The LBDS Hercules sample of millijansky radio griffincharles@example.comGHz: I. Multi-colour photometry



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\#1<span><span> \#1</span></span> \#1<span><span> \#1</span></span> @mathgroup@group @mathgroup@normal@group<span>eur</span><span>m</span><span>n</span> @mathgroup@bold@group<span>eur</span><span>b</span><span>n</span> @mathgroup@group @mathgroup@normal@group<span>msa</span><span>m</span><span>n</span> @mathgroup@bold@group<span>msa</span><span>m</span><span>n</span> ="019 ="016 ="040 ="336 ="33E == == == ==

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galaxies: active — galaxies: photometry — quasars: general — radio continuum: galaxies

Introduction
============

Essentially all low-redshift, powerful ($\rm P_{\rm 1.4~GHz}\ge \rm
P^*_{\rm 1.4~GHz} = 10^{25}$ <span>W Hz$^{-1}$ sr$^{-1}$</span>) radio galaxies are housed in normal giant elliptical galaxies. Thus radio selection has long been regarded as providing an efficient method of identifying high-redshift ellipticals. However, very radio-powerful high-redshift sources have proved virtually useless as probes of galaxy evolution due to the contaminating effects of the active galactic nucleus (AGN) at ultraviolet–infrared wavelengths (McCarthy <span>et al.</span> 1987; Tadhunter <span>et al.</span> 1992; Best, Longair & Röttgering 1996, 1997). Given the success of the Lyman-break technique for selecting high-redshift galaxies on the basis of their optical colours (Steidel <span>et al.</span> 1996, 1999), it might be presumed that radio galaxies are no longer of any importance for probing galaxy evolution. In fact, nothing could be further from the truth, since the identification of high-redshift galaxies at optical wavelengths is by necessity biased towards the bluest, most ultraviolet-active systems – such methods cannot detect old or dust-reddened sources. What is required is an <span>*optically unbiased*</span> selection method, such as radio selection at low flux densities. Unlike their high-power counterparts, faint radio sources have only weak emission lines (Kron, Koo & Windhorst 1985) and show little evidence of an alignment effect (Dunlop & Peacock 1993).

There are a number of radio surveys with millijansky flux density griffincharles@example.com GHz ($S_{1.4} \ga 1$ mJy). This limit is sufficiently <span>*faint*</span> that a large fraction of the sources potentially lie at high redshifts, and yet sufficiently <span>*bright*</span> that objects selected at this flux density are still predominantly radio galaxies rather than low-redshift starbursts (Hopkins <span>et al.</span>2000). Some of the more recent surveys are the FIRST survey (Becker, White & Helfand 1995; White <span>et al.</span> 1997), the NVSS (Condon <span>et al.</span> 1998), the VLA survey of the ELAIS regions (Ciliegi <span>et al.</span> 1999), and the ATCA survey of the Marano Field (Gruppioni <span>et al.</span> 1997). In order to study the evolution of the hosts of these radio sources, it is essential to identify optical/infrared counterparts to a majority of the radio sources. This has not yet been achieved for any of these recent surveys. This paper presents essentially complete optical identifications for a subsample of the Leiden–Berkeley Deep Survey (LBDS; Windhorst, van Heerde & Katgert 1984a), together with infrared $K$-band observations of 85% of the optically identified sources. A companion paper (Waddington <span>et al.</span>2000a; hereafter Paper II) will present the results of the spectroscopic observations and photometric redshift estimates of these sources.

The layout of the paper is as follows. In section 2 the radio observations and previous work using the LBDS are reviewed, and the resolution corrections for the sources are recalculated. In section 3 the optical identifications and photometry of sources in the Hercules sample are presented. The infrared observations are presented in section 4. Finally, section 5 is a discussion of the properties of the sample as a whole and of a number of the individual sources, and compares the $K$-band magnitude distribution to that of brighter radio surveys. Unless otherwise stated, a cosmology with $H_0 =
50$ <span>km s$^{-1}$ Mpc$^{-1}$</span>, $\Omega_0 = 1$ and $\Lambda = 0$ is assumed.

The Leiden–Berkeley Deep Survey
===============================

The LBDS began with a collection of multi-colour prime focus plates that had been acquired with the 4-m Mayall Telescope at Kitt Peak for the purpose of faint galaxy and quasar photometry @Kron80 [@Koo82]. Several high latitude fields were chosen in the selected areas SA28 (referred to as Lynx), SA57, SA68 and an area in Hercules. The fields were selected on purely optical criteria, such as high galactic latitude ($b^{ II} \ga 35\degr$) and minimum H column density, resulting in a random area of sky from the radio perspective. Nine of these fields were then surveyed with the 3-km Westerbork Synthesis Radio Telescope (WSRT) at 21 cm (1.412 GHz) with a 125 beam @Windhorst84a. These observations yielded noise limited maps with $\sigma=0.12$–0.28 mJy in 12 hours, with absolute uncertainties in position of order 04 and in flux of order 3–5%. A total of 471 sources were found, out of which a complete sample of 306 sources was selected. This complete sample is defined by: (1) a peak signal-to-noise $S_{\rm p}/N \ge 5\sigma$, corresponding to $S_{\rm p} \ge 0.6$–1.0 mJy; and (2) a limiting primary beam attenuation of $-7$ dB, which corresponds to a radius of 0464, or an attenuation factor $A(r)\le 5$. With this attenuation radius, the WSRT field then covers the same area as the Mayall 4-m plates. Images were also made at the resolution of the 1.5-km WSRT ($\sigma=0.27$ mJy; Windhorst <span>et al.</span> 1984a) and at 50 cm (0.609 GHz) with the 3-km WSRT ($\sigma=0.48$ mJy; Windhorst 1984). The radio data for the two Hercules fields are summarised in Table \[radiotable\].

<span>13.0cm</span>

  -------------- --------------------------- ------------------ ------------------ ---------------------- ------------ ------------------ ---------------- ------- ----- -------
  Name              3<span>RA (J2000)</span>    $S_{1.4}$ (mJy)    $S_{0.6}$ (mJy)  $\alpha^{1.4}_{0.6}$   ${\cal R}$   $\psi$ $\arcsec$   $\phi$ $\degr$    $W$         
                   3<span>Dec (J2000)</span>   $\Delta S_{1.4}$   $\Delta S_{0.6}$    $\Delta \alpha$                     $\Delta\psi$                                   
                                                                                                                                                                         
  53W002                                  17                 14              14.75          50.1             126.1            1.10               R           0.8    90    1.00
                                          50                 15               30.4         (4.3)             (7.0)           (0.12)                         (0.2)        
  53W004                                  17                 14              36.66          54.5              64.5            0.20               U           1.4    78    1.00
                                          50                 10               26.3         (4.2)             (3.6)           (0.11)                           -          
  53W005                                  17                 14              36.61          7.6               19.0            1.09               E          11.9    56    1.06
                                          50                 28               23.5         (1.3)             (1.9)           (0.23)                           -          
  53W008                                  17                 15               3.87         306.6             597.2            0.79               R           1.9    58    1.00
                                          49                 54               18.6         (26.9)            (31.0)          (0.12)                         (0.5)        
  53W009                                  17                 15               3.55          92.7             128.1            0.38               R          20.0    36    1.00
                                          50                 21               31.4         (6.7)             (7.0)           (0.11)                         (2.1)        
  53W010                                  17                 15               5.48          8.1               15.1            0.73               R          11.0    100   1.07
                                          50                 10               19.1         (0.8)             (1.2)           (0.16)                         (4.5)        
  53W011                                  17                 15               6.29          3.5               2.8             0.28               U           8.8     0    1.64
                                          49                 55               46.6         (0.7)               -               -                              -          
  53W012                                  17                 15               9.14          47.6              67.3            0.41               E          20.0    49    1.00
                                          50                  0               26.0         (3.8)             (3.6)           (0.11)                           -          
  53W013                                  17                 15              14.47          3.7               2.7             0.39               U          10.5    125   1.70
                                          49                 53               55.6         (0.8)               -               -                              -          
  53W014                                  17                 15              18.00          5.3               2.7             0.81               E           2.9    169   1.21
                                          50                  0               31.2         (0.7)               -               -                              -          
  53W015                                  17                 15              23.60         184.6             355.1            0.78               R          16.1    126   1.00
                                          50                 13               13.3         (11.8)            (18.6)          (0.10)                         (1.6)        
  53W019                                  17                 15              46.86          6.8               12.5            0.72               E           3.2    139   1.17
                                          50                 30                7.0         (0.9)             (1.4)           (0.20)                           -          
  53W020                                  17                 15              48.69          6.7               16.6            1.07               R           4.0    45    1.00
                                          50                 25                0.5         (0.6)             (1.4)           (0.14)                         (0.5)        
  53W021                                  17                 16               4.89          4.7               11.6            1.07               E          12.9    25    1.18
                                          50                 20               41.5         (0.4)             (1.0)           (0.14)                           -          
  53W022                                  17                 16               9.26          11.8              16.9            0.43               E          21.8    67    1.26
                                          50                 24               18.0         (1.0)             (1.4)           (0.14)                           -          
  53W023                                  17                 16              10.22         109.9             229.1            0.87               R           9.3    65    1.00
                                          50                  5               34.0         (6.3)             (11.7)          (0.09)                         (1.0)        
  53W024                                  17                 16              11.20          10.3              16.4            0.55               U           1.4    11    1.00
                                          49                 56               48.8         (0.8)             (1.0)           (0.12)                           -          
  53W025                                  17                 16              22.71          1.1               2.7             1.03               U           8.7     0    10.68
                                          50                 16               57.8         (0.2)               -               -                              -          
  53W026                                  17                 16              28.38          21.1              39.2            0.74               R           3.5    138   1.00
                                          49                 47               12.8         (2.0)             (2.1)           (0.13)                         (4.0)        
  53W027                                  17                 16              26.81          8.3               16.2            0.80               E          26.8    127   2.35
                                          50                 23               54.5         (1.1)             (1.8)           (0.20)                           -          
  53W029                                  17                 16              29.26          22.2              18.3            0.23               U           1.4     0    1.00
                                          50                 20               22.1         (1.3)             (1.2)           (0.10)                           -          
  53W030                                  17                 16              43.01          1.4               2.3             0.60               U           1.0     0    3.63
                                          50                  9               40.3         (0.2)               -               -                              -          
  53W031                                  17                 16              46.32         116.5             210.2            0.70               R           4.1    111   1.00
                                          49                 56               44.4         (6.9)             (10.6)          (0.09)                         (0.5)        
  53W032                                  17                 16              46.99          10.5              20.5            0.80               E          22.4    155   1.23
                                          49                 48               51.5         (2.1)             (1.6)           (0.26)                           -          
  53W034                                  17                 16              54.16          10.9              25.3            1.00               E          40.2    38    1.88
                                          50                  0               39.2         (1.4)             (1.8)           (0.17)                           -          
  53W035                                  17                 16              55.76          4.4               3.0             0.44               U           1.3    133   1.46
                                          50                 18               39.5         (0.4)             (0.6)           (0.27)                           -          
  53W036                                  17                 16              56.46          3.2               9.0             1.24               U           6.5     0    1.29
                                          50                 29                2.7         (0.3)             (0.9)           (0.18)                           -          
  53W037                                  17                 16              59.72          6.6               16.3            1.07               E           3.6    66    1.00
                                          50                 19               16.2         (0.4)             (1.2)           (0.12)                           -          
  53W039                                  17                 17               2.00          3.4               6.8             0.82               U          11.4     2    1.57
                                          50                 25               29.0         (0.4)             (1.0)           (0.22)                           -          
  53W041                                  17                 17              19.19          9.4               19.8            0.88               U           1.4    151   1.01
                                          49                 49               18.3         (0.9)             (1.1)           (0.14)                           -          
  53W042                                  17                 17              24.12          6.6               16.1            1.07               R           1.3     0    1.26
                                          49                 48               26.1         (0.8)             (1.0)           (0.17)                         (0.5)        
  -------------- --------------------------- ------------------ ------------------ ---------------------- ------------ ------------------ ---------------- ------- ----- -------

<span>13.0cm</span>

  -------------- --------------------------- ------------------ ------------------ ---------------------- ------------ ------------------ ---------------- ------- ----- ------
  Name              3<span>RA (J2000)</span>    $S_{1.4}$ (mJy)    $S_{0.6}$ (mJy)  $\alpha^{1.4}_{0.6}$   ${\cal R}$   $\psi$ $\arcsec$   $\phi$ $\degr$    $W$         
                   3<span>Dec (J2000)</span>   $\Delta S_{1.4}$   $\Delta S_{0.6}$    $\Delta \alpha$                     $\Delta\psi$                                   
                                                                                                                                                                         
  53W043                                  17                 17              29.71          2.7               9.6             1.52               E           2.7     0    1.65
                                          50                 18               52.8         (0.3)             (0.9)           (0.17)                           -          
  53W044                                  17                 17              36.90          1.8               3.8             0.92               R           2.0     0    3.47
                                          50                  3                4.6         (0.3)             (0.5)           (0.23)                         (0.5)        
  53W045                                  17                 17              41.47          1.5               2.4             0.58               U           1.0    17    5.32
                                          50                 15               44.0         (0.3)               -               -                              -          
  53W046                                  17                 17              53.27          63.1             112.6            0.69               R           3.2    143   1.03
                                          50                  7               51.4         (3.2)             (5.7)           (0.09)                         (0.5)        
  53W047                                  17                 18               7.89          23.9              42.0            0.67               R           1.4    94    1.00
                                          50                 22               44.6         (1.6)             (2.3)           (0.10)                         (0.5)        
  53W048                                  17                 18              11.17          11.5              22.6            0.81               R           1.3    90    1.00
                                          50                 24                1.1         (1.1)             (1.7)           (0.14)                         (0.5)        
  53W049                                  17                 18              11.26          95.1             188.9            0.81               E          30.9    78    1.00
                                          50                 33               13.8         (8.0)             (10.2)          (0.12)                           -          
  53W051                                  17                 18              30.19         141.6             294.3            0.87               R          19.6    30    1.00
                                          49                 48               32.5         (8.3)             (14.8)          (0.09)                         (1.6)        
  53W052                                  17                 18              34.18          8.6               16.1            0.74               R           2.2     9    1.03
                                          49                 58               53.0         (0.6)             (1.0)           (0.10)                         (0.5)        
  53W054A                                 17                 18              47.12          3.9               2.8             0.39               U          12.5    50    1.57
                                          49                 45               49.6         (0.6)             (0.4)           (0.24)                           -          
  53W054B                                 17                 18              49.87          3.0               2.1             0.42               U          12.5    50    1.73
                                          49                 46               12.4         (0.4)             (0.3)           (0.25)                           -          
  53W057                                  17                 19               7.33          2.9               2.2             0.36               R           1.0    122   3.33
                                          49                 45               45.1         (0.6)               -               -                            (0.5)        
  53W058                                  17                 19              19.12          1.4               2.2             0.52               U          11.3    45    6.68
                                          49                 57               47.8         (0.3)               -               -                              -          
  53W059                                  17                 19              20.47          18.7              40.0            0.90               U           3.0    97    1.00
                                          50                  0               19.2         (1.0)             (2.1)           (0.09)                           -          
  53W060                                  17                 19              25.08          9.7               21.1            0.93               U           1.4    66    1.02
                                          49                 28               44.6         (1.4)             (1.3)           (0.19)                           -          
  53W061                                  17                 19              27.37          2.6               2.3             0.15               R          12.3    72    2.35
                                          49                 43               59.7         (0.4)               -               -                            (5.4)        
  53W062                                  17                 19              31.97          1.7               2.2             0.28               U           1.4     0    6.46
                                          49                 59                6.5         (0.3)               -               -                              -          
  53W065                                  17                 19              40.11          5.3               14.5            1.21               U           1.4     0    1.00
                                          49                 57               39.3         (0.4)             (0.9)           (0.11)                           -          
  53W066                                  17                 19              42.97          4.1               8.8             0.91               U           1.4     0    1.12
                                          50                  1                4.5         (0.3)             (0.7)           (0.13)                           -          
  53W067                                  17                 19              51.63          23.2              45.8            0.81               E          12.6    101   1.00
                                          50                 10               55.4         (1.4)             (2.5)           (0.10)                           -          
  53W068                                  17                 19              59.72          3.9               5.1             0.33               U           1.0    31    1.26
                                          49                 36                9.5         (0.5)             (0.6)           (0.20)                           -          
  53W069                                  17                 20               2.49          3.7               7.8             0.87               R           1.6     0    1.18
                                          49                 44               51.1         (0.3)             (0.9)           (0.17)                         (0.5)        
  53W070                                  17                 20               6.18          2.6               2.5             0.04               U           1.4    107   1.96
                                          50                  6                1.7         (0.3)               -               -                              -          
  53W071                                  17                 20              11.34          2.8               9.3             1.43               U           1.4    132   1.89
                                          50                 17               17.1         (0.6)             (0.9)           (0.26)                           -          
  53W072                                  17                 20              29.56          6.6               7.6             0.17               U           1.4    25    1.13
                                          50                 22               37.6         (1.3)             (1.0)           (0.29)                           -          
  53W075                                  17                 20              42.41          96.1             185.3            0.78               U           1.2     0    1.00
                                          49                 43               49.0         (6.0)             (9.6)           (0.10)                           -          
  53W076                                  17                 20              56.09          1.4               3.0             0.89               R           1.0     0    3.99
                                          49                 40                1.1         (0.3)               -               -                            (0.5)        
  53W077                                  17                 21               0.21          7.8               16.1            0.87               R          16.8    82    1.54
                                          49                 48               31.4         (0.8)             (1.6)           (0.17)                         (4.2)        
  53W078                                  17                 21              18.20          2.0               3.1             0.53               R           0.7     0    3.38
                                          50                  3               35.2         (0.4)               -               -                            (0.5)        
  53W079                                  17                 21              22.79          13.3              13.9            0.05               U           1.4    39    1.00
                                          50                 10               31.3         (1.0)             (1.3)           (0.14)                           -          
  53W080                                  17                 21              37.53          27.6              54.2            0.80               E          10.4    35    1.00
                                          49                 55               37.2         (1.8)             (3.0)           (0.10)                         (0.5)        
  -------------- --------------------------- ------------------ ------------------ ---------------------- ------------ ------------------ ---------------- ------- ----- ------

<span>13.0cm</span>

  -------------- --------------------------- ------------------ ------------------ ---------------------- ------------ ------------------ ---------------- ------- ----- ------
  Name              3<span>RA (J2000)</span>    $S_{1.4}$ (mJy)    $S_{0.6}$ (mJy)  $\alpha^{1.4}_{0.6}$   ${\cal R}$   $\psi$ $\arcsec$   $\phi$ $\degr$    $W$         
                   3<span>Dec (J2000)</span>   $\Delta S_{1.4}$   $\Delta S_{0.6}$    $\Delta \alpha$                     $\Delta\psi$                                   
                                                                                                                                                                         
  53W081                                  17                 21              37.90          12.2              24.7            0.84               U           1.4     0    1.00
                                          49                 57               58.0         (0.8)             (1.6)           (0.11)                           -          
  53W082                                  17                 21              37.70          2.0               6.5             1.41               U           1.4     0    2.28
                                          50                  8               27.7         (0.4)             (1.0)           (0.29)                           -          
  53W083                                  17                 21              49.00          5.0               9.0             0.70               U           1.4     0    1.00
                                          50                  2               40.1         (0.5)             (1.1)           (0.19)                           -          
  53W085                                  17                 21              52.54          4.3               12.8            1.29               U           1.4     0    1.04
                                          49                 54               34.5         (0.4)             (1.1)           (0.16)                           -          
  53W086                                  17                 21              57.74          4.9               6.7             0.35               R           1.3    124   1.52
                                          49                 53               34.5         (0.7)             (1.1)           (0.26)                         (0.5)        
  53W087                                  17                 21              59.11          5.8               15.8            1.18               E           2.9    106   1.02
                                          50                  8               43.7         (0.8)             (1.6)           (0.20)                           -          
  53W088                                  17                 21              58.89          14.9              13.7            0.10               U           1.4    22    1.00
                                          50                 11               53.5         (1.4)             (1.2)           (0.15)                           -          
  53W089                                  17                 22               1.17          2.5               7.3             1.29               E           3.2    178   2.12
                                          50                  6               53.2         (0.5)             (1.1)           (0.30)                           -          
  53W090                                  17                 22              23.89          2.1               4.1             0.83               U           9.3     0    2.50
                                          49                 56               44.5         (0.4)               -               -                              -          
  53W091                                  17                 22              32.73          22.1              66.0            1.30               E           4.0     0    1.00
                                          50                  6                1.8         (2.0)             (3.9)           (0.13)                           -          
  -------------- --------------------------- ------------------ ------------------ ---------------------- ------------ ------------------ ---------------- ------- ----- ------

$*$ The source has multiple radio components – the coordinates correspond to the average position of all the components.

$\dagger$ WSRT data only @Windhorst84a – all other sources have VLA positions and morphologies @Oort87 [@Oort88a]. All coordinates have been converted to a J2000 equinox.

Following this selection of the radio sample, the photographic plates were searched for optical counterparts to the radio sources (Windhorst, Kron & Koo 1984b). Large astrographic plates were used to measure the positions of 30–40 secondary standards based on the positions of AGK-3 astrometric standard stars. These secondary standards were then used to calibrate the Mayall prime focus plates for each field in the survey. The radio and optical position errors combine to give an error ellipse around the co-ordinates of the radio source within which one expects to find the optical identification of the source. For the complete sample, 171 of the 306 radio sources were identified in this way, to $U^+$, $J^+ \simeq 23.5$ mag and $F^+$, $N^+ \simeq 21.5$–22.5 mag. The expected number of real identifications was 53% for the whole survey, while for the Hercules fields the identification percentage was somewhat higher at 65% (47 out of 72 sources). As will be discussed in Paper II, there is some evidence for large-scale structure in Hercules, which may explain the higher identification rate in these two fields.

Magnitudes for each of these objects were measured from digital scans of the plates @Kron85. Absolute calibrations were made for most of the fields using photoelectric observations of stars in the fields and transforming the derived $UBV$ zero-points to the photographic $U^+J^+F^+N^+$ system. For the two Hercules fields, however, no photoelectric zero-points were available. They had to be estimated by assuming that the sensitivity of the Hercules plates was the same as for plates (with the same emulsion and filter) taken of another field for which photometric calibrations were available. The resulting errors in the photometry (0.2–0.3 mag) are thus larger for Hercules than the rest of the sample. Redshifts were measured for approximately 60 of the LBDS identifications, of which 16 were in Hercules @Kron85.

One of the major limiting factors in using the LBDS for statistical studies of radio source evolution has been the incomplete optical identification of the sample and the limited number of redshifts available. To obtain complete identification and spectroscopic data on the whole 306-source survey was a major long-term project, due to the size of the survey area (several square degrees), so here attention is focused on a subsample of 72 sources. The two Hercules fields were chosen for this detailed study because they had the largest number of optical identifications already available. In addition, the highest redshift object yet known in the LBDS (53W002 at $z=2.390$) was found in these fields. Optical and infrared observations have been acquired over many years and are presented here for the first time in their entirety. First, some of the relevant highlights of previous work in the LBDS will be reviewed and the radio observations of Hercules will be summarised.

Previous work in the LBDS
-------------------------

Results from the photographic identifications were presented by Kron <span>et al.</span> (1985). About 20% of the identifications were quasars and there were two stars. The galaxies were separated into bright ($F^+<18$) and faint ($18<F^+<21.5$), red ($J^+-F^+>1.2$–2.8) and blue ($J^+-F^+<1.2$–2.8) classes. The red radio galaxies (both bright & faint classes) were identified as giant ellipticals with extended radio emission – "classical" powerful radio galaxies. The bright, blue galaxies were exclusively spirals with unresolved radio structure and a very narrow range in power ${\mathop{{\rm log}_{10}}}P_{1.4} =
22.1 \pm 0.1$. The faint, blue galaxies frequently had irregular optical morphologies (interactions, mergers or compact galaxies), and higher radio/optical flux ratios than normal spirals, suggesting they were a population distinct from the brighter blue sources.

Thuan <span>et al.</span> (1984) observed 48 sources in the LBDS in the near-infrared $JHK$-bands, to $K\simeq 17.5$ mag. They discovered that the optical–infrared colours of the faint radio galaxies were due to their stellar populations, showing no correlation with their radio flux or power. Less than 10% of the red radio galaxies had evidence for non-thermal infrared emission. The colours of the red galaxies were consistent with those of distant ($z\ga 0.2$) non-evolving or passively-evolving luminous giant ellipticals, such as observed in the 3CR survey @Lilly84. The optical/infrared colours of the faint blue radio galaxies were indicative of low-luminosity and/or star-forming galaxies.

High-resolution maps of many of the LBDS sources were griffincharles@example.com GHz with the Very Large Array (VLA), in order to investigate the radio morphologies of weak radio sources @Oort87 [@Oort88a]. The median angular size of the radio samples was found to decrease with decreasing flux density, to $\sim 2$ at 1–10 mJy and $\la
griffincharles@example.com–1.0 mJy. This was attributed to the combined effects of a change in the population and a decrease in the intrinsic size of radio sources at lower (radio) luminosity. Approximately 90% of the red galaxies were resolved by the 14 beam, but half of the blue radio galaxies remained unresolved. There was evidence in the sample for a decrease in intrinsic size with increasing redshift – a factor of 4 from $z=0$ to $z=0.5$. The morphological information and radio positions from this survey have been incorporated into Table \[radiotable\]. Radio observations have also been made of the LBDS at additional frequencies, for example: 4.86 GHz (6 cm) by Donnelly, Partridge & Windhorst (1987), 327 MHz (92 cm) by Oort, Steemers & Windhorst (1988). Deeper VLA observations were also made of the Lynx-2 field, reaching 5-$\sigma$ limiting fluxes of 0.2 griffincharles@example.com GHz @Windhorst85 and $\sim 20$ $\griffincharles@example.com GHz @Windhorst93.

Several sources drawn from the LBDS Hercules sample have also been the subject of individual investigations. The most widely-studied of these is 53W002, which, at $z=2.390$, is the most distant source to date in the whole LBDS @Windhorst91. A total of 67 orbits with the <span>*Hubble Space Telescope (HST)*</span> have now been devoted to 53W002 and its companions. Windhorst, Keel & Pascarelle (1998) used these data to investigate the alignment effect and evolution of this relatively weak high-redshift radio galaxy. Narrow-band images of the field around the galaxy led Pascarelle et al. (1996a,b) to discover a group of emission-line objects at $z\simeq 2.4$ around the radio source, which they suggested were subgalactic clumps that would eventually collapse into a few massive galaxies today.

Spectroscopic observations with the Keck Telescope of two of the reddest sources (53W069 & 53W091) have enabled detailed models of their spectra to be used to estimate their ages. 53W091 was found to have a likely age of 3.5 Gyr at $z=1.552$ @Dunlop96 [@Spinrad97], and a best-fitting age of 4.0 Gyr was determined for 53W069 at $z=1.432$ @Dey97 [@Dunlop99]. However, other authors have suggested that the age of 53W091 is nearer to 1.5–2.0 Gyr @Bruzual97 [@Yi00]. In addition to 53W002, <span>*HST*</span> observations of several other LBDS Hercules sources have been published: 53W044 & 53W046 @Keel93 [@Windhorst94] and 53W069 & 53W091 @Waddington00b.

Sample completeness and source weights
--------------------------------------

Before reviewing the radio properties of the LBDS Hercules sample, it is necessary to discuss the completeness of the sample and the associated weighting of radio sources. Given the selection criteria of the LBDS ($S_{\rm p}/N \ge 5\sigma$, $A(r) \le 5$), the sample will be complete only for certain ranges in total flux density $S_\nu$, angular size $\psi$ and the component flux ratio $f$. Here, we summarize the discussion of the completeness, that is given in full in Windhorst <span>et al.</span> (1984a).

Due to the primary beam attenuation (i.e. the sensitivity of the telescope decreases with radial distance from the pointing centre), the observed signal-to-noise of a given source will depend on where it is on the map. For example, a source that lies just above the 5-$\sigma$ cut at the centre of the map would have fallen below the cut if it happened to lie at the edge, and it would then not be included in the sample. Assuming the primary beam is isotropic, then the correction for this incompleteness is a simple, geometrically-determined weight in the source counts and optical identification statistics. Every radio source is weighted inversely proportional to the area over which it could have been seen, before it dropped below the 5-$\sigma$ threshold.

This primary beam weight is $$W_{\rm pb} = \left( {{0.464}\over{r_{\rm lim}}} \right)^2
\label{wpb}$$ where $r_{\rm lim}$ is the distance from the beam centre (in degrees) at which the source would fall below the 5-$\sigma$ cut: $$r_{\rm lim} = {{1}\over{61.191 \times \nu}} \arccos \left[ \left( 
  {{S_{\rm p}}\over{N}} \right) {{A(r_{\rm obs})}\over{5}} 
  \right]^{-{1\over6}}.
\label{wpb1}$$ Here, $\nu$ is the frequency in GHz, $S_{\rm p}/N$ is the observed peak signal-to-noise, and the attenuation ($A$) at the distance ($r_{\rm obs}$) from the beam centre where the source was observed is given by Windhorst <span>et al.</span> (1984a) as $$A(r_{\rm obs}) = \cos^{-6} \left( 61.191 \times \nu \times r_{\rm obs} \right).
\label{attenuation}$$

A second, more complicated, source of incompleteness is the resolution/population bias – a resolved source of a given sky flux $S_{^{\rm TOT}}^{_{\rm SKY}}$ will drop below the 5-$\sigma$ cut-off more easily than a point source of the same $S_{^{\rm TOT}}^{_{\rm
SKY}}$. Thus the completeness depends on the distribution of source angular sizes and component flux ratios. The determination of, and statistical corrections for, this incompleteness were found by processing Monte Carlo simulations of artificial data using the same algorithms as the real data. They are detailed in Windhorst <span>et al.</span>(1984a), to which one is referred. Higher resolution (arcsecond) VLA images have subsequently shown that the median angular size of radio sources is a function of flux density, decreasing monotonically from $\sim 20$ at 1 Jy to $\sim
2$ at 1 mJy. Windhorst, Mathis & Neuschaefer (1990) showed that this resulted in an overestimate of the original resolution correction, which was based on the lower resolution WSRT data, by a factor of approximately twenty-five percent. The revised source weights were computed following equation (14) of Windhorst <span>et al.</span>(1984a), incorporating the revised angular sizes, as follows: $$W_{\rm res} = 1 + {{58\arcsec}\over{{\rm HPBW}_\alpha}} \exp 
   \left( {{-2.71 (S_{\rm TOT}/N)}\over{(S_{\rm p}/N)_{\rm cut-off}}} \right).
\label{wres}$$ Here, ${\rm HPBW}_\alpha=12\arcsec$ is the half-power beam-width of the observations, $S_{^{\rm TOT}}/N$ is the total observed signal-to-noise of the source and $(S_{\rm p}/N)_{\rm cut-off}=5$ is the selection criterion of the sample. The statistical errors in this correction were shown to be a few percent at the $S_{^{\rm TOT}}\simeq
10\sigma$ level, increasing to about 10% at $S_{^{\rm TOT}}\simeq
5\sigma$ @Windhorst90.

The total weight of each source is then the multiple of the primary beam and resolution weights: $$W = W_{\rm pb} \times W_{\rm res}.
\label{wtotal}$$ These revised weights are given in the last column of Table \[radiotable\], and are plotted in Fig. \[hercweights\]. This figure clearly shows how the weights rise exponentially near the survey flux density limit of 1 mJy. By applying a flux density limit of 2 mJy to the sample, the "completeness" is increased significantly from 56% to 76% – here defining the "completeness" as the ratio of the number of sources actually detected to the total weighted number of sources. There are 9 sources with 1 mJy $\le S_\nu <
2$ mJy that are excluded, with an average weight of 5 (a "completeness" of 20%). Being the faintest objects, they have the largest errors and their effect on the sample is greatly exaggerated by the high weights. Therefore an a posteriori "2-mJy sample" is defined, consisting of those 63 sources with $S_{1.4} \ge 2$ mJy. This will used in preference to the full Hercules sample in some of the statistical studies that follow in this and subsequent papers. It must be emphasized that following application of these weights, the incompleteness of the sample is fully corrected for and so it is, in effect, <span>*complete*</span>.

Radio properties of the Hercules sample
---------------------------------------

The radio data for the Hercules sample are summarized in Table \[radiotable\]. The coordinates are from the VLA 1.4 GHz observations where available @Oort87 [@Oort88a], otherwise the WSRT co-ordinates are used @Windhorst84a. The 1.4 GHz and 0.6 GHz fluxes ($S_{1.4}$ and $S_{0.6}$ respectively) and the resulting spectral indices ($\alpha^{1.4}_{0.6}$, where $S_\nu \propto
\nu^{-\alpha}$) are from the WSRT data @Windhorst84 [@Windhorst84a]. The radio morphological data are taken from Oort et al. (1987) where available, otherwise the WSRT data are shown. Column 6 (${\cal R}$) notes whether the source is unresolved (U), resolved (R) or extended (E). An unresolved source consists of one component that is not distinguishably larger than the WSRT beam; a resolved source consists of one component whose extent is larger than the beam; and a source is classified as extended if it is clearly resolved into two (the classical double) or more components. Column 7 is the largest angular size ($\psi$) of the source in arcseconds, or an upper limit to $\psi$ for unresolved sources. The position angle ($\phi$) of the largest angular size is given in degrees east of north. The weights ($W$) have been recalculated as discussed in the previous section and are given in the final column.

The flux density distribution of all 72 sources is presented as a histogram in Fig. \[hercflux\]. The median flux is 3.0 mJy, and for the 2-mJy sample the median is 6.6 mJy. The dashed line in the figure is the predicted distribution based on a 5<span>$^{\rm th}$</span>-order polynomial fit to the 1.4 GHz differential source counts of Windhorst & Waddington (2000). The fit was based on a sample of 10575 sources drawn from a large number of recent radio surveys. The overall agreement between data and model is indicative that the Hercules sample being used here is a fair representation of the full LBDS and indeed other surveys. We note that there is a small excess of bright sources at $S_\nu > 80$ mJy, although, given the small area of the Hercules field, this may not be significant.

In Fig. \[hercalpha\] the distribution of 1.4–0.6 GHz (21–50 cm) spectral indices is plotted, for both the full Hercules sample and the 2-mJy sample (taking $S_\nu \propto \nu^{-\alpha}$). Not all sources were griffincharles@example.com GHz and thus those have only upper limits to their spectral index (indicated by the hatched histogram). The median spectral index of those sources with detections at both frequencies (i.e. <span>*excluding*</span> upper limits) is $\alpha_{\rm med}\simeq 0.8$ for both samples. Taking into account the 0.6 GHz flux limits gives lower and upper limits to the median spectral index itself: $0.05<\alpha_{\rm med}<0.74$ for the full sample, and $0.74<\alpha_{\rm med}<0.79$ for the 2-mJy sample. Given the relatively few sources without spectral indices in the 2-mJy sample, the true $\alpha_{\rm med}$ is well constrained and we will adopt a value of 0.77 in subsequent work. Nearly half the full Hercules sample is without spectral index information, thus the small lower limit to $\alpha_{\rm med}$ above. However, we do not expect the true value to differ significantly from that of the 2-mJy sample, given that Donnelly <span>et al.</span> (1987) found that the median spectral index in the Lynx-2 area of the LBDS remains at $\alpha_{\rm
med} \simeq 0.75$ down to $S_{1.4}\simeq 0.25$ mJy, when griffincharles@example.com GHz.

Optical identifications and photometry
======================================

Twenty-five of the seventy-two sources in Hercules remained unidentified on the multi-colour Mayall photographic plates. These deep, sky-limited plates reached limiting magnitudes of $U^+ <
23.3$ mag, $J^+ < 23.7$ mag, $F^+ < 22.7$ mag and $N^+ < 21.1$ mag, roughly corresponding to a giant elliptical galaxy at $z\la 1$ @Windhorst84b [@Kron85]. Thus the unidentified sources were potentially the most important for investigating the high-redshift evolution of the faint radio source population. In order to complete the survey, deep CCD images were obtained of the unidentified radio sources.

Observations with the Palomar 200-inch
--------------------------------------

The Hercules field was observed on the 200-inch Hale telescope at Palomar Observatory between 1984 and 1988 (Table \[4shobs\]), using the <span>4-Shooter</span> CCD camera @Gunn87. This camera consists of four simultaneously exposed $800\times800$ pixel Texas Instruments CCDs, covering a nearly contiguous field of $\sim 9\arcmin\times9\arcmin$, at a scale of 0.332 arcsec pixel$^{-1}$. The total field of view is split by a reflecting pyramid into four separate beams which go to one each of the detectors. Poor reflections at the edges of the pyramid results in a strip of $\approx 10$ of sky between the CCDs which is not exposed, but $>$95% of the field is imaged by the detectors. One simultaneous exposure of the four CCDs is defined as a <span>*frame*</span>.

  ------------------------- ---------------
  Dates                     Telescope
                            
  1984 July 31 – August 2   Hale 200-inch
  1985 June 16 – June 18    Hale 200-inch
  1986 July 31 – August 3   Hale 200-inch
  1987 May 27 – May 28      Hale 200-inch
  1987 July 26 – July 29    Hale 200-inch
  1988 June 7 – June 8      Hale 200-inch
  1992 July                 UKIRT 3.8-m
  1993 May 15 – May 17      UKIRT 3.8-m
  1997 June 1 – June 4      UKIRT 3.8-m
  ------------------------- ---------------

  : Summary of observing runs\[4shobs\]\[hercukirt\]

Sixteen separate pointings of the telescope were used in order to observe all of the unidentified radio sources (Fig. \[radiomap\]). Multiple observations were made through Gunn $g$, $r$ and $i$ filters over the six runs. Photometric standard stars were observed each night, normally at the start, middle and end of observing. Many of the nights were not photometric, though in almost all cases at least one photometric frame was obtained in each filter for each source. During the 1984 run, a problem with the <span>4-Shooter</span> dewar resulted in liquid nitrogen coolant being spilled onto the pyramid thus obscuring much of the frame. Although taken in otherwise photometric conditions, these images were only occasionally used in the analysis, in cases where the target had not been observed at a later date and where the radio source was not affected by the spilt liquid nitrogen. The May 1987 run was used for spectroscopy and also an attempt to observe 53W043 by occulting a very bright star in the field that obscured the radio source. The July 1987 run was primarily spectroscopic data but a few images were also obtained.

Data reduction methods
----------------------

The images were processed in a standard manner @Neuschaefer92 [@Neuschaefer95a], but with some important differences. Examination of several bias frames confirmed that there was no two-dimensional structure to the bias (the mean counts in a $10
\times 10$ pixel box varied by $< 0.3$% across the image). For each exposure a first order spline was fitted to the 16-column bias strip and subtracted from across the image. The next step is normally to remove the dark current, however, the <span>4-Shooter</span> CCDs have a very low dark current, which the observers considered to be negligible. Tests on the two best dark frames showed that the counts were comparable to the noise in the bias frames for exposures of about 1000 s (corresponding to a dark current of $<
10^{-3}$ e$^-$ s$^{-1}$ pixel$^{-1}$), thus they were not used in the processing.

Flat-field images of the inside of the telescope dome were made at the beginning and end of each night. These images were the average of eight exposures of 7–10 seconds each for $g$ and 2–4 seconds each for $r$ and $i$. For each observing run, the mean of all the flat-field images was calculated, after scaling and rejection of bad pixels, to give a single flat-field for the whole of the run. The mean value of all the pixels in all four CCDs of the flat-field frame was calculated, and each image divided by this single value. Scaling in this way corrected for the global sensitivity differences between the four CCDs, assuming that they had been uniformly illuminated.

In some of the $g$ and $r$ images and in almost all the $i$ images, large-scale gradients remained across the CCDs, following division by the appropriate flat-field. Neuschaefer & Windhorst (1995) determined that the features in $g$ and $r$ were due to scattered light rather than sensitivity variations in the CCDs. Such global gradients were not important, as variations in the background of each target were removed at the photometry stage. The features in the $i$-band images posed a more serious problem, as they appeared to have two distinct sources. First, there were large-scale gradients across the images of a few percent of the sky background (larger than in $g$ and $r$), similar in appearance to the flat-field pattern itself. Rather than being scattered light, it is suggested that this was due to the different spectral characteristics of the night sky compared with the lamp used to illuminate the flat-fields, which was supported by the observation that the problem was most significant near twilight when the sky was changing most rapidly. This was then an extra <span>*multiplicative*</span> correction. The second problem with the $i$ images was that of fringing due to the strong night sky lines, on a smaller scale than the large gradients. This is an <span>*additive*</span> correction that scales with the brightness of the sky background.

Following Neuschaefer & Windhorst (1995), who actually only considered the fringing, an $i$-band 'superflat' was constructed. Most of the $i$-band data were taken in the June 1988 run, in which there were approximately 50 $i$-band exposures. Observations of the same region of sky were offset by 10–20 and repeated no more than three or four times during the run, thus all the frames were effectively pointing at different parts of the sky. Following infrared imaging techniques, a superflat was constructed from the median of all 50 frames. This produced a high signal-to-noise picture of the sky flat-field, devoid of all sources. The flattened $i$-band images were divided by the superflat in order to remove the large-scale features. The fringing pattern was also removed by this process, although it is really an additive error. If fringing had been the dominant problem, then a scaled version of the superflat should have been subtracted from the images. This was done for several frames and the results compared with those obtained by dividing by the superflat. There was no visual difference between the results of the two methods, nor were they statistically different (both methods increased the sky noise by 0.5–1.0%). For the $i$-band observations in earlier years there were not enough independent exposures to construct a superflat, however using the 1988 superflat often improved the images from these earlier runs.

Finally, the observations from different years were combined to produce an image of each radio source in the $g$, $r$ and $i$ filters. The images were registered using three or four unsaturated stars – most images only required a linear offset, although a 07 rotation was applied to the 1988 data. The images were then stacked, rejecting any remaining cosmic rays or bad pixels, in those cases where there were sufficient exposures to make this possible.

Optical identifications
-----------------------

The astrometry was performed on the $r$-band images in general. Occasionally the radio source was not visible in $r$, in which case either the $g$ or $i$ image was used. The Cambridge APM Guide Star Catalogue @Lewis97 was used to find 10–20 secondary standards in each image of interest. This catalogue is based on digitised scans of the first epoch Palomar Observatory Sky Survey, which has an internal accuracy of 01–02, and is accurate to 05 externally. A six-coefficient linear model was fitted to the <span>4-Shooter</span>images, yielding root-mean-square residuals of $0\farcs5 \pm
0\farcs1$.

The 1.4 GHz radio coordinates from Table \[radiotable\] were converted to pixel coordinates on the <span>4-Shooter</span> images. The errors in the radio positions are typically 05–10. Combining these in quadrature with the optical astrometry errors defines a circle about the predicted coordinates of the source, with a 1-$\sigma$ radius of 07–12, within which $\sim 68$% of the optical counterparts to the radio sources are expected to be found. Strictly, the errors in right ascension and declination are not equal and the search area should be an ellipse @Windhorst84b, however with an ellipticity of typically 0.1–0.2 the assumption of symmetrical errors was adequate for all identifications. Given the faintness of many of the sources, an optical identification was considered to be real only if the source was detected in at least two passbands. This requirement had the potential to exclude very red or very blue objects, but in practice no candidate identification was rejected on this basis.

A total of 47 sources were observed, of which 25 had not been identified on the Mayall photographic plates. Of these sources, new optical identifications for 19 are proposed here, 3 have been published elsewhere (53W002, 53W069, 53W091) and only 3 sources remain unidentified (53W037, 53W043, 53W087). Of the new identifications, 53W054 which was previously classified as a two-component radio source has now been reclassified as two independent objects with solid identifications (53W054A & 53W054B). Two sources have new identifications compared with those in Windhorst <span>et al.</span>(1984b): 53W051 has a close optical counterpart where it was previously associated with a source offset along the radio axis; and 53W022 is identified with a fainter source 5to the north-west of the original candidate. The coordinates of all the identifications are given in Table \[photmaster\] and the <span>4-Shooter</span>images are presented in Fig. \[images\].

<span>15.0cm</span>

  -------------- --------------------------- ------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ -------- ----------
  Name              3<span>RA (J2000)</span>    $z$          $g$     $r$          $i$          $J$          $H$          $K$       References           
                   3<span>Dec (J2000)</span>   Type   $\Delta g$  $\Delta r$   $\Delta i$   $\Delta J$   $\Delta H$   $\Delta K$                        
                                                                                                                                                        
  53W002                                  17     14        14.70    2.390        23.42        23.26        23.13        20.71        20.04      18.87   W91, W98
                                          50     15         29.9      G          (0.12)       (0.09)       (0.10)       (0.16)       (0.17)     (0.12)  
  53W004                                  17     14        36.62      -          24.38        24.05        23.25          -          19.78      19.27   
                                          50     10         25.4      G          (0.22)       (0.16)       (0.11)         -          (0.16)     (0.27)  
  53W005                                  17     14        36.73     0.95        23.34        23.02        21.73          -            -        16.97   II, T84
                                          50     28         23.1      G          (0.30)       (0.30)       (0.30)         -            -        (0.25)  
  53W008                                  17     15         3.90    0.733        20.61        20.31        20.02        17.68          -        16.57   B82, T84
                                          49     54         18.2      Q          (0.06)       (0.04)       (0.05)       (0.28)         -        (0.21)  
  53W009                                  17     15         3.56    1.090        17.57        17.72        18.30        16.42        16.12      15.15   K85, T84
                                          50     21         30.8      Q          (0.30)       (0.30)       (0.30)       (0.10)       (0.11)     (0.11)  
  53W010                                  17     15         5.35     0.48        21.08        19.35        19.33        17.10        16.38      15.47   II, T84
                                          50     10         19.7      G          (0.30)       (0.05)       (0.30)       (0.14)       (0.15)     (0.07)  
  53W011                                  17     15         6.06      -          21.45        20.61        20.29        18.27        17.54      17.10   NK
                                          49     55         45.6      G          (0.06)       (0.04)       (0.05)       (0.15)       (0.12)     (0.15)  
  53W012                                  17     15         9.10    1.328        23.97        23.98        23.41          -          20.75      19.25   II
                                          50      0         25.5      G          (0.11)       (0.11)       (0.10)         -          (0.39)     (0.40)  
  53W013                                  17     15        14.36      -          24.79        24.77        25.12          -           21.1      20.37   
                                          49     53         56.7      G          (0.18)       (0.19)       (0.33)         -            -        (0.51)  
  53W014                                  17     15        17.79      -          23.55        23.16        22.83          -            -        18.46   
                                          50      0         29.7      Q          (0.08)       (0.06)       (0.07)         -            -        (0.16)  
  53W015                                  17     15        23.64    1.129        19.41        18.91        19.37          -            -        16.18   II, NK
                                          50     13         13.1      Q          (0.30)       (0.30)       (0.30)         -            -        (0.16)  
  53W019                                  17     15        46.84    0.542        22.40        21.22        20.91          -            -        16.57   II, NK
                                          50     30          6.3      Q?         (0.30)       (0.06)       (0.30)         -            -        (0.25)  
  53W020                                  17     15        48.63    0.100        17.73        16.86        17.01        15.36        14.60      14.21   K85, T84
                                          50     24         59.7      G          (0.30)       (0.05)       (0.30)       (0.07)       (0.06)     (0.06)  
  53W021                                  17     16         4.75      -            -          22.56        21.51          -          18.38      16.37   T84
                                          50     20         42.2      G            -          (0.30)       (0.30)         -          (0.45)     (0.15)  
  53W022                                  17     16         8.99    0.528        21.84        21.32        20.64          -            -        16.78   II
                                          50     24         17.3      G          (0.30)       (0.06)       (0.30)         -            -        (0.06)  
  53W023                                  17     16        10.32     0.57        22.12        21.00        20.08        17.28        16.71      15.85   II, NK
                                          50      5         33.4      G          (0.30)       (0.30)       (0.30)       (0.17)       (0.14)     (0.08)  
  53W024                                  17     16        11.19    1.961        20.65        21.01        20.64          -            -        16.77   H96, NK
                                          49     56         48.7      Q          (0.30)       (0.30)       (0.30)         -            -        (0.32)  
  53W025                                  17     16        22.65      -          23.10        22.90        21.74          -            -        18.09   NK
                                          50     16         59.1      ?          (0.30)       (0.30)       (0.30)         -            -        (0.60)  
  53W026                                  17     16        28.27     0.55        22.23        21.44        20.70          -            -        16.39   II, T84
                                          49     47         12.2      G          (0.30)       (0.30)       (0.30)         -            -        (0.21)  
  53W027                                  17     16        26.52    0.403        22.56        22.63        21.66          -            -        19.74   II
                                          50     23         53.5      G?         (0.30)       (0.09)       (0.30)         -            -        (0.38)  
  53W029                                  17     16        29.24      -          23.06        22.06        22.09          -            -        16.86   NK
                                          50     20         22.0      Q          (0.30)       (0.30)       (0.30)         -            -        (0.32)  
  53W030                                  17     16        42.98     0.35        21.07        20.04        19.61        16.74        16.06      15.54   II, NK
                                          50      9         40.1      G          (0.30)       (0.30)       (0.30)       (0.16)       (0.11)     (0.11)  
  53W031                                  17     16        46.39    0.628        22.21        21.09        19.95        17.28        16.46      15.84   K85, NK
                                          49     56         43.6      G          (0.30)       (0.30)       (0.30)       (0.08)       (0.07)     (0.04)  
  53W032                                  17     16        47.15     0.37        19.51        18.48        18.17        16.60        15.87      15.21   II, NK
                                          49     48         46.9      G          (0.07)       (0.07)       (0.04)       (0.12)       (0.10)     (0.14)  
  53W034                                  17     16        54.45    0.281        22.38        22.18        22.87          -            -        19.50   II
                                          50      0         34.4      G          (0.30)       (0.30)       (0.30)         -            -        (0.25)  
  53W035                                  17     16        55.75      -          23.74        23.66        23.39          -          20.03      19.04   
                                          50     18         38.8      ?          (0.10)       (0.09)       (0.13)         -          (0.20)     (0.25)  
  53W036                                  17     16        56.56      -          21.69        21.86        21.76          -            -        19.05   
                                          50     29          3.4      Q?         (0.30)       (0.30)       (0.30)         -            -        (0.20)  
  53W037                                                              -            -           25.0          -            -            -         20.7   
                                                                      -            -            -            -            -            -          -     
  53W039                                  17     17         1.60    0.402        20.94        19.26        18.75        16.54        15.71      15.01   K85, NK
                                          50     25         28.8      G          (0.09)       (0.05)       (0.03)       (0.11)       (0.10)     (0.06)  
  53W041                                  17     17        19.02      -          26.31        25.07        26.26          -            -         20.8   
                                          49     49         17.6      ?          (0.43)       (0.23)       (0.91)         -            -          -     
  53W042                                  17     17        24.07      -          24.80        25.68        25.11          -            -         20.8   
                                          49     48         22.9      ?          (0.17)       (0.47)       (0.37)         -            -          -     
  -------------- --------------------------- ------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ -------- ----------

<span>15.0cm</span>

  -------------- --------------------------- ------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ -------- -------------
  Name              3<span>RA (J2000)</span>    $z$          $g$     $r$          $i$          $J$          $H$          $K$       References           
                   3<span>Dec (J2000)</span>   Type   $\Delta g$  $\Delta r$   $\Delta i$   $\Delta J$   $\Delta H$   $\Delta K$                        
                                                                                                                                                        
  53W043                                                              -            -           23.0          -            -            -          -     
                                                                      -            -            -            -            -            -          -     
  53W044                                  17     17        36.88    0.311        19.93        18.99        18.57        16.40        15.28      14.63   W94
                                          50      3          4.6      G          (0.30)       (0.30)       (0.30)       (0.19)       (0.07)     (0.08)  
  53W045                                  17     17        41.51     0.30        20.49        19.29        18.79        16.63        15.92      15.08   II, NK
                                          50     15         42.8      G          (0.06)       (0.03)       (0.03)       (0.12)       (0.11)     (0.11)  
  53W046                                  17     17        53.37    0.528        21.39        20.34        19.69        17.27        16.46      15.94   W94
                                          50      7         51.8      G          (0.30)       (0.30)       (0.30)       (0.10)       (0.08)     (0.12)  
  53W047                                  17     18         7.89    0.534        21.87        20.73        20.24        17.31        16.56      15.76   II, NK
                                          50     22         44.9      G          (0.30)       (0.30)       (0.30)       (0.12)       (0.10)     (0.12)  
  53W048                                  17     18        11.18    0.676        22.38        21.01        20.16        17.56        16.55      15.68   II, NK
                                          50     24          1.4      G          (0.30)       (0.30)       (0.30)       (0.12)       (0.07)     (0.06)  
  53W049                                  17     18        11.29     0.23        21.86        20.70        19.99        17.85        16.75      16.15   II, NK
                                          50     33         12.7      G          (0.09)       (0.03)       (0.03)       (0.15)       (0.12)     (0.15)  
  53W051                                  17     18        30.28      -          24.55        22.84        21.87          -            -        17.23   
                                          49     48         30.2      G?         (0.11)       (0.05)       (0.04)         -            -        (0.07)  
  53W052                                  17     18        34.14     0.46        22.37        21.20        20.63          -          17.85      16.90   II, T84
                                          49     58         50.9      G          (0.30)       (0.30)       (0.30)         -          (0.32)     (0.16)  
  53W054A                                 17     18        47.32      -          24.52        23.93        23.30          -          19.52      18.34   
                                          49     45         48.4      G          (0.26)       (0.16)       (0.13)         -          (0.14)     (0.13)  
  53W054B                                 17     18        50.10      -          24.26        24.04        23.59          -          20.79       19.8   
                                          49     46         14.5      ?          (0.18)       (0.15)       (0.17)         -          (0.34)       -     
  53W057                                  17     19         9.87      -          24.75        25.29        26.14          -           21.9      21.22   
                                          48     45         44.5      G          (0.15)       (0.21)       (0.59)         -            -        (0.51)  
  53W058                                  17     19        18.71    0.034        15.92        15.42        15.05          -            -        11.92   K85
                                          49     57         41.0      G          (0.09)       (0.05)       (0.04)         -            -        (0.01)  
  53W059                                  17     19        20.33      -          24.53        24.59        23.92          -          20.09      19.20   
                                          50      0         20.3      G?         (0.17)       (0.18)       (0.18)         -          (0.20)     (0.19)  
  53W060                                  17     19        25.31      -          26.52        25.52        25.76          -            -         20.8   
                                          49     28         45.8      G          (0.53)       (0.26)       (0.45)         -            -          -     
  53W061                                  17     19        27.40      -          21.95        21.26        20.81          -            -        17.39   T84
                                          49     43         59.6      Q?         (0.30)       (0.30)       (0.30)         -            -        (0.26)  
  53W062                                  17     19        31.92     0.61        22.54        21.25        20.54          -          17.13      17.09   II, NK, T84
                                          49     59          6.2      G          (0.11)       (0.06)       (0.05)         -          (0.20)     (0.25)  
  53W065                                  17     19        39.78    1.185        23.26        22.92        22.52          -            -        18.80   II
                                          49     57         39.3      G          (0.08)       (0.06)       (0.05)         -            -        (0.21)  
  53W066                                  17     19        42.95      -          24.59        24.60        24.60          -          21.34       19.3   
                                          50      1          3.1      G?         (0.18)       (0.20)       (0.32)         -          (0.32)       -     
  53W067                                  17     19        51.56    0.759        24.06        21.76        21.70          -          18.38      18.95   II
                                          50     10         55.6      G          (0.13)       (0.07)       (0.05)         -          (0.06)     (0.20)  
  53W068                                  17     19        59.66      -          22.66        22.54        22.65          -            -        19.36   
                                          49     36          9.3      ?          (0.08)       (0.05)       (0.05)         -            -        (0.28)  
  53W069                                  17     20         2.52    1.432        26.49        25.04        24.35        20.25        19.75      18.53   D97, D99
                                          49     44         51.0      G          (0.60)       (0.22)       (0.14)       (0.14)       (0.18)     (0.11)  
  53W070                                  17     20         6.07      -          24.55        22.34        21.81          -            -        16.89   
                                          50      6          1.7      G          (0.20)       (0.10)       (0.05)         -            -        (0.07)  
  53W071                                  17     20        11.42    0.287        21.46        21.09        20.94          -          18.83        -     K85, NK
                                          50     17         17.4      G          (0.30)       (0.30)       (0.30)         -          (0.26)       -     
  53W072                                  17     20        29.54    0.019        15.71        15.27        15.04          -            -          -     K85
                                          50     22         38.0      G          (0.30)       (0.30)       (0.30)         -            -          -     
  53W075                                  17     20        42.34    2.150        22.16        21.35        20.73          -          18.14      16.74   K85, T84
                                          49     43         48.7      Q          (0.08)       (0.05)       (0.04)         -          (0.37)     (0.23)  
  53W076                                  17     20        55.96    0.390        20.85        19.47        19.03        16.77        16.13      15.56   K85, T84
                                          49     40          2.8      G          (0.30)       (0.30)       (0.30)       (0.11)       (0.11)     (0.10)  
  53W077                                  17     21         1.34     0.80        22.92        21.47        20.68          -          17.86        -     II, NK
                                          49     48         34.4      G          (0.30)       (0.30)       (0.30)         -          (0.20)       -     
  53W078                                  17     21        18.22     0.27        20.00        19.18        18.59        16.25        15.55      14.91   II, T84
                                          50      3         35.3      G          (0.30)       (0.30)       (0.30)       (0.09)       (0.11)     (0.06)  
  53W079                                  17     21        22.84    0.548        21.79        20.23        19.67        17.56        16.67      15.86   K85, NK
                                          50     10         30.2      G          (0.07)       (0.04)       (0.03)       (0.09)       (0.09)     (0.09)  
  54W080                                  17     21        37.50    0.546        18.29        18.41        18.09        16.72        15.84      15.02   K85, T84
                                          49     55         36.6      G          (0.12)       (0.10)       (0.04)       (0.06)       (0.10)     (0.09)  
  -------------- --------------------------- ------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ -------- -------------

<span>15.0cm</span>

  -------------- --------------------------- ------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ -------- -------------
  Name              3<span>RA (J2000)</span>    $z$          $g$     $r$          $i$          $J$          $H$          $K$       References           
                   3<span>Dec (J2000)</span>   Type   $\Delta g$  $\Delta r$   $\Delta i$   $\Delta J$   $\Delta H$   $\Delta K$                        
                                                                                                                                                        
  53W081                                  17     21        37.87    2.060        24.84        24.64        24.57          -            -        18.91   S97a
                                          49     57         57.1      ?          (0.20)       (0.23)       (0.29)         -            -        (0.21)  
  53W082                                  17     21        37.62      -          26.92        25.79        25.43          -          21.73      21.36   
                                          50      8         27.4      G          (0.60)       (0.38)       (0.31)         -          (0.34)     (0.68)  
  53W083                                  17     21        48.92    0.628        22.60        22.20        21.01          -            -        17.34   II
                                          50      2         40.1      G          (0.30)       (0.30)       (0.30)         -            -        (0.10)  
  53W085                                  17     21        52.54     1.35        22.57        22.59        22.24        18.40          -        16.87   II, NK, T84
                                          49     54         33.7      Q          (0.11)       (0.11)       (0.05)       (0.32)         -        (0.16)  
  53W086                                  17     21        57.67     0.40        23.91        22.36        21.25          -          17.29      16.41   II, T84
                                          49     53         33.7      G          (0.13)       (0.11)       (0.04)         -          (0.21)     (0.10)  
  53W087                                                              -            -           25.0          -            -            -         19.3   
                                                                      -            -            -            -            -            -          -     
  53W088                                  17     21        58.92    1.773        24.46        24.30        24.03          -            -        19.83   S97a
                                          50     11         52.4      G?         (0.12)       (0.13)       (0.13)         -            -        (0.29)  
  53W089                                  17     22         1.02    0.635        25.09        24.70        24.41          -            -         19.2   II
                                          50      6         51.7      ?          (0.21)       (0.19)       (0.33)         -            -          -     
  53W090                                  17     22        24.04    0.094        17.68        17.13        16.61          -            -        13.84   K85
                                          49     56         42.7      G          (0.12)       (0.11)       (0.04)         -            -        (0.02)  
  53W091                                  17     22        32.71    1.552        25.99        25.88        24.37         20.5         19.5      18.67   D96, S97b
                                          50      6          1.4      G          (0.49)       (0.48)       (0.19)       (0.1)        (0.1)      (0.13)  
  -------------- --------------------------- ------ ------------ ------------ ------------ ------------ ------------ ------------ ------------ -------- -------------

$*$ The object classification is based on the optical appearance, and spectral features when available. The sources are divided into "galaxies" and "quasars" where: G (G?) is a clearly (most likely) extended source; Q (Q?) is a (most likely) stellar object; and sources denoted as ? are too faint to classify.

$\dagger$ Coordinates are taken from Windhorst <span>et al.</span>(1984b) and converted to a J2000 equinox. Photometry is taken from Kron <span>et al.</span> (1985) and transformed from $J^+F^+N^+$ data using equations \[gritrans\]–\[gritrans1\].

$\ddagger$ $g$ & $i$ photometry is taken from Kron <span>et al.</span>(1985) and transformed from $J^+F^+N^+$ data using equations \[gritrans\]–\[gritrans1\].

$\P$ Spectroscopy and infrared photometry references: Butcher, private communication (1982; B82); Dey (1997; D97); Dunlop <span>et al.</span> (1996; D96); Dunlop (1999; D99); Hall <span>et al.</span> (1996; H96); Kron <span>et al.</span> (1985; K85); G. Neugebauer, P. Katgert <span>et al.</span>, private communications (NK); Spinrad, private communication (1997; S97a); Spinrad <span>et al.</span> (1997; S97b); Thuan <span>et al.</span>(1984; T84); Waddington (1998; W98); Waddington <span>et al.</span> (2000a; paper II); Windhorst <span>et al.</span> (1991; W91); Windhorst <span>et al.</span>(1994; W94).

Three radio sources were not identified either on the photographic plates or in the <span>4-Shooter</span> CCD observations, and a few comments can be made concerning their nature. The first of these, 53W043, is located 5 from a $R=14$ mag star, and lies within the wings of the star's point spread function (PSF) in the <span>4-Shooter</span> data. The PSF of the photographic plates is smaller than that of the CCDs, giving an upper limit to the brightness of the optical counterpart of $F^+ > 23$ mag. Counterparts to 53W037 and 53W087 were not identified on good <span>4-Shooter</span>images, even after both smoothing the images and stacking the $g$, $r$ & $i$ images together. For both sources, an upper limit of $r >
25$ mag was calculated. Neither source was detected in the infrared (see §4 below), with limits of $K>20.7$ mag for 53W037 and $K>19.3$ mag for 53W087. Both these objects are extended, steep-spectrum radio sources, suggesting that they may be classical radio galaxies. If so, then the faintness of their host galaxies suggests that they are either at very high redshift, or are obscured by dust, or are dusty high-redshift sources @Waddington99.

<span>15cm</span>

<span>15cm</span>

<span>15cm</span>

<span>15cm</span>

<span>15cm</span>

<span>15cm</span>

<span>15cm</span>

Photometry
----------

The photometric calibration of the <span>4-Shooter</span> images was done in two stages, due to the non-photometric conditions of a significant number of the observing nights. For most of the sources, at least one exposure had been taken on a photometric night which could therefore be calibrated accurately. This calibrated exposure was then used to bootstrap a zero-point for the non-photometric mosaic of all the exposures.

The apparent magnitude of a source ($m$) is defined by $$m = m_{\rm inst} + k \cdot \overline{{\rm sec}z} + C \cdot (g-r) +
  z_{\rm p}
\label{mageqn1}$$ where $m_{\rm inst}$ is the instrumental magnitude, $k$ is the extinction coefficient for a given filter, $\overline{{\rm sec}z}$ is the time-averaged airmass, $C$ is the colour coefficient for the filter, $(g-r)$ is the instrumental colour of the source, and $z_{\rm
p}$ is the zero-point. Higher order terms are not included due to the limited number of standard star observations available.

For each night of the observing runs, there were between three and eight observations of Gunn standard stars made. These were taken throughout the night at different airmasses and in all three filters. To avoid saturation, the standard stars were observed with the telescope out of focus. Instrumental magnitudes in a 30–40 circular aperture were measured for each star, on every night that the log sheets recorded as being photometric. True apparent magnitudes ($m_0$) were taken from a list of both published and unpublished standards available at the telescope @Thuan76 [@Wade79; @Kent85]. Equation \[mageqn1\] was then fitted to the data ($m_0-m_{\rm inst}$, ${\rm sec}z$, $g-r$) using a linear least squares method. This gave best-fitting values for $k$, $z_p$ and $C$ for each night. The colour coefficients are not expected to change from night to night and the fitted values were indeed consistent, thus a weighted average over all the nights in a run was used. A second least squares fit was then performed with $C$ fixed at its average value, and values for $k$ and $z_{\rm p}$ were found for each photometric night. For the non-photometric mosaics, the extinction and colour coefficients were taken as the mean of the values over all the runs (Table \[kccoeffs\]). Note that these values are consistent with those assumed by Neuschaefer & Windhorst (1995), who used the same instrument and telescope, over a similar period of time (1984–1988).

For each photometric image containing a radio source, the automated image detection program <span>pisa</span> @Draper96 was used to calibrate 20–80 sources in the image. The search parameters were chosen such that a source was defined as having at least eight contiguous pixels with values greater than 5-$\sigma$ above the background. Such conservative parameters ensured that only good signal-to-noise sources were detected in the relatively short photometric exposure. The corresponding non-photometric, deep mosaic was then analysed in the same way with <span>pisa</span>. The mean difference in magnitude between each source, as observed in the mosaic and in the calibrated exposure, then allowed the zero-point of the non-photometric mosaic to be bootstrapped from the calibrated photometric image.

  -------- ---------------- ----------------
   Filter   $\overline{k}$   $\overline{C}$
                            
    $g$     $-0.28\pm0.05$   $0.16\pm0.02$
    $r$     $-0.14\pm0.03$   $0.10\pm0.01$
    $i$     $-0.11\pm0.02$   $0.05\pm0.01$
  -------- ---------------- ----------------

  : Mean extinction & colour coefficients<span data-label="kccoeffs"></span>

For five sources (53W010, 53W019, 53W020, 53W022, 53W027), only $r$-band observations from the 1984 run were available so no colour correction could be applied to them. In addition, only two standard star observations were available for each of the two nights, which was inadequate to determine both the extinction and zero-points. Thus, the mean extinction coefficient from Table \[kccoeffs\] was adopted, and the zero-point calculated from the observed magnitudes of the standards. For five other sources (53W080, 53W081, 53W085, 53W086, 53W090), no photometric calibrations were available for the $g$ and $r$ images. The zero-points adopted for these mosaics were taken as the mean of the zero-points for all the other observations in the sample. This is reflected in the slightly larger errors for these sources in Table \[photmaster\].

The sky background subtraction for each source was done using a method based upon the image reduction package <span>cassandra</span> by D. P. Schneider, adapted to run as an <span>iraf</span> task using the <span>apphot</span> package for the numerical work. A rectangular box (typically 10–20 on a side) surrounding the source, and excluding any other objects, was cut out of the mosaic image. A plane was fitted to this box, excluding from the fit a circle centered on the source, and the sky was subtracted from the image. Photometry was performed using a circular aperture of 40, 75 or 100 diameter (depending on the extent of the source), with the sky statistics determined over the remainder of the box. This enabled a large asymmetric sky aperture to be used, which is not possible with the basic <span>apphot</span>, in addition to providing a better measure of the sky background than is possible with an annulus around the object.

During testing of this method an error was found in the way that <span>apphot</span> calculates magnitude errors for faint objects. <span>apphot</span> makes the approximation $\ln (1+\Delta) \approx \Delta$ which for faint sources overestimates the error by as much as 0.1–0.2 magnitudes. This was corrected by including the second, and for good measure the third, order terms in the expansion: $\ln (1+\Delta)
\approx \Delta - \Delta^2 / 2 + {\Delta^3 / 3}$. The apparent magnitude was then calculated from equation \[mageqn1\] using the coefficients in Table \[kccoeffs\] and the appropriate zero-points. The results are presented in Table \[photmaster\]. The errors quoted are the quadratic sum of the instrumental magnitude errors from <span>apphot</span> (shot-noise in the object aperture, sky-noise), and the errors in the determination of $k$, $C$ and $z_{\rm p}$.

In order to compare those radio sources with photographic magnitudes, $J^+F^+N^+$, to those sources with <span>4-Shooter</span> Gunn magnitudes, $gri$, it was necessary to convert one photometric system to another @Fukugita95. Windhorst <span>et al.</span> (1991)derived transformations from the Gunn system to the photographic system, and inverting these gives the required equations: $$\begin{aligned}
\label{gritrans}
g & = & 0.69{J^+} + 0.31{F^+} - 0.19\\
r & = & 1.14{F^+} - 0.14{J^+} + 0.34\\
i & = & {N^+} + 0.75
\label{gritrans1}\end{aligned}$$ For those sources without <span>4-Shooter</span> observations, the optical magnitudes in Table \[photmaster\] are photographic magnitudes from Kron <span>et al.</span>(1985) transformed to the Gunn system using these equations. An error of 0.3 magnitudes is assigned to each of these values, corresponding to the quadratic sum of the error in the transformations (0.1 mag) and the error in the photographic magnitudes (0.2–0.3 mag). For the eighteen sources with both photographic and <span>4-Shooter</span> Gunn photometry, the transformed photographic magnitudes are compared with the <span>4-Shooter</span> data in Fig. \[gritranscomp\]. It can be seen that the transformations are in good agreement with the data for $gri \la 22$–23 mag; fainter than this, the $J^+F^+N^+$ magnitudes are close to the detection limits of the photographic plates and are less reliable.

Infrared photometry
===================

Infrared data are crucial to understanding high-redshift galaxies. Beyond $z \sim 1$, optical observations sample the restframe ultraviolet emission of galaxies and the restframe optical emission has shifted into the near-infrared. Thus in order to properly compare sources at high-$z$ with those at low-$z$, the analysis must move to longer wavelengths. The $K$-band has long been recognized as a valuable window through which to investigate radio galaxies, and so we sought to obtain $K$ magnitudes for the complete Hercules sample.

Observations with the UK Infrared Telescope
-------------------------------------------

Approximately half the sample has been observed during three major observing runs at the 3.8-m UK Infrared Telescope, Mauna Kea, Hawaii (Table \[hercukirt\]). The first two runs (1992 & 1993) used the infrared camera IRCAM, a 62$\times$58-pixel InSb array with a scale of 0.62 arcsec pixel$^{-1}$. All these observations were done in the $K$-band. The 1997 run used the upgraded camera IRCAM3, which had 256$\times$256 pixels with a scale of 0.286 arcsec pixel$^{-1}$. Deep $K$ images were obtained for sources which had not previously been detected, together with $H$-band observations of several galaxies for which $H$ was considered important for constraining the redshift. Additional observations of some sources were made during associated projects and via the UKIRT Service Observing programme.

A standard jittering procedure was used to obtain a median-filtered sky flat-field simultaneously with the data. Nine 3-minute exposures were made, each offset by 8 (1992 & 1993) or 15 (1997) from the first position, resulting in a central area around the radio source with a maximal exposure time of 27 minutes, surrounded by a border of low signal-to-noise data. This was repeated two or three times for the faintest sources. Observations of faint standard stars were taken to calibrate the data.

Data reduction and calibration
------------------------------

For all three UKIRT runs, the image processing stage in the reduction was performed at the telescope by the observers. This consisted of the following steps: (i) a dark frame observed prior to the nine-exposure sequence was subtracted from each image; (ii) a normalised flat-field was constructed by taking the median of the nine exposures; (iii) each exposure was then divided by the flat-field; (iv) an extinction correction was applied; (v) the images were registered and finally combined into a mosaic after rejection of known bad pixels.

The standard star observations were reduced in the same manner, and the instrumental magnitude (corrected for extinction) calculated. Comparison with the known apparent magnitude then yielded a zero-point. Standards were observed regularly and the zero-points were found to vary by $<0.05$ mag throughout each photometric night. Colour coefficients are small in the infrared and were not determined.

Photometry was performed on each of the mosaics using the same method as for the optical data (§3.5), with the exception of the 1992 observations for which the sky background was determined from the mean of $\simeq 5$ circular apertures placed randomly around the source. The results are presented in Table \[photmaster\] and Fig. \[images\]. In addition to the 36 new observations described here, Table \[photmaster\] contains infrared data published by Thuan <span>et al.</span> (1984) for sixteen sources, unpublished data from G. Neugebauer, P. Katgert <span>et al.</span> (private communications) for a further twenty sources, and data on five other galaxies referenced in the notes to the table.

Discussion of the multi-colour photometry
=========================================

The results of the optical and infrared photometry are discussed in this section, and compared with both earlier results from the LBDS and with results from other radio surveys. Discussion of redshift-dependent properties will be presented in Paper II, following analysis of the new spectroscopic data.

Notes on individual sources
---------------------------

Before investigating the photometric properties of the sample as a whole, the optical, infrared & radio observations of some individual sources are worth noting.

53W002 – This $z=2.390$ radio galaxy has been the subject of much study (see §2.1). Comparing the optical and infrared colours recorded in Windhorst <span>et al.</span> (1991) with those here, shows that they are fully consistent within the errors, although there is some discrepancy between the optical magnitudes. This may be explained by noting that Windhorst et al. use "total" magnitudes which are brighter than the 4 aperture magnitudes in Table \[photmaster\] – indeed, application of the same method to these data produces consistent results. It is important to note that the <span>*colours*</span> of faint sources are not significantly affected by aperture size so long as the aperture is larger than the seeing disk, which it is in all cases here.

53W011 & 53W013 – There was originally some concern that these two sources may have been confused with the grating rings in the WSRT observations, however both have optical counterparts and so are retained in the sample.

53W014 – Optical counterpart griffincharles@example.com-$\sigma$ from the radio position. A second object, 5 to the north-east, at 3.7-$\sigma$, may also be a possible identification.

53W022 – New identification compared with Windhorst <span>et al.</span>(1984b). This object looks as if it could be physically associated with the brighter old identification in the $r$-band. At $K$, the two objects are distinct and very similar in appearance.

53W032 – A $z=0.370$ galaxy at the centroid of a double radio source. The <span>4-Shooter</span> images reveal extended emission to the north-east, reminiscent of a tidal tail. Note also that component A is coincident with an $r\simeq 20.3$ mag source, although component B does not have an optical counterpart.

53W035 & 53W089 – These sources each appeared on two independent mosaics, enabling the repeatability of the photometry to be confirmed.

53W054A & 53W054B – Originally classified as the lobes of a classical double radio source @Windhorst84a, they are now considered to be two distinct sources. Both have solid identifications in the optical, and 53W054A is also identified in the infrared.

53W057 – $K$ is a marginal (2-$\sigma$) detection at the north-east end of the elongated source in $g$. The brighter source at 6 to the west is also a possible identification, at 2-$\sigma$ from the radio position.

53W058 – The radio source is in the arm of a bright spiral galaxy at $z=0.034$. The coordinates given in Table \[photmaster\] are for the centre of the galaxy; the position of the radio emission is marked in Fig. \[images\].

53W067 – The optical counterpart is 48 (8-$\sigma$) from the radio position but has \[O<span>ii</span>\] and Ca H & K lines identified in the spectrum, at a redshift of 0.759 (Paper II). The fainter source to the south-east, originally proposed as the identification (at a separation of 1.2-$\sigma$), was identified as an M-type star from spectroscopy with the Keck telescope (Spinrad, Dey & Stern, 1997, private communication).

53W069 & 53W091 – These two red sources at $z\simeq1.5$ have been extensively studied with both the Keck Telescope and the <span>*Hubble Space Telescope*</span>. Their rest-frame ultraviolet spectra are consistent with an evolved stellar population of ages 3–4 Gyr @Dey97 [@Dunlop96; @Dunlop99; @Spinrad97], and their rest-frame optical morphologies are dominated by $r^{1/4}$ elliptical profiles @Waddington00b.

General properties of the sample
--------------------------------

The apparent magnitude distribution is of cosmological interest because it is closely related to the radio source redshift distribution. Broadly speaking, the fainter a source is (in optical/infrared wavebands), the more distant it is expected to be. Although complicated by evolutionary effects, in the absence of spectroscopic data the magnitude distribution has been an important tool in studying radio galaxies.

The optical data are shown in Fig. \[grinumbers\] and the infrared data in Fig. \[irnumbers\]. In addition to the full Hercules distributions, the 2-mJy sample is shown as hatched histograms. The first issue that is apparent from these figures is the greater depth of the new observations. The limiting magnitudes of the Kron <span>et al.</span>(1985) photographic data correspond to $g\simeq
23.0$ mag, $r\simeq 22.3$ mag and $i\simeq 21.5$ mag. The <span>4-Shooter</span> data extend some 3–4 magnitudes fainter in all passbands. The infrared $K$-band data are similarly about four magnitudes deeper than the Thuan <span>et al.</span> (1984) results. The $griK$ data are essential complete, approximately half the sources have $H$-band measurements and only one-third of the sample has been observed in $J$.

It is clear from Figs. \[grinumbers\] & \[irnumbers\] that the number of galaxies per magnitude interval does not continue to increase down to the magnitude limit, but rather turns over at $r \sim
22$ mag. This immediately points to evolution of some form in the radio source population – if the radio sources formed an homogeneous class of object present throughout the history of the universe, the numbers would continue to increase towards the magnitude limit. This turnover was hinted at in the $N^+$ magnitude distribution of the whole LBDS @Windhorst84b and is clearly confirmed for the Hercules subsample here. Excluding the 1 mJy $\le S_{1.4} < 2$ mJy sources does not significantly change the shape of the magnitude distributions, but it does <span>*increase*</span> the median magnitude – i.e. the faintest radio sources are not in general the faintest sources at optical/infrared wavelengths. This would suggest that the faintest radio sources are lower (radio) luminosity objects at lower redshift, rather than radio-powerful objects at high redshift. Some caution must be applied to this conclusion however, given that these sources are few in number (9) but have large weights ($\ga$2.5).

In Fig. \[multikband\], the LBDS $K$-band magnitude distribution is compared with the results of three other radio samples with near complete infrared data. The Parkes Selected Regions (PSR) data are principally taken from Dunlop <span>et al.</span> (1989). Only sources in their four-region subsample, for which the $K$-band data are essentially complete, are used (the 12$^{\rm h}$ and 13$^{\rm h}$ regions are poorly covered in the infrared). The 1-Jansky sample of Allington-Smith (1982) is a complete sample of 59 radio sources with 1 Jy $< S_\nu < 2$ Jy at 408 MHz. Lilly, Longair & Allington-Smith (1985) presented infrared observations of 53 of these sources, which are plotted in the third panel of Fig. \[multikband\]. Finally, a complete sample of 90 radio galaxies was selected from the 173-source 3CR catalogue of Laing, Riley & Longair (1983). Nearly complete $K$-band data was obtained for this 3CR sub-sample @Lilly84, which excludes all quasars, and is shown in the last panel of the figure. For the first three samples, both galaxies and quasars are shown. The LBDS panel also includes the 2-mJy sample for comparison.

As first pointed out by Dunlop <span>et al.</span> (1989), the 1-Jansky radio galaxies are biased towards larger $K$ magnitudes than the (radio) brighter 3CR galaxies. However, a similar shift is not seen between the 1-Jansky and PSR sources, a further factor of two fainter in flux. Dropping another factor of $\sim$200 in flux, the LBDS galaxies are seen here to have much the same distribution as the 1-Jansky and PSR galaxies. The median $K$ magnitudes for the four samples are 15.3 (3CR), 16.5 (1-Jy), 16.5 (PSR) and 16.8 (LBDS). To the extent that the $K$ magnitude of a powerful radio galaxy is a good estimator of its redshift, this result implies that although the 1-Jansky galaxies are consistent with being high-redshift counterparts of the 3CR galaxies, these same sources are not seen at even higher redshifts in the fainter samples. (Note that a median spectral index of $\alpha=0.8$ was used to bring the flux limits of the samples to a common frequency for this comparison.)

Although the number of sources is small, the same effect is not seen in the quasar distributions. The median $K$ magnitude of quasars in the fainter three samples increases with decreasing flux limit: 16.1 (1-Jy), 16.3 (PSR) and 16.8 (LBDS). This may suggest that the quasar population is not changing as rapidly as the radio galaxy population. It must be noted, however, that the decrease in restframe optical/infrared flux between the 1-Jansky and LBDS quasars (a factor of $\sim 2$) is certainly not comparable to the drop in radio flux (a factor of $\sim 400$) – i.e. if the $K$ magnitude is a fair redshift estimator, the LBDS quasars must be less luminous in the radio than the 1-Jansky quasars.

Fig. \[lbdscolmag\] presents colour–magnitude diagrams for the Hercules sample. To compare these results with those of Kron <span>et al.</span>(1985), note that the colours are related by $(g-r)
\sim (J^+ - F^+) - 0.5$ and $(r-i) \sim (F^+ - N^+) - 0.4$ (from equations \[gritrans\]–\[gritrans1\]). It can be seen that the colours of the new identifications are comparable to those of the photographic identifications at $r\la 22$ mag. There is some bias towards bluer $g-r$ (and to a lesser extent, $r-i$) colours at the fainter magnitudes. In particular, there is a deficit of faint ($r>23$ mag), red ($g-r>0.5$, $r-i>1$) radio sources compared with field galaxy surveys of comparable depth @Neuschaefer92 [@Neuschaefer95a]. This is consistent with a continuation of the faint blue radio galaxy population that Kron <span>et al.</span> (1985) found at brighter magnitudes.

The sources classified as quasars (Q & Q?) tend to have bluer optical colours on average than the galaxies, as one would expect from the dominance of the AGN at ultraviolet/optical wavelengths in such sources. (Recall that the classification was based on morphology, not colour.) The "galaxy" class includes objects of unknown identity (?), which dominate at the faintest magnitudes. Figs. \[lbdscolmag\](a), (b) & (f) suggest that the bluest of these objects may in fact be quasars. Fig. 6 of Dunlop <span>et al.</span>(1989) shows that essentially all PSR sources with $K \ga 15$ and $R-K \la 3$ are quasars. Comparing that figure with Fig. \[lbdscolmag\](f) here, shows that the same cannot be said for the LBDS – only one of these faint blue objects is of uncertain classification (53W068) and one is a probable quasar (53W036), while the other three are G (53W034, 53W067) and G? (53W027). The LBDS quasars have a much broader range of colours than those in the PSR, perhaps a consequence of their weaker AGN.

Figs. \[lbdscolmag\](c), (d) & (e) show the distribution of near-infrared colours with apparent magnitude. In considering these figures, it must be remembered how incomplete these data are (only one-third of the sample has $J$-band data, only one-half has been observed in the $H$-band). There appears to be a linear correlation between $i-J$ colour and $i$ magnitude in Fig. \[lbdscolmag\](c), however this may simply be due to the absence of faint $J$-band photometry – at any given $i$ magnitude it is the reddest sources in the sample that would have been preferentially detected at $J$. The dispersion of the $J-H$ colours (0.2 mag), defined as the standard deviation about the mean colour, is 2–3 times smaller than the dispersion in the optical colours. This is probably due to the incomplete infrared data, but may also be a genuine property of the sample. The smaller scatter may indicate that the infrared emission is dominated by stellar light from the host galaxies, rather than emission from the AGN which tends to dominate at bluer wavelengths and can vary significantly from one source to another.

To summarize, the optical identification of the 72-source LBDS Hercules sample is essentially complete (only three sources remain unidentified). Approximately 85% of the sources have also been identified in the near-infrared $K$-band and a programme to obtain complete $J$- and $H$-band data is ongoing. Paper II will present the results of work to measure redshifts for this sample from both direct spectroscopy and by using photometric estimation techniques. This is now the most comprehensive sample of radio-selected sources available at millijansky flux density levels, and is ideally suited to study the evolution of the 1.4 GHz radio luminosity function (for AGN) out to very high redshifts – a topic to be addressed in forthcoming papers.

Acknowledgments {#acknowledgments .unnumbered}
===============

We thank M. Oort and S. Anderson for contributing to the Palomar observations; T. Keck for assisting with the processing of the <span>4-Shooter</span>data; and P. Katgert, G. Neugebauer, H. Spinrad and D. Stern for allowing us to include some unpublished data. The Hale Telescope at Palomar Observatory is owned and operated by the California Institute of Technology. The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the PPARC. This work was supported by a PPARC research studentship (to IW); and by NSF grants AST8821016 & AST9802963 and NASA grants GO-2405.01-87A, GO-5308.01-93A & GO-5985.01-94A from STScI under NASA contract NAS5-26555 (to RAW).

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