6.2.3 Population Statistics for X-Ray Samples
The EMSS and HGLS XBL samples, which went down to fairly low X-ray fluxes, ~ 2 x 10-13 erg cm-2 s-1 in the 0.3-3.5 keV band, revealed a decided flattening of the counts at low flux, in marked contrast to the steep X-ray log N - log S curves for other kinds of AGN. Padovani and Urry (1990) compared predictions of the FR I unified scheme with the X-ray counts from these two samples (plus the HEAO-1 A-2 sample) and found good agreement for a bulk Lorentz factor x ~ 3 and a ratio of Intrinsic jet luminosity to unbeamed luminosity f ~eq 0.1. The total number of BL Lac objects was ~14% of the number of FR I galaxies, with more than 90% of the BL Lacs at lower X-ray luminosities than currently observed, and the critical angle separating BL Lacs from FR Is was c ~ 30°.
Since then, the EMSS-derived X-ray luminosity function of BL Lac objects has been published (Morris et al. 1991; Wolter et al. 1994) and now we can fit it directly. We compare our beaming predictions with the X-ray luminosity function for the EMSS subsample of 30 BL Lacs with fx 2 x 10-13 erg cm-2 s-1, assuming no evolution (which is consistent at the ~ 2 level with the observational data; Wolter et al. 1994; see also Sec. 6.2.2). We follow the method of Avni and Bahcall (1980) to take into account the fact that the volume surveyed in the EMSS is a function of limiting flux. Redshifts, fluxes, and sky coverage were taken from Wolter et al. (1994). Five objects in the sample have no redshift determination; these were initially excluded from the sample but their presence was taken into account by multiplying the normalization of the resulting luminosity function by 30/25.
Figure 16 shows the luminosity function (solid line) from the fitted beaming model of Padovani and Urry (1990) compared to the observed LF for the EMSS sample for no evolution (filled circles). The model agrees very well with the data (2 0.3), especially considering that the parameters for the model were optimized for the number counts. If instead we use the anti-evolving X-ray luminosity function of Wolter et al. (1994), with = -0.14, then by increasing Rmax (the ratio between the maximum luminosities of the parent and beamed populations) from 250 (as in Padovani and Urry 1990) to 1000 we get the dot-dashed line in Fig. 16. The ratio between BL Lacs and FR Is increases to about 30%, x ~ 2.9, f ~ 1.1, and c ~ 47°. This is a much poorer fit to the data (2 2.5) but given the uncertainties in the X-ray luminosity function of FR Is (see below), one cannot definitely rule out this case.
|Figure 16. The local differential X-ray luminosity functions of low-luminosity radio-loud AGN. The observed LF of FR I galaxies is represented by a broken power law (dashed line). The observed LFs for the EMSS XBL sample (no evolution: filled circles; anti-evolution: open squares) are fitted by beaming models for the non-evolving case (solid line) and the anti-evolving case (dash-dotted line); data and evolution estimate from Wolter et al. (1994). Error bars correspond to 1 Poisson errors (Gehrels 1986).|
The redshift distribution of the EMSS is difficult to reproduce. Despite the fact that beaming in the zero evolution case fits the observed LF better, it cannot reproduce the peak in N(z) at z ~ 0.2-0.3, whereas our fit to the anti-evolving LF does. Browne and Marchã (1993) have suggested that recognition problems affecting low-luminosity BL Lacs whose light is swamped by the host galaxy, typically a bright elliptical (Sec. 5.4), might explain the unusual redshift distribution and anti-evolution of the EMSS XBL. Padovani and Giommi (1995) have shown through numerical simulations, however, that although recognition problems have some effect, they are probably not strong enough to affect these properties so drastically.
A complication in applying beaming models to the X-ray band stems from the uncertainties in the X-ray luminosity function of FR Is. These are due to its bivariate nature, small statistics, and the non-detection in X-rays of ~ 30% of the complete radio-selected sample (which was already small). ROSAT will eventually produce an X-ray selected sample of FR Is, or at least complete X-ray data on a sizeable radio-selected sample of these objects. Already one interesting ROSAT result is the identification of resolved (thermal) and unresolved X-ray emission in radio galaxies, as assumed by Padovani and Urry (1990). The beaming model discussed in this section predicts ratios of intrinsic-jet to extended X-ray flux in the range 0.1-1, marginally inconsistent with the observed ratios of nonthermal to thermal emission for six low-luminosity radio galaxies of 1-5 (Worrall and Birkinshaw 1994). The disagreement is even worse because in radio galaxies the jets should be de-amplified (for ~ 3, < 1 for > 45°; Appendix A). Further high-resolution X-ray observations will put more constraints on the f-parameter.
The XBL samples are still relatively small. Larger XBL samples are now being optically identified, including the HEAO-1 LASS sample (Schwartz et al. 1989; Laurent-Muehleisen et al. 1993) and the Einstein Slew Survey Sample (Elvis et al. 1992; Schachter et al. 1993; Perlman et al. 1995). In addition, the ROSAT All-Sky Survey should produce large numbers of new BL Lac objects - our beaming model for the X-ray samples predicts roughly two objects per square degree down to fx = 10-14 erg cm-2 s-1 in the 0.3-3.5 keV band - some of which have already been identified (Bade et al. 1994). With these new data we will be able to address the beaming hypothesis with better statistics.