8.1. Structured Component
A diffuse, non-isotropic, optical background is produced in the Milky Way by scattering of the optical interstellar radiation field (ISRF) by Galactic dust. The same dust is heated by the UV ISRF, causing it to produce thermal IR emission. It is not surprising, therefore, that the thermal Galactic emission seen in the IRAS 100 µm maps correlates well with the surface brightness of the optical diffuse Galactic light (DGL), as both are proportional to the column density of the dust and the intensity of the ambient ISRF along the line of sight. In Tables 6 and 7, we give a representative summary of the observed correlations between optical and 100 µm fluxes for regions with low to moderate 100 µm intensities (N(HI)< 5 × 1020 cm-2, I100 < 5 MJy sr-1) and a range of Galactic orientations.
As evident from those results, there is only moderate agreement concerning the exact scaling relations between the optical DGL and thermal emission at any wavelength. Measurement errors in the IR, optical, and UV intensities are > 10% in most cases and are one cause for variations between results. However, asymmetry in the scattering phase function of Galactic dust also contributes to the variable scaling relations seen between different lines of sight. Strong forward scattering causes lower optical surface brightnesses at both high latitudes (|b| > 50°) and at longitudes away from the Galactic Center (130° < l < 230°) (see Draine & Lee 1984, and references therein; Onaka & Kodaira 1991; Witt, Friedmann, & Sasseen 1997). Both trends are evident from the data shown in Tables 6 and 7.
While these results suggest a range of appropriate correlation factors, they do not identify a single appropriate scaling law for our purposes for two reasons. First, variability in the measured IR-optical and UV-optical correlations is evident within a single cloud, as well as between clouds (see, for example, Figures 5 & 6 in GT89 and Table 1 in Laureijs, Mattila, & Schnur 1987). This suggests that the observed systems may be dense enough that self-shielding and further complications come into play. These clouds have been selected precisely because the optical and IR emission is bright enough to be readily observed: while the IR flux levels and N(HI) column densities of the clouds listed in Tables 6 and 7 are low enough that the molecular gas fraction does not affect the correlation between dust column density (or extinction) and N(HI), they are still roughly a factor of 10 higher than the values for our observed field, for which I100 ~ 0.4 MJy sr-1(N(HI) ~ 0.47 × 1020 cm-2, or E(B - V) ~ 0.009 mag). Second, while empirical relations between the scattered and thermal DGL have have been published in the far-UV and at optical B- and R-bands, the expected surface brightness from scattering at 3000Å is not clear from these results. Neither the optical depth of interstellar dust nor the ISRF is a monotonic function of wavelength between 1600Å and 4500Å (see Savage & Mathis 1979 and Mathis, Mezger, & Panagia 1983).
To better understand the contribution of non-isotropic DGL over the full range of our observations, we have used a basic scattering model to predict the scattered light from dust. We then compare the results of this model to the observed DGL at UV and optical wavelengths.
Assuming the Galactic cirrus along the line of sight in question is optically thin (extinction, A < 1.08 mag), the surface brightness of scattered light off of interstellar dust can be expressed as
in which j is the flux of the radiation field in ergs s-1 cm-2 sr-1 Å-1; is the effective albedo of the dust; is the optical depth; and the term in brackets is the back-scattered intensity in terms of Galactic latitude, b, and the average phase function of the dust, g (Jura 1979). For strong forward scattering, g ~ 1; for isotropic scattering, g ~ 0. We take the ISRF flux, j, from the Mathis et al. (1983) estimate for the Solar Neighborhood (10 kpc from the Galactic center). As our observations are b = 60° from the Galactic plane and l = 206.°6 from the Galactic center, this estimate is probably slightly high. We take the dust albedo from the results of Draine & Lee (1984), which are based on an exponential distribution in grain sizes suggested by Mathis, Rumpl & Nordsieck (1977).
The optical depth of Galactic dust, , is well known to correlate strongly with hydrogen column density (see Savage & Mathis 1979, Boulanger & Pérault 1988, and references therein). It is not surprising, then, that the thermal emission, I100, also correlates well with hydrogen column density. While optical depth is a physical manifestation only of the column density of dust, I100 is also affected by the strength of the ISRF. We therefore use the observed I100 and I100/N(HI) as calibrated by Boulanger & Pérault (1988) from the IRAS 100 µm maps to obtain an effective optical depth for our observations as follows. Optical depth can be written as a function of optical extinction and dust column density as
in which R = A / E(B - V) is the usual expression for the normalized extinction. Several groups find N(HI) / E(B - V) between 48 × 1020 and 50 × 1020 cm-2mag-1 from measurements of the HIdensities from 21cm line emission strength and the reddening to globular clusters and star counts (Bohlin, Savage & Drake 1978, Burstein & Heiles 1982, Knapp & Kerr 1974). To get an effective optical depth (weighted by the ISRF field strength which is at issue for scattering), we use the relation found by Boulanger et al. (1996) for the low-column density regime (N(HI) < 5 × 1020 cm-2): I100 / N(HI) 0.85 MJy sr-1/(1020cm-2). (3) The fluxes in our field are roughly 0.4 MJy sr-1, or 0.47 × 1020cm-2. The predicted scattered fluxes from this model are shown in Table 8. Scattering angle is not considered in this model. Consequently, this estimate is conservative in the sense that it should over-predict the DGL for our observations, as the line of sight to our field is away from the Galactic center and the dust is forward scattering.
This scattering model reproduces the observed flux ratios with reasonable accuracy in the range 1600-4500Å (see Tables 7 and 6 at b > 45). The phase function changes by less than 10% at latitudes |b| > 50°, so the values shown in Table 8, for which |b| = 50° was used, are generally representative for high latitude fields. However, as noted by GT89, optical colors (B - R) and (R - I) are redder than a basic scattering model predicts. GT89 find values of I(R) / I(B) = 3.2, 2, and 1.7 and I(I) / I(R) = 2.3, 2.1, and < 1.5 in three different fields. By comparison, the ratios we predicted are I(R) / I(B) = 1.4 and I(I) / I(R) = 0.95. A significant H contribution as the explanation for the red colors is ruled out by GT89. Variable scattering asymmetry with wavelength is another possible explanation, but strong wavelength dependence in the range 4500-9000Å has never been observed in the lab or in space (Witt et al. 1997, Onaka & Kodaira 1991, Laureijs et al. 1987). The most plausible explanation is suggested by observations of reflection nebulae, which have high N(HI) and show red fluorescence from molecular hydrogen, hydrogenated amorphous hydrocarbons, and polycyclic aromatic hydrocarbons. The relevance of such contributions to fields with 10 times lower N(HI) and I100, as is the case for our data, is not clear, as the density of molecular gas correlates only with high column densities, N(HI) > 5 × 1020cm-2. The results of GT89, in fact, do show that the degree of reddening is well correlated to the average I100 emission but not structure within the cloud. Self-shielding, local optical depth and local ISRF may be responsible for strong variations in the correlation between color and molecular gas density both in and between fields (Stark 1992, 1995). It seems conservative, therefore, to adopt optical colors found for the fields with the lowest IR flux in the GT89 sample, listed in Table 7. Note that the IR flux in the 2 lower flux fields (denoted "ir2" and "ir3") is still more than a factor of 10 higher than in our own.
In summary, we estimate the optical flux in our field using our scattering model for < 4500Å, and adjust the predicted scattering model at redder wavelengths to match the average colors observed by GT89: I(R) / I(B) ~ 1.8 and I(I) / I(R) ~ 2.0. We apply this correction in the sense of increasing the long wavelength fluxes over that predicted by our models, so that the DGL estimate we use is, if anything, higher than is appropriate, although given the small total flux associated with the DGL even a large fractional decrease in our estimate of the DGL would have a negligible impact on our EBL results. The resulting spectrum is flat in I, with a value of roughly 0.9-1.0 × 10-9 ergs s-1 cm-2 sr-1 Å-1 from 3000-9000Å. We note, also, that our scattering model was not dependent on Galactic longitude, which, again, makes ours a conservative overestimate of the DGL contribution to the total sky background, and our measurement of the EBL, therefore, a conservative underestimate in this regard.
3 A slightly different scaling, I100/N(HI) 0.53 MJy sr-1/(1020cm-2), is seen in from the DIRBE results (Boulanger et al. 1996). The difference is attributed to a well known calibration offset in the IRAS maps. Since we are using IRAS fluxes, we use the IRAS correlation. Back.