Interstellar cirrus

Emission from the interstellar medium dominates the sky brightness at wavelengths longer than 70 $\mu$m at high galactic latitudes, shifting to 45 $\mu$m at galactic latitudes around $10^\circ$. In the galactic plane, the interstellar medium dominates at all wavelengths except around 20 $\mu$m. The implication for Spitzer is that zodiacal light is the dominant background for IRAC, IRS, and MIPS 24$\mu$m except at very low galactic latitude, while the interstellar medium dominates for the MIPS 160 $\mu$m.

The distribution of interstellar dust is irregular, so there is no acceptable analytical model even at the factor of 2 level. Therefore we take a different approach, which is to use a template map of the interstellar medium at one wavelength. We will scale this template map by a `generic' spectrum of the interstellar medium, which can be convolved with each of the Spitzer filters.

The interstellar template we used is the one developed by Schlegel, Finkbeiner, & Davis (1998), hereafter `SFD'. The SFD map was created using both the DIRBE far-infrared data (with its accurate calibration) and the IRAS 100 $\mu$m map (with its higher angular resolution). SFD have processed the IRAS data even beyond what was done for the ISSA, with an additional deglitching, Fourier destriping, offset correction to the DIRBE offsets, gain scaling based on the DIRBE vs. IRAS correlation, and smoothing to a round $6.5^\prime$ resolution. The SFD maps are all-sky maps of the brightness at 100 $\mu$m of the interstellar medium, with a temperature correction factor. The dust temperature was calculated from the DIRBE 100-240$\mu$m maps, and the temperature correction factor adjusts the brightness of each pixel in the map by the ratio of a blackbody at the local temperature to that at a nominal temperature of T₀=18.2 K.

  

Figure: Average spectrum of the interstellar medium, combining observations from various telescopes as labeled. From 3-5 and 16-100 $\mu$m, the continuum is a logarithmic interpolation between broad-band observations at 3.5, 4.9, 12, 25, 60, and 100 $\mu$m. From 5-16 $\mu$m and longward of 100 $\mu$m, actual spectral data were used. At 3.28 $\mu$m a synthetic line profile was normalized to match the observed ratio of integrated line brightness to the continuum at 100 $\mu$m. This spectrum should be accurate to within at least a factor of 2.

   

Table 1: Broad-band spectrum of the Interstellar Medium^a

wavelength ($\mu$m)	3.5	4.9	12	25	60	100	140	240
intensityb, IA	0.0018	0.0029	0.046	0.048	0.17	1	1.70	1.30
color corr., KA	1	1	1.02	1.23	0.91	0.92	0.94	0.99

^abased on Arendt et al. (1998) ^brelative to that at 100 $\mu$m

We can therefore create an all-sky, any-wavelength estimate of the brightness of the interstellar medium with the following model:

$$I_\nu(l,b) = \frac{D_{100}^Q(l,b)}{K_{100}(T[l,b])} \frac{B_\nu(T[l,b])}{B_{100}(T[l,b])} (100/\lambda)^2,$$ (1)

where D₁₀₀^Q is the SFD 100 $\mu$m DIRBE+IRAS map, $B_\nu(T)$ is the Planck function at frequency $\nu$ and temperature T, $\lambda$ is the wavelength, and K₁₀₀(T) is the color correction factor for a source with a $\nu^2 B_\nu(T)$ spectrum in the DIRBE 100 $\mu$m waveband. The index (l,b) represents galactic coordinates. The temperatures T(l,b) for each sky region were calculated by SFD. Using the final `dust map,' D^T, of SFD, we can rewrite the previous equation as

$$I_\nu(l,b) = D^T(l,b) \frac{B_\nu(T[l,b])}{K_{100}(T_0)B_{100}(T_0)} (100/\lambda)^2,$$ (2)

where T₀=18.2 is the nominal dust temperature. This version is more simple to evaluate because D_T is already provided by SFD, and the only color correction needed is at the nominal temperature.

The interstellar background model described in the previous paragraph will only account for the part of the sky brightness due to large grains in thermal equilibrium with the interstellar radiation field. In the mid-infrared, a different population of grains dominates the sky brightness (by many orders of magnitude). This emission consists is due to cooling of grains and large molecules that are heated to high temperatures by single interstellar photons. The spectrum contains strong, broad features at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.6 $\mu$m. The brightness of the average interstellar medium was well determined in broad bands by DIRBE. The brightness of the interstellar medium, I_A, scaled to a 100 $\mu$m brightness of 1 MJy sr^-1 is shown in Table 1. We also include color correction factors for each of these, using the tables from the DIRBE Explanatory Supplement (Hauser et al. 1998) and the local spectral shape of I_A. A broad-band estimate of the interstellar spectrum relative to 100 $\mu$m, within the range 3.5-240 $\mu$m, can be obtained by interpolating I_A/K_A to the desired wavelength. We will use a logarithmic interpolation (i.e. interpolate in $\log \lambda$ vs. $\log I_\nu$). From 5 to 16.5 $\mu$m, we can do better by using the spectrum of a diffuse cloud measured by ISO. The spectrum of a small cloud in the $\rho$ Oph region, reported by Boulanger et al. (1996), was scaled so that its integral over the DIRBE 12 $\mu$m waveband matches the value of I_A/K_A listed in Table 1. The final resulting spectrum is shown in Figure 3 (Reach & Boulanger 1997)). The spectrum longward of 16 $\mu$m is very smooth because we have not included an spectral lines. Spectral lines due to dust are known to exist in this range, but it is not known whether such features are generic for interstellar dust or are present only in the special regions so far observed. These features are generally of low-contrast, less than 20% on average. Shortward of 5 $\mu$m, there are no sensitive spectra of the diffuse interstellar medium, but we can at least include the very strong 3.3 $\mu$m feature, normalized to match the observations made with the Arome balloon telescope (Giard et al. 1994). We presume a line centered at 3.28 $\mu$m with a full-width at half-maximum of 0.1 $\mu$m.

One problem with the background model described here is that the mid-infrared and far-infrared emission have been found not to be perfectly correlated on the sky. Therefore, the use of a single generic spectrum for the interstellar medium can be questioned. Boulanger et al. (1988, 1990) have found that the ratio of 12 $\mu$m to 100 $\mu$m brightness varies from 0.25 to 5 times the average value. The color variations were found in studies of molecular clouds and the environment of an H II region. It is likely that the range of variation away from such regions is smaller, although a significant range has also been found for isolated, low-column density clouds (Heiles et al. 1988). In light of this problem, it would certainly seem better to use actual mid-infrared data for the background estimator, rather than scaling the far-infrared data. However, the mid-infrared observations of the interstellar medium are of significantly lower quality than the far-infrared data, and are only useful for clouds near stars or in the galactic plane. For such regions, the observer will have to resort directly to the IRAS data at 12 $\mu$m, which we can expect them to do in any event because such regions are also very complicated spatially. At higher galactic latitudes, Arendt et al. (1998) found the 12 $\mu$m broad-band intensity (which contains several PAH lines) to be well-correlated with that at 100 $\mu$m, and Giard et al. (1994) found that the 3.3 $\mu$m PAH line brightness does not vary strongly with respect to the 100 $\mu$m brightness on large scales over a significant portion of the galactic plane. Therefore, except around regions locally excited by starlight, our model is likely to be be accurate to better than a factor of 2, which will suffice for the uses we envision here.