A&A 387, 422-428 (2002)
T. Beckert1 - W. J. Duschl2,1
1 - Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
2 - Institut für Theoretische Astrophysik, Tiergartenstraße 15, 69121 Heidelberg, Germany
Received 24 April 2001 / Accepted 18 March 2002
We have calculated stationary models for accretion disks around super-massive black holes in galactic nuclei. Our models show that below a critical mass flow rate of advection will dominate the energy budget while above that rate all the viscously liberated energy is radiated. The radiation efficiency declines steeply below that critical rate. This leads to a clear dichotomy between AGN and normal galaxies which is not so much given by differences in the mass flow rate as by the radiation efficiency. At very low mass accretion rates below synchrotron emission and Bremsstrahlung dominate the SED, while above the inverse Compton radiation from synchrotron seed photons produce flat to inverted SEDs from the radio to X-rays. Finally we discuss the implications of these findings for AGN duty cycles and the long-term AGN evolution.
Key words: accretion, accretion disks - black hole physics - radiation mechanisms: non-thermal - galaxies: active - galaxies: nuclei
Seyfert Galaxies, on the other hand, are spiral galaxies which host an AGN. Activity in the nucleus, which is powered by accretion into a BH, can be discriminated against starbursts in Seyferts from radio and X-ray observations. Radio cores and jets with brightness temperatures above 108 K have been detected in some Seyferts (Ulvestad et al. 1999; Mundell et al. 2000; Falcke et al. 2000). Their flux stability over several years exculdes radio supernovae as the power supply. The X-ray emission shows rapid variability and in some cases a redshifted Fe K line, which is an indicator of relativistic motion in the accretion disk around the BH. The masses of BHs in some Seyfert 1 galaxies have been measured by reverberation mapping of variable and correlated continuum and line emission (Peterson & Wandel 2000). These measurements are in reasonable agreement with the relation of enclosed mass ( ) versus velocity dispersions in bulges of normal galaxies (Gebhardt et al. 2000). It is therefore reasonable to assume the existence of supermassive BH in most elliptical galaxies and spirals with bulges.
While in the high luminosity objects both jet and accretion disk can be identified in the spectrum, the situation is different in less luminous AGNs like weak Seyfert Galaxies and LINERs. But even here small scale jets are commonly found (Falcke et al. 2000) and argue for the existence of BHs. For instance NGC 4258 is an interesting transition object showing both an outer irradiated thin accretion disk and a small scale radio jet. A geometrically thin standard accretion disk close to the black hole can not be identified, but the ionizing X-rays maybe produced at the base of the jet, which can be identical with the proposed advection-dominated accretion flow (ADAF) within (Gammie et al. 1999; : Schwarzschild radius). At even lower luminosities the Galactic Center (Sgr A*) with a BH mass of (Genzel et al. 1997) is the only visible AGN with a power output of . A comparable object in any other galaxy (spiral or elliptical) would not be seen as an AGN. Assuming an spherical and adiabatic Bondi inflow, cooled only by Bremsstrahlung, gives an radiation efficiency (Frank et al. 1992). Bremsstrahlung will be emitted in X-rays and the Chandra detection (Baganoff et al. 2001) of erg s-1 is consistent with a mass accretion rate of yr-1and an efficiency of . The sub-mm luminosity of Sgr A* is about 30 times larger than the X-ray flux and makes Sgr A* a unique object. We will discuss a specific ADAF model for Sgr A* in Sect. 3. The Bondi flow faces at least two problems: it does not allow for any possible angular momentum of the inflow and does not include magnetic fields, which lead to synchrotron emission at radio frequencies and synchrotron self-compton cooling. Both can be accounted for in ADAF models. They provide a reasonable explanation for the spectral energy distribution (SED) of Sgr A* with a mass accretion of yr-1and a radiative efficiency of 10-5. Beside the basically unresolved radio core of Sgr A*, it is not possible to identify a jet in the Galactic Center.
In this paper we will explore the hypothesis, that most of the normal galaxies without substantial AGN activity contain supermassive black holes some of which have been active during the quasar phase 0.3 < z < 5 (z being the cosmological redshift) and are quietly accreting in an ADAF mode today. Spectral properties of ADAFs with rather large mass accretion rates are explored in Sect. 2. The total luminosities and spectral energy distributions are of interest for weak AGNs (Ho 1999). We investigate the transition from standard thin disk accretion to ADAFs and vice versa as an upper limit in the mass accretion rate for ADAFs in Sect. 4. The combined consequences for accretion in normal galaxies are discussed in Sect. 5.
|Figure 1: Spectral energy distribution (SED) for ADAF models with a black hole mass of . The mass accretion rates are yr-1. The scale-free accretion rate for this BH is . The spectral energy flux increases for increasing mass accretion rate with an exception at , which is plotted with a dashed curve.|
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|Figure 2: SED for an ADAF around a black hole. The mass accretion rate is corresponding to /yr. The seed photon flux is represented as dashed line, the first and second Compton humps are dash-dotted and dotted respectively. Further Comptonization is important but individual humps are smeared out. Only the total SED is shown as solid line. The dependence of the spectral shape on the black hole mass is weak, while the total flux scales with the mass accretion rate according to Eq. (2).|
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From the described model we can construct spectral energy distributions (SED) for different mass accretion rates. The mass of the central BH has only a weak influence on the SED, which is not included in the scaling of to the Eddington accretion rate, and is not considered here. We assume a mass of for the SED in Fig. 1, appropriate for the Galactic Center, with a corresponding Eddington limit of yr-1 (in this paper we define the Eddington accretion rate with an efficiency ) and use the scale free accretion rate in the following discussion. The spectral luminosity in Fig. 1 scales as the black hole mass, . For comparision we show in Fig. 2 the SED for an ADAF arround a black hole with . Figure 5 demonsttrates that the radiation efficiency for this flow is independend of the black hole mass.
The SEDs for between and are shown in Fig. 1. The presented model spectra are accurate above 30 GHz, and they show that the synchrotron emission rises in flux from 1033 to 1037 erg s-1and shifts in frequency from Hz to Hz at and back to smaller frequency for larger . Above the Thomson optical depth for synchrotron photons from central regions around is significant, and Compton scattering broadens the synchrotron peak and make it less prominent, compared to the IC emission. The dominating peak in the IC part of the spectrum, which can be identified between the synchrotron and the Bremsstrahlung peaks at Hz, is the second Compton peak of twice scattered synchrotron photons. The synchrotron seed photons are produced in a region closer to the BH than the Compton scattered radiation. So the seed photon flux for first Compton scattering is anisotropic, and most synchrotron photons are scattered back into a high density and high temperature region with the largest optical depth. The second Compton peak is therefore the dominant one, and the asymmetry between even and odd scattering order decreases thereafter, because the photon field to be scattered becomes more and more isotropic. The SED becomes flat or inverted due to multiple IC scattering above 1014 Hz for . The Bremsstrahlung peak will only be recognized below . The peak does not shift very much in frequency as the maximum of electron temperature only varies between K and K, where the highest are achieved at very close to the horizon and the photons from that radius are significantly redshifted.
|Figure 3: Normalized flux (see Eq. (1)) at 86 GHz (solid line), in K (dash-dotted) and V band (dotted), at 1 keV (dashed) and 100 keV (3dotted-dashed) as a function of mass accretion rate. The models are calculated for a black hole. The efficiency in Eq. (1) is 10% and the SED is assumed to peak at 100 keV.|
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One major prediction of ADAF models is the different evolution of
observable flux in different frequency bands. This is expressed in
the scale-free spectral luminosity .
We scale the radiation
to the total, frequency integrated luminosity of the
specific model from Eq. (2) and define
The enigmatic radio source Sgr A* in the Galactic Center is
coincident with the center of gravity of an enclosed mass of
It was considered to be one of the test cases
for ADAF models (Narayan et al. 1998), but the SED of the
source poses three problems for standard ADAFs. (1) The observed
radio spectrum is much flatter than predicted, so that only the
sub-mm bump (Falcke 1999) is nowadays attributed to the
accretion flow. Most of the radio emission at cm-wavelength must
then be produced by an outflow or jet (Falcke & Markoff
2000). (2) The X-ray spectrum as derived from Chandra
observations (Baganoff et al. 2002) has a different slope
than expected from thermal bremsstrahlung coming from the ADAF.
(3) The observed rapid variability in X-rays (Baganoff et al.
2001) restricts the size of the variable emitting region
to less than
The spectrum at high X-ray fluxes
is harder than at low flux levels. This can be explained by
inverse Compton emission of relativistic electrons in a jet
(Markoff et al. 2001) but even a jet has to be powered by an
accretion process and bremsstrahlung emission of the accreting gas
is unavoidable. In contrast to these recent scenarios, here we
present an ADAF-wind infall model, where the gas in the accretion
flow is heated by wind infall at all radii (Beckert 2000) with a steeper density profile
than normal ADAFs. The synchrotron emission
dominates the SED (Fig. 4) due to a strongly magnetised
|Figure 4: Spectral energy distribution (SED) for an ADAF model with a wind infall appropriate for Sgr A*. The black hole mass is and the mass accretion rate at the last stable orbit yr-1 corresponding to . This special model is briefly described in Sect. 3. The dashed line shows the synchrotron and bremsstrahlung emission. The first three inverse Compton stages are given as dash-dotted lines. The total spectrum (thick line) has a remarkably flat radio slope consistent with the observations.|
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The wind infall is assumed to be strong and rotates with of the ADAF. The flow is magnetically dominated with and the radiative efficiency is larger than in the other models presented in this paper due to the larger electron temperature and the stronger magnetic fields, which leads to increased synchrotron emission. Viscosity is described by an -parametrisation with , lower than for the other ADAF models in Sect. 2, but convection is still expected to be unimportant (Narayan et al. 2000). This model gives a good fit to the radio spectrum but the problem with the X-ray observation persists.
|Figure 5: Radiation efficiency as a function of mass accretion rate with efficiency to compare with the expectation for efficient radiation cooling. Model calculations are made for a black hole (symbol: stars), for (diamonds), and for a (triangles) black hole. The estimated errors for the numerical convergence of assumed and posteriori derived are given for the black hole. The data are fitted with Eq. (2).|
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Another local criterion for the existence of ADAFs is given by the
imbalance of Bremsstrahlung cooling and viscous heating. At large
radii the electron cooling rate, which is coupled to the ion
heating rate by the radiation efficiency, decreases faster than
Coulomb coupling between thermal ions and electrons. The electron
temperature is therefore close to the ion temperature at
these radii. The ions are close to the viral temperature as long
as the radiative efficiency is significantly smaller than 1,
which is the case for all calculated models here. In the region
are equal, the
Bremsstrahlung cooling, which dominates at large radii, decreases
as r-5/2, while the viscous heating falls off as r-3. At
a critical outer radius, the radiative efficiency is 1 and no ADAF
is possible at larger radii. This outer radius is found to be
Furthermore, our numerical models show that the relation outlined by Eq. (7) holds for the entire range of investigated. In the following we will use the value as derived by interpolating our numerical models (Eq. (2)).
The existence of with the properties discussed above translates into a fairly sharp transition between an active and an inactive state of a galaxy. As soon as falls below the radiation efficiency of the accretion decreases dramatically. In other words, already a relatively small change in the mass flow rate around suffices to "switch off" an AGN, and vice versa. The difference between a normal and an active galaxy is then not due to a difference in which is as large as the difference in luminosities between the two classes. A much more important reason is the steep decline in the radiation efficiency for the accretion rates below which the disk turns advection-dominated.
Our numerical models predict . This is in good agreement with observations (e.g., Peterson & Wandel 2000, who find AGN only in the luminosity range between and 1 of the Eddington luminosity, or - equivalently - the Eddington mass accretion rate). In our interpretation the lack of galactic nuclei below is not due to a lack of galaxies with mass accretion rates below but rather due to the steep decline of radiation efficiency below this critical value.
For a supermassive black hole of mass
give an average accretion rate
over its age
If, in addition, we assume, that the age of the BH is not very
much shorter than the age of its host galaxy and thus the Hubble time
(at the location of the black hole),
As discussed above, the mass
of a black hole define an upper limit for its
average mass accretion rate. During phases of activity, the mass
flow rate must be larger than
Let us - for
the purpose of a crude estimate - assume that we have only two
states, namely the AGN phase, characterized by a mass flow
a period of time of
and a normal
galaxy phase for which the mass flow rate
smaller so as to maintain the average value
Let us, moreover, assume
then we get for the duty cycle
Derivation of a more detailed luminosity evolution of an AGN sample requires, however, a treatment more detailed than the above order-of-magnitude estimates. In particular it has to be investigated whether real-world galaxies can maintain a sufficiently high supply of matter for the accretion process over long enough a period of time. This then involves, for instance, questions about the accretion time scales and the long-term development of mass reservoirs. This topic, however, is beyond the scope of the present paper and will be addressed separately (Duschl & Strittmatter, in prep.)
At the same time, this means that - at accretion rates around - small changes in the mass flow rate are sufficient to cause a strong difference in radiation efficiency and thus nuclear luminosity. In other words, the crossing of acts almost like a switch which turns AGNs on and off.
Finally, the combination of the black holes' masses and the mass accretion rate allowed us to put constraints on the duty cycle of AGN. It turned out that the most active AGN can maintain this level of activity only for rather short time scales (of the order of some 107 years).
We wish to thank the referee, Dr. Suzy Collin, for her very helpful report on this paper. This work was in part supported by the Deutsche Forschungsgemeinschaft, DFG, through grant SFB439/C2.