Effect of superstrong magnetic fields on thermonuclear reaction rates on the surface of magnetars

A simple and efficient screening model for studying the effects of superstrong magnetic fields （such as those of magnetars） on thermonuclear reaction rates on magnetar surfaces is proposed in this paper. The most interesting thermonuclear reactions, including hydrogen burning by the CNO cycle and helium burning by the triple alpha reaction, are investigated on the surface ofmagnetars. We find that the superstrong magnetic fields can increase the thermonuclear reaction rates by many orders of magnitude. The enhancement may have a dramatic effect on the thermonuclear runaways and bursts on the surfaces of magnetars.     

Screened Thermonuclear Reaction Rates on Magnetar Surfaces

Improving Salpeter＇s method, we discuss the effect of superstrong magnetic fields （such as those of magnetars） on thermonuclear reaction rates. These most interesting reactions, including the hydrogen burning by the CNO cycle and the helium burning by the triple alpha reaction, are investigated as examples on the magnetar surfaces. The obtained result shows that the superstrong magnetic fields can increase the thermonuclear reaction rates by many orders of magnitude. The enhancement may have significant influence for further study research of the magnetars, especially for the x-ray luminosity observation and the evolution of magnetars.     

Effect of Superstrong Magnetic Fields on Nuclear Energy Generation Rate in the Crust of Neutron Stars

This paper shows that superstrong magnetic fields （such as those of magnetars） can increase the energy generation rate many times in the crust of neutron stars. This result undoubtedly not only influences the cooling of neutron stars and the X-ray luminosity observed of neutron stars but also the evolution of neutron stars.     

超强磁场对中子星外壳层核素56Fe,56Co,56Ni,56Mn和56Cr电子俘获过程中微子能量损失的影响

研究了超强磁场对中子星外壳层核素⁵⁶Fe,⁵⁶Co,⁵⁶Ni,⁵⁶Mn和⁵⁶Cr电子俘获过程中微子能量损失的影响.结果表明,就大部分中子星表面的磁场B<10¹³G,超强磁场对中微子能量损失率的影响很小.对于一些磁场范围为10¹³—10¹⁵G的超磁星,超强磁场可使中微子能量损失率大大降低,甚至超过5个数量级.     

Magnetar crust electron capture for $$^{}$$Co and $$^{56}$$56Ni

Based on the relativistic mean-field effective interaction principle and random phase approximation theory in superstrong magnetic fields (SMFs), we present an analysis of the influence of SMFs on the electron Fermi energy, nuclear blinding energy, single-particle level structure and electron capture for \(^{55}\)Co, and \(^{56}\)Ni by the shell-model Monte Carlo method in the magnetar’s crust. The electron capture rates increase by two orders of magnitude due to an increase in the electron Fermi energy and a change in single-particle level structure by SMFs. Then the rates decrease by more than two orders of magnitude due to an increase in the nuclear binding energy and a reduction in the electron Fermi energy by SMFs.     

Electron capture of nuclides 52,53,54, 55, 56Fe in magnetars

Based on the theory of relativity in superstrong magnetic fields (SMFs), we have carried out an estimation on electron capture (EC) rates of nuclides ^{52,53,54,55,56}Fe in the SMFs in magnetars. The rates of change of electronic fraction (RCEF) in the EC process are also discussed. The results show that the EC rates increase greatly and even exceeds by 4 orders of magnitude (e.g. ⁵⁴Fe, ⁵⁵Fe and ⁵⁶Fe) in SMF. On the contrary, the RCEF decreases largely and even exceeds by 5 orders of magnitude in the SMF.     

Hydrogen-like atom in a superstrong magnetic field: Photon emission and relativistic energy level shift

Following our previous work, additional arguments are presented that in superstrong magnetic fields B ? (Zα)² B ₀, B ₀ = m ² c ³/e? ≈ 4.41 × 10¹³ G, the Dirac equation and the Schrödinger equation for an electron in the nucleus field following from it become spatially one-dimensional with the only z coordinate along the magnetic field, “Dirac” spinors become two-component, while the 2 × 2 matrices operate in the {0; 3} subspace. Based on the obtained solution of the Dirac equation and the known solution of the “onedimensional” Schrödinger equation by ordinary QED methods extrapolated to the {0; 3} subspace, the probability of photon emission by a “one-dimensional” hydrogen-like atom is calculated, which, for example, for the Lyman-alpha line differs almost twice from the probability in the “three-dimensional” case. Similarly, despite the coincidence of nonrelativistic energy levels, the calculated relativistic corrections of the order of (Zα)⁴ substantially differ from corrections in the absence of a magnetic field. A conclusion is made that, by analyzing the hydrogen emission spectrum and emission spectra at all, we can judge in principle about the presence or absence of superstrong magnetic fields in the vicinity of magnetars (neutron stars and probably brown dwarfs). Possible prospects of applying the proposed method for calculations of multielectron atoms are pointed out and the possibility of a more reliable determination of the presence of superstrong magnetic fields in magnetars by this method is considered.     

Electron capture rates for iron group nuclei at the surface of magnetar

Effects of an ultra-strong magnetic field on electron capture rates for 55Co are analyzed in the nuclear shell model and under the Landau energy levels quantized approximation in the ultra-strong magnetic field, and the electron capture rates on 10 abundant iron group nuclei at the surface of a magnetar are given. The results show that electron capture rates on 55Co are increased greatly in the ultra-strong magnetic field, by about 3 orders of magnitude generally. These conclusions play an important role in future study of the evolution of magnetars.     

Resonant nuclear reaction ~(23)Mg(p,γ) ~(24)Al in strongly screening magnetized neutron star crust

Based on the relativistic theory of superstrong magnetic fields(SMF), by using three models those of Lai(LD), Fushiki(FGP), and our own(LJ), we investigate the influence of SMFs due to strong electron screening(SES) on the nuclear reaction ~(23)Mg(p,γ) ~(24)Al in magnetars. In a relatively low density environment(e.g., ρ_7 0.01)and 1 B_(12) 10~2, our screening rates are in good agreement with those of LD and FGP. However, in relatively high magnetic fields(e.g., B_(12) 10~2), our reaction rates can be 1.58 times and about three orders of magnitude larger than those of FGP and LD, respectively(B_(12), ρ~7 are in units of 10~(12)G, 10~7 g cm~(-3)). The significant increase of strong screening rate can imply that more ~(23)Mg will escape from the Ne-Na cycle due to SES in a SMF. As a consequence,the next reaction, ~(24)Al(+β, ν) ~(24)Mg, will produce more ~(24)Mg to participate in the Mg-Al cycle. Thus, it may lead to synthesis of a large amount of A20 nuclides in magnetars.     

Magnetic collapse of a neutron gas: Can magnetars indeed be formed?

A relativistic degenerate neutron gas in equilibrium with a background of electrons and protons in a magnetic field exerts its pressure anisotropically, having a smaller value perpendicular to than along the magnetic field. For critical fields the magnetic pressure may produce the vanishing of the equatorial pressure of the neutron gas. Taking this as a model for neutron stars, the outcome could be a transverse collapse of the star. This fixes a limit to the fields to be observable in stable neutron star pulsars as a function of their density. The final structure left over after the implosion might be a mixed phase of nucleons and a meson condensate, a strange star, or a highly distorted black hole or black ”cigar”, but not a magnetar, if viewed as a superstrongly magnetized neutron star. However, we do not exclude the possibility of superstrong magnetic fields arising in supernova explosions which lead directly to strange stars. In other words, if any magnetars exist, they cannot be neutron stars. Received: 25 November 2002 / Revised version: 25 February 2003 / Published online: 5 May 2003     

Effect of strong magnetic field on electron capture of iron group nuclei in crusts of neutron stars

In this paper electron capture on iron group nuclei in crusts of neutron stars in a strong magnetic field is investigated. The results show that the magnetic fields have only a slight effect on electron capture rates in a range of 10$^{8}-10^{13}$G on surfaces of most neutron stars, whereas for some magnetars the magnetic fields range from 10$^{13}$ to 10$^{18}$~G. The electron capture rates of most iron group nuclei are greatly decreased, reduced by even four orders of magnitude due to the strong magnetic field.     

Neutrino energy loss by electron capture in magnetic field at the crusts of neutron stars

Based on the p-f shell model,the effect of strong magnetic field on neutrino energy loss rates by electron capture is investigated.The calculations show that the magnetic field has only a slight effect on the neutrino energy loss rates in the range of 108-1013 G on the surfaces of most neutron stars.But for some magnetars,the range of the magnetic field is 1013-1018 G,and the neutrino energy loss rates are greatly reduced,even by more than four orders of magnitude due to the strong magnetic field.     

Neutrino energy loss by electron capture in magnetic field at the crusts of neutron stars

Based on the p-f shell model, the effect of strong magnetic field on neutrino energy loss rates by electron capture is investigated. The calculations show that the magnetic field has only a slight effect on the neutrino energy loss rates in the range of 10⁸—10¹³G on the surfaces of most neutron stars. But for some magnetars, the range of the magnetic field is 10¹³—10¹⁸G, and the neutrino energy loss rates are greatly reduced, even by more than four orders of magnitude due to the strong magnetic field.     

Magic ultramagnetized nuclei in explosive nucleosynthesis

Direct evidence of the presence of ⁴⁴Ti and content of the isotope in the supernova remnant Cassiopeia A are obtained from the analysis of gamma-ray spectrum of the remnant. A significant excess of observational ⁴⁴Ti volume on predictions of supernova models can be explained as the magnetization effect in the process of explosive nucleosynthesis. The formation of chemical elements is considered accounting for superstrong magnetic fields predicted for supernovae and neutron stars. Using the arguments of nuclear statistical equilibrium, a significant effect of magnetic field on the nuclear shell energy is demonstrated. The magnetic shift of the most tightly ??bound?? nuclei from the transition metals of iron series to titanium leads to an exponential increase in the portion of ⁴⁴Ti and, accordingly to a significant excess of the yield of these products of nucleosynthesis.     

Cold neutral plasma in a quantizing magnetic field

The chemical potential of a relativistic and an ultrarelativistic electron gas and the energy of an ultrarelativistic electron gas at T = 0 are expressed analytically as functions of the magnetic field. The possible application of these expressions to the investigation of super-compressed matter in the presence of superstrong magnetic fields is discussed.     

The Coulomb problem in superstrong B: Atomic levels and critical nuclei charges

The spectrum of atomic levels of hydrogen-like ions originating from the lowest Landau level in an external homogeneous superstrong magnetic field is obtained. The influence of the screening of the Coulomb potential on the values of critical nuclear charges is studied.     

Effect of superstrong magnetic field on electron screening at the crusts of neutron stars

The influences of electron screening (ES) and electron energy correction (EEC) are investigated by superstrong magnetic field (SMF). We also discuss in detail the discrepant factor between our results and those of Fushiki, Gudmundsson and Pethick (FGP) in SMF. The results show that SMF has only a slight effect on ES when B < 109 T on the surfaces of most neutron stars. Whereas for some magnetars, SMF influence ES greatly when B > 109 T . For instance, due to SMF the ES potential may be increased about 23.6% and the EEC may be increased about 4 orders of magnitude at ρ/μe = 1.0 × 106 mol/cm3 and T9 = 1. On the other hand, the discrepant factor shows that our results are in good agreement with FGP’s when B < 109 T . But the difference will be increased with increasing SMF.     

Very high-frequency gravitational waves from magnetars and gamma-ray bursts

Extremely powerful astrophysical electromagnetic(EM) systems could be possible sources of highfrequency gravitational waves(HFGWs). Here, based on properties of magnetars and gamma-ray bursts(GRBs), we address "Gamma-HFGWs"(with very high-frequency around 10~(20) Hz) caused by ultra-strong EM radiation(in the radiation-dominated phase of GRB fireballs) interacting with super-high magnetar surface magnetic fields(～10~(11) T).By certain parameters of distance and power, the Gamma-HFGWs would have far field energy density ?gw around10~(-6), and they would cause perturbed signal EM waves of～10~(-20) W/m~2 in a proposed HFGW detection system based on the EM response to GWs. Specially, Gamma-HFGWs would possess distinctive envelopes with characteristic shapes depending on the particular structures of surface magnetic fields of magnetars, which could be exclusive features helpful to distinguish them from background noise. Results obtained suggest that magnetars could be involved in possible astrophysical EM sources of GWs in the very high-frequency band, and Gamma-HFGWs could be potential targets for observations in the future.