Radio Source Evolution & Unified Schemes
C. A. Jackson, PASA, 16 (2), in press.

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Contents Page: Volume 16, Number 2

Space density evolution:When do these sources exist ?

We have tested the dual-population unified scheme in a two-stage process: Firstly we find a simple space density evolution model for the parent radio sources and secondly a set of beaming parameters which replicate the observed source counts at high frequencies. Full details of this analysis is given in Jackson & Wall (1999) so only a brief outline is presented in this section.

The first stage of our analysis adopts a simple parametric form for the evolution of the FRI and FRII populations. To describe the evolution, we adopt an evolution function, F(P,z), which modifies the local radio luminosity function to give the radio luminosity function at any epoch, i.e.

$\rho(P,z) = \rho_{0}(P) F(P,z)$ . The function adopted describes exponential `luminosity-dependent density evolution' (LDDE), (

$F(P,z) = \exp M(P) \tau(z)$ ), where $\tau(z)$ is the look-back time in units of the Hubble time. For Einstein-de-Sitter ( $\Omega$ =1) geometry this is given by

$\tau(z) = (1 - (1 + z)^{-1.5})$ . We also apply a redshift cutoff to the populations to mirror the observed behaviour of powerful radio sources (e.g. Shaver et al. (1996)), modifying the evolution function so that it peaks at z_c/2, then declines to zero at the cut-off redshift z_c:

F = F(P,z) for $z \le z_c/2$ ,

F = F(P,z_c - z) for

$z_c/2 < z \le z_c$ and

F = 0 for z > z_c.

The evolution rate M is set between 0 and M_max as a function of radio power P:

$M(P) = M_{max} \frac{\log_{10}P - \log_{10}P_{1}}{\log_{10}P_{2} - \log_{10}P_{1}}$ for

$P_{1} \leq P \leq P_{2}$ ,

M(P) = 0 for P < P₁, i.e. no evolution of radio sources of radio power less than P₁,

and

M(P) = M_max for P > P₂, i.e. sources of radio power greater than P₂ undergo maximal evolution.

The choice of this evolution function is constrained by (i) the evidence for differential evolution of radio sources, with the most powerful sources having undergone significantly more evolution that those of lower-radio power (Longair 1966), (ii) that an exponential form is required to fit the strong cosmic evolution to relatively modest redshifts (Doroshkevich, Longair & Zeldovich 1970) and (iii) that there is a `turnover' in the space density of powerful sources at high redshift, representing the epoch of peak AGN activity. Other simple forms of exponential evolution have been tested using the latest radio source count data and have been found to be less successful (Jackson 1997).

To determine an evolution model for the FRI and FRII parent populations we use radio samples which are free from orientation bias. Low-frequency radio samples ( $\nu <$ 400 MHz) comprise sources whose radio emission is from extended, steep-spectrum regions. This extended emission swamps any emission from the (potentially boosted) core of the source. We use the source count from the 3CRR sample at 178 MHz (Laing, Riley & Longair 1983) and that from the 6C survey at 151 MHz (Hales, Baldwin & Warner 1988) to fit a parametric model of space density evolution which best reproduces the observed source count. The best-fit model is the parameter set which yields the $\chi^{2}$ -minimum between the observed and model source counts, where this minimum is found using the AMOEBA downhill simplex method in multi-dimensions (Press et al. 1992). The model fit has strong luminosity-dependent density evolution of the FRII population coupled with no evolution of the FRI population. The FRII population has its maximum space density around $z \sim$ 2.8. The most powerful FRIIs have space density enhancement factors $\sim$ 10⁴ (comoving) relative to their local space density (Figure 2). Shaver et al. (1996) have found similar space density enhancement factors for a sample of flat-spectrum (i.e. beamed) radio sources of high radio power (

$\log_{10} P_{2.7 \rm\thinspace GHz} >$ 27 W Hz^-1 sr^-1.

Testing the orientation-dependence of the dual-population unified scheme uses the derived evolution model to predict the radio source count at radio frequencies which comprise both parent sources and their beamed-progeny. We describe the Doppler beaming of the radio core/jets in terms of a Lorentz factor, $\gamma$ and the intrinsic core-to-extended flux ratio, R_c, for each parent population, then randomly orientate the sources to produce the total source count comprising beamed and unbeamed sources. A model fit to the observed 5 GHz count is determined by the $\chi^{2}$ -minimum using AMOEBA to search the beaming parameter space.

As discussed in Jackson & Wall (1999), the fitted beaming parameters are in agreement with those measured observationally - for example the critical angle inferred for the FRII population is $\sim7^{\circ}$ , concurring with 6 - 7 $^{\circ}$ determined by Best et al. (1995) for a sample selected from 3CR, and a Lorentz factor, $\gamma$ , of 8.5 is in accord with results from a large VLBI sample (Vermeulen 1995) and estimates of $\gamma\sim$ 10 for highly-beamed sources such as 3C 273 (Davis, Unwin & Muxlow 1991) Additional tests of the model predictions against observed radio source samples at intermediate frequencies have also been made: e.g. comparing the model and observed fraction of core-dominated sources at 2.7 GHz. The clear decline in the fraction of core dominated sources found in a complete sample (totalling 3412 sources) towards lower flux densities is clearly predicted by the dual-population unified scheme (Figure 3). This decline arises due to the very strong cosmic evolution of the FRII population. That our model reproduces observational results such as this is a real strength of the dual-population unified scheme.