Hypergeometric solutions to Schr\"odinger equations for the quantum Painlev\'e equations

We consider Schr\"odinger equations for the quantum Painlev\'e equations. We present hypergeometric solutions of the Schr\"odinger equations for the quantum Painlev\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\"odinger equations for the quantum Painlev\'e equations and those of the KZ equation or the confluent KZ equations.Comment: 17 pages; Journal of Mathematical Physics (Vol.52, Issue 8) 201

Polarized emission from strongly magnetized sources

Anomalous X-ray pulsars (AXPs) and Soft gamma repeaters (SGRs) form together a single class of astrophysical sources, commonly associated to magnetars. New-generation X-ray polarimeters will play a key role in assessing the nature of these sources by directly probing the star magnetic field. In the highly magnetized environment radiation is expected to be strongly polarized and such a measure will be easily within reach of IXPE and eXTP. Polarization measurements will eventually confirm the presence of ultra-strong magnetic fields, probing the magnetar scenario. In this work we will discuss theoretical expectations for the polarization signature of AXPs and SGRs and present numerical simulations for the detector response of the polarimeters currently under construction. We will also show how these sources can be used to test vacuum birefringence, a QED effect predicted by Heisemberg and Euler in the Thirties and not experimentally verified as yet

Importance of Compton scattering to radiation spectra of isolated neutron stars

Model atmospheres of isolated neutron stars with low magnetic field are calculated with Compton scattering taking into account. Models with effective temperatures 1, 3 and 5 MK, with two values of surface gravity log(g)g = 13.9 and 14.3), and different chemical compositions are calculated. Radiation spectra computed with Compton scattering are softer than the computed with Thomson scattering at high energies (E > 5 keV) for hot (T_eff > 1 MK) atmospheres with hydrogen-helium composition. Compton scattering is more significant to hydrogen models with low surface gravity. The emergent spectra of the hottest (T_eff > 3 MK) model atmospheres can be described by diluted blackbody spectra with hardness factors ~ 1.6 - 1.9. Compton scattering is less important for models with solar abundance of heavy elements.Comment: Proceedings of the 363. WE-Heraeus Seminar on: Neutron Stars and Pulsars (Posters and contributed talks) Physikzentrum Bad Honnef, Germany, May.14-19, 2006, eds. W.Becker, H.H.Huang, MPE Report 291, pp.173-17

Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation

We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.Comment: 13 pages, 3 figure

On the compactness of the isolated neutron star RX J0720.4-3125

The data from all observations of RX J0720.4-3125 conducted by XMM-Newton EPIC-pn with the same instrumental setup in 2000-2012 were reprocessed to form a homogenous data set of solar barycenter corrected photon arrival times registered from RX J0720.4-3125. A Bayesian method for the search, detection, and estimation of the parameters of an unknown-shaped periodic signal was employed as developed by Gregory & Loredo (1992). A number of complex models (single and double peaked) of light curves from pulsating neutron stars were statistically analyzed. The distribution of phases for the registered photons was calculated by folding the arrival times with the derived spin-period and the resulting distribution of phases approximated with a mixed von Mises distribution, and its parameters were estimated by using the Expected Maximization method. Spin phase-resolved spectra were extracted, and a number of highly magnetized atmosphere models of an INS were used to fit simultaneously, the results were verified via an MCMC approach. The phase-folded light curves in different energy bands with high S/N ratio show a high complexity and variations depending on time and energy. They can be parameterized with a mixed von Mises distribution, i.e. with double-peaked light curve profile showing a dependence of the estimated parameters (mean directions, concentrations, and proportion) upon the energy band, indicating that radiation emerges from at least two emitting areas. The genuine spin-period of the isolated neutron star RX J0720-3125 derived as more likely is twice of that reported in the literature (16.78s instead of 8.39s). The gravitational redshift of RX J0720.4-3125 was determined to $z=0.205_{-0.003}^{+0.006}$ and the compactness was estimated to $(M/M_{Sun})/R(km)=0.105 \pm 0.002$.Comment: Comments: 19 pages, 15 figures and 5 tables, Astronomy and Astrophysics accepted. arXiv admin note: text overlap with arXiv:1108.389

Theoretical And Experimental Studies Of Collision-Induced Electronic Energy Transfer From v=0-3 Of The E(0g+) Ion-Pair State Of Br2: Collisions With He And Ar

Collisions of Br(2), prepared in the E(0(g)(+)) ion-pair (IP) electronic state, with He or Ar result in electronic energy transfer to the D, D(\u27), and beta IP states. These events have been examined in experimental and theoretical investigations. Experimentally, analysis of the wavelength resolved emission spectra reveals the distribution of population in the vibrational levels of the final electronic states and the relative efficiencies of He and Ar collisions in promoting a specific electronic energy transfer channel. Theoretically, semiempirical rare gas-Br(2) potential energy surfaces and diabatic couplings are used in quantum scattering calculations of the state-to-state rate constants for electronic energy transfer and distributions of population in the final electronic state vibrational levels. Agreement between theory and experiment is excellent. Comparison of the results with those obtained for similar processes in the IP excited I(2) molecule points to the general importance of Franck-Condon effects in determining vibrational populations, although this effect is more important for He collisions than for Ar collisions