Issue |
A&A
Volume 494, Number 3, February II 2009
|
|
---|---|---|
Page(s) | 905 - 913 | |
Section | Extragalactic astronomy | |
DOI | https://doi.org/10.1051/0004-6361:200811005 | |
Published online | 22 December 2008 |
A correlation between the spectral and timing properties of AGN
I. E. Papadakis1,2 - M. Sobolewska2 - P. Arevalo3 -
A. Markowitz4 - I. M. MHardy3 -
L. Miller5 - J. N.
Reeves6 - T. J. Turner7,8
1 - Physics Department, University of Crete, PO Box 2208,
71003 Heraklion, Crete, Greece
2 - i IESL, Foundation for Research and Technology, 71110 Heraklion, Greece
3 - School of Physics and Astronomy, University of Southampton, Southampton
S017 1BJ, UK
4 - Centre for Astrophysics and Space Sciences, University of California, San
Diego, Mail Code 0424, La Jolla, CA 92093-0424, USA
5 - Dept. of Physics, University of Oxford, Denys Wilkinson Building, Keble
Road, Oxford OX1 3RH, UK
6 - Astrophysics Group, School of Physical and Geographical Sciences, Keele
University, Keele, Staffordshire ST5 5BG, UK
7 - Department of Physics, University of Maryland Baltimore County, 1000
Hilltop Circle, Baltimore, MD 21250, USA
8 - Code 662, Exploration of the Universe Division, NASA/GSFC, Greenbelt, MD
20771, USA
Received 21 September 2008 / Accepted 4 December 2008
Abstract
Context. We present the results from a combined study of the average X-ray spectral and timing properties of 14 nearby AGN.
Aims. We investigate whether a ``spectral-timing'' AGN correlation exists, similar to the one observed in Cyg X-1, compare the two correlations, and constrain possible physical mechanisms responsible for the X-ray emission in compact, accreting objects.
Methods. For 11 of the sources in the sample, we used all the available data from the RXTE archive, which were taken until the end of 2006. There are 7795 RXTE observations in total for these AGN, obtained over a period of 7-11 years. We extracted their 3-20 keV spectra and fitted them with a simple power-law model, modified by the presence of a Gaussian line (at 6.4 keV) and cold absorption, when necessary. We used the best-fit slopes to construct their sample distribution function, and we used the median of the distribution, and the mean of the best-fit slopes, which are above the 80th percentile of the distributions, to estimate the mean spectral slope of the objects. The latter estimate is more appropriate in the case when the energy spectra of the sources are significantly affected by absorption and/or reflection effects. We also used results from the literature to estimate the average spectral slope of the three remaining objects.
Results. The AGN average spectral slopes are not correlated either with the black hole mass or the characteristic frequencies that were detected in the power spectra. They are positively correlated, though, with the characteristic frequency when normalised to the sources black hole mass. This correlation is similar to the spectral-timing correlation that has been observed in Cyg X-1, but not the same.
Conclusions. The AGN spectral-timing correlation can be explained if we assume that the accretion rate determines both the average spectral slope and the characteristic time scales in these systems. The spectrum should steepen and the characteristic frequency should increase, proportionally, with increasing accretion rate. We also provide a quantitative expression between spectral slope and accretion rate. Thermal Comptonisation models are broadly consistent with our result, and can also explain the difference between the spectral-timing correlations in Cyg X-1 and AGN, but only if the ratio of the soft photons' luminosity to the power injected to the hot corona is proportionally related to the accretion rate.
Key words: galaxies: active - galaxies: Seyfert - X-rays: galaxies
1 Introduction
The X-ray variability properties of AGN have been extensively studied during
the past twenty years. Significant progress has been achieved in the estimation
of their X-ray power spectral density functions (PSDs), which (among other
things) can be helpful in the search for characteristic time scales in these
objects. This progress has been made possible with the combined use of
monitoring RXTE light curves (which are up to 5-10 years long in many cases)
and shorter (1 to a few days long), high signal-to-noise, XMM-Newton and Chandra light curves. The results have shown that the PSD has a -2 power
law shape at high frequencies and then, below a characteristic ``break -
frequency'',
,
it flattens to a slope of
-1 (e.g.
Uttley et al. 2002; Markowitz et al. 2003;
M
Hardy et al. 2004).
Uttley & M
Hardy (2005, UM05 hereafter) list
estimates for 14 nearby AGN. Using these results, M
Hardy et al. (2006, M06 hereafter) demonstrated that the corresponding ``break timescale'',
,
increases with increasing black hole mass,
,
and for a given
,
it decreases with increasing accretion rate,
(in units of the Eddington limit).
Knowledge of the X-ray properties of the Galactic black hole binaries (GBHs) has also advanced substantially during the past twenty years. Power spectral studies of Cyg X-1 in particular have been advanced considerably. Pottschmidt et al. (2003, hereafter P03) for example have used many RXTE observations between 1998 and 2001 to study the long-term evolution of the PSD. They also studied the energy spectrum of the source and presented convincing evidence that its timing and spectral properties are closely linked: the characteristic time scales become shorter as the spectrum steepens. Axelsson et al. (2006, hereafter A06), using several archival RXTE observations, which cover all spectral states of the source, detected the same ``spectral-timing properties'' correlation as well. Shaposhnikov & Titarchuk (2006) also found that photon index and characteristic PSD frequencies are positively correlated in Cyg X-1.
The question whether AGN vary in a manner similar to that of GBHs is a long standing one. The availability of the better quality AGN light curves over the last few years (resulted from intense and extended RXTE monitoring campaigns to sample variability on very long time scales) has allowed a more quantitative comparison between AGN, Cyg X-1 and other GBHs (GRS1915+105 for example, in M06). In this work we used archival RXTE observations of 11 AGN, together with data from the literature for 3 more objects, to estimate their average spectral slope and compare it with the characteristic frequencies that have been detected in their power spectra. We show that a positive ``average spectral slope - characteristic frequencies'' correlation exists, and we argue that this correlation is driven by accretion rate, for a given black hole (BH) mass: objects with a higher accretion rate relative to the Eddington limit should also have a steeper spectrum and a shorter characteristic time scale. We also compared the spectral-timing relation we found in AGN with a similar relation that has been detected in one GBH binary, namely Cyg X-1. The two relations differ, but by an amount that can be explained if we take into account the BH mass difference in AGN and Cyg X-1. Our results support the idea that AGN and GBHs vary in the same way. They also have interesting implications regarding the nature of the X-ray source in AGN and GBHs.
2 Sample selection and data reduction
For the purposes of this study, we need to study AGNs with known
and average X-ray slopes. The sample of UM05 is the best choice given the
availability of the
estimates, and the fact that these objects
have been observed regularly with RXTE, over durations of at least a few years.
This is more than
1-2 orders of magnitude longer than the characteristic
time scale of the sources in our sample. Most probably then, we have observed
most of the possible flux and spectral variations that they exhibit.
Furthermore, the study of the same RXTE observations that were used to
estimate the power spectrum of the sources, offers us the possibility to
determine their underlying spectral index around the same period of the power
spectrum measurements.
Table 1: Black hole mass and timing properties of the AGN in the sample.
In Table 1 we list the 14 AGN in the UM05 sample, together with their
and
estimates. For 11 of these objects we
considered all the RXTE observations that were performed until the end of
2006; all data were taken from the public archive. Table 2 lists the date of the
first and last observation, and the total number of RXTE observations that we
have used (second and third column, respectively). For the remaining three
objects, namely NGC 4151, NGC 4258 and NGC 4395 we used data from literature to
determine their average spectral shape, as explained in Sects. 3.1, 3.2
and 3.3, below.
Table 2: Summary of the RXTE observations.
We used data from the Proportional Counter Array (PCA, Jahoda et al. 1996) only.
The typical duration of each observation was 1-2 ks. The data were
reduced using FTOOLS v.6.3. The PCA data were screened according to the
following criteria: the satellite was out of the South Atlantic Anomaly (SAA)
for at least 30 min, the Earth elevation angle was
,
the offset
from the nominal optical position was
,
and the parameter
ELECTRON-2 was
0.1. Appropriate PCA background
files
, were used to calculate background model energy spectra in the
3-20 keV band.
3 Spectral analysis
We extracted STANDARD-2 mode, 3-20 keV (where the PCA is most sensitive),
Layer 1, energy spectra from PCU2 only. After background subtraction, we used the XSPEC v.11.3.2 software package (Arnaud 1996) to fit a simple
``power-law + Gaussian line'' (to account for the K iron feature) to the spectrum of
each observation. We used PCA response matrices and effective area curves
created specifically for the individual observations by pcarsp. All
spectra were rebinned using grppha so that each bin contained more than
15 photons for the
statistic to be valid.
The simple ``power-law + Gausian'' (hereafter PLG) model fitted well almost all
of the individual RXTE spectra of the sources listed in Table 2. The only
exception is NGC 5506, which hosts a heavily reddened Narrow Line Seyfert 1
nucleus (Nagar et al. 2002). Its central source is absorbed by neutral matter
with column density of
cm-2 (Lamer et al. 2000;
Bianchi et al. 2003). For this reason we used a
``wabs
PLG'' model instead, with
fixed at
cm-2. This model fitted well most of the RXTE spectra of this source.
3.1 NGC 4395
NGC 4395 is a rather faint X-ray source, with an average 2-10 keV flux of
erg cm-2 s-1 (Shih et al. 2003),
which has not been observed by RXTE. Shih et al. have estimated a mean
spectral slope,
,
of
from the study of a
7 day long ASCA observation. Since
s for this
source (Vaughan et al. 2005), we can be reasonably confident that the ASCA observation sampled most of the flux/spectral variations that the source
displays. For this reason we adopted this value as the best estimate for its
average spectral shape.
3.2 NGC 4258
The nucleus of NGC 4258 is heavily obscured in the X-ray band. Absorption
column density estimates of the order of a few
cm-2 have
been reported in the past (Yang et al. 2007). The absorption also varies on time
scales of months and years (Fruscione et al. 2005). NGC 4258 has been observed
extensively by RXTE. There are 707 observations (obtained until the end of
2006) in the archive. We reduced the data for all of them, and fitted the
resulting spectra with a wabs
PLG model, keeping
fixed
at 1023 cm-2. The model fitted the RXTE spectra well. The mean
spectral slope is equal to 2.02.
Fruscione et al. (2005) found that the best-fit
values increase with
decreasing instrumental angular resolution. They argued that this is due to the
fact that a small extraction radius can isolate the central engine from the
surrounding soft nuclear emission. It is unsurprising then that the mean
spectral slope we estimated is similar to the best-fit value of
2.1 that
Fiore et al. (2001) reported from a study of BeppoSax data, and
significantly steeper than the values obtained from the Chandra and
XMM-Newton data analysis (Fruscione et al. 2005). For this reason, we used their results
from the spectral analysis of 9 Chandra and XMM-Newton observations, which were
performed between May 8 2000 and May 22 2002. The weighted mean of their best
fit spectral slopes is
,
which we adopt as the
average spectral slope estimate for this source.
3.3 NGC 4151
The X-ray spectrum of NGC 4151 is one of the most complex in AGNs, characterised by narrow and broad spectral features from soft to hard X-rays (e.g. Kraemer et al. 2005). The spectrum above 2 keV is affected by absorption from a neutral absorber, which may even be patchy, and from warm material photionised by the central continuum (e.g. Beckmann et al. 2005; de Rosa et al. 2007).
NGC 4151 has been observed regularly by RXTE. Data from 506 observations
performed until the end of 2006 are stored in the archive. A simple PLG model
yields
in 241 out of the 506 spectra. The use of a partial
covering fraction absorption model, ``pcfabs
PLG'', with the
covering fraction and
fixed at 0.55 and
cm-2 (de Rosa et al. 2007) improved the quality of the model fit but there
are still more than a hundred spectra that the model could not fit well. Given
the complexity of the NGC 4151 spectrum and the low spectral resolution of PCA,
it is not safe to use a more complex model to fit the RXTE data. Using the
results of de Rosa et al. (2007), based on the spectral study of 8 BeppoSax observations from January 1996 to December 2001, we found that the
weighted mean of the best fit spectral slopes is
.
4 Results
4.1 The mean spectral slope
The top panel in Fig. 1 shows the sample distribution function of the Mrk 766
best-fit spectral slope values,
.
A Gaussian fits well this
distribution. This is the case with 5 more sources, namely: NGC 5548,
PG 0804+761, NGC 3516, NGC 5506 and Ark 564. In the middle and bottom panels of
the same figure we plot the
distribution functions in the
case of NGC 3227 and NGC 4051. An extended tail towards low
values can
be seen in both cases. In NGC 3227, these low-
values correspond to the
transient absorption by a gas cloud of column density in late 2000 and early
2001 (Lamer et al. 2003). As for NGC 4051, it is well
established that it shows rather unusual (among AGN) low flux states, which
last from weeks to months, during which the X-ray spectrum becomes extremely
hard (Uttley et al. 2004, and references therein). Less pronounced tails towards
low
values were also observed in the spectral slope distribution
functions of Fairall 9, NGC 3783 and MCG -06-30-15.
Given the asymmetry in the spectral slope distributions we observe in some
cases, we used the median of the distribution as an estimate of the mean
spectral slope,
,
for all sources in our sample. The
results are listed in the second column of Table 3. The numbers in the
parentheses correspond to the standard deviation of the
distributions. They indicate the scatter of the individual
about their mean, and are representative of the typical range of the spectral
slopes that we observe for each object. In the case of NGC 4258 and NGC 4151,
the standard deviation is corrected for the contribution of the error of the
individual best-fit
values, which in some cases was quite large. In the
case of NGC 4395, the error listed is the one reported by Shih et al. (2003).
![]() |
Figure 1: The spectral slope distribution function of Mrk 766 ( top panel), NGC 3227 ( middle panel) and NGC 4051 ( bottom panel). |
Open with DEXTER |
Table 3: The mean spectral slope estimates.
4.2 The ``intrinsic'' spectral shape of AGNs
We found that most objects show significant spectral variations (the results
from a detailed analysis of these variations will be presented elsewhere). If
the
variations correspond to variations of the intrinsic
continuum slope,
,
then
will be
representative of the average
as well. However, the AGN
X-ray spectra, in some cases at least, are strongly affected by the presence of
warm absorbing material even at energies above 2 keV. For example, significant
warm absorbing effects have been observed in NGC 3516 (Turner et al. 2005),
NGC 3783 (Reeves et al. 2004), MCG -06-30-15 (Miller et al. 2008)
and Mrk 766 (Turner et al. 2007). In this case,
will be a
biased estimate of
.
It is even possible that the spectral variations we observed are mainly caused
by variations in a complex and multi-layered absorber, while
remains constant (e.g. Turner et al. 2007; Miller et al. 2008). If that is the
case, then, for each individual spectrum,
,
where
(as any absorption effects always
result in flatter spectra). Since we expect
to be different from
one observation to the other (due to changes in the covering factor, ionization
state of the absorber etc.), then
,
where
is the mean of all the
individual
s, and should be negative, hence
.
It has also been suggested that the observed spectral variations are caused by
the combination of a highly variable (in flux) power-law (with
= constant) and a constant reflection component (e.g., Taylor et al. 2003; Ponti et al. 2006; Miniutti et al. 2007). Even in this
case, we expect that
(with
), hence
.
The point is that, if the 2-20 keV spectrum is affected by absorption and/or
reflection effects, then
will be a biased estimator
of
.
One way to minimise the bias is to estimate the mean
spectral slope using only the largest
for each object since,
in this case,
will be minimum. For this reason, we estimated the
mean of the
which are larger than the 80th percentile of the
distribution (i.e. the value below which 80 percent of the observations fall).
In the case of NGC 4258, we used the mean of the three steepest
values
of Fruscione et al. (2005) as an estimate of
.
Similarly, in the case of NGC 4151 we considered the mean of the two
steepest
values of de Rosa et al. (2007).
The
estimates are also listed in Table 3. The
numbers in the parentheses correspond to the standard deviation of the points
in the 20% upper part of the
distributions, and indicate
the scatter of these points about
.
The 80/20 dividing
line is somehow arbitrary, and is mainly determined by the need to retain a
sizable sample of
values to estimate their mean in the case
of sources with small number of observations. In any case, our results do not
change significantly when we use the 90th or 70th percentile of the distribution
for the sources with more than 800 observations. Furthermore, the
values are closer to spectral slope estimates which
are resulted when complex, and more realistic, models are fitted to high
quality X-ray spectra. For example, in Mrk 766, Miller et al. (2007) derive
from the ``principal component analysis'' (fit to
eigenvector 1). In NGC 3516, Turner et al. (2005) derive
and
from XMM-Newton observations at 2 different epochs. In MCG
-6-30-15, the absorption model in Miller et al. (2008) derives a best-fit of
(from the Suzaku data analysis) and
from the study of the XMM-Newton long looks. In comparison,
Minutti et al. (2007) in their blurred reflection model also derive a steep
from the Suzaku data. Finally, in NGC 4051, in a
recent paper by Terashima et al. (2008, PASJ, submitted), based on absorption
fits to Suzaku data, derive
.
The average
difference between these spectral slope estimates and
is less than
0.1. Therefore,
should be more
representative of the intrinsic spectral slope of each source, if absorption
and/or reflection effects are significant.
4.3 The ``spectral-timing'' relation in AGN
Filled squares in the upper panel of Fig. 2 indicate the ``mean spectral slope
vs characteristic frequency'' relation for the AGN in our sample, using the
values listed in Table 3 and the
estimates listed in Table 1. The plot in the middle panel shows the ``mean
spectral slope vs. BH mass'' relation, and in the bottom panel we plot
as a function of the characteristic frequency
multiplied by the BH mass of each object (using the BH mass estimates listed in
Table 1). We call the product
as the
``normalised characteristic frequency'',
(in units of
Hz
). The crosses in the bottom panel of Fig. 2 indicate the
``mean spectral slope vs.
'' relation when we used
(instead of
)
as a measure of
the mean spectral slope for the sources in our sample.
Visual inspection of Fig. 2 suggests that, although the mean spectral slope does
not correlate with BH mass, it may correlate positively with
,
and
even more so with
:
objects with steeper spectra have shorter
characteristic frequencies as well. We reached the same conclusion even when we
replaced
with
in the first
two panels of Fig. 2. To quantify the correlation of the mean spectral slope
with
,
BH mass, and
,
we used the Kendall's
test. The test was performed in the log-log space, and the results
(
and
,
i.e. the probability that, under the hypothesis there
is no correlation,
could be this large or larger just by chance) are
listed in Table 4. We accepted a correlation to be ``significant'' if
.
Values in third column of Table 4 are the test results when we
use
instead of
.
![]() |
Figure 2:
Top panel: The ``
|
Open with DEXTER |
The Kendall's
results imply that only the ``mean spectral slope vs.
'' correlation is strong (i.e.
)
and significant. This
is true irrespective of whether we use
or
.
The correlation remains significant even if we
omit Ark 564 (i.e. the source with the softest spectrum and the highest
characteristic frequency):
,
for the
-
relation, and
,
when we use
instead of
.
We therefore conclude that, although the mean spectral slope does not
correlate significantly either with power spectrum break frequency or with
the BH mass, it does correlate positively with the break frequency when
normalised to the BH mass of each object
.
To investigate whether a straight line or a power law model fits best the
AGN spectral-timing relation, we considered the 10 AGN that have well measured
PSD breaks and we fitted their ``average spectral slope - normalised frequency''
data with a straight line in both the linear and log-log space, taking into
account the errors on both the
and
(or
)
values. We found that the power-law model (i.e. a straight
line in the log-log space) describes better the observed spectral-timing
relation. For example, the linear model fit to the (
,
)
data resulted in a
value of 25.1 for 8 degrees of
freedom (d.o.f.). A linear model to the logarithm of the same data set resulted
in 17.6 for 8 d.o.f. To quantify if this change in
is significant, we
computed the ``ratio of likelihoods'',
L1/L2 (Mushotzky 1982). It is
defined as
L1/L2 = exp
exp
,
where
and
are the chisquare for the line fits in the
logarithmic and linear spaces, respectively. We found that
L1/L2=42.5.
This result suggests that a power law is
40-45 times more likely, than a
straight line, to be the ``correct'' model for the spectral-timing data plotted
in the bottom panel of Fig. 2.
To derive the best-fit power law parameter values, we used the ``ordinary least
squares bisector'' method of Isobe et al. (1990) to fit the
[(
,
(
)] data with a straight line
of the form
(
.
The best-fit
parameter values are
and
(the best-fit model
is indicated by the solid line in the bottom panel of Fig. 2). The dashed line
in Fig. 2 indicates the best-fit straight line model to the
[log
,
log
]
data. The best-fit
parameter values in this case are
and
.
In
other words, a power-law model of the form
fits well the (
) data, while in the case of the (
) data the best-fit power-law model is
.
We note that although the
best-fit slopes are small, they are significantly different than zero. The
best-fit parameter values are consistent within the errors and their weighted
mean value is
and
.
We therefore
conclude that the spectral-timing relation in AGN is well parametrised by a
power-law model of the form:
.
According to M06, the PSD break frequency depends on both the BH mass and
accretion rate approximately as follows:
.
Consequently,
should depend on
only. Given this observational result, the
relation we found can be translated to a
relation. In other
words, our results suggest that the mean spectral slope in AGN correlates
positively with
:
objects with higher accretion rate should
also have steeper spectra (on average).
In the case of Comptonisation models, where thermal electrons in a corona above
the disc upscatter soft photons emitted by the disc of temperature
,
the produced X-rays have a power-law spectrum. When a soft photon of initial
energy
is Compton scattered in the corona, it acquires an energy
,
on average, where A is the Compton amplification factor
defined as
(
and
are the power used to heat the corona and the intercepted soft luminosity,
respectively). The produced X-rays have a power-law spectrum whose slope,
,
depends on the temperature and optical depth of the corona. In
general, one expects that when
increases, the corona cooling will be
more efficient. Consequently, its temperature should decrease and the resulting
X-ray spectrum will be steeper (i.e.
will increase).
Table 4:
The Kendaull's
test results for the correlations plotted in
Fig. 2.
Using the numerical Comptonisation code of Coppi (1999, eqpair in XSPEC), which is applicable in the case of a soft photon source located in the
centre of a static, isothermal spherical corona, Beloborodov (1999) derives a
relationship between
and
for different disc
temperatures,
.
For
few
,
which is applicable in
AGN, he finds that
.
For low
mass black holes like Cyg X-1, where
few
,
.
In the case of a
non-static, outflowing corona, Malzac et al. (2001) found
similar results:
and
.
We found that
which, when
combined with the
result of M06,
implies that
.
Consequently, thermal Comptonisation model predictions, i.e.
0.10, are consistent
with our results, i.e.
,
but only if
.
5 Comparison with Cyg X-1
To compare the spectral-timing behaviour of AGN with that of Galactic black hole X-ray binary systems, we considered the extensive spectral and timing observations of the best studied GBH, Cyg X-1. To maximise the spectral-timing range, we considered all available information, covering ``hard'' state observations (from P03 and A06) and ``soft'' and ``intermediate'' states (from A06).
It is important that a consistent measure of characteristic break-frequency is
used for all the Cyg X-1 and AGN data. In the soft state the PSD of Cyg X-1 is
well described by a power-law with only one ``bend'', with slope -1 at low
frequencies and
-2 at high frequencies. This shape is sometimes also
parametrised as a power-law of slope -1 with an exponential cut-off (model 5 of
A06). This shape also fits well the PSDs of almost all AGN that have been
studied so far (except for Akn564, for which a double Lorentzian model fits
best, M
Hardy et al. 2007). For the soft state PSDs of Cyg X-1
therefore, we considered from model 5 of A06, the best-fit ``turnover'' or
``bend'' frequency at which the PSD slope bends from -1 to -2.
In the hard state, the PSD of GBHs such as Cyg X-1 can be fitted either as a
doubly bending power-law of slope 0 at the lowest frequencies, slope -1 at
intermediate frequencies, and slope -2 at the highest frequencies or, where
the signal-to-noise ratio is higher, as the sum of a number of Lorentzian-shaped
components. Both P03 and A06 have opted for the second option, in modeling the
Cyg X-1 PSD in the hard and intermediate state. To include therefore the hard
state Cyg X-1 PSD observations, we must use the Lorentzian which, in the bending
power-law parametrization, is closest to the frequency at which the slopes
change from -1 to -2. In the observations of P03, that Lorentzian is
referred to as ,
and has an average frequency around 2 Hz. In the
analysis of A06 (and also of Axelsson et al. 2005), the hard
and intermediate state PSD is parametrised by the sum of two Lorentzians but
also with the addition of a weak cut-off power-law. The Lorentzian with the
higher frequency corresponds to
of P03 and so we used the frequency of
that Lorentzian here
.
In order to measure
,
P03 fit their spectra with a ``power-law
+ multi-temperature disc-black body + reflection'' model from which the
of the power-law can be taken. A06 list (20-9)/(4-2) keV
hardness ratios (HR). We have used the empirical relationship between
and HR of Axelsson et al. (2005) to convert HR into
.
The resulting Cyg X-1 data are shown in Fig. 3. Open and filled circles indicate
the (
)
data for Cyg X-1 where
is the centroid
frequency of the ``second'' Lorentzian in the P03 and A06 model fits to the
Cyg X-1 PSD, respectively. These data define the Cyg X-1 spectral-timing relation
in its hard state. Crosses indicate the (
)
data for
Cyg X-1, where
is the ``bend'' frequency of the ``bending'' power-law
model which fits best the Cyg X-1 PSD in its soft state, according to A06 (their
model 5). To convert the observed frequencies (both
and
)
to
we assumed a black hole mass of 15
,
intermediate
between the two published estimates of 10
(Herrero et al. 1995) and
20
(Ziolkowski 2005). We can see that the Cyg X-1 hard and soft
state data form a smooth continuous distribution in the spectral-timing plane
shown in Fig. 3.
![]() |
Figure 3:
(Both panels) Filled and open circles indicate the
spectral-timing data for Cyg X-1 in its hard state, using data from P03 and
A06, respectively. Crosses indicate the spectral-timing data for Cyg X-1 in
its soft state using data from A06. Filled squares indicate the ``mean spectral
slope - normalised characteristic frequency'' data for the AGN in our sample,
when we consider the
|
Open with DEXTER |
Filled squares in the top and bottom panels of Fig. 3 indicate the ``spectral
slope - characteristic frequency'' relation for the AGN in our sample, when we
use the
and
values,
respectively. Although in both Cyg X-1 and AGN the characteristic frequencies
increase as the energy spectrum steepens, Fig. 3 shows clearly that the
respective ``
'' relations are not the same.
This difference can be explained by the fact that the accretion disc is hotter
in Cyg X-1 than in AGN. So, for example, in the case of an outflowing corona, as
stated in Sect. 4.3,
in AGN but
in Cyg X-1. If
,
both in AGN and Cyg X-1, then we expect
that
and
.
Using the
relation of M06, these relations can be written as follows:
and
.
As a result, in the case when
,
we should expect that
,
i.e.
(in the case of a static corona, we expect
a similar relation, i.e.
). Open squares in both panels of Fig. 2 indicate the AGN data
when we transform
to
.
The
agreement now between the Cyg X-1 and AGN ``spectral slope - characteristic
frequency'' relation is good (a more detailed derivation of the relation between
and
in the case of thermal
Comptonisation models is presented in Sect. 6.2).
6 Discussion and conclusions
We have used 7795 RXTE observations of 11 AGN, obtained over a period of
7-11 years, to extract their 3-20 keV spectra. We fitted them with a simple
``power-law + Gaussian line'' model, and we used the best-fit slopes to construct
their sample distribution function. We used the median of the distributions, and
the mean of the best-fit slopes which are above the 80th percentile of the
distributions, to estimate the mean spectral slope of the objects (the latter
estimate is more appropriate in the case when the energy spectra of the sources
are significantly affected by absorption and/or reflection effects). We also
used results from literature to estimate the average spectral slope of three
more objects. The fourteen AGN that we consider in this work are nearby, X-ray
bright objects, whose X-ray light curves have been studied in the past. Their
PSDs have been accurately estimated, and characteristic ``break frequencies''
have been detected in them.
When we combine the mean spectral slope estimates with the
estimates listed in UM05, we find that: objects with steeper mean energy
spectra have shorter characteristic time scales as well. This is the first time
that such a ``spectral - timing'' correlation is detected in AGN. The results we
reported in Sect. 4.3 suggest that this spectral-timing relation in AGN can be
parametrised as follows:
.
6.1 The spectral-timing correlation in AGN
The easiest way to explain this correlation is to assume that, for an AGN with a
given BH mass, the accretion rate determines both the PSD characteristic
frequencies (this has already been shown by M06) and their energy spectral shape
as well: the higher the accretion rate, the steeper the mean energy spectrum
will be. Such a positive
relation in AGN has
already been suggested/shown in the past (e.g. Porquet et al. 2004;
Bian 2005;
Shemmer et al. 2006; Saez et al. 2008). A positive
relation has also been detected recently in 7 GBHs by Wu & Gu (2008), when they
accrete at a rate higher than
of the Eddington limit. Our results are
consistent with the results reported in these papers.
Using the M06 results, we calculate that
Hz
.
When we replace
in the relation of
we
found in this work, we find that:
.
This formula between spectral slope and accretion rate could be
helpful in deriving a rough estimate for the accretion rate of the distant AGN
that are detected in deep X-ray surveys, assuming that their variability
properties are similar to the properties of nearby AGN (this is supported by
recent studies, see e.g. Papadakis et al. 2008).
In the context of thermal Comptonisation models,
can
affect the spectral slope
as it controls the strength of the soft disc
photons, hence the cooling of the thermal plasma in the X-ray emitting corona.
The greater the cooling by seed photons incident on the plasma, the softer the
resulting X-ray power-law spectra are. Indeed, we found that Comptonisation
models are consistent with the
relation that our
results imply, but only if
.
6.2 The comparison with Cyg X-1
Both P03 and A06 have used data from RXTE observations that lasted for
1-2 ks, and were performed every
5-10 days over a period of many years.
If ``time scales'' scale with BH mass in accreting objects, then 1-2 ks in
Cyg X-1 should correspond to a period of at least
3-6 years in objects
with
times the mass of the black hole in Cyg X-1 (like most
AGN in our sample). This suggests that each one of the AGN points in Fig. 3
corresponds to just one of the Cyg X-1 points plotted in the same figure. We
found that the AGN and Cyg X-1 ``
'' relations are
similar but not the same. In Sect. 5 we discussed briefly some implications of
this result. In the paragraphs below we discuss the implications of our results
in more detail.
The main aim of the discussion below is to investigate the constrains that the AGN spectral-timing relation, and its comparison with the similar relation in Cyg X-1, impose on thermal Comptonisation models, based on the particular assumption that both the spectral and timing properties of accreting systems are driven by accretion rates variations. We point out that other interpretations are also possible; see for example Kylafis et al. (2008) for an alternative explanation of the Cyg X-1 spectral-timing relation, which does not assume that X-rays are produced by thermal Comptonisation. We also point out that, given the small number of objects in our sample, and the unavoidable uncertainty in the derived parameters of the AGN spectral-timing relation, the values of the various parameters in the equations below are somehow uncertain.
As we showed in Sect. 6.1, the AGN spectral-timing relation and the
M06 results imply that
.
If
X-rays in AGN are produced by thermal Comptonisation, we expect
that
.
Therefore, the observations
(i.e.
)
are consistent with the
thermal Comptonisation model predictions
(
), only if
![]() |
(1) |
An obvious implication of this result is that, if a certain fraction, say







Suppose that X-rays from Cyg X-1 in its low/hard state (LH) are also produced
by thermal Comptonisation. In this case, thermal Comptonisation models predict
that
,
or
![]() |
(2) |
if we accept that Eq. (1) holds in this case as well. According to Körding et al. (2007), the normalisation of the








![]() |
(3) |
The dashed line in the top panel of Fig. 3 indicates this relation. The agreement between the predicted


- a)
- X-rays from the AGN we studied are produced by thermal Comptonisation. The
relation we observe is consistent with the predictions of thermal Comptonisation models but only if the
ratio, and hence the
ratio as well, increase proportionally with accretion rate;
- b)
- X-rays in Cyg X-1 are also produced by thermal Comptonisation. Taking into
account the fact that the normalisation of the
relation is
8 times smaller in Cyg X-1 than in the AGN in our sample (Körding et al. 2007), the predicted
relation agrees well with the Cyg X-1 data up to
;
- c)
- in the case when
, we expect that (
, and
(using Eq. (1)). Consequently,
and, since
, AGN should operate on a lower accretion rate than Cyg X-1 when the spectral slope is the same in both systems. Furthermore, since
and
(when
), then
implies that
, and
. Therefore, when the spectral slope is the same (and less than
2.1-2.2) in AGN and Cyg X-1, the former should operate at a lower accretion rate but their characteristic time scales should be shorter than those in Cyg X-1 (when normalised to the respective BH mass), because the normalisation of the AGN
relation is significantly larger than the normalisation of the respective Cyg X-1 relation in LH state.









The discrepancy between the predicted spectral-timing relation and the Cyg X-1
data when
and
cannot be explained by the
fact that the normalisation of the
relation
increases by a factor of
8 in the high/soft state. If that were the
case, the spectral-timing relation in this state should be similar to the one
defined by Eq. (3), but with a smaller normalisation (opposite to
what we observe).
One possibility is that the
relation
(Eq. (1)) changes in the high/soft state. However, in this case we would have
to accept that the X-ray source does not operate in the same way in AGN
and Cyg X-1: when
,
both Cyg X-1 and the AGN in our sample
follow the same
relation (M06, Körding
et al. 2007). Therefore, as long as
,
a given
value implies the same accretion rate in both systems. The fact that the
AGN spectral-timing relation is valid up to
should
then imply that, for the same accretion rate, the ``
- accretion rate'' relation is different in AGN and Cyg X-1.
In Cyg X-1,
implies that
,
and hence
.
Another possible explanation then for the discrepancy between the Cyg X-1 data
and the predicted spectral-timing relation above
is the
following: Eq. (1) holds until
,
at
which point the hot corona is significantly cooled down, and the thermal X-ray
emission component is weak. It is possible then that at high accretion rates a
separate, possibly non-thermal, X-ray component emerges, and dominates the
X-ray emission in the soft state. If that is the case, the
relation we have assumed above is not valid, hence the
predicted spectral-timing relation does not fit the data any more.
Even if the picture drawn above is correct, there are important issues regarding
the relation between AGN and GBH states which still remain unresolved. In
particular, the answer to the question whether the AGN in our sample are
``soft'' or ``hard'' state systems is far from clear. There are indications that
they are analogous to Cyg X-1 in its soft state. For example, the radio emission
in Cyg X-1 in its LH state is enhanced. On the other hand, Panessa et al. (2007)
have shown that, for the same
ratio, the radio luminosity
of Seyfert galaxies is
8-10 times lower than the radio luminosity of
hard-state GBHs, even when the BH mass difference is properly taken into account
(7 of the objects in our sample are also included in their sample). Furthermore,
the AGN in our sample follow the soft-state ``characteristic time scale -
accretion relation'' in GBHs, and a ``bending'' power-law is the dominant
component in the power spectrum of those objects with good enough light curves
to accurately study their PSD (e.g. NGC 4051, M
Hardy et al. 2004;
NGC 3227 and NGC 5506, UM05; MCG 6-30-15, M
Hardy et al. 2005; and
perhaps NGC 3783, Summons et al. 2007), implying a soft-state like PSD in these
objects. High quality light curves for low accretion rate AGN are necessary to
investigate whether any AGN with hard-state like power spectra exist or not.
However, although the radio emission strength and the timing properties of many
objects in our sample are soft-state like, their spectral properties are not, as the average spectral slope is smaller than 2.1 in most cases. If
indeed the spectral hard-to-soft state transition corresponds to
,
at which point the thermal corona emission is weak,
and a different component dominates the X-ray emission, then we should expect
this transition to happen when
in AGN. Given the AGN
relation, this slope corresponds to
.
At even higher normalised frequencies, we should then
expect the AGN spectral-timing relation to break (like in Cyg X-1 at
). Obviously, more data are necessary to confirm that this is
indeed the case in AGN.
The data so far suggest that while in AGN the timing properties transition
from hard-to-soft state happens at least as low as
,
the spectral properties transition should happen at much higher accretion
rates. This is opposite to what we observe in Cyg X-1, where both the spectral and
timing properties change from the hard to soft state, at the same accretion rate
(indicated by the value
.
Perhaps the timing
properties in accreting objects are determined by accretion disc variations
only, and the hard-to-soft state transition materialises at a certain accretion
rate, irrespective of whether the soft disc luminosity is strong enough for
,
i.e. strong enough to cool down the hot corona.
In this case, we would expect the AGN hard-to-soft timing properties transition
to appear at
as well. Due to the cooler disc
temperature though, the AGN spectral soft-to-hard state transition happens at
higher accretion rates (i.e. at a higher
value in the
spectral-timing plane of Fig. 3). Further progress in understanding the relation
between AGN and GBHs can be made when we know how the accretion rate determines
the characteristic frequency in accreting compact objects (assuming that it is
just the accretion rate that determines
in these systems).
Acknowledgements
We would like to thank the referee, P.O. Petrucci, for valuable comments which helped us to improve the paper significantly. I.E.P. and M.S. acknowledge support by the EU grant MTKD-CT-2006-039965. M.S. also acknowledges support by the the Polish grant N20301132/1518 from Ministry of Science and Higher Education.
References
- Arnaud, K. A. 1996, Astronomical Data Analysis Software and Systems V, ed. G. Jacoby, & J. Barnes, ASP Conf. Ser., 101, 17 (In the text)
- Axelsson, M., Borgonovo, L., & Larsson, S. 2005, A&A, 438, 999 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Axelsson, M., Borgonovo, L., & Larsson, S. 2006, A&A, 452, 975 [NASA ADS] [CrossRef] [EDP Sciences] (A06) (In the text)
- Beckmann, V., Shrader, C. R., Gehrels, N., et. al. 2005, ApJ, 634, 939 [NASA ADS] [CrossRef] (In the text)
- Beloborodov, A. M. 1999, in High Energy Processes in Accreting Black Holes, Ed., J. Poutanen & R. Svensson, ASP, San Francisco, 295 (In the text)
- Bianchi, S., Balestra, I., Matt, G., Guainazzi, M., & Perola, G. C. 2003, A&A, 402, 141B [NASA ADS] [CrossRef] (In the text)
- Bian, W. 2005, ChJAS, 5, 289 [NASA ADS] (In the text)
- Botte, V., Ciroi, S., Rafanelli, P., & Di Mille, F. 2004, AJ, 127, 3168 [NASA ADS] [CrossRef]
- Coppi, P. S. 1999, in High Energy Processes in Accreting Black Holes, Ed., J. Poutanen & R. Svensson, ASP, San Francisco, 375 (In the text)
- de Rosa, A., Piro, L., Perola, G. C., et al. 2007, A&A, 463, 903 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Fiore, F., Pellegrini, S., Matt, G., et al. 2001, ApJ, 556, 150 [NASA ADS] [CrossRef] (In the text)
- Fruscione, A., Greenhill, L. J., Filippenko, A. V., et al. 2005, ApJ, 624, 103 [NASA ADS] [CrossRef] (In the text)
- Herrero, A., Kudritzki, R. P., Gabler, R., Vilchez, J. M., & Gabler, A. 1995, A&A, 297, 556 [NASA ADS] (In the text)
- Herrnstein, J. R., Moran, J. M., Greenhill, L. J., et al. 1999, Nature, 400, 539 [NASA ADS] [CrossRef]
- Jahoda, K., Swank, J. H., Giles, A. B., et al. 1996, Proc. SPIE, 2808, 59 (In the text)
- Isobe, T., Feigelson, E. D., Akritas, M. G., & Babu, G. J. 1990, ApJ, 364, 104 [NASA ADS] [CrossRef] (In the text)
- Körding, E. G., Migliari, S., Fender, R., et al. 2007, MNRAS, 380, 301 [NASA ADS] [CrossRef] (In the text)
- Kraemer, S. B., George, I. M., Crenshaw, D. M., et al. 2005, ApJ, 633, 693 [NASA ADS] [CrossRef] (In the text)
- Kylafis, N. D., Papadakis, I. E., Reig, P., Giannios, D., & Pooley, G. G. 2008, A&A, 489, 481 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Lamer, G., Uttley,
P., & M
Hardy, I. M. 2000, MNRAS, 319, 949 [NASA ADS] [CrossRef] (In the text)
- Lamer, G., Uttley,
P., & M
Hardy, I. M. 2003, MNRAS, 342, 41 [NASA ADS] [CrossRef] (In the text)
- Malzac, J., Beloborodov, A. M., & Poutanen, J. 2001, MNRAS, 326, 417 [NASA ADS] [CrossRef] (In the text)
- Markowitz, A., Edelson, R., Vaughan, S., et al. 2003, ApJ, 593, 96 [NASA ADS] [CrossRef] (In the text)
-
M
Hardy, I. M., Papadakis, I. E., Uttley, P., Page, M. J., & Mason, K. O. 2004, MNRAS, 348, 783 [NASA ADS] [CrossRef] (In the text)
-
M
Hardy, I. M., Gunn, K. F., Uttley, P., & Goad, M. 2005, MNRAS, 359, 1469 [NASA ADS] [CrossRef] (In the text)
-
M
Hardy, I. M., Köerding, E., Knigge, C., Uttley, P., & Fender, R. P. 2006, Nature, 444, 730 [NASA ADS] [CrossRef] (M06) (In the text)
-
M
Hardy, I., Arevalo, P., Uttley, P., et al. 2007, MNRAS, 382, 985 [NASA ADS] (In the text)
- Miller, L., Turner, T. J., & Reeves, J. N. 2008, A&A, 483, 437 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Miniutti, G., Fabian, A. C., Anabuki, N., et al. 2007, PASJ, 59, 315 (In the text)
- Mushotzky, R. F. 1982, ApJ, 256, 92 [NASA ADS] [CrossRef] (In the text)
- Nagar, N. M., Oliva, E., Marconi, A., & Maiolino, R. 2002, A&A, 391, L21 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Panessa, F., Barcons, X., Bassani, L., et al. 2007, A&A, 467, 519 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Papadakis, I. E. 2004, MNRAS, 348, 207 [NASA ADS] [CrossRef]
- Papadakis, I. E., Brinkmann, W., Negoro, H., & Gliozzi, M. 2002, A&A, 382, L1 [NASA ADS] [CrossRef] [EDP Sciences]
- Papadakis, I. E., Reig, P., & Nandra, K. 2003, MNRAS, 344, 993 [NASA ADS] [CrossRef]
- Papadakis, I. E., Chatzopoulos, E., Athanasiadis, D., et al. 2008, A&A, 487, 475 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Peterson, B. M., Ferrarese, L., Gilbert, K. M., et al. 2004, ApJ, 613, 682 [NASA ADS] [CrossRef]
- Ponti, G., Miniutti, G., Cappi, M., et al. 2006, MNRAS, 368, 903 [NASA ADS] [CrossRef] (In the text)
- Porquet, D., Reeves, J. N., O'Brien, P., & Brinkmann, W. 2004, A&A, 422, 85 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Pottschmidt, K., Wilms, J., Nowak, M. A., et al. 2003, A&A, 407, 1039 [NASA ADS] [CrossRef] [EDP Sciences] (P03) (In the text)
- Reeves, J. N., Nandra, K., George, I. M., et al. 2004, ApJ, 602, 648 [NASA ADS] [CrossRef] (In the text)
- Saez, C., Chartas, G., Brandt, W. N., et al. 2008, AJ, 135, 1505 [NASA ADS] [CrossRef] (In the text)
- Shaposhnikov, N., & Titarchuk, L. 2006, ApJ, 643, 1098 [NASA ADS] [CrossRef] (In the text)
- Shemmer, O., Brandt, W. N., Netzer, H., Maiolino, R., & Kaspi, S. 2006, ApJ, 646, L29 [NASA ADS] [CrossRef] (In the text)
- Shih, D. C., Iwasawa, K., & Fabian, A. C. 2003, MNRAS, 341, 973 [NASA ADS] [CrossRef] (In the text)
- Summons, D. P.,
Arevalo, P., M
Hardy, I. M., Uttley, P., & Bhaskar, A. 2007, MNRAS, 378, 649 [NASA ADS] [CrossRef] (In the text)
- Taylor, R. D.,
Uttley, P., & M
Hardy, I. M. 2003, MNRAS, 342, L31 [NASA ADS] [CrossRef] (In the text)
- Turner, T. J., Kraemer, S. B., George, I. M., Reeves, J. N., & Bottorff, M. C. 2005, ApJ, 618, 155 [NASA ADS] [CrossRef] (In the text)
- Turner, T. J., Miller, L., Reeves, J. N., & Kraemer, S. B. 2007, A&A, 475, 121 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
- Uttley, P., &
M
Hardy, I. M. 2005, MNRAS, 363, 586 [NASA ADS] (UM05) (In the text)
- Uttley, P.,
M
Hardy, I. M., & Papadakis, I. E. 2002, MNRAS, 332, 231 [NASA ADS] [CrossRef] (In the text)
- Uttley, P., Taylor,
R. D., & M
Hardy, I. M. 2004, MNRAS, 347, 1345 [NASA ADS] [CrossRef] (In the text)
- Vaughan, S., & Fabian, A. C. 2003, MNRAS, 341, 496 [NASA ADS] [CrossRef]
- Vaughan, S., Iwasawa, K., Fabian, A. C., & Hayashida, K. 2005, MNRAS, 356, 524 [NASA ADS] [CrossRef] (In the text)
- Woo, J.-H., & Urry, C. M. 2002, ApJ, 579, 530 [NASA ADS] [CrossRef]
- Wu, Q., & Gu, M. 2008, ApJ, 682, 212 [NASA ADS] [CrossRef] (In the text)
- Ziolkowski, J. 2005, MNRAS, 358, 851 [NASA ADS] [CrossRef] (In the text)
Footnotes
- ...
files
- We used the latest background model for the faint objects, pca_bkgd_cmfaintl7_eMv20051128.mdl available from the RXTE Guest Observer Facility.
- ... object
- We got the same results when
we excluded from the sample the three sources for which the mean spectral slope
estimation was not based on the analysis of a large number of
RXTE observations. For example we found that
in the case of the ``
-
'' relation (
,
, and
in the case of the ``
-
'' relation, and
,
in the case of the ``
-
'' relation.
- ... here
- We note that if band-limited PSD power is fitted
by Lorentzians, the Lorentzian at the upper band limit will lie at a slightly
lower frequency than the bend frequency, if the same PSD is fitted by a bending
power-law (cf. Akn564, M
Hardy et al. 2007). The difference, however, is typically only a factor of 2 or less, much less than the range of frequencies covered here, and so we do not try and take account of it here.
- ... expect
- The discussion in these paragraphs is based on the assumption of an outflowing corona, hence we adopt the results of Malzac et al. (2001). Similar conclusions can also be drawn if we assume a static corona.
All Tables
Table 1: Black hole mass and timing properties of the AGN in the sample.
Table 2: Summary of the RXTE observations.
Table 3: The mean spectral slope estimates.
Table 4:
The Kendaull's
test results for the correlations plotted in
Fig. 2.
All Figures
![]() |
Figure 1: The spectral slope distribution function of Mrk 766 ( top panel), NGC 3227 ( middle panel) and NGC 4051 ( bottom panel). |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Top panel: The ``
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
(Both panels) Filled and open circles indicate the
spectral-timing data for Cyg X-1 in its hard state, using data from P03 and
A06, respectively. Crosses indicate the spectral-timing data for Cyg X-1 in
its soft state using data from A06. Filled squares indicate the ``mean spectral
slope - normalised characteristic frequency'' data for the AGN in our sample,
when we consider the
|
Open with DEXTER | |
In the text |
Copyright ESO 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.