Thin magnetic hydrogen atmospheres and the neutron star RX J1856.5–3754

RX J1856.5–3754 is one of the brightest nearby isolated neutron stars, and considerable observational resources have been devoted to it. However, current models are unable to satisfactorily explain the data. We show that our latest models of a thin, magnetic, partially ionized hydrogen atmosphere on top of a condensed surface can fit the entire spectrum, from X-rays to optical, of RX J1856.5–3754, within the uncertainties. In our simplest model, the best-fit parameters are an interstellar column density N _H≈1×10²⁰ cm^?2 and an emitting area with R ^∞≈17 km (assuming a distance to RX J1856.5–3754 of 140 pc), temperature T ^∞≈4.3×10⁵ K, gravitational redshift z _g ～0.22, atmospheric hydrogen column y _H≈1 g cm^?2, and magnetic field B≈(3–4)×10¹² G; the values for the temperature and magnetic field indicate an effective average over the surface.     

Search for the sources of cosmic rays with energies above 10<Superscript>20</Superscript> eV

The sources of ultrahigh energy cosmic rays (UHECRs, E >10¹⁸ eV) are still unknown, mainly due to the loss of the direction to the source after the deflection of cosmic rays’ (CRs) trajectories in the galactic and extragalactic magnetic fields. With the increase in CR energy (rigidity), the influence of the magnetic field weakens; therefore, the most promising approach is to search for the sources of events with the highest energy. In our work, we expand the existing UHECR (E > 10²⁰ eV) sample from 33 to 42 events by calibrating the AUGER events. The sample is characterized by the presence of an event triplet in a circle of radius 3°. The highest-energy event is still the shower (E = 3.2 × 10²⁰ eV) detected with the Fly’s Eye fluorescent detector (FE-event) in 1993. The possible sources of the triplet and the FE-event are analyzed. Taking into account the deflection of CR trajectories in the extragalactic and galactic magnetic fields, it is shown that transient sources of the FE-event and the triplet may be galaxies with active star formation, where CRs are accelerated by newborn millisecond pulsars. Among the galactic sources, the potential candidates are young pulsars that might have had millisecond periods at birth and giant magnetar flares.     

Contribution of Cosmic Rays from Sources with a Monoenergetic Proton Spectrum to the Extragalactic Diffuse Gamma-Ray Emission

The extragalactic sources of ultra-high-energy (E > 4 × 10¹⁹ eV) cosmic rays that make a small contribution to the flux of particles recorded by ground-based arrays are discussed. We show that cosmic rays from such sources can produce a noticeable diffuse gamma-ray flux in intergalactic space compared to the the data obtained with Fermi LAT (onboard the Fermi space observatory). A possible type of active galactic nuclei (AGNs) in which cosmi-ray protons can be accelerated to energies 10²¹ eV is considered as an illustration of such sources. We conclude that ultra-high-energy cosmic rays from the AGNs being discussed can contribute significantly to the extragalactic diffuse gamma-ray emission. In addition, a constraint on the fraction of the AGNs under consideration relative to the BL Lac objects and radio galaxies has been obtained from a comparison with the Fermi LAT data.     

Cosmic ray acceleration in hypernova remnants expanding in wind bubbles of Wolf-Rayet progenitor stars

The determination of the origin of cosmic rays with observed energies in excess of 10¹⁷ eV that exceed the expected energies of cosmic rays accelerated by supernova remnants in the galaxy is a pressing problem in modern astrophysics. Hypernova remnants are one of the possible galactic sources of cosmic rays with energies of up to 10¹⁹ eV. Hypernovae constitute a class of extremely powerful supernova explosions, whose supposed progenitors are massive Wolf-Rayet stars. We analyze the special aspects of acceleration of cosmic rays in hypernova remnants that expand in wind bubbles of Wolf-Rayet progenitor stars. We show that these cosmic rays may attain maximum energies of 10¹⁸ eV even with a relatively conservative choice of acceleration parameters and account for tens of percent of the total cosmic ray flux observed in the vicinity of the earth in the energy range of 10¹⁶–10¹⁸ eV if the galactic hypernova explosion rate in the modern epoch reaches ? _S ～ 10^?4 year^?1.     

Pulsations of microwave emission and flare plasma diagnostics

We consider the modulation of nonthermal gyrosynchrotron emission from solar flares by the ballooning and radial oscillations of coronal loops. The damping mechanisms for fast magnetoacoustic modes are analyzed. We suggest a method for diagnosing the plasma of flare loops that allows their main parameters to be estimated from peculiarities of the microwave pulsations. Based on observational data obtained with the Nobeyama Radioheliograph (17 GHz) and using a technique developed for the event of May 8, 1998, we determined the particle density n≈3.7×10¹⁰ cm^?3, the temperature T≈4×10⁷ K, and the magnetic field strength B≈220 G in the region of flare energy release. A wavelet analysis for the solar flare of August 28, 1999, has revealed two main types of microwave oscillations with periods P₁≈7, 14 s and P₂≈2.4 s, which we attribute to the ballooning and radial oscillations of compact and extended flare loops, respectively. An analysis of the time profile for microwave emission shows evidence of coronal loop interaction. We determined flare plasma parameters for the compact (T≈5.3×10⁷ K, n≈4.8≈10¹⁰ cm^?3, B≈280 G) and extended (T≈2.1≈10⁷ K, n≈1.2≈10¹⁰ cm^?3, B≈160 G) loops. The results of the soft X-ray observations are consistent with the adopted model.     

Dynamics of the flows accreting onto a magnetized neutron star

We investigate the unsteady column accretion of material at a rate \(10^{15} g s^{ - 1} \leqslant \dot M \leqslant 10^{16} g s^{ - 1}\) onto the surface of a magnetized neutron star using a modified first-order Godunov method with splitting. We study the dynamics of the formation and evolution of a shock in an accretion column near the surface of a star with a magnetic field 5×10¹¹≤B≤10¹³ G. An effective transformation of the accretion flow energy into cyclotron radiation is shown to be possible for unsteady accretion with a collisionless shock whose front executes damped oscillations. The collisionless deceleration of the accreting material admits the conservation of a fraction of the heavy nuclei that have not been destroyed in spallation reactions. The fraction of the CNO nuclei that reach the stellar atmosphere is shown to depend on the magnetic field strength of the star.     

Multiyear observations of the galaxy Mk 501

Data of six-year observations of very high energy (E > 10¹¹ eV) gamma-ray flux from the active galactic nucleus Mk 501 obtained using the ground-based GT-48 telescope are analyzed and compared with the 2–10 keV X-ray data obtained using the ASM instrument onboard the RXTE satellite. A positive correlation between the average annual X-and gamma-ray fluxes is demonstrated.     

On the MOND external field effect in the solar system

In the framework of the MOdified Newtonian Dynamics (MOND), the internal dynamics of a gravitating system s embedded in a larger one S is affected by the external background field E of S even if it is constant and uniform, thus implying a violation of the Strong Equivalence Principle: it is the so-called External Field Effect (EFE). In the case of the solar system, E would be A _cen≈10^?10 m?s^?2 because of its motion through the Milky Way: it is orders of magnitude smaller than the main Newtonian monopole terms for the planets. We address here the following questions in a purely phenomenological manner: are the Sun’s planets affected by an EFE as large as 10^?10 m?s^?2? Can it be assumed that its effect is negligible for them because of its relatively small size? Does E induce vanishing net orbital effects because of its constancy over typical solar system’s planetary orbital periods? It turns out that a constant and uniform acceleration, treated perturbatively, does induce non-vanishing long-period orbital effects on the longitude of the pericenter ? of a test particle. In the case of the inner planets of the solar system and with E≈10^?10 m?s^?2, they are 4–6 orders of magnitude larger than the present-day upper bounds on the non-standard perihelion precessions \(\Delta\dot{\varpi}\) recently obtained with by E.V. Pitjeva with the EPM ephemerides in the Solar System Barycentric frame. The upper limits on the components of E are E _x ≤1×10^?15 m?s^?2, E _y ≤2×10^?16 m?s^?2, E _z ≤3×10^?14 m?s^?2. This result is in agreement with the violation of the Strong Equivalence Principle by MOND. Our analysis also holds for any other exotic modification of the current laws of gravity yielding a constant and uniform extra-acceleration. If and when other corrections \(\Delta\dot{\varpi}\) to the usual perihelion precessions will be independently estimated with different ephemerides it will be possible to repeat such a test.     

Small-scale anisotropy of cosmic rays with energies above 3×1018 eV based on data from the Yakutsk EAS facility

We analyze the directions of the arrival of cosmic rays with energies E ₀≥3×10¹⁸ eV and zenith angles θ≤45° recorded by the Yakutsk extensive air shower (EAS) facility during 1974–2000. They are shown to have a small-scale structure with scale sizes of 5°–10°. Enhanced particle fluxes compared to the expected levels for random distributions at (4–5)σ are observed from the Galactic and Supergalactic planes.     

Observations of active galactic nuclei with GT-48 gamma-ray telescope in 2007–2009

Results of observations of active galactic nuclei with the gamma-telescope GT-48 during 2007?C2009 are presented. It is shown that the very-high-energy (E > 10¹² eV) gamma radiation from galaxies 3C 66A, Mrk 421, Mrk 501, and BL Lac is variable.     

On origin of ultra high energy cosmic rays

Propagation of UHE protons through CMB radiation leaves the imprint on energy spectrum in the form of Greisen–Zatsepin–Kuzmin (GZK) cutoff, bump (pile-up protons) and dip. The dip is a feature in energy range 1×10¹⁸–4×10¹⁹ eV, caused by electron-positron pair production on CMB photons. Calculated for power-law generation spectrum with index γ _g =2.7, the shape of the dip is confirmed with high accuracy by data of Akeno—AGASA, HiRes, Yakutsk and Fly’s Eye detectors. The predicted shape of the dip is robust: it is valid for the rectilinear and diffusive propagation, for different discretenesses in the source distribution, for local source overdensity and deficit etc. This property of the dip allows us to use it for energy calibration of the detectors. The energy shift λ for each detector is determined by minimum χ ² in comparison of observed and calculated dip. After this energy calibration the absolute fluxes, measured by AGASA, HiRes and Yakutsk detectors remarkably coincide in energy region 1×10¹⁸–1×10²⁰ eV. Below the characteristic energy E _c ≈1×10¹⁸ eV the spectrum of the dip flattens for both diffusive and rectilinear propagation, and more steep galactic spectrum becomes dominant at E<E _c . The energy of transition E _tr<E _c approximately coincides with the position of the second knee E _2kn , observed in the cosmic ray spectrum. The dip-induced transition from galactic to extragalactic cosmic rays at the second knee is compared with traditional model of transition at ankle, the feature observed at energy ∼1×10¹⁹ eV.      

Ion acceleration and Alfvén wave generation at the Earth’s bow shock

The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10^?2–1 Hz and their spectral peak with a wave amplitude βB ～ B comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10^?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.     

Hydrogen atom in intense magnetic field

The structure of a hydrogen atom situated in an intense magnetic field is investigated. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength,H _a ?5×10⁹G. Fields in excess ofH _a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrödinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrödinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2×10¹⁰G and 2×10¹² G. It is found that at 2×10¹² G the lowest energy eigenvalue is changed from ?13.6 eV to about ?180 eV in agreement with previous variational computations.     

Formation of the spectrum of ultra-high-energy cosmic rays: Effect of extragalactic magnetic fields and expected contribution of individual sources

The effect of the extragalactic magnetic field on the propagation of ultra-high-energy cosmic rays (UHECRs) is investigated. We use the infrared galaxy catalog IRAS PSCz to reconstruct the magnetic field distribution in the Local Universe. The magnetic field induction is considered as a power function of the galactic infrared luminosity density: B = Kρ^β. In contrast to some earlier studies in which the exponent β = 2/3 corresponded to the freezing-in condition, the parameters K and β are estimated from the field inductions normalized by the expected maximum inductions (strong field) and minimum inductions (weak field) in galaxy clusters and voids, respectively. Maps of angular deflections of UHECRs are presented for these magnetic field models. We found that the protons with energies E > 4 × 10¹⁹ eV are not significantly deflected from their sources in a sphere with a radius of 100 Mpc only in the case of the weak magnetic field model (the deflections are comparable to the errors of modern detectors). The effect of the extragalactic magnetic field on the UHECR spectrum is investigated, with Virgo A and Arp 299 taken as potential sources.     

Local galactic field of forces and the interstellar matter

The density distributions of the two main components in interstellar hydrogen are calculated using 21 cm line data from the Berkeley Survey and the Pulkovo Survey. The narrow, dense component (state I of neutral hydrogen) has a Gaussianz-distribution with a scale-height of 50 pc in the local zones (the galactic disk). For the wide, tenuous component (hydrogen in state II) we postulate a distribution valid in the zones where such a material predominates (70 pc?z? 350 pc the galactic stratum) i.e., $$n_H \left( z \right) = n_H \left( 0 \right)exp \left( { - \left( {z/300{\text{ }}pc} \right)^{3/2} } \right).$$ Similar components are found in the dust distribution and in the available stellar data reaching sufficiently highz-altitudes. The scale-heights depend on the stellar type: the stratum in M III stars is considerably wider than in A stars (500–700 pc against 300 pc). The gas to dust ratio is approximately the same in both components: 0.66 atom cm^?3 mag^?1 kpc in the galactic plane. A third state of the gas is postulated associating it the observed free electron stratum at a scale-height of 660 pc (hydrogen fully ionized at high temperatures). The ratio between the observed dispersions in neutral hydrogen (thermal width plus turbulence) and the total dispersions corresponding to the real inner energies in the medium is obtained by a comparison with the dispersion distribution σ(z) of the different stellar types associated with the disk and the stratum $$\sigma ^2 \left( {total} \right) = \sigma ^2 \left( {21{\text{ cm line}}} \right) \cdot {\text{ }}Q^2 ,$$ from which we graphically obtainedQ ²=2.9 ± 0.3, although that number could be lower in the densest parts of the spiral arms. Its dependence on magnetic field and cosmic rays is analysed, indicating equipartition of the different energy components in the interstellar medium and consistency with the observed values of the magnetic field: i.e., fluctuations with an average of ～ 3 μG (associated with the disk) in a homogeneous background of ～ 1 μG (associated with the stratum). A minimum and maximumK _z-force are obtained assuming extreme conditions for the total density distribution (gas plus stars). TheK _z-force obtained from the interstellar gas in its different states using approximations of the Boltzmann equation is a reasonable intermediate case between maximum and minimumK _z. The mass density obtained in the galactic plane is 0.20±0.05M _⊙ pc^?3, and the results indicate that the galactic disk is somewhat narrower and denser than has usually been believed. The effects of wave-like distributions of matter in thez-coordinate are analysed in relation with theK _z-force, and comparisons with theoretical results are performed. A qualitative model for the galactic field of force is postulated together with a classification of the different zones of the Galaxy according to their observed ranges in velocity dispersions and the behaviour of the potential well at differentz-altitudes. The disk containing at least two-thirds of the total mass atz<100 pc, the stratum containing one-third or less of the total mass atz≤600–800 pc, and the halo at higherz-altitudes with a small fraction of such a mass which is difficult to evaluate.     

The effects of ultra-strong magnetic fields on electron capture rates for iron group nuclei in the outer crust of magnetars

Based on the work of Wang et al. (Chin. Phys. Lett. 29:049701, 2012), we re-investigated electron capture on iron group nuclei in the outer crust of magnetars and studied magnetar evolution. Effects of ultra-strong magnetic field on electron capture rates for ⁵⁷Co have been analyzed in the nuclear shell model and under the Landau-level-quantization approximation, and the electron capture rates and the neutrino energy loss rates on iron group nuclei in the outer crust of magnetar have been calculated. The results show that electron capture rates on ⁵⁷Co are increase greatly in the ultra-strong magnetic field, and above 3 orders of magnitude generally; and the neutrino energy loss rates by electron capture on iron group nuclei increase above 3 orders of magnitude in the range from B=4.414×10¹³ G to B=4.414×10¹⁵ G. These conclusions play an important role in future studying the evolution of magnetar. Furthermore, we modify the expressions of the electron chemical potential (Fermi energy) and phase space factor by introducing Dirac δ-function, and select appropriate parameters of temperature T, magnetic field B and matter density ρ in the our crust, thus our results will be reliable than those of Wang et al.     

Magnetic field decay of magnetars in supernova remnants

In this paper, we modify our previous research carefully, and derive a new expression of electron energy density in superhigh magnetic fields. Based on our improved model, we re-compute the electron capture rates and the magnetic fields’ evolutionary timescales t of magnetars. According to the calculated results, the superhigh magnetic fields may evolve on timescales ～(10⁶?10⁷) yrs for common magnetars, and the maximum timescale of the field decay, t≈2.9507×10⁶ yrs, corresponding to an initial internal magnetic field B ₀=3.0×10¹⁵ G and an initial inner temperature T ₀=2.6×10⁸ K. Motivated by the results of the neutron star-supernova remnant (SNR) association of Zhang and Xie (2011), we calculate the maximum B ₀ of magnetar progenitors, B _max～(2.0×10¹⁴?2.93×10¹⁵) G when T ₀=2.6×10⁸ K. When T ₀～2.75×10⁸?1.75×10⁸ K, the maximum B ₀ will also be in the range of ～10¹⁴?10¹⁵ G, not exceeding the upper limit of magnetic field of a magnetar under our magnetar model. We also investigate the relationship between the spin-down ages of magnetars and the ages of their SNRs, and explain why all AXPs associated with SNRs look older than their real ages, whereas all SGRs associated with SNRs appear younger than they are.     

Influence of the Variations of Current Sheet Parameters on the Acceleration of Electrons

By the test particle method, we have investigated the kinematic characteristics of the electrons in the reconnecting current sheet with a guiding magnetic field B_z after they are accelerated by the supper-Dreicer electric field E_z. Firstly, the influence of the guiding magnetic field B_z on the particle acceleration is discussed under the assumption that B_z is constant in magnitude but different in orientation with respect to the electric field. In this case, the variation of the B_z direction directly leads to the variation of electron trajectories and makes electrons leave the current sheet along different paths. If B_z is parallel to E_z, the pitch angles of the accelerated electrons are close to 180°. If B_z is anti-parallel to E_z, the pitch angles of the accelerated electrons are close to 0°. The orientation of the guiding magnetic field just makes the electric field accelerate selectively the electrons in different regions, but does not change the energy distribution of electrons, and the finally derived energy spectrum is the common power-law spectrum E^?γ. In typical coronal conditions, γ is about 2.9. The further study indicates that the magnitude of γ depends on the strengths of the guiding magnetic field and reconnecting electric field, as well as the scale of the current sheet. Then, the kinematic characteristics of the accelerated electrons in the current sheet with multiple X-points and O-points are also studied. The result indicates that the existences of the X-points and O-points have the particles constrained in the accelerating region to obtain the maximum acceleration, and the final energy spectrum has the characteristics of multi-power law spectra.     

The solar modulation of electrons in the heliosphere

The propagation and modulation of electrons in the heliosphere play an important part in improving our understanding and assessment of the modulation processes. A full three-dimensional numerical model is used to study the modulation of galactic electrons, from Earth into the inner heliosheath, over an energy range from 10 MeV to 30 GeV. The modeling is compared with observations of 6–14 MeV electrons from Voyager 1 and observations at Earth from the PAMELA mission. Computed spectra are shown at different spatial positions. Based on comparison with Voyager 1 observations, a new local interstellar electron spectrum is calculated. We find that it consists of two power-laws: In terms of kinetic energy E, the results give E ^?1.5 below ～500 MeV and E ^?3.15 at higher energies. Radial intensity profiles are computed also for 12 MeV electrons, including a Jovian source, and compared to the 6–14 MeV observations from Voyager 1. Since the Jovian and galactic electrons can be separated in the model, we calculate the intensity of galactic electrons below 100 MeV at Earth. The highest possible differential flux of galactic electrons at Earth with E=12 MeV is found to have a value of 2.5×10^?1 electrons m^?2?s^?1?sr^?1?MeV^?1 which is significantly lower (a factor of 3) than the Jovian electron flux at Earth. The model can also reproduce the extraordinary increase of electrons by a factor of 60 at 12 MeV in the inner heliosheath. A lower limit for the local interstellar spectrum at 12 MeV is estimated to have a value of (90±10) electrons m^?2?s^?1?sr^?1?MeV^?1.     

Ballistic and diffusive components in the dynamic spectra of ultrahigh energy cosmic rays from nearby transient sources

Ultrahigh energy cosmic rays (UHECRs, E > 10¹⁸ eV) from extragalactic sources deviate in the galactic and intergalactic magnetic fields, which explains the diffusive character of their propagation, the isotropization of their total flux, and the absence of UHECR clusters associated with individual sources. Extremely high energy cosmic rays (E > 10^19.7 eV) are scattered mainly in localized magnetized structures, such as galaxy clusters, filaments, etc., with a mean free path of tens of megaparsecs; therefore, in the case of nearby transient sources, a substantial contribution to the observed flux is expected from unscattered and weakly scattered particles, which may be a decisive factor in the identification of these sources. We propose a method for calculating the time evolution of the UHECR energy spectra based on analytical solutions of the transport equation with the explicit determination of the contributions from scattered and unscattered particles. As examples, we consider the cases of transient activity of the nearest active galactic nucleus, Centaurus A, and the acceleration of UHECRs by a young millisecond pulsar.