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Astron. Astrophys. 353, 575-582 (2000)

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3. Analysis and results

3.1. X-ray lightcurve

The 0.1-1.0 keV LECS and 1.8-10 keV MECS lightcurves of both observations are shown in Fig. 2 together with the hardness ratios (LECS counts between 4-10 keV divided by those between 0.1-1.0 keV). The ordinate extrema are the same for both on-states, but the time axes have different scales, with the main-on state plots expanded by about a factor of 2. Eclipse intervals based on the orbital ephemeris of Deeter et al. (1991) and assuming an on-state eclipse duration of 5.5 hour are indicated.

[FIGURE] Fig. 2. MECS 1.8-10 keV (upper panels) and LECS 0.1-1.0 keV (middle panels) lightcurves obtained during the main- (left) and short-on state (right) observations with a binning of 1024 s. Note the different temporal scales. The predicted eclipse times and durations, using the ephemeris of Deeter et al. (1991), are indicated with dashed lines. The intervals M1 and S1 to S4, used to extract continuum spectra, are indicated by horizontal bars (see Sect. 3.2). Times are seconds since the start of each observation. The lower panels show the LECS hardness ratio (4.0-10 keV/0.1-1.0 keV) plotted with a binning of 4096 s

A number of new and interesting features are evident. Soon after the start of the main-on state observation there is an interval of dipping activity (the modulation is much stronger in the LECS than the MECS, consistent with the known energy dependence of dipping), followed by a dip-free interval and a longer interval of deep dipping at the end of the observation. The short-on state observation covers parts of 4 orbital cycles and includes 3 eclipse intervals. Both the LECS and the MECS show a gradual reduction in count rate, with this effect being more pronounced in the LECS, such that the fourth orbital cycle appears to be absent, whereas a small modulation is still visible in the MECS. Superposed on this decay are the eclipses and what is normally taken to be dipping activity. However, this appears to be present for up to 20 hrs during each orbital cycle, whereas the main-on state dip duration is usually 5-10 hr (see e.g., Reynolds & Parmar 1995; Scott & Leahy 1999). During the first three orbital cycles, the centroid of the emission occurs at successively earlier orbital phases, while for the fourth orbital cycle no strong variation within the cycle is observed. This is also seen in the hardness ratio plot which shows intervals of increased hardness (consistent with increased absorption) that occur progressively earlier in each of the first 3 (and possibly the fourth) orbital cycles. The peaks of the MECS centroids and the increases in LECS hardness ratio seen in Fig. 2 are separated by an average of [FORMULA]1.4 days. This means that the intervals of strong absorption march back by [FORMULA]7 hr each orbital cycle. This rapid marching back is in strong contrast to the main-on state dips which have a period only 0.5 hr less than the orbital one (Scott & Leahy 1999). There may also be a narrow intensity dip in the MECS lightcurve, similar to those seen in the on-state, towards the end of the second cycle of the short-on state.

3.2. X-ray spectrum

In order to study the spectral evolution during the parts of the 35 day cycle observed here, 5 phase averaged spectra were extracted. The selected intervals are indicated in Fig. 2 and are labelled as M1 and S1 to S4. Interval M1 covers a dip-free part of the main-on state, while S1 and S2 cover the peaks of the first two short-on orbital cycles and have a similar overall intensity to M1. Interval S3 covers part of the third short-on orbital cycle, where the LECS intensity is severely reduced, while S4 covers most of the final short-on cycle, which may also include low-state emission.

The spectra were rebinned to oversample the full width half maximum (FWHM) of the energy resolution by a factor 3 and to have additionally a minimum of 20 counts per bin to allow use of the [FORMULA] statistic. Additionally a 2% systematic error was added to the uncertainties. Events were selected in the energy ranges 0.1-4.0 keV (LECS) and 1.8-10 keV (MECS) where the instrument responses are well determined and sufficient counts obtained. The photoelectric absorption cross sections of Morisson & McCammon (1983) and the solar abundances of Anders & Grevesse (1989) are used throughout. A factor was included in the spectral fitting to allow for normalization uncertainties between the instruments. This was constrained to be within the usual range of 0.8-1.0 (LECS/MECS) during all fitting.

Initially, all 5 spectra were fit with the absorbed power-law and blackbody continuum together with 2 broad Gaussian emission features at [FORMULA]1 keV and [FORMULA]6.4 keV as used by O97. The ASCA Solid-State Imaging Spectrometer (SIS) results of Mihara & Soong (1994) indicate that the [FORMULA]1 keV feature may be better modeled as two narrow lines at at 0.91 keV and 1.06 keV, at least in the low-state. Since the full-width half maximum (FWHM) energy resolution of the LECS is 0.2 keV at 1 keV, these features are not well resolved in the LECS and so the broad feature was replaced by two narrow lines with the energies fixed at the above values in all subsequent fits. We refer to this as the "standard" model. The fit results presented in Table 1 indicate that this model adequately describes the M1, S1, S2 and S4 spectra, but not the S3 spectrum where a [FORMULA] of 383 for 83 degrees of freedom (dof) is obtained. The fit quality of the S2 spectrum is somewhat worse than to the M1, S1, and S4 spectra. This may be because of unresolved variability which was not excluded from the accumulation (see the upper and middle panels of Fig. 2). The S4 spectrum is significantly harder and the equivalent width (EW) of the Fe-K line is higher than the other spectra (Table 1). There is no comparable change in the EW of the Fe-L lines. The intense Fe-K feature is clearly visible in the S4 spectrum shown in Fig. 3. There is no significant change in Fe-K line energy between the spectra. The equivalent blackbody radii are [FORMULA]200 km for intervals M1, S1 and S2, decreasing to [FORMULA]150 km during S3 and [FORMULA]70 km during S4. The ratio of 0.1-10.0 keV flux in the blackbody component compared to the powerlaw is 16% for all the spectra except S3, where is it 9%.

[FIGURE] Fig. 3. LECS and MECS Her X-1 spectra during the main-on (M1) and short-on states (S1, S3, and S4). The solid lines show the unfolded spectrum obtained with the "standard" spectral model (see Table 1), while for S3 a partially covering absorber is used (see Table 2). The contributions from the blackbody and power-law components are indicated separately. The same scales have been used for all four panels. The effect of the large amount of absorption required in the S3 spectral fits is clearly seen as a change in the spectral slope around 2 keV


Table 1. Spectral fit parameters and 90% confidence uncertainties for the phase-averaged spectral fits. The spectra have been fit with the "standard" model. The energies of the narrow Fe-L lines were fixed at the best-fit ASCA values in Mihara & Soong (1994). The equivalent blackbody radius assumes a distance of 6.6 kpc (Reynolds et al. 1997). The (0.1-10 keV) intensity is for all spectral components


Table 2. Partial covering fit results to the S3 and S4 spectra. The energies of the narrow Fe-L lines were fixed at the best-fit ASCA values in Mihara & Soong (1994). f is the fraction of the flux that undergoes extra absorption, [FORMULA]

The effects of significant absorption are clearly seen in the S3 spectrum as a change in spectral shape and increased curvature in the 1-3 keV range (see Fig. 3). This implies an absorption of [FORMULA][FORMULA] atom cm-2. However, substantial flux remains [FORMULA]0.5 keV, which should be completely absorbed with such a high absorption. There are a number of possible explanations for such behavior: (1) the presence of separate "scattered" and "absorbed" spectral components, (2) partial covering of the emitting region(s), and (3) absorption by partially ionized material such that the low Z materials responsible for the majority of the absorption [FORMULA]0.5 keV are significantly ionized, while the higher Z elements are not. Possibilities (1) and (2) cannot be spectrally distinguished and are referred to as "partial covering", although this should be taken to include the possibility of separate scattering and absorbing regions. Partial covering can be modeled using the pcfabs model in XSPEC . Here a fraction, f, of the emission undergoes extra absorption, [FORMULA], while the rest is absorbed by a low value of [FORMULA], as before. The partial covering model gives an acceptable fit to the S3 spectrum (a [FORMULA] of 115.7 for 82 dof), while that of an ionized absorber (the absori model in XSPEC ) is somewhat worse ([FORMULA] for 83 dof). We therefore do not pursue further the ionized absorber fits since the partial covering model provides a better fit.

As previously stated, the "standard model" gives a significantly harder spectrum ([FORMULA]) for interval S4 than for the other spectra, where the average is [FORMULA]0.8. We have investigated whether this apparent hardness may result from a large amount of intrinsic absorption which, if not modeled correctly, results in an anomalously hard spectral slope determination. The partial covering model was also fit to the S4 spectrum, even though the "standard" model provides an adequate description of the spectrum ([FORMULA] for 84 dof). This gives a partial covering fraction of [FORMULA] and extra absorption, [FORMULA], of [FORMULA] atom cm-2. The best-fit value of [FORMULA] is now [FORMULA], much closer to the values obtained in the other fits. This suggests that an explanation for the hard spectra (relative to the peak of the main-on state where [FORMULA]) seen at times from Her X-1 is the effects of large amounts of unresolved absorption, together with partial covering.

3.3. Pulse period and profile

The Her X-1 pulse periods were determined using only the non-dip and non-eclipse data obtained during the main- and short-on state observations. First, the arrival times of the photons were corrected to the solar system barycenter. Then the arrival times were additionally corrected to the Her X-1 center of mass using the ephemeris of Deeter et al. (1991). The periods were obtained with an epoch-folding technique using the MECS data, while the (1[FORMULA]) uncertainties were determined by fitting the arrival times of sets of 6 averaged profiles. During the main- and short-on states the best-fit periods are 1.2377268[FORMULA]0.0000009 s and 1.2377272[FORMULA]0.00000015 s, respectively.

The pulse profiles obtained by folding the data with these best-fit periods in different energy bands are shown in Fig. 4. The well-known, strongly energy-dependent, pulse profile of Her X-1 is evident. In general, the main-on state profiles all exhibit greater modulation depth than those obtained during the short-on state. The smooth almost sinusoidal 0.1-1.0 keV profiles are dominated by emission from the blackbody and Fe-L lines, while the 2-4 keV and 4-10 keV profiles are dominated by the power-law. The 2-4 keV main-on state profile is more sharply peaked and has a larger amplitude than that obtained during the short-on state. The 1-2 keV energy range clearly marks the transition between the profiles dominated by these different spectral components and it has a very structured appearance. In this energy range the difference in profiles is the largest between the two on-states.

[FIGURE] Fig. 4. Pulse profiles in 4 energy bands for the main- (left) and short-on (right) state observations. The 0.1-1 keV and 1-2 keV profiles are from the LECS and the 2-4 keV and 4-10 keV profiles from the MECS. Pulse phase 0.0 is defined as the maximum of the 4-10 keV folded lightcurves. The profiles are repeated for clarity

3.4. Pulse phase resolved spectrum

The data obtained during intervals S1 and S2 (short-on) and M1 were used to investigate the pulse phase dependence of the spectrum. Only the S1 and S2 intervals were included in the low-state accumulation since the spectra obtained during S3 and S4 are clearly different from those obtained elsewhere in the low-state. Both sets of data were divided into 10 equal phase bins, which gives comparable (within a factor of two) statistics. (Note that this is half the number of phase bins used by O97, since the total number of counts in both observations is much smaller than that in the SVP observation.) The spectra were rebinned and energy selected as above. The 10 phase-resolved spectra were fit using the "standard model" except that [FORMULA], the Fe-L line energies, the Fe-K line energy and width and LECS/MECS relative normalization were fixed at their best-fit values obtained from the fits to the phase-averaged spectra (Table 1). The best-fit values from the M1 and S1 fits were used for the main- and short-on states phase resolved fits, respectively.

The fits to the phase-resolved spectra give acceptable values of [FORMULA] of typically 0.9-1.3 for 80-110 dof. Fig. 5 shows the variations in best-fit spectral parameters as a function of pulse phase. Variations in all the fit parameters, except the strengths of both Fe lines and the blackbody kT are evident. Comparison of the left- and right-hand panels of Fig. 5 shows that the phase differences between the blackbody and power-law normalizations are approximately the same for the main- and short-on states. The amplitude of variation of the power-law component is smaller during the short-on state observation ([FORMULA]25%), compared to during the main-on state observation ([FORMULA]%). The intensity of the Fe-L line appears to be relatively constant. The phase dependence of the Fe-K line intensity is not well determined, but is consistent with having the same behavior as the power-law normalization, or with having no variation with pulse phase. This is in contrast to the Ginga results of Choi et al. (1994), where the blackbody and Fe-K line normalizations appear to be correlated.

[FIGURE] Fig. 5. Best-fit spectral parameters as a function of pulse phase for the main- (left) and short-on (right) state observations. The units of normalization are: for the power-law: Photons at 1 keV, cm-2 keV-1 s-1, for the Gaussian features: Photons cm-2 s-1, and for the blackbody: L39/d[FORMULA], where L39 is the source luminosity in 1039 erg s-1 and d[FORMULA] is the source distance in units of 10 kpc. Note that the power-law index, [FORMULA], was kept constant. Uncertainties denote the 68% confidence interval for 1 parameter of interest ([FORMULA]). Phases are arbitrary, but identical for each observation

The ratio of the blackbody to power-law fluxes are, during the main-on state, 18% and 15% for the pulse minima and maxima, respectively and 16% and 20% during the short-on state. Similar values can be derived from O97. This means that the reprocessing fraction is similar in all the observations, implying that the amount of reprocessing does not depend strongly on [FORMULA]. The best-fit equivalent blackbody radii are consistent with being identical between the main-on and the beginning (S1 and S2) of the short-on at [FORMULA]210 km, while in the latter phases of the short-on it decreases to [FORMULA]100 km. This may indicate that about 75% the blackbody reprocessing site is obscured during the later parts of the short-on state.

A cross-correlation between the best-fit power-law and blackbody normalizations obtained during the main- and short-on states reveals that in both cases the phase difference is consistent with a separation of [FORMULA]. This value is marginally consistent with the phase difference of [FORMULA] obtained earlier in the main-on state by O97. However, due to the broad, asymmetric profiles that are different in each observation (see Fig 5 and O97) it is difficult to reliably measure the pulse phase difference between the two components and so probe any changes of (relative) positions of the emission and reprocessing regions.

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Online publication: December 17, 1999