Several evolution models have been proposed for GPS sources, in which GPS sources subsequently evolve into CSS sources and large-scale doubles (Hodges & Mutel 1987, Fanti et al. 1995, Readhead et al. 1996, O'Dea & Baum 1997). In these models, the age ratio of large size objects to GPS sources is typically ~ 103. The much larger fraction (say 10%) of GPS in radio surveys therefore implies that young radio sources have to substantially decrease in radio luminosity (a factor ~ 10) when evolving to large scale radio sources. Readhead et al. (1996) find from their CSO statistics that the luminosity evolution from 10 pc to 150 Kpc is consistent with a single power-law decrease. This in contrast to O'Dea & Baum (1997) who find that the number of GPS and CSS sources per bin of log projected size is constant from 100 pc to 6 Kpc, indicating that GPS and CSS sources must decline in luminosity at a faster rate than the classical 3CR doubles. The number count and linear size statistics used in these studies, are all averaged over a wide redshift range and only cover the brightest objects in the sky. However, as is shown in figure 2, in flux density limited samples the redshift distribution of GPS galaxies is significantly different from that of large size radio galaxies. This suggests that the interpretation of the number count statistics is not so straightforward.
Figure 2. (Top) The cumulative redshift distributions of GPS galaxies from the Stanghellini et al. sample (1998) and of 3CR galaxies. (Left) Schematic representation of the intra-galactic medium and the proposed luminosity evolution scenario for radio sources. (Right) The Local Luminosity Function of young radio sources derived from the faint and bright GPS samples. The solid and dashed lines represent simulated luminosity functions for extended and young objects respectively.
The bias of GPS galaxies towards higher redshifts than large size radio galaxies provides an important clue about the luminosity evolution of radio sources. It implies that GPS galaxies are biased towards higher radio power than extended objects in flux density limited samples. If GPS and large size radio sources are identical objects, just observed at different phases pf the life cycle, their cosmological density evolution, e.g. their birth functions with redshift, should be the same. Since their lifetimes are short compared to the Hubble time, the redshift distributions of the GPS galaxies, and the objects they evolve to, should also be the same. The bias of GPS sources towards higher redshifts and radio powers therefore implies that their luminosity function must be flatter than that of large size radio sources. We argue that the luminosity evolution of the individual objects strongly influences their collective luminosity function, and propose an evolution scenario in which GPS sources increase in luminosity and large size sources decrease in luminosity with time. In the simplified case, in which source to source variations in the surrounding medium can be ignored, the luminosity of a radio source only depends on its age and jet power. Sources in a volume based sample are biased towards older ages and lower jet powers for populations of both GPS and large size sources. Low jet powers result in low luminosity sources. The higher the age of a large size source, the lower its luminosity, but the higher the age of a GPS source, the higher its luminosity. This means that for a population of large size sources the jet power and age bias strengthen each other resulting in a steep luminosity function, while they counteract for GPS sources, resulting in a flatter luminosity function.
The luminosity evolution proposed is expected for a ram-pressure confined radio source in a surrounding medium with a King-profile density. In the inner parts of the King profile, the density of the medium is constant and the radio source builds up its luminosity, but after it grows large enough the density of the medium declines and the luminosity of the radio source decreases. An analytic model for radio sources with pressure confined jets has been developed by Kaiser & Alexander (1997). Interestingly, they showed that the properties of the bow shock and the surrounding gas force radio sources to grow in a self-similar way, provided that the density of the surrounding gas falls off less steeply than 1 / r2. X-ray observations of large nearby ellipticals show that their hot ISM follows a King distribution well, and have a core radius of typically 500-1000 pc (Trinchieri, Fabianno & Canizares 1986). Hence the predicted change in luminosity evolution can be expected to occur between the GPS and the CSS phases.
A way to test this luminosity scenario is to determine the local luminosity functions (LLF) for GPS galaxies and large size radio sources and compare it with simulated luminosity functions for a population of radio sources undergoing the proposed luminosity evolution. Unfortunately, only 4 GPS galaxies at z < 0.2 are present in the combined faint and bright GPS samples, too small a number to construct a LLF directly. However, since it can be assumed that the cosmological number density evolution for the young sources is the same as for old sources, the cosmological evolution of the luminosity function as derived for steep spectrum (eg. large size) sources (Dunlop & Peacock 1990) can be used to derive a LLF for young radio sources from the total faint and bright GPS samples. The combination of the bright and faint GPS samples is not straightforward, since they are selected in very different ways. This introduces a relatively uncertain correction factor of ~ 3 for the number densities derived from the faint sample. The result is shown in figure 2. A radio source population is simulated having random ages between 0 and 1000 time-units and jet powers over a range of 200, distributed with a powerlaw of -1.69, chosen to result in a slope of the luminosity function of large size sources at low radio powers of 0.69 in log, as determined by Dunlop & Peacock (1990). The objects younger than 1 time-unit are designated as GPS sources, and increase in luminosity with time, while the older sources decrease in radio luminosity. Assuming that the boundary between the GPS and large size phases is at 105 year, the age-limit of the large size radio sources in the simulation is 108 years. The resulting luminosity functions were scaled in such way that the break in the luminosity function of the large scale sources overlaps with what is found by Dunlop & Peacock for steep spectrum sources. Although the uncertainties are large and several free parameters enter the simulation, figure 2 shows that the shape of the LLF of GPS galaxies is as expected. This scenario is also consistent with the high number densities of GPS sources at bright flux density levels, since at the high luminosity end, the simulated LLF of GPS galaxies is only slightly lower than that of large size galaxies.