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Astron. Astrophys. 322, 719-729 (1997)

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4. Temporal analysis

4.1. Flux variability

NGC 4051 is known to be rapidly variable. The X-ray light curve of the present observation is shown in Fig. 3.

[FIGURE] Fig. 3a and b. a X-ray lightcurve of NGC 4051, binned to time intervals of 400 s for the total energy range. b Correlation of soft (0.1-0.5 keV) and hard (0.5-2.4 keV) countrate normalized to the mean countrate in the corresponding energy interval. The dotted line represents a linear relation.

The source is variable by about a factor of 6 within a day. In order to test whether the amplitude of variability is the same in the low and high energy region of the ROSAT band, we have divided the total observed flux in a soft (0.1 keV [FORMULA] 0.5 keV) and a hard (0.5 keV [FORMULA] 2.4 keV) component and normalized each to the mean flux in the corresponding band. (We note that only in this section do we use this 'tight' definition of 'soft' band. Throughout the rest of the paper, the term 'soft excess' more losely refers to a component somewhere in the ROSAT energy band without implying it to be located exclusively below 0.5 keV.) The soft band is dominated by the cold-absorbed powerlaw component, whereas the dominant feature of the warm absorber, the oxygen absorption edge, is located in the hard band. We find essentially correlated variability between both components (Fig. 3 b), although there is a slight trend for the source to be softer when fainter.

4.2. Spectral variability

To check for variability of the warm absorption feature in more detail, we have performed warm-absorber fits to individual subsets of the total observation (referred to as 'orbits' hereafter). The warm column density, [FORMULA], is not expected to vary on short timescales and was fixed to the value determined for the total observation. The same was done for the unabsorbed powerlaw index [FORMULA] = -2.3 (but see comment below). The best-fit ionization parameter turns out to be essentially constant over the whole observation despite strong changes in the intrinsic luminosity (Fig. 4). If the warm material reacted instantaneously to variations in the ionizing luminosity, a clear correlation between U and L would be expected. Given the fact that there are time gaps in the observation and slightly delayed reactions might have escaped observation, one would still expect U to scatter as strongly as L. The constancy of U provides a limit on the density of the warm gas. Its recombination timescale [FORMULA] is conservatively estimated from the lack of any reaction of the warm material during the long low-state in orbit 7 (at t = 46 000 - 48 000 s after [FORMULA] ; cf. Fig. 3a), resulting in [FORMULA] sec. The upper limit on the density is given by

[EQUATION]

where [FORMULA] is the ion abundance ratio of the metal ions dominating the cooling of the gas and the last term is the corresponding recombination rate coefficient [FORMULA] (Shull & Van Steenberg 1982 with coefficients A = 6.71 [FORMULA], X = 0.726 from Aldrovandi & Pequignot 1973). Oxygen is a major coolant, and given its ionization structure for the best-fit warm absorber model (with an ion abundance ratio of [FORMULA] and a recombination rate coefficient of [FORMULA] = 0.57 [FORMULA] cm3 /s) this yields [FORMULA] [FORMULA] cm-3.

[FIGURE] Fig. 4. Ionization parameter U in dependence of the intrinsic X-ray luminosity (parameterized as the powerlaw flux at 10 keV, in photons/cm2 /s/keV), resulting from warm absorber fits to individual orbits of the total observation. The errors correspond to 95.5 % confidence. The dashed line reflects the expected dependence of U on flux if the warm gas reacted immediately to changes in the ionizing luminosity. Within the error bars, U is constant throughout the total observation.

For the above analysis, the intrinsic powerlaw index was fixed to the value derived for the total observation, [FORMULA] = -2.3. In fact, when fitting the X-ray spectra of individual orbits, this value always turns out to still represent the best description of the data. Due to the lower number of photons in each orbit, these datasets are less restrictive concerning the values of the fit parameters. However, Fig. 3b already indicates that no strong spectral changes occured, although simultaneous variations of different components that simulate a constant countrate ratio cannot be excluded. To set limits on the variability of [FORMULA] within the present observation we have fixed the powerlaw index to -1.9. Re-fitting the low-state (a hardening of the spectrum when the source is less bright would mirror the trend that is observed at higher energies, e.g. Matsuoka et al. 1990), no satisfactory description of the data can be achieved, with a change [FORMULA] = 39 as compared to the former best fit.

The spectrum during the first orbit (i.e. the first [FORMULA] 800 s) of the total observation, corresponding to a high-state in source flux, shows evidence for an additional black-body-like spectral component with [FORMULA] 0.12 keV and an unabsorbed flux of 7.7 [FORMULA] erg/cm2 /s in the ROSAT band, consistent with former observations of a soft excess during source high-states (Pounds et al. 1994, Mihara et al. 1994). If, again, [FORMULA] = - 1.9 is enforced, and the parameters of the black body are left free to vary, an additional very soft excess with [FORMULA] 40 eV reproduces the observation. However, a very large column of the warm material is found in this case to compensate the flatter intrinsic powerlaw, log [FORMULA] = 23.4. If this model applied, a strong change in the column density (by about a factor of 5) during the high-state would have to be invoked, which seems rather unrealistic.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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