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Astron. Astrophys. 326, 885-896 (1997)

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5. Model fits to the IUE and ROSAT data

We have performed [FORMULA] fits to the UV to soft X-ray continuum spectra of the 31 sample quasars in order to investigate whether the observed spectra are indeed in agreement with our model, i.e. whether satisfactory best-fit minimum [FORMULA] values are achieved and the resulting accretion disk model parameters are in line with our general understanding of the quasar phenomenon.

As already mentioned in the introduction, in order to separate the accretion disk emission from the underlying hard power law spectrum, where available we took the spectral index for the hard power law from the literature (Einstein Observatory, EXOSAT, GINGA; Malaguti et al., 1994). Otherwise, a canonical value of 0.7 was adopted. X-ray variability between the observation in the soft and hard X-ray bands was allowed for by treating the normalization of the hard power law spectrum as a free parameter. The spectral indices and references used are listed in Table 4.

We have not included infrared and optical data in the spectral analysis, because such measurements were not available for all of the sample members and many different emission components (non-thermal synchrotron emission, thermal dust emission, BLR and NLR line emission, emission from the host galaxy) would needlessly complicate the analysis. Emission components at low frequencies which in addition to the accretion disk also contribute to the emission in the UV range were incorporated into the model by assuming a power law component with spectral index [FORMULA] and an exponential cutoff in the extreme UV range ([FORMULA] Hz) which mainly represents the non-thermal synchrotron component.

Interstellar low energy X-ray absorption is included in our spectral fits by using the galactic hydrogen column densities by Stark et al. 1992 and Elvis et al. 1989 and by applying the cross sections by Morrison & Mc Cammon (1983 ). Note that the de-reddening of the UV data, based on the same hydrogen column densities, was already applied to the data prior to the spectral fitting (see Sect. 2). We did not consider intrinsic absorption in the accretion disk model fitting. This is justified as no evidence for intrinsic absorption was found in our spectral power law fits and, generally, high luminosity objects (i.e. quasars as opposed to lower luminosity AGN) at moderate redshifts are not expected to show large amounts of intrinsic absorption.

The total fit function thus includes three components with a total of six free parameters:

1. Accretion disk model with four free parameters (M, [FORMULA], [FORMULA], [FORMULA])

2. Underlying hard power law with a slope taken from the literature (free normalization)

3. Soft power law with [FORMULA] and a cutoff in the EUV (free normalization).

The accretion rate [FORMULA] is measured in units of the Eddington accretion rate [FORMULA], where [FORMULA] is the Eddington luminosity, [FORMULA] is the efficiency of accretion, and [FORMULA] is the Thomson opacity. One additional parameter of the accretion disk model, the specific angular momentum [FORMULA] of the black hole was fixed at [FORMULA], i.e., we have considered only the non-rotating case with [FORMULA].

To compare the accretion disk model with observations, we calculated model spectra for a fixed grid in 4 dimensional parameter space consisting of 980 data points (see Table 3). At intermediate points within the grid, model spectra were computed by linear interpolation.


Table 3. Grid of accretion disk model parameters


Table 4. Table of the resulting fit parameters. [FORMULA]: Spectral index of the underlying hard power law. [FORMULA] mean value of Exosat and Ginga observations; [FORMULA] additional HEAO data. All data are taken from Malaguti et al. 1994 . [FORMULA] was set to 0.7 where no measurements were available. All parameters are given with their upper ([FORMULA]) and lower (-) 1 [FORMULA] -errors. If there is no value in the list (-) the error exceeds the parameter boundary. Masses are in units of [FORMULA] and accretion rates are in units of the Eddington accretion rate.

Simultaneous fits of the ROSAT and IUE data were performed by folding the model X-ray fluxes with the response of the ROSAT PSPC detector to determine the ROSAT count rates predicted by our model in each spectral bin. The UV fluxes predicted by the model were compared directly with the de-reddened IUE continuum fluxes (see Sect. 3). Model fluxes were calculated from the source luminosities emitted by the accretion disk by assuming a Hubble constant [FORMULA] and [FORMULA]. Note that in particular the best-fit central masses M are dependent on these assumptions, i.e., M is approximately proportional to [FORMULA]. Statistical errors of the best-fit parameters were determined by calculating a [FORMULA] grid in parameter space. The region defined by [FORMULA], corresponding to the 68 % value of the cumulative [FORMULA] -distribution for 4 degrees of freedom, was then used to construct the upper and lower 1 [FORMULA] errors of the fit parameters.

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998