The ordinary URCA process in the presence of positrons and large magnetic fields

The effect of positron capture on the ordinary URCA neutrino luminosity in a zero magnetic field is investigated for several values of the degeneracy parameter and the range of temperatures 5×10⁸K–5×10¹⁰K. The rate for this process is then compared with those in large magnetic fields (on the order ofH _c =m ² c ³/eh=4.414×10¹⁰ G). The results indicate that positron capture reduces the effect of large magnetic fields on this process at high temperatures.     

Neutrino reactions in strong magnetic field

We present the energy losses due to several neutrinos processes: (1) synchrotron neutrinos, (2) pair annihilation neutrinos, (3) plasmon neutrinos, and (4) photoneutrinos in the presence of a superstrong magnetic field. Numerical results are tabulated and illustrated for several values of densities and temperatures. In the low density regime (10⁷ g cm^–3) the presence of a magnetic field decreases the luminosity, whereas the opposite is true at higher densities. This last effect is however almost entirely due to the existence of a new process the synchrotron neutrinos that disappear whenH0. Even though the overall effect can only be quantitatively ascertain after a complete cooling computation is performed, one should however expect a much lower temperature for neutron star surface than the one computed in theH=0 case.     

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.     

The proton-proton reaction and related reactions in an intense magnetic field

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH _q =m ² c ³/e=4.414×10¹³G. For fields greater thanH _q , the proton-proton reaction rates are enhanced linearly with (=H/H _q ).The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T ₉5) and low fields (1). For instance, _pep(H)=0.04 _pep(O) at =10^–3,T ₉=10. For relatively high fields (>1) and low temperatures (T ₉2), the reaction rates are enhanced approximately linearly with . In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (₆/_e10). At high densities (₆/_e10) the reaction rates are unaffected by the magnetic field.     

The URCA process in convective cores

A Monte Carlo simulation has been carried out for URCA processes in a degenerate convective stellar core, such as would be obtained following degenerate carbon ignition. We find energy loss rates substantially less than obtained by Paczynski in his vibrational approximation for this process. We conclude that the loss rates should be computed by direct integration over the convective core assuming a uniform ratio of the abundances of the URCA pair.     

On the interaction between the URCA process and convection

The influence of the URCA process (β-decay, electron capture) on convective stability is investigated and a stability criterion is derived. The criterion contains the Schwarzschild criterion and the thermohaline convection. It is found that URCA may cause convective instability to an otherwise stable medium, but it cannot stabilize an unstable medium, only the growth rate is affected. A numerical example for the Na²³?Ne²³ URCA pair shows the regions in the ?-T plane where instability is caused (assuming given abundances of the isotopes). The evolution of C-O core of an evolved 3.5M _⊙–8M _⊙ star may be affected by formation of convective regions even prior to C¹² ignition.     

Vertical motions in an intense magnetic flux tube

Solar Physics - The nature of convective instability in a slender magnetic flux tube is explored. A sufficient condition for stability is derived for the case of anarbitrary temperature profile in...     

Vertical motions in an intense magnetic flux tube

It is of interest to examine the effect of radiative relaxation on the propagation of waves in an intense magnetic flux tube embedded in a stratified atmosphere. The radiative energy loss (assuming Newton's law of cooling) leads to a decrease in the vertical phase-velocity of the waves, and to a damping of the amplitude for those waves with frequencies greater than the adiabatic value ( ) of the tube cut-off frequency. The cut-off frequency is generalized to include the effects of radiative relaxation, and allows the waves to be classified as mainly progressive or mainly damped. The phase-shift between velocity oscillations at two different levels and the phase-difference between temperature and velocity perturbations are compared with the available observations.Radiative dissipation of waves propagating along an intense flux tube may be the cause of the high temperature (and excess brightness) observed in the network.     

Vertical motions in an intense magnetic flux tube

In a recent discussion of intense photospheric magnetic fields we gave an expansion procedure that lead to a tractible system of differential equations governing vertical motions in a slender flux tube embedded in a quiescent environment. Transverse variations were taken into account in our discussion. In support of this expansion scheme we considered the special case of a straight flux tube in a uniform atmosphere. Wilson (1978, 1979b) has now criticised our treatment of this special case. We discuss his objections here, and show them to be without foundation.The cause of the disparity between our results and his lies not in a breakdown of the slender flux tube approximation but rather in the differing assumptions as to the nature of pressure variations in the tube's exterior. We generalize the slender flux tube approximation in a uniform tube, and obtain the governing dispersion relation. This dispersion relation contains, as special cases, both the results of Roberts and Webb (1978) and those of Wilson (1979a).     

Vertical motions in an intense magnetic flux tube

The recent discovery of localised intense magnetic fields in the solar photosphere is one of the major surprises of the past few years. Here we consider the theoretical nature of small amplitude motions in such an intense magnetic flux tube, within which the field strength may reach 2 kG. We give a systematic derivation of the governing expansion equations for a vertical, slender tube, taking into account the dependence upon height of the buoyancy, compressibility and magnetic forces. Several special cases (e.g., the isothermal atmosphere) are considered as well as a more realistic, non-isothermal, solar atmosphere. The expansion procedure is shown to give good results in the special case of a uniform basic-state (in which gravity is negligible) and for which a more exact treatment is possible.The form of both pressure and velocity perturbations within the tube is discussed. The nature of pressure perturbations depends upon a critical transition frequency, _p , which in turn is dependent upon depth, field strength, pressure and density in the basic (unperturbed) state of the tube. At a given depth in the tube pressure oscillations are possible only for frequencies greater than _p for frequencies below _p exponentially decaying (evanescent) pressure modes occur. In a similar fashion the nature of motions within the flux tube depends upon a transition frequency, _v . At a given depth within the tube vertically propagating waves are possible only for frequencies greater than _v ; for frequencies below _v exponentially decaying (evanscent) motions occur.The dependence of both _v and _p on depth is determined for each of the special cases, and for a realistic solar atmosphere. It is found that the use of an isothermal atmosphere, instead of a more realistic temperature profile, may well give misleading results.For the solar atmosphere it is found that _v is zero at about 12 km above optical depth ₅₀₀₀= 1, thereafter rising to a maximum of 0.04 s^–1 at some 600 km above ₅₀₀₀ = 1. Below ₅₀₀₀ = 1, in the convection zone, _v has a maximum of 0.013 s^–1. The transition frequency, _p , for the pressure perturbations, is peaked at 0.1 s^–1 just below ₅₀₀₀ = 1, falling to a minimum of 0.02 s^–1 at about one scale-height deeper in the tube     

The galaxy luminosity function in clusters and the field

We present the results from a CCD survey of the B -band luminosity function of nine clusters of galaxies, and compare them to published photographic luminosity functions of nearby poor clusters like Virgo and Fornax, and also to the field luminosity function. We derive a composite luminosity function by taking the weighted mean of all the individual cluster luminosity functions; this composite luminosity function is steep at bright and faint magnitudes and is shallow in-between.
All clusters have luminosity functions consistent with this single composite function. This is true both for rich clusters like Coma and for poor clusters like Virgo.
This same composite function is also individually consistent with the deep field luminosity functions found by Cowie et al. and Ellis et al., and also with the faint end of the Las Campanas Redshift Survey R -band luminosity function, shifted by 1.5 mag. A comparison with the Loveday et al. field luminosity function, which is well determined at the bright end, shows that the composite function, which fits the field data well fainter than M _B=−19, drops too steeply between M _B=−19 and −22 to fit the field data there.     

Neutrino emission from plasmons in strong magnetic fields

We show, contrary to previously published results, that magnetic fields of astrophysical interest have negligible effects on the emission rate of neutrinos from plasmons.     

The time-delayed solar cycle luminosity modulation by sub-surface magnetic flux tubes

In order to explore the mechanism of the solar cycle luminosity change observed by the Active Cavity Radiometer Irradiance Monitor (ACRIM) I experiment on board of the spacecraft Solar Maximum Mission, we examined running mean time profiles of the daily ACRIM data from the declining phase of solar cycle 21 to the rising phase of solar cycle 22. By comparing them with those of the daily sunspot number, integrated surface magnetic field flux, integrated He I 10830 Å line equivalent width data, and two kinds of data sets of the daily integrated Ca II K line index as indices of the surface magnetic activities, we found (i) that the running mean time profiles of the six independent data sets have several peaks and valleys in common in one solar cycle with time intervals on the order of a few hundreds of days, and (ii) that the peaks and valleys of the ACRIM data profiles followed the peaks and valleys of all the other five indices of the surface activities by 40 to 60 days. This time delay phenomenon suggests (i) that the luminosity modulation was not directly caused by dark and bright features of the surface magnetic activities that the other five indices represent, and (ii) that the missing sunspot radiative flux which was blocked by sub-surface magnetic flux tubes of sunspots and sunspot groups should be re-radiated 40 to 60 days after the surface emergence of the magnetic flux tubes. The concept of the time delay resolves the enigma of the missing sunspot radiative flux and the enigma of the ACRIM experiment that the luminosity dropped when a sunspot or a sunspot group appeared on the surface while the yearly mean of the luminosity decreased and increased along with the decrease and increase of the yearly sunspot number of the 11-year solar cycle. A model of the mechanism to understand these phenomena is presented and its application to other stars is suggested.     

Skinning process stability of the magnetic field in the solar active regions

Skinning process stability of the magnetic field in homogeneous plasma is studied. A set of magnetohydrodynamic equations is used. Dependence of electrical conductivity on the plasma parameters and radiation intensity in grey-body approximation are taken into account. The investigation is carried out on the model problems in linear approximation and by means of numerical solution of MHD equations. Threshold of stability and critical gradient of magnetic field in skin-layer are obtained. The model of the phenomenon proposed in the paper indicates on overheating instability of plasma with electric current in large gradient magnetic field zones as a possible trigger mechanism of solar flare origin.     

The effect of rotation on the luminosity of magnetic stars

The effect of rotation and a general magnetic field on the luminosity, radius, and effective temperature of the upper Main-Sequence stars has been investigated using a perturbation analysis. The magnetic field profile prevailing inside the star is assumed to have both poloidal and toroidal components. The case of constant as well as differential rotation is admitted. Model calculations indicate that these stellar parameters modify considerably as a result of coupling between rotation and the magnetic field.     

Dynamo action in the presence of an imposed magnetic field

Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Material flows of an evolving magnetic field

The possibility of material flows to trace out the magnetic field configuration is examined through numerical simulations. In particular, the evolution of a magnetic arcade due to differential motions of its footpoints is considered. With the use of numerical scheme based on the method of projected characteristics and newly derived proper boundary conditions, it is shown that material flows develop to outline the configuration of evolving magnetic field. Physical implications of the results are discussed.     

Strong cosmic-ray scattering in an anisotropic random magnetic field

We calculate the kinetic coefficients and the transport mean free paths of high-energy particles parallel to the regular magnetic field in the approximation of a large-scale anisotropic random magnetic field by using a nonlinear collision integral, i.e., by taking into account the processes of strong random scattering. We consider the diffusion of solar and Galactic cosmic rays by two-dimensional turbulence. Strong random scattering by two-dimensional turbulence is shown to reduce the parallel transport mean free path several fold. The momentum dependence of the parallel mean free path does not change, Λ_∥ ∝ p^2?v. In the case of strong random scattering by turbulence formed by several modes, the parallel transport mean free path is Λ_∥ ∝ p. We show that two-dimensional turbulence can make a major contribution to the parallel transport mean free paths of cosmic rays in the heliosphere and the interstellar medium.