A&A 413, 843-859 (2004)
DOI: 10.1051/0004-6361:20031532

ISO deep far-infrared survey in the "Lockman Hole''

III. Catalogs and source counts at 90 & 170 $\mu$m

K. Kawara ¹ - H. Matsuhara ² - H. Okuda ^2,3 - Y. Taniguchi ⁴ - Y. Sato ¹ - Y. Sofue ¹ - K. Wakamatsu ⁵ - S. Oyabu ¹ - D. B. Sanders ⁶ - L. L. Cowie ⁶

1 - Institute of Astronomy, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo, 181-0015, Japan
2 - Institute of Space and Astronautical Science (ISAS), 3-1-1 Yoshinodai, Sagamihara, Kanagawa, 229-8510, Japan
3 - Gunma Astronomical Observatory, Gunma 377-0702, Japan
4 - Astronomical Institute, Tohoku University, Aoba, Sendai 980-77, Japan
5 - Department of Physics, Gifu University, Gifu 501-11, Japan
6 - Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

Received 28 May 2003 / Accepted 25 September 2003

Abstract
We present the catalogs and source counts for the C_90 (reference wavelength of 90 $\mu$m) and C_160 (170 $\mu$m) bands, which were extracted from our analysis of an ISO deep far-infrared survey conducted as part of the Japan/UH ISO cosmology project. The total survey area is $\sim$0.9 deg² in two fields within the Lockman Hole. The analysis consists of source extraction using the IRAF DAOPHOT package and simulations carried out by adding artificial sources to the maps to estimate the detection rate, the flux bias, the positional accuracy, and the noise. The flux calibration was performed using the Sb galaxy UGC06009 - the photometric error was estimated to be $\sim$50% at C_90 and $\sim$65% at C_160. The total noise estimated from the simulation is dominated by the confusion noise due to the high source density. The confusion noise is $\sim$20 mJy at C_90 and $\sim$35 mJy at C_160, which is much larger than the instrumental noise which is at the level of a few mJy or less. The catalogs were constructed by selecting 223 C_90 sources and 72 C_160 sources with a Signal to Noise Ratio (SNR) of three or greater. The distribution of the observed associations between C_90 and C_160 sources indicates that the $1 \sigma$ positional errors are $\sim$20 $^{\prime \prime }$ and $\sim$35 $^{\prime \prime }$ at C_90 and C_160, respectively. The corrections for the detection rate and the flux bias are significant for sources fainter than 200 mJy at C_90 and 250 mJy at C_160. Most of the sources detected both at C_90 and C_160 have a F(C_160)/F(C_90) color redder than the Sb galaxy UGC 06009. Such a red color could result from reddening due to the flux bias or a K-correction brightening due to the effect of redshift. Red sources brighter than 200 mJy at C_160 may be very luminous galaxies like Arp 220 at moderate redshift. The source counts are derived by applying the corrections for the detection rate and flux bias. The resultant counts are quite consistent with the constraints derived from the fluctuation analysis performed in Paper II. The C_160 counts are also consistent with the results from the FIRBACK project. Our C_90 survey, which is 2-3 times deeper than those previously published, reveals an upturn in the count slope at around 200 mJy. While recent models give a reasonable fit to the C_160 counts, none of them are successful in accounting for the upturn in the C_90 counts. If the upturn is caused by ultraluminous IR galaxies, their redshifts would need to be at  $z \sim 0.5$, implying a major event in galaxy evolution at moderate redshift.

Key words: galaxies: evolution - galaxies: starburst - cosmology: observations - infrared: galaxies

1 Introduction

The IRAS all-sky survey opened up a new window on galaxy evolution, and showed that a significant fraction of the bolometric luminosity of all galaxies is emitted at far-infrared wavelengths through reprocessing by dust of UV/optical light from both stars and active galactic nuclei (AGN). The far-infrared spectra of galaxies peak in the wavelength range 25-200 $\mu$m. Cirrus-dominated normal galaxies have an emission peak at 100-200 $\mu$m, while infrared-luminous starburst galaxies peak near 60 $\mu$m, and Seyfert galaxies often show a peak near 25 $\mu$m (Sanders & Mirabel 1996 and references therein). The infrared luminosity as observed by IRAS is $\sim$30% of the total energy output of galaxies in the local Universe (Soifer & Neugebauer 1991). The detection of the CIB (Cosmic Infrared Background) with the COBE satellite at far-infrared and submillimeter wavelengths (e.g. Puget et al. 1996) indicates that the integrated luminosity from thermal dust emission is comparable to or greater than that of the integrated UV/optical light of galaxies in the Hubble Deep Field (HDF) (Guiderdoni et al. 1997), implying a potentially larger contribution from dust-enshrouded star formation than that inferred from the rest-frame optical/UV at high redshift. As discussed by Steidel et al. (1999 and references therein), at high redshift where optical observations are sampling the rest-frame optical/UV, the SFR density derived from optical observations (e.g. Madau et al. 1996) may be substantially underestimated as a result of absorption by dust.

The next step is to resolve the CIB into individual sources. The sub-millimeter common-user bolometer array (SCUBA) on the 15 m James Clerk Maxwell Telescope (JCMT) is now able to resolve a substantial fraction of the CIB at 0.85 mm into luminous IR galaxies most of which appear to lie at high redshift, z > 1 (Smail et al. 1997; Hughes et al. 1998; Barger et al. 1998; Scott et al. 2002; Sato et al. 2002). In the mid- and far-infrared, various surveys have been conducted with the European Space Agency (ESA) Infrared Space Telescope (ISO: Kessler 1996), which was in operation between 1995 and 1998. Most of the deep ISO mid-infrared surveys were performed in the 6.7 $\mu$m (LW2) and/or 15 $\mu$m (LW3) bands. 6.7 $\mu$m surveys are useful for looking at stellar systems at high redshift (Serjeant et al. 1997; Taniguchi et al. 1997; Flores et al. 1999a; Altieri et al. 1999; Sato et al. 2003; Oliver et al. 2002). The cross-identification of 6.7 $\mu$m sources with SCUBA sources suggests that star formation with a SFR of  $10^3~M_{\odot}~{\rm yr}^{-1}$ can build up massive stellar systems of 5 $\times$ $10^{11}~M_{\odot}$ by redshift z = 1-2 (Sato et al. 2002). 15 $\mu$m surveys carried out by different groups to different depths, probed emission both from warm dust and the unidentified infrared bands at 6-13 $\mu$m in star forming galaxies (Serjeant et al. 1997; Flores et al. 1999b; Aussel et al. 1999; Altieri et al. 1999; Elbaz et al. 1999; Oliver et al. 2002). The 15 $\mu$m counts show an excess at 400 $\mu$Jy by a factor of $\sim$10 (Elbaz et al. 1999), requiring strong cosmic evolution of the mid-infrared emission of galaxies. The excess could be largely attributable to bright and massive galaxies at z < 1.5 (Elbaz et al. 1999).

The CIB has a major peak at wavelengths 100-200 $\mu$m that is presumably due primarily to emission from cool dust (e.g., Hauser & Dwek 2001). If the rest-frame SEDs of starburst galaxies peaking at 60-100 $\mu$m are responsible, this might imply a high SFR at $z \sim 0.5{-}1$, corresponding to a major event in galactic evolution.

The far-infrared imaging instrument ISOPHOT (Lemke et al. 1996) onboard ISO was used to carry out deep far-infrared surveys in a $\sim$0.9 deg² area in the LH using the 90 $\mu$m and 170 $\mu$m bands (Kawara et al. 1998; Matsuhara et al. 2000), in 4 deg² in the Marano fields and northern ELAIS fields using the 170 $\mu$m band as part of the FIRBACK project (Puget et al. 1999; Dole et al. 2001), in 12 deg² of the ELIAS fields using the 90 $\mu$m band (Oliver et al. 2000; Efstathiou et al. 2000), in 0.4 deg² in the SA57 field using the 60 $\mu$m and 90 $\mu$m bands (Linden-Vørnle et al. 2000), and in 1.6 deg² in eight fields at wavelengths between 90 $\mu$m and 180 $\mu$m (Juvela et al. 2000). The far-infrared source counts derived by the various groups are in agreement with strongly evolving models of the starburst galaxy population. While the resolved sources brighter than 180 mJy at 170 $\mu$m account for less than 10% of the CIB (Dole et al. 2001), the constraints from the fluctuation analysis by Matsuhara et al. (2000) indicate that sources brighter than 35 mJy at 90 $\mu$m and 60 mJy at 170 mJy contribute 5-40% of the CIB.

This is our third paper reporting results from our ISO deep far-infrared survey that was conducted at 90 $\mu$m and 170 $\mu$m in the LH. The survey was made as part of the Japan/UH ISO cosmology program using ISAS guaranteed time. Paper I (Kawara et al. 1998), reported that the source counts at 90 $\mu$m and 170 $\mu$m are much greater than expected from a no-evolution model. The high counts at 170 $\mu$m have been confirmed by Puget et al. (1999). Paper II (Matsuhara et al. 2000), used fluctuation analysis to place constraints on the source counts down to a level of 35 mJy at 90 $\mu$m and 60 mJy at 170 $\mu$m. These constraints suggest a steep slope in the source counts versus flux, implying strong galaxy evolution, most likely at moderate redshift (e.g., Takeuchi et al. 2001). In the current paper, we describe our source extraction method, perform simulations to estimate the reliability and completeness of our survey, construct the catalogs of far-infrared sources, derive the source counts at 90 $\mu$m and 170 $\mu$m, and discuss the implications of our results.

2 Observations and Image processing

We have carried out a far-infrared survey in the LH using ISOPHOT, which was an imaging photopolarimeter onboard ISO. The LH is a region of the sky with the smallest HI column density (Lockman et al. 1986), and thus the far-infrared confusion noise caused by infrared cirrus is expected to be a minimum in this region (Gautier et al. 1992).

The survey was performed in two fields, LHEX and LHNW, between revolutions 194 and 215 (May 28 and June 19, 1996). Each field extends approximately $44\hbox {$^\prime $ }$ $\times$ $44\hbox {$^\prime $ }$. The center of the LHEX field is at  $\alpha = 10^{\rm h}52^{\rm m}00^{\rm s} \ \delta = +57\hbox{$^\circ$ }21\hbox{$^\prime$ }30\hbox{$^{\prime\prime}$ }$ (J2000), and LHNW is at  $\alpha = 10^{\rm h}33^{\rm m}55^{\rm s} \ \delta = +57\hbox{$^\circ$ }46\hbox{$^\prime$ } 20\hbox{$^{\prime\prime}$ }$ (J2000). LHEX contains the field in which the ROSAT Deep Survey was carried out (Hasinger et al. 1998). Our ISOPHOT observations were made using the PHT22 raster mapping mode in the C_90 band (reference wavelength 90 $\mu$m) and the C_160 band (reference wavelength 170 $\mu$m) (see $ISO\ Handbook\ Volume\ V$).

Each $44\hbox {$^\prime $ }$ $\times$ $44\hbox {$^\prime $ }$ field consists of four rasters. The area covered by each raster is approximately $22\hbox {$^\prime $ }$ $\times$ $22\hbox {$^\prime $ }$. Four rasters making one field were executed and completed in a single revolution, except for LHNW at C_160, so that the position angles of all of the rasters are almost the same on the sky. For C_90, each raster has 18 $\times$ 18 raster points with raster steps of 69 $^{\prime \prime }$ corresponding to a 1.5 pixel overlap in both directions in the spacecraft (Y, Z) coordinate system. The integration time per raster point was 16 s. Within the maximum redundancy region, each part of sky was thus observed by four different pixels resulting in a total integration time per sky position of 64 s (4 $\times$ 16 s). For C_160, each raster has 27 $\times$ 14 raster points with raster steps of 46 $^{\prime \prime }$ corresponding to a 1.5 pixel overlap in the Y axis and raster steps of 92 $^{\prime \prime }$ corresponding to a one pixel overlap in the Z axis. The integration time per raster point was 20 s. Within the maximum redundancy region, each part of the sky was observed eight times by four different pixels and thus the total integration time per sky position was 160 s (8 $\times$ 20 s).

Our image processing consists of two stages. At the first stage, the PHT Interactive Analysis (PIA) version 7.3 (Gabriel et al. 1997) was used, starting with the edited raw data (ERD) created via the off-line processing version 7.0. The AOT/Batch processing mode of PIA was employed using the defaultparameters to reduce the ERD to the Astronomical Analysis Processing (AAP) level. This standard reduction includes discarding some of the readouts at the beginning of the integration ramps, linearization and deglitching of the ramps on the ERD level, signal deglitching and drift recognition at the Signal-per-Ramp Data (SRD) level, reset interval normalization, signal deglitching, dark current subtraction, and vignetting correction on the Signal-per-Chopper Plateau (SCP) data level. At the end of this stage, maps were produced at the Astronomical Analysis Processing (AAP) level in mapping mode using median brightness values. These are called AAP maps in this paper. Each AAP map corresponds to the respective $22\hbox {$^\prime $ }$ $\times$ $22\hbox {$^\prime $ }$ raster.

Figure 1: The left column shows C_90 (90 $\mu$m) and C_160 (170 $\mu$m) maps of the  $44\hbox {$^\prime $ }$ $\times$ $44\hbox {$^\prime $ }$ LHEX field, while the right column shows the same for LHNW. Each field is made up of four $22\hbox {$^\prime $ }$ $\times$ $22\hbox {$^\prime $ }$ sub-fields (see text). The median filtered maps have been rebinned onto a $2.3\hbox {$^{\prime \prime }$ }$/pixel grid for C_90 and a $4.6\hbox {$^{\prime \prime }$ }$/pixel grid for C_160. The IRAF GAUSS routine is then applied with $\sigma = 6$ for smoothing the images. Sources with $SNR \ge 3$ are plotted on the C_90 and C_160 maps. The SNRs are coded by the filled circles; the largest circles represent sources with SNR> 6, the second with SNR= 6-5, the third with SNR = 5-4, and the smallest with SNR= 4-3. Flux calibration was performed using UGC 06009(IRAS F10507+5723) which is the only cataloged IRAS source in our survey fields. It is noted that all "sources" detected within 46 $^{\prime \prime }$ at C_90 (1/3 of the detector array) and 92 $^{\prime \prime }$ at C_160 (1/2 of the array) from the outer bounds of the survey fields are not plotted because the sensitivity in these outer boundary regions is significantly poorer than the inner regions due to fewer redundant observations. The "+" (plus) symbols represent the sources detected by Linden-Vørnle et al. (2000).

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The AAP maps, in particular for the C_90 band, are greatly affected by a slow drift in the responsivity. No sources can be recognized because of the overwhelming lattice pattern. At the second stage, we have developed the so-called median filtering technique to remove the slow responsivity drift. As shown in Figs. 1 and 2 in Paper I, median filtering dramatically reduces the responsivity drift and many sources become recognizable in the map. It should be noted that the AAP C_160 map is almost identical to that from the median filtered signal map, implying that the detectors used for the C_160 band were stable and suffered little from responsivity drift.

Figure 1 shows the mosaiced maps of LHEX and LHNW, which are made from the median filtered signal. The resultant maps of the four sub-fields are first rebinned onto a 2.3 $^{\prime \prime }$/pixel grid for C_90 and a 4.6 $^{\prime \prime }$/pixel grid for C_160, and then combined into the 44$^\prime$ $\times$ 44$^\prime$ maps. Finally, the IRAF gauss routine was applied with  $\sigma = 6$ for smoothing the maps.

3 Source extraction and photometry

3.1 Source extraction

The IRAF DAOPHOT package (Davis 1994) was used to extract sources from the maps for the following reasons; (1) as shown in Fig. 1, the maps are very crowded, often blending the light of two or more sources, and (2) FWHM measurements of brightness profiles of bright sources indicate that all of their FWHMs are not extended more than two detector pixels and thus they should be detected as point sources. DAOPHOT has indeed been developed to perform stellar photometry in crowded fields (Stetson 1987) such as in the cores of globular clusters. In DAOPHOT, the positions and relative magnitudes of point sources are determined by using a numerical fitting technique to match the given Point Spread Function (PSF) to the observed light distribution. Where the light of two or more sources is blended, it fits a model in which two or more of the expected PSFs are superimposed by shifting each model PSF in position and scaling in intensity until a satisfactory fit of the overall model to the image data is achieved. IRAS F10507+5723, the brightest source in our survey, was used to define the PSFs because the light distribution for IRAS F10507+5723 is typical of what is expected when a point source is observed in our survey.

The following sequence from (1) to (6) was performed for extracting sources: (1) DAOFIND was used to find sources on the original map and produce a list of x and y positions of the sources; (2) PHOT was used on the original map to obtain aperture photometry and sky values for the sources in the list; (3) ALLSTAR was used to do simultaneous PSF-fitting for all the sources found on the original map, reject poorly fitted sources, and produce a list of sources and a subtracted map from which the listed sources are subtracted; (4) DAOFIND, PHOT, and ALLSTAR were used on the subtracted maps to identify sources that had been previously hidden by brighter sources, with the procedure repeated until all the significant sources were extracted from the subtracted maps; (5) PFMERGE was used to merge the original and all the other lists obtained from the subtracted maps and produce the new merged list; (6) ALLSTAR was used on the original image to do simultaneous PSF-fitting for all the sources in the merged list and produce the final list of sources.

DAOPHOT fits the PSF to the data within the specified fit-radius of 62 $^{\prime \prime }$ for C_90 and 124 $^{\prime \prime }$ for C_160, and computes the fitted flux and flux error. The flux error is derived from a combination of the residuals from the fitting and the uncertainty of the local sky values. The SNR for source detection is a division of the flux by the flux error, both of which DAOPHOT returns. However, such SNRs should not be regarded as true, because the flux error is calculated by using values in sub-pixels which are not themselves independent. We thus scaled the flux error in such a way that the average of the flux errors given by DAOPHOT agrees with that of the differences between the given and measured fluxes of artificial objects in simulations that will be discussed later. Figure 1 plots sources extracted by DAOPHOT on (top) the LHEX C_90 and C_160 maps and (bottom) the LHNW C_90 and C_160 maps. The detected sources have $SNR \ge 3$, which is our detection threshold in this paper.

3.2 Flux calibration

Flux scaling is done by using the same standard source as described in Paper I. This standard source is IRAS F10507+5723, which has ISO band fluxes, F(C_90) = 1218 mJy and F(C_160) = 1133 mJy. IRAS F10507+5723 is the only cataloged IRAS source in our survey fields, and it is the brightest source in our survey fields. It is identified with a Sb galaxy UGC 06009 (Thuan & Sauvage 1992). The IRAS fluxes are F(60 $\mu$m) = 533 $\pm$ 59 mJy and F(100 $\mu$m) = 1218 $\pm$ 292 mJy (IRAS FSC 1990). Its flux ratio, F(100 $\mu$m)/F(60 $\mu$m) = 2.29, can be fit with a combination of IR cirrus and starburst spectra (Pearson & Rowan-Robinson 1996), if 76% of the 100 $\mu$m flux comes from the cirrus component. This predicts F(C_160)/F(100 $\mu$m) = 0.93, which implies F(C_160) = 1133 mJy. F(C_90) is simply assumed to be identical to F(100 $\mu$m) because the central wavelength at the C_90 band is 95 $\mu$m which is close enough to the IRAS's 100 $\mu$m band. A large error may be associated with the F(C_160) flux density. For example, combining recent model spectra by Dale et al. (2001) with the same IRAS flux ratio implies F(C_160)/F(100 $\mu$m) = 1.15, leading to a F(C_160) value greater than the former by $\sim$25%, which is comparable to the IRAS flux error.

Figure 2: Comparison with the C_90 flux by Linden-Vørnle et al. The mean ratio of ours to those in Linden-Vørnle et al. are 1.03 and the mean deviation from the line for ratio = 1 (dashed line) is 25% of the flux. The dotted lines denote flux deviations of $\pm$25%. The flux values by Linden-Vørnle et al. are multiplied by a factor of 1.63 so that the C_90 flux of Lockman E4_1 is equal to the IRAS value.

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The following arguments suggest that our flux calibration is associated with a larger source of error than those discussed so far. Our IRAF flux calibration results in 14.4 MJy sr^-1 at C_90 and 5.17 MJy sr^-1 at C_160 for the sky background. These are 3.5 times and 1.9 times greater than the COBE values (Paper I). Note that the intensity of interplanetary dust emission varies little with solar elongation at such high ecliptic latitude ( $\beta \sim 45^{\circ}$). The discrepancy can be mostly attributed to the flux loss in the PSF wings and to transients in the detector signals.

The fluxes for IRAS F10507+5723 were determined from the light within the apertures used by the aperture photometry routine PHOT. The radii of the apertures are 69 $^{\prime \prime }$ for C_90 and 138 $^{\prime \prime }$ for C_160. The fractions of the PSFs, taken from the calibration files PC1FOOTP.FITS and PC2FOOTP.FITS, passing through the apertures are 0.92 for both C_90 and C_160. Note that the PSFs given in the calibration files agree with the theoretical model PSFs that take into account the ISO primary mirror, secondary mirror, and tripod (Okumura 2000).

The transient effects in the ISOPHOT data have been analyzed and discussed by Acosta-Pulido et al. (1999). When the illumination changes, a generally observed effect in the transients is an instantaneous signal jump followed by a slow rise of the signal until stabilization is reached. The instantaneous signal jumps are $\sim$0.30 of the stabilized value at C_90 with the C100 detectors and $\sim$0.85 at C_160 with the C200 detectors. For the C200 detectors, the time constant for the slow rise is $\sim$40 s (see Fig. 5 in Lagache & Dole 2001). In our 20 s integration, the signal reaches a level of 0.91. Hence, the correction for the transient effect is 0.88 (i.e., average of 0.85 and 0.91) at C_160 for point sources. Note that such a correction should not be applied to the sky background because its spatial distribution is extremely smooth and flat. For the C100 detectors, the time constant is longer than that for the C200 detectors, and it takes several hundreds of seconds to reach stabilization of the signal (see Fig. 7 in Acosta-Pulido et al. 1999). In our 16 s integratio, the signal reaches a level of $\sim$0.60. Thus, the correction for the transients is roughly $\sim$0.45 at C_90.

After applying the corrections to the point source for the effects of the PSFs and the transients, the IRAS flux scaling gives sky background values that are 1.45 and 1.55 times greater than the COBE values. Thus, our calibration may overestimate the fluxes by 45% at C_90 and 55% at C_160. Taking all of the errors into account, the total errors associated with our flux calibrations are estimated to be 50% at C_90 and 65% at C_160; i.e., in the case of C_160, a 25% error for the IRAS 100 $\mu$m flux, 25% for the model prediction, and 55% for the deviation from the COBE flux.

Table 1: Identification with sources in Linden-Vørnle et al.

3.3 Comparison with Linden-Vørnle et al.

Linden-Vørnle et al. (2000) have reduced our C_90 data in the LHEX and LHNW fields by using the PIA with median filtering similar to our image processing. They then used SExtractor to detect and measure sources. Their flux calibration is based on the calibration files supplied with PIA v7.31(e). IRAS F10507+5723 then has a C_90 flux of 747 mJy, which is 1.63 times smaller than the IRAS value. To be consistent with our flux scaling, their C_90 fluxes are multiplied by 1.63 in the following discussion.

They detected 8 sources that are brighter than 269 mJy. In Fig. 1, these sources are marked by a "+" symbol. As can be seen from the maps, these are the brightest sources in our observations. Table 1 identifies their sources with our sources having a $SNR \ge 3$. Two of their eight sources are resolved into two sources, while two are not detected because the SNRs are less than 3. One of the two resolved sources, called E4_3 by Linden-Vørnle et al. (2000), is also resolved into two sources in high spatial resolution VLA observations (De Ruiter et al. 1997), suggesting that DAOPHOT is a useful tool for extracting far-infrared sources in crowded fields. It is also possible that the two undetected sources are extended or that they are multiple sources, where DAOPHOT has failed to fit PSFs with sufficient SNRs.

Figure 2 compares the Linden-Vørnle et al. fluxes with ours. After multiplying by 1.63, the mean ratio of our fluxes to their fluxes is 1.03 and the mean deviation from the line of ratio = 1 is 25% of the flux, thus being in agreement within 25%. As can be recognized from Table 1 and Fig. 2, their flux errors are approximately two or three times smaller than ours. As will be discussed in Sect. 4.2, our flux error is estimated from the simulations, and thus it includes the confusion noise due to the high source density which is a dominant noise source in our survey observation. On the other hand, Linden-Vørnle et al. (2000) did not perform simulations, thus their flux error does not include such confusion noise. This could explain why their flux errors are two to three times smaller than ours.

4 Simulations and noise

4.1 Simulations

To estimate the errors and bias in detection, photometry, and astrometry, we have carried out simulations using artificial objects. In crowded fields where the detection limits are controlled by the confusion noise, strong Eddington/Malmquist noise is expected. Near the detection limit, more sources are scattered to brighter fluxes (e.g., Oliver 2002). In fact, in crowed fields there is a good chance of having more than one source within a photometric aperture resulting in the two sources being detected as a single brighter source. This results in overestimating the flux (flux bias) and thus the number of bright sources.

It would be ideal to add the signals of artificial sources to the ERD data in such a way that all of the routines used in the data reduction can be checked by the simulations. However, such simulations are very time-consuming and require complete knowledge of such systematic effects as transient behavior of the detectors and incident stray light. However, because of our incomplete understanding of such effects, we decided to perform the simulation by adding artificial objects to the original maps shown in Fig. 1.

Detections and measurements were made on simulation maps, to which artificial objects were added by using the same set of DAOPHOT parameters as used to detect sources in the original maps. The simulations were repeated by changing the positions and fluxes of artificial objects until a statistically sufficient number of objects had been detected. The fluxes given in the simulations range from 50-200 mJy for C_90 and from 70-280 mJy for C_160 in steps of 0.15 dex ( $\sqrt{2} \times$). The results from the simulations are summarized in Figs. 3 and 4. The top panels in Fig. 3 indicate the expected flux bias; the ratio of the measured flux over the given flux increases as the given flux decreases. The bottom panels show a rapid slowdown of the growth in source counts toward the faint end of the flux range. In other words, the detection rates rapidly decrease as the flux decreases.

Table 2: Corrections for source confusion estimated from simulation.

Figure 3: Summary of the simulations for detection of C_90 (left panels) and C_160 (right panels) sources. The top panels plot the flux given to artificial objects against the flux measured by DAOPHOT. The dotted lines denote the ideal case where the given flux is identical to the measured flux. Due to Eddington/Malmquist bias, the ratio of the measured flux to the given flux increases as the given flux decreases. The bottom panels shows the detection rates as a function of the measured flux. The crosses represent the values of the corrections applied to the source counts (see Table 2).

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Figure 4: Accuracy of the catalog data estimated from the simulations for C_90 (left panels) and C_160 (right panels) sources. The top panels show the ratio of the flux measured by DAOPHOT to the flux given to artificial sources. The error bars associated with the flux ratio represent a standard deviation as defined by  $\sqrt{\frac{1}{N-1}\sum_{j=0}^{N-1}(x_j - \overline{x})^2}$ where N represents the number of artificial sources detected by DAOPHOT, while the error bars on the measured flux are the standard deviations divided by $\sqrt {N}$. The middle panels show the standard deviations of the measured flux. The dotted lines fitted to the simulation data are given by  $\sqrt {\sigma _0^2 + \sigma _f^2}$ where $\sigma _0$ = constant and $\sigma _f$ = a $\times$ (measured flux): $\sigma _0$ = 20 mJy and a = 0.16 for C_90 and $\sigma _0$ = 35 mJy and a = 0.20 for C_160. The bottom panels show the standard deviations of the positional differences between measured and given positions.

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The derived correction factors to the source counts are given in Table 2. The values of the correction factors listed in the table are marked by crosses in Fig. 3. It can reasonably be assumed that sources brighter than 400 mJy are free from the effects of Eddington/Malmquist bias. As one can see from this table and Fig. 3, the corrections for source confusion are important for determining source counts. For example, 30% of the 100-141 mJy C_90 sources are detected as 1.78$\times$ brighter sources, while 64% of the 200-283 mJy C_160 sources are detected as 1.31$\times$ brighter sources.

4.2 Noise

The PIA provides a determination of the signal uncertainty at the individual raster positions. This PIA noise can be used to estimate the instrument noise (Kiss et al. 2001). With PIA Ver8.1, we have produced uncertainty maps. The median filtering technique reduces the PIA noise significantly, namely 2$\times$ and 5$\times$ smaller than those without this technique at C_90 and C_160, respectively. The typical 1 $\sigma$ noise levels are 1.3 mJy per  $46\hbox{$^{\prime\prime}$ }\times 46\hbox{$^{\prime\prime}$ }$ pixel at C_90 and 0.6 mJy per $92\hbox{$^{\prime\prime}$ }$ $\times$ $92\hbox{$^{\prime\prime}$ }$ pixel at C_160, after the IRAS-based flux calibration is applied. These values correspond to 3.1 mJy within a PSF-fitting radius of 62 $^{\prime \prime }$ at C_90 and 1.4 mJy within a 124 $^{\prime \prime }$ radius at C_160. As will be discussed later, the instrumental noise is much smaller than that estimated from the simulations.

The confusion noise due to IR cirrus should not be a dominant noise source given the low level of the total HI column density for our two LH fields. Analyzing the brightness fluctuation at C_90 and C_160 in our fields, Matsuhara et al. (2000) in Paper II found that the spatial power spectrum was flat at low spatial frequencies (f < 0.1 arcmin^-1) and was slowly decreasing toward higher frequencies. These spectra are quite different from the power-law spectra expected from IR cirrus, and are well explained by randomly distributed sources (i.e., galaxies). In addition, a point-to-point comparison between C_90 and C_160 brightness shows that the slope of the linear fit is quite different from that expected from IR cirrus (Paper II; Juvela et al. 2000).

Following the technique described by Dole et al. (2001), the total noise including the confusion noise due to the high number density of sources, can be estimated from the results of the simulations. In this technique, the difference between the measured and given fluxes of the artificial objects is regarded as the noise. The middle panels in Fig. 4 show 1 $\sigma$ dispersions of the differences in flux as a function of the measured flux. The dispersions increase with the fluxes. It is reasonable to approximate the dispersions by a quadratic sum of  $\sqrt {\sigma _0^2 + \sigma _f^2}$, where $\sigma _0$ is constant and $\sigma _f$ is proportional to the flux (i.e.,$\sigma _f$ = a $\times$ flux). The dotted lines in the figures represent $\sigma _0$ = 20 mJy with a = 0.16 for C_90 and $\sigma _0$ = 35 mJy with a = 0.2 for C_160. The $\sigma _0$ values, corresponding to the noise at zero flux, are much greater than the instrumental noise and the noise due to IR cirrus fluctuations. Thus, we conclude that our observations are limited by the confusion noise due to the high density of galaxies. Our confusion noises are $\sim$20 mJy at C_90 and $\sim$35 mJy at C_160. These values are consistent with the value of 45 mJy derived from the C_160 source counts by Dole et al. (2001) and those from the fluctuation analysis of C_90 and C_160 brightness by Kiss et al. (2001).

The standard rule of thumb is that confusion becomes important at 1/30 of a source per beam (Hogg 2001). One sigma confusion noise can be represented as $\sigma^2_{\rm conf}(S_{\nu}) = -\Omega_{\rm bm}\int_0^{S_{\nu}}S^2[{\rm d}N(S)/{\rm d}S]{\rm d}S$ by integrating sources fainter than $S_{\nu}$ falling within one beam $\Omega_{\rm bm}$ (e.g., Helou & Beichman 1990; Lagache & Puget 2000) . Assuming the cumulative number counts down to $S_{\nu}$ to be a power law function of the flux density, namely, $N(S_{\nu}) = KS^{\alpha}_{\nu}$, we have $\sigma_{\rm conf}(S_{\nu}) = [-\alpha/(2+\alpha)\Omega_{\rm bm}N(S_{\nu})]^{1/2}S_{\nu}$. Our cumulative source counts have forms of  $N \propto S^{-3.2}$ at C_90 and  $N \propto S^{-2.9}$ at C_160. Hence, at the 3 $\sigma$ limit, namely $S_{\nu} = 3 \sigma_{\rm conf}$, the number of sources for $\alpha = -3$ is $\Omega_{\rm bm}N(S_{\nu})$ = 1/27. In our source counts, the number of sources brighter than the 3 $\sigma _0$ noise levels are 1.5 $\times$ 10⁶ and 3.5 $\times$ 10⁵ per steradian at C_90 and C_160, respectively. Because the beam solid angles are $46\hbox{$^{\prime\prime}$ }$ $\times$ $46\hbox{$^{\prime\prime}$ }$ for C_90 and  $92\hbox{$^{\prime\prime}$ }$ $\times$ $92\hbox{$^{\prime\prime}$ }$ for C_160, the numbers of sources per beam are 1/13 at C_90 and 1/14 at C_160. Our analysis has thus pushed the confusion limited flux levels beyond the classical limit by a factor of two in terms of sources per beam. This may be largely attributed to use of DAOPHOT for source extraction. As already pointed out, DAOPHOT has been developed to do stellar photometry in crowded fields like the cores of globular clusters. In hoping that DAOPHOT would push the confusion limit to a fainter flux level, we decided to use it for source extraction.

5 Catalogs, positional accuracy, and IR colors

5.1 Separate catalogs for C_90 and C_160 sources

Table 3: Cumulative numbers of sources.

To construct the ISO far-infrared catalogs that will be used in the subsequent analysis, we have selected sources with SNR > 3, excluding areas near the edges of the maps. The redundancy of the observations along the edges of the maps is less than for the inner regions, implying poorer sensitivity near the edges. The widths of these edges correspond to the size of the detector, namely 46 $^{\prime \prime }$ at C_90 and 92 $^{\prime \prime }$ at C_160. As given in Table 3, the total survey areas are 0.904 deg² at C_90 and 0.885 deg² at C_160. C_90 and C_160 observations were not performed in the same revolution so that each has a different roll angle, resulting in some small areas where observations were only performed at a single band. The common areas in which both C_90 and C_160 observations were made are 0.426 deg² for LHEX and 0.431 deg² for LHNW. The total common area is thus 0.857 deg², which is 95% of the total area observed at C_90 and 97% at C_160.

The catalogs are given in Tables 4-7. As summarized in Table 3, the numbers of sources listed in the catalogs are 223 at C_90 and 72 at C_160; thus there are 295 entries in total. The first column of the catalogs gives the names of sources. C_90 and C_160 sources in LHEX are prefixed 1EX and 2EX, respectively, and those in LHNW are prefixed 1NW and 2NW, respectively. The three digits following the prefix are running numbers given by DAOPHOT. Therefore, 2NW007 means the 7th source in LHNW detected in the C_160 band. Columns 2 and 3 give the right ascension and declination (J2000). The errors in position estimated from the simulations are given in the bottom panels of Fig. 4. They are estimated to be 20 $^{\prime \prime }$ at C_90 and 35 $^{\prime \prime }$ at C_160. As will be discussed in the next subsection, these errors are consistent with those estimated from Fig. 5. Column 4 shows the flux density in mJy along with the error. Column 5 gives the SNR estimated from DAOPHOT photometry. The flux errors for sources fainter than 400 mJy are estimated from the simulations as shown in the middle panels of Fig. 4. For brighter sources, the flux errors are simply the flux divided by the SNR. No correction for flux bias was applied to the flux density values given in the catalogs. Notes are given in Col. 6. The area observed at C_90 differs slightly from that at C_160 due to field rotation; therefore some sources were only observed at either C_90 or C_160. Such sources are marked "*'' in the last column.

5.2 Cross-association catalogs of C_90 and C_160 sources

Figure 5: The distributions of associations between C_160 and C_90 sources as a function of distance, where distance is an angular separation from a C_160 source to the nearest C_90 source. The top panel shows the observed 65 associations with a distance of 300 $^{\prime \prime }$ or less. The middle panel represents background associations expected from uniformly-distributed, random positions of sources. The bottom panel shows the difference between the observed and background associations, thus presumably real associations only plus statistical fluctuation. The dotted curve in the top and bottom panels represents the distributions for the case that all associations are physically real and the positional errors are identical to those estimated by the simulations (i.e., $\sigma _{{\rm C\_160}}$ = 35 $^{\prime \prime }$ and $\sigma _{{\rm C\_90}}$ = 20 $^{\prime \prime }$). In the top panel, 84% of the observed association with distances less than 50 $^{\prime \prime }$ are expected to be real.

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Table 4: C_90 (90 $\mu$m) sources in LHEX.

Table 5: C_90 (90 $\mu$m) sources in LHNW.

Table 6: C_160 (170 $\mu$m) sources in LHEX.

To merge the separate catalogs, C_160 sources were cross-associated with C_90 sources. To do this, C_160 sources were coupled to the nearest C_90 source and their angular separations were computed. This was done for 70 C_160 sources that were all "detected" at C_90. The results are given in the top panel of Fig. 5. The distribution of the observed associations consist of real physical associations and fault background associations that are produced by chance. To estimate the number of background associations, we generated C_90 and C_160 sources at positions which are distributed at random. The number of sources and the field areas are the same as those where the observations were performed. This operation was repeated 50 times so that a statistically sufficient number of background associations were obtained. The distribution of background associations are given in the middle panel of Fig. 5. The background is normalized in such a way that the total number of background associations within a distance range (i.e., angular separation) 100-300 $^{\prime \prime }$ is equal to that of observed associations in the same distance range. The difference between the observed and the background associations, which presumably represents real associations only (plus statistical fluctuation), is given in the bottom panel of Fig. 5. The dotted lines in Fig. 5 show the distribution for the real associations with positional errors of 20 $^{\prime \prime }$ and 35 $^{\prime \prime }$ for C_90 and C_160 sources, respectively. These errors are obtained through the simulations. Judging from a comparison between the top panel (observed associations) and the bottom panel (presumably real associations plus statistical fluctuation), 85% of the observed associations with a distance of 50 $^{\prime \prime }$ or less are real.

Table 7: C_160 (170 $\mu$m) in LHNW.

The cross-association catalogs are given in Tables 8 and 9. All the associations with a distance of 50 $^{\prime \prime }$ or less are regarded as real, and listed in the catalogs.

Table 8: C_160 (170 $\mu$m) sources associated with C_90 (90 $\mu$m) sources in LHEX.

Table 9: C_160 (170 $\mu$m) sources associated with C_90 (90 $\mu$m) sources in LHNW.

Columns 1 and 2 give the names of C_160 and C_90 sources, respectively, followed by right ascension and declination measured at C_160 in Cols. 3 and 4. Columns 5 and 6 show the flux density in mJy along with the errors. The errors for sources fainter than 400 mJy are estimated from the simulations, while those for brighter sources are simply the flux density divided by the SNR. Column 7 gives the flux density ratio of C_160 over C_90. The distance is given in arcsec in Col. 8. In Cols. 9 and 10, SNRs for C_160 and C_90 are given, respectively.

Table 10: Source counts without the corrections.

Figure 6: The C_160 flux plotted versus the ratio of the C_160 flux to the C_90 flux. The upper panel shows error bars, while the error bars are omitted in the bottom panel. The solid lines are predictions for the flux-color relations at various redshifts for M 82, Arp 220, and 10 $\times$ Arp 220. The numbers given just to the right of the crosses are redshifts; z = ..., 0.02, 0.04, 0.06,... for M 82, z = ..., 0.2, 0.4, 0.6, ... for Arp 220, and so on. Flux bias makes the flux brighter and the color redder. The dotted lines represent the flux-color relations without the effect of the flux bias. UGC 06009 is the standard source used for the flux calibration.

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5.3 IR colors

32 C_160 sources are listed in the cross-association catalogs. The diagrams plotting the F(C_160) flux versus the IR color i.e., the flux ratio F(C_160)/F(C_90) are shown in Fig. 6. The upper panel shows error bars, while error bars are omitted from the bottom panel. The errors shown in the upper panel do not include the errors associated with the flux calibration. As discussed above, the flux calibration errors are estimated to be 50% at C_90 and 65% at C_160. In the diagrams the relative positions of all the data points are fixed to each other, but they can move tanslationally up to 65% in the flux axis and 80% in the color axis. The standard source UGC 06009 for the flux calibration is plotted as a filled circle. As discussed in Sect. 3.2, UGC 06009 is likely to be a cirrus dominated Sb galaxy and is expected to have a red F(C_160)/F(C_90) color. Nonetheless, most of our sources are redder than UGC 06009. There are three possible reasons making the color red. These are reddening due to flux bias, K-correction brightening (in particular at C_160 due to reshift), and the presence of very cold dust.

Table 11: Source counts after corrections for the detection rate and flux bias.

Figure 7: The source count versus flux-density relations plotted for ISO far-infrared sources in the Lockman Hole. The top panels show differential counts for C_90 sources on the left and C_160 sources on the right. The data connected by the dashed line are those without the corrections. The vertical error bars shown are statistical errors only i.e., $\sqrt {N}$ where N is the number of sources. The data connected with the solid line are those after the corrections for the detection rate and the flux bias. The horizontal error bar gives the flux uncertainty obtained from the simulations, and the vertical error bar includes the uncertainty in the detection rate derived from the simulations. The bottom panels are the same as the top panels, but for cumulative counts. The regions enclosed by the dot lines are constraints derived from a fluctuation analysis on the present data performed in Paper II.

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Figure 8: The number versus flux-density relations for ISO far-infrared sources in the Lockman Hole are compared with other observations and various models. The top panels show the differential counts for C_90 sources on the left and C_160 sources on the right. The filled circles are from the present data after corrections for the detection rate and the flux bias, the open diamonds are from the ISO C_90 ELAIS survey, the plus signs are from the IRAS 100 $\mu$m counts by Efstathiou et al. (2000), and the open squares are from the FIRBACK survey (Dole et al. 2001). The solid and dashed lines represent the evolution #3 and no-evolution models by Takeuchi et al. (2001), respectively, the dotted lines represent model E by Guiderdoni et al. (1998), and the dash-dot lines represent a model based on the 15 $\mu$m source counts by Chary & Elbaz (2001). The middle panels show the cumulative counts. The filled circles, open diamonds, plus signs, and open diamonds are the same as in the top panels. The "$\times$" symbols are from Linden-Vørnle et al. (2000). The regions enclosed by the dash-dot lines represent constraints from a fluctuation analysis that was performed on the present data in Paper II. The solid, dashed, and dotted lines are the same as in the top panels. The bottom panels are the same as the middle panels, except for the long-dashed and dash-dot-dot lines which represent the models by Rowan-Robinson (2001) and by Franceschini et al. (2001), respectively.

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To examine the first two causes, the flux-color relations for starburst galaxy M 82, ultra-luminous IR galaxy Arp 220, and 10 $\times$ Arp 220 at various redshifts are overlaid in the panels by the solid and dotted lines. These relations are calculated based on the SEDs of M 82 (Efstathiou et al. 2000 and references therein), and the ultra-luminous IR galaxy Arp 220 (Rigopoulou et al. 1996; Klaas et al. 1997). The solid lines include the effect of the flux bias given in the upper panels of Fig. 3 and Table 2, while the dotted lines represent the case without this effect. The flux bias makes the flux brighter and the color redder, and the effect becomes more significant as the flux decreases. The figures imply that a significant fraction of faint sources below 200 mJy at C_160 are starburst galaxies like M 82 and their intrinsic blue colors are reddened by the flux bias. On the other hand, bright sources above 200 mJy with a red color could be dominated by very luminous galaxies such as Arp 220 at moderate redshifts. In addition, there may be a contribution from galaxies having very cold dust (Alton et al. 1998; Haas et al. 1998). The large errors associated with the flux calibration hampers further insight into the flux-color diagrams. Precise measurements of the far-infrared flux for our calibration source UGC 06009 (IRAS F10507+5723) are required from future missions like SIRTF and ASTRO-F.

6 Source counts

The cumulative and differential source counts are tabulated in Table 10. These are "raw'' counts derived from Table 3 without any corrections. To obtain "true'' counts, the corrections for flux bias and the detection rate should be applied to the un-corrected counts. This is done by using the correction factors tabulated in Table 2, and the resultant corrected counts are given in Table 11. The corrected counts, both in differential and cumulative forms, are compared with the un-corrected counts in Fig. 7. The differential counts are plotted in the top panels, and the cumulative counts in the bottom panels. The data connected by solid lines are corrected counts and those dashed lines are un-corrected counts. The zones enclosed by the dotted lines in the bottom panels are constraints derived from the fluctuation analysis performed on the present survey data in Paper II. It is very encouraging to know that the results from the different methods, i.e., the fluctuation analysis in Paper II and the source extraction in this work, are consistent with each other. It should be noted that the corrections become significant in the flux range below 200 mJy at C_90 and below 250 mJy at C_160, underscoring the importance of the simulations.

Our corrected source counts are compared with other observations and models in Fig. 8. The differential counts for C_90 sources are plotted on the left of the top panels and C_160 sources on the right, and the cumulative counts are given in the middle and bottom panels. The filled circles are from the present work, the open diamonds from the ISO C_90 ELAIS survey (Efstathiou et al. 2000), the "+'' (plus) symbols from the IRAS 100 $\mu$m counts reported by Efstathiou et al. (2000), the "$\times$'' (cross) symbols are from Linden-Vørnle et al. (2000), and the open squares are from the FIRBACK C_160 survey (Dole et al. 2001). The regions enclosed by the dash-dot lines are constraints on the cumulative counts that were derived from the fluctuation analysis in Paper II.

As can be seen in the right panels, our C_160 counts are consistent with the results by Dole et al. (2001). The essence of our work is shown in the left panels. It is clear that our C_90 observations are 2-3 times deeper than those previously published and that there is an upturn in the count slope at $\sim$200 mJy for C_90 which has never been recognized with the depth of the previous surveys. To explore the nature of the sources, the source counts are compared with various models. The dash-dot lines in the top panels show the model by Chary & Elbaz (2001), based on the differential number counts at 15 $\mu$m, especially the "knee'' in the count slope at 0.4 mJy (Elbaz et al. 1999). Far-infrared counts are predicted by utilizing the correlations between far-infrared and 15 $\mu$m fluxes. In their model, the SFR density peaks at z = 0.8 with a value 30$\times$ greater than the local value, and gradually decreases towards higher redshift. The solid and dashed lines in the top and middle panels represent the evolution #3 and no-evolution models by Takeuchi et al. (2001), respectively, where they assumed a spike in the star formation history; the SFR density peaks at z = 0.5-0.8 where it is 30$\times$ greater than in the local universe, while at higher redshift it is only 3$\times$ the local value to be consistent with the CIB. The dotted lines illustrate the model of scenario E by Guiderdoni et al. (1998) that yields the maximum counts of far-infrared sources among their models. In scenario E, the SFR density is 3$\times$ the local value at  $z \sim 0.5$ and peaks at $z \sim2.5$ with a density of 10$\times$ the local value. The models by Rowan-Robinson (2001) and Franceschini et al. (2001) are overlaid in the bottom panels by using the long-dashed and dash-dot-dot lines, respectively. In the models by Rowan-Robinson and Franceschini et al., the SFR densities rapidly increase with redshift, from peaks at $z \sim 1$. The densities are $\sim$$6\times$ the local value at z = 0.5, and $\sim$$20\times$ the local value at z = 1.

While the models give a reasonable fit to the C_160 counts, all of them, except for the one by Chary & Elbaz (2001), fail to account for the upturn in the C_90 counts. Unfortunately, Chary & Elbaz (2001) only plotted the prediction down to 200 mJy at 90 $\mu$m. The model by Takeuchi et al. (2001) is also consistent with the C_90 counts down to 200 mJy, but it underestimates the differential counts by a factor of three at 100 mJy. The model by Takeuchi et al. (2001) is characterized by a spike in the star formation history - the luminosity density from  z = 0.5 - 0.8 is $20\times$ the local value. Thus a spike with a three times higher ($60 \times$ the local value) and a $3 \times$ narrower redshift range, for example from  z = 0.5- 0.6, would be worth exploring. If the upturn in the C_90 counts is caused by ultraluminous IR galaxies, their redshifts would be at  $z \sim 0.5$. It is urgent to identify the optical counterparts of the faint C_90 sources because these sources would result from a major event of galaxy evolution at moderate redshift. Unfortunately, our C_90 survey is the only ISO survey that detects sources to a depth of 100 mJy at C_90. Thus, it is not clear whether the C_90 upturn can be seen in all directions or if it is specific to the direction of our fields and we are just looking at the high density part of the large scale structure of the galaxy distribution. In future missions such as SIRTF and ASTRO-F, surveys in similar bands are planned and thus should add further information on such questions. Our survey using a 60 cm diameter aperture telescope is heavily limited by the confusion noise due to the high density of far-infrared emitting galaxies, and the correction for the effect of the source confusion is significant, hampering further insight on the nature of sources detected in our survey. For SIRTF and ASTRO-F, with telescope diameters similar to ISO, the super-resolution technique with a carefully designed sampling density would minimize such confusion. Otherwise, we must wait for the Herschel 3.5 m telescope and the SPICA 3.5 m telescope being planned by ISAS.

7 Summary and conclusions

An ISO deep far-infrared survey was conducted in the C_90 (reference wavelength of 90 $\mu$m) and C_160 (170 $\mu$m) bands in two fields of the Lockman Hole (LHEX and LHNW), covering a combined area of $\sim$0.9 deg². This paper presents the catalogs and source counts. Paper I discussed image processing and reported initial results, while Paper II used a fluctuation analysis of the brightness distribution to derive constraints on the source counts. A summary of the results presented in this paper follows:

• The IRAF DAOPHOT package was used to detect and measure sources.
• Flux calibration was performed using IRAS F10507+5723 (Sb galaxy UGC 06009). The errors associated with this IRAS based calibration are estimated to be 50% at C_90 and 65% at C_160.
• The catalogs were constructed, selecting 223 C_90 sources and 72 C_160 sources with SNR > 3, where the error includes the confusion noise due to the high source density.
• Simulations were performed by adding artificial sources in order to estimate the detection rate, the flux bias due to Eddington/Malmquist bias, the positional accuracy, and the total noise including the confusion noise due to the high source density.
• The distribution of the observed associations between C_90 and C_160 sources indicates that the $1 \sigma$ positional errors are 20 $^{\prime \prime }$ and 35 $^{\prime \prime }$ at C_90 and C_160, respectively, which agrees with the results from the simulations.
• The total noise in our observations is dominated by the confusion noise due to the high source density. The confusion noise is $\sim$20 mJy at C_90 and $\sim$35 mJy at C_160 which is much larger than the instrumental noise which is at the level of a few mJy or less.
• Corrections for the detection rate and the flux bias are significant for sources fainter than 200 mJy at C_90 and 250 mJy at C_160.
• Most of the sources detected both at C_90 and C_160 have a F(C_160)/F(C_90) color redder than the Sb galaxy UGC 06009. Such a red color could result from reddening by the flux bias or K-correction brightening at C_160 due to the effect of redshift. Red sources brighter than 200 mJy at C_160 may be very luminous galaxies like Arp 220 at moderate redshift.
• The source counts are derived by applying the corrections for the detection rate and flux bias. The resultant counts are quite consistent with those derived from the fluctuation analysis performed in Paper II.
• Our C_160 counts are consistent with the results of Dole et al. (2001).
• Our C_90 observations are 2-3 times deeper than those previously published, and there is an upturn in the count slope at around 200 mJy at C_90 which was not previously recognized given the depth of the previous surveys.
• While recent models give a reasonable fit to the C_160 counts, none of them are successful in accounting for the upturn at the C_90 counts. If the upturn was caused by ultraluminous IR galaxies, their redshifts would be at  $z \sim 0.5$, implying a major event of galaxy evolution at moderate redshift.

Acknowledgements

We would like to thank the ISOPHOT team, in particular Carlos Gabriel for many helpful discussion. T. T. Takeuchi has kindly made his models available in differential count form.

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