Photometric reverberation mapping of 3C120

We present the results of a five month monitoring campaign of the local active galactic nuclei (AGN) 3C120. Observations with a median sampling of two days were conducted with the robotic 15cm telescope VYSOS-6 located near Cerro Armazones in Chile. Broad band (B,V) and narrow band (NB) filters were used in order to measure fluxes of the AGN and the H_beta broad line region (BLR) emission line. The NB flux is constituted by about 50% continuum and 50% H_beta emission line. To disentangle line and continuum flux, a synthetic H_beta light curve was created by subtracting a scaled V-band light curve from the NB light curve. Here we show that the H_beta emission line responds to continuum variations with a rest frame lag of 23.6 +/- 1.69 days. We estimate a virial mass of the central black hole M_BH = 57 +/- 27 * 10^6 solar masses, by combining the obtained lag with the velocity dispersion of a single contemporaneous spectrum. Using the flux variation gradient (FVG) method, we determined the host galaxy subtracted rest frame 5100A luminosity at the time of our monitoring campaign with an uncertainty of 10% (L_AGN = 6.94 +/- 0.71* 10^43 ergs^-1). Compared with recent spectroscopic reverberation results, 3C120 shifts in the R_BLR - L_AGN diagram remarkably close to the theoretically expected relation of R-L^0.5. Our results demonstrate the performance of photometric AGN reverberation mapping, in particular for efficiently determining the BLR size and the AGN luminosityComment: 11 pages, 11 figures, Published in Astronomy and Astrophysic

Modelling photometric reverberation data -- a disk-like broad-line region and a potentially larger black hole mass for 3C120

We consider photometric reverberation mapping, where the nuclear continuum variations are monitored via a broad-band filter and the echo of emission line clouds of the broad line region (BLR) is measured with a suitable narrow-band (NB) filter. We investigate how an incomplete emission-line coverage by the NB filter influences the BLR size determination. This includes two basic cases: 1) a symmetric cut of the blue and red part of the line wings, and 2) the filter positioned asymmetrically to the line centre so that essentially a complete half of the emission line is contained in the NB filter. Under the assumption that the BLR size is dominated by circular Keplerian orbits, we find that symmetric cutting of line wings may lead to overestimating the BLR size by less than 5%. The case of asymmetric half-line coverage, similar as for our data of the Seyfert 1 galaxy 3C120, yields the BLR size with a bias of less than 1%. Our results suggest that any BLR size bias due to narrow-band line cut in photometric reverberation mapping is small and in most cases negligible. We used well sampled photometric reverberation mapping light curves with sharp variation features in both the continuum and the Hbeta light curves to determine the geometry type of the Hbeta BLR for 3C120. Modelling of the light curve, under the assumption that the BLR is essentially virialised, argues against a spherical geometry and favours a nearly face-on disk-like geometry with inclination i = 10 +/- 4 deg and extension from 22 to 28 light days. The low inclination may lead to a larger black hole mass than the derived when using the average geometry scaling factor f=5.5. We discuss deviations of Seyfert 1 galaxies from the M_BH - sigma relation.Comment: 9 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio

Writhe of center vortices and topological charge -- an explicit example

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.Comment: 33 latex pages, 10 figures incorporating 14 ps files. Furthermore, the time evolution of the vortex line discussed in this work can be viewed as a gif movie, available for download by following the PostScript link below -- watch for the cute feature at the self-intersection poin

Size and disk-like shape of the broad-line region of ESO399-IG20

We present photometric reverberation mapping of the narrow-line Seyfert 1 galaxy ESO399-IG20 performed with the robotic 15 cm telescope VYSOS-6 at the Cerro Armazones Observatory. Through the combination of broad- and narrow-band filters we determine the size of the broad-line emitting region (BLR) by measuring the time delay between the variability of the continuum and the H_alpha emission line. We use the flux variation gradient method to separate the host galaxy contribution from that of the active galactic nucleus (AGN), and to calculate the 5100A luminosity L_AGN of the AGN. Both measurements permit us to derive the position of ESO399-IG20 in the BLR size -- AGN luminosity R_BLR-L_AGN^0.5 diagram. We infer the basic geometry of the BLR through modelling of the light curves. The pronounced sharp variability patterns in both the continuum and the emission line light curves allow us to reject a spherical BLR geometry. The light curves are best fitted by a disk-like BLR seen nearly face-on with an inclination angle of 6+/-3 degrees and with an extension from 16 to 20 light days.Comment: 9 pages, 13 figures, Published in Astronomy and Astrophysic

Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge

Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in the Maximal Abelian Gauge are discussed. These condensates turn out to be related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.

A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions

Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for publication in the EPJ

Level spacings for weakly asymmetric real random matrices and application to two-color QCD with chemical potential

We consider antisymmetric perturbations of real symmetric matrices in the context of random matrix theory and two-color quantum chromodynamics. We investigate the level spacing distributions of eigenvalues that remain real or become complex conjugate pairs under the perturbation. We work out analytical surmises from small matrices and show that they describe the level spacings of large random matrices. As expected from symmetry arguments, these level spacings also apply to the overlap Dirac operator for two-color QCD with chemical potential.Comment: 23 pages, 6 figures, 1 animation; minor corrections, references added, as published in JHE

The history of Shtokman field development

Let's twist again! The first highly enantioselective asymmetric reaction in which a chiral reaction medium is the sole source of chirality is presented. The aza‐Baylis–Hillman reaction in an ionic liquid with a chiral anion, whose design is based on mechanistic insights, gave products with up to 84 % ee

On topological charge carried by nexuses and center vortices

In this paper we further explore the question of topological charge in the center vortex-nexus picture of gauge theories. Generally, this charge is locally fractionalized in units of 1/N for gauge group SU(N), but globally quantized in integral units. We show explicitly that in d=4 global topological charge is a linkage number of the closed two-surface of a center vortex with a nexus world line, and relate this linkage to the Hopf fibration, with homotopy $\Pi_3(S^3)\simeq Z$; this homotopy insures integrality of the global topological charge. We show that a standard nexus form used earlier, when linked to a center vortex, gives rise naturally to a homotopy $\Pi_2(S^2)\simeq Z$, a homotopy usually associated with 't Hooft-Polyakov monopoles and similar objects which exist by virtue of the presence of an adjoint scalar field which gives rise to spontaneous symmetry breaking. We show that certain integrals related to monopole or topological charge in gauge theories with adjoint scalars also appear in the center vortex-nexus picture, but with a different physical interpretation. We find a new type of nexus which can carry topological charge by linking to vortices or carry d=3 Chern-Simons number without center vortices present; the Chern-Simons number is connected with twisting and writhing of field lines, as the author had suggested earlier. In general, no topological charge in d=4 arises from these specific static configurations, since the charge is the difference of two (equal) Chern-Simons number, but it can arise through dynamic reconnection processes. We complete earlier vortex-nexus work to show explicitly how to express globally-integral topological charge as composed of essentially independent units of charge 1/N.Comment: Revtex4; 3 .eps figures; 18 page