivalent area of 2.′′ 2 × 5.′′8 of the rectangular aperture employed in this study. By substituting the scaled parameters into Eq. (1) from Venkataramani et al. (2016), we obtained log(Q${}_{{\text{C}}_2}$) = 27.65. However, we note again that these band fluxes might not be accurate because of the airmass mismatch between the standard star and 2P, but they do explain the inverse relationship with the polarization degrees, as shown below.

Fig. 1 Dust intensity map (panel a) and its radial profile (panel b) after we subtracted the gas components from the observed signals on UT 2017 February 19 by IAO/MITSuME. (a) The photocenter of 2P is markedas a red cross. The contours on 2P are spaced linearly down to one-fifth of the central brightness level (i.e., 95, 70, 45, and 20% flux with regard to the peak flux). The negative velocity (− v) and antisolar (r⊙) vectors projected on the celestial plane are shown as solid and dashed arrows, respectively. North is up and east is left. “S” letters in the bottom right corner denote the remnants of background stars. Panel b: The surface brightness profile of the near-nuclear coma with respect to the radial distance. We binned the radial distance logarithmically over 1.′′ 0–13.′′0, and averaged the data points at intervals of 0.′′5 radial distance each. All brightness points are normalized at the innermost point (0.′′ 2 from the photocenter). The upper solid and lower dashed lines exhibit gradients of −1 and − 1.5, which are typical of cometary dust expanding with initial ejection speed under the solar radiation field (Jewitt & Meach 1987). The blue vertical line at 5.′′ 8 denotes the apertureradius we used.

Fig. 2 Flux (panel a), P (panel b), and θr (panel c) of 2P observed on UT 2017 February 21 by HHO/HONIR as a function of wavelength. In panel a, we name the branches of discernible line emissions. The red line is a median-smoothed line of the original black points within the size of wavelength resolution. In panel b, the binned-average P is calculated within a rectangle region of 2.′′2 × 5.′′8. We mark the analyzed emission lines with the vertical lines in panels a and b. In panel c, the horizontal red line denotes the average θr of 0°.4.

3.2 Continuum polarization

At first glance, the observed P has an inverse relationship with the line emission flux (Figs. 2a and b). The local minima are found around the emission peaks (the verticallines). Figure 2b shows an almost flat continuum spectrum. From this data, we obtain the polarimetric color of −1.0 ± 0.9 % (1000Å⁾⁻¹.

To derive an average P_cont (i.e., for the dust), we extracted the continuum signals, avoiding the polarimetric data at the wavelengths of the line emissions described in the catalog of Brown et al. (1996). Wavelengths of the continua used to estimate the average P_cont are 0.680–0.690, 0.720–0.730, 0.760–0.770, 0.845–0.870, 0.880–0.910, 0.930–0.935, and 0.945–0.970 μm. We then transformed P_cont into the polarization degree of the continuum with respect to the normal vector of the scattering plane (P_{cont, r}) as follows: $$P_{\text{cont},\text{r}}=P_{\text{cont}}\cos \left(2{\theta }_{\text{r}}\right)$$(1)

and $${\theta }_{\text{r}}={\theta }_{\text{P}}-\left(\varphi \pm {90}^{°}\right),$$(2)

where ϕ is the position angle of the scattering plane (the plane of Sun-comet-observer), whose sign satisfies the condition of 0° ≤ (ϕ ± 90°) ≤ 180° (Chernova et al. 1993). The ϕ value at the time of this sppol observation was 56°.3. From Eqs. (1)–(2), we obtain P_{cont, r} = 33.8 ± 2.7% at λ = 0.68–0.97 μm at the effective wavelength of λ_eff = 0.82 μm. θ_r is shown in Fig. 2c. The polarization vector is aligned nearly perpendicularly to the scattering plane (i.e., the average of θ_r = 0°.4 over the region of 0.50–0.97 μm), but exhibits a downward trend as the wavelength increases (which would be a real feature because we corrected for the wavelength dependence in θ_r using data of strongly polarized stars, but we know no plausible physical reason for the dust property).

As indicated by the dust image (Fig. 1a), whose flux is ~22.5 times brighter than the predicted one of the 2P nucleus, the dust continuum measured in this study should be dominated by the coma dust. This assumption can also be supported by comparison with Jewitt (2004), who performed the narrowband imaging polarimetry on/around the nucleus: (i) the aperture size in this study (1550 km × 4080 km) is 1.5–4.0 times larger than the coverage of his data, and (ii) the heliocentric distance in this study (0.54 au) is nearly twice smaller than those of Jewitt (2004). This suggests more significant contribution of dust coma with respect to the nucleus as a result of theincreasing solar incident flux.

To derive the phase angle dependence of P_{cont, r}, we searched the published narrowband data of 2P to minimize the influence of the gas emission, but found no consistent dataset whose radial distance matches ours. The physical distances from the nucleus we cover are 2–3, and 4 times larger than the data in Jewitt (2004; λ_eff = 0.526 μm; open diamonds in Fig. 3a) and Jockers et al. (2005; λ_eff = 0.642 μm; open squares in Fig. 3a), respectively. Meanwhile, for the broadband data in Böehnhardt et al. (2008; filled triangles in Fig. 3a) obtained at the large heliocentric distance (r_h = 2.7–2.1 au), most of the polarized signals they obtained came from the bare nucleus, so that it could hardly be included in the line with our study as the dust signals.

Our P_{cont, r} (33.8 ± 2.7%) at α = 75°.7 is already significantly higher than the average P_{cont, r} of the dust-rich comets (the thin solid line in Fig. 3a). Thus, instead of compiling the published data, assuming that an ensemble polarimetric response of the dust of 2P as a function of phase angle is morphologically similar with those of other comets (i.e., a bell-shaped curve having a minimum P_min at α ~ 10°, a maximum P_max at α ~ 100°, and an inversion angle α₀ at α ~ 15°–20°), we multiplied the average P_{cont, r} distribution of dust-rich comets by the constant (1.5) to match our sppol data.

We fit the published narrowband data using the empirical phase function written in Penttilä et al. (2005): $$P_{\text{cont},\text{r}}(\alpha )=b{\left(\sin \alpha \right)}^{c_1}\sin \left(\alpha -{\alpha }_0\right)\cos {\left(\frac{\alpha }{2}\right)}^{c_2},$$(3)

where b, c₁, c₂, and α₀ are constants to characterize the profile. For comparison, we show the profiles of high- and low-P_max comets in the archive data (Kiselev et al. 2006) (λ_eff = 0.67 μm) in Fig. 3a, whose parameters are determined to be b = 33.25 ± 1.66%, c₁ = 0.85 ± 0.04, c₂ = 0.39 ± 0.02, and α₀ = 21°.90 ± 1°.10 for the high-P_max comets and b = 17.78 ± 0.89%, c₁ = 0.61 ± 0.03, c₂ = 0.14 ± 0.01, and α₀ = 21°.90 ± 1°.10 for the low-P_max ones (Kwon et al. 2017). As a result, we derive the maximum polarization degree of P_max ≳ 40% at the phase angle of α_max ≈ 100° (thick red solid line in Fig. 3a). This P_max value is approximately 12% higher than the average P_max of high-P_max comets (≈28%) defined by Levasseur-Regourd et al. (1996). We note that the expected P_max roughly coincides with the dust coma polarization values of the published data of 2P at high phase angles, ensuring that the large P_{cont, r} is a common nature of dust from the comet.

Fig. 3 Phase angle dependence of Pcont, r (panel a) and Pgas, r (panel b). In panel a, the thick solid line shows the trend of the 2P continuum component weighted by the data errors. The solid and dashed lines denote the average trends of high- and low-Pmax comets, respectively. The filled symbols denote the data used in fitting, and open symbols are the excluded ones. The solid curve in panel b denotes the empirical phase function of fluorescence lines (Öhman 1941). The molecules analyzed in this study are expressed as stars. The meanings of the different symbols are given in the legend at the top left panel. Open stars of C2 bands and of CN(3,1) are enlarged to avoid mutual overlapping.

3.3 Molecule polarization

For the molecular polarization analysis, we excluded two NH₂ regions at the central wavelengths of λ_c = 0.60 and 0.63 μm to prevent the leverage of foreign gas (O(¹D) and C₂). The analyzed regions are marked by the vertical lines in Fig. 2b, whose central wavelengths are λ_c = 0.51, and 0.55 μm for C₂ Swan bands, λ_c = 0.66, 0.70, and 0.74 μm for NH₂ α bands, and λ_c = 0.79, 0.81, 0.92 and 0.94 μm for CN bands (the so-called CN-red system). We tabulate the detailed information of molecular bands we analyzed and their polarization degrees in Table 2. We first subtracted the continuum signals determined in Sect. 3.2 and derived the polarization degrees of line emissions in the same manner as P_cont. In this process, we confirmed that molecules have inherent nonzero P_gas values at the observed phase angle. Figure 4 zooms in on the corresponding regions to show each analyzed molecule in panels a–i.

To identify the wavelengths and intensities of molecular emissions, we calculated the distribution of fluorescent lines in optical wavelengths (0.4–1.0 μm) at the sppol observing geometry of 2P, and we used the fluorescence excitation models of C₂ (Shinnaka et al. 2010), NH₂ (Kawakita et al. 2000), and CN (Shinnaka et al. 2017). In the NH₂ model, we assumed the fluorescence equilibrium condition and fixed an ortho-to-para abundance ratio of 3.2, which is a typical value found in comets (Shinnaka et al. 2016). In the C₂ and CN models, we assumed that the rotational energy levels in the ground vibronic state are maintained to the Boltzmann distribution for a given excitation temperature. The given temperatures for the C₂ and CN models are 4000 K (a typical value found in comets; Rousselot et al. 2012) and 289 K (close to the fluorescence equilibrium condition; Shinnaka et al. 2017), respectively.

Figure 4 shows the polarization degrees of the gas components (i.e., P_gas), where the solid lines are the weighted means of P_gas within the wavelength resolution (Δλ ~ 0.002 μm). We overplot the corresponding branches for the C₂ and CN transitions at the top of the figures. C₂ bands are attributed to both P and R branches, and most of CN-red bands are dominated by Q branches (more details are described in Sect. 4.1). On average, we obtain P_gas = 8.0 ± 1.0% and P_gas = 7.2 ± 0.4% for the (0,0) and (3,4) transitions of the C₂ swan band, respectively, and P_gas = 8.4 ± 1.3%, P_gas = 3.8 ± 1.2%, P_gas = 5.8 ± 0.7%, and P_gas = 18.5 ± 3.1% for each CN-red (2,0), (3,1), (1,0), and (2,1) transition. For NH₂ α bands, due to their feeble fluxes embedded in the continuum signal, we zoom in on the very near regions of the line centers and obtain P_gas = 4.0 ± 1.0%, P_gas = 3.7 ± 0.5%, and P_gas = 7.0 ± 0.8% for (0,7,0), (0,6,0), and (0,10,0) transitions, respectively.

4 Discussion

4.1 Polarization of C₂, NH₂, and CN-red molecules

Öhman (1941) suggested two principal mechanisms of comet polarization: polarized light by dust continuum (P_cont), and by fluorescent molecule emissions (P_gas). The latter follows a empirical phase function: $$P_{\text{gas}}(\alpha )=\frac{p_{90}{\sin }^2\alpha }{1+p_{90}{\cos }^2\alpha },$$(4)

where p₉₀ denotes the maximum polarization value at α = 90°, which was derived as 7.7% (a limiting value of P_gas with a high rotational quantum number of diatomic molecules that was theoretically determined from the ¹ Π −¹Σ transition of the Zeeman splitting in the magnetic field (Mrozowski 1936). Since then, phase angle dependence of P_gas has been mainly discussed in terms of the observed P_gas values beingconsistent or inconsistent with the profile of Eq. (4) (hereafter the reference P_gas profile).

Le Borgne et al. (1987) compared the observed P_gas of C₂ (λ_c = 0.51 μm), CN-violet (λ_c = 0.38 μm), and OH (λ_c = 0.31 μm) molecules of comet 1P/Halley and 103P/Hartley-Good via narrowband imaging polarimetry to the reference P_gas profile in Öhman (1941; Fig. 3b). They found that P_gas values of C₂ and CN-violet follow the reference P_gas profile well, whereas those of the OH band were nearly five times smaller than the curve. They could not find any explanation for this deviation. Sen et al. (1989) also measured the P_gas of CN-violet, C₃, CO⁺, C₂, and H₂ O⁺ molecules of comet 1P/Halley via narrowband imaging polarimetry. They found agreement for CN-violet, C₃, and C₂, but deviations of CO⁺ and H₂ O⁺ from the reference P_gas profile. Recently, Borisov et al. (2015) measured the P_gas of C₂ of C/2013 R1 (Lovejoy) via spectropolarimetry and confirmed its distribution along the fluorescent phase curve. For the P_gas of NH₂ α bands, Kiselev et al. (2004) used the differential imaging method to extract the gas signal and derived P_gas of (mainly) NH₂(0, 7, 0) as ≈3% for 2P at α = 80°.5 and for C/1999 J3 (LINEAR) at α = 61°.6. In the same manner, Jockers et al. (2005) derived P_gas of NH₂(0, 7, 0) of 2P during its 2003 apparition as ≈7% at α = 90° (purple squares and diamonds in Fig. 3b). The P_gas of the CN-red system has not yet been reported in refereed journals.

We compare our P_gas values with the published data in Fig. 3b. Green, purple, and red present the P_gas values of C₂, NH₂ α, and CN-redsystem molecules, respectively. The stars were obtained by us, and the squares and diamonds are quoted from the references described in the top left corner. The reference P_gas profile described by Eq. (4) with p₉₀ = 7.7% is drawn asthe black solid line. Figure 3b confirms that our P_gas of C₂ of 2P follows the curve well in terms of measurement accuracy, whereas the P_gas of NH₂ and CN-red molecules deviate greatly. Overall, NH₂ molecules have lower P_gas values thanthose found by Öhman (1941). By contrast, the P_gas values of CN-red molecules present fairly large variations of P_gas for each transition of the molecule.

We conjecture that the phase angle distribution of P_gas would be related to the type of molecular transitions. Le Borgne & Crovisier (1987) proposed a possible range of P_gas, as determined by the types of transitional behaviors, complementing the theories of Mrozowski (1936) and Öhman (1941), who considered a single case of polarization by fluorescent molecular emissions. For molecules, a possible range of P_gas can be determined by the relative dominance among the P, Q, and R branches of molecular transition (Le Borgne & Crovisier 1987). The P and R branches are induced by the fluorescence excitation of Δ J = +1 and Δ J = −1, respectively, whereas the resonant Q-branch results from the transition of Δ J = 0, where J is the total angular momentum quantum number. A possible range of P_gas induced by the fluorescence is P_gas = 0–7.7%, whose limiting value agrees with the P₉₀ = 7.7% (Le Borgne & Crovisier 1987). Meanwhile, the dynamic range of P_gas induced by resonant Q branch is much wider (i.e., −14% to +19% without consideration of hyperfine structure of molecules) than those of the P and R branches.

Our fluorescence excitation model (see Sect. 3.3) shows the relative contribution of each molecular branch to reproduce the observed band emissions of 2P. Two strong C₂ swan bands of 2P (Figs. 4a and b) are mainly triggered by the fluorescent P and R branches, while the intensity of the resonant Q branch therein is much weaker (i.e., ≲10^-3) than the intensities of P and R. By contrast, most of the CN-red bands (A² Π − X²Σ^-) spanning the wavelengths of 0.78–0.94 μm (Figs. 4c–e) are caused largely by Q branches, and the relative influence of P and R in these intervals is negligible as <10^-2 times. In thecase of CN(2,1) at λ ~ 0.94 μm (Fig. 4f), the dominant transition occurs by the R branch. However, both (1) the comparable intensities of the Q and R branches (i.e., 10^-1 < flux(Q/R) < 1) for this band and (2) the weak continuum-subtracted signal make it hard to interpret this result clearly. For NH₂, its transitions have systematic differences with the cases of diatomic C₂ and CN, so we must consider three vibrational (symmetric, bending, and asymmetric) modes induced by its structural form of XY₂ (X and Y denote different atomic species). For now, we have no theoretical interpretation to explain the systematically lower P_gas of the NH₂ α band than C₂ at the given phase angle, but we can infer that our result for NH₂ is consistentwith previous molecular observations.

Fig. 4 Panels a and b: Pgas of C2 (0,0) and C2 (3,4), respectively. Panels c–f: Pgas of the CN(2,0), CN(3,1), CN(1,0), and CN(2,1) transitions, panels g–i: those of the NH2 (0,7,0), (0,6,0), and (0,10,0) α bands, respectively. Solid lines are median-smoothed within the wavelength resolution (i.e., Δ λ ~ 0.002 μm), and the background gray dashed lines present the modeled distributions of line emissions under the fluorescence equilibrium at the observation geometry of 2P. The right axis of panels a–i was arbitrarily scaled for visibility. More detailed information is described in the text.

4.2 Polarimetric anomaly of the 2P continuum

It has been conventionally suggested that two polarimetric groups of comets exist, that is, the high-P_max and low-P_max groups (Levasseur-Regourd et al. 1996). The former tends to be dust rich, and the latter is mainly gas rich. Recently, Kwon et al. (2017) noted that C/2013 US10 (Catalina), which was originally categorized in the low-P_max group, can be classified into the high-P_max group after subtracting the gas influence. This evidence suggests that the polarimetric signals in the low-P_max group might be largely contaminated by the gas emissions and that the two polarimetric classes do not necessarily result from the difference of dust physical properties. From the research, it is also inferred that cometary dust particles have a unified polarimetric property and show a phase angle dependence similar to that of high-P_max comets. It is important, however, to note that the 2P continuum data do not coincide with the majority of comets (Fig. 3a), even though the gas contaminations were adequately subtracted. As mentioned above, our flux data contain ambiguity due to the airmass mismatch between our target and the standard star. However, sppol data provide more reliable results because we derive them by comparing the ordinary and extraordinary components of light taken simultaneously using the Wollaston prism, which eliminates the ambiguity of atmospheric influence without flux calibration. Thus, the large polarization is probably attributable to an inherent scattering property of 2P dust and the nuclear surface. However, what causes the 2P continuum to deviate from a population of normal comets?

P_cont,r tends to increase via Rayleigh scattering as the abundance of small (<submicron) dust particles increases (Bohren & Huffman 1983). It is likely that the fragility of dust can increase under solar heat due to the evaporation of the gluing volatile matrix. This effect would result in the disaggregation of dust receding from the nucleus and would generate smaller constituent particles in the coma, as proposed in previous polarimetric research of 2P (Jewitt 2004). Similarly, scattered light by neutral gas components can enhance the P_cont,r. However, the enhancement by small particles is probably not the case of large P_cont,r for 2P. We do not find any evidence of a small dust population that extended along the antisolar direction of the extra-solar radiation pressure. In Fig. 1a, the dust cloud was elongated nearly perpendicularly to both the antisolar and negative orbital velocity vectors, most likely because of a population of compact large grains ejected from an active region via a jet of 2P (Sekanina 1988). Our radial profile of the dust intensity map (Fig. 1b) also indicates the absence of significant disintegration of outward dust particles within the aperture radius we considered (the vertical line at 5.′′ 8 from the photocenter). All brightness points are located in between the slopes of −1 and −1.5, which are typical of cometary dust expanding with initial ejection speed under the solar radiation field (Jewitt & Meach 1987), supporting our discussion point. In addition, our sppol data do not show an obvious increase in P_cont,r at shorter wavelengths, where the contribution of small Rayleigh scattering particles should be dominant in the signal to increase the polarization degree. We note, however, that our result does not refute the hypothesis of disaggregation in a smaller radial scale. Because the spatial resolution of Jewitt (2004; 0.′′ 22 per pixel) is nearly one-third of Fig. 1a (0.′′72 per pixel), with 2–3 times smaller aperture size, we are unable to verify the hypothesis of disaggregation of porous in the innermost of dust coma.

There are several possibilities to increase P_cont. The so-called Umow effect indicates that P_max has an inverse correlation with the geometric albedo, which implies that multiple scattering among individual particles or constituent monomers in dust aggregates reduces P_max (see, e.g., Zubko et al. 2011). However, the geometric albedo of the 2P dust particles (0.01–0.04 for the large dust grain, Sarugaku et al. 2015, and 0.03–0.07 for the nucleus, Fernández et al. 2000) shows albedos that are typical of general cometary dust (~0.04; Kolokolova et al. 2004) and nuclei (0.02–0.06; Lamy et al. 2004), although their results include large errors in the albedo measurements.

We speculate that the unique dust size distribution of 2P would lead to a larger P_cont,r compared to those of other comets. As mentioned in Sect. 1, the dominance of large grains (i.e., a paucity of small grains) from2P has been suggested by the observations of the featureless spectra (Lisse et al. 2004) and the unique morphology of the dust cloud with the dust trail structure (Reach et al. 2000; Epifani et al. 2001; Ishiguro et al. 2007; Sarugaku et al. 2015). Such a dust trail should be produced by large compact dust grains that are less sensitive to the solar radiation pressure. It is thus probable that the large opaque compact particles suppress multiple scattering in a single particle such that the surface single-scattering signals are magnified to increase the P_max values. The polarimetric measurement in the laboratory indicate that large dust-free rocks tend to retain higher P_max values than submillimeter-size grains do, although the experiment demonstrated that planetary surfaces where inter-particle multiple scattering should occur, unlike an optically thin cometary dust cloud (Geake & Dollfus 1986).

2P has the shortest orbital period of 3.3 yr of the Jupiter-Family comets, and it has a small perihelion distance (q ~ 0.3 au), which means that 2P can be an object more susceptible to solar radiation (e.g., photon pressure and solar heat) than other comets. It is also suggested that 2P resides in the inner solar system for a long time to be decoupled with Jupiter gravity (Levison et al. 2006). Taking account of the unique orbital properties as well as our polarimetric results, we conjecture that small dust grains have been lost from the surface and the circumnucleus environment by the gas drag force and from the dust mantle layer, which consists of mainly fall-back boulder-size rocks. The sintering effect by solar heat near the perihelion may also contribute to create coherent large dust particles on/around the surface of 2P, as suggested for 1566 Icarus and 3200 Phaethon (Ishiguro et al. 2017; Ito et al. 2018). Additionally, the packing effect of fluffy particles, which is caused by a sublimation of volatile materials on dust grains, can reduce the empty space in the conglomerated fluffy dust, removing multiple scattering within particles (Mukai & Fechtig 1983). Although the real physical mechanism for the large P_cont of the comet is not yet clear, such an unusual environment could be related to the polarimetric anomaly.

Acknowledgements

We thank the referee, H., Boehnhardt, whose constructive comments improved our manuscript. The observational data were obtained under the framework of a campaign program in the Optical and Infrared Synergetic Telescopes for Education and Research (OISTER). This work at Seoul National University was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST), No. 2015R1D1A1A01060025. Y.G.K is supported by the Global Ph.D. Fellowship Program through the NRF funded by the Ministry of Education (NRF-2015H1A2A1034260). Y.S. was supported by Grant-in-Aid for JSPS Fellows Grant No. 15J10864.

References

All Tables

All Figures

Fig. 1 Dust intensity map (panel a) and its radial profile (panel b) after we subtracted the gas components from the observed signals on UT 2017 February 19 by IAO/MITSuME. (a) The photocenter of 2P is markedas a red cross. The contours on 2P are spaced linearly down to one-fifth of the central brightness level (i.e., 95, 70, 45, and 20% flux with regard to the peak flux). The negative velocity (− v) and antisolar (r⊙) vectors projected on the celestial plane are shown as solid and dashed arrows, respectively. North is up and east is left. “S” letters in the bottom right corner denote the remnants of background stars. Panel b: The surface brightness profile of the near-nuclear coma with respect to the radial distance. We binned the radial distance logarithmically over 1.′′ 0–13.′′0, and averaged the data points at intervals of 0.′′5 radial distance each. All brightness points are normalized at the innermost point (0.′′ 2 from the photocenter). The upper solid and lower dashed lines exhibit gradients of −1 and − 1.5, which are typical of cometary dust expanding with initial ejection speed under the solar radiation field (Jewitt & Meach 1987). The blue vertical line at 5.′′ 8 denotes the apertureradius we used.

In the text

Fig. 2 Flux (panel a), P (panel b), and θr (panel c) of 2P observed on UT 2017 February 21 by HHO/HONIR as a function of wavelength. In panel a, we name the branches of discernible line emissions. The red line is a median-smoothed line of the original black points within the size of wavelength resolution. In panel b, the binned-average P is calculated within a rectangle region of 2.′′2 × 5.′′8. We mark the analyzed emission lines with the vertical lines in panels a and b. In panel c, the horizontal red line denotes the average θr of 0°.4.

In the text

Fig. 3 Phase angle dependence of Pcont, r (panel a) and Pgas, r (panel b). In panel a, the thick solid line shows the trend of the 2P continuum component weighted by the data errors. The solid and dashed lines denote the average trends of high- and low-Pmax comets, respectively. The filled symbols denote the data used in fitting, and open symbols are the excluded ones. The solid curve in panel b denotes the empirical phase function of fluorescence lines (Öhman 1941). The molecules analyzed in this study are expressed as stars. The meanings of the different symbols are given in the legend at the top left panel. Open stars of C2 bands and of CN(3,1) are enlarged to avoid mutual overlapping.

In the text

Fig. 4 Panels a and b: Pgas of C2 (0,0) and C2 (3,4), respectively. Panels c–f: Pgas of the CN(2,0), CN(3,1), CN(1,0), and CN(2,1) transitions, panels g–i: those of the NH2 (0,7,0), (0,6,0), and (0,10,0) α bands, respectively. Solid lines are median-smoothed within the wavelength resolution (i.e., Δ λ ~ 0.002 μm), and the background gray dashed lines present the modeled distributions of line emissions under the fluorescence equilibrium at the observation geometry of 2P. The right axis of panels a–i was arbitrarily scaled for visibility. More detailed information is described in the text.

In the text