5 Discussion and conclusions

In this paper, we have considered the apparent discrepancies between independent central mass estimates for the paradigmatic object Mkn 501. Our main conclusions can be summarized as follows:

(1) Estimates inferred from host galaxy observations using the reported, statistical correlations for the central velocity dispersion and the bulge luminosity reveal a tendency for the central BH mass in Mkn 501 to be larger than $\sim$ $5 \times 10^8~M_{\odot}$. If verified by further investigations, this would exclude both the standard binary scenario, where the jet is emitted from the less massive BH, and several high energy emission models proposed so far. However, as the correlations still show substantial intrinsic scatter and large uncertainties due to the use of limited samples - especially with respect to the high mass end - the accuracy of this estimate should be treated with caution. In particular, we have shown that the central mass limit could be easily up to a factor of (2-3) smaller, thus allowing for the standard binary scenario, in which case a simple explanation for the divergent mass estimates from emission models and host observations appears possible.

(2) Independent mass estimates from high energy emission models suggest a mass for the jet emitting BH in Mkn 501 which is smaller than $\simeq$ $6 \times 10^7~M_{\odot}$. However, this estimate is quite model-dependent and so cannot be used as a universally valid constraint. In particular, emission models have been developed for Mkn 501 where a central BH mass up to ten times larger appears quite possible.

(3) If a binary BH interpretation for the periodical variability (cf. RMI) is appropriate in the case of Mkn 501, the jet dominating the emission has to be produced by the less massive (secondary) BH. Using characteristic jet parameters and assuming both Eddington-limited accretion and a binary separation comparable to the gravitational one, we have shown that the combined central (primary + secondary BH) mass should be smaller than $\simeq$ $3 \times 10^8 ~M_{\odot}$. The binary model particularly permits a system with $m=6 \times 10^7 M_{\odot}$ and $(m+M)\simeq (1.5{-}2)\times 10^8~M_{\odot}$, possibly allowing for a convergence of constraints from emission models and host observations.

(4) If further research clearly establishes a high central BH mass $\sim$ $10^9~ M_{\odot}$ in Mkn 501, this would call for a change of fundamental assumptions and/or a modification of the parameter space regarded to be typical in the context of several high energy emission models. The only way to avoid this conclusion seems to be the assumption of a highly unequal BBHS with the jet dominating the emission produced by the less massive and the central mass dominated by the primary BH. However, it then appears no longer be possible to explain the observed periodicity via the orbital motion. On the other hand, even in the case of a high central mass, a binary model for the observed periodicity may be still possible provided the jet is produced by the primary BH. Yet, for the binary to be near or above the separation at which gravitational radiation becomes dominant, one then requires the earlier binary evolution to pass through phases of super-Eddington accretion and/or decreased conversion efficiency $\eta < 0.1$. Such conditions need not necessarily be ad hoc but have already been considered in the context of galaxy evolution and the growth of massive BH (e.g. Collin et al. 2002; Yu & Tremaine 2002).

In view of Mkn 501 as a paradigmatic object, bringing its mass estimates to convergence continues to be an important task. Further research on the parameter space of emission models and the careful observations of nearby galaxies will be particularly valuable in order to minimise the uncertainties in the statistical correlations, to evaluate the impact of host observations on high energy emission models, and to assess the plausibility of a BBH model.

Acknowledgements

We are grateful to J. Heidt for fruitful discussions about the host of Mkn 501, and C. Hettlage and R. Hessman for a helpful reading of the manuscript. F.M.R. gratefully acknowledges support under DFG MA 1545/8-1.