A&A 406, 7-13 (2003)
DOI: 10.1051/0004-6361:20030728
Research Note
A. F. Zakharov1,2,3 - S. V. Repin4
1 - National Astronomical Observatories, Chinese Academy of Sciences, 100012
Beijing, PR China
2 - Institute of Theoretical and Experimental Physics,
25, B. Cheremushkinskaya st., Moscow 117259, Russia
3 - Astro Space Centre of Lebedev Physics Institute, 84/32,
Profsoyuznaya st.,
Moscow 117810, Russia
4 - Space Research Institute, 84/32,
Profsoyuznaya st.,
Moscow 117810, Russia
Received 7 March 2003 / Accepted 18 April 2003
Abstract
Recent X-ray observations of microquasars and Seyfert galaxies
reveal broad emission lines in their spectra, which can arise in
the innermost parts of accretion disks. Simulations indicate that
at low inclination angle the line is measured by a distant
observer as characteristic two-peak profile. However, at high
inclination angles (>
)
two additional peaks arise.
This phenomenon was discovered by Matt et al. (1993) using the
Schwarzschild black hole metric to analyze such effect. They
assumed that the effect is applicable to a Kerr metric far beyond
the range of parameters that they exploited. We check and confirm
their hypothesis about such a structure of the spectral line shape
for the Kerr metric case. We use no astrophysical assumptions
about the physical structure of the emission region except the
assumption that the region should be narrow enough.
Positions and heights of these extra peaks drastically
depend on both the radial coordinate of the emitting region
(circular hot spot) and the inclination angle. We find that the
best conditions to observe this effect are realized at
and
and may exist in microquasars or
low-mass black holes in X-ray binary systems, because there is
some precession (and nutation of accretion disks) with not very
long time periods (see, for example, the SS433 binary system). The
line profiles for different inclination angles and radial
coordinates are presented. To analyze the influence of disk
models on the spectral line shapes we simulate the line profiles
for the Shakura-Sunyaev disk model for accretion disks with the
high inclination.
Key words: black hole physics - line: profiles - X-rays individuals: SS433
More than ten years ago it was predicted that profiles of lines
emitted by AGNs and X-ray binary systems could have an asymmetric double-peaked shape
(e.g. Chen et al. 1989; Matt et al. 1993; Dumont & Collin-Souffrin 1990; Robinson et al. 1990; Fabian et al. 1989).
Generation of the broad
fluorescence lines as a result
of irradiation of a cold accretion disk was discussed by many
authors
(see, for example, Matt et al. 1991, 1992a; Matt & Perola 1992; Matt et al. 1993; Bao 1993; Martocchia et al. 2002 and references therein).
Recent X-ray observations of Seyfert galaxies, microquasars
and binary systems
(Fabian et al. 1995; Tanaka et al. 1995; Nandra et al. 1997a,b; Malizia et al. 1997; Sambruna et al. 1998; Yaqoob et al. 2001; Ogle et al. 2000; Miller et al. 2002 and references therein) confirm these
considerations in general and reveal broad emission lines in their
spectra with characteristic two-peak profiles.
A comprehensive
review by Fabian et al. (2000)
summarizes the detailed discussion of
theoretical aspects of possible scenarios for generation of broad
iron lines in AGNs. These lines are assumed to arise in the
innermost parts of the accretion disk, where the effects of
General Relativity (GR) must be taken into account, otherwise it
appears very difficult to find a natural explanation for observed
line profile.
Numerical simulations of the line structure
are be found in a number of papers
(Ma 2002; Laor 1991; Fanton et al. 1997; Kojima 1991; Pariev & Bromley 1998,1997; Pariev et al. 2001; Bromley et al. 1997; Bao et al. 1994; Rauch & Blandford 1994; Bao & Stuchlik 1992; Bao 1993; Rauch & Blandford 1993; Ruszkowski M. 2000). They indicate that the accretion disks in Seyfert
galaxies are usually observed at the inclination angle close to
or less. This occurs because according to the
Seyfert galaxy models, an opaque dusty torque surrounds the
accretion disk which does not allow us to observe the disk at
larger inclination angles.
However, at inclination angles
,
new
observational manifestations of GR could arise. (Matt et al. 1993 discovered such phenomenon for a Schwarzschild black hole,
moreover the authors predicted that their results could be
applicable to a Kerr black hole over the range of parameters
exploited.)
The authors mentioned that this problem was not
analyzed in detail for a Kerr metric case and it would be
necessary to investigate this case. Below we do not use a specific
model on surface emissivity of accretion (we only assume that the
emitting region is narrow enough). But general statements (which
will be described below) can be generalized to a wide disk case
without any problem. Therefore, in this paper we check and confirm
their hypothesis for the Kerr metric case and for a Schwarzschild
black hole using other assumptions about surface emissivity of
accretion disks. In principle, such a phenomenon could be observed
in microquasars and X-ray binary systems where there are neutron
stars and black holes with stellar masses.
In Sect. 3 we discuss disk models used for simulations. In Sect. 4 we present the results of simulations with two extra peaks in the line profile. These extra peaks exist because of the gravitational lens effect in the strong field approximation of GR. In Sect. 5 we discuss results of calculations and present some conclusions.
We used an approach discussed in detail in papers by
Zakharov (1991,1994), Zakharov & Repin (1999,20002a), Zakharov & Repin (2003,2002b), Zakharov et al. (2002).
The approach was used in particular to simulate spectral line
shapes. For example, Zakharov et al. (2002) used this approach to simulate
the influence of a magnetic field on spectral line profiles. This
approach is based on results of a qualitative analysis
(which was done by Zakharov 1986, 1989 for different types of geodesics near a Kerr black hole).
The equations of photon motion in the Kerr metric are reduced to
the following system of ordinary differential equations
in dimensionless Boyer-Lindquist coordinates
(Zakharov 1991,1994; Zakharov & Repin 1999):
![]() |
(3) |
![]() |
(4) |
Solving Eqs. (1)-(6) for
monochromatic quanta emitted by a ring we can calculate a specral
line shape
which is registered by a distant
observer at inclination angle
.
The numerical integration has been performed using the combination of the Gear and Adams methods (Gear 1971) and realized as the standard package by Hindmarsh (1983), Petzold (1983), Hiebert & Shampine (1980). We obtain the entire disk spectrum by summation of sharp ring spectra.
To simulate the structure of the emitted line it is necessary
first to choose a model for the emissivity of an accretion disk.
We exploit two different models, namely we consider a narrow and
thin disk moving in the equatorial plane near a Kerr black hole as
the first model and as we analyze the inner wide part of an
accretion disk with a temperature distribution which is chosen
according to the Shakura & Sunyaev (1973) with fixed inner and outer radii
and
as the second model.
Usually a power law is
used for wide disk emissivity
(see, for example, Laor 1991; Martocchia et al. 2002; Martocchia & Matt 1996; Matt et al. 1991; Martocchia et al. 2000). However, other models for
emissivity can not be excluded for such a wide class of accreting
black holes, therefore, to demonstrate how another emissivity law
could change line profiles we investigate such a emissivity law.
First, we assume that the source of the emitting quanta is a narrow thin disk rotating in the equatorial plane of a Kerr black hole. We also assume that the disk is opaque to radiation, so that a distant observer situated on one disk side cannot measure the quanta emitted from its other side.
For the sake of computational simplicity we suggest that the
spectral line is monochromatic in its co-moving frame. It can
really be adopted because even at T = 108 K the thermal line
width
![]() |
For second case of the Shakura-Sunyaev disk model, we assume
that the local emissivity is proportional to the surface element
and and T4, where T is a local temperature.
The emission intensity of the ring is proportional to its area.
The area of the emitting ring (width )
differs in the Kerr
metric from its classical expression
and should
be replaced with
For simulation purposes we assume that
the emitting region lies entirely in the innermost region of the
-disk (zone a) from
to
and the emission is monochromatic in the co-moving
frame
.
The frequency of this emission set as unity
by convention.
![]() |
Figure 1:
Line profiles for
high inclination angles,
![]() |
Open with DEXTER |
Spectral line profiles of a narrow ring observed at large inclination
angles
and different radii r are shown in
Fig. 1 (a Kerr metric generalization of Fig. 1 from
Matt et al. 1993 which was drawn using calculations for the
Schwarzschild case). The ring is assumed to move in the equatorial
plane of a Kerr black hole with an almost extreme rotation
parameter
a = 0.9981. The inclination angle increases from left
to right and the radial coordinate from bottom to top. The figure
indicates that there are practically no new specific features of
profiles, thus, the line profile remains one-peaked with a
maximum close to
and a very long red wing without
any significant details.
For the lowest radii there are no signatures of multiple peaks of
spectral line shapes even for high inclination angles (the bottom
row in Fig. 1 which corresponds to
).
Increasing the radius to
,
an additional
blue peak arises in the vicinity of the blue maximum at the
highest inclination angle
.
The red maximum
is so small that no details can be distinguished in its
structure. At lower inclination angles
the blue maximum also has no details and the entire line
profile remains essentially one-peaked.
For
additional details in the blue peak
appear for
.
Thus, for
we
have a fairly clear bump, at
it changes into a
small complementary maximum and for
this
maximum becomes well-distinguished. Its position in the last case
differs significantly from the main maximum:
,
.
When further increasing the radius the red maximum also
bifurcates. This effect becomes visible for
and
.
Thus, for
we have only a
faintly discernible (feebly marked) bump, but for
both complementary maxima (red and blue) arise. For
we have already four maxima in the line
profile:
,
,
,
.
Note that the splitting for
the blue and red maxima is not equal, moreover,
.
For
the profile becomes more narrow,
but the complementary peaks appear very distinctive. We have a
four-peak structure for
.
It is interesting
to note that for
the energy of the blue
complementary peak is close to its laboratory value.
Note that the effect almost disappears when the radial coordinate
becomes less than ,
i.e. for the orbits which could exist
only near a Kerr black hole.
![]() |
Figure 2:
Details of a hot spot line profile for the most
distinctive case with
![]() ![]() ![]() |
Open with DEXTER |
![]() |
Figure 3:
Details of the line structure for an ![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
Figure 2 demonstrates the details of the spectrum
presented in the top row in Fig. 1. Thus, the left
panel includes all the quanta emitted by a hot spot at
with
at infinity (the mean value could
be counted as
if the quanta distribution would be
uniform there) but with much higher resolution than in
Fig. 1. The spectrum has four narrow distinctive
maxima separated by lower emission intervals. In the right panel,
which includes all the quanta with
,
the right complementary maxima is even higher
than the main one. The blue complementary maxima still remains
lower than its main counterpart, but it increases rapidly its
intensity with increasing inclination angle. It follows
immediately from the comparison of the left and right panels. The
"oscillation behavior" of the line profile between the maxima has
a pure statistical origin and is not caused by the physics
involved.
As an illustration, a spectrum of an entire accretion disk at
high inclination angles in the Schwarzschild metric is shown in
Fig. 3. (In reality we have calculated geodesics for
the quanta trajectories in the Schwarzschild metric using the same
Eqs. (1)-(6) as for a Kerr metric, but assuming
there a = 0.01.) The emitting region (from 3 to
)
lies
as a whole in the innermost region of the
-disk
(the detailed description of this model was given by Lipunova & Shakura 2002; Shakura & Sunyaev 1973).
As follows from Fig. 3, the blue peak may consist of the two components, whereas the red one remains unresolved.
The complicated structure of the line profile at large inclination angles is explained by the multiple images of some pieces of the hot ring. We point out that the result was obtained in the framework of GR without any extra physical and astrophysical assumptions about the character of the radiation etc. For a Kerr black hole we assume only that the radiating ring is circular and narrow.
The problem of multiple images in the accretion disks and extra peaks was first considered by Matt et al. (1993) (see also Bao & Stuchlik 1992; Bao 1993; Bao et al. 1994, 1996). Using numerical simulations Matt et al. (1993) proved the statement for the Schwarzschild metric and suggested that the phenomenon is applicable to a Kerr metric over the range of parameters that the authors have analyzed. They noted also that it is necessary to perform detailed calculations to confirm their hypothesis. We verified and confirmed their conjecture without any assumptions about a specific distribution of surface emissivity or accretion disk model (see Figs. 1 and 2).
We confirmed also their conclusion that extra peaks are generated by photons which are emitted by the far side of the disk, therefore we have a manifestation of gravitational lensing in the strong gravitational field approach for GR.
Some possibilities to observe considered features of spectral line profiles were considered by Matt et al. (1993), Bao (1993). The authors argued that there are non-negligible chances to observe such phenomenon in some AGNs and X-ray binary systems. For example, Bao (1993) suggested that NGC 6814 could be a candidate to demonstrate such a phenomenon (but Madejski et al. 1993 found that the peculiar properties of NGC 6814 are caused by a cataclysmic variable like an AM Herculis System).
However, it is clear that in general the probability to observe
objects where one could find such features of spectral lines is
small. Moreover, even if the inclination angle is very close to
,
the thickness of the disk (shield or a torus around
an accretion disk) may not allow us to look at the inner part of
accretion disk. Here, discuss astrophysical situations when the
the inclination angle of the accretion disk is high enough.
About 1% of all AGN or microquasar systems could have an
inclination angle of the accretion disk >
.
For
example, Kormendy et al. (1996) found that NGC 3115 has a very high
inclination angle about of
(Kormendy & Richstone 1992 discovered a
massive dark object
(probably a massive black
hole) in NGC 3115). Perhaps we have a much higher probability to
observe such a phenomenon in X-ray binary systems where black
holes with stellar masses could be. Taking into account the
precession which is actually observed for some X-ray binary
systems (for example, there is a significant precession of the
accretion disk for the SS433 binary system
(Cherepashchuk 2002)
, moreover since the
inclination of the orbital plane is high (
for
this object) sometimes we may observe almost edge-on accretion
disks of such objects. Observations indicated that there is a
strong evidence that the optically bright accretion disk in SS433
is in a supercritical regime of accretion. The first description
of a supercritical accretion disk was given by Shakura & Sunyaev (1973). Even
now such a model is discussed to explain observational data for SS433 (Cherepashchuk 2002). We used the temperature distribution from
the Shakura-Sunyaev model (Lipunova & Shakura 2002; Shakura & Sunyaev 1973) for the inner
part of accretion disk to simulate shapes of lines which could be
emitted from this region (Fig. 3). Therefore, we
should conclude that the properties of spectral line shapes
discovered by Matt et al. (1993) are confirmed also for such emissivity
(temperature) distributions which correspond to the Shakura-Sunyaev model.
Thus, such properties of spectral line shapes are robust enough with respect to wide variations of rotational parameters of black holes and the surface emissivity of accretion disks as it was predicted by Matt et al. (1993). In this work their conjecture was confirmed not only for the Kerr black hole case but also for other dependences of surface emissivity of the accretion disk.
Acknowledgements
A.F.Z. is grateful to E. F. Zakharova for the kindness and support necessary to complete this work. AFZ would like to thank Dipartimento di Fisica Universita di Lecce, INFN, Sezione di Lecce and the National Astronomical Observatories of the Chinese Academy of Sciences for a hospitality and profs. F. DePaolis, G. Ingrosso, J. Wang and Dr. Z. Ma for very useful discussions.S.V.R. is very grateful to Prof. E. Starostenko, Dr. A. Salpagarov and Dr. O. Sumenkova for the possibility of working on this problem.
This work was supported by the National Natural Science Foundation of China, No. 10233050. This work has been partly supported also by the Russian Foundation for Basic Research, grant 00-02-16108.
The authors thank the anonymous referee for useful remarks.