X-ray spectroscopy
Testing strong gravity in
active galactic nuclei
Andy Fabian reviews advances in understanding the processes in accretion
disks around black holes using broad iron lines. This paper was presented to
the Royal Astonomical Society as the George Darwin Lecture 1997.
T
here is now much evidence for the presence of black holes in the universe, in
systems ranging from galactic binaries
such as Cygnus X1 (Bolton 1972; Webster and
Murdin 1972) through the nuclei of galaxies
such as NGC 4258 (Miyoshi et al. 1995) and
the massive elliptical galaxy M87 (Ford et al.
1995). One approach has been to use optical or
radio spectroscopy to determine the mass of a
dark central object using Kepler’s law to combine velocities inferred from Doppler shifts of
spectral lines with a radius found from imaging
or a binary motion. For the galactic centre,
stellar proper motions have been used (Eckart
and Genzel 1996) to determine the velocities.
The results generally indicate the presence of a
large mass within a small radius, and the only
class of object that will fit in there without
overproducing light is a black hole.
These are impressive results but they do not
probe very close to the black hole. Although
the work pushes the limits of angular resolution, the small radii at which material is being
observed are still about 100 000 gravitational
radii. (A gravitational radius is defined as
GM/c2, where G is the gravitational constant, c
the velocity of light and M the mass of the
hole. The gravitational radius of the Earth is
about 1.5 mm, for the Sun it is about 1.5 km
and for a billion solar mass black hole it is
1.5 billion km or about 100 au. The event
horizons for a non-spinning Schwarzschild,
and a maximally spinning Kerr, black hole are
at two and one gravitational radii respectively.)
Even if the resolution could be improved
enormously, the approach is limited since the
atoms, ions and molecules that are being
-ray spectroscopy has proved to be
a powerful tool with which to
probe the innermost parts of
accretionary disks around massive
black holes – reaching up to 10 000
times as close as optical and radio
measurements. Observations of the
fluorescent iron line are consistent
X
10
observed cannot survive very close to the black
hole, where most matter is ionized by the high
velocities and temperatures. The small trace of
iron in matter accreting into the black hole
does, however, retain electrons, because of the
large positive charge of the nucleus. Its spectral
line, which is in the X-ray band, does provide
another approach with which the near environment of the black hole can be observed and
mapped. Using this approach, velocities of
100 000 km s–1, rather than only 1000 km s–1,
can now be measured.
The source of X-ray emission from
active galaxies
For the X-ray approach to work there must be
matter orbiting close to the black hole. From
Kepler’s law, matter orbits at different radii
with different speeds. Viscosity then acts on
these differential motions causing the gas to
spiral slowly inwards, thereby forming an
accretion disk and releasing its gravitational
energy. The rate at which the gas accretes in
active galaxies means that an enormous power
is released in a small region. This is the source
of the luminous X-ray emission from quasars
and active galaxies that has long been thought
to originate close to the black hole. In standard
accretion models, particularly those of accretion disks, most of the radiation emerges
within about 20 gravitational radii and, with
the high temperatures implied by simple
thermodynamic considerations, the bulk of the
radiation occurs in the X-ray band. The rapid
X-ray variability that is common in Seyfert 1
galaxies is a further indication that the X-rays
do originate in very compact regions. If we
with a disk and flaring corona model in
Seyfert 1 galaxies. As new instruments
have increased the spectral resolution
available, it has become possible to
distinguish between rotating and nonrotating black holes on the basis of
their different effects on the iron line.
Gravitational red shifts demonstrate the
look at the X-ray light curves of many
Seyfert 1 galaxies, we see chaotic variability
that is qualitatively similar to that seen from
Cygnus X1. No definite periods are seen, but
variability with factors of two changes on
timescales of days, hours and, in a few extreme
examples, below 1000 seconds. Indeed, one
observation of the Seyfert 1 galaxy
MCG–6-30-15 has shown variation by a factor
of almost 2 in less than 100 seconds. That indicates that we are dealing with a very compact
object where the emission region is smaller
than 100 lts in size, yet its X-ray luminosity is
1043 erg s–1. The most extreme variability is
seen in narrow-line Seyfert 1 galaxies, such as
IRAS 13224-3809, which with ROSAT has
been seen (Boller et al. 1997) to undergo variations by factors of up to 70. Its isotropic luminosity ranges from that of a quasar around
1045 erg s–1 down to that of a more modest
Seyfert galaxy of a few times 1043 erg s–1.
Chaotic X-ray variability is suggestive of emission from close to a black hole but in no way
demonstrates it.
X-ray line emission from Seyfert 1
galaxies
Theoretical and other indications of X-ray line
emission from accretion disks in the late 1980s
and the discovery (Pounds et al. 1990; Matsuoka et al. 1990) with the Ginga satellite of
distinct line emission in the spectrum of
Seyfert 1 galaxies provided a diagnostic tool
with which to study the inner regions of the
accretion flow around a massive black hole.
The spectral feature discovered is due to
X-ray fluorescence from what is normally
importance of strong gravity and the
need for a general relativistic
description of these accretion disks.
Future instruments will make
observations of the broad iron line
routine, bringing a wealth of new
information that will establish strong
gravity as an observational science.
August/September 1997 Vol 38 Issue 4
X-ray spectroscopy
August/September 1997 Vol 38 Issue 4
(a)
Kerr black hole (a/M = 0.998, Rin = 1.23 rg, Rout =15 rg, inc = 30°)
1
0.8
0.6
E/E0
0.4
0.2
0
(b)
Kerr black hole (a/M = 0.998, Rin = 1.23 rg, Rout =15 rg, inc = 75°)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
E/E0
(c)
1.0
Schwarzschild
30°
photon intensity
called “cold” iron. “Cold” in this context
means that the iron retains at least its K- and
L-shell electrons, so the temperature of such
cold iron could still be several million degrees.
The important issues are that the iron ion
retains those electrons into the smallest radii of
the accretion disk and the product of abundance and fluorescent yield is highest for iron.
Studies with the Ginga satellite demonstrated
that the X-ray fluorescence is produced by the
process of reflection. The flaring corona above
the accretion disk sends X-rays both to us and
to the disk. Although most of the photons
striking the disk are absorbed, some are backscattered in our direction by electrons and
some are absorbed by K-shell electrons of iron
that de-excite by emission of a photon at
6.4 keV – the fluorescent iron line – which is
the other component of the reflection spectrum
(George and Fabian 1991). The disk and flaring corona model appears to work very well
and can explain the chaotic variability and the
shape of the spectrum.
To understand why such an emission line is
so valuable for studying the gravity of the central black hole, consider what is happening in
the accretion disk. Matter close to the black
hole is going very fast, and matter further away
is going slowly. If the gravitational field could
be thought of as purely Newtonian, we would
see the emission line symmetrically broadened
by the Doppler effect in the manner that is
commonly seen in cataclysmic variables and
also from radio observations of spiral galaxies
in the 21 cm line. The broadest part of the line
comes from the innermost part of the disk.
When, however, we are considering a disk
around a black hole, the velocities close to the
black hole become very high and we have to
start considering relativity. First, special relativity implies two effects. One is beaming,
which causes the approaching side of the disk
to appear brighter than the receding side. And
because moving clocks run slow, there is also a
transverse Doppler effect. Second, because we
are dealing with a disk deep in the gravitational potential well of the black hole, we have
to include the gravitational redshift, and any
other general relativistic effects, which means
that the broadest parts of the line coming from
the innermost parts of the disk are going to be
shifted yet further to lower frequencies with
respect to the narrow parts of the line that
originate from the outer part. The net result
(Fabian et al. 1989) is a very broad skewed
emission line with essentially two peaks or
horns: a blue horn that is going to be fairly
close to the rest frequency of the emission, and
is brighter than the red horn, which is spread
out into a red tail. (Red and blue here just
mean photon energies below and above the
rest energy of the line.) The red tail is, of
course, from the receding and innermost parts
60°
0.5
Kerr
30°
0.0
3
4
5
6
photon energy (keV)
7
8
1 Computer images of the appearance of an accretion disk around a black hole with
a spin parameter of 0.998 and inclinations of (a) 30° and (b) 75°, kindly generated by
Youri Dabrowski and Anthony Lasenby. (b) is similar to the image shown by Bromley
et al. (1997). The colours have been chosen so that blue and green indicate that line
emission will appear blue-shifted from its laboratory frequency; orange and red
appear red-shifted. (c) shows the line profile in photon energy space from Fabian et
al. (1989) and Laor (1991). The noise in the profiles is numerical. Note the blue and
red horns to the lines, as described in the text.
11
X-ray spectroscopy
of the disk where transverse Doppler and gravitational redshifts are important. The predicted
line shape can be seen in the figures, first in the
pictorial representation of the accretion disk
(1a and b) and secondly (1c) in the graphical
representation, which shows the energy spread
of the line. Such line profiles were first predicted by us back in 1989, building on work by
Chen, Halpern and Filippenko (1989), who
were modelling emission from hydrogen lines
at larger radii in accretion disks. (Recombination of hydrogen, which is very highly ionized but very abundant, can be detected from
the mildly relativistic regime of disks.)
Ginga was unable to resolve the line clearly.
It was not until the launch of the Japanese–US
satellite ASCA (Tanaka et al. 1994) in February
1993 that there was a detector in orbit capable
of showing the clear shape of the emission line.
The reason for this is that ASCA carries sensitive, low-background CCD detectors that have
excellent spectral resolution (160 eV) around
the energy of the iron line (6.4 keV). First indications that the lines in active galactic nuclei
were broad came from an observation of
MCG–6-30-15 (the galaxy mentioned earlier
and shown in figure 2), then work with
Mushotzky et al. (1995) on several other
galaxies indicated that the line had the right
shape: it was broad, implying velocities
exceeding 50 000 km s–1, and possibly skewed.
However, because there were only a few hundred photons in each line, per day of observing
(the typical observation length), it was not
clear that the line was due to a relativistic disk.
We needed a much longer exposure in order to
see clearly the skew nature of the line.
The observation that enabled us to do this
was of MCG–6-30-15 and lasted four-and-ahalf days in the summer of 1994. The spectrum
from that observation (Tanaka et al. 1995) is
shown in figure 3. The results of the two CCD
detectors have been summed together and the
power-law continuum is not shown. What is
12
X-ray emission coming from within about
20 Schwarzschild radii. This is certainly consistent with most theories of accretion around
a massive black hole and serves to support
them. The strength of the red tail of the line
(the tail to lower energies) indicates the presence of gravitational redshifts and is therefore
beginning to demonstrate that we are really
dealing with strong gravity and the need for a
general relativistic description of the situation.
Alternative models
Nevertheless, we must consider alternatives for
the formation of the line. One possibility raised
by Czerny et al. (1991) is that of Comptonization. Is it possible that we have a narrow iron
emission line that is then being spread out by
repeated electron scattering? (The broadening
would then be due to the Compton effect.)
That has been considered by us (Fabian et al.
1995) and generally we find that such a possibility does not hold. A high Thomson depth in
electrons of about 5 is required in cold electrons, with temperatures of less than about
0.25 keV. This is a rather bizarre requirement:
the gas needs at the same time to be extremely
highly ionized and, although we do not have
high-energy observations simultaneously with
any ASCA broad line observations, such a
Comptonizing medium would give a break in
the continuum at an energy of about 20 keV.
Other observations, such as from OSSE on the
3 The broad iron line as observed
from MCG–6-30-15 with ASCA
(Tanaka et al. 1995). The results
from both CCDs have been
summed. The red line shows the
best-fitting model for an accretion
disk with inclination 30±3° and
inner and outer radii of 6 and
20 gravitational radii.
1.5 × 10 – 4
line flux (ph cm –2 s –1 keV –1)
Fig. 2: Optical image of MCG–6-30-15 (from the
Digitized Sky Survey, copyright National
Geographic, UKSTU and the AAO). The galaxy lies in
the constellation of Centaurus and is at a
cosmological redshift of 0.008.
seen is the deviation from the best fitting
power-law spectrum. There is a clear and very
sharp drop in the spectrum at about 6.5 keV, a
peak around 6.2–6.4 keV and a broad red tail
extending down well below 5 keV. The
coloured line in figure 3 shows the best-fitting
relativistic disk model, assuming a Schwarzschild or non-rotating black hole. The inclination of the disk is about 30±3° and its outer
radius, i.e. the radius within which most of the
emission originates, is about 20 gravitational
radii. This is certainly consistent with the idea
of an accretion disk around a non-rotating
black hole. The reason why we can be so precise about the inclination is because of the
sharp drop in the line at 6.5 keV, which is
clearly seen because of the excellent resolution
of the CCDs. Were the inclination to be higher,
this sharp drop would spread out to 7 keV and
possibly higher. In that case there would be a
larger component of the motion along our line
of sight and that emission, of course, is blueshifted. Observations of other objects, such as
IRAS 18325-5926 by Iwasawa et al. (1996a)
where the line does extend up well above
6.5 keV, do show a disk of larger inclination,
perhaps 50°.
The long observation of MCG–6-30-15
remains the best and clearest example of a
broad iron line. Observations of about two
dozen other Seyfert 1 and other active galaxies,
including some radio-loud ones, have been
10 – 4
5 × 10 – 5
0
3
4
5
6
energy (keV)
analysed by several groups and generally show
the presence of a strong, broad 6.4 keV line
(although very luminous quasars do not). Nandra et al. (1997) and Reynolds (1997) have systematically studied these data in the ASCA
archives and found that broad iron lines are
common. Nandra et al. have shown, by summing the spectra, that the broad line is skewed
with a strong red tail. The picture that this
yields is one of accretion disks with a typical
inclination of about 30° and the bulk of the
7
8
9
Compton Gamma-Ray Observatory, show that
such a break is not present.
An alternative possibility is that we are seeing
something of an iron edge. After all, we are
producing the fluorescent photons by the
absorption of incident photons above the iron
photoelectric absorption edge of 7.1 keV.
However, in the spectrum of standard cold
reflection spectrum we do not expect to see the
iron edge unless we have extremely good data.
The reason is that, although there is a lot of
August/September 1997 Vol 38 Issue 4
X-ray spectroscopy
The strength of the iron line
One property of the iron line that needs some
consideration is its strength, which is surprisingly high. The equivalent width of the line is
about 380 eV. When we first started predicting
such lines we expected them to have an equivalent width of about 150 eV, based on certain
assumptions about abundances. The most
likely explanation for the high equivalent
width of the line is that the abundance of iron
in Seyfert 1 nuclei is slightly above, by about a
factor of a few, the solar value.
I stressed at the beginning the similarity
between the variability of Seyfert 1 galaxies in
X-rays and Cygnus X1. They also have similar
spectral shapes, and it is plausible that the
disk–corona model also applies to Cygnus X1.
One might ask then why broad iron lines are
not detected in that case too. When Cygnus X1
and other galactic black hole candidates have
been observed with ASCA, and before that
with Ginga, a large broad edge feature was
seen instead of a line. This has generally been
regarded as a puzzle. However, it is possible
that in the case of the stellar mass black hole
disks, which are much more compact than
those around massive black holes (scaling in
terms of the Eddington luminosity and mass),
it is likely that they are much hotter than those
in the active galaxies. The iron in such disks is
therefore likely to be fairly highly ionized; oxygen in particular will be highly ionized. There
is then a large contrast between the absorption
above the iron K-edge and the relative lack of
absorption below it, with the result that the
August/September 1997 Vol 38 Issue 4
edge appears large in the reflected spectrum. It
is also possible that any line produced from the
ionized disk is destroyed through resonant
scattering and the Auger effect, as discussed in
work with Ross et al. (1996). Therefore for an
ionized disk what we expect to see is a large
edge. This, and any emission line, is then
blurred in energy by the same Doppler and
gravitational redshifts as for a cold disk. The
net result is mostly a blurred edge, as observed.
The data obtained so far (Ebisawa et al. 1995)
appear superficially consistent with this picture, although alternative models are possible.
Variability of the line shape
As already discussed, the continuum in these
objects is extremely variable. During the fourand-a-half day observation of MCG–6-30-15,
we saw an overall variation by a factor of 2–3
and rapid variations on timescales of 1000 s
and longer. There was one period during the
observation when it was relatively bright and
another period when it was relatively faint. We
can, in principle, measure the mass of the black
hole if we can determine the time delay
between a change in the continuum and the
subsequent change in the line in response.
However, for MCG–6-30-15 the timescale is
likely to be less than 1000 s, and in that time
we only detect one or two counts from the line.
We need at least a hundred times the count rate
of ASCA in order to follow such rapid line
Then, depending on whether a flare is on the
approaching or receding side of the disk, or
whether it is further or closer in radius, so the
blue or red parts of the line respond the most.
Thus as the source varies, the line shape can
change just because the flares either move or
occur at different places. With that in mind we
looked carefully at the data on MCG–6-30-15
to see if line profile changes were apparent
(Iwasawa et al. 1996b).
The bright flare during the source observation does show a different line profile. In this
case the line appears to be narrow and centred
on 6.4 keV. It is actually broader than the
instrumental response but narrower than the
standard line that is seen from the source. This
can be explained if the flare is taking place
above the approaching side of a disk at about
10 gravitational radii. Both the continuum and
the line are then beamed along our line of
sight, which can perhaps explain why the iron
line during the flare is narrow. Such an effect
could have a very large influence on the continuum if the inclination is much higher than the
30° of MCG–6-30-15, and it will be even larger if the photon index of the source is greater.
The narrow-line Seyfert 1 galaxies, such as
IRAS 13224-3809, could be at high inclinations and certainly have much larger photon
indices. Relativistic beaming due to disk
motions could thus explain the giant persistent
variability seen from that source. If the inclina4 The broad iron line from
MCG–6-30-15 as observed during
the deep minimum of the 4.5 day
observation (Iwasawa et al.
1996b). The best-fitting Kerr
model is shown by the red line.
1.5 × 10 – 4
line flux (ph cm –2 s –1 keV –1)
absorption by the iron edge, there is also a lot
of absorption due to oxygen at energies below
7.1 keV, so the contrast at the edge is very
small. The sharp drop that is seen in the
observed spectrum is at 6.5 keV, not at the iron
edge energy of 7.1 keV, so a redshift is
required. If it were due to a highly ionized
absorber, for example FeXXV or FeXXVI,
then we would require an even larger redshift
to produce a sharp feature at 6.5 keV, and that
redshift has to be very precise, occurring at
some particular velocity or from some particular radius. We have also considered partialcovering models that also require red-shifting.
After fitting a variety of such models to the
data, the residuals still resemble the broad line.
None of the simple alternative models that we
have considered match the data well. Certainly
the best fit is with the broad emission line of a
relativistic disk. It is worth pointing out here
that we have also looked carefully at instrumental effects. Seyfert 2 galaxies, for example,
which are expected to show a narrow line, do
indeed show a very sharp narrow line generally in agreement with the instrumental response.
Broad iron line features are not seen below
6 keV in clusters of galaxies.
10 – 4
5 × 10 – 5
0
4
6
energy (keV)
variations and thereby do what is called reverberation mapping. However, because there is a
large variation observed from this object, it is
likely that it comes from a small number of
coronal flares and those flares may well move
around on the disk. The flares, for example,
could be due to the reconnection of magnetic
fields amplified by the differential motions in
the disk, and the situation could be somewhat
similar to, only very much scaled up from, that
on the surface of the Sun as seen in X-rays.
8
tion is 70° to 80°, then the variability is boosted by more than an order of magnitude, solely
due to flares occurring on the approaching side
of a disk.
Most of the line during the variations in
MCG–6-30-15 looks the same as it did for the
total line shape. However, when the flux is at a
minimum we see no sharp line at all. The line
is very broad with a much larger red tail than
for the rest of the observation. In this case,
shown in figure 4, the line appears to extend
13
X-ray spectroscopy
a/M
launched, XMM in 1999
from about 6.4 keV down
1.00
and ASTRO-E in 2000. All
to well below 4 keV, and is
20%
of these missions have
relatively strong. What we
50%
higher spectral resolution,
have to explain is how the
75%
and XMM and Astro-E in
line can be even more red0.95
particular have much highshifted than for the
90%
er throughput at the iron
Schwarzschild case. We do
95%
line energies. This is going
not expect, of course, the
to mean that observations
inclination of the disk to
0.90
98%
of the broad iron line,
have changed, but we do
including its variability,
need a larger redshift. This
99%
will be routine. Looking
can be obtained if we go
ahead perhaps 10 years to
closer to the black hole
99.5%
0.85
missions that are on the
than the 6 gravitational
drawing-board now, such
radii, which is the inner
as HTXS and XEUS with
radius of a disk around a
99.9%
square metres of collecting
Schwarzschild or non0.80
area, the increase in
rotating black hole. The
15
20
25
30
35
throughput may exceed a
simplest way to get closer
inclination (°)
factor of 100, so that reverto such a black hole is to
beration mapping becomes
have it spinning (i.e. it is a Fig. 5: Probability contours for inclination and spin parameter for the line shown in fig. 4
possible. This means that a
Kerr black hole). In this (from Dabrowski et al. 1997).
means more fluorescence and less escaping
variety of objects, both radio-loud and radiocase the radius of marginal stability for a disk
directly to us. An important factor here is how
quiet, can have both masses and spin paramemoves inwards, bringing larger gravitational
the disk is illuminated. If flares occur just
ters determined, as well as inclinations and
redshifts as the spin of the disk increases. What
above the disk and co-rotate with it, then the
innermost disk radii. The distribution of emisis shown in the figure is the prediction for a
enhancement in line strength is only about
sion regions and flare sizes, the interaction of
maximally spinning black hole. For this we
20%. If instead the irradiation of the disk is by
jets, and many other properties can begin to be
assume a spin parameter of 0.998 (work by
a source that is not co-rotating, but is essenunderstood. We can explore the complexities
Thorne [1974] has shown that this is the maxtially stationary above the centre of the disk,
of light bending, frame dragging and other
imum spin parameter for an accreting black
then, as shown by Martocchia and Matt
properties of the Kerr metric, and start to seek
hole). The agreement is reasonable and sug(1996), the effect can be large. The continuum
and explore observables for alternative gravigests that the black hole in MCG–6-30-15 is
is bent toward the disk and away from our line
tational theories. Strong gravity is becoming an
indeed spinning rapidly. At this stage the only
of sight and as seen by the disk it is blueobservational science. ●
line profiles available for fitting to the data
shifted, therefore much brighter and giving rise
were those for a Schwarzschild non-spinning
to much more fluorescence.
black hole and one with a maximum spinning
A C Fabian is Royal Society Professor in Astronomy
These are only possible explanations for the
black hole that had been produced by Laor
at the Institute of Astronomy, Madingley Road,
line profile changes and much more work is
(1991). In recent work with Dabrowski et al.
Cambridge CB3 0HA, UK.
needed. They do illustrate how the strong grav(1997), who have computed line profiles for a
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[1976]). More radiation striking the disk
other objects. In 1998 AXAF should be
Webster B L and Murdin P 1972 Nature 235 37.
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August/September 1997 Vol 38 Issue 4