OPTICAL AND NEAR-INFRARED POLARIMETRY FOR A HIGHLY DORMANT COMET 209P/LINEAR

Polarimetric observations of 209P were conducted for five nights in 2014 April–May using two telescopes: the Hiroshima Optical and Near-infraRed camera (HONIR) on the 1.5-m Kanata telescope (hereafter Kanata) at the Higashi-Hiroshima Astronomical Observatory, Hiroshima, and the visible Multi-Spectral Imager (MSI) on the 1.6-m Pirka telescope (Pirka) at Hokkaido University's Nayoro Observatory in Hokkaido, Japan. In the imaging polarimetric mode, each instrument employs a Wollaston prism beam-splitter and a rotatable half-wave plate modulator, which produces reliable data sets taking ordinary and extraordinary images simultaneously at four position angles θ = 0°, 45°, 225, and 675. HONIR provides a simultaneous optical and near-infrared imaging polarimetry in a sequence of exposures. The detectors consist of a 2048 × 4096 pixel Hamamatsu Photonics fully depleted back-illuminated CCD with a pixel scale of 15 μm for optical channel and a 2048 × 2048 pixel Raytheon VIRGO-2K HgCdTe array with a pixel scale of 20 μm for infrared channel, respectively (Akitaya et al. 2014). MSI enables optical polarimetric measurements using the EM-CCD camera (Hamamatsu Photonics C9100-13), which employs a back-thinned 512 × 512 pixel frame transfer CCD with a pixel scale of 16 μm (Watanabe et al. 2012). We observed 209P with HONIR/Kanata and MSI/Pirka at large phase angles, that is, 855–995 (R_C-band) and 855–899 (J-band). We employed a non-sidereal (cometary motion) tracking with MSI/Pirka, and a sidereal tracking with HONIR/Kanata. The exposure times were chosen ranging from 45 to 180 s depending on the detected fluxes and the apparent motion of 209P. Note that the apparent motion of the comet was fast in late 2014 May (5''–7'' minute⁻¹ with respect to the sidereal tracking) so that we chose short exposure times to reduce the risk of tracking errors of these telescopes. Details of those observations are summarized in Table 1.

Observed raw data were processed in the standard manner for astronomical imaging data. All object frames were bias subtracted, flat fielded, and cosmic ray corrected using the IRAF reduction package. Figure 1 shows the processed images, which are produced by summing up the reduced ordinary images. We found that the cometary tail was faint in the image on UT 2014 April 23 but became obvious in the R_C-band image in 2014 May. The tail extended between the Sun–comet vector and the negative heliocentric velocity vector, which is typical of cometary dust tails (rather than ion tails). On the contrary, the tail was not detected in the J-band image due to the low signal-to-noise ratio (S/N). We noticed the comet was slightly stretched in the apparent direction of movement in the image taken with HONIR/Kanata because we could not employ a comet-tracking mode with the Kanata telescope (theoretically, it stretched by 18 on May 23, 28 on May 1, and 37 on May 17, comparable to or slightly larger than the FWHM in HONIR images).

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Imaging polarimetric data have often been analyzed to produce the two-dimensional polarization maps (Furusho et al. 1999, 2007; Jones & Gehrz 2000; Hadamcik et al. 2013). However, since the dust tail was too faint to permit us to make a map, we examined the spatial variation of the linear polarization degrees in the following manner: We first extracted individual source fluxes on the ordinary and extraordinary images by means of the IRAF apphot task. Each flux was numerically integrated over the desired circular aperture and the sky background was subtracted using the surrounding annulus (i.e., aperture photometry). We set the aperture size ranging from one to five times the full width at half-maximum (FWHM, 26–35) of 209P. The extracted intensities are used to obtain the Stokes parameters normalized by the intensity, Q/I, and U/I, which are given by:

$$\begin{eqnarray}&&\displaystyle \frac{Q}{I}=\left(1-\sqrt{\displaystyle \frac{{I}_{{\rm{e}},0}/{I}_{{\rm{o}},0}}{{I}_{{\rm{e}},45}/{I}_{{\rm{o}},45}}}\right)/\left(1+\sqrt{\displaystyle \frac{{I}_{{\rm{e}},0}/{I}_{{\rm{o}},0}}{{I}_{{\rm{e}},45}/{I}_{{\rm{o}},45}}}\right),\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&\displaystyle \frac{U}{I}=\left(1-\sqrt{\displaystyle \frac{{I}_{{\rm{e}},22.5}/{I}_{{\rm{o}},22.5}}{{I}_{{\rm{e}},67.5}/{I}_{{\rm{o}},67.5}}}\right)/\left(1+\sqrt{\displaystyle \frac{{I}_{{\rm{e}},22.5}/{I}_{{\rm{o}},22.5}}{{I}_{{\rm{e}},67.5}/{I}_{{\rm{o}},67.5}}}\right),\end{eqnarray} \tag{ 2 }$$

where ${I}_{{\rm{o}},{\rm{\Psi }}}$ and ${I}_{{\rm{e}},{\rm{\Psi }}}$ are the ordinary and extraordinary intensities at the half-wave plate angles Ψ in degree (Kawabata et al. 1999). The degree of linear polarization (P) and the position angle of polarization (θ_P) were calculated as

$$\begin{eqnarray}&&P=\sqrt{{\left(\displaystyle \frac{Q}{I}\right)}^{2}+{\left(\displaystyle \frac{U}{I}\right)}^{2}},\end{eqnarray} \tag{ 3 }$$

and

$$\begin{eqnarray}&&{\theta }_{P}=\displaystyle \frac{1}{2}{\mathrm{tan}}^{-1}\left(\displaystyle \frac{U}{Q}\right),\end{eqnarray} \tag{ 4 }$$

respectively (Tinbergen 1996). For each night, we corrected for the instrumental polarization, the polarization bias, and the position angle zero-point using the results for the polarized and unpolarized standard stars. The polarization quantity (P_r) and the position angle of the polarization plane (θ_r) referring to the scattering plane (Zellner & Gradie 1976) were expressed as the following:

$$\begin{eqnarray}&&{P}_{r}=P\mathrm{cos}(2{\theta }_{r}),\end{eqnarray} \tag{ 5 }$$

and

$$\begin{eqnarray}&&{\theta }_{r}={\theta }_{P}-(\phi \pm 90^\circ ),\end{eqnarray} \tag{ 6 }$$

where ϕ is the position angle of the scattering plane (see Table 1), and the sign inside the bracket is chosen to satisfy $0^\circ$ $\leqslant$ (ϕ ± $90^\circ$) $\leqslant \;180^\circ$ (Chernova et al. 1993). In Table 2, we summarize the results of the polarization degrees (P and P_r) and the position angles (${\theta }_{P}$ and θ_r), which are derived from the multiple data sets at each night.

From this point on, we tried to distinguish the nuclear flux from the coma flux. In general, the optical depth of most cometary comae is small relative to the nucleus. It is unclear for the flux contrast between the nucleus and the coma (Lamy et al. 2004, p. 223). We chose the data from two nights (UT 2014 May 4 and 19) obtained with Pirka to allow the use of the precise non-sidereal tracking. The radial profiles of 209P were obtained from the co-added frames, which used only ordinary intensities at the four half-wave plate angles. Stellar radial profiles were defined from the standard star images in the same night. These data were converted into the one-dimensional azimuthally averaged surface brightness by the pradprof task in IRAF. The profile parameters were determined by the best fit model with the Moffat point-spread function fitting function (Moffat 1969). The reduced magnitudes of the nucleus on these two nights, R = 19.92 ± 0.26 mag and R = 20.02 ± 0.26 mag, were calculated using an empirical formula, R = 16.24 + 0.04α (Ishiguro et al. 2015). Figure 2 shows the radial profiles 209P (open circles) together with nucleus model (solid line) on these two nights. It is clear that the observed fluxes are dominated by the nucleus at the radial distance within ∼2 × FWHM, while by the coma beyond ∼2 × FWHM.

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To distinguish the nuclear polarization degrees from the coma polarization degree, we made a plot of the polarization degrees taken with different aperture sizes with respect to the ratio of the modeled nuclear flux to the observed flux, f_n/c (Figure 3). We considered the error associated not only with the S/N and the uncertainty in the sky background determination, but also with the uncertainty of the nuclear magnitude model (i.e., 0.26 mag, Ishiguro et al. 2015). In Figure 3, the data with smaller apertures are plotted in the upper right, while the data with larger apertures are plotted in the lower left. This trend implies that the cometary nucleus is more polarized than the coma. In principal, the P-intercept (i.e., f_n/c = 0) is supposed to approach the coma polarization degree while the intersection with f_n/c = 1 approaches the nuclear polarization degree. We thus assumed that the data points in Figure 3 can be fitted with a simple linear function, P = (P_n − P_c) × f_n/c + P_c, where P_n and P_c are polarization degrees of the nucleus and coma, respectively, and derived these values by the method of least squares.

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In Table 2, the position angle of the strongest electric vectors, θ_P, is in good agreement with those of normal vector to the scattering plane projected on the celestial plane, ${\theta }_{\perp }$ (see Table 1) to an accuracy of a few degrees. For a spherical body, θ_P is supposed to align to the normal vector of the scattering plane, and therefore, θ_P = ${\theta }_{\perp }.$ Although the radar image of 209P showed an irregular shape (Howell et al. 2014), such a regional irregularity may be smoothed out by integrating the flux through the disk. These high polarizations for nucleus indicate a light scattering feature on an object a few kilometers in size (2.5 × 3.2 km, Ishiguro et al. 2015). Since the polarization degree for an airless body is primarily controlled by the surface albedos, the low albedo of the nucleus (the geometric albedo P_v ∼ 0.05, Ishiguro et al. 2015) would result in the high polarization degree. However, we are unable to confirm this because of a lack of precedent for such dark airless bodies (typically P_v < 0.1).

The following studies were shown potential for becoming the high polarization degree (∼30%) of the dark bodies around α = 95°. There are studies of near-nuclear polarization for 2P/Encke (P_v = 0.05 ± 0.02, Fernández et al. 2000). High and low polarizations have been reported to P = 34.9% ± 1.7% at α = 946 (P = 39.9% ± 2.9% when corrected for the NH₂ contamination) in the red domain (662/5.9 nm) (Jockers et al. 2005) and P = 11% ± 3% at α = 929 in the green domain (526/5.6 nm) (Jewitt 2004) respectively. Considering the contamination by the gaseous species, both studies were measured through the narrow band filter for the same appearance. Note the difference that only the spectral gradient is incompletely explained as pointed out by Hadamcik & Levasseur-Regourd (2009). Polarization of dark airless bodies at the high phase angle were obtained P = 24.5% ± 4% at α = 81° for the Martian satellites Phobos (P_v = 0.07, Zellner & Capen 1974) and P = 22% ± 4% at α = 74° for Deimos(P_v = 0.07, Thomas et al. 1996) in the orange domain (570 nm), while these measurements by Mariner-9 may contain significant systematic errors (Noland et al. 1973). Thus, more observations of dark asteroids are needed to investigate the positive polarization at the higher phase angle.

For the coma, such positive polarization with a maximum of P_max = 25%–30% around α = 95° in the red domain was reported in previous studies of the high P_max comets (see Figure 4). Our measurements for the coma are consistent with them. We found from HONIR measurements that the wavelength dependence of the polarization for the mixture of the nucleus and coma was negligibly small, that is, P = 30% ± 3% in R_C-band and P = 27% ± 5% in J-band at α = 899 with the aperture size of 1–3 × FWHM, although the error of the measurement was not good enough to compare with previous studies.

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Figure 4 shows the phase angle dependence of the polarization degrees of the nucleus and coma. For comparison, we show the previous studies for cometary comae at phase angles larger than about 80° and two red continuum lines through the use of the database of comet polarimetry (Kiselev et al. 2005). Our data shows a moderate increase from 835 to 995 and no clear peak. There are known to be two classes of comets in terms of the maximum polarization P_max, so-called "high-polarization comets" and "low-polarization comets." Levasseur-Regourd et al. (1996) reported that these two classes of comets have similar polarization properties at α < 40° but are bifurcated at larger phase angles. The high-polarization comets have the peak polarization ${P}_{\mathrm{max}}\;\sim$ 25%–28% around α = 90°–100°, while the low-polarization comets have ${P}_{\mathrm{max}}\;\sim$ 15% around the same phase angle. In addition, Levasseur-Regourd et al. (1996) described the high-polarization comets as tending to be classified as dusty comets, while the low-polarization comets tend to be classified as gassy comets based on optical spectra. However, the latter case was evaluated as a misleading definition due to the gas contaminations through the broadband filter (Kiselev et al. 2004, 2001; Jewitt 2004). In the near-nucleus region, the polarizations of some low-polarization comets reach to those of high-polarization comets (Kolokolova et al. 2007).

First of all, we would like to discuss the contamination of polarization degree by gas emissions. The observed polarization degrees of comets are known to be occasionally contaminated by gas emissions that reduce the observed polarization degree. In fact, gas-rich comets tend to display low polarization degrees probably because of the depolarization of the gas emission (Kiselev et al. 2001). However, we found that the observed spectra of the 209P coma showed no detectable gas emission in the wavelength range in which we deduced the polarization degree. Figure 5 shows the optical spectra on UT 2014 May 27, only about a week after our polarimetric run, taken at the Nishi-Harima Astronomical Observatory with the Medium and Low-dispersion Long-slit Spectrograph (MALLS) attached to the Nayuta 2.0-m telescope. We employed the lowest-resolution grating (150 line mm⁻¹), 8''-slit, and the order cut filter of WG320, ensuring the available spectrum at the wavelength 500–730 nm with the spectral resolution R ∼ 90. Note that the continuum slope might be affected by insufficient calibration of the flux with the standard star taken at slightly different airmass. We normalized the obtained reflectance spectrum at 550 nm and subtracted the continuum by the spline interpolation. Figure 5 shows the continuum-subtracted spectrum with the typical emission lines labeled (Brown et al. 1996).

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There are clearly no detectable emission lines in the coverage of our R_C filter, dispelling the gas contamination. Similar results are reported through spectroscopic observation on UT 2014 April 9 that a spectrum in the 350–600 nm range reveals no CN, C₂, or C₃ emission features (Schleicher 2014). Although there might be time variation in the intensity of gas emission, we conjecture that the variation would be small in our polarimetric data because the R_C-band monitoring magnitudes did not change over this period (Ishiguro et al. 2015).

We distinguished the polarization of the nucleus P_n = 30%–31% from that of the coma P_c = 29%–30% taking account of the signal with different apertures (see Section 2.3). These two values are not necessarily the same, because we observe the scattered light from the coma dust grains in the former, while we observe the reflected light from a kilometer-sized body in the latter. As shown in Figure 4, a comparison between observations performed in other comets indicates a lower trend for the coma polarizations of 209P. We may nevertheless underestimate the polarization degrees for the coma due to a very slight gas contamination.

The polarization of the nucleus (P_n) seems to show higher than the coma (P_c) but the differences are insignificant to the accuracy of our measurement. Figure 6 compares the polarization degrees of the nucleus with those of asteroids at phase angles larger than about 60° from the asteroid polarimetric database (Lupishko 2014). All asteroids in the database show polarization degrees remarkably lower than 209P. The phase-polarization curve of (4179) Tautatis is well studied among these asteroids. Ishiguro et al. (1997) determined the phase angle of the maximum polarization at ${\alpha }_{\mathrm{max}}$ = 107° ± 10°. Although we cannot determine ${\alpha }_{\mathrm{max}}$ of 209P with our measurement, we conjecture that our polarimetric measurement was performed around the maximum polarization degree because both the S-type asteroid and cometary coma show the maximum values around the phase angle we measured. For a better understanding of the polarization properties of the nucleus and coma dust at large phase angles, we derived the P_max using the Lumme and Muinonen function (Goidet-Devel et al. 1995; Penttilä et al. 2005):

$$\begin{eqnarray}&&{P}_{\alpha }=b{\left(\mathrm{sin}\alpha \right)}^{{c}_{1}}{\left(\mathrm{cos}\left(0.5\alpha \right)\right)}^{{c}_{2}}\mathrm{sin}\left(\alpha -{\alpha }_{0}\right),\end{eqnarray} \tag{ 7 }$$

where b, c₁, c₂ and α₀ are constant parameters. According to Penttilä et al. (2005), parameters b and α₀ affect the amplitude and slope of polarization and the inversion angle, and the other two parameters, the powers c₁ and c₂, control shapes the phase curve. Because the phase angle coverage of our data is limited, we first fit the phase-polarization relations for comets or asteroids, and then derived P_max of 209P. Therefore, assuming that the nucleus was essentially identical to low-albedo asteroids(P_v < 0.1), we deduced P_max of the nucleus is 30.8% at ${\alpha }_{\mathrm{max}}$ of 96° with the fitted parameters b = 34.81%, c₁ = 0.7838, c₂ = 0.2400 and α₀ = 1788. For the coma, assuming that the fitted parameters c₁ = 0.7904, c₂ = 0.2418 and α₀ = 2159 for high-polarization comets and keeping b as a free parameter, we deduced P_max of the coma is 29.6% with ${\alpha }_{\mathrm{max}}$ = 98°.

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Our P_max values are higher polarization than other high-polarization comets and known airless bodies. It was suggetsed that the presence of jets and arcs in the ambient coma correlated with regions of higher polarization (Hadamcik et al. 1997; Tozzi et al. 1997; Furusho et al. 1999). However, according to Ishiguro et al. (2015), such structures were not identified for 209P. Trends are shown as that are similar to the case with cometary nuclei split into fragments (e.g., C/1999 S4 Hadamcik & Levasseur-Regourd 2003c and 73P Bonev et al. 2008), whereas 209P is obvious without such an outburst. Therefore the correlation between cometary activity and polarization excess are considered to be unsuitable for 209P. Some physical properties such as grain size distribution and porosity (Hadamcik et al. 2002, 2006; Hanner 2003) may enhance the polarization degree of 209P, although we have no observational evidence to study these properties.

Asteroids show a similar trend of the phase-polarization relation having the maximum polarization at α = 90°–120°(Ishiguro et al. 1997; Kiselev et al. 1999) but the polarization degrees of these asteroids are significantly lower than that of the 209P nucleus (see Figure 6). Note that only a few asteroids including (1685) Toro, (4179) Toutatis (214869) 2007 PA₈ were observed at large phase angles and they are classified as S-type asteroids. The S-type asteroids show very similar phase-polarization relations. Unique data concerning E-type asteroids, which was obtained from (33342) 1998 WT₂₄, indicated P_max at α = 72° (Kiselev et al. 2002). The linear polarization of (2100) Ra-Shalom (C-type) was measured up to a moderate phase angle (α = 50°). The C-type asteroid shows large P at α ≳ 20°, although P_max for C-type asteroids has not been determined yet. Since S-type asteroids generally have albedos larger than those of C-type asteroids and E-type asteroids have albedos larger than others, it seems that P_max for asteroids would have a correlation between albedo and P_max.

A slope of the linear region at the inversion angle h (as the solid line in Figure 6 shows) was derived as 0.30%/° ± 0.01%/° from the phase-polarization curve. This polarimetric slope h was slightly steeper than the mean value of C-type objects (0.282%/° ± 0.025%/°, Gil-Hutton & Cañada-Assandri 2012). The relation between the geometric albedo P_v and the slope h has been found from the studies of the scattering properties (Gehrels & Gradie 1974; Dollfus et al. 1989; p. 594), and is the following:

$$\begin{eqnarray}&&\mathrm{log}\ {{P}}_{{\text{}}v}={C}_{1}\ \mathrm{log}\ h+{C}_{2},\end{eqnarray} \tag{ 8 }$$

where C₁ and C₂ are the constants. These recent values were presented as C₁ = –1.207 ± 0.067 and C₂ = –1.892 ± 0.141 by Masiero et al. (2012). The geometric albedo for the nucleus of 209P is calculated ${0.05}_{-0.02}^{+0.03}$ on these constraints, which are consistent findings for Ishiguro et al. (2015) and 0.049 ± 0.020 as the average albedo of the potential dormant comets (Kim et al. 2014).

This P_max–albedo relationship has long been known as the Umov law. Since the effect is observed on the moon, Mercury and Mars, the Umov law could essentially be applicable to asteroids and comets. The law is described as (Dollfus 1998):

$$\begin{eqnarray}&&{P}_{\mathrm{max}}={C}_{3}\left(d\right){{P}}_{{\text{}}v}^{-{C}_{4}},\end{eqnarray} \tag{ 9 }$$

where P_v is the geometric albedo. C₃ is a constant, originally proposed C₄ = 1 by Umov. Also, ${C}_{3}\left(d\right)$ depends a grain size d of the regolith.

Dollfus (1998) investigated how C₃ and C₄ change according to the grain size. Figure 7 shows the albedo versus P_max plot of 209P together with the Umov function modified by Dollfus (1998) and Shevchenko & Skobeleva (1995). The geometric albedo of 209P was unknown, so we adopted ${0.05}_{-0.02}^{+0.03}$ as the likely estimate from Equation (8). We also plotted the data of (1685) Toro, (4179) Tautatis, (33342) 1998 WT₂₄, (214869) 2007 PA₈ referring to the geometric albedo of 0.29 ± 0.13 (Masiero et al. 2012), 0.32 ± 0.11 (Kraemer et al. 2005), 0.56 ± 0.20 (Harris et al. 2007), and 0.29 ± 0.09 respectively. It is likely the albedo–P_max relation can be explained by the Umov law. Although the errors of albedos are too large to enable the regolith sizes on these bodies to be determined, we can safely say that our 209P data favors large ($\gg 1$ μm) particle sizes. Submicron-sized particles were probably well accommodated by gas outflow and lost over time by repeated comet activities.

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