HIGH-RESOLUTION IMAGING OF THE GEGENSCHEIN AND THE GEOMETRIC ALBEDO OF INTERPLANETARY DUST

All data in this paper were taken with WIZARD. A detailed description of the instrument is given in Usui et al. (2002), Ishiguro et al. (2002, 2003), and Ueno et al. (2005, 2007). In this section, we briefly describe the instrument and report on its performance based on the data reduction results.

WIZARD was developed to cover a wide-extended zodiacal light and the Gegenschein. It consists of a camera head and a wide-field lens (Figure 1). The system was mounted on an equatorial mounting. We employed a back-illuminated full-frame CCD chip, EEV CCD 42–80 (27.6 × 55.3 mm; 2048 × 4096 pixels), placed in a compact N₂-cooled cryogenic dewar (Kadel Engineering Corp.). During observations, the CCD temperature was maintained at around 180 K. The optical system was designed by the Genesia Corporation. It has a large image circle (60 mm in diameter) to cover the whole imaging area of the CCD. The focal ratio and the focal length are 2.8 and 32.5 mm, respectively. With the camera head, it gives a field of view of 46° × 92° with a pixel resolution of 14. Figure 2 shows the transmittance of the optical filter used for zodiacal light observations. It covers a wavelength range of 440–520 nm, avoiding prominent airglow emissions and artificial emission light. In particular, it was designed not to transmit O i airglow at 557.7 nm and artificial mercury vapor light at 435.8 nm. In addition, sodium beacons at 589.2 nm as laser guide stars are nowadays problematic for astronomical observations. The transmittances at these wavelengths are negligible: 0.35% at 435.8 nm (Hg), 0.19% at 557.7 nm O i, and 0.0008% at 589.2 nm (Na), respectively. The CCD clock pattern and the operation commands were prepared on a Linux host computer and sent to the CCD chip through a COGITO-3 system. COGITO-3 is a programmable control system for imaging devices specifically designed for scientific purposes and was developed by Ueno and Wada at ISAS/JAXA. It contains three units: a sequencer board, an A/D board, and a driver board. The analog signal obtained was converted to digital on the COGITO-3 A/D board and transferred to the host computer via a PCI–VME bus interface adapter.

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The analog signal in each pixel was sampled 16 times to reduce the readout noise. In addition, during CCD readout, we turned off the pulse motor used for star tracking to reduce noise associated with the motor drive unit. Consequently, the readout noise was reduced to the level of 20–25 e⁻. To monitor the zero level of the CCD, we recorded the overscan data by reading 50 dummy pixels before and after each row. For confirmation, we examined the stability of the zero intensity level using dark frames obtained at the intervals of the light frame. We found that the standard deviation of the zero level in each frame was ≲10 e⁻. Using the overscan region, we determined the zero level to an accuracy of 4 e⁻. The typical brightness of the Gegenschein plus airglow was about 1.1 e⁻ s⁻¹. With an exposure time of 600 s, the uncertainty of the zero intensity level (i.e., 4 e⁻) was small enough (0.6% of the Gegenschein plus airglow brightness, i.e., 660 e⁻) to derive the brightness of the Gegenschein plus airglow. In addition, background noise becomes dominated by photon noise from the natural night sky background rather than the readout noise. For this reason, we fixed the exposure time of 600 s for our Gegenschein observations.

An image taken by a wide-field camera generally shows strong vignetting. The detected intensity around the optical center is thus brighter than that at the edge of the frame. A flat-field correction is essential to obtain accurate intensity maps of the zodiacal light and the Gegenschein. It is, however, difficult to obtain flat data using WIZARD because of its huge field of view. We investigated flat-fielding for different spatial scales, that is, by considering optical vignetting as a low-frequency component and pixel-to-pixel variation in the sensitivity as a high-frequency component. We examined the optical vignetting by observing bright stars at different positions on the CCD chip. We confirmed that the weather conditions were stable and the air masses of these stars were constant during the exposures, suggesting that the brightnesses of these light sources were stable enough to examine the vignetting. Figure 3 shows the vignetting function across the CCD chip. From the measurement, we found that the detected intensity was almost constant within 20° from the optical center and reduced by 15% at 38° and 30% at 47°. For reference, we compare the vignetting function with those of previous CCD observations of the Gegenschein (James et al. 1997; Ishiguro et al. 1999a), in which commercial products for single-lens reflex cameras were used. It is clear that the optics for WIZARD is well designed to suppress the vignetting throughout a large portion of the CCD chip. Small-scale (pixel-to-pixel) fluctuations of the CCD sensitivity were examined by taking images with a Labsphere integrating sphere. We found that the pixel-to-pixel responsivity variation was negligibly small (≲0.3%).

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The performance of WIZARD, which are critical for estimating the error in the measurements, are summarized in Table 1.

In normal operation, we began observation soon after the end of evening twilight. We took a couple of images successively without slewing the camera to its next position. Since the motor controller for star-tracking was turned off for about three minutes after exposures for the CCD readout, the position of celestial objects moved about one degree on the CCD chip. This observation strategy enables us to distinguish small-scale structures of the Gegenschein from instrumental artifacts associated with uneven sensitivity of the instrument.

We performed a sequence of observations of the zodiacal light and the Gegenschein with WIZARD between 2003 March and 2006 November on Mauna Kea. Our observations were supported by the Subaru telescope (National Astronomical Observatory of Japan) and the InfraRed Telescope Facility (ITRF; NASA and Institute for Astronomy, University of Hawaii). We observed zodiacal light and the Gegenschein for 45 nights under photometric conditions. We selected Gegenschein data taken at high Galactic latitude near the zenith. In total, 14 nights of data in different seasons of the year were analyzed for the present study. We summarize the observation conditions of these data in Table 2. Gegenschein data were not available in May–July and December–January because the antisolar point was close to the Galactic plane (Figure 4).

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Table 1. Summary of the WIZARD Performance

Field of view	49°×98°
Pixel resolution	1435
Gain factor	0.825 (e−/ADU)
Readout noise	20–25 (e−)
Stability of the CCD zero level	≲10 (e−) or
	≲0.6% of the Gegenschein brightness
Vignetting	30% (at 47° from the optical center)
Pixel-to-pixel responsivity variation	≲0.3%

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The night sky brightness observed from the ground consists of those of zodiacal light including the Gegenschein, integrated starlight of unresolved stars, diffuse Galactic light, and pseudo-continuum airglow (Leinert et al. 1998). These light sources are attenuated by scattering of atmospheric molecules and aerosols. At the same time, the scattered component in Earth's atmosphere results in a diffuse light source. Dumont (1965) introduced the concept of effective optical depth for diffuse light sources, which is different from that for point sources. Later, Hong et al. (1998, 2002) developed the idea by solving radiative transfer in an anisotropically scattering spherical atmosphere of the Earth. It is difficult to reduce zodiacal light data in high-air-mass (i.e., large zenith distance) regions owing to the considerable contributions of the atmospheric diffuse light and the strong zenith extinction, although some intensive studies were conducted to obtain the absolute brightness of the zodiacal light from ground-based observatories (Kwon et al. 2004; Dumont 1965). The data reduction of the Gegenschein is, however, relatively easy. The Gegenschein appears near the zenith around midnight on Mauna Kea, where the contaminations from airglow and zenith extinction are smallest in the sky. The typical brightness of atmospheric diffuse light components was 20 S_☉10 and had a weak slope of 10%–20% of the Gegenschein brightness over a 40° field of view in Gegenschein exposures, where 1 S_☉10 is equivalent to the flux of a solar-type star of magnitude 10 distributed over one degree squared (Leinert et al. 1998). Inadequate reduction for these atmospheric components does not tend to lead to a misunderstanding of the morphology of the Gegenschein. In addition to these diffuse light sources mentioned above, there remain a number of point sources. Stars brighter than a visual magnitude of 12–14 (depending on the Galactic latitude) were resolved by our observations. We subtracted point sources brighter than magnitude 12 using the USNO–B2.0 catalog (Monet et al. 2003). The detected pixel data were replaced by the median values of circumjacent pixels.

For the most part, the data were analyzed as follows: first, the raw data were reduced using the overscan region as a bias level plus flat-field data. The flux calibration factor and the optical depth of the point sources are determined by aperture photometry of field stars at various air masses. Since we applied a nonstandard filter, we constructed a photometric standard star catalog for WIZARD data. An empirical formula is applied to convert from the Johnson–Cousins system into the WIZARD system, that is, M_WZD = V + α(B − V), where α is the color conversion factor and B and V are B-band and V-band magnitudes, respectively. To derive the coefficient α, we selected 56 stars in BSC Ver. 5 in an air-mass range of 1.00–1.07. Since the typical extinction coefficient on Mauna Kea in the WIZARD band was ∼0.15, atmospheric extinction did not change the stellar magnitude by ≳0.01 magnitude in this sky area, which is adequate to derive the coefficient α. The result is shown in Figure 5. In the figure, the bottom axis denotes the instrumental magnitude measured by aperture photometry, and the perpendicular axis denotes the magnitude in the WIZARD system (M_WZD). The best-fit parameter was found to be α = 0.605 ± 0.005.

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Unresolved starlight brightness plus diffuse Galactic light brightness were subtracted by using Pioneer 10 and 11 data, which was obtained beyond the inner solar system (i.e., outside the zodiacal cloud) and the USNO–B2.0 catalog (Monet et al. 2003). Although the central wavelength of WIZARD (460 nm) is slightly longer than that of the Pioneer blue band (440 nm), we used the Pioneer data without color correction. The contribution from unresolved starlight (stars fainter than magnitude 12) was estimated to be 20 S_☉10 (or 10% of the Gegenschein brightness) at a Galactic latitude of 25° and 10 S_☉10 (or 5% of the Gegenschein brightness) at a Galactic latitude of 50° (Leinert et al. 1998). The intensity of the airglow was subtracted using Barbier's function (Barbier 1944; Barbier et al. 1961), whereas the intensity of the multiple-scattering component in Earth's troposphere was not subtracted because of its weak contribution in our data around the Gegenschein. The extinction coefficients of Earth's atmosphere were obtained through stellar photometry, while the effective optical depths for the extended sources were obtained using the QDM_sca code by adjusting the particle albedo ω and the asymmetry factor g (Hong et al. 1998, 2002) to match the brightness of previous zodiacal light observations (Levasseur-Regourd & Dumont 1980). Some of the unknown parameters such as the intensity of the airglow at zenith and scaling factor of starlight brightness by Pioneer to our system were determined empirically to fit our data to the zodiacal light brightness in Levasseur-Regourd & Dumont (1980). We derived the Gegenschein brightness in the range of 165–190 S_☉10. Throughout this data reduction, we found that there is an uncertainty of ±10–15 S_☉10 in the absolute brightness. This uncertainty is mainly caused by inadequate subtraction of atmospheric diffuse light sources and imperfect correction of the zenith extinction, although instrumental effects such as scattered light inside the camera cannot be ruled out. It is, however, emphasized that the relative intensity distribution of ≲20° structures is reliable in our data set because it cannot be influenced by the inevitable atmospheric and instrumental effects.

Figure 6 shows snapshots of the Gegenschein in ecliptic coordinates. The long axis was nearly parallel to the ecliptic and stretched in the east–west direction. The morphology was symmetrical with respect to the line at an ecliptic longitude with respect to the Sun of λ − λ_☉ = 180°, where λ and λ_☉ denote the ecliptic longitude and ecliptic longitude of the Sun. Looking at the morphologies closely, we see a truncated oval shape whose eastern and western edges are angular rather than round. As the antisolar point is approached, the shape changes from truncated oval to round. There is a prominent peak at the antisolar point.

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It is clear that the brightness distribution shifted northward on February 17 and southward on October 12 (Figure 6). We found that the Gegenschein morphology deviated to the south in August–October and to the north in February–April. This trend is consistent with the result of Ishiguro et al. (1998), who mentioned that the overall brightness distribution shifted southward in September but shifted northward in March. The annual variation can be explained by the 3D zodiacal cloud model having a plane of symmetry deviated southward during August and November and northward during February and April, as previously noticed in Ishiguro et al. (1998). We discuss the annual variation in Section 3.2.

Figure 7 shows the surface brightness profile of the Gegenschein on October 12 at three different longitudes. These profiles show a convex feature over the ecliptic latitude range β = −3° to 1°. The flat-topped profiles were detected for the first time through the infrared observation of zodiacal emission (Low et al. 1984). They were also recorded for the Gegenschein (Ishiguro et al. 1999a; Mukai et al. 2003). Recent theoretical studies have showed that features in the profiles are associated with materials generated by recent catastrophic collisions in the main-belt asteroid region (Nesvorný et al. 2003, 2006). However, the convex structure is not clear in the profile of λ − λ_☉ = 180°. Instead, it exhibits a steep increase at β = 0°.

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Despite the annual variation in the overall shape, we found that the maximum position coincided with the antisolar point through the observation runs. Neither east–west nor north–south displacement was detected in the profiles at λ − λ_☉ = 180°. Figure 8 shows the ecliptic latitude of the maximum intensity at λ − λ_☉ = 180°. For comparison, we show photoelectric and photographic data compiled by Roosen (1970b) as well as previous CCD data. Our results are inconsistent with those in Roosen (1970b), James et al. (1997), Ishiguro et al. (1998), and Mukai et al. (2003), but they are consistent with the recent measurement from space by SMEI (Buffington et al. 2009). It should be emphasized that our measurement is the most reliable of all observational data so far because of the better spatial resolution.

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In this chapter, we analyze the annual variation in the morphology and the peak position by conducting 3D zodiacal cloud model simulations.

The surface brightness of the zodiacal light as seen by an observer in the ecliptic plane at an ecliptic latitude β and an ecliptic longitude λ − λ_☉ with respect to the Sun can be described as a double integral over the size distribution and along the line of sight. As an approximation, we assume the following.

• 1.  
  The size distribution of dust particles in the zodiacal cloud is independent of their position in interplanetary space.
• 2.  
  The albedo and scattering phase functions of dust particles are independent of position.
• 3.  
  The zodiacal cloud has a plane of symmetry and is axisymmetric with respect to an axis perpendicular to the plane of symmetry.
• 4.  
  Dust grains are sufficiently far from the Sun that we can regard the Sun as a point source.

Under these assumptions, the brightness of the zodiacal light is given by

$\begin{eqnarray} I_{ZL}(\lambda -\lambda _{\odot }, \beta) &=& \int _{0}^{\infty } \int _{0}^{\infty } F(r_h) n(x,y,z) \nonumber\\ &&\times f(s)\,\sigma _{{\rm sca}}(s)\,\phi (\theta; s) \,ds\,dl, \end{eqnarray} \tag{ 1 }$

where dl and θ denote the line element and the scattering angle, respectively, and s is the particle radius. f(s) is the differential size distribution of the particles with a radius of s. σ_sca(s) is the cross section of the particles. ϕ(θ; s) characterizes the distribution of scattered intensity with θ. The incident solar flux F(r_h) can be replaced by F_☉(r₀/r_h)², where F_☉ denotes the solar flux at the heliocentric distance r_h = r₀. n(x, y, z) is the number density of the cloud particles in ecliptic coordinates with respect to the Sun, where the x axis points from the Sun toward the vernal equinox, the z axis is perpendicular to the ecliptic plane, and the y axis completes a right-handed orthogonal coordinate system. The geometry and the notations are summarized in Figure 9.

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For simplification, the mean volume scattering phase function Φ(θ) and the mean total scattering cross section $\bar{\sigma }_{{\rm scat}}$ are defined by

$\begin{equation} \int _{0}^{\infty } f(s)\,\sigma _{{\rm scat}}(s)\,\phi (\theta;s)\,ds \equiv \bar{\sigma }_{{\rm scat}} \,\Phi (\theta), \end{equation} \tag{ 2 }$

with a normalization condition, that is,

$\begin{equation} \int _{4\pi } \Phi (\theta) \,d\Omega = 1. \end{equation} \tag{ 3 }$

The mean volume scattering phase function was empirically derived from the zodiacal light observations (Leinert et al. 1976; Hong 1985; Lamy & Perrin 1986). Figure 10 (left) shows an example of the mean volume scattering phase function given by Hong (1985) and Lamy & Perrin (1986). It has a strong peak in the forward direction, an isotropic component at intermediate scattering angle, and a slight enhancement in the backward direction.

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The spatial distribution of dust particles has been discussed (Giese et al. 1986; Giese & Kneissel 1989; Kelsall et al. 1998). In the early years of research, the spatial distribution was of a form separable into radial and vertical terms, that is,

$\begin{equation} n(r_h;\beta ^{\prime })=n_0 \left(\frac{r_h}{r_0}\right)^{-\nu } \,h(\beta ^{\prime }), \end{equation} \tag{ 4 }$

where n₀ is the reference dust number density on the symmetry plane at heliocentric distance r_h = r₀. The radial power law is motivated by the radial distribution expected for particles under the effect of Poynting–Robertson drag, which results in ν = 1 for dust particles in circular orbit; h(β') describes how the dust number density reduces as we move away from the symmetry plane. Various axisymmetric distribution models were proposed. Among them, the ellipsoid model,

$\begin{equation} h(\beta ^{\prime }) = [ (1+6.5 \sin \beta ^{\prime })^2]^{-0.65}, \end{equation} \tag{ 5 }$

and the fan model,

$\begin{equation} h(\beta ^{\prime })= \exp (-2.1 |\sin \beta ^{\prime }|), \end{equation} \tag{ 6 }$

were often applied in phenomenological model calculation in the literature (e.g., Giese & Kneissel 1989). The plane of symmetry was derived by different authors (see, e.g., Kwon et al. 2004, who obtained i_sym ∼ 2° and Ω_sym = 80°, and Mukai et al. 2003, who obtained i_sym = 203 ± 050 and Ω_sym = 54°–64°). A sophisticated model, in which localized dust condensations as well as the axisymmetric smooth component are considered, was suggested on the basis of infrared observations with the Cosmic Background Explorer's Diffuse Infrared Background Experiment (COBE/DIRBE; Kelsall et al. 1998). It consists of a smooth diffuse component that has a plane of symmetry of i_sym = 203 ± 0017 and Ω_sym = 777 ± 06, three asteroidal dust components, and circumsolar ring components.

We began with a comparison of the ellipsoid model and the fan model. We assumed a plane of symmetry of i_sym = 2° and Ω_sym = 80° based on previous studies (Kwon et al. 2004; Kelsall et al. 1998). The radial power law exponent ν = 1.3 is assumed. We confirmed that ν does not change the Gegenschein morphology significantly within ∼30° from the antisolar point. The mean volume scattering phase function in Hong (1985) was applied. We should note here that the power-law exponent ν is insensitive to the morphology of the Gegenschein, as already pointed out by Hong (1985). For this reason, we did not give much attention to ν in this paper. The results are shown in Figure 11. The systematic change in north–south asymmetry is explained qualitatively by these models. The model morphologies are, however, different from the observed ones in that they have protruding edges toward the eastern and western directions (see the arrows in Figure 11). No peak in the antisolar direction appears in these modeled images. These mismatches cannot be explained by different values of i_sym and Ω_sym, suggesting that the classical models are inadequate for explaining the observed distribution of interplanetary dust particles.

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Next, we applied the infrared model of Kelsall et al. (1998). Because the model was constructed to fit the data in near- and far-infrared wavelengths, no scattering phase function was provided for optical wavelengths. We again applied the scattering phase function in Hong (1985). The upper panels in Figure 12 show the results using only the smooth component of the infrared model, while the middle panels show the results using all the components. From the comparison between top and middle panels, it is clear that the angular shape is associated with fine-scale structure, in particular, the dust-band components. Both the north–south asymmetry and the angular edge along the east–west direction were reproduced by the model (Figures 12(c) and (d)). It is interesting to note that the model was constructed based on infrared observations and yet fit the optical zodiacal light as well. In addition, the infrared observations covered the zodiacal emission at solar elongations of 64°–124°. Both the observed wavelengths and the solar elongation angle of the infrared observations differ from those of our observations. Nevertheless, the infrared model matches the Gegenschein in the visible wavelength range.

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In Figures 12 and 6, we would like to draw attention to the antisolar point, where the brightness spike is clearly seen in our observational images but not visible in the model image. The difference is also seen in Figure 13, where the observed brightness profile around the antisolar point does not match the observed one. This is probably because the backscattering part of the scattering phase function is inadequate for reproducing the observed spikes. Since the scattering phase function has so far been derived using low-resolution data, it is likely that the backscattering part within ∼1° has not been considered yet. For this reason, we modified the scattering phase function by multiplying it by a term used in Kaasalainen et al. (2003),

$\begin{equation} \Phi ^{\prime }(\theta)=\left\lbrace 1 + A \exp \left(-\frac{\pi -\theta }{B}\right)\right\rbrace \Phi (\theta), \end{equation} \tag{ 7 }$

where A and B are fitting parameters and Φ(θ) is the original scattering phase function in Hong (1985). We derived A = 0.15 and B = 0.021 (or 12) to match the observed images. With the modified scattering phase function, we fit the surface brightness profiles (see Figures 12 (e) and (f), indicated by arrows, and also Figure 13).

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