Radio/gamma-ray time delay in the parsec-scale cores of active galactic nuclei

We report the detection of a non-zero time delay between radio emission measured by the VLBA at 15.4 GHz and gamma-ray radiation (gamma-ray leads radio) registered by the Large Area Telescope (LAT) on board the Fermi Gamma-Ray Space Telescope for a sample of 183 radio and gamma-ray bright active galactic nuclei (AGNs). For the correlation analysis we used 100 MeV - 100 GeV gamma-ray photon fluxes, taken from monthly binned measurements from the first Fermi LAT catalog, and 15.4 GHz radio flux densities from the MOJAVE VLBA program. The correlation is most pronounced if the core flux density is used, strongly indicating that the gamma-ray emission is generated within the compact region of the 15 GHz VLBA core. Determining the Pearson's r and Kendall's tau correlation coefficients for different time lags, we find that for the majority of sources the radio/gamma-ray delay ranges from 1 to 8 months in the observer's frame and peaks at about 1.2 months in the source's frame. We interpret the primary source of the time delay to be synchrotron opacity in the nuclear region.Comment: 5 pages, 2 figures, 2 tables, accepted by the Astrophysical Journal Letters; minor corrections to the text are made; full table 1 in electronic form can be extracted from the preprint sourc

Sharp distortion growth for bilipschitz extension of planar maps

This note addresses the quantitative aspect of the bilipschitz extension problem. The main result states that any bilipschitz embedding of $\mathbb R$ into $\mathbb R^2$ can be extended to a bilipschitz self-map of $\mathbb R^2$ with a linear bound on the distortion.Comment: 9 pages. Slightly expanded introduction, added reference