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Astron. Astrophys. 342, 665-670 (1999)

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2. Sample selection

We based our survey on a sample of sources selected from the IRAS Faint Source Catalog (FSC; Moshir et al. 1992). Since our project involves the optical identification of faint sources, it is important to avoid spurious FSC sources (resulting from e.g., small-scale structure in 60 µm cirrus). We therefore selected a survey area where diffuse 60 µm emission is faint (cf. the IRAS 60 µm maps presented by Rowan-Robinson et al. (1991b)). The area selected consists of the 4 hour R.A. (B1950.0) interval between [FORMULA] and [FORMULA], at Dec. (B1950.0) less than [FORMULA] and Galactic latitude less than [FORMULA]. We also used a 60 µm flux cutoff of [FORMULA], since below this value the FSC becomes rapidly less complete. The region selected contains 3057 60 µm FSC sources brighter than [FORMULA] over an area of [FORMULA]. Stars and nearby galaxies were rejected by excluding all sources detected at 12 µm, leaving 2719 objects in the sample. As a further safeguard against spurious sources, we used the FSC flux quality indicators and cirrus flag, to retain in the sample only those sources with a high-quality detection at 60 µm and no confusion by cirrus. Since the spectral energy distribution (SED) of ULIGs peaks in the rest-frame 60 µm region, ULIGs at [FORMULA] will have flux densities rising monotonically with wavelength in the IRAS bands. Therefore the resulting sample was further reduced by retaining only sources detected at both 60 and 100 µm. However, following Clements et al. (1996), sources with [FORMULA] (where [FORMULA] and [FORMULA] are the 100 and 60 µm flux densities as given in the FSC) were excluded, since such cold sources most likely arise from small-scale structure in Galactic cirrus. Finally, we rejected sources with associations in other catalogs as indicated in the FSC, thus limiting our sample to 313 objects. As shown in Sect. 5, these strict selection criteria make our survey a sparse (approximately 1 in 8) but unbiased survey for infrared galaxies with [FORMULA] over the 1079deg2 survey area.

In order to select from our sample the most distant objects, we define the FIR loudness R by


(see Clements et al. 1996), where [FORMULA] is the 60 µm luminosity, [FORMULA] the luminosity in the B band, B the B-band magnitude, and [FORMULA] the 60 µm flux density in Jy. The bivariate B-60 µm luminosity function has been derived by Saunders et al. (1990), who show that R increases monotonically with [FORMULA]. This dependence accounts for the fact that the high luminosity cutoff of the luminosity function is much sharper in the optical regime than in the infrared. Therefore, [FORMULA] can be combined with the apparent B band magnitude to calculate R and hence obtain a crude estimate of the far-IR luminosity and distance of the object. An approximate B magnitude of the most luminous sources in our sample can be estimated as follows. For the cosmological parameters adopted here, a ULIG with [FORMULA] will have [FORMULA] if it is at [FORMULA]. Using the bivariate luminosity function of Saunders et al. (1990), 95% of these will have [FORMULA], and they will have a mean absolute B magnitude of [FORMULA], or an apparent magnitude [FORMULA] at [FORMULA]. At these magnitudes, sources can be identified on optical Schmidt survey plates. Furthermore, since the IRAS error ellipse for our sample sources is typically [FORMULA], and the extragalactic source density at [FORMULA] is about 1000 per square degree, there is only about a 2% probability of chance superpositions at these magnitudes. Therefore, ULIGs in the FSC can be identified in optical Schmidt surveys and selected based on their [FORMULA]/[FORMULA] ratio. This method has been succesfully used by Clements et al. (1996), to find 91 ULIGs with a median redshift between 0.2 and 0.3, and a maximum redshift of 0.43, by selecting only [FORMULA] objects from FSC sources identified on Schmidt plates. This reasoning suggests that HyLIGs could be found in the same way, but selecting only sources with [FORMULA] (e.g., [FORMULA] has [FORMULA]). However, a HyLIG with [FORMULA] will have [FORMULA] at [FORMULA], and a most likely [FORMULA]. Such sources are below the plate limit of common Schmidt surveys, while with deeper imaging the density of faint sources becomes so high, that reliable identification is no longer possible without additional information. In order to circumvent these problems we have first obtained a sample of candidate distant HyLIGs by selecting those sources for which no reliable identification can be found on optical Schmidt plates, or which have very faint optical counterparts. Optical follow-up (see Sect. 3) was then used to obtain the correct identifications and redshifts for the candidates. We note that the existence of faint but reliable FSC sources without optical counterparts above the typically [FORMULA] limit of Schmidt surveys has been noted by several groups (Wolstencroft et al. 1986; Rowan-Robinson 1991; Sutherland et al. 1991; Clements et al. 1996; Oliver et al. 1996a). Our programme is the first published project to systematically identify these optically faint and potentially very distant sources.

We carried out an identification programme for our FSC sources on the U.K. Schmidt Telescope southern sky survey plates, digitized using the COSMOS plate scanning machine (Yentis et al. 1992). The COSMOS catalog provides [FORMULA] magnitudes to a completeness limit of [FORMULA], positions, major and minor axis lengths, position angles, and for objects with [FORMULA] a classification as star or galaxy, based on an algorithm described by Heydon-Dumbleton et al. (1989). The identifications were performed using the likelihood ratio method (see Sutherland & Saunders (1992) for a detailed discussion). Briefly, the method assigns to every optical source a likelihood ratio


where r is the distance between the FSC and optical positions in a coordinate system where the IRAS error ellipse is a circle of unity radius,


In these expressions, [FORMULA] and [FORMULA] are the major and minor axes of the FSC error ellipse, [FORMULA] and [FORMULA] are the position differences of the optical source with respect to the FSC source projected on these axes, and [FORMULA] is the density of objects brighter than the candidate object.

In calculating L, it is important to take into account possible errors in the star/galaxy classification performed by COSMOS. We noted that a number of FSC sources had counterparts with a very high value of L, which were however classified by COSMOS as stellar, but with axial ratios significantly exceeding unity. During our observing programme described in Sect. 3 we obtained B-band images of 19 of these, covering a range of magnitudes and axial ratios. In these 19 fields, we found that all objects classified as stellar by COSMOS, were in fact galaxies if they had [FORMULA] and axial ratio exceeding 1.27. Some objects with lower axial ratios were also misclassified as stellar. We therefore reclassified all objects with [FORMULA] and axial ratio greater than 1.27 as galaxies. In calculating L for objects classified as galaxies, we computed [FORMULA] taking into account only objects having the same classification. For objects classified as stellar or having [FORMULA] (making them too faint for useful classification), the calculation of [FORMULA] took into account all sources, regardless of classification. This method allows for the possibility of misclassification, while still somewhat favouring objects classified as galaxies.

In Eq. (2) the simplifying assumption is made that the position errors in the FSC are Gaussian. This assumption is approximately correct for small r, but the FSC position error distribution has wings which are stronger than Gaussian ones (Sutherland & Saunders 1992; Clements et al. 1996; Bertin et al. 1997). In order to take these wings into account, all optical sources classified as galaxies were assigned [FORMULA] if they were within [FORMULA] from the FSC position and had [FORMULA].

The identification process consisted of calculating L as described above for every optical object within [FORMULA] of the FSC position. Following Clements et al. (1996), we consider an optical identification reliable for [FORMULA]. Of our sample of 313 FSC sources, 302 had identifications with [FORMULA]. Of the remaining 11, 5 were found to have [FORMULA] objects within [FORMULA] of the FSC positions, which present plausible identifications given the non-Gaussian wings of the FSC position error distribution. The remaining 6 had no plausible optical counterpart with [FORMULA]. The best "identifications" for these FSC sources had [FORMULA]. These 6 sources thus form our sample of candidate HyLIGs. We note that [FORMULA], which has [FORMULA] and is located outside the IRAS FSC error ellipse, would also have been selected by this method, if it was located within our survey area.

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© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999