Novel calibrations of virial black hole mass estimators in active galaxies based on X-ray luminosity and optical/NIR emission lines

Accurately weigh the masses of SMBH in AGN is currently possible for only a small group of local and bright broad-line AGN through reverberation mapping (RM). Statistical demographic studies can be carried out considering the empirical scaling relation between the size of the BLR and the AGN optical continuum luminosity. However, there are still biases against low-luminosity or reddened AGN, in which the rest-frame optical radiation can be severely absorbed/diluted by the host and the BLR emission lines could be hard to detect. Our purpose is to widen the applicability of virial-based SE relations to reliably measure the BH masses also for low-luminosity or intermediate/type 2 AGN that are missed by current methodology. We achieve this goal by calibrating virial relations based on unbiased quantities: the hard X-ray luminosities, in the 2-10 keV and 14-195 keV bands, that are less sensitive to galaxy contamination, and the FWHM of the most important rest-frame NIR and optical BLR emission lines. We built a sample of RM AGN having both X-ray luminosity and broad optical/NIR FWHM measurements available in order to calibrate new virial BH mass estimators. We found that the FWHM of the H$\alpha$, H$\beta$ and NIR lines (i.e. Pa$\alpha$, Pa$\beta$ and HeI$\lambda$10830) all correlate each other having negligible or small offsets. This result allowed us to derive virial BH mass estimators based on either the 2-10 keV or 14-195 keV luminosity. We took also into account the recent determination of the different virial coefficients $f$ for pseudo and classical bulges. By splitting the sample according to the bulge type and adopting separate $f$ factors we found that our virial relations predict BH masses of AGN hosted in pseudobulges $\sim$0.5 dex smaller than in classical bulges. Assuming the same average $f$ factor for both populations, a difference of $\sim$0.2 dex is still found.Comment: 11 pages, 2 figures, 4 tables, accepted for publication on A&

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

A higher grading affine algebraic construction of integrable hierarchies, containing the Wadati-Konno-Ichikawa (WKI) hierarchy as a particular case, is proposed. We show that a two-component generalization of the Sch\" afer-Wayne short pulse equation arises quite naturally from the first negative flow of the WKI hierarchy. Some novel integrable nonautonomous models are also proposed. The conserved charges, both local and nonlocal, are obtained from the Riccati form of the spectral problem. The loop-soliton solutions of the WKI hierarchy are systematically constructed through gauge followed by reciprocal B\" acklund transformation, establishing the precise connection between the whole WKI and AKNS hierarchies. The connection between the short pulse equation with the sine-Gordon model is extended to a correspondence between the two-component short pulse equation and the Lund-Regge model

The algebraic structure behind the derivative nonlinear Schroedinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schr\" odinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of a $\hat{s\ell}_2$ Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows, respectively. The equivalence between the latter and the massive Thirring model is explicitly demonstrated also. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation.Comment: references adde