Cross-spectral analysis of the X-ray variability of Mrk 421

Using the cross-spectral method, we confirm the existence of the X-ray hard lags discovered with cross-correlation function technique during a large flare of Mrk 421 observed with BeppoSAX . For the 0.1--2 versus 2--10keV light curves, both methods suggest sub-hour hard lags. In the time domain, the degree of hard lag, i.e., the amplitude of the 3.2--10 keV photons lagging the lower energy ones, tends to increase with the decreasing energy. In the Fourier frequency domain, by investigating the cross-spectra of the 0.1--2/2--10 keV and the 2--3.2/3.2--10 keV pairs of light curves, the flare also shows hard lags at the lowest frequencies. However, with the present data, it is impossible to constrain the dependence of the lags on frequencies even though the detailed simulations demonstrate that the hard lags at the lowest frequencies probed by the flare are not an artifact of sparse sampling, Poisson and red noise. As a possible interpretation, the implication of the hard lags is discussed in the context of the interplay between the (diffusive) acceleration and synchrotron cooling of relativistic electrons responsible for the observed X-ray emission. The energy-dependent hard lags are in agreement with the expectation of an energy-dependent acceleration timescale. The inferred magnetic field (B ~ 0.11 Gauss) is consistent with the value inferred from the Spectral Energy Distributions of the source. Future investigations with higher quality data that whether or not the time lags are energy-/frequency-dependent will provide a new constraint on the current models of the TeV blazars.Comment: 11 pages, 6 figures, accepted by MNRA

Three dimensional imaging of short pulses

We exploit a slightly noncollinear second-harmonic cross-correlation scheme to map the 3D space-time intensity distribution of an unknown complex-shaped ultrashort optical pulse. We show the capability of the technique to reconstruct both the amplitude and the phase of the field through the coherence of the nonlinear interaction down to a resolution of 10 $\mu$m in space and 200 fs in time. This implies that the concept of second-harmonic holography can be employed down to the sub-ps time scale, and used to discuss the features of the technique in terms of the reconstructed fields.Comment: 16 pages, 6 figure

Nonlinear space-time dynamics of ultrashort wave packets in water

We have monitored the space\u2013time transformation of a 150-fs pulse undergoing self-focusing and filamentation in water, by means of the nonlinear gating technique. We have observed that pulse splitting and subsequent recombination apply to axial temporal intensity only, whereas the space-integrated pulse profile preserves its original shape