182
A. Patruno and A. L. Watts
Another interesting finding has been the correlation or anti-correlation between
the fractional amplitude of the fundamental (where most of the pulse power is
observed) and the time of arrival of the pulsations of some AMXPs. The most
prominent example is XTE J1807-294 where high/low fractional amplitude pulses
arrive systematically earlier/later than predicted by the timing model. This finding,
and a similar anti-correlation between the time of arrivals and the X-ray flux, may
be evidence for a hot spot moving on the NS surface [259]. Similar conclusions
were reached by other authors to explain the timing noise observed in the timing
residuals of several AMXPs [123, 239, 253, 287]. Some of these observations can
be understood in terms of the hot spot wandering model described in Sect. 4.4.2.1
although no final confirmation of the models has yet been put forward. Despite
many open problems that need to be solved (such as why such correlations are not
observed in AMXPs like SAX J1808.4-3658) the moving hot spot model help us to
understand the AMXP pulse formation process.
Soon after the first AMXP discovery, it was realized that the lowest energy
(“soft”) photons that compose the pulsations arrive on average later than the high
energy (“hard”) photons [67]. In SAX J1808.4-3658, hard photon arrival times
tend to saturate at some energy E 10 keV, with soft photons at about 2 keV
accumulating a lag of about 0.08 rotational cycles (or 200 μs). Similar behaviour
was soon discovered in other five AMXPs: XTE J0929-314 (0.14 cycles [99]), XTE
J1751-305 (0.06 cycles, [111]), XTE J1814-338 (0.016 cycles, [350]), XTE J1807294 (0.1 cycles, [60]) and in the intermittent pulsar HETE J1900.1-2455 (0.07
cycles, [101]). In IGR J00291+5934, soft lags were observed with hard photons
leading by 0.06 cycles at 6–8 keV [88]. Above this energy, harder photons (E 8
keV) start to gradually reduce their lead until at energies of 30–100 keV there are
no phase lags with respect to the soft photons (at ∼2 keV). The origin of these
lags is poorly understood, and has been discussed in terms of the different angular
distribution (“fan” and “pencil” beams) of a two spectral component model [278]
or in terms of Compton down-scattering of hard X-ray photons from the cold disk
plasma or the NS surface [86]. Detailed study of the soft lags in SAX J1808.43658 [124] suggests that they have a flux dependence, with the lag being almost
zero at high fluxes, increasing steadily at lower fluxes and then decreasing again
below a flux threshold coincident with the onset of the rapid decay. This may be
linked with the changing properties of the accretion disk as it transitions towards
the propeller phase.
4.5.2 Pulse Shape Evolution
Most AMXPs with strong harmonic content show pulse shape variability that
often correlates with the stage of the outburst. The pulse profiles observed in
different outbursts of SAX J1808.4-3658 have characteristic shapes that can be
associated with the specific stage of the outburst (e.g., rise, peak, decay, etc.;
see [123, 142, 159]). There is a very strong linear anti-correlation between the
A. Patruno and A. L. Watts
Another interesting finding has been the correlation or anti-correlation between
the fractional amplitude of the fundamental (where most of the pulse power is
observed) and the time of arrival of the pulsations of some AMXPs. The most
prominent example is XTE J1807-294 where high/low fractional amplitude pulses
arrive systematically earlier/later than predicted by the timing model. This finding,
and a similar anti-correlation between the time of arrivals and the X-ray flux, may
be evidence for a hot spot moving on the NS surface [259]. Similar conclusions
were reached by other authors to explain the timing noise observed in the timing
residuals of several AMXPs [123, 239, 253, 287]. Some of these observations can
be understood in terms of the hot spot wandering model described in Sect. 4.4.2.1
although no final confirmation of the models has yet been put forward. Despite
many open problems that need to be solved (such as why such correlations are not
observed in AMXPs like SAX J1808.4-3658) the moving hot spot model help us to
understand the AMXP pulse formation process.
Soon after the first AMXP discovery, it was realized that the lowest energy
(“soft”) photons that compose the pulsations arrive on average later than the high
energy (“hard”) photons [67]. In SAX J1808.4-3658, hard photon arrival times
tend to saturate at some energy E 10 keV, with soft photons at about 2 keV
accumulating a lag of about 0.08 rotational cycles (or 200 μs). Similar behaviour
was soon discovered in other five AMXPs: XTE J0929-314 (0.14 cycles [99]), XTE
J1751-305 (0.06 cycles, [111]), XTE J1814-338 (0.016 cycles, [350]), XTE J1807294 (0.1 cycles, [60]) and in the intermittent pulsar HETE J1900.1-2455 (0.07
cycles, [101]). In IGR J00291+5934, soft lags were observed with hard photons
leading by 0.06 cycles at 6–8 keV [88]. Above this energy, harder photons (E 8
keV) start to gradually reduce their lead until at energies of 30–100 keV there are
no phase lags with respect to the soft photons (at ∼2 keV). The origin of these
lags is poorly understood, and has been discussed in terms of the different angular
distribution (“fan” and “pencil” beams) of a two spectral component model [278]
or in terms of Compton down-scattering of hard X-ray photons from the cold disk
plasma or the NS surface [86]. Detailed study of the soft lags in SAX J1808.43658 [124] suggests that they have a flux dependence, with the lag being almost
zero at high fluxes, increasing steadily at lower fluxes and then decreasing again
below a flux threshold coincident with the onset of the rapid decay. This may be
linked with the changing properties of the accretion disk as it transitions towards
the propeller phase.
4.5.2 Pulse Shape Evolution
Most AMXPs with strong harmonic content show pulse shape variability that
often correlates with the stage of the outburst. The pulse profiles observed in
different outbursts of SAX J1808.4-3658 have characteristic shapes that can be
associated with the specific stage of the outburst (e.g., rise, peak, decay, etc.;
see [123, 142, 159]). There is a very strong linear anti-correlation between the