Spectrum and Pulse Profile Formation in Strong-Field X-ray Pulsars

D.K. Galloway1

School of Mathematics and Physics, University of Tasmania, Hobart, Australia 7001
Research Center for Theoretical Astrophysics, University of Sydney, Camperdown NSW 2006

I present the results of an analytic and modelling study of X-ray pulsar emission. Satellite X-ray observations of the binary pulsars GX 1+4 and RX J0812.4-3114 made using the Rossi X-ray Timing Explorer (RXTE) and the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma Ray Observatory (CGRO) were analysed to quantify source variations with time and pulse phase. A numerical model simulating X-ray emission from pulsars in terms of Compton scattering of photons within a neutron star accretion column has been developed to test the consistency of the analysis results and to further investigate the spectral and pulse profile formation.

Mean Proportional Counter Array (PCA) spectra of both pulsars over the range 2-40 keV are adequately fitted with a Comptonization model, with blackbody source spectrum T0 approx 1-1.3 keV, plasma temperature Te approx 6-10 keV, and optical depth tau approx 2-6. The source spectrum temperature is consistent with an origin at the neutron star polar cap, with Compton scattering taking place primarily in the hot plasma of the accretion column. Both the fitted optical depth and plasma temperature vary significantly with the source flux. The wide range of source luminosity spanned by archival observations of GX 1+4 offers evidence for two distinct spectral states above and below LX approx 1.4 * 1037 erg s-1 (2-20 keV, assuming a source distance of 10 kpc). GX 1+4 additionally exhibits dramatic hourly variations in neutral column density nH indicative of density variations in the stellar wind from the giant companion.

Pulse profiles from GX 1+4 vary dramatically over timescales as short as 6 h. Low-order Fourier decomposition of pulse profiles in the 20-50 keV band from BATSE monitoring of the source, in addition to the pulse profiles observed by RXTE over a broader energy range have been used to investigate the relationship between source flux and profile asymmetry suggested on the basis of previously published profiles. The asymmetry of the pulse profiles (as measured by the asymmetry parameter alpha, Greenhill et al. 1998) exhibits large variation which decreases as the flux increases. No significant relationship is suggested by the recent data, although the span in flux is significantly narrower than from historical profiles which cover the 1970s during which the source was consistently very bright.

Pulse-phase spectroscopy of RXTE data from GX 1+4 and RX J0812.4-3114 support the interpretation of the sharp dips in the pulse profile as `eclipses' of the emission region by the accretion column. The dip phase corresponds with the closest approach of the column axis to the line of sight, and the additional optical depth experienced by photons escaping from the column in this direction gives rise to both the decrease in flux and increase in the fitted tau measured at this phase. Analysis of the arrival time of individual dips in GX 1+4 provides the first measurement of azimuthal wandering of a neutron star accretion column. The column longitude varies stochastically with standard deviation 2-6 degrees depending on the source luminosity. Measurements of the phase width of the dip both from mean pulse profiles and individual eclipses demonstrates that the dip width is proportional to the flux. The variation is consistent with that expected if the azimuthal extent of the accretion column depends only upon the Keplerian velocity at the inner disc radius, which varies as a consequence of the accretion rate Mdot.

A numerical model using a Monte-Carlo approach has been developed to investigate the behaviour of the emission model suggested by the analysis results. The model simulates Comptonization of a source of blackbody photons emitted from the polar cap of a canonical neutron star in a semi-infinite cylindrical accretion column. The mean spectra vary with both inclination angle and magnetic colatitude (the source aspect). For certain ranges of aspect the pulse profiles exhibit dips similar to those observed in GX 1+4 and RX J0812.4-3114, although not as sharp. Pulse phase spectroscopy of the model data confirms the increase in fitted tau coincident with the dip. Latitudinal variations in density across the column, suggested as a possible source of profile asymmetry, result in significant asymmetry only if the brightness of the two poles is unequal.

1 present address: Monash Centre for Astrophysics, Monash University, Clayton VIC 3800

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1st June 2001