3. THE SUBMILLIMETER BACKGROUND

The COBE data have provided detections of the CIB at some wavelengths and limits elsewhere within the spectral range of the two instruments. Since foreground sources and the CMB dominate the observed sky brightness in all directions throughout the 1-1000 µm spectral range, all of these results require discrimination and removal of non-CIB contributions. Assessment of the reality of a potential CIB measurement therefore requires careful analysis of the random and systematic uncertainties in the residuals from the measured sky brightness. The residual must also be demonstrated to be isotropic, and not likely to arise from any unmodeled foreground.

Quantitative results from all of the investigations described here are listed in Table 1. Error bars for reported detections are 1. Upper and lower limits are shown at the 95% CL, with actual values and 1 uncertainties shown in parentheses. The third column indicates whether some degree of isotropy was demonstrated. The fourth column indicates whether the investigators claimed a detection (yes), a possible detection (tentative), or a limit (no). The designation ``no'' is also used for any case where the result is less than 3 times the quoted uncertainty. For illustrative purposes, the values shown in bold type in Table 1 are plotted in Figure 1.

Table 1. COBE Diffuse Infrared Background Measurements

	I	Isotropy	Detection	Reference
(µm)	(nW m-2 sr-1)	test passed
1.25	< 75 (33±21)	no	no	Hauser et al. 1998
1.25	< 68 (27±21)	no	no	Dwek & Arendt 1998
1.25	< 57 (27.8±14.5)	no	no	Wright 2000
2.2	< 39 (15±12)	no	no	Hauser et al. 1998
2.2	23.1±5.9	yes	yes	Wright & Reese 2000
2.2	22.4±6.0	no	tentative	Gorjian et al. 2000
2.2	19.9±5.3	yes	yes	Wright 2000
3.5	< 23 (11±6)	no	no	Hauser et al. (1998)
3.5	14.4±4.6	no	tentative	Dwek & Arendt 1998
3.5	11.0±3.3	no	tentative	Gorjian et al. 2000
3.5	12.4±3.2	yes	yes	Wright & Reese 2000
4.9	< 41 (25±8)	no	no	Hauser et al. 1998
4.9	< 36 (23±6)	no	no	Dwek & Arendt 1998
12	< 468 (192±138)	no	no	Hauser et al. 1998
12-100	< 15	no	no	Kashlinsky et al. 1996b
25	< 504 (192±156 )	no	no	Hauser et al. 1998
60	< 75 (21±27)	no	no	Hauser et al. 1998
60	28.1±7.2	yes	tentative	Finkbeiner et al. 2000
100	< 34 (22±6)	no	no	Hauser et al. 1998
100	> 5 (11±3)	no	no	Dwek et al. 1998
100	23.4±6.3	no	yes	Lagache et al. 2000
100	24.6±8.4	yes	tentative	Finkbeiner et al. 2000
140	32±6.5	yes	tentative	Schlegel et al. 1998
140	25±7	yes	yes	Hauser et al. 1998
140	< 28 (15.3±6.4)	no	no	Lagache et al. 1999
140	< 47 (24.2±11.6)	no	no	Lagache et al. 2000
240	17±2	yes	tentative	Schlegel et al. 1998
240	13.6±2.5	yes	yes	Hauser et al. 1998
240	11.4±1.9	no	yes	Lagache et al. 1999
240	< 25 (11.0±6.9)	no	no	Lagache et al. 2000
200-1000	(see Figure 1)	yes	tentative	Puget et al. 1996
200-1000	a ( / 0)k B(T)	yes	yes	Fixsen et al. 1998 (a)
200-1000	a ( / 0)k B(T)	yes	yes	Lagache et al. 1999 (b)
(a) a = (1.3 ± 0.4) × 10-5, k = 0.64 ± 0.12, T = (18.5 ± 1.2) K, 0 = 100 µm
(b) a = 8.8 × 10-5, k = 1.4, T = 13.6 K, 0 = 100 µm

Since the DIRBE team provided extensive foreground models, some of which have been used by other investigators, it is convenient to describe the results and methods of the DIRBE team first. The DIRBE team searched for the CIB in the data from all 10 DIRBE wavelength bands, and results based upon the final photometric reduction of the DIRBE data were reported by Hauser et al. (1998). Since there is no direction in the sky devoid of foreground radiation from the solar system and Galaxy, the faintest measured sky brightness at each wavelength is a conservative upper limit on the CIB. These dark sky limits (95% CL) are I < 398, 151, 64, 193, 2778, 2820, 315, 94, 73, and 28 nW m^-2 sr^-1 at 1.25, 2.2., 3.5, 4.9, 12, 25, 60, 100, 140 and 240 µm respectively. While these limits are free of model assumptions, they are too dominated by foreground sources to be of cosmological interest.

After modeling and removing the contributions from all foreground sources, the DIRBE team found isotropic residuals exceeding 3 only at 140 and 240 µm, as indicated in Table 1. The DIRBE team further argued that these residuals could not plausibly arise from unmodeled components of the solar system or Galaxy (Dwek et al. 1998), and concluded that the CIB had been measured at those wavelengths. At all other DIRBE wavelengths they reported CIB upper limits (95% CL) based upon the residuals and estimated uncertainties. They also determined a lower limit at 100 µm based on the argument that a thermal source producing the spectrum detected at 140 and 240 µm could not be fainter than this level at 100 µm (Dwek et al. 1998).

Figure 1. Summary of COBE-based CIB measurements. Detections are shown with 2 uncertainties. Upper limits are given at the 2 level. References are listed in Table 1. The curves at submillimeter wavelengths are from Fixsen et al. 1998 (dark wiggly curve from 200-1000 µm, representing the average of their three approaches); and Puget et al. 1996 (light curves from 150-1000 µm with break at ~ 500 µm: upper curve has no correction for emission correlated with ionized gas, lower curve has the correction).

The interplanetary dust contribution presents the most difficult problem except at the longest wavelengths, since it dominates the measured sky brightness from 1-140 µm even at high galactic and ecliptic latitude (see Figure 2, Hauser et al. 1998). The contribution from the IPD was determined by fitting a parameterized model of the spatial distribution and scattering and radiative properties of the dust cloud to the apparent annual variation of the sky brightness over the whole sky (Kelsall et al. 1998). Though this model was quite successful, reproducing the seasonal variation well and leaving evident map artifacts only at the few percent level, the uncertainties in the small residual differences between the measured brightness and the model are still quite substantial. Furthermore, it is not possible to determine a unique IPD model from sky brightness measurements from within the cloud. Kelsall et al. considered a number of different shapes for the cloud density distribution which gave comparably good fits to the time dependence, and estimated the model uncertainty by the spread in residual values at high Galactic latitude between these models.

Arendt et al. (1998) described the DIRBE team methods for determining the contribution of Galactic sources. Discrete bright sources within the Galaxy and the Magellanic Clouds were blanked out of the DIRBE maps. The contribution from discrete Galactic sources fainter than the DIRBE direct detection limit (about 5th magnitude at 2.2 µm) was calculated from 1.25 to 25 µm using a faint source model based on the SKY model of Wainscoat et al. (1992). The SKY model fits star count data over many wavelengths very well.

The contribution from the interstellar medium (ISM) was identified by its angular variation over the sky. The 100 µm map, after removal of the IPD contribution and an estimated value of the 100 µm CIB, was used as a template for ISM emission. The estimate of the 100 µm CIB was obtained by correlating 100 µm emission with H I column density at well-studied dark fields near the North Ecliptic Pole and the Lockman Hole and extrapolating the correlation to zero H I column density. This correlation is linear at low column densities. If all of the Galactic infrared emission were correlated with H I gas, extrapolation of this correlation to zero column density would yield the extragalactic light. If there is additional infrared emission associated with other gas components not correlated with H I, this procedure would not yield accurate results. Arendt et al. (1998) chose these two fields because the molecular gas has also been mapped, and low limits on the contribution from ionized gas could be set using pulsar dispersion measures and H measurements. The residual maps at all wavelengths other than 100 µm, after removal of the IPD contribution and blanking of bright sources, were correlated with the ISM template to determine a global color for each. The template was then scaled by that color and subtracted from each map. These final residual maps were tested for positive residuals and isotropy at high galactic latitude where foregrounds are least bright. Note that an error in the estimated 100 µm CIB would not have affected the isotropy tests of the residual maps, only the brightness of the residual. The uncertainty in the estimated 100 µm CIB was included in estimating the CIB uncertainties at all other wavelengths. The residual maps at 140 and 240 µm showed significant, isotropic residuals in dark regions of the sky, but the most precise determination of the brightness of the residual at these wavelengths was obtained by correlating the emission at these wavelengths with H I column density in the dark fields in the Lockman Hole and North Ecliptic Pole regions, as described above. To remove the ISM from the 100 µm map for purposes of looking for an isotropic residual at 100 µm, the H I map of Stark et al. (1992) was used as the ISM template. The final 100 µm residual map did not pass the isotropy tests.

Prior to publication of the DIRBE team results, a tentative identification of the CIB using DIRBE data was reported by Schlegel, Finkbeiner, & Davis (1998). In the course of preparing Galactic reddening maps based on the far infrared data from IRAS and DIRBE, they removed the zodiacal emission contribution using the DIRBE 25 µm map as a template. Correlating the residual maps with H I maps they found a significant constant additional term at 140 and 240 µm which they identified as a possible measurement of the CIB. However, they were not certain that the residual constant could not be an instrumental effect. They were therefore not confident that the CIB had been detected, and noted that the results of the DIRBE team would be more definitive. As Table 1 shows, their tentative values for the CIB are consistent with those of Hauser et al. (1998) within the stated uncertainties.

Puget et al. (1996) reported the first tentative identification of the CIB. Analyzing the initial release of FIRAS data, they concluded that there was a residual uniform background from 200 µm to 2 mm in excess of contributions from the CMB, interplanetary dust, and interstellar dust. They constructed a simple model for the IPD brightness based upon DIRBE 25 and 100 µm data and the assumption that the zodiacal emission is only a function of ecliptic latitude. They extrapolated this model to longer wavelengths assuming I ³. Since the IPD contribution to the sky brightness at these wavelengths is small, an accurate IPD model is not required. They assumed that the interstellar emission at high galactic latitude and low H I column density is traced by H I, and that the submillimeter emission correlated with H I can be represented by a single temperature medium with a ² emissivity law. They also made a correction for infrared emission associated with ionized gas not correlated with the H I, which significantly reduced their residual at the shortest wavelengths (200-400 µm). Their residual maps showed no significant gradients with galactic latitude or longitude, so the residual background was at least approximately isotropic. Figure 1 shows the residual spectra of Puget et al. with and without the ionized gas correction, with a break around 500 µm due to the shift between the FIRAS high and low frequency channels. The lower intensity curve includes the correction for Galactic emission from ionized gas.

A more extensive analysis of the FIRAS data, based upon the final photometric reduction of those data, was presented by Fixsen et al. (1998). They subtracted the CMB contribution and a contribution from interplanetary dust using an extrapolation of the DIRBE team model (Kelsall et al. 1998) out to 500 µm. They used three different methods to look for an isotropic residual distinct from emission from the ISM. One method assumed that the ISM spectrum is the same in all directions, but the intensity is spatially varying. The second method assumed that the neutral and ionized phases of the ISM are traced by a combination of maps of H I 21-cm line emission and of C II (158 µm) line emission. The latter was mapped over the sky by FIRAS (Bennett et al. 1994). Each component, including a term proportional to the square of the H I intensity, was allowed to have a distinct spectrum. In the third method, they assumed that the ISM emission is traced by a linear combination of the DIRBE ISM maps at 140 and 240 µm (Arendt et al. 1998), each term again having its own spectrum. Though each of these methods is subject to quite different systematic errors, the three methods yielded a consistent residual isotropic background, providing confidence that this is a robust determination of the submillimeter spectrum of the CIB. Figure 1 shows the mean spectrum found by Fixsen et al., which is consistent with the DIRBE results of Hauser et al. (1998). Table 1 gives an analytic representation of the mean CIB found by Fixsen et al.

Lagache et al. (1999) extended the study of the far infrared emission of the Galaxy at high galactic latitude using FIRAS data, finding a component of the emission not correlated with H I emission but which follows a csc(b) law. They attributed this emission to the warm ionized medium in the Galaxy. Subtracting the emission associated with these two gas-phase components from the mean FIRAS spectrum in low H I column density regions, they obtained the spectrum of the CIB longward of 200 µm. The result is consistent, within the uncertainties, with that of Fixsen et al. (1998). An analytic representation of this result is given in Table 1. They also obtained reduced values of the DIRBE residual in the Lockman Hole region at 140 and 240 µm. As shown in Table 1, the 240 µm value is within 1 of the Hauser et al. (1998) value, and the 140 µm value, which differs by less than 2, is positive by < 3 and therefore most confidently provides an upper limit.

Recently, Lagache et al. (2000) extended the study of infrared emission from the warm ionized medium using data from the Wisconsin H Mapper (WHAM) sky survey of Reynolds et al. (1998). They analyzed diffuse emission regions covering about 2% of the sky at high galactic latitude. Assuming a constant electron density so they could relate emission measure to H⁺ column density, they found a marginally better correlation of infrared emission at FIRAS resolution with a linear combination of H I and H⁺ column density than with H I alone. Their results suggest that 20-30% of the far-infrared emission at high galactic latitudes is uncorrelated with H I gas. Their resulting values for the CIB at submillimeter wavelengths are consistent with those of Fixsen et al. (1998) and Lagache et al. (1999). At 140 and 240 µm their results are consistent with those of Hauser et al. (1998), but with residuals less than 3 positive due to the small sky area analyzed and the uncertainties in the WHAM data. They obtained a significantly positive residual at 100 µm similar to that of Hauser et al. (1998), but did not demonstrate that this residual was isotropic.