POLARIZATION SPECTRUM OF NEAR INFRARED ZODIACAL LIGHT
OBSERVED WITH CIBER

The zodiacal light (ZL) arises from sunlight scattered by the interplanetary dust (IPD) in the optical and the near-infrared , and from thermal emission from IPD in the mid- and far-infrared . Measuring the ZL is important for understanding the structure of the IPD distribution and physical properties of the IPD, such as their size distribution, composition, shape, and complex refractive index. In addition, information obtained from ZL measurements is important for future studies of dust disks of exoplanetary systems. . Because the IPD grains of these sizes fall into the Sun , IPD dating to the early solar system is unlikely to exist today. A continuous supply of IPD particles is necessary to maintain the zodiacal cloud.

The source of the IPD is assumed to comprise both comets and asteroids, but the relative importance of each has not been settled. Nesvorný et al. (2010, 2011) compared their dynamical simulations of the IPD with the Infrared Astronomical Satellite (IRAS) data suggesting that 85 $\sim 95\%$ of the observed mid-infrared emission is produced by particles from Jupiter-family comets (JFCs) and $<10\%$ by dust from long-period comets. Fernández et al. (2006) showed that the geometric albedo of comet 162P/Siding Spring (P/2004 TU₁₂), which is largest radii among known JFCs, is $0.059\pm 0.023$ in H band, $0.037\pm 0.014$ in R band, and $0.034\pm 0.013$ in V band. Soderblom et al. (2002) also observed the JFC 19P/Borrelly and derived a geometric albedo of $0.03\pm 0.05$. The IPD is also known to be a low albedo (Kelsall et al., 1998) and has similarities to the comet nucleus. Yang & Ishiguro (2015) derived the spectral gradient of IPDs as $S^{\prime}=8.5\pm 1.0\%/100$ nm at 460 nm, and combining with the albedo showed that $>90\%$ of the IPDs originate from comets or D-type asteroids. The ZL spectra measured by the Near Infrared Spectrometer (NIRS) on board the Infrared Telescope in Space (IRTS) and the Cosmic Infrared Background Experiment (CIBER) show silicate-like features at 0.9 and 1.6 $\mu$m (Matsumoto et al., 1996; Tsumura et al., 2010), comparable to fresh and active comets or S-type asteroids. A combination of amorphous and crystalline silicate grain features is found in ZL spectrum between 9 and 11$\mu$m (Ootsubo et al., 1998; Reach et al., 2003; Ootsubo et al., 2009).

The ZL scattered by an optically thin cloud of IPDs presents a systematic polarization. The linear polarization degree $P$ of sunlight scattered by IPD surfaces is usually defined as the difference between the intensities polarized along the planes perpendicular, $I_{\perp}$, and parallel, $I_{\parallel}$, to the scattering plane:

According to Kelsall et al. (1998), the ZL intensity $I_{\lambda}$ observed at wavelength $\lambda$ as the integral along the line of sight $s$ is expressed as:

where $n(X,Y,Z)$ is the three-dimensional density of the IPD, $A_{\lambda}$ is the albedo at wavelength $\lambda$, $F^{\odot}_{\lambda}$ is the solar flux, and $\Phi_{\lambda}(\Theta)$ is the phase function at scattering angle $\Theta$. Since the polarization properties of scattered light depend on the scattering angle and the composition of the IPD, the origin of the IPD can be investigated by the polarization spectrum of ZL at various fields. For example, the cometary dust ejected from comets is studied by polarization measurements. Zubko et al. (2014) studied dust in comet C/1975 V1 (West) and reproduced the polarization measurement by models with Mg-rich silicate and amorphous carbon. Lasue et al. (2009) also studied dust of comet C/1995 O1 Hale-Bopp and 1P/Halley based on the polarization measurement and implied that the cometary dust can be explained by mixture of a non-absorbing silicate-type material and a more absorbing organic-type material.

A few studies report polarization measurements of the ZL. Leinert et al. (1998) summarized the ZL polarization measured from space in the visible and the near-infrared, and the degree of polarization is largely dependent on the helio-ecliptic longitude to first order. At visible wavelengths, and shows little wavelength dependence (Weinberg & Hahn, 1980; Pitz et al., 1979; Leinert & Blanck, 1982). In the near-infrared, only Berriman et al. (1994) has measured the polarization of the ZL from space by the Diffuse Infrared Background Experiment (DIRBE) aboard on the Cosmic Background Explorer (COBE) in discrete photometric bands at 1.25, 2.2, and 3.5 $\mu$m. This result shows that the degree of polarization of the ZL is about 10 $\sim 20\%$ at solar elongation $\epsilon$ = 90^∘.

In this paper, we report a ZL polarization spectrum measurement from the Low Resolution Spectrometer (LRS) onboard CIBER. The purpose of polarization observation by LRS was to separate polarized ZL from unpolarized EBL, and to identify spectral features by studying the wavelength dependence of polarization. Our result is the first measurement of the ZL polarization spectrum in the near-infrared.

CIBER, designed to study the diffuse near-infrared emission above the Earth’s atmosphere (Zemcov et al., 2013), housed three instruments including a two broad-band imagers (Bock et al., 2013), a narrow band spectrometer (Korngut et al., 2013), as well as the LRS designed to measure the spectrum of diffuse light in 0.8$\leq\lambda\leq$ 1.8 $\mu$m (Tsumura et al., 2013) with a wavelength resolution of $\lambda/\Delta\lambda~{}=~{}15$-30. Fore optics of the LRS brings an image of the sky to focus on a mask containing 5 slits as shown in Figure 1, each spanning a field of view (FOV) of 5${}^{\circ}\times$2.7^′ sampled by a 256$\times$256 pixel HgCdTe array. This array hosts a cold shutter assembly for dark current measurement.

CIBER conducted observations four times, on February 2009, July 2010, March 2012, and June 2013. The payload was successfully recovered and refurbished after the first three flights. Because the polarizers were only installed in the third flight, we mainly use the third flight data in this paper. At the third flight, we used NASA Black Brant IX¹¹1For details on the launch vehicles, Sounding rocket handbook (http://sites.wff.nasa.gov/code810/files/SRHB.pdf). two-stage vechicles launched from the White Sands Missile Range in New Mexico, USA. The apogee on the flight was 330km, providing a total exposure time of $\sim$ 240 seconds. The raw data, which are non-destructively sampled by the integrating detectors, were telemetered to the ground from the rocket during the flight. The celestial attitude control system achieved a pointing stability of $<$ 8^′′. Details about the CIBER payload and flight performance are written in Zemcov et al. (2013). See Tsumura et al. (2013) and Arai et al. (2015) for details of the LRS.

To measure the polarization spectrum, we installed wire-grid polarization film ²²2Manufactured by Asahikasei E-materials corporation. on the slit mask. The wire-grid polarization films with different transmittance axis were installed on eight different regions of the slit mask (Figure 1). Although the FOV of each polarizer is different, the ZL is smoothly distributed over the entire FOV and small field-to-field fluctuations if any can be corrected for. Therefore, if the integrated star light (ISL) and diffuse galactic light (DGL) can be removed, ZL polarization can be measured with this instrument.

The phase angles of the transmittance axis of the polarizer are labeled as $\theta$ = $0^{\circ},45^{\circ},90^{\circ},135^{\circ}$ (Figure 1). Note that the polarizing film in the lower left corner was mistakenly installed with the transmission axis rotated by 90 degrees during the final installation, but it was calibrated and launched as it was. Because the polarizing films were not installed on the center slit, the total spectrum of the sky brightness was also measured.

The observed fields are listed in Table 1. For the ZL analysis, the fields are selected based on ecliptic coordinates and solar elongation. The low ecliptic latitude field, Elat30, shows high ZL brightness. On the other hand, the high ecliptic latitude fields exhibit low ZL brightness. The North Ecliptic Pole (NEP) field, where the solar elongation is 90^∘, is selected because the polarization is expected to be maximum. As the solar elongation increases, the polarization is expected to decrease.

We describe the wavelength calibration, surface brightness calibration, and flat field correction, and polarization calibration in this section. The wavelength calibration, surface brightness calibration, and flat field correction are similar to Arai et al. (2015).

At first, we make the LRS image from individual time-ordered array readout frames. In Figure 5, we give examples of the LRS images in the third flight. The five vertical sections correspond to the five slits dispersed in the $x$ direction, and the four parallel sections correspond to the wire-grid polarizing films.

In order to measure the absolute spectrum of the sky brightness, we subtract the dark current and mask bright point sources from the LRS images. The dark current is estimated from the masked regions of each slit individually. The corners of the array are masked to avoid contamination by spurious signals emanating from the multiplexers of the detectors in the corners of each quadrant. To remove bright point sources, we average the photocurrent of each slit along the horizontal direction, then clip the pixels containing stars determined by the criterion that the band-averaged photocurrent is deviated from the mean of band-average photocurrent of all pixels by 2 $\sigma$, where $\sigma$ is the standard deviation of the photocurrent. We iterate this clipping procedure until the ratio of the number of rejected pixels to the remaining pixels is less than 0.1$\%$ of the total. To reject hot and dead pixels and the remaining faint point sources, pixels which are greater than 3 $\sigma$ from the mean are also excluded. Finally, we derive the sky spectrum, $I_{\rm sky}(\theta)$, through each polarization filter as shown in Figure 6.

Further details on the basic data reduction are described in Tsumura et al. (2010) and Arai et al. (2015).

After the basic data reduction, to derive the ZL polarization spectrum, we separate the mean ZL brightness, $I_{\rm ZL,mean}$, and the ZL brightness of the polarized component, $I_{\rm ZL,pol}$, from the measured sky brightness. We assume that the polarization components of the DGL, the ISL, and the EBL are negligible compared to the ZL as discussed in Section 7. The measured sky brightness of the polarized component $I_{{\rm sky,pol}}$ can then be assumed as $I_{{\rm sky,pol}}=I_{\rm ZL,pol}$.

The mean sky brightness comprises;

To derive $I_{\rm ZL,mean}$, the DGL, the ISL, and the EBL contributions need to be separated from the measured sky brightness (Matsuura et al., 2017). The DGL component, $I_{{\rm DGL}}(\lambda)$, is derived using its spatial distribution as traced by 100 $\mu$m emission on scales smaller than a degree (Arai et al., 2015). The ISL component, $I_{{\rm ISL}}(\lambda)$, is estimated by Monte-Carlo simulation of the star distribution in the FOV using the 2MASS catalogue (Skrutskie et al., 2006), taking into account the limiting magnitude and the effective slit efficiency of the LRS (Arai et al., 2015). The EBL component, $I_{{\rm EBL}}(\lambda)$, can be assumed as identical in all the fields, but with a lot of indeterminacy. To derive the fiducial unpolarimetric spectral shape of ZL, we calculate the difference between two fields,

where $i$ and $j$ indicate different observation fields. We assume that the EBL component is identical in all the fields, so $I_{{\rm EBL}}(\lambda)$ is canceled in Equation 5. We also estimate the ZL brightness, $I_{\rm ZL_{model}}$, at 1.25 $\mu$m of each field from the DIRBE/COBE-based ZL model (Kelsall et al., 1998), which are summarized in Table 1, and normalize the differences of $I_{\rm ZL,mean}$ with $I_{\rm ZL_{model}}$ at 1.25 $\mu$m. Because of deep airglow contamination, only the NEP, Elat-30 and BOOTES-B fields are available to derive the fiducial unpolarimetric spectral shape of ZL with polarization slit of the LRS. To improve the signal-to-noise ratio, we use not only the data with polarization slit but also that with center slit at the NEP and Elat-30 fields, and average these results. It is noteworthy that we could not use the data with center slit at the BOOTES-B field because the detector was not functioning properly. The airglow emission likely depends on atmospheric conditions and changes daily. The details of uncertainty of the airglow contamination are described in Section 7.

Figure 7 presents the fiducial mean spectral shape of ZL during the third flight. The difference in the ZL spectral shape between the second and third flights may be due to the timing of the observations and the calibration accuracy. In deriving the ZL polarization spectrum, we only use the ZL spectral shape of the third flight in terms of the instrumental systematic uncertainties.

To derive $I_{\rm ZL,pol}$, we fit the measured sky spectrum $I_{\rm sky}$ with Equation 2 to separate the polarized and unpolarized components. In Figure 8, we show the measured $I_{\rm sky}(\theta)$ at 1.26 $\mu$m as a function of $\theta$ in the NEP field, as an example of the analysis. The black curve presents best fit by Equation 2.

Finally, from Equation 3, the ZL polarization spectrum $P_{\rm ZL}(\lambda)$ can be expressed as,

Fig 14 contains the same data as Fig 11, but overplotted with the instrumental and astronomical systematic uncertainties. The systematic uncertainties include the instrumental calibrations, the contributions from airglow emission, and the diffuse brightness estimation. The total systematic uncertainty is the upper limit because we assume maximum polarization of residual faint stars, and the DGL.

In Figure 15, the ZL polarization has little wavelength dependence from visible to infrared. The similar scattering properties at different wavelengths suggest that large IPD grains contribute to the ZL polarization. This suggestion is supported by the fact that our observations are consistant with the ZL polarization calculated by the empirical scattering model in the visible band. The similar scattering properties at different wavelengths suggest that large IPD grains contribute to the ZL polarization. We provide another test for the IPD size by comparing the ZL polarization spectrum with the polarization of Mie scattering theories. We used five models with different particle radius ($x$=0.3, 0.5, 1, 3, and 10 $\mu$m) with a constant complex refractive index independent of wavelength, referring to $m=2.98+1.6i$ for graphite, a typical absorber. The wavelength dependence of the ZL polarization from visible to infrared is consistent with the Mie scattering model for large particles ($r>1~{}\mu$m). The observed degree of polarization is also roughly consistent with the Mie scattering model for large particles within the systematic uncertainty.

As shown in Figure 12, our results can also be reproduced by the Mie scattering with graphite, suggesting that the IPD is dominated by large particles ($r>1~{}\mu$m). The observed ZL polarization is not consistent with the Rayleigh scattering which would favor small IPD grain size . The Rayleigh scattering implies that the amount of scattering is inversely proportional to the fourth power of the wavelength. However, the ZL polarization spectrum shows little wavelength dependence, therefore disfavoring the Rayleigh explanation. In fact, the IPD is composed of several of these components, suggesting that the larger particles contribute more to ZL polarization than the smaller ones.

In Figure 15, we also consider the polarization of comet Hale Bopp extrapolated to 40^∘ phase angle. The polarization of cometary dust also has little wavelength dependence. This is consistent with our observed polarization and that of large absorbing materials, however, cometary dust also contains silicate. As reported by Ootsubo et al. (2009), the ZL spectrum exhibits crystalline silicate features at 9.3 and 11.35 $\mu$m. Silicate emission bands similar to comets were also detected in the ZL spectrum (Reach et al., 2003). Hanner (1999) also reported Mg-rich silicate features at 9.3 and 11.3 $\mu$m. Zubko et al. (2014) reproduced the polarization measurement in comet C/1975 V1 (West) by modeling a mixture of weakly and highly absorption particles with complex refractive indices $m=1.5+0i$ or $1.6+0.0005i$ and $2.43+0.59i$. This mixture corresponds to Mg-rich silicates and amorphous carbon. Lasue et al. (2009) also found evidences of a similar mixture comprising non-absorbing silicate-type and absorbing organic-type materials in the cometary dust of comet C/1995 O1 Hale-Bopp and 1P/Halley.

We cannot conclusively determine the origin of the IPD from our data alone. Further observation of comets and asteroids as well as theoretical modeling of the IPD scattering are required to reveal the origin of the IPD.

We will extend the ZL observation to shorter wavelengths using the second CIBER experiment, CIBER-2 (Takimoto et al., 2020). CIBER-2 was successfully launched in mid-2021 and its data will provide ZL spectrum at 0.5-2.5 $\mu$m. Future observations of ZL polarization spectra in the visible and near-infrared will help us understand the structural and physical properties of IPD. At the same time, the heliocentric IPD distribution will be observed by ZL observation from outside the Earth’s orbit (0.7-1.5 au) by the Hayabusa-2 extended mission (Hirabayashi et al., 2021). These missions will allow us to better probe the IPD origin.

To determine the size and composition of the IPD, we observed the linear polarization spectrum of the ZL at the near-infrared wavelengths from 0.8 - 1.8 $\mu$m with spectro-polarimetric function of the LRS/CIBER instrument. We subtracted the contributions of the ISL, the DGL, and the EBL from the total sky brightness to derive the ZL polarization spectrum. The ZL polarization spectrum shows little wavelength dependence, and the degree of polarization shows clear dependence on the ecliptic coordinates and the solar elongation. The measured degree of polarization and its solar elongation dependence are reproduced by the empirical scattering model in the visible band and also by a scattering model for large absorptive particles, while small particles cannot reproduce ($r<1~{}\mu$m). All of our results suggest that the IPD is dominated by large particles. The wavelength dependence of the ZL polarization in wide wavelength range including the visible band is similar to that of comet Hale-Bopp,