Quantitative comparison of filtering methods in lattice QCD

We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all these methods, when handled with care, reveal very similar topological structures. Hence, these common structures are free of ambiguities and faithfully represent infrared degrees of freedom in the QCD vacuum. As an application we discuss an interesting power-law for the clusters of filtered topological charge.Comment: 6 pages, 18 plots in 5 figures; final version as published in EPJ A; section 4 was adde

Laplacian modes probing gauge fields

We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.Comment: 43 pages, 26 figure

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

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

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

Doubly Periodic Instanton Zero Modes

Fermionic zero modes associated with doubly periodic SU(2) instantons of unit charge are considered. In cases where the action density exhibits two `instanton cores' the zero mode peaks on one of four line-segments joining the two constituents. Which of the four possibilities is realised depends on the fermionic boundary conditions; doubly periodic, doubly anti-periodic or mixed.Comment: 12 pages, 4 figure

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