MEASUREMENTS OF DIFFUSE SKY EMISSION COMPONENTS IN HIGH GALACTIC LATITUDES AT 3.5 AND 4.9 μm USING DIRBE AND WISE DATA

The ZL term I_i(ZL) is defined as

$$\begin{eqnarray}&&{I}_{i}({\rm{ZL}})={a}_{i}{I}_{i}({\rm{Kel}}),\end{eqnarray} \tag{ 3 }$$

where a_i is a free parameter and I_i(Kel) is the ZL intensity estimated by the Kelsall model with a default set of parameters (Kelsall et al. 1998). The Kelsall model is a parameterized physical model of interplanetary dust emission fitted to the seasonal variation in the sky brightness observed by DIRBE. To evaluate the typical scaling factor of the Kelsall model against the DIRBE data, we introduce the free parameter a_i. If the Kelsall model completely reproduces the seasonal variation observed by DIRBE, the parameter a_i is determined to be 1.0.

Diffuse 100 μm emission from interstellar dust has been suggested as a physically appropriate tracer of DGL (Brandt & Draine 2012). In fact, several studies have reported a good linear correlation between the intensities of diffuse optical to near-IR light and 100 μm emission (e.g., Matsuoka et al. 2011; Ienaka et al. 2013; Arai et al. 2015; Paper I). In their analysis of the translucent cloud MBM32 in the optical wavelengths, Ienaka et al. (2013) suggested that the linear correlation may break in the optically thick region where DGL itself suffers extinction by interstellar dust. In contrast, at 1–2 μm, Arai et al. (2015) and Paper I reported a linear correlation in the wide range of the 100 μm emission intensity, ∼0–10 MJy sr⁻¹, because optically thin fields are dominant in the high Galactic latitudes in the near-IR bands. We therefore expect the diffuse sky brightness at 3.5 and 4.9 μm to show linear correlation against diffuse 100 μm emission.

In the present analysis, we use the diffuse 100 μm emission map created by Schlegel et al. (1998), hereafter referred to as the "SFD map." The SFD map was created using the data collected with the Infrared Astronomical Satellite (IRAS) and DIRBE, from which point sources and the ZL contribution were removed. The different pixel scales between the SFD map (∼004 × 004) and the  = 90° DIRBE maps (∼032 × 032) cause photometric bias in the correlation analysis. We therefore apply an 8 × 8 pixel binning to the SFD map to obtain the same spatial resolution as that of the DIRBE  = 90° maps. The DGL term I_i(DGL) is then defined as

$$\begin{eqnarray}&&{I}_{i}({\rm{DGL}})={b}_{i}{I}_{{\rm{100}}},\end{eqnarray} \tag{ 4 }$$

where b_i is a free parameter and I₁₀₀ is the interstellar 100 μm emission intensity, defined as

$$\begin{eqnarray}&&{I}_{100}={I}_{{\rm{SFD}}}-0.78\;\mathrm{MJy}\;{\mathrm{sr}}^{-1},\end{eqnarray} \tag{ 5 }$$

with I_SFD being the diffuse 100 μm emission intensity of the binned SFD map. Lagache et al. (2000) derived the 100 μm EBL intensity of 0.78  ±  0.21 MJy sr⁻¹. In addition, Matsuoka et al. (2011) showed the intensity relation of the SFD map and the diffuse optical light observed by Pioneer 10/11, and found a correlation break below ∼0.8 MJy sr⁻¹ on the SFD map. Based on these results, we assume the isotropic EBL at 100 μm to be 0.78 MJy sr⁻¹, and subtract this from the intensity of the SFD map to obtain the 100 μm intensity associated with interstellar dust.

To estimate the ISL contribution in the  = 90° maps, we use the AllWISE source catalog created by the WISE mission (Wright et al. 2010) because the W1 (3.4 μm) and W2 (4.6 μm) bands are close to the DIRBE bands that interest us. The AllWISE catalog contains point and extended sources with the 5σ sensitivities of 16.9 and 16.0 mag in the Vega magnitude in the W1 and W2 bands, respectively.

To calculate the ISL intensity at each pixel in the DIRBE maps, we need to know beam profiles of the  = 90° maps. The intensity of the DIRBE  = 90° map is derived as the average of dozens of observations. Therefore, we should use an averaged beam of the daily map created in the manner described in Section 3.1.3 and Figure 2 of Paper I. The shape of the averaged beam at 3.5 and 4.9 μm is similar to that at 1.25 and 2.2 μm, with an FWHM ∼1°.

Because the spectral response function of WISE is different from that of DIRBE, we need to estimate the flux densities of the sources in the DIRBE bands at 3.5 and 4.9 μm from those in the W1 and W2 bands, respectively. In the wavelength range that interests us, a vast majority of the Galactic sources exhibit the Rayleigh–Jeans spectrum:

$$\begin{eqnarray}&&{F}_{\nu }\propto {\nu }^{2},\end{eqnarray} \tag{ 6 }$$

where F_ν is the flux density per unit frequency. Then, the conversion formula between the weighted-mean flux density in the WISE band (${F}^{{W}_{i}}$) and that in the DIRBE band (${F}^{{D}_{i}}$) is described as

$$\begin{eqnarray}&&{F}^{{D}_{i}}=\left(\displaystyle \frac{\int {F}_{\nu }{R}_{\nu }^{{D}_{i}}/\nu \;d\nu }{\int {R}_{\nu }^{{D}_{i}}/\nu \;d\nu }/\displaystyle \frac{\int {F}_{\nu }{R}_{\nu }^{{W}_{i}}/\nu \;d\nu }{\int {R}_{\nu }^{{W}_{i}}/\nu \;d\nu }\right){F}^{{W}_{i}}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&=\;{\alpha }_{i}{F}^{{W}_{i}},\end{eqnarray} \tag{ 8 }$$

where ${R}_{\nu }^{{D}_{i}}$ and ${R}_{\nu }^{{W}_{i}}$ are the spectral response functions of DIRBE and WISE in the i band, respectively, taken from the COBE/DIRBE explanatory supplement (1998) and Wright et al. (2010). Equation (7) adopts the formula of flux density at the isophotal wavelength, which was defined in Tokunaga & Vacca (2005). The derived conversion terms, α_i, are 0.902 and 0.882 at 3.5 and 4.9 μm, respectively. As described in Wright et al. (2010), F^W_i is defined as

$$\begin{eqnarray}&&{F}^{{W}_{i}}={F}_{0}^{{W}_{i}}{10}^{-0.4{m}_{i}},\end{eqnarray} \tag{ 9 }$$

where m_i is the magnitude of the source in the AllWISE catalog and ${F}_{0}^{{W}_{i}}$ is the zero magnitude at the WISE photometric system—306.681 and 170.663 Jy in the W1 and W2 bands, respectively. The magnitude of the AllWISE source is derived under an assumed source spectrum of F_ν ∝ ν⁻² (Wright et al. 2010). As described in Table 1 of Wright et al. (2010), the difference of the flux density between the sources of the Rayleigh–Jeans spectrum F_ν ∝ ν² and F_ν ∝ ν⁻² is less than 1%. Similarly, the intensity of the DIRBE map is estimated by assuming F_ν ∝ ν⁻¹ (COBE/DIRBE explanatory supplement 1998), and the divergence from the spectrum of F_ν ∝ ν² is less than ∼2%. These differences associated with the color correction are small in comparison to the ISL term derived in the following section.

In the AllWISE catalog, we should select only point sources (Galactic stars). The probability of each source being an extended object is indicated by the digit 0, 1, 2, 3, 4, or 5 in the "ext_flg" of the catalog. The probability increases as the digit increases (see the AllWISE documentation). We select the sources with ext_flg of 0, 1, 2 as the Galactic stars. The selected sources form more than 99% of all AllWISE sources.

To all sources that satisfy the above criteria and are brighter than the 5σ sensitivity limits in the AllWISE catalog (W1 = 16.9 and W2 = 16.0 mag), we apply Equation (7) and calculate their integrated intensities, I_i(DISL), assuming the averaged DIRBE beam profiles. These maps are described in the panels (b) and (b') of Figure 1. We then define the ISL term as

$$\begin{eqnarray}&&{I}_{i}({\rm{ISL}})={c}_{i}{I}_{i}({\rm{DISL}}),\end{eqnarray} \tag{ 10 }$$

where c_i is a free parameter that reflects the contributions of fainter sources than the AllWISE sensitivity limits and the effect of the photometric calibration difference between DIRBE and WISE. Equation (10) also assumes that the ISL intensity of fainter sources (W1 > 16.9 and W2 > 16.0 mag) has a spatial distribution same as that of brighter sources, I_i(DISL).

The residual emission, which includes EBL, is assumed to be independent of the region. It is expressed as I_i(Resid) and defined as

$$\begin{eqnarray}&&{I}_{i}({\rm{Resid}})={d}_{i},\end{eqnarray} \tag{ 11 }$$

where d_i is a free parameter.

Prior to fitting, we remove regions that might perturb the analysis. First, the analyzed region is limited to the high Galactic latitude of $| b| \gt 35^\circ ,$ where the optical depth at the wavelengths of interest is sufficiently small and the linear combination model (Equation (12)) is valid because there is no attenuation of I_i(Resid). In the same field, Paper I confirmed linear correlations at 1.25 and 2.2 μm. Second, the AllWISE sources in the ecliptic longitude range of 447 ∼ 548 or 2309 ∼ 2387, which were observed during the early three-band Cryo phase of the WISE mission, are reported to have missing or elevated uncertainty at the W1 band. These regions were excluded in the analysis at 3.5 μm. Third, Kelsall et al. (1998) pointed out that their model leaves systematic residuals in the low ecliptic latitudes of $| \beta | \lt 15^\circ$ at 4.9 μm. We therefore limit the region to $| b| \gt 35^\circ$ and $| \beta | \gt 20^\circ$ in the analysis at 4.9 μm.

We must also conduct additional limitation. First, the magnitudes of some bright sources in the AllWISE catalog are only given as the 2σ upper limits due to the large photometric uncertainty. We mask the surrounding regions of such sources. Second, the regions around the sources brighter than W1 = 4 mag are removed to reduce the photometric uncertainty. About 30% of the region is removed by the mask around the bright sources. Third, we blank out the regions around the Magellanic Clouds and probable Galactic extended sources listed in the Explanatory Supplement to the 2MASS All Sky Data Release and Extended Mission Products (Cutri et al. 2003). Fourth, we limit our analysis to the regions of I₁₀₀ < 6 MJy sr⁻¹ in which Galactic extinction is assumed to be negligible. Finally, outliers in the ISL intensity are excluded by applying 2σ clipping to the ISL intensities I_i(DISL).

To determine the parameters a_i, b_i, c_i, and d_i (Equation (13)), we minimize the following χ² function in each band:

$$\begin{eqnarray}&&{\chi }_{i}^{{\rm{2}}}=\displaystyle \sum _{j}\displaystyle \frac{{[{I}_{i}({\rm{Obs}})-{I}_{i}({\rm{Model}})]}^{{\rm{2}}}}{{\sigma }_{i}^{{\rm{2}}}}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&=\;\displaystyle \sum _{j}\displaystyle \frac{{[{I}_{i}({\rm{Obs}})-{a}_{i}{I}_{i}({\rm{Kel}})-{b}_{i}{I}_{{\rm{100}}}-{c}_{i}{I}_{i}({\rm{DISL}})-{d}_{i}]}^{{\rm{2}}}}{{\sigma }_{i}^{{\rm{2}}}},\end{eqnarray} \tag{ 15 }$$

where "j" refers to the pixels used in the fitting. The total uncertainty, σ_i, at each pixel is calculated as follows:

$$\begin{eqnarray}&&{\sigma }_{i}^{{\rm{2}}}={\sigma }_{i}{({\rm{Obs}})}^{{\rm{2}}}+{b}_{i}^{{\rm{2}}}{\sigma }_{{\rm{100}}}^{{\rm{2}}}+{c}_{i}^{{\rm{2}}}{\sigma }_{i}{({\rm{DISL}})}^{{\rm{2}}},\end{eqnarray} \tag{ 16 }$$

where σ_i(Obs), σ₁₀₀, and σ_i(DISL) are the standard deviations of the intensities of the  = 90° map, that of the 100 μm emission, and that of the ISL intensity I_i(DISL), respectively. We adopt the value σ₁₀₀ = 0.35 MJy sr⁻¹ derived by Ienaka et al. (2013). The σ_i (DISL) at each pixel is calculated in the same way as I_i(DISL), convolved with the DIRBE beam profile (see Section 2.2.3):

$$\begin{eqnarray}&&{\sigma }_{i}{({\rm{DISL}})}^{2}={[{\alpha }_{i}{10}^{-0.4{m}_{i}}]}^{2}{\sigma }_{{F}_{{\rm{0}}}^{{W}_{i}}}^{2}\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&+\;{[-0.4(\mathrm{log}10){10}^{-0.4{m}_{i}}{\alpha }_{i}{F}_{{\rm{0}}}^{{W}_{i}}]}^{2}{\sigma }_{{m}_{i}}^{2}\end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray}&&+\;{[{F}_{{\rm{0}}}^{{W}_{i}}{10}^{-0.4{m}_{i}}]}^{2}{\sigma }_{{\alpha }_{i}}^{2},\end{eqnarray} \tag{ 19 }$$

where ${\sigma }_{{F}_{0}^{{W}_{i}}},$ ${\sigma }_{{m}_{i}}$, and ${\sigma }_{{\alpha }_{i}}$, respectively, denote the uncertainties of the zero magnitude in the WISE band (4.600 and 2.560 Jy in the W1 and W2 bands, respectively (Wright et al. 2010)), that of the magnitude of each AllWISE source, and that of the conversion factor α_i, set to be 1% of α_i. Sources with no uncertainty entry in the AllWISE catalog are assigned an uncertainty, ${\sigma }_{{m}_{i}}$, of 0.5 mag.

As indicated by the blue and green curves in Figure 5, Brandt & Draine (2012) estimated the spectra of the starlight scattered by the plane-parallel-distributed dust grains, based on the different dust models of Zubko et al. (2004), hereafter ZDA04, and Weingartner & Draine (2001), hereafter WD01, respectively, with the de-reddening correction of the original ISRF estimation derived by Mathis et al. (1983), hereafter MMP83, and the stellar population synthesis model of Bruzual & Charlot (2003), hereafter BC03. Brandt & Draine (2012) used the BC03 model with solar metallicity and a star formation rate of $\propto \mathrm{exp}(-t/5\;{\rm{Gyr}})$, where t denotes the timescale in units of Gyr. As summarized in Chapter 23 of Draine (2011), both the ZDA04 and the WD01 models are composed of graphite, silicate, and PAH materials. However, they differ in the size distributions of the grains. The half-mass radius, a_0.5 (50% of the total mass in grains with the radius a > a_0.5), is 0.06 and 0.07 μm for the graphite and silicate grains, respectively, in ZDA04, but is 0.12 μm for both grains in WD01, leading to a much greater mass in a > 0.2 μm in WD01. Draine (2011) pointed out that the WD01 model better reproduces the observed extinction curve from ultraviolet to the near-IR wavelengths, as derived by Fitzpatrick (1999).

In addition to the scattering component of DGL, the orange curves in Figure 5 represent the expected spectra of the near-IR emission from interstellar dust, a mixture of amorphous silicate and carbonaceous grains including PAH (Draine & Li 2007; hereafter DL07). As shown in Figure 12 of DL07, the increase in the PAH abundance directly causes high-intensity dust emission in the near-IR. In Figure 5, we show the three DL07 models in which the mass fraction between PAH particles and total dust, q_PAH, is different, i.e., q_PAH = 0.5%, 1.8%, or 4.6%. To compare with the values obtained in the general interstellar fields, the scaling factor against the ISRF intensity of MMP83, U, is set to U = 1,—corresponding to the ISRF intensity for the solar neighborhood. In the literature, the value of U = 1 has been adopted in the general interstellar field throughout the sky (e.g., Dwek et al. 1997; Li & Draine 2001; Draine & Li 2007; Compiègne et al. 2011). All model spectra in Figure 5 show the distinct PAH feature of the C–H stretching mode at 3.3 μm. In DL07, the intensity of the dust emission is calculated as λI_λ/N_H (erg s⁻¹ sr⁻¹ H⁻¹), where N_H denotes hydrogen column density. To convert N_H to the diffuse 100 μm intensity, we use the ratio of 100 μm emission to H I column density derived from the DIRBE data at high-latitude regions of $| b| \gt 25^\circ$–18.6 nWm⁻² sr⁻¹/10²⁰ cm⁻² (Arendt et al. 1998).

Compared with the values of the DL07 spectra convolved with each DIRBE band (asterisks in Figure 5), the present result at 3.5 μm falls between the model with q_PAH = 4.6% and that with q_PAH = 1.8%. At 4.9 μm, the present result prefers the model with q_PAH = 4.6%, without the large uncertainty caused by the regional variation in the decomposition analysis (see Section 3.1). As shown in Figure 16 of DL07, the IR emission colors obtained by the Spitzer/IRAC (Infrared Array Camera) observation toward several regions of the lower Galactic latitudes (Flagey et al. 2006) are closer to that of the DL07 model with q_PAH = 4.6%. Compiègne et al. (2011) also modeled the high-latitude dust emission with the PAH parameter of 7.7%. The dust emission intensity at 3–5 μm is comparable between their model and the DL07 model of q_PAH = 4.6%; the difference between the two models falls within ∼20% in that wavelength range (see Figure 6 of Compiègne et al. 2011). Combining the present values with these results, it is probable that q_PAH is above ∼2% in the high-latitude region.

In the previous analysis of DIRBE data, Arendt et al. (1998) derived the intensity ratios of DGL to 100 μm emission only in low-latitude regions of $| b| \lt 30^\circ$ (filled black circles in Figure 5). At 3.5 μm, their low-latitude result is comparable to the present high-latitude value. This indicates that the PAH abundance does not greatly change throughout the general interstellar field in the Milky Way, except in the region of the Galactic plane. At 4.9 μm, the result of Arendt et al. (1998) is two times higher than that of the model spectra; Li & Draine (2001) thus suggested an additional opacity for the ultra-small grain component to explain this excess. However, such components may not be required by our result at 4.9 μm, without the uncertainty of regional variation.

The intensities of the DL07 models with q_PAH = 4.6% are a few times lower than that obtained with AKARI (Tsumura et al. 2013b; solid black curve in Figure 5) in the continuum spectra. The low-latitude result of AKARI ($5^\circ \lt | b| \lt 15^\circ$) may cause such a difference. It is suspicious that U = 1 can be adopted in the low-latitude region because of its higher ISRF. Unfortunately, Tsumura et al. (2013b) did not find the DGL feature in the high-latitude region, probably due to the low signal-to-noise ratio of the observation, the same as in the reanalysis of the IRTS data (Matsumoto et al. 2015).

To maintain consistency with the results at optical wavelengths (Matsuoka et al. 2011; Ienaka et al. 2013), Paper I and Arai et al. (2015) have both suggested a bluer DGL spectrum at 1–2 μm, fitted to the twice-scaled ZDA04 model spectra (blue curves in Figure 5). However, there is no firm reason to allow the scaling of the model to fit the observed results. In addition, the size distribution of the dust grains differs between the DL07 and ZDA04 models; DL07 adopts the WD01 model, which better reproduces the observed extinction curve (Fitzpatrick 1999). Therefore, it may be premature to conclude that the scattering components of DGL have a bluer spectrum with a larger contribution of smaller dust grains. Figure 5 shows that the original model spectra based on the WD01 model (green curves) can be fitted to the observed results of Paper I and Arai et al. (2015) without violating the present results at 3.5 and 4.9 μm. In this case, the observed results of Matsuoka et al. (2011) are larger than the model spectra by a factor of two. To explain this discrepancy, the albedo of the dust grains in the optical wavelengths should be larger than the DGL model of Brandt & Draine (2012) without a change in the albedo in the near-IR. By solving the simple radiative transfer of light through the dust slab, Ienaka et al. (2013) expressed the parameters b_i as functions of albedo and optical depth (see Appendix of Ienaka et al. 2013). According to the solution of their equation, only an ∼20% increase in the visual albedo can enhance the parameter b_i by a factor of two. This small change in the optical albedo in the model of Brandt & Draine (2012) may explain the excess values of Matsuoka et al. (2011).

For a further study of interstellar dust using DGL, both precise spectroscopic observations of DGL with high signal-to-noise ratios and DGL models that simultaneously reproduce scattering and thermal emission components will be needed.

For the residual emission components d_i, we estimate the additional uncertainties associated with the absolute gain of DIRBE, faint galaxies, and the ZL model.

Hauser et al. (1998) reported uncertainties of 3.1% and 3.0% in the absolute gain of DIRBE at 3.5 and 4.9 μm, respectively. The values of these uncertainties correspond to percentages of the derived parameter d_i, and appear in the row "Gain" in Table 1.

The AllWISE catalog may contain unresolved faint galaxies, which should be added to the uncertainty budget of the parameter d_i. Levenson et al. (2007) estimated the contribution of such galaxies at 3.5 μm of 0.04 nWm⁻² sr⁻¹, which corresponds to galaxies of K_s < 14.3 mag in the 2MASS PSC. Assuming this value is of the same order as the AllWISE sources, we adopt this as the uncertainty of faint galaxies at 3.5 μm. Generally, the spectrum of a galaxy does not drastically change between 3.5 and 4.9 μm. We then set the same value at 4.9 μm. These uncertainties are listed in the "Galaxies" row in Table 1.

As described in Kelsall et al. (1998), the uncertainty of the Kelsall model is estimated as the intensity difference between the two ZL models at the north Galactic pole (NGP) where the difference is reported to be the largest. This uncertainty is 2.1 and 5.9 nWm^{− 2} sr⁻¹ at 3.5 and 4.9 μm, respectively, listed in the row "ZL model" in Table 1.

The quadrature sum of the uncertainties of the parameter d_i is presented in the row "Quadrature sum" in Table 1. For the parameter d_i, the uncertainties associated with the regional variation in the parameter and the Kelsall model dominate over the other uncertainties.

To test the isotropy of the residual emission, Figure 6 illustrates I_i(Obs) − I_i(ZL) − I_i(ISL) − I_i(DGL) with the parameters d_i being functions of the Galactic latitude b (panels (a) and (a')) and the ecliptic latitude β (panels (b) and (b')) in both bands.

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Other than in the region where b ≳ 60°, the residual emission shows similar trends at 3.5 and 4.9 μm as functions of Galactic latitude; it increases toward the low Galactic latitudes (panels (a) and (a')). Paper I found the same trend in the analysis of the residual emission at 1.25 and 2.2 μm with the 2MASS data and suggested two explanations for this trend. One was the simply modeled ISL term, I_i(ISL) = c_iI_i(2MASS), where I_i(2MASS) denotes the integrated intensity of the 2MASS sources below the detection limit. Such a trend could be caused if the spatial distribution of intensity as a function of Galactic latitude differs between I_i(2MASS) and the ISL of stars fainter than the detection limits of 2MASS. Another was the contribution of the faint stars that were not detected in the 2MASS PSC due to the masking effect of the nearby bright sources. Such faint stars increase as the number density of the bright sources increases toward the lower Galactic latitudes. These explanations can be applied to the present study, which evaluates ISL using the AllWISE sources in the same way as the 2MASS PSC in Paper I.

In the region of b ≳ 60°, the residual emission shows the inverse behavior: it increases toward NGP. To investigate this phenomenon, we plot I_i(Obs) − I_i(ZL) and I_i(ISL) + I_i(DGL) with the residual emission in Figure 7. Reasonably, the modeled Galactic components I_i(ISL) + I_i(DGL) increase toward the low Galactic latitudes. In contrast, I_i(Obs) − I_i(ZL) shows the same feature as the residual emission in the b ≳ 60° region, indicating that the trend is caused by I_i(ZL). The fact that such a feature is larger at 4.9 μm than at 3.5 μm is then reasonable because of the stronger ZL component at 4.9 μm. However, the reason why such a feature is seen only at b ≳ 60° is unclear. For one thing, Kelsall et al. (1998) pointed out that the intensity differences between the different ZL models are largest in the NGP region. Such difficulty in the modeling of ZL near the NGP region may be related to the trend at b ≳ 60°.

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As a function of ecliptic latitude, the residual emission is relatively constant at 3.5 μm, but is systematically larger toward the lower-ecliptic latitudes at 4.9 μm (panels (b) and (b') of Figure 6). This indicates the difficulty of modeling of ZL at 4.9 μm, where the ZL intensity is much stronger than that at 3.5 μm. In addition to the high intensity of the ZL at 4.9 μm, the incompleteness of the ZL model in the band may contribute to the large scatter of the other components—DGL, ISL, and the residual emission (see Figure 4). In this situation, there seems to be room for improvement on the ZL model, though it is generally difficult.

Though the residual emissions show some amount of scatter as functions of b and β, they are within the typical scatter derived by the regional variation in the parameters d_i (see Table 1 and Section 3.1), because such regional variation naturally includes the dependence of b and β. Such scatter as functions of b and β is also comparable to the estimated systematic uncertainty of the Kelsall model (Table 1). For the isotropy measurement of the residual emissions, we therefore use the "Scatter" value (Table 1) as the conservative values. In our analysis, the deviation of the residual emission from the isotropy is then less than ∼30% of the residual intensity at 3.5 μm. This deviation from the isotropy is larger than that of ≲10% at 1.25 and 2.2 μm (Paper I), partly because the residual emission intensity at 3.5 μm is more than two times smaller than those at 1.25 and 2.2 μm. We do not discuss the isotropy of the residual emission at 4.9 μm due to the very large scatter.

In Figure 8, we compare the resultant residual emissions of Paper I and the present study with those of previous studies. As illustrated in Figure 5, the present DGL result at 3.5 μm in the high Galactic latitudes is comparable to the results obtained at low Galactic latitudes (Arendt et al. 1998) within the uncertainty. This leads to the same level of residual emissions as in the previous studies adopting the DGL result derived by Arendt et al. (1998) at 3.5 μm (Gorjian et al. 2000). At 4.9 μm, the residual emission is not significantly detected due to large uncertainty associated with the ZL subtraction, same as the previous studies (Hauser et al. 1998; Tsumura et al. 2013c).

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The intensity of the residual emission changes according to the different ZL models; using the Kelsall model or Wright (1998)'s model, several studies have reported large residual emissions at 1.25 and 2.2 μm (Gorjian et al. 2000; Cambrésy et al. 2001; Levenson et al. 2007; Tsumura et al. 2013c; Matsumoto et al. 2015; Paper I), which are two to five times the observed or modeled IGL intensity (e.g., Madau & Pozzetti 2000; Totani et al. 2001; Stecker et al. 2006; Mazin & Raue 2007; Franceschini et al. 2008; Finke et al. 2010; Domínguez et al. 2011). Because such large residual emissions also exceed most of the γ-ray constraints of EBL (e.g., Aharonian et al. 2006; Abramowski et al. 2013), it is difficult to regard them as being entirely of extragalactic origin. In addition, Paper I suggested that IGL, together with the contributions of all of the exotic extragalactic sources estimated so far, including Pop-III stars (Fernandez & Zaroubi 2013; Inoue et al. 2013), IHL (Zemcov et al. 2014), direct collapse black holes (Yue et al. 2013), and dark stars (Maurer et al. 2012), cannot account for the excess residual emission, especially at 1.25 μm. Therefore, it is probable that part of the excess emission comes from the local universe.

Compared with the residual emissions at 1.25 and 2.2 μm, the present result at 3.5 μm is relatively small, approaching the IGL level and γ-ray constraints. Combined with the results of Paper I, the spectrum of the near-IR residual isotropic emission has the Rayleigh–Jeans spectrum, consistent with the previous studies. In contrast, a large gap exists between the two results in the optical wavelengths: Matsuoka et al. (2011) and Bernstein (2007). Because the results of Matsuoka et al. (2011) were obtained from the Pioneer 10/11 observation beyond 3 AU from the Earth, where the ZL contribution is negligible, the residual emission may be regarded as the optical EBL intensity. If this is true, the intensity gap between Matsuoka et al. (2011) and Bernstein (2007) can be attributed to the unmodeled ZL contribution.

The present decomposition analysis, which deals with the integrated light of each emission component cannot identify where the residual emission comes from. As mentioned above, part of the residual emission can arise from the local universe, such as the Milky Way or solar system due to the contradiction against the γ-ray constraints. In their interpretation of the derived isotropic residual emissions at 140 and 240 μm, Dwek et al. (1998) suggested that the Galactic component cannot produce the residual intensity because an unreasonably large gas and dust mass is needed. From this point of view, the "isotropic DGL component," the counterpart of the isotropic far-IR emission from ISM, is unlikely to contribute to the residual emission in the optical to near-IR wavelengths. Recently, Lehner et al. (2015) reported the presence of the massive circumgalactic medium around the Andromeda galaxy. However, it is very unclear that such component also exists around the Milky Way and creates the isotropic emission.

Another possible origin of the residual emission may be within the solar system, including ZL. As reported by Dwek et al. (2005), the spectrum of near-IR excess residual emission is similar to the ZL spectrum. In addition, some isotropic components associated with ZL can be added to the Kelsall model because absolute measurement of ZL is impossible from the orbit of the Earth (Hauser et al. 1998). However, such isotropic ZL components have not been observationally confirmed and it is suspicious that they would have the same spectrum as the currently measured ZL. To reveal whether the residual emission components include the ZL contribution, the EXo-Zodiacal Infrared Telescope (EXZIT), one of the science instruments of the Solar Power Sail spacecraft planned for launch in 2020s, will be useful; this mission is planned to observe the universe in the near-IR wavelengths beyond the interplanetary dust region (Matsuura et al. 2014). EXZIT will reveal the three-dimensional structure of interplanetary dust and the absolute EBL intensity without the uncertainty of the ZL model.