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

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5. Discussion

5.1. SED and ionization parameter

The ionization parameter of the warm absorber, as determined from the X-ray absorption spectrum, is [FORMULA]. Here, the EUV-SED incident on the absorber enters in two ways: (i) by contributing to the total number of photons irradiating the warm gas (Eq. (1)) and (ii) by its influence on the ionization structure of the absorber via its spectral shape. In the following, we discuss constraints on the EUV-SED and the resulting number rate Q of photons above the Lyman limit. It should be noted, however, that the X-ray part of the SED is the one most important in determining the depth of the metal absorption edges, in creating highly ionized ions by K-shell photoionization.

A lower limit on the number of photons in the unobserved EUV-part of the SED is estimated by a powerlaw interpolation between the flux at 0.1 keV (from X-ray spectral fits) and the Lyman-limit (by extrapolating the observed UV spectrum), which was used for the present modeling. This gives [FORMULA] s-1.

Q can also be deduced from the H [FORMULA] luminosity. The minimal number of hydrogen-ionizing photons isotropically emitted by the central continuum source is given by the total observed H [FORMULA] luminosity. Assuming [FORMULA] K and using Tables. 2.1 and 4.2 of Osterbrock (1989) results in [FORMULA] 1012 [FORMULA]. The mean observed [FORMULA] = 7.8 [FORMULA] erg/s (Rosenblatt et al. 1992) yields [FORMULA] s-1. It is interesting to note that this is of the same order as the lower limit determined from the assumption of a single powerlaw EUV-SED, suggesting the existence of an additional EUV component in NGC 4051. (Alternatively, it would imply that broad line region (BLR) plus narrow line region (NLR) completely cover the central source (i.e. the covering factor is unity) in contrast to what is observed in the soft X-ray spectrum, i.e. there is no evidence for strong cold absorption in excess of the Galactic value.) However, such an EUV component cannot be identified with the black-body-like soft X-ray excess seen in source high-states (Sect. 4.2; Pounds et al. 1994, Mihara et al. 1994) which turns over already in the soft X-ray region, negligibly contributing to the EUV luminosity. Neither is there a measurable black-body continuum component in the ultraviolet (Edelson & Malkan 1986).

A third approach to Q is via the ionization-parameter-sensitive emission-line ratio [OII] [FORMULA] 3727/[OIII] [FORMULA] 5007 (e.g. Penston et al. 1990). This method makes use of the fact that the [OII]/[OIII] ratio is rather insensitive to the spectral shape of the ionizing continuum (although it tends to overestimate the number of photons, if the emission line region in question contains density inhomogeneities or a large fraction of matter-bounded clouds; Schulz & Komossa  1993). The oxygen ratio, as measured by Malkan (1986) yields an ionization parameter for the NLR of [FORMULA] - -2.5. To determine Q, the mean density and distance of the narrow line region have to be known. The density was estimated from the emission line ratio [SII] [FORMULA] 6716/[SII] [FORMULA] 6731 (Veilleux 1991) to be [FORMULA] cm-3 and the distance assumed to be [FORMULA] pc (consistent with Schmitt & Kinney 1996), leading to [FORMULA] s-1.

An additional EUV component may also explain the observational trend that broad emission lines and observed continuum seem to vary independently in NGC 4051 (Osterbrock & Shuder 1982, Peterson et al. 1985, Rosenblatt et al. 1992), as expected if the observed optical-UV continuum variability is not fully representative of the EUV regime.

As noted in Sect. 3.2 there are hints for such an EUV bump in the present X-ray spectrum, although the evidence is rather weak due to the softness of the component. A similar very soft excess, based on much better photon statistics, has been found in the ROSAT spectrum of the narrow-line quasar TON S180 (Fink et al. 1996).

Given the evidence for an EUV bump in NGC 4051 in excess of a simple powerlaw, we have verified that such a component (parameterized as a black body; Sect. 3.2) does not change the fit parameters of the warm absorber within the given error bars except for contributing to U.

An intense IR spectral component, however, leads to a strong heating of the gas and the best-fit ionization parameter decreases somewhat. Underabundant metals (see next section) lead to an increase in the fit value of U. There is approximately a factor of 2 uncertainty in U resulting from this ignorance of continuum shape and chemical composition.

[FIGURE] Fig. 5. UV- to X-ray spectrum of NGC 4051. The thin solid line corresponds to the unabsorbed SED chosen for modeling. The thick solid line in the X-ray region shows the best-fit warm-absorbed spectrum corrected for Galactic cold absorption, whereas the crosses correspond to the absorbed spectrum. The dot-dashed line represents the black body with kT = 13 eV that was mentioned in Sect. 3.2. The arrow marks the Lyman limit and the two horizontal bars indicate the amplitude of flux variability when the data are binned to orbits.

5.2. Properties of the warm absorber

5.2.1. Column density and abundances

The warm hydrogen column density of the absorber is [FORMULA] = 22.7, adopting solar abundances; an assumption that is usually made. The actual abundances are a priori unknown and might deviate from that by a factor of several. There are indications for underabundant metals in the extended emission line regions of some Seyfert galaxies (e.g. Tadhunter et al. 1989) and in the narrow line regions of Seyfert 2 galaxies by a factor of 1/2 to 1/3 compared to the solar value (Komossa & Schulz 1994). Marshall et al. (1993) constructed a model for the warm electron scattering medium in NGC 1068 (which, in general, might be one component to identify the warm absorber with; and the temperature of which is comparable to that found for the absorber in NGC 4051) with underabundant oxygen of 1/5 [FORMULA] solar. Depleted gas-phase oxygen abundances are also found by Sternberg et al. (1994) in molecular gas in the central region of NGC 1068, and material evaporating from the torus might be another reservoir for warm absorbing material. X-ray spectral fits do not constrain the abundances. An approach to estimate the chemical composition within the inner region of active galaxies is by emission lines. For the narrow line region, the intensity ratio [OIII] [FORMULA] 4363/[OIII] [FORMULA] 5007 is a good abundance indicator via its temperature sensitivity. Using published emission line intensities of NGC 4051 (Dibai & Pronik 1968, Malkan 1986), we find [FORMULA] [OIII] [FORMULA] 4363/[OIII] [FORMULA] 5007 [FORMULA] -0.7, indicative of a rather high temperature and correspondingly low abundances.

Running fits with reduced metal abundances of 1/5 [FORMULA] solar results in a larger total warm column density, [FORMULA] = 23.38, reflecting the fact that the depth of the absorption feature is dominated by oxygen.

5.2.2. Density

The density of the warm gas is not important in determining the X-ray spectral shape at a fixed time. A limit was drawn from the variability behaviour (Sect. 4.2), which resulted in [FORMULA] [FORMULA] cm-3. We come back to this point in Sect. 5.3.1.

With [FORMULA] [FORMULA] cm-3, the thickness of the warm absorber is [FORMULA] cm.

5.2.3. Location

The location of the warm material is poorly constrained from X-ray spectral fits alone. The absorber might be part of the broad line region or situated farther outwards, e.g. in the narrow line region. The emission line contribution of an optically thin matter-bounded BLR component in active galaxies was discussed by Shields et al. (1995), who also particularly pointed out that this gas might act as an X-ray warm absorber.

Using [FORMULA] s-1 as derived from the powerlaw description of the EUV spectrum and the upper limit of the density of the warm gas as determined from the X-ray variability results in a distance of the absorber from the central power source of [FORMULA] cm. Conclusive results for the distance of the BLR in NGC 4051 from reverberation mapping, that would allow a judgement of the relative positions of both components, do not yet exist: Rosenblatt et al. (1992) find the optical continuum to be variable with large amplitude, but no significant change in the H [FORMULA] flux.

5.2.4. Influence of dust

Dust might be expected to survive in the warm absorber, e.g. depending on its distance from the central energy source. A rough estimate for the evaporation distance [FORMULA] of dust is provided by [FORMULA] pc, where L is the integrated continuum luminosity in 1046 erg/s (Netzer 1990), leading to [FORMULA] pc for NGC 4051.

Mixing dust of Galactic ISM properties (including both, graphite and astronomical silicate; Ferland 1993) with the warm gas in NGC 4051 and self-consistently re-calculating the models leads to maximum dust temperatures of 2200 K (graphite) and 3100 K (silicate), above the evaporation temperatures (for a density of [FORMULA] cm-3 and U, [FORMULA] of the former best-fit model; Sect. 3.2). For [FORMULA] cm-3, dust can survive throughout the absorber. However, it strongly changes the equilibrium conditions and ionization structure of the gas via strong photoelectric heating and collisional cooling. For relatively high ionization parameters, dust very effectively competes with the gas in the absorption of photons (e.g. Laor & Draine 1993).

An interesting point to pursue in this context is the following: An old puzzle is the lack of any transition region between BLR and NLR (judged from missing 'intermediate' line emission). Netzer & Laor (1993) proposed this to be due to the relatively more important influence of dust in an intermediate zone. Can the warm absorber be identified with this transition region ?

Firstly, re-running a large number of models, we find no successful fit of the X-ray spectrum. This can be traced back to the relatively higher importance of edges from more lowly ionized species, significantly changing the X-ray absorption spectrum and particularly a very strong Carbon edge. Secondly, independent evidence for non-dusty warm gas comes from the observed UV and EUV spectrum, if these components travel along the same path as the X-ray spectrum. The 2175 Å  bump in the UV spectrum of NGC 4051 is not particularly strong (e.g. Walter et al. 1994) and NGC 4051 is detected by EUVE (Marshall et al. 1995). (There are various possibilities to change the properties of dust mixed with the warm material. The one which minimizes the aforementioned observable features, i.e. weakens the 2175 Å  absorption and the 10µ IR silicon feature, and is UV gray, consists of a modified grain size distribution, with a dominance of larger grains (Laor & Draine 1993). However, again, such models do not fit the observed X-ray spectrum, even if silicate only is assumed to avoid a strong carbon feature and its abundance is depleted by 1/10.) Indubitably, the dust in NGC 4051 could be significantly different from the Galactic one. However, too many additional free parameters are introduced in this case to warrant a more detailed study.

We conclude that the soft X-ray spectrum of NGC 4051 is not dominated by a (Galactic-ISM-like)dusty warm absorber. We emphasize, however, that dusty warm absorbers might explain the low-energy absorption edges seen in some active galaxies (work in progress, for first results see Komossa & Fink 1996).

The absence of dust in the warm material would imply either (i) the history of the warm gas is such that dust was never able to form, like e.g. in an inner-disc driven outflow (e.g. Königl & Kartje 1994, Murray et al. 1995, Witt et al. subm.) or (ii) if dust originally existed in the absorber, the conditions in the gas have to be such that dust destruction is guaranteed. In the latter case, one obtains an important constraint on the density (location) of the warm gas, which then has to be high enough (near enough) to ensure the dust is destroyed. For the present case (and Galactic-ISM-like dust) only a narrow range in density around [FORMULA] cm-3 is allowed. For lower densities, dust can survive in at least part of the absorber and higher densities have already been excluded in Sect. 4.2.

5.2.5. Warm-absorber intrinsic line emission and covering factor

Constraints on the covering factor of the warm gas result from (i) its emissivity in emission lines, which has to be low enough not to predict line emission stronger than the observed one, and (ii) the desire to account for the rather large number of Seyferts which show evidence for warm absorption (e.g. Fabian 1996), leading to the expectation of a correspondingly large mean covering.

In particular, it is interesting to ask whether one of the emission line regions present in NGC 4051 (and in Seyfert galaxies in general), like the coronal line region, or the one responsible for the broad component seen in H [FORMULA] in NGC 4051, can be identified with the warm absorber.

In the case of NGC 4051, the maximal warm-absorber intrinsic H [FORMULA] emission predicted for the best-fit model is only about 1/220 of the observed [FORMULA]. Rescaling the strongest predicted optical emission line, [FeXIV] [FORMULA] 5303, correspondingly leads to an intensity ratio [FeXIV] [FORMULA] /H [FORMULA] 0.01. This compares to the observed upper limit of [FeXIV]/H [FORMULA] as estimated from a spectrum by Peterson et al. (1985) and it is consistent with a covering of the warm material of less or equal 100%.

Due to the low emissivity of the warm gas, no strong UV - EUV emission lines are produced (e.g. HeII [FORMULA] 1640 [FORMULA] /H [FORMULA], NeVIII [FORMULA] 774 [FORMULA] /H [FORMULA], FeXVI [FORMULA] 343 [FORMULA] /H [FORMULA]).

Consequently, no known emission line component in NGC 4051 can be fully identified with the warm absorber.

This conclusion still holds when the properties of the warm material are changed compared to the 'standard' assumptions (but note, that only one parameter is varied at a time): The strength of e.g. [FeXIV] is also dependent on the density and changes by a factor of several depending on the value of [FORMULA], but stays below the observed upper limit. For subsolar metal abundances of the absorber HeII [FORMULA] 1640 becomes the strongest line in the UV-optical region due to the increased helium column necessary to ensure the same column in metal ions and thereby the same strength of the absorption edges in X-rays. For metal abundances of 0.2 [FORMULA] solar, we find HeII [FORMULA] 1640 [FORMULA] /H [FORMULA]. A strong additional IR spectral component incident on the warm gas slightly influences the line emission, although again, there is no strong contribution to the optical-UV spectrum.

5.2.6. UV absorption lines

The ionization structure of the best-fit warm absorber model indicates that the expected UV absorption by e.g. C [FORMULA] or N [FORMULA] is low. A common UV - X-ray absorber has been found in some active galaxies by Mathur and collaborators (e.g. Mathur 1994). In the following we give the expected equivalent widths for the UV lines CIV [FORMULA] 1549, NV [FORMULA] 1240 and Ly [FORMULA] predicted by the warm absorber model. The column density in C [FORMULA] is [FORMULA] which yields [FORMULA] = 108.09 cm-1, where [FORMULA] = 1549 [FORMULA]  and f = 0.28 is the oscillator strength for CIV (Allen 1955). Performing a standard curve of growth analysis (Spitzer 1978) this evaluates to give an equivalent width of [FORMULA] / [FORMULA] = -4.02 [FORMULA] where the uncertainties refer to values of the velocity spread parameter b = 100 km/s (for '+') and 20 km/s (for '-') whereas the central value is calculated with b = 60 km/s. Correspondingly, we find for NV [FORMULA] 1240 [FORMULA] and [FORMULA] / [FORMULA] = -4.69 and for Ly [FORMULA] [FORMULA] and [FORMULA] / [FORMULA] = -3.04 [FORMULA]. HST spectra would allow to search for these absorption lines and thereby further constrain the properties of the warm material.

5.3. Time variability of the spectral components and comparison with other observations

5.3.1. Warm absorber

In the preceding discussion, photoionization equilibrium was assumed. That photoionization indeed plays an important role for the ionization of warm material is shown by a direct reaction of the absorber (i.e. the depth of the OVIII absorption edge) in MCG-6-30-15 to changes in the continuum (Otani et al. 1996). The equilibrium state of the gas depends on its reaction timescale compared to the timescale of changes in the continuum flux (see Krolik & Kriss 1995). In case the continuum variations are slow compared to the recombination timescale, the warm material re-adjusts to each continuum level, whereas a mean continuum is appropriate for modeling in the opposite case. The latter seems to apply to the present observation, with no reaction of the warm gas despite changes in the luminosity. However, in the long term there are changes in the ionization parameter of the gas: An earlier ROSAT observation shows both, lower mean luminosity and ionization parameter (McHardy et al. 1995; treating and re-fitting these data with the same data reduction procedures and model assumptions as carried out for the present observation yields [FORMULA] = 0.2, [FORMULA] = 22.45, [FORMULA] = -2.2 and an integrated (0.1-2.4 keV) luminosity of [FORMULA] erg/s). Although this might mean that the warm material follows long term trends in the luminosity but not the very short-time variability, the situation seems to be more complex. McHardy et al. (1995) and Guainazzi et al. (1996) find U to be variable within one day. McHardy et al. interpret an increase in U in two orbits as a time-delayed reaction of the absorber to a continuum high-state. The limit on the density of the ionized material estimated by Guainazzi et al. is [FORMULA] cm-3. (Note an uncertainty in the density estimate of a factor of several resulting from e.g. the exact values chosen for the temperature of the warm gas, the ion abundance ratio, and the estimated time interval.) Comparing these observations with the present one, the implications are either (i) time gaps just prevented observing a reaction of the warm gas within the current data, or (ii) the warm material does not see the luminosity changes in the present observation, or (iii) the density of the warm gas varies with time, or (iv) the ionization state of the absorber is not dominated by photoionization (see Krolik & Kriss 1995, Reynolds & Fabian 1995 for some alternatives). None of the possibilities can be decided upon with the present data, but we note the following:

Possibility (i) would nearly pin down the density of the warm absorber, to lie in a narrow range around 107 cm-3.

(ii) A scenario in which the warm gas does not see luminosity changes is one in which the variability is not intrinsic to the central continuum source but caused between the absorber and the observer. Wachter et al. (1988) proposed the existence of fast moving, dense blobs of matter within the inner region of active galaxies, partially blocking the line of sight to the continuum source. A similar scenario was invoked by Kunieda et al. (1992) to explain different flux states seen in a Ginga observation of NGC 4051. The present observation is consistent with the blob model, if the source were in state 'C' (in the terminology of Kunieda et al., referring to variable soft and constant hard observed flux). We lack simultaneous observations in the harder X-ray region but placing blobs with a column density of [FORMULA] cm-2, as proposed by Kunieda et al., along the line of sight would completely absorb the incident radiation in the ROSAT sensitivity range. In that case, no density constraint on the warm material could be derived. But the origin of the blobs and their fast movement (the latter in combination with their large number to account for the observed flux states) remain to be solved.

(iii) Time-dependent density occurs e.g. if the absorber is in the form of an expanding cloud or consists of inhomogeneous material e.g. in orbital motion. In the latter case variability of the observed warm column density is also expected, which indeed is observed. There is approximately a factor of 2 change in warm column between the two ROSAT observations, being separated by 2 years (Nov. '91 and Nov. '93), and a factor of larger than 10 compared to the ASCA data (April '93) of Mihara et al. (1994), who derived [FORMULA]. Guainazzi et al. (1996) find for a second ASCA observation (July '94) roughly [FORMULA] 22.3, and indications for variability in the OVII edge.

In this context, it is also interesting to note that the warm gas in NGC 4051 is located near an instable region in the [FORMULA] diagram. A possible 3 phase equilibrium of the ionized absorber in MCG-6-30-15 was discussed by Reynolds & Fabian (1995). The results of a similar analysis for NGC 4051 are shown in Fig. 6. Those regions of the equilibrium curve in which the temperature T is multi-valued for constant [FORMULA], i.e. pressure, allow for the existence of multiple phases in pressure balance. The parts with negative gradient correspond to thermally unstable equilibria. For comparison, the corresponding curves for metal abundances deviating from the solar value are shown.

[FIGURE] Fig. 6. Equilibrium gas temperature T against [FORMULA] for various SEDs incident on the gas and abundances of the gas. The solid line corresponds to the SED of NGC 4051 used for the modeling. The position of the warm absorber is marked. The other models correspond to a modification of either metal abundances of 0.2 [FORMULA] solar (lower dashed line) or 3 [FORMULA] solar (upper dashed line) or spectral shape; dot-dashed: additional EUV black body component as described in Sect. 3.2, dotted: 'mean Seyfert' continuum but with [FORMULA] = -1.5, for comparison.

5.3.2. Powerlaw component

The possibility of producing all observed spectral variability in NGC 4051 by warm absorption has been repeatedly mentioned (e.g. Matsuoka et al. 1990, Fiore et al. 1992, Mc Hardy et al. 1995). We find a significantly steeper powerlaw slope ([FORMULA] = -2.3) as compared to other observations (e.g. [FORMULA] = -1.88, Mihara et al. 1994). Consequently, not all soft X-ray spectral variability in NGC 4051 can be traced back to the influence of the warm absorber. In particular, the powerlaw slope is also steeper than is predicted by currently popular non-thermal pair models (e.g. Svensson 1994).

Short-timescale variability of [FORMULA] during one Ginga observation has been favoured by Matsuoka et al. (1990; and has recently been found in ASCA data, Guainazzi et al. 1996). In the Ginga data, when described by a powerlaw SED, a change of the 2-10 keV flux by a factor of 3-4 was accompanied by a change [FORMULA] = 0.4-0.5. During the present observation, we find [FORMULA] to be essentially constant despite changes in flux by a factor of larger than 4. This corroborates the complex and probably time-dependent behaviour of this source.

5.4. NLSy1 - character of NGC 4051

NLSy1 galaxies generally exhibit steep soft X-ray spectra and narrow Balmer lines (see Boller et al. 1996 for a recent detailed discussion). These properties are also shown by NGC 4051, in the sense that a simple powerlaw fit to the X-ray spectrum results in a rather steep powerlaw with [FORMULA] = -2.9 and the FWHM of H [FORMULA] is less than 1000 km/s. However, much of the X-ray spectral steepness of NGC 4051 is caused by the presence of the warm absorber. On the other hand, the intrinsic powerlaw slope is still steeper than the canonical one with [FORMULA] = -1.9. And an additional soft excess is seen in source high-states. This points to the complexity of NLSy1 spectra with probably more than one mechanism at work to cause the X-ray spectral steepness.

A dusty environment in NLSy1 galaxies was proposed as one explanation for the narrowness of their broad lines (Goodrich 1989). Dusty warm gas was suggested to exist in the infrared loud quasar IRAS 13349+2438, which has several properties in common with NLSy1 galaxies (Brandt et al. 1996). In case of NGC 4051 no successful description of the X-ray spectrum is achieved when compared to models including dust. The general trend holds that it is more difficult to produce steep soft X-ray spectra with dusty absorbers. On the contrary, the existence of relatively stronger absorption edges from more lowly ionized species generally leads to an effective flattening of the spectrum when the edges are not individually resolved.

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Online publication: June 5, 1998