【摘要】 本文对于天体的几何形状、自转、内应力、内部运动和自引力等提出假设,计算得到天体自转四极引力辐射功率公式改正的明显表达式,并估算了脉冲星PSR1937+214的引力辐射功率。更多还原

【Abstract】 The total power of gravitational radiation from rotating stars may be estimated by the well-known quadrupole radiation formula. However, in deriving the formula of quadrupole power radiated, the components of the stress energy tensor contain only term of rest-mass, which represents merely the effect of lowest order.The aim of this paper is to improve the formula of total quadrupole power radiated from a rotating star. Expressions of the power radiated ("total luminosity") have been derived by Epstein and Wagoner [3] by means of post-Newtonian approximation of the components of stress energy tensor containing terms of rest-mass, kinetic energy, potential energy and internal motion of the source. We apply their formulae to the gravitational radiation of a star rotating in the Newtonian limit. Thus, for geometrieal shape, rotation, internal motion, internal stress and self-gravity of a star, we make following simple assumptions:1. The stair is an ellipsoid of small equatorial eccentricity and can be approximated as a Maelaurin ellipsoid .Let α1, α2, α3 be the three semi-axes of the ellipsoid, and α1=α2. We have equation (3).2. The star rotates with a constant angular velocity in the Newtonian limit.3. Matter in the star may be described as a perfect fluid with ρ0, the rest-mass density and 77, the internal energy per unit mass of the matter, both to be constants. The actual density distribution is a function of ρ0, v, Π and U etc.4. The Newtonian potential in a star can be expressed in term of the potential in the Maclaurin ellipsoid as formulae (7)-(8d) that satisfy equation (9).We calculate mass-multipole-moment employing rotational coordinate transformation (5). Then, using (2)-(15), we obtain explicit expession (16) of the power radiated from a rotating star, after a somewhat lengthy calculation.For small l of (8d), arctg l can be expanded into a power series of l. We obtain further the expression (19). The first term in the bracket of (19) represents the quadrupole radiation, the second depends on internal motion, the third is general relativity effect due to self-gravity, and the last term is the effect of special relativity due to high rotational velocity in v2/c2 order.The expressions (16) and (19) are vald to estimate the power radiated from a fast-rotating neutron star. The power radiated from the pulsar PSR 1937+214 is estimated. By use of expression (16) and data in [4-6], it gives L/Lquadrupole=1.6.更多还原