3. Spectral analysis
3.1. Simple spectral models
A single powerlaw has been previously found to give a poor fit to the X-ray spectrum of NGC 4051. This also holds for the present observation (see Table 1). The resulting powerlaw slope is rather steep, , and strong residuals remain, with an unacceptable of 3.8. When the cold absorbing column density is left as a free parameter, a value slightly higher than the Galactic one is found. For all further fits described below, turned out to be either less than or about the same as the Galactic value and thus was fixed to the Galactic column of 0.13 cm-2 (Elvis et al. 1989; see also McHardy et al. 1995).
Table 1. X-ray spectral fits to NGC 4051 (pl = powerlaw, bb = black body, wa = warm absorber). Model 3 refers to the one with 'standard' assumptions (see text), in model 4 (and only in 4) the data corresponding to the short high-state in source flux (orbit 1) are excluded from the spectral fitting, in model 5 underabundant metals of 0.2 solar are chosen and in model 6 an IR spectral component as observed by IRAS is added. The errors are quoted at the 95.5% confidence level.
Although an improvement of the fit is obtained when adding a soft excess, this model does not provide a satisfactory description of the spectrum, either. Parameterizing the excess component as a black body (with normalization and temperature free) yields = 1.9 with a rather steep underlying powerlaw spectrum (Table 1).
Alternatively, the fit can be improved by adding an absorption edge which is thought to originate from warm gas along the line of sight. With the resulting best fit from a physical warm absorber model (next section) already in mind, the major absorption edges being those of OVII, OVIII and NeX, we modeled the X-ray spectrum with 3 single edges (of the form for ) superimposed on a powerlaw. The edge energies were fixed to the theoretical values ( = 0.74 keV, = 0.87 keV, = 1.36 keV) and the optical depths left free to vary. We find , , and a photon index .
3.2. Warm absorber models
The spectral absorption structure resulting from a physical absorber is more complex than a simple edge. Assuming the gas to be photoionized by continuum emission of the central pointlike nucleus and assuming it to be in photoionization equilibrium, we calculated a sequence of photoionization models using the code Cloudy (Ferland 1993).
The ionization state of the warm absorber can be characterized by the hydrogen column density of the warm material and the ionization parameter U, defined as
where Q is the number rate of incident photons above the Lyman limit, r is the distance between central source and warm absorber, c is the speed of light, and is the hydrogen density (fixed to 109.5 cm-3 unless noted otherwise). The X-ray absorption structure depends only very weakly on ( , where is the electron density) and remains unchanged for the range of densities discussed below, given the dominant physical processes; the essential parameter is the column density . Both quantities, and U, are determined from the X-ray spectral fits. Solar abundances (Grevesse & Anders 1989) were adopted if not stated otherwise. We have always assumed the continuum source to be completely covered by the absorber, i.e. no partial covering in which part of the intrinsic X-ray spectrum is seen directly, has been studied. Further, we assume the absorber to be one-component.
The observed spectral energy distribution (SED) of NGC 4051 is shown in Fig. 1. The one chosen for the modeling corresponds to the observed IR to UV spectrum in an intermediate brightness state (corrected for stellar contribution) extrapolated to the Lyman limit, a break at 10µm and an energy index = -2.5 -longwards, an X-ray powerlaw as self-consistently determined from the spectral fitting, and a break into the gamma-ray region at 100 keV.
Data in the NIR to UV spectral region were taken from Done et al. (1990) and are simultaneous but not contemporaneous to the present X-ray observation, although both represent an intermediate brightness state. Anyway, Done et al. (1990) and Hunt et al. (1992) find no short-timescale correlated IR/optical/UV - X-ray variability. Long-term trends are less certain, but Salvati et al. (1993) point to an X-ray high-state contemporaneous with a NIR high-state. The FIR spectrum of NGC 4051 observed by IRAS does not show a turnover shortwards of 100 µm. However, the IRAS points are thought to be contaminated by emission from cold dust of the surrounding galaxy (Edelson & Malkan 1986, Ward et al. 1987) and consequently are not seen by the warm material as a pointlike continuum source. Therefore, the nuclear SED was assumed to break at 10 µm and extend to the radio spectral region with = -2.5, consistent with the measured millimeter upper limit (Edelson et al. 1987). Anyway, the continuum -longwards the Lyman limit usually does not play an important role in determining the ionization state of the warm material and in particular the depth of the X-ray absorption features. (Later we comment on the influence of increased free-free heating, when an IR component as observed by IRAS is added to the nuclear spectrum.) The hard X-ray spectrum was assumed to follow the soft X-ray powerlaw (as was found to be a viable description of the ROSAT-Ginga and ASCA data; Pounds et al. 1994, Mihara et al. 1994, Guainazzi et al. 1996) and to break at 100 keV, in line with current observations of Seyferts (e.g. Kurfess 1994) and consistent with the observed gamma-ray upper limit (Maisack et al. 1995).
Fitting the warm absorber model to the X-ray spectrum of NGC 4051 results in an ionization parameter of , a warm column density of , and a photon index of = -2.3 (Table 1). The value of was pre-determined in a sequence of fits and then fixed to that value for further modelling (we did not attempt to tune the second digit of ; a change of results in = 24(10)). Further discussions and conclusions refer to this set of model parameters, if not stated otherwise. The electron temperature T of the warm gas is about 3 105 K. There is no evidence for a cold absorbing column larger than the Galactic one. The residuals from the best spectral fit are shown in Fig. 2 and the (unfolded) X-ray spectrum is displayed in Fig. 5. The absorption structure is dominated by highly ionized oxygen (OVIII) and neon. No strong iron edge around 7 keV is predicted (Fig. 5), consistent with higher-energy observations (e.g. Matsuoka et al. 1990). The intrinsic X-ray luminosity (i.e. the one prior to warm absorption) for this model in the 0.1 - 2.4 keV energy range is erg/s.
Netzer (1993) has discussed the consequences for the X-ray spectral shape of taking into account X-ray emission and reflection by the ionized absorbing gas. For the present observation of NGC 4051 the addition of an emission and reflection component to the X-ray spectrum, calculated with the code Cloudy for a covering factor of the warm material of 0.5, only negligibly changes the results ( = 22.70) due to the weakness of these components.
The warm absorber fit shown in Fig. 2 shows some residual structure between 0.1 and 0.3 keV. For completeness we note that an additional very soft excess component, parameterized as a black body, removes part of the residuals. Of course, the parameters of such a black body component are not well constrained from X-ray spectral fits. One with = 13 eV (corresponding to 150 000 K) and an integrated absorption-corrected flux (between the Lyman limit and 2.4 keV) of erg/cm2 /s fits the data. It contributes about the same amount to the ionizing luminosity as the powerlaw continuum used for the modeling and has the properties of the EUV spectral component for which evidence is presented in Sect. 5.1.
The observational data were compared to four further model sequences, which consisted of (i) a change in metal abundances of the warm gas up to 0.2 solar, (ii) the addition of dust with Galactic (ISM) properties to the gas, or a modification of the SED impinging on the absorber, by (iii) the addition of an EUV black body component with a temperature of = 100 000 K or 150 000 K contributing the same amount to the ionizing luminosity as the powerlaw component (the choice of these parameters is motivated and further discussed in Sects. 5.2.1, 5.2.4 and 5.1, respectively), or (iv) the inclusion of a strong IR spectral component as observed by IRAS.
The resulting best-fit model for reduced metal abundances of 1/5 the solar value is given in row 4 of Table 1. The low abundances are mostly reflected in an increase in the corresponding total hydrogen column , as expected due to the fact that oxygen (and neon) are most important in determining the absorption structure. An additional IR component strongly increases the free-free heating of the gas and the electron temperature rises. An additional black body component in the EUV with the properties given above has negligible influence on the X-ray absorption structure. Dusty models will be further commented on in Sect. 5.2.4.
3.3. Warm absorber plus soft excess ?
The intrinsic, i.e. unabsorbed, powerlaw with index = -2.3 is steeper than the Seyfert-1 typical one with -1.9. In fact, fixing the slope of the intrinsic powerlaw to = -1.9 (with U and as free parameters) leads to a significantly worse fit ( = 5.2). This still holds when all data points below 0.3 keV (which show some residual structure interpretable as a very soft excess, as mentioned above) are excluded from the spectral fitting ( = 4.3).
Since a soft excess on top of a flat powerlaw might mimick a single steeper powerlaw, we have performed some further tests to check, whether the data can be reconciled with = -1.9 plus a soft excess, parameterized as a black body. Firstly, we have fixed the black body temperature to the value found in an ASCA observation by Mihara et al. (1994), = 0.1 keV. In this case, the black body contribution is always found to be negligible (with a normalization of less than 10-10 ph/cm2 /s). When the other fit parameters, namely the ionization parameter of the warm absorber, are changed to enforce a black body contribution to the fit, remains far above acceptable values. Secondly, was left as an additional free parameter. In this case, a very soft excess is found, with 35 eV, ill-constrained by the ROSAT data, and the overall quality of the fit is not yet acceptable. Systematically steepening the underlying powerlaw, one is lead back to the model presented above, with = -2.3. Finally, all data points which correspond to the short high-state in source flux and which show some evidence for an additional soft excess ( 0.12 keV; detailed in Sect. 4.2) were excluded from the spectral fitting. The underlying powerlaw spectrum remains steep and the deduced parameters of the warm absorber remain unchanged within the error bars (Table 1, model 4).
© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998