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Astron. Astrophys. 332, 569-574 (1998)

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1. Introduction

To test the observational effects predicted by Einstein's general relativity theory and other gravitational theories in pulsar systems by means of high-precision timing observations as well as radio polarization observation is an important trend and topic in modern relativistic astrophysics(see e.g. Damour, Gibbons & Taylor 1988). In this paper, we propose a gravitational spin effect as a possible mechanism to explain the evolution of the pulsar magnetic inclination, the angle between the pulsar's rotation axis and its magnetic axis, a quantity which is well determined either by the radio polarization observations developed by Lyne & Manchester(1988, hereafter LM88) or if the complete radio core beam is obtained, by the estimation of the standard pulsar radiation theory developed by Rankin (Rankin 1993, hereafter R93). Both methods are remarkably consistent with each other despite systematic differences in a number of cases (see comments in Bhattacharya & Van den Heuvel 1991). The magnetic inclination has been extensively investigated by astronomers (LM88; R93; Candy & Blair 1986; Kuzmin & Wu 1992 ; Xu & Wu 1991) , because it plays a very important role in determining the structure of pulsar magnetospheres and the detailed radiation processes which occur. On the other hand, the high precision pulsar observation data can provide evidence to support and/or test gravitational theories. The topics studied here connect gravitational theories and observational astronomy.

The magnetic inclination evolution has been studied theoretically by many other researchers who all conclude that the alignment of the magnetic axis with rotational axis is a consequence of the Maxwell radiation torque (Davies & Goldstein 1970; Michel & Goldwire 1970; Ruderman & Cheng 1988). However, it has been pointed out that the neutron star magnetic field may originate from the alignment of the neutron intrinsic magnetic moments in the stellar crust region (Boccaletti, De Sabbata & Gualdi 1965; Silverstein 1969; O'Connell & Roussel 1972), in which case the coupling between intrinsic spin and the gravitational field will influence the evolution of the direction of the magnetic field. Physically, the coupling effects include a special relativity effect (Mashoon 1988; Hehl & Ni 1990), a torsion effect predicted by gauge theories of gravity (Hayashi & Shirafuji 1979; Hehl et al 1976) and the magnetic self interaction. These combine to give the following evolutionary equations for the field (Zhang et al 1992; Zhang 1993),

[EQUATION]

[EQUATION]

[EQUATION]

where [FORMULA] is the angular velocity of the pulsar, [FORMULA] the rotation correlated axial torsion term, [FORMULA], the Larmor frequency, g the Lande g-factor, [FORMULA] the neutron mass and [FORMULA] the neutron magnetic moment. Eq. (1) shows that the magnetic moment is rotating with a combined angular frequency given in Eq. (2). The physical meaning of each term in Eq. (2) is following (Zhang 1993). The first term is the torsion-spin effect which represents the non-Riemannian contribution of Metric-Affine Gravity. However, the Riemannian contribution of the metric part is the effect of a rotating gravitational field, which is equivalent to increase the rotation-spin effect by a factor of [FORMULA], where [FORMULA] is the Schwarzshild radius. The second term is the rotation-spin effect which represents the inertia centrifugal contribution of the rotation frame. The third term is the magnetic self interaction which represents the recovery effect when the spin deviates from the original main direction of the magnetic field. The post-Newtonian approximated torsion [FORMULA] inside a rotating star with constant density is given as follows (Nitsch 1980),

[EQUATION]

[EQUATION]

[EQUATION]

where G is the gravitational constant and c is the speed of light, and M and R are the mass and radius of the star, respectively. [FORMULA] and [FORMULA]. Our model is shown schematically in Fig. 1. On the surface of the earth, the absolute value of [FORMULA] is about [FORMULA] rad [FORMULA], which is beyond the level of present-day experimental detectability. However, on the surface of a neutron star, [FORMULA] 1 rad [FORMULA], for [FORMULA] = 100 rad [FORMULA].

[FIGURE] Fig. 1. A schematic representation of the model. The dipolar magnetic field, which is in the direction of vector [FORMULA], is formed in the crust region with crust depth [FORMULA]. The inclination angle between rotational axis and the magnetic polar axis is [FORMULA]. The spin is precessing around the combined angular frequency vector [FORMULA]. The angle between [FORMULA] and [FORMULA] is [FORMULA].
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© European Southern Observatory (ESO) 1998

Online publication: March 23, 1998
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