Completeness of the PG survey

Goldschmidt et al. [22] have found a systematic difference of 0.28 mag between the PG magnitudes and their own measurements for 25 PG stars, the PG magnitudes being too bright; they suggested that this difference was due to a zero-point error in the PG magnitude scale. The mean differences between the PG and photoelectric magnitudes for 105 stars is equal to 0.00 mag; this does not confirm the existence of an systematic offset in the PG scale. The quoted error for the PG photographic B magnitude is $\sigma$ = 0.29 mag [23]. The comparison with photoelectric magnitudes gives $\sigma$ = 0.37 mag (Fig. 4b).

 

Figure: (a) Plot of the differences between the APS O magnitudes and the photoelectric B magnitudes for 105 PG objects. (b) Plot of the differences between the PG photographic and the photoelectric B magnitudes for the same 105 objects. In the two figures, the straight lines represent the best fits through the data.

It has been suggested [58] that, on average, the PG magnitudes for QSOs are too bright; as we do not observe such an effect for the stars, we suggest that this is due to the QSO variability; QSOs are discovered preferentially when they are bright; when measured at an epoch different than the survey epoch they are found to be systematically weaker by a few tens of a magnitude [20].

 

$$\:\:\:z \:\,B b\:$$ Postion O M_B Name

0732+396 0.118 16.: 14.70 -24.6 X N F 25.1

0804+761 0.100 15.15 14.18 -24.4 X Y PF 31.0

0838+770 0.131 16.30 17.55 -22.0 X Y PF 32.7

0844+349 0.064 14.00 16.89 -20.7 X Y PF 38.0

0931+437 0.456 16.41 16.47 -25.8 X Y PF 47.4 US 737

0935+416 1.966 16.30 16.07 -29.6 - Y PF 48.3

0936+396 0.458 16.30 16.69 -25.6 - Y PF 48.6

0947+396 0.206 16.40 16.39 -24.1 X Y PF 50.7

0953+415 0.239 15.05 15.59 -25.3 X Y P 51.7

0959+685 0.773 16.28 16.01 -27.1 x Y F 42.0

1002+437 0.178 15.: 16.39 -23.8 X Y F 52.9

1007+417 0.613 15.: 16.04 -26.9 X Y F 54.2 4C 41.21

1048+342 0.167 15.81 15.94 -24.2 X Y PF 63.4

1049+617 0.421 16.66 16.62 -25.3 X Y F 50.4 4C 61.20

1100+772 0.313 15.86 15.93 -25.6 X Y PF 38.6 3C 249.1

1102+347 0.51 16.2 - -26.2 - N F 66.2 CSO 314

1112+668 0.544 17.0 16.53 -26.1 X Y F 47.9

1112+431 0.302 16.20 17.03 -24.4 - Y P 64.9

1114+445 0.144 16.05 15.11 -24.6 x Y PF 64.5

1115+407 0.154 16.02 14.57 -25.3 X Y PF 66.7

1121+422 0.234 16.02 15.84 -24.6 X Y PF 66.9

1137+661 0.650 16.50 16.25 -26.6 X Y F 49.7 3C 263.0

X: in the ROSAT All Sky Survey Bright Source Catalogue; x: in the ROSAT WGACAT Catalogue; R: in the NRAO VLA Sky Survey; Y: in the PG area; N: not in the PG area; O: APS O magnitudes; P: in the PG catalogue; F: in the FBS catalogue.

 

$$\:\:\:z \:\,B b\:$$ Position O M_B Name

1140+680 0.796 17.0 16.82 -26.8 X Y F 48.1

1147+673 1.02 16.7 16.69 -27.2 - Y F 49.1

1150+334 1.40 16.2 16.30 -28.8 R Y F 76.0 CSO 373

1229+710 0.208 15.4 15.66 -24.9 X Y F 46.3

1235+699 0.522 17.9 17.96 -24.5 x Y F 47.4

1242+342 0.717 17.3 17.52 -25.8 - Y F 83.1 CSO 919

1248+401 1.032 16.06 16.33 -28.0 X Y PF 77.3

1255+447 0.300 16.5 16.48 -24.9 X Y F 72.6

1309+355 0.184 15.45 15.64 -24.7 X Y PF 80.7

1322+659 0.168 15.86 15.71 -24.2 X Y PF 51.1

1324+448 0.331 17.: 18.09 -23.5 X Y F 71.1

1329+412 1.937 16.30 16.78 -29.1 - Y PF 73.8

1338+416 1.204 16.08 16.50 -28.1 - Y PF 72.5

1351+640 0.088 15.42 - -22.3 x Y PF 52.0

1402+436 0.320 15.: - -25.4 - Y F 68.0 CSO 409

1411+442 0.089 14.99 - -22.6 x Y PF 66.4

1444+407 0.267 15.95 - -24.9 X Y PF 62.7

1512+370 0.370 15.97 - -25.8 X Y PF 58.3 B2 1512+37

1526+659 0.345 17.0 16.90 -24.8 x Y F 44.4

1630+377 1.478 15.96 16.62 -28.5 x Y PF 42.9

1634+706 1.337 14.90 15.27 -29.7 x Y PF 36.6

1641+399 0.594 16.25 15.87 -26.7 X Y F 40.9 3C 345.0

X: in the ROSAT All Sky Survey Bright Source Catalogue; x: in the ROSAT WGACAT Catalogue; R: in the NRAO VLA Sky Survey; Y: in the PG area; N: not in the PG area; O: APS O magnitudes; P: in the PG catalogue; F: in the FBS catalogue.

The QSO counts are systematically affected by the photometric errors in B as these errors scatter many more objects toward brighter magnitudes than it does toward fainter magnitudes. Assuming that the error distribution is Gaussian, with dispersion $\sigma$, the correction to be applied to the observed counts is a factor 10 to the power of [$(b+1)\,\sigma^{2}/2$], where b is the slope of the integrated number-magnitude relation: logN(B) = $a + b \times B$ [18,53]. Assuming b = 0.75, if $\sigma$ = 0.27 mag, the true QSO surface densities are smaller by 1.16 than the observed ones; if $\sigma$ = 0.37, the correction is 1.32.

In principle the PG survey selected all objects with U-B < -0.46 (and brighter than B$\sim$16.2); however, the U-B colour was measured with a relatively large error (0.24 mag rms) which induced an incompleteness estimated at around 12% [53]. Moreover, in the interval 0.6 < z < 0.8, the strong Mgii$\lambda$2800 emission line is in the B filter which results in a much redder U-B colour than for neighbouring redshifts; as a result in this interval, the PG survey picked up too few quasars and was estimated to be only 72% complete [53].

The catalogue of mean UBV data on stars [44] contains 283 stars in the magnitude range 12.0 < B < 16.5 and with U-B < -0.40 in the full 10714 deg² area of the PG survey; 190 are included in the PG catalogue (there are 59 stars fainter than B = 16.5 in the PG area, but only two are included in the PG catalogue). Twenty four stars photoelectrically observed because they were in the PG catalogue [29,37] have been ignored. The overall completeness of the PG survey is therefore 64% (166/259). 67% (162/241) of the stars brighter than B = 16.2 were found in the PG survey, while only 22% (4/18) of those weaker than this were detected. The completeness of the PG survey for stars brighter than B = 16.2 rises from about 55% for U-B > -0.60 to 80% for U-B < -1.0. For PG QSOs (B < 16.2), the completeness should not be less than $\sim$70%.

There are 19 known non-PG QSOs in the FBS catalogue, listed in Table 4; 17 are within the limits of the PG survey, but twelve have APS O magnitudes weaker than 16.2 and may have been too weak for having been discovered by the PG survey. FBS 1641+399 is 3C 345.0, an optically violently variable, with a B magnitude ranging from 14.7 to 17.7 [30]; according to the published light-curve, during the epoch of the PG survey (Jan. 1973-May 1974) the object was always fainter than B = 16.4 and was most probably weaker than the plate limit. The published magnitudes for FBS 1402+436 are inaccurate and in poor agreement (B = 15$\pm$0.75 [12], B = 16 [49], V = 16.5 [27]), suggesting that this object could have been weaker than the PG limiting magnitude. We are left with only three bright FBS QSOs missing from the PG catalogue implying an incompleteness of 15% (assuming that the FBS is 70% complete). Two of them are in the z range (0.6-0.8) in which the U-B excess is reduced because of the presence of the Mgii line in the B filter which could explain their absence from the PG survey.

 

$$\:\,z \:B \:\,M_{B}$$ Name Position O b

HS 0806+6212 0806+62 0.173 16.5 16.12 -24.0 - Y 33.0

KUV 08126+4154 0812+41 1.28 16.4 15.91 -28.9 - Y 32.9

US 1329 0833+44 0.249 15.6 15.24 -25.7 X Y 37.0

KUV 09468+3916 0946+39 0.360 16.1 15.99 -25.8 X Y 50.6

RX J10265+6746 1022+68 1.178 15.0 - -29.6 - Y 43.9

KUV 11274+4133 1127+41 0.72 16.93 16.12 -27.0 - Y 68.1

HS 1312+7837 1312+78 2.00 16.4 15.84 -30.1 - N 38.7

CSO 1022 1351+36 0.284 16. - -25.3 - Y 73.9

RX J14249+4214 1422+42 0.316 15.7 - -25.8 X Y 65.7

B3 1621+392 1621+39 1.97 16.7 15.86 -30.0 X Y 44.7

RXS J16261+3359 1624+34 0.204 16.5 15.82 -24.7 X Y 43.8

RXS J17060+6857 1706+69 0.449 16.3 16.04 -26.2 X N 34.6

HS 1710+6753 1710+67 0.41 16.4 15.94 -26.1 - N 34.5

B2 1721+34 1721+34 0.206 15.46 - -25.0 X Y 32.2

X: in the ROSAT All Sky Survey Bright Source Catalogue; Y: in the PG area; N: not in the PG area; O: APS O magnitudes.

Wampler & Ponz [58] suggested that the incompleteness of the PG survey could be substantial. Goldschmidt et al. [22] found five new QSOs with B < 16.17 in a 330 deg² area included in the PG area where Green et al. [23] found only one; they got a surface density of 0.018 deg^-2, about three times larger than PG. We have obtained a spectrum of one of them (Q 1404-0455) which shows it to be a starburst galaxy at z = 0.029. For two others, the O magnitudes extracted from the APS database [48] are greater than 16.5; it is not clear if this is due to variability or to a difference in the magnitude scales. In these conditions, it seems hazardous to conclude to a gross incompleteness of the PG survey on the basis of these data. Köhler et al. [33] surveyed a 611 deg² area and concluded to an incompleteness of the BQS by a factor 2 to 3; they found eight QSOs brighter than B = 16.16, or 0.013 deg^-2. La Franca & Cristiani [36] have surveyed an area of 555 deg² in the magnitude range 15 < B < 18.75; they found that, for magnitudes brighter than B = 16.4, the QSO surface density (0.013 deg^-2, derived from seven objects) is a factor 2.2 higher than the PG value. Savage et al. [51] found 16 QSOs brighter than B = 16.16 in a 1500 deg² area or 0.011 deg^-2. These samples are quite small; the zero-point errors of their magnitude scales have not been determined. These results should, therefore, be considered as tentative.