Broad Iron Lines in Active Galactic Nuclei: Abstract. The broad lines in Active Galactic Nuclei (AGN) discovered recently have

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1 Broad Iron Lines in Active Galactic Nuclei: A possible test of the Kerr Metric? Jorn Wilms 1, Roland Speith 2, and Christopher S. Reynolds 3 1 Institut fur Astronomie und Astrophysik, Abt. Astronomie, Waldhauser Str. 64, D Tubingen, Germany 2 Institut fur Astronomie und Astrophysik, Abt. Theoretische Astrophysik, Auf der Morgenstelle 10, D Tubingen, Germany 3 JILA, University of Colorado, C. B. 440, Boulder, CO , U.S.A. Abstract. The broad lines in Active Galactic Nuclei (AGN) discovered recently have been interpreted as evidence for emission close to the central black hole. We briey describe the physical processes leading to the line emission, describe the computational methods used to compute the emerging line proles, and summarize the qualitative behavior of these lines. We present the observational evidence for the relativistic lines, concentrating on the properties of the line in MCG? , where the line prole shows strong indications that a Kerr black hole is present in the object. Finally, we show how future X-ray missions will help in deepening our understanding of the emission of broad iron lines from AGN. 1 Introduction As reviewed in several chapters of this volume, there is ample evidence for the presence of optically thick accretion disks in Active Galactic Nuclei (AGN) and in Galactic black hole candidates. While the high luminosity of AGN is a good indicator for the presence of a deep potential well, the evidence for the geometry of the accretion process has to rely mainly on indirect evidence from the UV, X-ray, and -ray spectrum. The ultraviolet excess seen in most AGN, the \big blue bump", and (probably) also the soft X-ray excess below 1 kev are usually assumed to originate in the accretion disk. At energies above 1 kev the spectrum of AGN can be roughly described by a power-law with a photon index of 1.7 and, at least in Seyfert galaxies, an exponential cuto above 100 or 200 kev. The current physical interpretation of this X-ray and -ray power-law component is that of Comptonization of the soft photons in a hot electron plasma, usually called an accretion disk corona, situated geometrically close to the accretion disk (Dove, Wilms & Begelman, 1997; Hua & Titarchuk, 1995; Haardt, Maraschi & Ghisellini, 1994, and references therein). See Svensson (1996) for a review of the radiation processes around AGN. Although the geometry of the X-ray producing region is still unclear, with possibilities ranging from \standard" thin accretion disks to more complicated accretion geometries as the advection dominated ows and the solutions proposed by Chakrabarti in this volume, there is general agreement that the high temperatures necessary for the production of

2 the hard radiation are only possible in the close vicinity of the black hole, closer than about 100 Schwarzschild radii, where relativistic eects are important. The X-ray and -ray radiation from Seyfert galaxies, therefore, should exhibit signatures that allow us to directly probe this region and perhaps even to nd physical processes enabling us to directly measure parameters of the black hole as its mass or its angular momentum. The availability of high sensitivity X-ray and -ray satellites in the past ten years has allowed the observational study of the broad band spectrum of AGN to search for such processes. Recently, extremely broad Iron uorescence lines have been observed in several Seyfert galaxies. The most convincing interpretation for these lines is that they are produced in a geometrically thin accretion disk close to the central black hole. If this interpretation is correct, the line proles are the best evidence for the existence of black holes known so far. In this review, we give a brief introduction to the eld. In x2 we describe the physical processes leading to line emission close to the black hole, i.e. Compton reection and uorescent line emission (x2.1), followed by a description of the computational methods used to calculate the emerging line proles (x2.2), and a summary of the qualitative behavior of the emitted lines (x2.3). In x3, we describe the observational evidence for the relativistic lines and give a summary of possible future observations. A recommended review of the subject, stressing the observational material, has recently been published by Fabian (1997). 2 Line Emission Close to the Black Hole 2.1 Compton Reection and Reprocessing One direct consequence of the Accretion Disk Corona model is that it requires the presence of a hot electron plasma with a temperature of a few 100 kev in the close vicinity of the cold accretion disk, which has a temperature of less than 10 6 K ( 0:1 kev). Due to the proximity of the cold material, hard X-rays emitted from the corona interact with the cold material, leading to observable spectral features. In a gas with kt < 0:2 kev, only Hydrogen and Helium are fully ionized. Most metals, i.e. elements with a nuclear charge number Z > 2, are only moderately ionized (Shull & Van Steenburg, 1982). Since the crosssection for photoabsorption is bf / E?3, most of the irradiating soft X-rays (i.e. photons with E < 10 kev) get photo-absorbed within the accretion disk. On the other hand, the cross-section for Compton scattering is almost equal to the Thomson cross section T (a constant), so that photons with high energies predominantly Compton scatter o the electrons in the disk. The threshold energy above which Compton scattering dominates is about 15 kev. Since the electrons in the accretion disk have low thermal velocities, Compton scattered X-ray photons with E 15 kev loose energy. The result of these two processes, photoabsorption and Compton scattering, is a \hump" of radiation in the spectrum emerging from the disk, peaking at about 30 kev(fig. 1; see also Lightman 2

3 & White, 1988; George & Fabian, 1991; Magdziarz & Zdziarski, 1995, and references therein). Such humps have indeed been found in many Seyfert galaxies, proving the presence of cold matter in these objects (Nandra & Pounds, 1994). Γ= Flux [arbitrary units] Fig. 1: Reection spectrum for a cold disk irradiated with a power-law with photon-index? = 1:9. From top to bottom, the plot shows the total emerging spectrum, the incident power-law, and the reection spectrum. Note the strong Iron K line at 6.4 kev and the Iron K line and Iron K edge at 7.1 kev. The spectrum was generated with our Monte Carlo code (Wilms, 1996, unpublished), using the cosmic abundances given by Grevesse & Anders (1989), photoabsorption cross-sections from Verner et al. (1993), and uorescence yields from Kaastra & Mewe (1993). In addition to the reection hump, the reprocessing of the irradiated X-rays within the accretion disk also leads to the production of emission lines in the X- ray spectrum below 10 kev. The absorption of an X-ray photon by the K-shell of an atom can lead to the emission of a K uorescence photon. For astronomical objects, features of Iron are especially abundant, since Iron has a high cosmic abundance and high uorescence yield (Fig. 1). Consistent with this picture, Iron features have been found in most Seyfert galaxies (Pounds et al., 1989). 2.2 Radiative Transfer in the Kerr Metric Since the spectrum is emitted close to the black hole, an observer at innity will see the spectrum of Fig. 1 \distorted" by relativistic eects, namely Doppler boosting and gravitational red-shift. In this section, we briey show how to take 3

4 care of these eects. Due to space limitations reasons, we can only sketch the important physics, for the details we refer to the literature referenced. The specic ux F o at frequency o as seen by an observer at innity is dened as the (weighted) sum of the observed specic intensities I o from all parts of the accretion-disk, F o = Z I o cos d (1) where is the solid angle subtended by the accretion disk as seen from the observer and is the angle between the direction to the disk and the direction of the observed photon. Since the black hole (=AGN) is assumed to be very far away from the observer (=us), we can safely set cos = 1. Thus, we \only" have to compute the specic intensity I o at innity from the spectrum emitted on the surface of the accretion disk, I e. In an axisymmetric accretion disk, I e is a function of the radial distance of the point of emission from the black hole, r e, and of the inclination angle, i e, of the emitted photon, measured with respect to the normal of the accretion disk. Due to Doppler boosting and gravitational red-shift, the observed frequency o is related to the emitted frequency e by g = o e = z where z is the red-shift of the photon. According to Liouville's theorem, the phase-space density of photons, proportional to I= 3, is constant along the path of propagation of the photon (the null-geodesic). It is therefore possible to express eq. (1) in terms of the emitted specic ux on the accretion disk: F o = Z I o 3 o 3 o d = Z I e 3 e 3 o d = Z (2) g 3 I e (r e ; i e ) d; (3) In other words, the computation of the emerging spectrum breaks down to the computation of the \red-shift" g. In the weak eld limit, when r=m 3 in geometric units, and in the Schwarzschild metric, g and therefore the line prole emitted by the accretion disk, can be evaluated analytically. Proles computed this way have been presented, e.g., by Fabian et al. (1989) for the Schwarzschild case, and by Chen & Halpern (1989) in the weak eld limit. In most cases, however, the computation has to be done in the Kerr metric since the accreting black hole will be sped up by the accreted material (Thorne, 1974). The \brute force" approach to the computation of g in the Kerr metric is the direct integration of the trajectory of the photon in the Kerr metric (Bromley, Chen & Miller, 1997; Karas, Vokrouhlicky & Polnarev, 1992, and references therein). This approach allows the computation of exact line proles even in the case of very complicated geometries, like thick accretion disks, but is very expensive: The computation of one line prole takes several hours on a typical workstation, and several tens of minutes on a supercomputer (Bromley, Chen 4

5 & Miller, 1997, quote a computation time of 15 minutes on a Cray T3D with 128 nodes for the computation of one line prole). It is clear, therefore, that ray-tracing is not suitable for the analysis of X-ray observations, where a direct comparison between the measured data and the theory is to be made using a 2 minimization method. The second way to compute the observed ux was rst used by Cunningham (1975) who noted that the observed ux from eq. (3) can be expressed by F o = Z T (i e ; r e ; g)i e (r e ; i e ) dg r e dr e (4) where the integration is carried out over all possible \red-shifts" g and over the whole surface of the accretion disk. This form is well suited for fast numerical evaluation. All relativistic eects are hidden in the transfer-function T. We refer to Cunningham (1975), Laor (1991), Speith, Riert & Ruder (1995), and the references in these works for the technical details. Numerical values for T from the computations of Laor (1991) are available in FITS-format as part of the popular X-ray analysis package XSPEC (Arnaud, 1996). For detailed studies, a FORTRAN 77 code is available (Speith, Riert & Ruder, 1995). This code needs about 5 minutes on a DEC Alpha machine (233 MHz) to compute T for one value of i e. The evaluation of the line prole afterwards takes almost no time. 2.3 The Emerging Line Prole In Figs. 2 to 4 we illustrate the relativistic eects on the emerging line prole. Due to its astrophysical importance, we chose the Iron uorescence line at 6.4 kev for our examples. To facilitate the translation to other lines, we indicate the redshift on the upper abscissa of the gures. All line proles have been computed with the code of Speith, Riert & Ruder (1995). In our computations we assumed a geometrically thin, optically thick Keplerian accretion disk to be the source of the line radiation. We note that our adopted velocity prole is dierent from the proles resulting from the thick accretion disks presented by Chakrabarti elsewhere in this volume. The local emissivity of the line on the disk was parameterized as I e (r e ; i e ) / (1 + a) b r? (5) where a, b, and are free parameters, and where = cos i e. This parameterization is sucient for most practical work (Bao, Hadravana & stgaard, 1994). For optically thick material, a; b = 0, for the optically thin case, a = 0, b =?1, and for general limb-darkening, a 6= 0, b = 0. In our computations, the disk was assumed to be optically thick. For realistic accretion disks, the coecient for the radial emissivity,, is in the range between 2 and 3 (the comparison with observations, x3, indicates 3). Common to all line proles is a characteristic double-horned shape (Fig. 2). This shape is due to the Doppler eect, with the line emitted from material 5

6 z=(e e /E o ) o I νo [arbitrary units] o 20 o 30 o 40 o 50 o 60 o Fig.2: Line prole as a function of the inclination angle i o for a = 0:9981 and = 0:5. 70 o 80 o receding from the observer being red-shifted, and the line emitted from material moving towards the observer being blueshifted. Contrary to accretion-disks around normal stars, the emitted line prole is not symmetric: relativistic boosting results in the blue wing of the line to be much stronger than the red wing (it is customary in astronomy to call lower energies \red" and higher energies \blue", even when talking about lines in other energy bands than the optical). In addition to the Doppler boosting, the line is also red-shifted due to the gravitational red-shift. The inuence of both eects on the line prole is dependent on the observers' inclination angle i o : For a disk seen almost face on (i.e. i o close to 0 ), the gravitational red-shift dominates. With larger and larger i o, Doppler eects become dominant. The broadest parts of the prole are due to material emitted very close to the black hole, as is evident from Fig. 3, where line proles for dierent emissivity coecients are shown. For large, most of the line emission takes place close to the last stable orbit, so that these proles are the broadest. Note that for values of > 2 the red wing of the prole gets weaker until it is almost undetectable. For the same emissivity coecient, the blue wings of lines emitted from disks around Schwarzschild and Kerr black holes are almost indistinguishable (Fig. 4), the red wings, however, are very dierent since in the Kerr case the radius of marginal stability, i.e. the inner edge of the accretion disk, is closer to the black hole than in the Schwarzschild case. Therefore, the red wing of the line can extend to much lower energies than in the Schwarzschild case. These eects from regions close to the last stable orbit, are the most promising for measuring 6

7 I νo [arbitrary units] z=(e e /E o ) i o = 40 o Fig.3: Line prole as a function of the coecient of radial emissivity,, where the emitted intensity prole is I e / r? (eq. (5)), for a black hole with a = 0:5. To emphasize the dierent proles, the lines have been ux-normalized z=(e e /E o ) I νo [arbitrary units] i o = 40 o Fig.4: Line prole for dierent angular momenta a = J=M of the Kerr black hole for an inclination of i o = 40 and = 3. 7

8 general relativistic eects around Kerr black holes (Laor, 1991). Photon Flux [10-5 ph cm -2 s -1 kev -1 ] MCG Fig. 5: Average line prole of MCG? , as observed with ASCA. The best- t power-law continuum has been subtracted (after Tanaka et al., 1995, Fig. 2). 3 Observational Evidence for Broad Iron Lines 3.1 The Case of MCG? The rapid evolution of moderate resolution X-ray detectors in the past decade nally made the discovery of relativistically broadened Iron lines possible. The best candidate for such a line is the Seyfert galaxy MCG? Here, the Japanese Advanced Satellite for Cosmology and Astrophysics (ASCA) discovered a strongly broadened Iron feature, with a full width at zero intensity of km/sec (Tanaka et al., 1995, Fig. 5). Comparing Fig. 5 with Fig. 2 shows that such a prole has to come from a disk that is seen close to face-on, since the blue-wing of the line is still very close to the rest-frame energy of the line. Fitting the data with the theoretical line models shows that the observed line prole is consistent with that emitted by an accretion disk seen at an inclination of 30 3 (Tanaka et al., 1995). As we showed in the last section, the line proles from Schwarzschild and Kerr black holes are very similar, with the main dierence being in the very red parts of the line. For determining the type of the black hole, therefore, a more careful analysis of the observation of MCG? has to be done. Iwasawa et al. (1996) looked at the temporal changes of the Iron line prole during the 4.5 days of the ASCA observation and correlated the prole with the observed variability of MCG? They were able to nd 8

9 three distinct \states" of the line: for times where MCG? was close to its average ux (Fig. 6b), the prole is similar to the average prole shown in Fig. 5, at times where the ux was very large (Fig. 6a), the line prole is very narrow and centered at 6.4 kev. Finally, when the source intensity is very small (Fig. 6c), the line is very broad and extends down to about 4 kev. This large width is only possible if the line is emitted from material inside six gravitational radii, i.e. inside the marginally stable orbit for a Schwarzschild black hole. Such an emission is only possible if the central object is a Kerr black hole where the disk can extend to smaller radii. Photon Flux [10 ph/(s cm kev)] a) b) c) Fig. 6: Variability of the uorescent iron line in MCG? , the dierent panels show the line prole for phases with high ux (a) down to phases where the continuum ux was very small (after Iwasawa et al., 1996, Fig. 7) If this interpretation of the line variability is true, then the observations present the rst direct evidence for rotating black holes. Although various objections have been raised against the interpretation of the line as a relativistic line, most objections can be rejected on physical grounds (Fabian et al., 1995) 1. There is strong evidence that the broad Iron line of MCG? is not a special case, but that broad Iron lines are a common phenomenon. In a recent study, Nandra et al. (1997) analyzed ASCA observations of 18 Seyfert 1 galaxies. 1 See, however, the objections by Reynolds & Begelman (1997) that could weaken the result for the angular momentum of the central black hole. 9

10 They nd evidence for broad lines with a strong asymmetry of the proles to the red in all 14 objects in which they could detect a line. Nandra et al. (1997) were able to explain these lines with relativistic line proles, but due to the poor signal to noise ratio they could not distinguish between lines from Kerr or Schwarzschild black hole accretion disks. 3.2 The Future: AXAF, XMM, and Such Although the ASCA results are very exciting and have undoubtfully opened the door to directly observing relativistic eects in AGN, more detailed observations are needed. With the currently planned next generation X-ray missions, the American Advanced X-ray Astrophysics Facility (AXAF; launch 1998), the Russian Spectrum-X/ (SXG, launch 1998), the European X-ray Multiple Mirror mission (XMM; launch 1999), and the US-Japanese Astro E (launch 2000), we will be able to use X-ray instruments with a much higher energy resolution and larger eective areas than presently available. The huge eective area of XMM will allow us to probe for temporal variability in the line on much smaller time-scales than presently possible: With XMM we might be able to study the time-delay between uctuations in the continuum and the reaction of the line to these uctuations, allowing us to directly probe the geometry of the accretion ow. The large energy resolution of AXAF and Astro E will enable us to measure line proles with a much higher resolution than ever before, which should help us to distinguish without doubt between the current relativistic models for the broad line emission. In the framework of the European EPIC consortium for XMM, two of us (J.W. and C.S.R.) have proposed an uninterrupted 100 ksec observation of MCG? The signal to noise ratio of such an observation will be much higher than that of Fig. 6, making the study of the line variability on short time-scales possible. Our future ability to observe relativistic eects happening on a large scale close to 10 8 M black holes look very positive indeed. Acknowledgments J.W. thanks Prof. N. Straumann for his enthusiastic suggestion to write this review and to Prof. F. W. Hehl for his invitation to include the review in these proceedings. We thank J. Dove, I. Kreykenbohm, K. Pottschmidt, T. Rauch, and R. Staubert for helpful discussions. References Arnaud, K. A., 1996, in Astronomical Data Analysis Software and Systems V, ed. J. H. Jacoby, J. Barnes, (San Francisco: Astron. Soc. Pacic), 17 Bao, G., Hadravana, P., stgaard, E., 1994, ApJ, 435, 55 Bromley, B. C., Chen, K., Miller, W. A., 1997, ApJ, 475, 57 Chen, K., Halpern, J. P., 1989, ApJ, 344,

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