Quasi-stellar objects and evolution of galaxies

In view of the striking similarities between Quasi-Stellar Objects on the one hand and the nuclei of N galaxies, Seyfert galaxies, radio galaxies and normal galaxies on the other, the possibility that QSOs might belong to an early phase in the evolutionary sequence of galaxies is explored. In this connection, considering the fact that nebulosities have been detected around five QSOs, the implications of the hypothesis that a QSO consists of a bright central object embedded in an extended nebulosity have been examined. In particular, the ratio a between the intensity of the bright central object and that of the surrounding nebulosity in the visual band of wavelengths has been calculated by the colour-given method for a sample of 81 QSOs with emission redshiftz0.76. This ratio a has been used to calculate the apparent visual magnitudem(V) and the absolute visual magnitudeM(V) of the bright central object (Nu) as well as that of the surounding nebulosity (Neb) of the QSOs in the sample and a criterion has been proposed as to the detectability of the surrounding nebulosities. Similar calculations have been made for N galaxies, Seyfert galaxies and normal galaxies. It is found that the values of log a, M(V) _Nu and M(V) _Neb for the four classes of extragalactic objects show a definite trend and suggest an evolutionary sequence: QSOsN galaxiesSeyfert galaxiesnormal galaxies.     

The critical and the saturation content of magnetic monopoles in rotating relativistic objects

Both the critical content _c ( N _m /N _B , whereN _m ,N _B are the total numbers of monopoles and nucleons, respectively, contained in the object), and the saturation content _s of monopoles in a rotating relativistic object are found in this paper. The results are:

Criculation in rotating degenerate objects

It is shown that due to degeneracy rather high Eddington-Vogt circulation velocities occur in cooling white dwarfs. The conclusion is that in fast rotating white dwarfs angular momentum is redistributed within a time scale short compared to the cooling time of the star. This might be important for the theory of very oblate rotating white dwarfs.It is shown that similar mechanisms work in the interior of degenerate, rotating cores of evolved stars, where circulations are driven by contraction energy and by neutrino losses. The circulations redistribute the core's matter within time scales shorter than or comparable with the evolution time scale.     

Oscillations of fluid disks rotating around compact objects

Frequency of global axisymmetric oscillations of a perfect fluid disk rotating around a compact object is investigated by trial function method. A formula for the frequency of local radial oscillation is presented.     

Extracting information from the gravitational redshift of compact rotating objects

Essential macroscopic internal properties of compact objects can be related to each other with the help of General Relativity. A somewhat familiar example is the relationship between the compactness M/R and the gravitational redshift for nonrotating bodies. Rotation poses new challenges when trying to relate observed or potentially observed quantities such as the graviational redshift, mass, radius, and angular velocity. Using a perturbative approach, we present an analytical approximation whose purpose is to relate these quantities. Two main results are highlighted: Derivation of a new maximal angular velocity depending only on the mass of the object and a possible estimate of the radius from a measurement of the gravitational redshift.     

On a uniformly rotating magnetic polytrope

The equilibrium general magnetic field inside a magneto-rotating star, assumed to be a polytrope, has been determined more accurately, for large general magnetic field. Furthermore the effect of such field on the structure and oscillations of a slowly rotating polytrope has been studied forn=1,0, 1.5, 2.0, and 3.0.     

Nonlinear pseudo-radial oscillation of a rotating magnetic star

The nonlinear pseudo-radial mode of oscillation of a rotating magnetic star is studied. It is shown that for a general rotational field, the coupling between magnetic field and rotation tends to reduce the average rotational energy parameterT. This result in a lowering of the maximum pulsation amplitudeq _max, which depends on strength of rotation and magnetic field. The configuration tends, therefore, to a new equilibrium state at lower value ofq _max. The analytic solution of the pulsation equation for the case ofy=5/3 in the presence of rotation and magnetic field has also been derived in the Appendix.     

Rigidly rotating modes of the solar magnetic field

Discrete rigidly rotating components (modes) of the large-scale solar magnetic field have been investigated. We have used a specially calculated basic set of functions to resolve the observed magnetic field into discrete components. This adaptive set of functions, as well as the expansion coefficients, have been found by processing a series of digitized synoptic maps of the background magnetic field over a 20-year period. As a result, dependences have been obtained which describe the spatial structure and the temporal evolution of the 27-day and 28-day rigidly rotating modes of the Sun's magnetic field.The spatial structure of the modes has been compared with simulations based on the known flux-transport equation. In the simulations, the rigidly rotating modes were regarded as stationary states of the magnetic field whose rigid rotation and stability were maintained by a balance between the emergence of magnetic flux from stationary sources located at low latitudes and the horizontal transport of flux by turbulent diffusion and poleward directed meridional flow. Under these assumptions, the structure of the modes is determined solely by the horizontal velocity field of the plasma, except for the low-latitude zone where sources of magnetic flux concentrate. We have found a detailed agreement between the simulations and the results of the data analysis, provided that the amplitude of the meridional flow velocity and the diffusion constant are equal to 9.5 m s^–1 and 600 km² s^–1, respectively.The analysis of the expansion coefficients has shown that the rigidly rotating modes undergo rapid step-like variations which occur quasi-periodically with a period of about two years. These variations are caused by separate surges of magnetic flux in the photosphere, so that each new surge gives rise to a rapid replacement of old large-scale magnetic structures by newly arisen ones.     

Structure and evolution of supermassive rotating magnetic polytropes

The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of General Relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radiusmass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.Receipt delayed by postal strike in Great Britain.     

Exact MHD solutions for rotating,magnetic stars

Simple exact solutions of the magnetohydrodynamic equations are found for rotating, magnetic stars. The velocity and magnetic field are axisymmetric and purely toroidal, and the magnetic energy density equals the kinetic energy density. For constant mass density, the solution reduces to that of Chandrasekhar (1956), which is stable even against non-axisymmetric perturbations. For an ideal gas equation of state, the condition for radiative thermal equilibrium is solved to lowest order in the non-spherical perturbation. The velocity, magnetic field and non-spherical pressure and temperature perturbations all vanish within cones centered around the rotation axis, |cos |>x _i a zero of a Legendre polynomial. Low-order, long-period stellar oscillations may be excited by MHD instabilities near the equatorial region which become damped near the axis.     

A general relativistic model for magnetic monopole-infused compact objects

Emergent concepts from astroparticle physics are incorporated into a classical solution of the Einstein-Maxwell equations for a binary magnetohydrodynamic fluid, in order to describe the final equilibrium state of compact objects infused with magnetic monopoles produced by proton-proton collisions within the intense dipolar magnetic fields generated by these objects during their collapse. It is found that the effective mass of such an object’s acquired monopolar magnetic field is three times greater than the mass of its native fluid and monopoles combined, necessitating that the interior matter undergo a transition to a state of negative pressure in order to attain equilibrium. Assuming full symmetry between the electric and magnetic Maxwell equations yields expressions for the monopole charge density and magnetic field by direct analogy with their electrostatic equivalents; inserting these into the Einstein equations then leads to an interior metric which is well-behaved from the origin to the surface, where it matches smoothly to an exterior magnetic Reissner-Nordström metric free of any coordinate pathologies. The source fields comprising the model are all described by simple, well-behaved polynomial functions of the radial coordinate, and are combined with straightforward regularity conditions to yield expressions delimiting several fundamental physical parameters pertaining to this hypothetical astrophysical object.     

Formation of a plasmasphere in a rotating magnetic field

Stationary flows of planetary plasmaspheres are analysed within the framework of magnetohydrodynamics. The necessary conditions for existence of a laminar axisymmetric plasma flow around the planet are formulated. A general solution of the problem is obtained for a plasma with the magnetic viscosity greatly exceeding the hydrodynamic one. It has been ascertained that the flow features are strongly dependent on the azimuthal component of the magnetic field. Detailed calculations are performed for a magnetic field similar to a dipole. A strong difference between rather slow-rotating plasmaspheres with plasmapauses and rather fast-rotating continuous plasmaspheres has been revealed. Results of the calculations are useful to explain some properties of the Jovian plasmasphere.     

Evolution of collapse nonuniformity for rotating magnetic interstellar clouds

We investigate the formation and evolution of isothermal collapse nonuniformity for rotating magnetic interstellar clouds. The initial and boundary conditions correspond to the statement of the problem of homogeneous cloud contraction from a pressure equilibrium with the external medium. The initial uniform magnetic field is collinear with the angular velocity. Fast and slow magnetosonic rarefaction waves are shown to be formed and propagate from the boundary of the cloud toward its center in the early collapse stages. The front of the fast rarefaction wave divides the gas mass into two parts. The density, angular velocity, and magnetic field remain uniform in the inner region and have nonuniform profiles in the outer region. The rarefaction wave front surface can take both prolate and oblate shapes along the rotation axis, depending on the relationship between the initial angular velocity and magnetic field. We derive a criterion that separates the two regimes of rarefaction wave dynamics with the dominant role of electromagnetic and centrifugal forces. Based on analytical estimations and numerical calculations, we discuss possible scenarios for the evolution of collapse nonuniformity for rotating magnetic interstellar clouds.     

The behaviour of the magnetic lines of a rotating system

The behaviour of a magnetic line has been studied under continuous injection of plasma. Under increasing density the existence of three zones of possible concentration has been shown. For values greater than a critical valueD=0, withD suitably defined, one zone disappears, whilst the other two degenerate into one.     

A new numerical scheme for structures of rotating magnetic stars

We have developed a new numerical scheme for obtaining structures of rapidly rotating stars with strong magnetic fields. In our scheme, both poloidal and toroidal magnetic fields can be treated for stars with compressibility and infinite conductivity. By introducing the vector potential and its integral representation, we can treat the boundary condition for the magnetic fields across the surface properly. We show structures and distributions of magnetic fields as well as the distributions of the currents of rotating magnetic polytropic stars with polytropic index   N = 1.5  . The shapes of magnetic stars are oblate as long as the magnetic vector potential decreases as 1/ r when   r →∞  . For extremely strong magnetic fields, equilibrium configurations can be of toroidal shapes.     

The magnetic field of a rotating cloud and magneto-rotational explosions

The contraction of a massive rotating plasma cloud with the magnetic field perpendicular to the axis of rotation and extending to infinity is considered. At some stage the contracting cloud reaches a state of dynamic quasi-stationary equilibrium. The change of the magnetic field in the cloud atmosphere before its arrival at the quasi-stationary state (stage I) and also in the process of quasi-equilibrium (stage II) are studied.At stage I an essential change of the external magnetic field geometry occurs, namely the formation of zero (neutral) lines and the transformation of the field into a quasi-radial one. Given certain conditions, the reconnection of the field lines in neutral X-type points may occur with the formation of closed loops. In this case the flux of field lines, which connect the contracting cloud with infinity, decreases asymptotically as (R/R _i)^2/3, whereR/R _i is the ratio of the present radius to initial one.After the cloud arrives at the state of dynamic equilibrium (stage II) a considerable increasing of the magnetic field occurs due to twisting of the field lines by rotation. The field strength increases up to some threshold after which instability suddenly occurs. As a result of cumulation occurring in the zero-line direction, and the subsequent dynamic dissipation, the ejection of relativistic particles and plasma in both directions along the rotational axis takes place. The magnetic field restores itself rapidly due to the continual twisting and this leads to the appearance of repeated explosions.The tension of the magnetic field lines as well as plasma outflow carry away the angular momentum. Its diminution determines the rate of secular gravitational contraction. During the contraction the rotational energy increases, so that recurrent bursts, being of magneto-rotational nature are based, finally, on the gravitational energy reservoir.According to our calculations of the time-interval for repetition of explosions, the energy output and certain other parameters, we are able to explain repeated bursts in the nuclei of galaxies and quasars observed, in particular, in the appearance of radio-variability.Extended version of the paper read at All-Moscow Astrophysical Seminar in Sternberg Astronomical Institute 3rd April 1969.