Binary stars and the fundamental initial mass function

We have carried out Monte Carlo simulations in which we generate a random pairing of objects drawn from a pre-assumed single-star power-law initial mass function (IMF), which we call the fundamental IMF. We show how the mass functions of primary stars and secondary stars and the mass function of the total mass of systems (if we could resolve them) differ from the underlying fundamental IMF for different slopes of this IMF. We also compare our results with the observed IMF, the binary frequency and the binary mass-ratio distributions for field stars and conclude that the fundamental IMF of subsolar mass stars could be steeper than is currently believed. In other words, the low-mass turn-over of the observed ('apparent') IMF could be spurious, if the main-sequence binary fraction of field stars is close to 100 per cent (perhaps owing to invisible companions).     

Exact anisotropic polytropic cylindrical solutions

In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential \(z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)\) and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for \(\eta =1,~2\).     

On surface tension for compact stars

In an earlier analysis it was demonstrated that general relativity gives higher values of surface tension in strange stars with quark matter than neutron stars. We generate the modified Tolman-Oppenheimer-Volkoff equation to incorporate anisotropic matter and use this to show that pressure anisotropy provides for a wide range of behaviour in the surface tension than is the case with isotropic pressures. In particular, it is possible that anisotropy drastically decreases the value of the surface tension.     

Massive compact dwarf stars and C-field

The effect of C-field in high density matter has been studied. We find that the negative energy and negative pressure of the C-field helps in formation of massive compact stable neutron stars of mass ∼ 0.5 solar mass which is in the range of 0.01 to 1.0 solar mass of recently observed dwarf stars.     

Charged anisotropic models for quark stars

We perform a detailed physical analysis for a class of exact solutions for the Einstein–Maxwell equations. The linear equation of state consistent with quark stars has been incorporated in the model. The physical analysis of the exact solutions is performed by considering the charged anisotropic stars for the particular nonsingular exact model obtained by Maharaj, Sunzu and Ray. In performing such an analysis we regain masses obtained by previous researchers for isotropic and anisotropic matter. It is also indicated that other masses and radii may be generated which are in acceptable ranges consistent with observed values of stellar objects. A study of the mass-radius relation indicates the effect of the electromagnetic field and anisotropy on the mass of the relativistic star.     

Low mass stars

Low mass stars contribute an important fraction to the mass of our Galaxy. Due to the faintness of these stars a direct investigation of their space distribution and kinematics can be carried out only in the immediate solar neighbourhood. This fact emphasizes the importance of the Third Catalogue of Nearby Stars (CNS3) as a probe of the stellar content of our galaxy.A preliminary version (Gliese and Jahreiss, 1991) of the CNS3 was recently released. Based on this version the spatial distribution of the nearby red dwarf stars is discussed. An infrared and a bolometric luminosity function is presented and compared with independent determinations from photometric surveys. An outlook is given on the expectation for the next decade due to the various surveys presently carried out or planned for the near future.     

Exact solution of the equation of transfer with planetary phase function

We have considered the transport equation for radiative transfer to a problem in semi-infinite atmosphere with no incident radiation and scattering according to planetary phase function w(1 + xcos ). Using Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. The emergent intensity is in agreement with that of Chandrasekhar (1960).     

Accretion effects on compact members of binary stars

We explore the change in the period of axial rotation and in the radius of a magnetized compact star in a binary system, induced by the accretion on it of mass with angular momentum from the surface of its non-compact companion. No specific assumption is made concerning the accretion model, and the primary’s interior is described by the Fermi-Dirac statistics for degenerate matter. The rate of change with time of the period and radius is expressed in terms of the compact primary’s physical parameters and total absolute luminosity. The conditions are fully derived under which the above changes can be positive, negative or even vanish. In the case of the millisecond pulsars in binary X-ray sources the predicted values of the period time derivative, depending on the values of the accretion rate and. the absolute luminosity, can be positive or negative—if not vanishing—and they fall absolutely in the range 10⁻²¹ −10⁻¹⁷ ss⁻¹, in good agreement with current observational data. The corresponding rate of change of radius, either positive or negative, fall in the range of 10⁻³ −10⁻¹ cm y⁻¹. Finally, it is proved that the well-known bursters can be explained by thermonuclear flash due to gravitational instability in the accreted matter, but their explanation as a result of direct contraction could be possible only for quite high accretion rates (>10⁻⁷ M ⊙ y⁻¹). This last result indicates that, in contrast to the accretion-induced change in period, which can be of either sign irrespective of the primary’s age, the accretion-induced non-catastrophic contraction is impossible, while according to repent results the contraction in general is possible for young compact objects.     

Critical accretion flow of gas onto compact stars

The critical accretion flow of gas onto compact stars with mass of 0.6M is investigated by numerical integrations of the time-dependent hydrodynamic equations in the sphericallysymmetric and optically thick case. For the compact stars surrounded by such a dense cloud of gas, the radiation pressure force decelerates the infall gas significantly and free fall regime of the gas is not at all attained. This results in incident low velocities at the standing shock front close to the stellar surface, low temperatures of the gas around the compact stars, and no X-ray in white dwarfs but soft X-rays in neutron stars, respectively. Some applications of the results to the X-ray sources are discussed.     

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.