Forum Springer Astron. Astrophys.
Forum Whats New Search Orders

Astron. Astrophys. 342, 736-744 (1999)

Previous Section Next Section Title Page Table of Contents

3. Time evolution of spectral parameters

3.1. Dip lightcurves

The full lightcurve of the July 26 pre-eclipse dip is shown in Fig. 1. Gaps in the data stream are due to passages through the South Atlantic Anomaly and due to the source being below the spacecraft horizon. The dip ingress, which occurred at orbital phase [FORMULA], is characterized by a rapid decrease in intensity by a factor 3 within 80 s. The RXTE observation corresponds to a 35 d phase of [FORMULA], that is the observation took place 4 to 5 days after the Turn-On of the Main High State. From the behavior of the lightcurve in Fig. 1 we estimate that the dip egress takes place close to the end of the observation, when the count rate again reaches the pre-dip level. Under this assumption the duration of the dip was 6.5 hours.

[FIGURE] Fig. 1. Lightcurve during the dip of the RXTE observation in July 1996, 16 s resultion. Top x-axis: Time [UT]

In order to describe the time evolution of spectral parameters we use two complementary methods: First, we divide the whole dip lightcurve into segments of 16 s duration and perform spectral fits to each of these segments (Sect. 3.2). Secondly, we use color-color diagrams to model the time evolution of the column density (Sect. 3.3).

3.2. Spectral modeling

As was mentioned in Sect. 1, the common explanation for the dips is that of photoabsorption and scattering by foreground material. The photon spectrum ([FORMULA]) resulting from this process can be well described by a partial covering model of the form


where [FORMULA] is the photoabsorption cross section per hydrogen atom (Morrison & McCammon 1983), [FORMULA] is the Thomson cross section, and [FORMULA] is the number of electrons per hydrogen atom ([FORMULA] is the electron column density). In Eq. (1), the continuum emission is modeled as the sum of two power laws, one of which is photo-absorbed by cold matter of column density [FORMULA], as well as Thomson scattered out of the line of sight by electrons in the cold material. The second power law is not modified by the absorber, indicating that this additional (scattering) component comes from a geometrically much larger, extended region and thus is not affected by the photoabsorption. To this continuum, an iron emission line (described by a Gaussian) is added, which remains unabsorbed to simplify the spectral fitting process.

Two-component models similar to that of Eq. (1) have previously been shown to yield a good description of the dip spectra, while other simpler models were found to result in unphysical spectral parameters. As we mentioned in Sect. 2, to avoid response matrix uncertainties and problems with the exponential cutoff and the cyclotron resonance feature we include only data from 3 to 18 keV in our analysis. This approach results in a simpler spectral model than that used by Choi et al. 1994 and Leahy et al. 1994, who included the whole Ginga LAC energy band from 2 to 37 keV in their analysis. Since [FORMULA], except for the highest values of [FORMULA], photoabsorption will virtually not influence the spectrum above [FORMULA]10 keV, such that the inclusion of data measured up to 18 keV is sufficient for the determination of the continuum strength. As we show in Fig. 2, neither the exponential cut-off nor the cyclotron resonance feature at [FORMULA]35 keV need to be taken into account when restricting the upper energy threshold to 18 keV, as significant deviations between the data and the model are observed only for energies above 18 keV. We, therefore, conclude that between 3 and 18 keV, additional continuum components do not affect the spectrum. When holding the power law index constant at its pre-dip value, from our spectral fits of the dip data we obtain acceptable [FORMULA] values ([FORMULA]). Introducing additional freedoms by leaving the photon index as a free parameter in the fit does not significantly improve the results. Therefore, we do not have to include high energy data to determine the continuum parameters.

[FIGURE] Fig. 2. 16 s PCA spectrum taken outside of the dip, modeled with the spectral shape from Eq. 1 over the energy interval used for our analysis of the dip-spectra. Significant deviations from the power-law continuum model appear only at energies above 18 keV, indicating that a power-law is sufficient in describing the data below 18 keV.

In different attempts to fit the 16 s time resolved spectra without explicitly allowing for Thomson scattering of the absorbed component we found that the absorbed intensity which was then a free parameter was strongly anticorrelated with the column density. The relation between [FORMULA] and [FORMULA] from a fit of a spectral model that does not take account of Thomson scattering is shown in Fig. 3a. The observed anticorrelation reflects the exponential [FORMULA]-dependence of the Thomson scattering factor and led us to the conclusion that absorption and Thomson scattering may not be separated. We, therefore, use the model of Eq. (1) and hold the continuum parameters fixed to their measured pre-dip values: a single power law of photon index 1.06 plus an emission line feature from ionized iron at 6.7 keV with width of [FORMULA] keV ([FORMULA] at 3-18 keV for 30 degrees of freedom). The normalization of the absorbed power law, [FORMULA], was also fixed to its pre-dip value, [FORMULA]. Finally, the ratio [FORMULA] was set to 1.21, appropriate for material of solar abundances. We emphasize that fixing the parameters to their normal state values assumes that the intrinsic spectral shape of the source does not change during the dip and that variations of the observed spectrum are due to the varying column density only. This is justified by the apparent constancy of the lightcurve outside the dip. Particularly, if [FORMULA] is free in the fit, we observe an increase of this parameter for very high [FORMULA], which is not clearly systematic (see Fig. 3b). Such a correlation between [FORMULA] and [FORMULA] seems to indicate an additional dependence of [FORMULA] on the column density (next to the Thomson scattering already taken into consideration in the spectral model). Rather than being due to real variations of the absorbed intensity, we consider this relation to be produced artificially by the fitting process: Variations of [FORMULA] during the dip might come about as compensation for slight misplacements of the column density. Any remaining correlation in Fig. 3b might contain a possible contribution from slight variations in the absorbed continuum. Due to the limited energy resolution of the detector, however, [FORMULA] and [FORMULA] are strongly correlated. Therefore, a slight real variation is not convincingly separable from the artificial one.

[FIGURE] Fig. 3a and b. Dependency of the absorbed intensity [FORMULA] on the column density [FORMULA] for variations of the two component model: a  model without inclusion of Thomson scattering, and b  model with free [FORMULA]. In subfigure a the line represents the exponential Thomson factor [FORMULA] for [FORMULA]. Uncertainties have been omitted for clarity.

To summarize, the remaining free parameters of the spectral model are the iron line normalization, [FORMULA], the normalization of the unabsorbed component, [FORMULA], and the column density, [FORMULA].

We divide the dip observation into 16 s intervals and obtain 941 spectra, covering the energy range from 3 to 18 keV. After subtracting the background, which has been modeled on the same 16 s basis, the individual spectra were fitted with the model of Eq. (1). Typical [FORMULA] values obtained from these fits are between 0.5-1.5 for 37 degrees of freedom, indicating that our simple spectral model is sufficient to describe the data.

The temporal behavior of the column density mirrors that of the lightcurve (Figs. 4a and b). This supports the assumption that the underlying cause for both is absorbing material whose presence in the line of sight blocks off the X-ray source and thus leads to a modification of the spectral shape due to energy dependent absorption and energy independent scattering as well as a corresponding reduction in the 3 to 18 keV flux. The highest value measured for the column density is about [FORMULA], comparable to that found in previous measurements (Reynolds & Parmar 1995). The variation of the measured count rate with [FORMULA] is shown in Fig. 5 together with the count rates predicted by our partial covering model. The transition from the dip to the normal state is manifested in the break of the slope around 1500 cps. The figure indicates that due to the 3 keV energy threshold of the PCA, the instrument is sensitive only to values of [FORMULA] of about [FORMULA] and above. This also explains why we measure [FORMULA] for the out-of-dip data just before dip-ingress, a value which is rather high compared to the value for absorption by the interstellar medium along the line of sight ([FORMULA], Mavromatakis 1993).

[FIGURE] Fig. 4a-d. Time evolution of bestfit parameters from spectral fitting in 16 s intervals: a  PCA count rate for the energy interval from 3.5 to 17 keV, b  [FORMULA], where [FORMULA] is measured in [FORMULA], c  normalization of the unabsorbed power law, [FORMULA], in [FORMULA] at 1 keV, d  normalization of the Gaussian emission line. Uncertainties shown are at the 90% level for one parameter. For clarity, the error bars are only shown for every 20th data point.

[FIGURE] Fig. 5. PCA count rate in the band from 3 to 18 keV as a function of the measured column density. The line represents the count rates predicted by the model of Eq. (1). Inset: typical [FORMULA] uncertainty for [FORMULA].

The normalization of the unabsorbed component, [FORMULA], is found to stay almost constant during the whole dip, indicating that the whole variability of Her X-1 during the dip is due to absorption and scattering in the intervening material. The absolute value of [FORMULA] is quite small (about 2.5% of [FORMULA]).

The normalization of the iron line, [FORMULA], also shows some decline during phases of high column density. Note, however, that in our spectral model the line feature is not absorbed and scattered. The remaining variation can in principle be explained by partial covering of the line emitting region.

3.3. Color-color diagrams

As an alternative to spectral fitting, the development of the column density can be visualized by color-color diagrams which show the behavior of broad band X-ray count rates (cf. Leahy 1995 for earlier results from Ginga data). We define four energy bands covering approximately the same range as our spectral analysis (Table 1). We then define modified X-ray colors by [FORMULA], [FORMULA], and [FORMULA] where [FORMULA] is the count rate in band i. For any given spectral model, a theoretical color can be obtained by folding the spectral model through the detector response matrix. If the only variable parameter in the model is [FORMULA], the resulting colors are found to trace characteristic tracks in the color-color diagram. Comparing these tracks with the measured data it is possible to infer the temporal behavior of the column density (see below).


Table 1. Energy bands defined for the analysis of colors.

As an example, Fig. 6a displays typical theoretical tracks for two possible spectral models for Her X-1. The dotted track represents a model without an unabsorbed component (called the one-component model henceforth), while the solid line is the track computed for a partial covering model. The form of this partial covering model is identical to Eq. (1) with the exception that the iron line is also absorbed and scattered. We used photoabsorption cross sections from Verner & Yakovlev 1995 and Verner et al. 1996 in the computation of the diagrams. The difference between these cross sections and those from Morrison & McCammon 1983 used in Sect. 3.2 is negligible, though. The typical shape of the tracks is due to the [FORMULA] proportionality of the absorption cross section [FORMULA]: for low values of [FORMULA] only the lower bands are influenced by the absorbing material, while for high values of [FORMULA] all bands are influenced. In both cases the model track starts at the low [FORMULA]-values in the upper right corner of the diagram marked by the square which describes the situation before the dip. Moving along the track the column density increases. For low values of [FORMULA], the tracks of both models are similar since the influence of absorption is negligible. For larger [FORMULA] the lower energy bands are increasingly affected by absorption. At a critical value of [FORMULA] the unabsorbed component begins to dominate the low energy bands in the partial covering model. Since the unabsorbed component has, by definition, the same shape as the non-dip spectrum, the track turns towards the low-[FORMULA] color. In the one-component model, the absence of an unabsorbed component leads to a further decrease in flux in the low energy bands that is only stopped by response matrix and detector background effects.

[FIGURE] Fig. 6. a  Theoretical track of a partial covering model (solid line) and a model without unabsorbed component (dashed line) in a color color diagram for spectral parameters typical for Her X-1. Labels on the curve refer to column densities (in [FORMULA]). b -d Color-color diagrams and best fit partial covering models for the dip of the RXTE observation.

For each of the energy bands defined in Table 1 we generate a background subtracted lightcurve of 32 s resolution and obtain the color-color diagrams shown in Fig. 6b-d. The data line up along a track which is curved similar to the theoretical tracks of Fig. 6a. The accumulation of data points in the upper right corner of the diagrams of Fig. 6b-d consists of the out-of-dip data, where the colors remain constant and the column density is at its lowest value. As noted above, the early turn of the observed tracks in the color-color diagram suggests the presence of an unabsorbed spectral component in the data. To quantify this claim, we compare theoretical tracks from the partial covering model to the data. This is done by varying the relative contributions of [FORMULA] and [FORMULA] to the total spectrum such that the total normalization of the incident spectrum, [FORMULA], is kept at its pre-dip value. Except for the normalizations, all other spectral parameters are fixed at their pre-dip values (cf. Sect. 3.2). We define the best fit model to be the model in which the root mean square distance between the track and the data is minimal (cf. Fig. 6). Not surprisingly, the ratio between [FORMULA] and [FORMULA] found using this method is similar to the average ratio found from spectral fitting, about 3%.

Using this best fit model, [FORMULA] as a function of time is found by projecting the measured colors onto the track. The projection provides slightly different values of [FORMULA] for each color-color diagram examined. Major discrepancies are due to projection onto a wrong part of the model curve in the region where the curve overlaps with itself. To even out these discrepancies we calculated the median of [FORMULA] from all three color-color diagrams used in our analysis. The time development of [FORMULA] found from the color-color diagrams is in good agreement with the [FORMULA] resulting from the spectral fits (Fig. 7).

[FIGURE] Fig. 7. Comparison of the time development of [FORMULA] as found from different methods: Upper panel: [FORMULA] from color-color diagrams, lower panel: [FORMULA] from spectral fitting.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999