General features of GX 1+4 pulse profiles

Pulse profiles obtained from GX 1+4 can be broadly classified into two classes which have generally been found during the two distinct eras - the 1970's high intensity spin-up era and the later low intensity, principally spin-down, era. These are illustrated in Figure 1 and Figure 2 respectively. The low energy profiles in both classes have a characteristic narrow 'dip' or primary minimum. The width corresponds to only 5%-10% of the period and is not always obvious in data from the 1970's when sampling rates were relatively low. We define the bottom of the 'dip' as phase zero for the system. At other phases the profiles can be complex; particularly at low energies. At higher energies the profile is generally simpler and the phase of deepest minimum corresponds to that of the low energy 'dip' (Doty et al. 1981; White et al. 1983). A secondary minimum is sometimes present at phase (e.g. Doty et al. 1981; Makishima et al.1988; Greenhill et al. 1989; Paul et al. 1997).

  
Figure 1: Typical pre-1980 (type A) pulse profiles from GX 1+4. a) low (1.5-3 keV) energy band and b) the high (30-40 keV) band (Doty et al. 1981). The error limits are 0.6% and 1.0% respectively. The phasing has been changed to suit the definition in section 2.

Other significant features are sometimes observed in the GX 1+4 pulse profiles. Greenhill et al. (1993) observed a remarkable change in pulse shape at energies above 60 keV. A narrow emission 'spike' appeared at the phase (0.5) of the lower energy secondary minimum. Dotani et al. (1989) observed a very narrow emission 'spike' at the position of primary minimum (phase zero) in 1-7 keV data. White et al. (1983) observed a phase reversal with the low energy 'notch' (1-7 keV) being replaced at higher energies by an emission peak. Considerable variation between successive individual pulses was reported by Elsner et al. (1985).

The emission peak is frequently asymmetric, particularly at higher energies. This can be used to classify the profiles into two classes. Class A profiles (Fig 1) have the trailing edge (i.e. the section of pulse profile at the highest phase) brightest - using our definition of phase 0. These are found, almost exclusively, in data obtained during the high intensity state. Typical examples are in Doty et al. (1981); White et al. (1983) and Elsner et al. (1985). During the low intensity, mostly spin-down state, since 1986, the pulses are generally either symmetric or have the opposite asymmetry with the leading edge brightest, i.e. they have the section of pulse profile at lower phases brightest. We designate these class B. Examples are in Makashima et al. (1988); Greenhill et al. (1989); Mony et al. (1991), Storey et al. (1998).

  
Figure 2: Post-1980 (type B) pulse profiles in a) the low energy (0.5-10 keV) ASCA data (Kotani et al. 1997) and b) the high energy (20-75 keV) band (Greenhill et al. 1993). The error limits in the ASCA data are too small to display. The phasing has been changed to suit the definition in section 2.

Classification into two classes is somewhat arbitrary since many profiles are almost symmetric. The shape appears to depend in a complex way upon X-ray luminosity and whether the pulsar is spinning up or down. We know of no examples of class B profiles being observed during the high state in the 1970's when spin-up appears to have been almost continuous. Since 1986, when the luminosity was generally lower and occasional brief episodes of spin-up have punctuated an average spin-down of the pulsar, the profiles have mostly been symmetric or class B.

Class A profiles have, however, been observed on several occasions. During RXTE observations lasting 34 hours on 19-21 July, 1996 the profiles changed from class B to class A (Giles et al. 1998). This occurred at all energies from 2-60 keV. The change occurred after a short interval when the intensity became very low ( in the 10-60 keV energy range). At about the same time as the RXTE measurements the BATSE experiment on GRO detected a brief X-ray flare and transition from pulsar spin-down to spin-up (Chakrabarty et al. 1997). A detailed analysis of this event will be published elsewhere (Giles et al. 1998). In March 1991 Laurent et al. (1993) recorded class A profiles during high energy (40-77 keV) measurements with the SIGMA experiment on GRANAT. We note, however, that the X-ray intensity during the SIGMA measurements was at a level comparable to that during the short-lived BATSE spin-up episode in 1996. BATSE was not operational at this time and it is possible that a short term spin-up event was under way during the SIGMA measurements. In October 1991, when the X-ray luminosity was slightly lower, the profiles were symmetric (Laurent et al. 1993). Similarly, in September 1990 Kotani et al. (1998) detected class A (trailing edge bright) profiles during Ginga satellite measurements. The X-ray luminosity was relatively high at the time. A year later the luminosity was much lower and the profiles were symmetric.

We have investigated the dependence of the asymmetry upon X-ray luminosity using a number of published high energy (E>20 keV) profiles for which the phase of primary minimum could be identified and for which spectral intensities are available. We use only the high energy data since the complexity of the low energy profiles makes it difficult to quantify their asymmetry. Furthermore, published profiles are not in general strongly dependent on energy above 20 keV. Hence valid comparisons can be made between data sets covering somewhat different energy ranges. The intensity at 20 keV is taken as an overall indicator of X-ray luminosity . This was estimated in some cases by extrapolation from higher energies assuming a power law spectrum with a photon index of 2.

We define an asymmetry parameter as the ratio of the pulsed flux between phases 0.5 and 0.75 to the pulsed flux between phases 0.25 and 0.5. Hence class A profiles have and class B have . In the absence of a phase link between published observations we assume the phase of primary minimum is phase zero. In some data sets (e.g. White et al. 1983) the minimum is broad with indications of a possible weak emission feature with phase width superimposed on the minimum. In these cases we have assigned phase 0 to the minimum of a smoothed curve fit to the principal modulation. This causes considerable uncertainty in the time of phase 0 but is justified by the close agreement with the time of the low energy 'dip' in the data sets where this was known.

The relationship between and is illustrated in Figure 3. It seems likely that a correlation exists although more data points are required to verify this. The form of the relationship depends strongly on the choice of phase 0 and this is poorly defined. Clearly large profiles were observed when was high in the 1970's and has been smaller since the mid 1980's when was generally low. This does not, however, prove a direct causal relationship between and . The RXTE measurements by Giles et al. (1998) suggest that depends also on whether the pulsar is spinning up or down. The transition from class A to class B profiles (small to large ) occurred when was very low. We note however that the transition was followed by a large increase in and a brief resumption of spin-up (Chakrabarty et al. 1997). We suggest therefore that the change in profile was a consequence of a transition in the accretion flow which led to the resumption of spin-up and subsequent large increase in . A similar brief episode of spin-up probably occurred at about the time of the SIGMA measurements in March 1991 (Laurent et al. 1993)

  
Figure 3: Asymmetry parameter vs 20 keV intensity ( ) for published hard X-ray (>20 keV) measurements. a) White et al. 1983), b) Doty et al. (1981), c) Greenhill et al. (1993), d) Kendziorra et al. (1982), e) Laurent et al. (1993), f) Maurer et al. (1982), g) Mony et al. (1989)

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