On a New Construction of Pseudo BL-Algebras

We present a new construction of a class pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop $A$. Using two injective mappings from one set, $J$, into the second one, $I$, and with an identical copy $\overline A$ with the reverse order we construct a pseudo BL-algebra where the lower part is of the form $(\overline A)^J$ and the upper one is $A^I$. Starting with a basic commutative hoop we can obtain even a non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with non-commuting negations. We describe the construction, subdirect irreducible kite pseudo BL-algebras and their classification

On the BL Lacertae objects/radio quasars and the FRI/II dichotomy

In the frame of unification schemes for radio-loud active galactic nuclei (AGNs), FR I radio galaxies are believed to be BL Lacertae (BL Lac) objects with the relativistic jet misaligned to our line of sight, and FR II radio galaxies correspond to misaligned radio quasars. The Ledlow-Owen dividing line for FR I/FR II dichotomy in the optical absolute magnitude of host galaxy-radio luminosity (M_R-L_Rad) plane can be translated to the line in the black hole mass-jet power (M_bh-Q_jet) plane by using two empirical relations: Q_jet-L_Rad and M_bh}-M_R. We use a sample of radio quasars and BL Lac objects with measured black hole masses to explore the relation of the jet power with black hole mass, in which the jet power is estimated from the extended radio emission. It is found that the BL Lac objects are clearly separated from radio quasars by the Ledlow & Owen FR I/II dividing line in the M_bh-Q_jet plane. This strongly supports the unification schemes for FR I/BL Lac object and FR II/radio quasar. We find that the Eddington ratios L_bol/L_Edd of BL Lac objects are systematically lower than those of radio quasars in the sample with a rough division at L_bol/L_Edd 0.01, and the distribution of Eddington ratios of BL Lac objects/quasars exhibits a bimodal nature, which imply that the accretion mode of BL Lac objects may be different from that of radio quasars.Comment: 4 pages, 2 figures, accepted by ApJ

Unification of Radio Galaxies and Their Accretion/Jet Properties

We investigate the relation between black hole mass, M_bh, and jet power, Q_jet, for a sample of BL Lacs and radio quasars. We find that BL Lacs are separated from radio quasars by the FR I/II dividing line in M_bh-Q_jet plane, which strongly supports the unification scheme of FR I/BL Lac and FR II/radio quasar. The Eddington ratio distribution of BL Lacs and radio quasars exhibits a bimodal nature with a rough division at L_bol/L_Edd~0.01, which imply that they may have different accretion modes. We calculate the jet power extracted from advection dominated accretion flow (ADAF), and find that it require dimensionless angular momentum of black hole j~0.9-0.99 to reproduce the dividing line between FR I/II or BL Lac/radio quasar if dimensionless accretion rate mdot=0.01 is adopted, which is required by above bimodal distribution of Eddington ratios. Our results suggest that black holes in radio galaxies are rapidly spinning.Comment: To appear JAA in Jun

Testing the FR I/BL Lac unifying model with HST observations

Hubble Space Telescope (HST) observations provide a novel way of testing unified models for FR I radio sources and BL Lac objects. The detection of extended dust discs in some radio galaxies provides information on their jet orientation. Given this, the strength of the compact nuclear sources of FR I and BL Lacs can be compared with model predictions. As a pilot project, we selected five radio galaxies which show extended nuclear discs in the HST images. The relative orientation of the projected radio-jets and of the extended nuclear discs indicates that they are not perpendicular, as the simplest geometrical model would suggest, but that they form an angle of ~ 20 - 40 degrees with the symmetry axis of the disc: a significant change of orientation occurs between the innermost AGN structure and the kpc-scale. Nevertheless, the discs appear to be useful indicators of the radio sources orientation since the angles formed by the disc axis and the jet with the line of sight differ by only ~ 10 - 20 degrees. At the center of each disc an unresolved nuclear source is present. We compared its luminosity with the optical core luminosity of BL Lacs selected for having similar host galaxy magnitude and extended radio luminosity. The BL Lac cores are between 2 E2 and 3 E5 times brighter than the corresponding radio galaxies ones. The FR I/BL Lac core luminosity ratio shows a suggestive correlation with the orientation of the radio galaxies with respect to the line of sight. The behavior of this ratio is quantitatively consistent with a scenario in which the emission in the FR I and BL Lac is dominated by the beamed radiation from a relativistic jet with Doppler factor ~ 5 - 10, thus supporting the basic features of the proposed unification schemes.Comment: 11 pages, 10 figures, submitted to MNRAS, revised versio

Does the unification of BL Lac and FR I radio galaxies require jet velocity structures?

We explore the viability of the unification of BL Lacs and FR I radio galaxies by comparing the core emission of radio galaxies with those of BL Lacs of similar extended radio power, taking advantage of the newly measured optical nuclear luminosity of FR I sources. The spectral properties of complete samples are also studied in the radio-optical luminosity plane: starting from the Spectral Energy Distribution (SED) of BL Lacs, we calculate the predicted luminosity of FR I nuclei in the frame of a simple one--zone model, by properly taking into account the relativistic transformations. We find that the bulk Lorentz factors required by the spread in the observed luminosities in all bands are significantly smaller than those implied by other, both observational and theoretical, considerations. This discrepancy is also reflected in the fact that FR I nuclei are over-luminous by a factor of 10-10^4, with respect to the predictions, both in the radio and in the optical band. In order to reconcile these results with the unification scheme, velocity structures in the jet are suggested, where a fast spine is surrounded by a slow (but still relativistic) layer so that the emission at different angles is dominated by different velocity components: the fast one dominates the emission in BL Lacs while the slow layer dominates the emission in misaligned objects. Furthermore for the lowest luminosity BL Lacs it has to be also postulated that their beaming factor in the radio band is lower than in the optical (and X-ray), as would result from deceleration of the jet. The self-consistency of the unification model therefore requires that both intrinsic differences in the SED and different beaming properties play a substantial role in characterizing the phenomenology of these sources.Comment: 10 pages, 11 figures, revised version, to be published in A&