SIMBAD references

We demonstrate that a log-linear relation does not provide an adequate description of the correlation between the masses of super massive black holes (SMBHs, M_bh) and the velocity dispersions of their host spheroid (σ). An unknown relation between logM_bhand logσ may be expanded to second order to obtain a log-quadratic relation of the form log(M_bh) =α+βlog(σ/200km/s) +β₂[log(σ/200km/s)]². We perform a Bayesian analysis using the local sample described in Tremaine et al., and solve for β, β₂and α, in addition to the intrinsic scatter (δ). We find unbiased parameter estimates of β= 4.2 ± 0.37, β₂= 1.6±1.3 and δ= 0.275±0.05. At the 90 per cent level the M_bh-σ relation does not follow a uniform power law. Indeed, over the velocity range 70 ≲σ≲ 380 km/s the logarithmic slope d logM_bh/d logσ of the best-fitting relation varies between 2.7 and 5.1, which should be compared with a power-law estimate of 4.02 ± 0.33. The addition of the 14 galaxies with reverberation SMBH masses and measured velocity dispersions to the local SMBH sample leads to a log-quadratic relation with the same best fit as the local sample. However, the addition of the reverberation masses increases the significance of the log-quadratic contribution, yielding a value of β₂that is non-zero at the 5σ level. Furthermore, assuming no systematic offset, single epoch virial SMBH masses estimated for active galactic nuclei (AGNs) follow the same log-quadratic M_bh-σ relation as the local sample, but extend it downward in mass by an order of magnitude. The log-quadratic term in the M_bh-σ relation has a significant effect on estimates of the local SMBH mass function at M_bh≳ 10⁹M_☉, leading to densities of SMBHs with M_bh≳ 10¹⁰M_☉that are several orders of magnitude larger than inferred from a log-linear M_bh-σ relation. We also estimate unbiased parameters for the SMBH-bulge mass relation using the sample assembled by Häring and Rix. With a parametrization log(M_bh) =α_bulge+β_bulge log(M_bulge/10¹¹M_☉) +β_2,bulge[log(M_bulge/10¹¹M_☉)]², we find β_bulge= 1.15±0.18 and β_2,bulge= 0.12±0.14. We determined an intrinsic scatter δ_bulge= 0.41±0.07 which is ∼50 per cent larger than the scatter in the M_bh-σ relation.