Statistical evaluation of the flux cross-calibration of the XMM-Newton EPIC cameras

The second XMM-Newton serendipitous source catalogue, 2XMM, provides the ideal data base for performing a statistical evaluation of the flux cross-calibration of the XMM-Newton European Photon Imaging Cameras (EPIC). We aim to evaluate the status of the relative flux calibration of the EPIC cameras on board XMM-Newton (MOS1, MOS2, and pn) and investigate the dependence of the calibration on energy, position in the field of view of the X-ray detectors, and lifetime of the mission. We compiled the distribution of flux percentage differences for large samples of 'good quality' objects detected with at least two of the EPIC cameras. The mean offset of the fluxes and dispersion of the distributions was then found by Gaussian fitting. Count rate to flux conversion was performed with a fixed spectral model. The impact on the results of varying this model was investigated. Excellent agreement was found between the two EPIC MOS cameras to better than 4% from 0.2 keV to 12.0 keV. MOS cameras register 7-9% higher flux than pn below 4.5 keV and 10-13% flux excess above 4.5 keV. No evolution of the flux ratios is seen with time, except at energies below 0.5 keV, where we found a strong decrease in the MOS to pn flux ratio with time. This effect is known to be due to a gradually degrading MOS redistribution function. The flux ratios show some dependence on distance from the optical axis in the sense that the MOS to pn flux excess increases with off-axis angle. Furthermore, in the 4.5-12.0 keV band there is a strong dependence of the MOS to pn excess flux on the azimuthal-angle. These results strongly suggest that the calibration of the Reflection Grating Array (RGA) blocking factors is incorrect at high energies. Finally, we recommend ways to improve the calculation of fluxes in future versions of XMM-Newton source catalogues.Comment: 11 pages, 10 figures, 3 tables. Abridged Abstract. Accepted for publication in Astronomy and Astrophysic

Perfectly invisible PT\mathcal{PT}-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry

We investigate a special class of the $\mathcal{PT}$-symmetric quantum models being perfectly invisible zero-gap systems with a unique bound state at the very edge of continuous spectrum of scattering states. The family includes the $\mathcal{PT}$-regularized two particle Calogero systems (conformal quantum mechanics models of de Alfaro-Fubini-Furlan) and their rational extensions whose potentials satisfy equations of the KdV hierarchy and exhibit, particularly, a behaviour typical for extreme waves. We show that the two simplest Hamiltonians from the Calogero subfamily determine the fluctuation spectra around the $\mathcal{PT}$-regularized kinks arising as traveling waves in the field-theoretical Liouville and $SU(3)$ conformal Toda systems. Peculiar properties of the quantum systems are reflected in the associated exotic nonlinear supersymmetry in the unbroken or partially broken phases. The conventional $\mathcal{N}=2$ supersymmetry is extended here to the $\mathcal{N}=4$ nonlinear supersymmetry that involves two bosonic generators composed from Lax-Novikov integrals of the subsystems, one of which is the central charge of the superalgebra. Jordan states are shown to play an essential role in the construction.Comment: 33 pages; comments and refs added, version to appear in JHE

General Criterion for the existence of Supertube and BIon in Curved Target Space

The supertube and BIon spike solutions are examined in a general curved target space. The criteria for the existence of these solutions are explicitly derived. Also the equation which the general BIon solution should satisfy is derived.Comment: 12 pages, no figur

Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study

We investigate anticipated synchronization between two periodically driven deterministic, dissipative inertia ratchets that are able to exhibit directed transport with a finite velocity. The two ratchets interact through an unidirectional delay coupling: one is acting as a master system while the other one represents the slave system. Each of the two dissipative deterministic ratchets is driven externally by a common periodic force. The delay coupling involves two parameters: the coupling strength and the (positive-valued) delay time. We study the synchronization features for the unbounded, current carrying trajectories of the master and the slave, respectively, for four different strengths of the driving amplitude. These in turn characterize differing phase space dynamics of the transporting ratchet dynamics: regular, intermittent and a chaotic transport regime. We find that the slave ratchet can respond in exactly the same way as the master will respond in the future, thereby anticipating the nonlinear directed transport

ac-driven Brownian motors: a Fokker-Planck treatment

We consider a primary model of ac-driven Brownian motors, i.e., a classical particle placed in a spatial-time periodic potential and coupled to a heat bath. The effects of fluctuations and dissipations are studied by a time-dependent Fokker-Planck equation. The approach allows us to map the original stochastic problem onto a system of ordinary linear algebraic equations. The solution of the system provides complete information about ratchet transport, avoiding such disadvantages of direct stochastic calculations as long transients and large statistical fluctuations. The Fokker-Planck approach to dynamical ratchets is instructive and opens the space for further generalizations

Supersphere

The spherical D2-brane solution is obtained without RR external background. The solution is shown to preserve $(1/4)$ supersymmetries. The configurations obtained depend on the integration constant $R_0$. For $R_0 \neq 0$ the shape of the solution is a deformed sphere. When, however, $R_0 = 0$, the D2-brane system seems to exhibit a brane-anti-brane configuration.Comment: 11 pages, 2 figure