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Astron. Astrophys. 361, 407-414 (2000)

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5. Discussion

We attribute the origin of the residual PSDs to the random distributions of faint sources which can no longer be identified as individual sources due to the source confusion. Another piece of evidence which supports this interpretation is the 170 µm/90 µm brightness ratio of the FIR background emission. In Fig. 5 we show the point-to-point comparison between the 90 µm and the 170 µm sky brightness. Here we examine the residual images after masking pixels around the sources with [FORMULA]. In order to match the spatial resolution between 90 µm ([FORMULA] FWHM) and 170 µm ([FORMULA] FWHM) images, one wavelength band image is convoluted with the other wavelength band beam profile. Although the scatter is large, the plot shows linear correlation with a slope of unity. This background color is quite different from that expected for the IR cirrus (about 3.1), and can be interpreted as a typical FIR color of galaxies contributing to the fluctuation. The fluctuation color due to faint galaxies depends on their redshift, and their SEDs. The relations between the FIR flux ratio and the redshift for SEDs of the cirrus dominated galaxy, the pure starburst galaxy (Efstathiou et al. 2000; Efstathiou & Siebenmorgen 2000), and the mixture of these two SEDs which represents a star-forming galaxy's SED like IRAS F10507+5723, are shown in Fig. 6. The flux ratio of [FORMULA] is attained at [FORMULA] for a pure starburst galaxy, while a cirrus dominated galaxy or a star-forming galaxy with a small contribution from starburst component must be local ([FORMULA]).

[FIGURE] Fig. 5. Point-to-point comparison between the 90 µm sky brightness and the 170 µm one in the Lockman Hole. The brightness is not absolute one, but is offset from the median brightness. In this plot the pixels around the bright sources ([FORMULA]mJy for 90 µm, [FORMULA]mJy for 170 µm) are not shown. In order to avoid the error due to the difference of the beam size between the two bands, the 90 µm images are convoluted with the 170 µm beam profile (144" FWHM). The solid line showing the IR cirrus color vector is taken from Lagache et al. (1999), which is 17.5 K gray-body with an emissivity proportional to [FORMULA].

[FIGURE] Fig. 6. FIR color vs redshift (z) relation for the cirrus dominated galaxy and the starburst galaxy. (Top) the ratio of [FORMULA] to [FORMULA], (bottom) the ratio of [FORMULA] to [FORMULA]. The model FIR SEDs are taken from Efstathiou et al. (2000) and Efstathiou & Siebenmorgen (2000). The dash-dotted lines represent the color-z relation of an example of the mixed SED, cirrus: starburst = 0.75: 0.25 at 100 µm.

From Fig. 6 we can also justify the flux calibration based on the IRAS fluxes of F10507+5723. If we adopt the ISO 90 µm flux determined by PIA and the theoretical PSFs, then [FORMULA] which is the color of a pure-starburst galaxy, while the ISO flux ratio [FORMULA] is much larger than that expected for any nearby ([FORMULA]) galaxies.

The local cirrus dominated galaxies are not likely to be the dominant sources responsible for the fluctuations, since such galaxies are relatively bright at optical wavelength and hence the source number density in the Lockman Hole at optical wavelength would exceed the observed one by more than an order of magnitude: as shown in Table 1 we obtained source density of about [FORMULA] sources/sr ([FORMULA]) at [FORMULA] mJy. Using the averaged SED of normal galaxies given by Schmidt et al. (1997), the B magnitude of a 100 mJy source at 90 µm is estimated to be about 16 mag. Reported B-band source counts above B = 16 mag is only a few sources per square degrees (Kirschner et al. 1979; Ellis 1983). Hence the galaxies responsible for the fluctuations must be heavily extincted at optical wavelengths, which is a well-known feature of starburst galaxies. In conclusion, the major source of the brightness fluctuations is most probably the star-forming galaxies located at [FORMULA] extincted at optical wavelengths.

In the plot of the 90 µm counts in Fig. 4, the IRAS counts are also plotted. These were originally the 60 µm counts, in which the flux is scaled by the factor [FORMULA]m)/[FORMULA]m)=2.1. This scaling factor is derived by the IRAS source counts at relatively high fluxes ([FORMULA]) (Rowan-Robinson et al. 1986), and is consistent with the color of normal galaxies with a partial contribution from starburst. Thus, if such galaxies dominate the 60 µm counts down to 110 mJy, this scaling is valid. We used the complete differential source counts down to 110 mJy by Lonsdale et al. (1990) and Bertin et al. (1997), and as shown in Fig. 4 the scaled counts are in good agreement with the model counts given by Guiderdoni et al. (1998). Since the integrated counts down to 150 mJy is much larger than the model counts, the integrated counts must show a steep rise between 150 mJy and 240 mJy, which, however, could not be observed in the IRAS 60 µm counts due to the source confusion (Hacking & Houck 1987). Further studies from space like ASTRO-F and SIRTF will judge if this steep rise is real.

Finally, we mention on the impact of the present work to the cosmic infrared background (CIB). Hauser et al. (1998) reported an upper limit of 1.1 MJy/sr at 100 µm and a positive detection of the CIB of 1.2 MJy/sr at 140 µm and 1.1 MJy/sr at 240 µm. Lagache et al. (1999) reported lower values of the CIB: [FORMULA] MJy/sr at 140 µm and [FORMULA] MJy/sr at 240 µm by further subtracting the dust emission associated with the diffuse ionized gas. Lagache et al. (2000) also reported the CIB at 100 µm: [FORMULA] MJy/sr. By summing the fluxes of all detected sources above 150 mJy, we obtained an integrated brightness of the CIB of 0.031 MJy/sr at 90 µm and 0.050 MJy/sr at 170 µm. If we consider the constraints on the number counts for [FORMULA] shown in Fig. 4, then the integrated brightness would be 0.09 - 0.30 MJy/sr at 90 µm for sources above 35 mJy and 0.053-0.15 MJy/sr at 170 µm for source above 60 mJy. Hence, 5-40 per cent of CIB can now be attributed to the integrated light of discrete sources above [FORMULA] which are responsible for the fluctuations.

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© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000