Describing neutron stars by the relativistic mean field theory

Neutron stars are studied in the framework of the relativistic mean field theory of interacting nucleons, hyperons, and mesons. Within the hadronic freedom, the cores of neutron stars are found to be dominated by hyperons when the density is sufficiently high. The influence of hyperon coupling constants on the transition from a neutron star to a hyperon-dominated strange neutron star is also investigated. It is found that the transition density gets its minimum value when the ratio of hyperon coupling constant to nucleon's takes the value of 0.65, and the calculated maximum mass of the neutron star is 1.4 M which lies within the range of the observational results.     

An equation of state for super-dense matter and the structure of neutron stars

We modify Walecka's mean field method by regarding the nucleons as point sources when considering the vector meson field and obtain a new softer equation of state. Applying the latter to the structural equations of neutron stars gives a maximum mass of 1.7 M⊙ amd a rotational inertia of 1.62 × 10⁴⁵gcm². in good agreement with observations. The use of our improved mean field method reduces considerably the differences in the mass and rotational inertia given by relativistic and non-relativistic calculations.     

Comparisons and connections between mean field dynamo theory and accretion disc theory

The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi‐analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha‐viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha‐accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Implications of mean field accretion disc theory for vorticity and magnetic field growth

In addition to the scalar Shakura–Sunyaev α _ss turbulent viscosity transport term used in simple analytic accretion disc modelling, a pseudo-scalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and each hemisphere is separately studied. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudo-scalar terms have been studied, and can lead to large-scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent with those required for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former pseudo‐scalar can more easily reverse sign in the two cases.     

Analysis of the effect of a mean velocity field on a mean field dynamo

We study semi-analytically and in a consistent manner the generation of a mean velocity field     by helical magnetohydrodynamical (MHD) turbulence, and the effect that this field can have on a mean field dynamo. Assuming a prescribed, maximally helical small-scale velocity field, we show that large-scale flows can be generated in MHD turbulent flows via small-scale Lorentz force. These flows back-react on the mean electromotive force of a mean field dynamo through new terms, leaving the original α and β terms explicitly unmodified. Cross-helicity plays the key role in interconnecting all the effects. In the minimal τ closure that we chose to work with, the effects are stronger for large relaxation times.     

A ‘source surface theory’ corollary: The mean solar field-interplanetary field correlation

The correlation of the mean solar magnetic field and the interplanetary magnetic field reported by Wilcox et al. (1969) and Severny et al. (1970) has been interpreted by comparing the relationship of the measurement of the mean solar field with the physics involved in the formation of the interplanetary field. The high correlation observed is thus interpreted as a fortuitous correspondance between two integrals. The high correlation thus provides further support for the source surface model involved in these calculations. A new method is then suggested for observing the mean solar field that might improve the correlations slightly.     

Treatment of a static spherically symmetric matter distribution on the basis of the projective unified field theory

In order to confront the Projective Unified Field Theory with physical experience it is appropriate to apply this theory also to astrophysical objects, for mathematical reasons in particular to a static spherically symmetric matter distribution as a rough model for a star (e.g. neutron star or another exotic compact object). The problem mentioned is treated here as far as possible analytically in order to prepare the basis for the numerical approach.     

Comparison of the mean photospheric magnetic field and the interplanetary magnetic field

The mean photospheric magnetic field of the sun seen as a star has been compared with the interplanetary magnetic field observed with spacecraft near the earth. Each change in polarity of the mean solar field is followed about 4 1/2 days later by a change in polarity of the interplanetary field (sector boundary). The scaling of the field magnitude from sun to near earth is within a factor of two of the theoretical value, indicating that large areas on the sun have the same predominant polarity as that of the interplanetary sector pattern. An independent determination of the zero level of the solar magnetograph has yielded a value of 0.1±0.05 G. An effect attributed to a delay of approximately one solar rotation between the appearance of a new photospheric magnetic feature and the resulting change in the interplanetary field is observed.     

Mathematical theory of the origin of matter

It is shown that from a simple and elegant action it is possible to obtain: (i) the equations of classical dynamics, (ii) Schrödinger's equation, (iii) the dynamical equation of special relativity, (iv) scale-invariant gravitation including general relativity, (v) the mathematical theory of the origin of matter, and (vi) the potential function of inflationary theory.When the action term in question is related to the electromagnetic theory an ugly feature arises, however. There must be a multiplication by a small dimensionless number of order 10^–38. If this ugly feature is to be avoided, matter must be taken to originate, not as particles observed in the laboratory but as Planck particles. The decay of each such particle into 10¹⁹ hadrons then explains the genesis of numbers of order 10³⁸ that appear in physics and cosmology. It also raises questions concerning primordial nucleosynthesis which were discussed in the preceding paper.     

The decay of the mean solar magnetic field

We have analyzed the effects that differential rotation and a hypothetical meridional flow would have on the evolution of the Sun's mean line-of-sight magnetic field as seen from Earth. By winding the large-scale field into strips of alternating positive and negative polarity, differential rotation causes the mean-field amplitude to decay and the mean-field rotation period to acquire the value corresponding to the latitude of the surviving unwound magnetic flux. For a latitudinally broad two-sector initial field such as a horizontal dipole, the decay is rapid for about 5 rotations and slow with a t ^–1/2 dependence thereafter. If a poleward meridional flow is present, it will accelerate the decay by carrying the residual flux to high latitudes where the line-of-sight components are small. The resulting decay is exponential with an e-folding time of 0.75 yr (10 rotations) for an assumed 15 m s^–1 peak meridional flow speed.E.O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

Cosmic-ray streaming perpendicular to the mean magnetic field

The distribution function of cosmic rays streaming perpendicular to the mean magnetic field in a turbulent medium is re-examined. Urch's (1977) discovery that, in quasilinear theory, the flux is due to particles at 90° pitch angle is discussed and shown to be consistent with previous formulations of the theory. We point out that this flux of particles at 90° cannot be arbitrarily set equal to zero, and hence we dismiss the alternative theory which proceeds from this premise. A further, basic inconsistency in Urch's new transport equation is demonstrated, and the connection between quasilinear theory and compound diffusion is discussed.     

Rosseland and Planck mean opacities for primordial matter

We present newly calculated low-temperature opacities for gas with a primordial chemical composition. In contrast to earlier calculations, which took a pure metal-free hydrogen/helium mixture, we take into account the small fractions of deuterium and lithium as resulting from standard big bang nucleosynthesis. Our opacity tables cover the density range  −16 < log ρ[g cm⁻³] < −2  and the temperature range of  1.8 < log  T [K] < 4.6  , while previous tables have usually been restricted to   T > 10³ K  . We find that, while the presence of deuterium does not significantly alter the opacity values, the presence of lithium gives rise to major modifications of the opacities, at some points increasing it by approximately two orders of magnitude relative to pure hydrogen/helium opacities.     

Three-dimensional model for generation of the mean solar magnetic field

A three-dimensional (non-axisymmetric) model for the solar mean magnetic field generation is studied. The sources of generation are the differential rotation and mean helicity in the convective shell. The system is described by two equations of the first order in time and the fourth order in space coordinates. The solution is sought for in the form of expansion over the spherical function Y_n^m. The modes of different m are separated. A finite-difference scheme similar to the Peaceman-Rachford scheme is constructed so to find coefficients of the expansion depending on the time and radial coordinates. It is shown that a mode with a smaller azimuthal number m is primarily excited. The axisymmetric mode m = o describes the 22 year solar cycle oscillations. The modes of m o have no such periodicity, the oscillate with a period of rotation of the low boundary of the solar convective shell, The solutions which are symmetric relative to the equator plane are excited more easily compared with the antisymmetrical ones. The results obtained are confronted to the observational picture of the non-axisymmetric large-scale solar magnetic fields.     

Dynamical friction in a mean field approximation

An exact formula is derived for the average frictional force acting upon a ‘test’ star which moves along a prescribed trajectory amongst a collection of ‘field’ stars which are characterized by a Maxwellian distribution of velocities. In the limit that the actual stellar trajectories may be approximated by their average forms, as determined by the mean gravitational field, one obtains a relatively simple expression which establishes an important connection with the fluctuation-dissipation theorem. For the case of an infinite, homogeneous system, one recovers Chandrasekhar's classical result. Alternatively, by allowing for the possibility of nearly periodic motion, one is led to new and intriguing phenomena.     

Excitation of non-axially symmetric modes of the Sun's mean magnetic field

The kinematic dynamo equations for the mean magnetic field are solved with an asymptotic method of the WKB type. The excitation conditions and main characteristics of the non-axially symmetric modes for a given distribution of the sources are obtained. Utilization of the helioseismologic data on the Sun's internal rotation permits an explanation, within the framework of dynamo theory, of the excitation of the main non-axially symmetric modes revealed in the Sun's magnetic field sector structure.     

A 14-day periodicity in the mean solar magnetic field

In the present paper we look for periodicities in the mean solar magnetic field observed at Stanford Observatory, using Fourier transform and autocorrelation techniques. Apart from the periodicity equal to that of the synodic rotational modulation of the Sun, other periods were also found by examining the time series formed at different epochs of the solar cycle. From the aforesaid analyses a 14-day periodicity has been confirmed, which is found to occur in all the cases taken under consideration.     

Unified theory of the interplanetary magnetic field

A simple model is used to present a unified picture of the polarity pattern of the interplanetary magnetic field observed during the solar cycle. Emphasis in this paper is on the field near solar maximum. The heliographic latitude dependence of the dominant polarity of the interplanetary magnetic field is explained in terms of weak poloidal (dipolar) field sources in the sun's photosphere. Unlike the Babcock theory, the author hypothesizes that the dipolar field exists at equatorial latitudes (0–20°), too, (as well as in polar regions) and that the major source of the interplanetary magnetic field observed near the ecliptic plane is the dipolar field from equatorial latitudes. The polarity of the interplanetary field data taken in 1968 and in the first half of 1969 near solar maximum may possibly be explained in terms of a depression of the dipolar field boundary in space. The effect on the solar wind of the greater activity in the northern hemisphere of the sun that existed in 1968 and in the first half of 1969 is believed responsible for this hypothesized depression, especially near solar maximum, of the plane separating the + and - dipolar polarity below the solar equatorial plane in space. Predictions are made concerning the interplanetary field to be observed near the ecliptic plane in each portion of the next solar cycle.