Astron. Astrophys. 361, 407–414 (2000) ASTRONOMY AND ASTROPHYSICS ISO deep far-infrared survey in the “Lockman Hole” II. Power spectrum analysis: evidence of a strong evolution in number counts?,?? H. Matsuhara1, K. Kawara2, Y. Sato1, Y. Taniguchi3, H. Okuda1, T. Matsumoto1, Y. Sofue2, K. Wakamatsu4, L.L. Cowie5, R.D. Joseph5, and D.B. Sanders5 1 The Institute of Space and Astronautical Science (ISAS), 3-1-1 Yoshinodai, Sagamihara, Kanagawa, 229-8510, Japan 2 Institute of Astronomy, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan 3 Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan 4 Faculty of Engineering, Gifu University, Gifu 501-1193, Japan 5 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Received 10 February 2000 / Accepted 27 June 2000 Abstract. We investigate the characteristics of FIR brightness 1. Introduction fluctuations at 90 µm and 170 µm in the Lockman Hole, In order to understand the history of galaxy formation and evo- which were surveyed with ISOPHOT aboard the Infrared lution, surveys at far-infrared (FIR) and submillimeter wave- Space Observatory (ISO). We first calculated the angular lengths are essentially important, since a large portion of star correlation function of each field and then its Fourier transform formation activity in the universe may be hidden by dust, pro- (the angular Power Spectral Density: PSD) over the spatial − hibiting optical and near-infrared studies due to the enormous frequency range of f =0.05–1 arcmin 1. The PSDs are found − extinction. The recent detection of the far-infrared Cosmic In- to be rather flat at low spatial frequencies (f ≤ 0.1 arcmin 1), frared Background (CIB) radiation by COBE, which appears to slowly decreasing toward higher frequencies. These spectra are have comparable brightness to the total intensity in deep optical unlike the power-law ones seen in the IR cirrus fluctuations, counts from the Hubble deep field (Fixen et al. 1998; Hauser and are well explained by randomly distributed point sources. et al. 1998; Lagache et al. 2000), indicates that the infrared- Furthermore, point-to-point comparison between 90 µm and bright galaxies are responsible for roughly half of the energy 170 µm brightness shows a linear correlation between them, released by nucleosynthesis. Variousdiscrete source surveys are and the slope of the linear fit is much shallower than that also being pursued from mid-infrared to submillimeter wave- expected from the IR cirrus color, and is consistent with the lengths. For example, source counts at 15 µm (Aussel et al. color of galaxies at low or moderate redshift (z<1). We 1998; Altieri et al. 1998; Elbaz et al. 1999), at 170 µm (Kawara conclude that the brightness fluctuations in the Lockman Hole et al. 1998 (paper I); Puget et al. 1999), and at 850 µm (Blain are not caused by the IR cirrus, but are most likely due to et al. 1999) have been reported. Using both CIB and these new faint star-forming galaxies. We also give the constraints on the number count data, modeling of the cosmic star formation his- galaxy number counts down to 35 mJy at 90 µm and 60 mJy tory has been attempted by many authors (Guiderdoni et al. at 170 µm, which indicate the existence of a strong evolution 1998; Dwek et al. 1998; Rowan-Robinson 1999; Tan et al. 1999; down to these fluxes in the counts. The galaxies responsible Ishii et al. 1999). All of them require a strong evolution in the for the fluctuations also significantly contribute to the cosmic star formation rate as we look back to high redshift (more than infrared background radiation. 10 times larger at z ' 1). Although the FIR deep survey is now considered a key ob- serving method for the exploration of the “optically dark side” Key words: galaxies: evolution – galaxies: starburst – cosmol- of the star formation history of galaxies (Guiderdoni et al. 1997), ogy: observations – infrared: ISM: continuum – infrared: galax- the detectivity of 1m-class space FIR telescopes is likely to be ies limited by the noise due to the fluctuation of the IR cirrus (Low et al. 1984), emission from the interstellar dust, even at high Send offprint requests to: [email protected] ? Galactic latitude (Helou & Beichman 1990). Hence a detailed Based on observations with ISO, an ESA project with instruments study of the IR cirrus fluctuations is highly important, especially funded by ESA member states (especially the PI countries: France, for the planning of the deep surveys intended with forthcoming Germany, the Netherlands, and the United Kingdom) and with the IR space telescopes such as ASTRO-F(IRIS) (Murakami 1998) participation of ISAS and NASA. ?? and SIRTF (Fanson et al. 1998). The ISOPHOT data presented in this paper was reduced using PIA, which is a joint development by ESA Astrophysics Division and the The spatial structure of the IR cirrus at 100 µm as measured ISOPHOT consortium. by IRAS was extensively studied by Gautier et al. (1992) and 408 H. Matsuhara et al.: ISO deep far-infrared survey in the “Lockman Hole”. I Abergel et al. (1996). From a Fourier analysis of the brightness As was done in Paper I, the observed fluxes as well as the distribution, Gautier et al. found that the Power Spectral Density brightness of the images are scaled based on the fluxes of the (PSD) of the brightness fluctuation at 100 µm follows a power- brightest source F10507+5723 (UGC 06009) measured with law function of the spatial frequency with an index of about 3 IRAS. Wefound that the flux calibration based on the FCS1 mea- below the spatial frequency corresponding to the IRAS beam surements underestimates the 90 µm flux of the IRAS source by − size (about 0.25 arcmin 1). They also found that the PSD is pro- a factor of 2.6, although it gives the mean brightness of the im- 3 portional to B0 , where B0 is the mean brightness of the IR cirrus. ages consistent with the COBE/DIRBE brightness within 25 The ISOPHOT (Lemke et al. 1996) onboard the ISO (Kessler per cent. The 170 µm flux of the IRAS source is assumed to be et al. 1996) is capable of observing the IR cirrus at wavelengths 1133 mJy as described in Paper I. The flux calibration based longer than 100 µm, with a better spatial resolution than that of on the FCS1 measurements again underestimates the 170 µm IRAS. Herbstmeier et al. (1998) analyzed the spatial character- flux by a factor of 1.5. For the 170 µm flux, we found that the istics of four fields measured by ISOPHOT, and obtained similar discrepancy is mostly due to an underestimate of the effective power-law spectra for relatively bright cirrus regions. Recently solid angle of the ISOPHOT detector. Puget et al. (1999) and Lagache & Puget (2000) have made a power spectrum analysis Lagache & Puget (2000) used an effective solid angle at 170 µm of the 170 µm image of the Marano 1 field, and found a signif- derived from Saturn footprint measurements, which is signifi- − icant excess at f =0.25–0.6 arcmin 1, which they attributed cantly larger than that used in the PIA. Here we assume theoreti- to the fluctuations due to unresolved extra-galactic sources. cal PSFs of a telescope with a 60 cm primary mirror and a 20 cm In this paper we investigate the characteristics of FIR bright- secondary mirror which agree well with those measured during ness fluctuations in the Lockman Hole, a region with a uniquely the ISOPHOT calibration observations (Muller¨ 2000). With this low HI column density (Lockman et al. 1986), and thus minimal assumption, the factors of 2.6 (90 µm) and 1.5 (170 µm) discrep- IR cirrus contribution to the fluctuations. Therefore the fluctua- ancies reduce to factors of 2.0 (90 µm) and 1.2 (170 µm). The tions in the Lockman Hole are likely to be dominated by faint, origin of the residual discrepancies is still unknown. However, distant galaxies (Helou & Beichman 1990; Herbstmeier et al. this is not problematic for the main results and conclusions of 1998) and the fluctuation analysis of FIR images will provide this paper as described in Sects. 4 and 5 as long as the fluxes of unique information on the number counts of infrared galaxies F10507+5723 determined by the IRAS faint source survey are even below the source-confusion limit, thus constraining the correct. parameters characterizing the number count models. Fig. 1 shows the images of LHEX and LHNW used for the This paper is organized as follows: Sect. 2 briefly describes fluctuation analysis, each of which is the largest square area the observations and data processing. Sect. 3 explains the power extracted from the mosaiced map (see Fig. 3 of Paper I) made spectrum analysis and examines the contribution by the IR cirrus up from four sub-field AAP maps. Each image is rebinned into fluctuations and also describes a simulation of the images and 103 × 103 pixels2 (C 90), 53 × 53 pixels2 (C 160 LHEX), or the PSDs. Sect. 4 describes the constraints on the galaxy number 51 × 51 pixels2 (C 160 LHNW). The plate scale is 2300/pixel counts. The nature of the sources responsible for the fluctuations for 90 µm maps, and 4600/pixel for 170 µm maps. is discussed in Sect. 5, and Sect. 6 gives the conclusions. 3. The power spectra and the simulation For each image shown in Fig. 1 the 2-dimensional angular cor- 2. Observation and data processing relation function C(x, y) was calculated from the brightness The FIR survey of the Lockman Hole, which was executed as distribution B(x0,y0): a part of Japan/UH cosmology program using the ISAS guar- C(x, y)=< (B(x ,y ) − B¯)(B(x + x, y + y) − B¯) > (1) anteed time, is described in Taniguchi et al.