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

1. Introduction

It is a well established fact that the maximum of the spectral energy distribution of quasars occures in the largely unobservable spectral range between the extrem UV and the soft X-ray domain. In many objects a steepening of the spectrum in the soft X-ray range as compared to the hard X-rays is observed which, in combination with the turnover of the spectrum in the UV range, suggests that these two components combine in the largely unobservable range between Hz and Hz to form the so called big blue bump emission. Continued attempts have been made to derive a self-consistent emission model which is able to account for this spectral component, the most probable scenario being thermal emission from an accretion disk around a central super-massive compact object.

The theory of standard geometrically thin -accretion disks is largely based on the paper of Shakura & Sunyaev (1973 ) and a general relativistic version presented by Novikov & Thorne (1973 ). It has soon turned out that simple accretion disk models based on multi-temperature blackbody emission from an optically thick accretion disk (Malkan & Sargent 1982 , Malkan 1983 ), at sub-Eddington accretion rates, are not sufficiently hot, or else that highly super-Eddington accretion rates would be required, for the accretion disk to emit an appreciable fraction of the radiation in the soft X-ray range (Bechtold 1987 ). A number of authors have improved this simple model by considering various effects on the structure and emission spectrum of the disk. Czerny & Elvis (1987 ), and Wandel & Petrosian (1988 ) calculated the radiative transfer by including free-free opacities and the effects of Comptonization in a simple analytic manner. Bound-free opacities as well as relativistic effects were included by Laor & Netzer (1989 ) and Laor et al. (1990 ). Most computations of model spectra to date, however, adopted a given vertical structure or made use of an averaging in the vertical direction. A detailed investigation of the emission spectrum was performed by Ross, Fabian, & Mineshige (1992 ), using the Kompaneets equation (Kompaneets 1957 ) to treat Compton scattering and including free-free and bound-free opacities of hydrogen and helium. They solved the vertical temperature structure and atomic level populations for a predetermined constant vertical density profile. A self-consistent solution of the vertical structure and radiative transfer is given by Shimura & Takahara (1993 ) and Shimura & Takahara (1995 ) for a Newtonian disk. In their viscosity description, they made the ad hoc assumption that the local heating rate is proportional to the mass density. In our approach (Dörrer et al. 1996 ), the vertical structure and radiation field of a disk around a Kerr black hole is calculated in a self-consistent way. Moreover, we use a different viscosity description. In Sect. 4 a short review of this model is given.

In the framework of the unified model the different properties of Active Galactic Nuclei are explained as being due to the different inclination angles under which the observer sees the accretion disk as well as various additional components such as absorbing material, emisssion line clouds or jets. The emission from the accretion disk is best studied in objects seen under intermediate inclination angles where the disk emission is neither obscured by an absorbing gas and dust torus nor is it swamped by beamed emission from a relativistic jet (in systems seen nearly face on). Such intermediate inclination angles are thought to lead to source properties as observed in radio-quiet quasars and Seyfert I galaxies. Thus, high signal-to-noise data, covering the spectral range from the UV to the soft X-ray range, of samples of such objects are best suited to investigate whether their broad-band spectra may be understood in terms of emission from an accretion disk. We have selected a sample of 31 radio-quiet quasars (see Sect. 2 for a discussion of the selection criteria), which were observed both by IUE in the energy range from 130 to 305 nm and by ROSAT in the energy range from 0.1 keV ( 3 nm) to 2.4 keV ( 0.5 nm) in order to investigate whether the UV and soft X-ray spectra of these objects are in agreement with predictions based on our accretion disk emission model.

The X-ray emission in the ROSAT energy band consists of at least two components, a hard power law component, extending to higher X-ray energies, beyond the ROSAT energy range, and a soft component, known under the name of soft X-ray excess emission, which in many AGN dominates the spectrum at energies below 0.5 keV and which is widely thought to originate in the inner part of an accretion disk. Testing the predictions of our accretion disk model thus requires to separate the contributions of these two emission components. Due to the limited energy resolution of ROSAT and also due to its limited spectral coverage at higher X-ray energies ( 2.4 keV), except for the brightest objects, this is not possible based on the ROSAT data alone. We therefore make use of published hard X-ray spectral slopes to separate the two emission components in our spectral fits. As a first approach we have compared spectra from deep ROSAT pointings with the hard power law spectra taken from the literature, to convince ourselves that soft excess emission is indeed present in almost all of the objects (see Sect. 3).

Things are further complicated by the fact that in the UV range different spectral components contribute to the emission. We treat this by including an additional power law component in our model fits extending from the IR with an exponential cutoff at around Hz. Details on the model fitting performed and on the resulting distributions of the four accretion disk model parameters central mass M, mass accretion rate , viscosity parameter , and the inclination angle can be found in Sect. 5. A similar study using data from the ROSAT All Sky Survey based on an earlier version of the present accretion disk model is presented by Friedrich et al. (1997). A brief comparison of the two models and a summary of basic results is given in Staubert et al. (1997).

© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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