Fundamental Solutions and Decay of Fully Non-local Problems

In this paper, we study a fully non-local reaction-diffusion equation which is non-local both in time and space. We apply subordination principles to construct the fundamental solutions of this problem, which we use to find a representation of the mild solutions. Moreover, using techniques of Harmonic Analysis and Fourier Multipliers, we obtain the temporal decay rates for the mild solutions

Scattering in the energy space for Boussinesq equations

In this note we show that all small solutions in the energy space of the generalized 1D Boussinesq equation must decay to zero as time tends to infinity, strongly on slightly proper subsets of the space-time light cone. Our result does not require any assumption on the power of the nonlinearity, working even for the supercritical range of scattering. No parity assumption on the initial data is needed

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

Circumstellar Disks revealed by HH/KK Flux Variation Gradients

The variability of young stellar objects (YSO) changes their brightness and color preventing a proper classification in traditional color-color and color magnitude diagrams. We have explored the feasibility of the flux variation gradient (FVG) method for YSOs, using $H$ and $K$ band monitoring data of the star forming region RCW\,38 obtained at the University Observatory Bochum in Chile. Simultaneous multi-epoch flux measurements follow a linear relation $F_{H}=\alpha + \beta \cdot F_{K}$ for almost all YSOs with large variability amplitude. The slope $\beta$ gives the mean $HK$ color temperature $T_{var}$ of the varying component. Because $T_{var}$ is hotter than the dust sublimation temperature, we have tentatively assigned it to stellar variations. If the gradient does not meet the origin of the flux-flux diagram, an additional non- or less-varying component may be required. If the variability amplitude is larger at the shorter wavelength, e.g. $\alpha < 0$, this component is cooler than the star (e.g. a circumstellar disk); vice versa, if $\alpha > 0$, the component is hotter like a scattering halo or even a companion star. We here present examples of two YSOs, where the $HK$ FVG implies the presence of a circumstellar disk; this finding is consistent with additional data at $J$ and $L$. One YSO shows a clear $K$-band excess in the $JHK$ color-color diagram, while the significance of a $K$-excess in the other YSO depends on the measurement epoch. Disentangling the contributions of star and disk it turns out that the two YSOs have huge variability amplitudes ($\sim 3-5$\,mag). The $HK$ FVG analysis is a powerful complementary tool to analyze the varying components of YSOs and worth further exploration of monitoring data at other wavelengths.Comment: 5 pages, 5 figures, accepted for publication in Astronomy and Astrophysic

Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra