Constraints on the Emission Geometry

It is important to note that the value of derived above represents the expected upper limit to the opening angle of the double-humped pulse. At moderate frequencies with respect to the cyclotron frequency, one would expect scattering to decrease the opening angle to a value less than the theoretical maximum (Kirk, Nagel and Storey 1986), and yet the maximum value is consistent with observations up to energies of several 10's of keV. This supports the arguments for a very high surface magnetic field on GX 1+4.

However, there are other possible causes for a wide opening angle. It is possible that a very wide polar cap is present which would produce a wider pulse than is produced by the flat polar cap model assumed here.

Alternatively, the wide pulses may be evidence for the existence of column geometry, rather than slab geometry in the emission region for GX1+4. Treatments of the radiation transfer in the strongly magnetized plasma of the emission region usually concentrate on two geometries of the emission region - usually termed slab and column geometries, depending on whether the deceleration region lies either close to the surface of the star,
( thought to occur in low to moderate luminosity pulsars), or on top of an accretion column at a distance from the surface which is not necessarily small compared to the diameter of the column. In this latter case, a significant fraction of the radiation from the emission region is emitted from the sides of the

post-shocked region, effectively increasing the projected area of the emission region at large angles with respect to the magnetic axis. This results in wider pulses than in the low luminosity case when the shock is a flat slab sitting on the surface and most emission comes from the top of the slab, as modelled above. The existence of column-shaped emission region geometry for GX 1+4 is consistent with the existence of a high surface magnetic field for this system. A high magnetic field results in the inner edge of the accretion disk being further from the star than for an average X-ray binary, which means that matter is channelled down a smaller range of field lines onto a narrower-than-average region of the neutron star surface. Thus, for even moderate luminosities, the restriction of the accretion funnel to a small region may result in a higher shock height, and thus wider pulses, than would be expected from an X-ray pulsar with the same luminosity but a slab-shaped emission region geometry. If column-shaped emission region geometry is applicable in GX 1+4, then one would not expect the formulae above to solely determine the pulse shape.

Greenhill et al. (1993) reported observations of a much narrower high frequency profile at energies from 75-114 keV. They postulated that scattering at moderate values was narrowing the pulse from the theoretically predicted shape. On the other hand, the high frequency pulse observed could be an interpulse. If the deep minimum is really the pulse centre then, as mentioned in Section 3.1, there is evidence for an extra component in the beam. In this case, the narrow high frequency pulse is at the phase where one would expect to observe an interpulse from a slab-shaped emission region. Alternatively, the combined effect of gravitational light bending and a column-shaped emission region can produce a narrow interpulse at the phase of the main pulse (Nollert et al. 1989). A higher magnetic field strength on the magnetic pole producing the interpulse may lead to a slower decrease in emission from this pole with frequency, thus leading to greater prominence of the interpulse as the frequency increases. A more detailed analysis of the pulse morphology of GX 1+4 is in preparation, together with analysis of XTE satellite data taken in 1996, which extends to higher frequencies than observations to date (Giles, Greenhill, Galloway, Storey and Swank, 1997, in preparation). The XTE satellite data should help to confirm the shape of the high frequency profile.

© Copyright Astronomical Society of Australia 1997