Possible evolution of dim radio quiet neutron star 1E 1207.4-5209 based on a B-decay model

Dim radio-quiet neutron star (DRQNS) 1E 1207.4-5209 is one of the most heavily examined isolated neutron stars. Wide absorption lines were observed in its spectrum obtained by both XMM-Newton and Chandra X-ray satellites. These absorption lines can be interpreted as a principal frequency centered at 0.7 keV and its harmonics at 1.4, 2.1 and possibly 2.8 keV. The principal line can be formed by resonant proton cyclotron scattering leading to a magnetic field which is two orders of magnitude larger than the perpendicular component of the surface dipole magnetic field (B) found from the rotation period (P) and the time rate of change in the rotation period (\.{P}) of 1E 1207.4-5209. Besides, age of the supernova remnant (SNR) G296.5+10.0 which is physically connected to 1E 1207.4-5209 is two orders of magnitude smaller than the characteristic age ($\tau$=P/2\.{P}) of the neutron star. These huge differences between the magnetic field values and the ages can be explained based on a B-decay model. If the decay is assumed to be exponential, the characteristic decay time turns out to be several thousand years which is three orders of magnitude smaller than the characteristic decay time of radio pulsars represented in an earlier work. The lack of detection of radio emission from DRQNSs and the lack of point sources and pulsar wind nebulae in most of the observed SNRs can also be partly explained by such a very rapid exponential decay. The large difference between the characteristic decay times of DRQNSs and radio pulsars must be related to the differences in the magnetic fields, equation of states and masses of these isolated neutron stars.Comment: 13 pages, 1 figur

Early phases of different types of isolated neutron star

Two Galactic isolated strong X-ray pulsars seem to be in the densest environments compared to other types of Galactic pulsar. X-ray pulsar J1846-0258 can be in an early phase of anomalous X-ray pulsars and soft gamma repeaters if its average braking index is ~1.8-2.0. X-ray pulsar J1811-1925 must have a very large average braking index (n~11) if this pulsar was formed by SN 386AD. This X-ray pulsar can be in an early phase of evolution of the radio pulsars located in the region P~50-150 ms and \.{P}~10$^{-14}-10^{-16}$ s/s of the P-\.{P} diagram. X-ray/radio pulsar J0540-69 seems to be evolving in the direction to the dim isolated thermal neutron star region on the P-\.{P} diagram. Possible progenitors of different types of neutron star are also discussed.Comment: to appear in the International Journal of Modern Physics

Effects of the background radiation on radio pulsar and supernova remnant searches and the birth rates of these objects

In different directions of the Galaxy the Galactic background radio radiation and radiation of complex star formation regions which include large number of OB associations have different influences on radio pulsar (PSR) and supernova remnant (SNR) searches. In this work we analyse the effects of these background radiations on the observations of PSRs at 1400 MHz and SNRs at 1000 MHz. In the interval l=0$^o$$\pm60^o$ the PSRs with flux F$_{1400}$$>$0.2 mJy and the SNRs with surface brightness $\Sigma$$>10^{-21}$ Wm$^{-2}$Hz$^{-1}$sr$^{-1}$ are observable for all values of l and b. All the SNRs with $\Sigma$$>3\times10^{-22}$ Wm$^{-2}$Hz$^{-1}$sr$^{-1}$ can be observed in the interval 60$^o$$<$l$<300^o$. We have examined samples of PSRs and SNRs to estimate the birth rates of these objects in the region up to 3.2 kpc from the Sun and also in the Galaxy. The birth rate of PSRs is about one in 200 years and the birth rate of SNRs is about one in 65 years in our galaxy.Comment: revised versio

Sturm-Liouville operators on time scales

We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have been obtained by various authors in the past.Comment: 12 page

Synoptic Sky Surveys and the Diffuse Supernova Neutrino Background: Removing Astrophysical Uncertainties and Revealing Invisible Supernovae

The cumulative (anti)neutrino production from all core-collapse supernovae within our cosmic horizon gives rise to the diffuse supernova neutrino background (DSNB), which is on the verge of detectability. The observed flux depends on supernova physics, but also on the cosmic history of supernova explosions; currently, the cosmic supernova rate introduces a substantial (+/-40%) uncertainty, largely through its absolute normalization. However, a new class of wide-field, repeated-scan (synoptic) optical sky surveys is coming online, and will map the sky in the time domain with unprecedented depth, completeness, and dynamic range. We show that these surveys will obtain the cosmic supernova rate by direct counting, in an unbiased way and with high statistics, and thus will allow for precise predictions of the DSNB. Upcoming sky surveys will substantially reduce the uncertainties in the DSNB source history to an anticipated +/-5% that is dominated by systematics, so that the observed high-energy flux thus will test supernova neutrino physics. The portion of the universe (z < 1) accessible to upcoming sky surveys includes the progenitors of a large fraction (~ 87%) of the expected 10-26 MeV DSNB event rate. We show that precision determination of the (optically detected) cosmic supernova history will also make the DSNB into a strong probe of an extra flux of neutrinos from optically invisible supernovae, which may be unseen either due to unexpected large dust obscuration in host galaxies, or because some core-collapse events proceed directly to black hole formation and fail to give an optical outburst.Comment: 11 pages, 6 figure

An integrable discretization of KdV at large times

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.Comment: 12 page

Approximation of the Sections of the Set of Trajectories of the Control System Described by a Nonlinear Volterra Integral Equation

Approximation of the sections of the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. The admissible control functions are chosen from the closed ball of the space Lp, p > 1, with radius µ and centered at the origin. The set of admissible control functions is replaced by the set of control functions, which includes a finite number of control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of control functions

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

Mimicking diffuse supernova antineutrinos with the Sun as a source

Measuring the electron antineutrino component of the cosmic diffuse supernova neutrino background (DSNB) is the next ambitious goal for low-energy neutrino astronomy. The largest flux is expected in the lowest accessible energy bin. However, for E < 15 MeV a possible signal can be mimicked by a solar electron antineutrino flux that originates from the usual 8B neutrinos by spin-flavor oscillations. We show that such an interpretation is possible within the allowed range of neutrino electromagnetic transition moments and solar turbulent field strengths and distributions. Therefore, an unambiguous detection of the DSNB requires a significant number of events at E > 15 MeV.Comment: 4 pages, 1 figur