Mon. Not. R. Astron. Soc. 000, 1–8 (2006) Printed 1 November 2018 (MN LATEX style file v2.2)
Timing evidence in determining the accretion state of the
Seyfert galaxy NGC 3783
D. P. Summons1,3⋆, P. Arévalo1 , I. M. McHardy1, P. Uttley2 and A. Bhaskar3
1School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
2Astronomical Institute ‘Anton Pannekoek’, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, the Netherlands
3School of Engineering Science, University of Southampton, Southampton SO17 1BJ, UK
Received /Accepted
ABSTRACT
Previous observations with the Rossi X-ray Timing Explorer (RXTE) have suggested
that the power spectral density (PSD) of NGC 3783 flattens to a slope near zero at low
frequencies, in a similar manner to that of Galactic black hole X-ray binary systems
(GBHs) in the ‘hard’ state. The low radio flux emitted by this object, however, is
inconsistent with a hard state interpretation. The accretion rate of NGC 3783 (∼ 7%
of the Eddington rate) is similar to that of other AGN with ‘soft’ state PSDs and
higher than that at which the GBH Cyg X-1, with which AGN are often compared,
changes between ‘hard’ and ‘soft’ states (∼ 2% of the Eddington rate). If NGC 3783
really does have a ‘hard’ state PSD, it would be quite unusual and would indicate
that AGN and GBHs are not quite as similar as we currently believe. Here we present
an improved X-ray PSD of NGC 3783, spanning from ∼ 10−8 to ∼ 10−3 Hz, based
on considerably extended (5.5 years) RXTE observations combined with two orbits
of continuous observation by XMM-Newton. We show that this PSD is, in fact, well
fitted by a ‘soft’ state model which has only one break, at high frequencies. Although
a ‘hard’ state model can also fit the data, the improvement in fit by adding a second
break at low frequency is not significant. Thus NGC 3783 is not unusual. These results
leave Arakelian 564 as the only AGN which shows a second break at low frequencies,
although in that case the very high accretion rate implies a ‘very high’, rather than
‘hard’ state PSD. The break frequency found in NGC 3783 is consistent with the
expectation based on comparisons with other AGN and GBHs, given its black hole
mass and accretion rate.
Key words: galaxies: active – galaxies: Seyfert – galaxies: NGC 3783 – X rays:
galaxies
1 INTRODUCTION
Super-massive black holes in active galactic nuclei (AGN)
and Galactic stellar-mass black hole X-ray binary sys-
tems (GBHs) both display aperiodic X-ray variability
which may be quantified by calculating the power spec-
tral densities (PSDs) of the X-ray light curves. The PSDs
can typically be represented by red-noise type power
laws (i.e. P (ν), the power at frequency ν, ∝ να where
α ∼ -1) with a bend or break (to α 6 -2) at a
characteristic PSD frequency. The time-scale, correspond-
ing to the bend-frequency, scales approximately linearly
with black hole mass from AGN to GBHs (McHardy
1988; Edelson & Nandra 1999; Uttley et al. 2002, 2005;
Markowitz et al. 2003; McHardy et al. 2004, 2005), albeit
⋆ E-mail: dps@astro.soton.ac.uk
with some scatter. However, the scatter is entirely accounted
for by variations in accretion rate, allowing scaling between
AGN and GBHs on time-scales from ∼ years to ∼ ms
(McHardy et al. 2006).
GBHs are observed in a number of distinct X-ray spec-
tral states which also have distinct X-ray timing proper-
ties. Two common states are the low/hard (hereafter ‘hard’)
and high/soft (hearafter ‘soft’) states. In the hard state, the
energy-spectrum is dominated by a highly variable power
law component and the PSDs are well fitted by multiple
broad Lorentzians. For use in AGN, where signal/noise is
lower than in GBHs, this PSD shape can be approximated by
a double-bend power law with slopes α = 0, -1 and -2, from
low to high frequency, where the high- and low-frequency
bends correspond to the strongest peaks in the Lorentzian
parameterisation. The breaks are typically separated by only
one to two decades in frequency. In the soft state, the en-
c© 2006 RAS
http://arxiv.org/abs/0704.0721v1
2 D. P. Summons et al
ergy spectrum is dominated by an approximately constant
thermal disc component which extends into the X-ray band
in GBHs but which in AGN is shifted down to the opti-
cal/UV band. Therefore, a meaningful comparison between
the PSDs of soft state GBH and AGN can only be made in
cases where the GBH power-law emission is strong enough
to show significant variability. Such GBHs are rare and the
best example is Cyg X-1 which shows a ‘1/f’ PSD over many
decades of frequencies (Reig et al. 2002). The soft state is
distinguished from the hard state by having only one, high
frequency, break in this power law, from slope -1 to -2.
It has been suggested that this pure simple broken or
cut-off power-law PSD shape is unique to the soft state of
Cyg X-1, which is a persistent source. However in transient
GBHs with similar X-ray spectra, the power law PSD com-
ponent may be seen in combination with broad Lorentzian
features (Done & Gierliński 2005). Axelsson et al. (2006)
also note that a mixed power law plus Lorentzian PSD is
also present in Cyg X-1 in lower luminosity, harder spectral
states, but as the luminosity rises the Lorentzian features
weaken and the power law PSD component strengthens un-
til, in the softest state, it completely dominates. Since the
softest spectral states of transient GBHs are dominated by
constant disc emission we cannot determine whether they
show a similar PSD shape to Cyg X-1.
However, a direct comparison of transient GBHs and
Cyg X-1 is complex, since the transients show much larger
luminosity changes, and complex hysteresis effects in spec-
tral hardness versus luminosity (e.g. Homan et al. 2001,
Belloni et al. 2005) which are not seen in Cyg X-1. There-
fore it is not clear that one can compare timing properties
between Cyg X-1 and transient GBHs simply as a function
of observed X-ray spectrum.
None the less, it is still interesting that the X-ray spec-
trum of Cyg X-1 never becomes totally disc-dominated,
and always contains a relatively strong variable component
whose PSD resembles that of X-ray bright AGN. If variabil-
ity originates, at least partly, in the disc, so power spectral
shape is related to the disc structure, that structure might
be severely disrupted during outbursts, thereby suggesting
a possible difference between the persistent Cyg X-1 and the
transient GBH sources. The similarities between the PSDs
of Cyg X-1 and AGN may also be related to the possible
similarities in accretion flows between AGN and Cyg X-1
noted by Done & Gierliński (2005).
To date, NGC 3783 and the Narrow Line Seyfert 1
Galaxy (NLS1) Ark 564 are the only AGN with suggested
second, low-frequency breaks in their PSDs (i.e. similar to
low/hard GBHs) and are both commonly referred to as be-
ing unusual (e.g. Done & Gierliński 2005). The power spec-
tral evidence for a second break in the case of Ark 564
is very strong (Pounds et al. 2001; Papadakis et al. 2002;
Markowitz et al. 2003, McHardy et al. in prep.). Of all the
AGN with good timing data, Ark 564 shows the highest
accretion-rate (possibly super-Eddington) so it would not be
surprising if it were in an unusual state, e.g. the ‘very high’
state where the PSD, in GBHs, also displays two distinct
breaks. The properties of NGC 3783, on the other hand, are
similar to those of AGN with proven soft-state PSDs (e.g.
NGC 3227, NGC 4051 McHardy et al. 2004, MCG-6-30-15
McHardy et al. 2005), and in particular it is radio quiet
(e.g. Reynolds 1997). In the hard state, GBHs are strong
radio sources whereas in the soft state the radio emission is
quenched (Corbel et al. 2000; Fender 2001; Körding et al.
2006). We also note that NGC 3783 has a more moder-
ate accretion rate than Ark 564 (∼ 7%), and more similar
to the other AGN mentioned above, and Cyg X-1 changes
from the hard to the soft state at around 2% of the Edding-
ton accretion rate (i.e. ṁE =0.02) (Pottschmidt et al. 2003;
Wilms et al. 2006; Axelsson et al. 2006). These two facts do
not lie easily with a hard state identification of NGC 3783.
Thus it would be surprising, and might indicate that our cur-
rent ideas regarding the scaling between AGN and GBHs are
not entirely correct, if NGC 3783 were proven to have a hard
state PSD. It is therefore important to determine whether
NGC 3783 does have a second, low frequency, break in its
PSD or not.
Markowitz et al. (2003) recognised the presence of a
break in the 2− 10 keV PSD of NGC 3783 at 4× 10−6 Hz
and found provisional evidence for a second lower-frequency
break at ∼ 2×10−7 Hz. Specifically, Markowitz et al. (2003)
rejected the possibility that the PSD is described by a single-
break power law with low-frequency slope -1, similar to other
AGN, at the 98% confidence level. In this paper we re-
investigate the evidence for the second break in the PSD of
NGC 3783, using new long-term monitoring data that cov-
ers the frequency range where the break appears to be. By
including additional RXTE archival data spanning several
years, along with short time-scale observations by XMM-
Newton, we will demonstrate that the improved PSD is
perfectly compatible with a single-bend power law, consis-
tent with the behaviour of the other moderately-accreting
Seyferts. In Section 2 we describe the observations and the
methods by which we extract the RXTE and XMM-Newton
light curves. In Sections 3 we discuss the PSD of NGC 3783
as produced from the RXTE and XMM-Newton observa-
tions, and compare it with various PSD models. In Section
4 we briefly review the implications of our observations.
2 OBSERVATIONS AND DATA REDUCTION
2.1 RXTE Data Reduction
From 1999 to 2006, NGC 3783 has been the target of various
monitoring campaigns with RXTE. These campaigns have
consisted of short, ∼1 ks duration, observations with the
proportional counter array (PCA, Zhang et al. 1993). We
have analysed the archival PCA STANDARD-2 data and
our own proprietary data with FTOOLS v6.0.2 using stan-
dard extraction methods. We use data from the top layers of
PCUs 0 and 2 up to 2000 May 12 and only top layer PCU 2
data from observations after this date. The remaining PCUs
were not used due to repeated breakdowns.
Data were selected according to the standard ‘good-
time’ criteria, i.e. target elevation < 10◦, offset pointing
< 0.02◦, and electron contamination < 0.1. The background
was simulated with the L7 model for faint sources using
PCABACKEST v3.0. The response matrices for each PCA
observation were calculated using PCARSP v10.1. The fi-
nal 2− 10 keV fluxes were calculated using XPSEC v12.2.1
by fitting a power law with galactic absorption to the PHA
data.
The RXTE data used in our analysis, together with the
c© 2006 RAS, MNRAS 000, 1–8
Accretion state of NGC 3783 3
Figure 1. RXTE long-term light curve of NGC 3783 in the 2-
10keV band.
Figure 2. RXTE intense sampling light curve in the 2-10 keV
band of NGC 3783.
sampling patterns, are listed in Table 1 and displayed in
Fig. 1. The early data (to MJD 52375) with 4 d sampling,
together with the 20 d period of 3 h sampling already pre-
sented by Markowitz et al. (2003) are followed, after a 2 year
gap, by our new long-term monitoring, with 2 d sampling.
As the gap is large compared to the duration of each moni-
toring campaign we will include data from each monitoring
campaign as separate lightcurves in our fits.
2.2 XMM-Newton Data Reduction
NGC 3783 was observed by XMM-Newton during revolu-
tions 371 and 372, between 2001 December 17 and 2001 De-
cember 21. Temporal analysis of these data were first pre-
sented by Markowitz (2005) who discusses the coherence,
frequency-dependent phase lags, and variation of high fre-
quency PSD slope with energy. Here we use these data to
constrain the high frequency part of the overall long and
short timescale PSD. We used data from the European Pho-
ton Imaging Cameras (EPIC) PN and MOS2 instruments,
which were operated in imaging mode. MOS1 was operated
in Fast Uncompressed Mode and we do not use those data
here. The PN camera was operated in Small Window mode,
using the medium filter. Source photons were extracted from
a circular region of 40′′ radius and the background was se-
Figure 3. XMM-Newton light curve in the 0.2–2 keV band of
NGC 3783.
lected from a source-free region of equal area on the same
chip. We selected single and double events, with quality
flag=0. The MOS2 camera was operated in the Full Win-
dow mode, using the medium filter. We extracted source
and background photons using the same procedure as for
the PN data and selected single, double, triple and quadru-
ple events. These data showed no serious pile-up when tested
with the XMM-SAS task epatplot.
We constructed light curves, for each detector and or-
bit, in the 0.2–2, 2–10 and 4–10 keV energy bands. We filled
in the ∼ 5 ks gap in the middle of orbit 371 light curves, and
some other much smaller gaps, by interpolation and added
Poisson noise. The resulting PN and MOS2 continuous light
curves were then combined to produce the final light curves
for each orbit. The combined, background subtracted, av-
erage count rates in the 0.2–10 keV band were 11.8 c/s for
orbit 371 and 15.8 c/s for orbit 372, and the 0.2-2 keV com-
bined light curve is shown in Fig. 3. Poisson noise dominates
the PSD on timescales shorter than 1000s, so the light curves
were binned into 200s bins.
3 POWER SPECTRAL MODELLING
3.1 Combining RXTE and XMM-Newton data
To determine the PSD over the largest possible frequency
range we combine the RXTE and XMM-Newton data. In
GBHs the break-frequency and slope of the PSD below the
break appear to be independent of the chosen energy band
(Cui et al. 1997; Churazov et al. 2001; Nowak et al. 1999;
Revnivtsev et al. 2000; McHardy et al. 2004). On the other
hand, the PSD normalisation and the slope above the break
are often energy-dependent (Markowitz 2005). Therefore,
when combining data from different instruments, it is prefer-
able to use similar energy ranges. The RXTE data are in
the 2–10 keV band and, for NGC 3783, that band has a
median photon energy of 5.7 keV. The XMM-Newton band
with the same median photon energy is 4.1–10 keV. How-
ever the count rate in that XMM-Newton band is low (2
c/s) so we only detect significant source power above the
Poisson noise level at frequencies below 10−4Hz. To probe
higher frequencies we can use the 0.2–2 keV XMM-Newton
data (8.8 c/s) but we must re-scale its PSD normalisation to
c© 2006 RAS, MNRAS 000, 1–8
4 D. P. Summons et al
Light curve Sampling interval Observation length Date Range [MJD]
RXTE Long-term 1 ∼4.36 days 1194.6 days 51180.5–52375.1
RXTE Long-term 2 ∼2.1 days 928.3 days 53063.4–53991.6
RXTE Intense monitoring ∼3.2 hours 19.9 days 51960.1–51980.1
XMM-Newton observations (2 orbits) 200-s 3.2 days 52260.8–52264.0
Table 1. Summary of the RXTE and XMM-Newton light curves used in the analysis of NGC 3783, including their sampling frequency
and date range.
that of the 4–10 keV PSD. We determined the scaling cor-
rection by producing PSDs in both energy bands and fitting
the same bending power law model to the noise-subtracted
data. On the assumption that the PSD shape below the high
frequency break is energy-independent, the combined RXTE
2–10 keV and XMM-Newton 0.2–2 keV PSD will then have
the shape of the 0.2–2 keV PSD.
3.2 Monte Carlo simulations
We use the Monte Carlo technique of Uttley et al. (2002)
(PSRESP), to estimate the underlying PSD parameters in
the presence of sampling biases. In this method we first
calculate the observed (or ‘dirty’) PSD, in parts, from the
observed lightcurves, using the Discrete Fourier Transform.
Here the PSD estimates are binned in bins of width 1.3ν,
where ν is the starting frequency by taking the average of
the log of power (Papadakis & Lawrence 1993). We require
a minimum of 4 PSD estimates per bin. We then compare si-
multaneously the dirty PSDs from each lightcurve with var-
ious model PSDs derived from lightcurves simulated with
the same sampling pattern as the real observations. We al-
ter the model parameters to obtain the best fit for any given
model. We refer the reader to Uttley et al. (2002) for a full
discussion of the method.
For each set of chosen underlying-PSD model param-
eters, we simulate red-noise light curves, as described by
Timmer & Koenig (1995). The RXTE light curves are sim-
ulated with time resolutions of 10.5 h, 5.0 h and 18 m for the
first and second long time-scale and the medium time-scale
light curves respectively. The simulated resolution, which is
10 times shorter than the typical sampling intervals of the
real observations, given in column 2 of Table 1, is to take into
account the effect of aliasing. These simulated light curves
were resampled and binned to match the real NGC 3783 ob-
servations. XMM-Newton light curves were simulated with
200-s resolution, as at shorter time-scales the underlying
varability power is negligible compared to the Poisson noise,
so aliasing does not play a role. The Poisson noise level was
not subtracted from the observed PSD but was added to
the simulated PSDs. To reproduce the effect of red-noise
leak, each light curve was simulated to be ∼300 times longer
than the real observation, and was then split into sections,
constituting 300 simulated light curves for each observed
lightcurve. The simulated model average PSD is evaluated
from this ensemble of PSD realisations, and the errors are
assigned from the rms spread of the realisations within a
frequency bin.
We present the results of several PSD model fits in an
attempt to quantify the underlying model shape that best
describes the PSD of NGC 3783, and associate an accep-
Figure 4. The best fit unbroken power law PSD of the combined
RXTE and XMM-Newton data. The solid lines represent the ob-
served data and the points with error bars exhibit the biased
model and the spread in individual realisations of the model. The
dashed line is the underlying model used to generate the simu-
lated PSD. The three lowest frequency data sets are from RXTE
observations and the high frequency data set (∼10−5 Hz) is from
the XMM-Newton observations. Note that the rise in power at
the highest frequencies is due to the photon Poisson noise.
tance probability with each model. We initially test a sim-
ple unbroken power law model. We next fit a power law with
a single-bend in the PSD, and then a model incorporating
a double-bend. We also fit a single-bend power law with a
Lorentzian component.
3.3 Unbroken power law model
To begin, we fitted a simple power law model to the data of
the form:
P (ν) = A
where A is the normalisation at a frequency ν0, and α
is the power law slope. We made 900 simulations and in Fig.
4 we show the best fit plotted in ν × Pν , which has a PSD
slope of -2.1. However, the fit is poor and this model can be
rejected with a probability > 99 %, or & 3 σ.
3.4 Single-bend power law model
Here we fit a single-bend power law to the data. This model
best describes the PSD of Cyg X-1 in the high/soft state,
and provides a good fit to the PSDs of the AGN NGC 4051
and MCG–6-30-15 (McHardy et al. 2004, 2005).
c© 2006 RAS, MNRAS 000, 1–8
Accretion state of NGC 3783 5
Figure 5. The best fit single-bend power law PSD of the com-
bined RXTE and XMM-Newton data. The various lines represent
the same data as seen in Fig. 4.
Figure 6. The best fit double-bend power law PSD of the com-
bined RXTE and XMM-Newton data. The various lines represent
the same data as seen in Fig. 4.
P (ν) =
A ναL
”αL−αH
Fig. 5 presents the observed PSD fitted with a single-
bend power law model, for which a good likelihood of accep-
tance is obtained (P = 44 %). The best fit bend-frequency is
νB = 6.2
+40.6
−5.6 × 10
−6 Hz, the high-frequency slope is αH =
−2.6+0.6
, and the low-frequency slope is αL = −0.8
−0.5.
The errors are 90% confidence limits, an asterisk indicates
that the limit is unconstrained. For αH the best fit value
is well within the searched parameter space but the degen-
eracy produced by red-noise leak in the probability at high
values of αH , means that the upper limit is not constrained
at the 90% confidence level. The confidence contours for the
main interesting parameters are plotted in Figs. 7 and 8. Ta-
ble 2 shows the single-bend power law best fit parameters to
the data. The best fit single-bend frequency obtained here is
consistent with the value found by Markowitz et al. (2003)
3.5 Double-bend power law model
Markowitz et al. (2003) provide tentative evidence that
Figure 7. Single-bend power law model: 68, 90, and 99% confi-
dence contours for the bend frequency, νB, and the high frequency
slope, −αH , for the single-bend power law fit to the combined
RXTE and XMM-Newton PSD.
Figure 8. Single-bend power law model: 68, 90, and 99% confi-
dence contours for the bend frequency, νB, and the low frequency
slope, −αL, for the single-bending power law fit to the combined
RXTE and XMM-Newton PSD.
a second, lower, frequency break exists in the PSD of
NGC 3783. Thus, we also fitted a more complex double-bend
power law model to see if the goodness-of-fit is improved sig-
nificantly. The double-bend power law model is given by:
P (ν) =
A ναL
”αL−αI
”αI−αH
where αI is the intermediate-frequency slope and νL
and νH are the low and high bend-frequencies respectively.
We fixed the low-frequency slope to zero, to avoid making
the simulations computationally prohibitive, and because a
low-frequency slope of zero would allow the best qualitative
comparison to the low state of Cyg X-1 (Nowak et al. 1999).
Fig. 6 presents the same observed PSD as in Fig. 5,
but fitted with the double-bend power law model. A good
likelihood of acceptance is obtained (P=64 %). The best-
fitting high bend-frequency is νH = 2.6
× 10−5 Hz, the
high-frequency slope is αH = −3.2
, the intermediate-
frequency slope is αI = −1.3
, the low-frequency bend is
νL = 1.7
×10−7 Hz. As before, we use 90% confidence lim-
c© 2006 RAS, MNRAS 000, 1–8
6 D. P. Summons et al
Model Normalisation αH αI αL νH νL Acceptance
(a) (Hz) (Hz) (%)
Single-bend 1.5× 10−4 −2.6
NA −0.8
+40.6
× 10−6 NA 44.4
Double-bend 1.0× 102 −3.2
0.0 2.6
× 10−5 1.7
× 10−7 63.9
Table 2. Best fit model parameters for the examined models to the combined RXTE and XMM-Newton PSD of NGC 3783. The errors
on the single- and double-bend fits are calculated from the 90% confidence intervals. The bend-frequency for the single-bend model, νB ,
is denoted here as νH . An asterisk indicates that the limit is unconstrained.
its. The added parameters allow extra freedom to find better
fit probabilities for any given set of double-bend parameters.
For this reason, the contour levels cover larger ranges in the
parameter space and therefore, most of the 90% contours
in our double-bend fit remain unbounded over the fitted
parameter space. The high-frequency slope is subject to the
same problems as in the single-bend model. Table 2 contains
a summary of the best-fitting model parameters.
The best-fitting low-frequency bend is found close to the
lowest frequencies probed by the data and, as seen in Fig. 9,
it is essentially unbounded down to the lowest measurable
frequency at the 68% confidence level. These facts suggest
that the second, low-frequency, bend might not be required
by the data and that the improvement in the fit might be
only due to the increased complexity of the model fitted.
The likelihood of acceptance is better in the double-
bend model than in the single-bend model, 64 versus 44 %
respectively, but there are more free parameters. In order
to determine the significance of this improvement, we per-
formed the following test. Using the best-fitting single-bend
PSD parameters, we generated 300 realisations of the sets of
RXTE and XMM-Newton lightcurves. Each realisation was
then fitted with the best-fitting double-bend parameters, ex-
actly as was done with the real data, and the distribution
of their fit probabilities was constructed. We found that 121
out of the 300 single-bend simulations have a higher fit prob-
ability than the real data, when fitted with the double-bend
model. Therefore, we conclude that the improvement in fit
probability is no more than may be expected from fitting a
model which is more complicated than required by the data:
the double-bend model does not represent a significant im-
provement.
3.6 Single-bend power law with a Lorentzian
component
We finally consider whether the observed PSD might be
best-described by adding a Lorentzian component, such as
are commonly used to describe broad-band noise compo-
nents in GBHs (e.g. Nowak 2000), to the single-bend power
law. We are motivated to consider this possibility because
the PSD of the intense-sampling RXTE light curve is not
very well described by either the single- or double-bend
power law model. Visual inspection of this light curve, shown
in Fig. 2, suggests that the variability is strongly concen-
trated on time-scales of around a day, or equivalently, fre-
quencies around 10−5 Hz, which is confirmed by the peak
seen in the corresponding section of the PSD, and the drop
in the same PSD at lower frequencies (∼ 10−6Hz). The
long-term monitoring PSDs, however, do not show a dip
at 10−6Hz, creating a large discrepancy in the PSD mea-
Figure 9. Double-bend power law model: 68, and 90% confi-
dence contours for the high bend-frequency, νH , and the low bend-
frequency, νL, for the double-bend power law fit to the combined
RXTE and XMM-Newton PSD.
surements at this frequency. A strongly peaked component
in the underlying PSD, at ∼ 10−5 Hz, could produce the
observed features. Such a component would appear as a
peak in a PSD that covered frequencies above and below
its peak-frequency, but would be insufficiently sampled by
the long-term monitoring campaigns; thus, its power would
be aliased into the highest frequencies of the longer time-
scale data, making them rise above the underlying model
level and causing the apparent disparity.
The Lorentzian profile is described by:
PLor(ν) =
ν2c + 4Q
2(νc − ν)2
where the centroid frequency νc is related to the peak-
frequency νp by νp = νc
1 + 1/4Q2 and the quality factor
Q is equal to νc divided by the full width at half maximum
of the Lorentzian. The variable A parameterizes the relative
contribution of the power law and Lorentzian components
to the total rms. Fitting a Lorentzian component in addition
to a single-bend power law provides a good fit (P=52 %).
The best-fitting Lorentzian contributes 20% of the variance
in the frequency range probed and its best-fitting parame-
ters are quoted in Table 3. Fig. 10 shows the observed PSD
compared with the best-fitting single-bend power law model
plus a Lorentzian component. The Lorentzian feature in the
model can reproduce qualitatively the spurious power at the
high frequency end of the long-term monitoring data and the
turn down effect observed in the intensive-sampling data.
To determine the significance of the Lorentzian compo-
nent fit we repeated the procedure used in determining the
c© 2006 RAS, MNRAS 000, 1–8
Accretion state of NGC 3783 7
νp νB Q A αL αH Acceptance
(Hz) (Hz) (%)
× 10−6 1.1
× 10−5 5.1
Table 3. Best fit single-bend power law with Lorentzian component model parameters to the combined RXTE and XMM-Newton PSD
of NGC 3783, where νp is the Lorentzian peak frequency, Q is its quality factor, νB is the power law bend frequency and αL and αH
are the power law slopes below and above the bend, respectively. The errors are calculated from the 68% confidence intervals, and an
asterisk indicates that the limit is unconstrained.
Figure 10. The best-fitting single-bend power law with a
Lorentzian component. The fit was done using the entire data
set but here we only show the Lorentzian region. As before, solid
lines represent the real data PSD, dashed lines represent the best-
fitting model and markers with error bars represent the model
distorted by sampling effets. The Lorentzian feature in the model
can reproduce qualitatively the spurious power at the high fre-
quency end of the long-term monitoring data and the turn down
effect observed in the intensive-sampling data.
significance of the double-bend model. We found that 222 of
the 300 single-bend simulated PSDs have a higher fit proba-
bility than the data, when fitted with the single-bend power
law plus Lorentzian model. This result indicates that the
increase in fit probability could be due to the added com-
plexity of the model, and that the improvement in the fit
over a simple bending power law is not significant.
4 DISCUSSION AND CONCLUSIONS
We have combined our own new RXTE monitoring data
with archival RXTE and XMM-Newton observations to
construct a high-quality PSD of NGC 3783 spanning five
decades in frequency.
We find that a ‘soft’ state model, with a single
bend at 6.2 × 10−6 Hz, similar to that found earlier by
Markowitz et al. (2003), a power law of slope approximately
-0.8 extending over almost three decades in frequency below
the bend, and slope above the bend of approximately -2.6
is a good fit to the data. We also find that a ‘hard’ state
model, with a double bend, fits the data, as does a model
with a single bend plus an additional Lorentzian compo-
nent. However the improvement in fit is marginal and, given
the additional free parameters, is not significant. Thus we
conclude that a simple ‘soft’ state model provides the most
likely explanation of the data.
Assuming a mass of 3 × 107M⊙ for NGC 3783
(Peterson et al. 2004), and an accretion rate of 7% of
the Eddington limit (Uttley & McHardy 2005, based on
Woo & Urry 2002), then NGC 3783 is still in good agree-
ment with the scaling of PSD break timescale as ∼ M/ṁE
between AGN and GBHs found by McHardy et al. (2006).
Our new fits, show that the PSD of NGC 3783 is per-
fectly consistent with a single-bend power law with low-
frequency slope of -1, in contrast with the earlier result of
Markowitz et al. (2003), who found that a similar model
was rejected tentatively at ∼ 98% confidence. The differ-
ence can be understood in terms of the improved long-term
data. Our new RXTE monitoring observations occur every 2
days, compared to 4 days previously, thereby increasing the
long term RXTE data set by a factor 2.6 and, in particular,
providing overlap at high frequencies with the RXTE inten-
sive monitoring data. The drop in long-timescale variability
power, evident in the older long term monitoring data is not
reproduced by the new long-term monitoring data, showing
that this drop could be just a statistical fluctuation. In addi-
tion, the very high frequencies are better constrained by the
2 orbits of XMM-Newton data than by the earlier Chandra
data used by Markowitz et al. (2003).
The classification of the PSD as being ‘soft’ state means
that NGC 3783 is no longer considered unusual amongst
AGN. The fact that this AGN is radio-quiet strongly sup-
ports the analogy with GBHs in the soft state. Also the ac-
cretion rate of NGC 3783 ( ṁE =0.07) (Uttley & McHardy
2005, based on Woo & Urry 2002) is similar to that
of other AGN with soft-state PSDs (e.g. NGC 3227
Uttley & McHardy 2005, NGC 4051 McHardy et al. 2004,
MCG-6-30-15 McHardy et al. 2005). This accretion rate is
above the rate at which the persistent GBH Cyg X-1 tran-
sits between hard and soft states in either direction and at
which other GBHs transit from the soft to hard state ( ṁE
=0.02) (Maccarone et al. 2003; Maccarone 2003). We note
that other transient GBHs in outburst, where the variable
power law emission in the soft state PSD is weak, can re-
main in the hard state to much higher accretion rates (∼ 2–
50% Homan & Belloni 2005) but it is not clear whether we
should expect similar PSD shapes to AGN for such outburst-
ing sources. Thus NGC 3783 remains compatible with other
moderately accreting AGN in being analogous to Cyg X-1
in the soft state. It is, of course, possible that the transition
rate might not be independent of mass. Observations do not
yet greatly constrain the transition rate as a function of mass
but the abscence of large deviations from the so-called ‘fun-
damental’ plane of radio luminosity, X-ray luminosity and
black hole mass (Merloni et al. 2003; Falcke et al. 2004) ar-
gues against a large spread in the transistion accretion-rates
(e.g. see Körding et al. 2006). In the case of Seyfert galaxy
c© 2006 RAS, MNRAS 000, 1–8
8 D. P. Summons et al
NGC 3227, the accretion rate is ∼ 1–2% and a ‘soft’ state
PSD is measured (Uttley & McHardy 2005), which suggests
that the transition accretion-rate in AGN should be at or
below that value.
Our observations, which show that NGC 3783 does not
have a highly unusual PSD, therefore confirm the growing
similarities between AGN and Galactic black hole systems
and leave only Arakelian 564, which is probably a very high
state object, as the only AGN showing clear double breaks
(or multiple Lorentzians) in its PSD (e.g. Arévalo et al.
2006, McHardy et al. in prep.).
ACKNOWLEDGEMENTS
We would like to thank the referee, Chris Done, for use-
ful comments and suggestions. This research has made use
of the data obtained from the High Energy Astrophysics
Science Archive Research Center (HEASARC), provided by
NASA’s Goddard Space Flight Center. We would like to
thank Information Systems Services (ISS) at the Univer-
sity of Southampton for the use of their Beowulf cluster,
Iridis2. PU acknowledges support from a Marie Curie Inter-
European Research Fellowship.
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c© 2006 RAS, MNRAS 000, 1–8
	INTRODUCTION
	OBSERVATIONS AND DATA REDUCTION
	RXTE Data Reduction
	XMM-Newton Data Reduction
	Power spectral Modelling
	Combining RXTE and XMM-Newton data
	Monte Carlo simulations
	Unbroken power law model
	Single-bend power law model
	Double-bend power law model
	Single-bend power law with a Lorentzian component
	Discussion and Conclusions

  Previous observations with the Rossi X-ray Timing Explorer (RXTE) have
suggested that the power spectral density (PSD) of NGC 3783 flattens to a slope
near zero at low frequencies, in a similar manner to that of Galactic black
hole X-ray binary systems (GBHs) in the `hard' state. The low radio flux
emitted by this object, however, is inconsistent with a hard state
interpretation. The accretion rate of NGC 3783 (~7% of the Eddington rate) is
similar to that of other AGN with `soft' state PSDs and higher than that at
which the GBH Cyg X-1, with which AGN are often compared, changes between
`hard' and `soft' states (~2% of the Eddington rate). If NGC 3783 really does
have a `hard' state PSD, it would be quite unusual and would indicate that AGN
and GBHs are not quite as similar as we currently believe. Here we present an
improved X-ray PSD of NGC 3783, spanning from ~10^{-8} to ~10^{-3} Hz, based on
considerably extended (5.5 years) RXTE observations combined with two orbits of
continuous observation by XMM-Newton. We show that this PSD is, in fact, well
fitted by a `soft' state model which has only one break, at high frequencies.
Although a `hard' state model can also fit the data, the improvement in fit by
adding a second break at low frequency is not significant. Thus NGC 3783 is not
unusual. These results leave Arakelian 564 as the only AGN which shows a second
break at low frequencies, although in that case the very high accretion rate
implies a `very high', rather than `hard' state PSD. The break frequency found
in NGC 3783 is consistent with the expectation based on comparisons with other
AGN and GBHs, given its black hole mass and accretion rate.

Mon. Not. R. Astron. Soc. 000, 1–8 (2006) Printed 1 November 2018 (MN LATEX style file v2.2)
Timing evidence in determining the accretion state of the
Seyfert galaxy NGC 3783
D. P. Summons1,3⋆, P. Arévalo1 , I. M. McHardy1, P. Uttley2 and A. Bhaskar3
1School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
2Astronomical Institute ‘Anton Pannekoek’, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, the Netherlands
3School of Engineering Science, University of Southampton, Southampton SO17 1BJ, UK
Received /Accepted
ABSTRACT
Previous observations with the Rossi X-ray Timing Explorer (RXTE) have suggested
that the power spectral density (PSD) of NGC 3783 flattens to a slope near zero at low
frequencies, in a similar manner to that of Galactic black hole X-ray binary systems
(GBHs) in the ‘hard’ state. The low radio flux emitted by this object, however, is
inconsistent with a hard state interpretation. The accretion rate of NGC 3783 (∼ 7%
of the Eddington rate) is similar to that of other AGN with ‘soft’ state PSDs and
higher than that at which the GBH Cyg X-1, with which AGN are often compared,
changes between ‘hard’ and ‘soft’ states (∼ 2% of the Eddington rate). If NGC 3783
really does have a ‘hard’ state PSD, it would be quite unusual and would indicate
that AGN and GBHs are not quite as similar as we currently believe. Here we present
an improved X-ray PSD of NGC 3783, spanning from ∼ 10−8 to ∼ 10−3 Hz, based
on considerably extended (5.5 years) RXTE observations combined with two orbits
of continuous observation by XMM-Newton. We show that this PSD is, in fact, well
fitted by a ‘soft’ state model which has only one break, at high frequencies. Although
a ‘hard’ state model can also fit the data, the improvement in fit by adding a second
break at low frequency is not significant. Thus NGC 3783 is not unusual. These results
leave Arakelian 564 as the only AGN which shows a second break at low frequencies,
although in that case the very high accretion rate implies a ‘very high’, rather than
‘hard’ state PSD. The break frequency found in NGC 3783 is consistent with the
expectation based on comparisons with other AGN and GBHs, given its black hole
mass and accretion rate.
Key words: galaxies: active – galaxies: Seyfert – galaxies: NGC 3783 – X rays:
galaxies
1 INTRODUCTION
Super-massive black holes in active galactic nuclei (AGN)
and Galactic stellar-mass black hole X-ray binary sys-
tems (GBHs) both display aperiodic X-ray variability
which may be quantified by calculating the power spec-
tral densities (PSDs) of the X-ray light curves. The PSDs
can typically be represented by red-noise type power
laws (i.e. P (ν), the power at frequency ν, ∝ να where
α ∼ -1) with a bend or break (to α 6 -2) at a
characteristic PSD frequency. The time-scale, correspond-
ing to the bend-frequency, scales approximately linearly
with black hole mass from AGN to GBHs (McHardy
1988; Edelson & Nandra 1999; Uttley et al. 2002, 2005;
Markowitz et al. 2003; McHardy et al. 2004, 2005), albeit
⋆ E-mail: dps@astro.soton.ac.uk
with some scatter. However, the scatter is entirely accounted
for by variations in accretion rate, allowing scaling between
AGN and GBHs on time-scales from ∼ years to ∼ ms
(McHardy et al. 2006).
GBHs are observed in a number of distinct X-ray spec-
tral states which also have distinct X-ray timing proper-
ties. Two common states are the low/hard (hereafter ‘hard’)
and high/soft (hearafter ‘soft’) states. In the hard state, the
energy-spectrum is dominated by a highly variable power
law component and the PSDs are well fitted by multiple
broad Lorentzians. For use in AGN, where signal/noise is
lower than in GBHs, this PSD shape can be approximated by
a double-bend power law with slopes α = 0, -1 and -2, from
low to high frequency, where the high- and low-frequency
bends correspond to the strongest peaks in the Lorentzian
parameterisation. The breaks are typically separated by only
one to two decades in frequency. In the soft state, the en-
c© 2006 RAS
http://arxiv.org/abs/0704.0721v1
2 D. P. Summons et al
ergy spectrum is dominated by an approximately constant
thermal disc component which extends into the X-ray band
in GBHs but which in AGN is shifted down to the opti-
cal/UV band. Therefore, a meaningful comparison between
the PSDs of soft state GBH and AGN can only be made in
cases where the GBH power-law emission is strong enough
to show significant variability. Such GBHs are rare and the
best example is Cyg X-1 which shows a ‘1/f’ PSD over many
decades of frequencies (Reig et al. 2002). The soft state is
distinguished from the hard state by having only one, high
frequency, break in this power law, from slope -1 to -2.
It has been suggested that this pure simple broken or
cut-off power-law PSD shape is unique to the soft state of
Cyg X-1, which is a persistent source. However in transient
GBHs with similar X-ray spectra, the power law PSD com-
ponent may be seen in combination with broad Lorentzian
features (Done & Gierliński 2005). Axelsson et al. (2006)
also note that a mixed power law plus Lorentzian PSD is
also present in Cyg X-1 in lower luminosity, harder spectral
states, but as the luminosity rises the Lorentzian features
weaken and the power law PSD component strengthens un-
til, in the softest state, it completely dominates. Since the
softest spectral states of transient GBHs are dominated by
constant disc emission we cannot determine whether they
show a similar PSD shape to Cyg X-1.
However, a direct comparison of transient GBHs and
Cyg X-1 is complex, since the transients show much larger
luminosity changes, and complex hysteresis effects in spec-
tral hardness versus luminosity (e.g. Homan et al. 2001,
Belloni et al. 2005) which are not seen in Cyg X-1. There-
fore it is not clear that one can compare timing properties
between Cyg X-1 and transient GBHs simply as a function
of observed X-ray spectrum.
None the less, it is still interesting that the X-ray spec-
trum of Cyg X-1 never becomes totally disc-dominated,
and always contains a relatively strong variable component
whose PSD resembles that of X-ray bright AGN. If variabil-
ity originates, at least partly, in the disc, so power spectral
shape is related to the disc structure, that structure might
be severely disrupted during outbursts, thereby suggesting
a possible difference between the persistent Cyg X-1 and the
transient GBH sources. The similarities between the PSDs
of Cyg X-1 and AGN may also be related to the possible
similarities in accretion flows between AGN and Cyg X-1
noted by Done & Gierliński (2005).
To date, NGC 3783 and the Narrow Line Seyfert 1
Galaxy (NLS1) Ark 564 are the only AGN with suggested
second, low-frequency breaks in their PSDs (i.e. similar to
low/hard GBHs) and are both commonly referred to as be-
ing unusual (e.g. Done & Gierliński 2005). The power spec-
tral evidence for a second break in the case of Ark 564
is very strong (Pounds et al. 2001; Papadakis et al. 2002;
Markowitz et al. 2003, McHardy et al. in prep.). Of all the
AGN with good timing data, Ark 564 shows the highest
accretion-rate (possibly super-Eddington) so it would not be
surprising if it were in an unusual state, e.g. the ‘very high’
state where the PSD, in GBHs, also displays two distinct
breaks. The properties of NGC 3783, on the other hand, are
similar to those of AGN with proven soft-state PSDs (e.g.
NGC 3227, NGC 4051 McHardy et al. 2004, MCG-6-30-15
McHardy et al. 2005), and in particular it is radio quiet
(e.g. Reynolds 1997). In the hard state, GBHs are strong
radio sources whereas in the soft state the radio emission is
quenched (Corbel et al. 2000; Fender 2001; Körding et al.
2006). We also note that NGC 3783 has a more moder-
ate accretion rate than Ark 564 (∼ 7%), and more similar
to the other AGN mentioned above, and Cyg X-1 changes
from the hard to the soft state at around 2% of the Edding-
ton accretion rate (i.e. ṁE =0.02) (Pottschmidt et al. 2003;
Wilms et al. 2006; Axelsson et al. 2006). These two facts do
not lie easily with a hard state identification of NGC 3783.
Thus it would be surprising, and might indicate that our cur-
rent ideas regarding the scaling between AGN and GBHs are
not entirely correct, if NGC 3783 were proven to have a hard
state PSD. It is therefore important to determine whether
NGC 3783 does have a second, low frequency, break in its
PSD or not.
Markowitz et al. (2003) recognised the presence of a
break in the 2− 10 keV PSD of NGC 3783 at 4× 10−6 Hz
and found provisional evidence for a second lower-frequency
break at ∼ 2×10−7 Hz. Specifically, Markowitz et al. (2003)
rejected the possibility that the PSD is described by a single-
break power law with low-frequency slope -1, similar to other
AGN, at the 98% confidence level. In this paper we re-
investigate the evidence for the second break in the PSD of
NGC 3783, using new long-term monitoring data that cov-
ers the frequency range where the break appears to be. By
including additional RXTE archival data spanning several
years, along with short time-scale observations by XMM-
Newton, we will demonstrate that the improved PSD is
perfectly compatible with a single-bend power law, consis-
tent with the behaviour of the other moderately-accreting
Seyferts. In Section 2 we describe the observations and the
methods by which we extract the RXTE and XMM-Newton
light curves. In Sections 3 we discuss the PSD of NGC 3783
as produced from the RXTE and XMM-Newton observa-
tions, and compare it with various PSD models. In Section
4 we briefly review the implications of our observations.
2 OBSERVATIONS AND DATA REDUCTION
2.1 RXTE Data Reduction
From 1999 to 2006, NGC 3783 has been the target of various
monitoring campaigns with RXTE. These campaigns have
consisted of short, ∼1 ks duration, observations with the
proportional counter array (PCA, Zhang et al. 1993). We
have analysed the archival PCA STANDARD-2 data and
our own proprietary data with FTOOLS v6.0.2 using stan-
dard extraction methods. We use data from the top layers of
PCUs 0 and 2 up to 2000 May 12 and only top layer PCU 2
data from observations after this date. The remaining PCUs
were not used due to repeated breakdowns.
Data were selected according to the standard ‘good-
time’ criteria, i.e. target elevation < 10◦, offset pointing
< 0.02◦, and electron contamination < 0.1. The background
was simulated with the L7 model for faint sources using
PCABACKEST v3.0. The response matrices for each PCA
observation were calculated using PCARSP v10.1. The fi-
nal 2− 10 keV fluxes were calculated using XPSEC v12.2.1
by fitting a power law with galactic absorption to the PHA
data.
The RXTE data used in our analysis, together with the
c© 2006 RAS, MNRAS 000, 1–8
Accretion state of NGC 3783 3
Figure 1. RXTE long-term light curve of NGC 3783 in the 2-
10keV band.
Figure 2. RXTE intense sampling light curve in the 2-10 keV
band of NGC 3783.
sampling patterns, are listed in Table 1 and displayed in
Fig. 1. The early data (to MJD 52375) with 4 d sampling,
together with the 20 d period of 3 h sampling already pre-
sented by Markowitz et al. (2003) are followed, after a 2 year
gap, by our new long-term monitoring, with 2 d sampling.
As the gap is large compared to the duration of each moni-
toring campaign we will include data from each monitoring
campaign as separate lightcurves in our fits.
2.2 XMM-Newton Data Reduction
NGC 3783 was observed by XMM-Newton during revolu-
tions 371 and 372, between 2001 December 17 and 2001 De-
cember 21. Temporal analysis of these data were first pre-
sented by Markowitz (2005) who discusses the coherence,
frequency-dependent phase lags, and variation of high fre-
quency PSD slope with energy. Here we use these data to
constrain the high frequency part of the overall long and
short timescale PSD. We used data from the European Pho-
ton Imaging Cameras (EPIC) PN and MOS2 instruments,
which were operated in imaging mode. MOS1 was operated
in Fast Uncompressed Mode and we do not use those data
here. The PN camera was operated in Small Window mode,
using the medium filter. Source photons were extracted from
a circular region of 40′′ radius and the background was se-
Figure 3. XMM-Newton light curve in the 0.2–2 keV band of
NGC 3783.
lected from a source-free region of equal area on the same
chip. We selected single and double events, with quality
flag=0. The MOS2 camera was operated in the Full Win-
dow mode, using the medium filter. We extracted source
and background photons using the same procedure as for
the PN data and selected single, double, triple and quadru-
ple events. These data showed no serious pile-up when tested
with the XMM-SAS task epatplot.
We constructed light curves, for each detector and or-
bit, in the 0.2–2, 2–10 and 4–10 keV energy bands. We filled
in the ∼ 5 ks gap in the middle of orbit 371 light curves, and
some other much smaller gaps, by interpolation and added
Poisson noise. The resulting PN and MOS2 continuous light
curves were then combined to produce the final light curves
for each orbit. The combined, background subtracted, av-
erage count rates in the 0.2–10 keV band were 11.8 c/s for
orbit 371 and 15.8 c/s for orbit 372, and the 0.2-2 keV com-
bined light curve is shown in Fig. 3. Poisson noise dominates
the PSD on timescales shorter than 1000s, so the light curves
were binned into 200s bins.
3 POWER SPECTRAL MODELLING
3.1 Combining RXTE and XMM-Newton data
To determine the PSD over the largest possible frequency
range we combine the RXTE and XMM-Newton data. In
GBHs the break-frequency and slope of the PSD below the
break appear to be independent of the chosen energy band
(Cui et al. 1997; Churazov et al. 2001; Nowak et al. 1999;
Revnivtsev et al. 2000; McHardy et al. 2004). On the other
hand, the PSD normalisation and the slope above the break
are often energy-dependent (Markowitz 2005). Therefore,
when combining data from different instruments, it is prefer-
able to use similar energy ranges. The RXTE data are in
the 2–10 keV band and, for NGC 3783, that band has a
median photon energy of 5.7 keV. The XMM-Newton band
with the same median photon energy is 4.1–10 keV. How-
ever the count rate in that XMM-Newton band is low (2
c/s) so we only detect significant source power above the
Poisson noise level at frequencies below 10−4Hz. To probe
higher frequencies we can use the 0.2–2 keV XMM-Newton
data (8.8 c/s) but we must re-scale its PSD normalisation to
c© 2006 RAS, MNRAS 000, 1–8
4 D. P. Summons et al
Light curve Sampling interval Observation length Date Range [MJD]
RXTE Long-term 1 ∼4.36 days 1194.6 days 51180.5–52375.1
RXTE Long-term 2 ∼2.1 days 928.3 days 53063.4–53991.6
RXTE Intense monitoring ∼3.2 hours 19.9 days 51960.1–51980.1
XMM-Newton observations (2 orbits) 200-s 3.2 days 52260.8–52264.0
Table 1. Summary of the RXTE and XMM-Newton light curves used in the analysis of NGC 3783, including their sampling frequency
and date range.
that of the 4–10 keV PSD. We determined the scaling cor-
rection by producing PSDs in both energy bands and fitting
the same bending power law model to the noise-subtracted
data. On the assumption that the PSD shape below the high
frequency break is energy-independent, the combined RXTE
2–10 keV and XMM-Newton 0.2–2 keV PSD will then have
the shape of the 0.2–2 keV PSD.
3.2 Monte Carlo simulations
We use the Monte Carlo technique of Uttley et al. (2002)
(PSRESP), to estimate the underlying PSD parameters in
the presence of sampling biases. In this method we first
calculate the observed (or ‘dirty’) PSD, in parts, from the
observed lightcurves, using the Discrete Fourier Transform.
Here the PSD estimates are binned in bins of width 1.3ν,
where ν is the starting frequency by taking the average of
the log of power (Papadakis & Lawrence 1993). We require
a minimum of 4 PSD estimates per bin. We then compare si-
multaneously the dirty PSDs from each lightcurve with var-
ious model PSDs derived from lightcurves simulated with
the same sampling pattern as the real observations. We al-
ter the model parameters to obtain the best fit for any given
model. We refer the reader to Uttley et al. (2002) for a full
discussion of the method.
For each set of chosen underlying-PSD model param-
eters, we simulate red-noise light curves, as described by
Timmer & Koenig (1995). The RXTE light curves are sim-
ulated with time resolutions of 10.5 h, 5.0 h and 18 m for the
first and second long time-scale and the medium time-scale
light curves respectively. The simulated resolution, which is
10 times shorter than the typical sampling intervals of the
real observations, given in column 2 of Table 1, is to take into
account the effect of aliasing. These simulated light curves
were resampled and binned to match the real NGC 3783 ob-
servations. XMM-Newton light curves were simulated with
200-s resolution, as at shorter time-scales the underlying
varability power is negligible compared to the Poisson noise,
so aliasing does not play a role. The Poisson noise level was
not subtracted from the observed PSD but was added to
the simulated PSDs. To reproduce the effect of red-noise
leak, each light curve was simulated to be ∼300 times longer
than the real observation, and was then split into sections,
constituting 300 simulated light curves for each observed
lightcurve. The simulated model average PSD is evaluated
from this ensemble of PSD realisations, and the errors are
assigned from the rms spread of the realisations within a
frequency bin.
We present the results of several PSD model fits in an
attempt to quantify the underlying model shape that best
describes the PSD of NGC 3783, and associate an accep-
Figure 4. The best fit unbroken power law PSD of the combined
RXTE and XMM-Newton data. The solid lines represent the ob-
served data and the points with error bars exhibit the biased
model and the spread in individual realisations of the model. The
dashed line is the underlying model used to generate the simu-
lated PSD. The three lowest frequency data sets are from RXTE
observations and the high frequency data set (∼10−5 Hz) is from
the XMM-Newton observations. Note that the rise in power at
the highest frequencies is due to the photon Poisson noise.
tance probability with each model. We initially test a sim-
ple unbroken power law model. We next fit a power law with
a single-bend in the PSD, and then a model incorporating
a double-bend. We also fit a single-bend power law with a
Lorentzian component.
3.3 Unbroken power law model
To begin, we fitted a simple power law model to the data of
the form:
P (ν) = A
where A is the normalisation at a frequency ν0, and α
is the power law slope. We made 900 simulations and in Fig.
4 we show the best fit plotted in ν × Pν , which has a PSD
slope of -2.1. However, the fit is poor and this model can be
rejected with a probability > 99 %, or & 3 σ.
3.4 Single-bend power law model
Here we fit a single-bend power law to the data. This model
best describes the PSD of Cyg X-1 in the high/soft state,
and provides a good fit to the PSDs of the AGN NGC 4051
and MCG–6-30-15 (McHardy et al. 2004, 2005).
c© 2006 RAS, MNRAS 000, 1–8
Accretion state of NGC 3783 5
Figure 5. The best fit single-bend power law PSD of the com-
bined RXTE and XMM-Newton data. The various lines represent
the same data as seen in Fig. 4.
Figure 6. The best fit double-bend power law PSD of the com-
bined RXTE and XMM-Newton data. The various lines represent
the same data as seen in Fig. 4.
P (ν) =
A ναL
”αL−αH
Fig. 5 presents the observed PSD fitted with a single-
bend power law model, for which a good likelihood of accep-
tance is obtained (P = 44 %). The best fit bend-frequency is
νB = 6.2
+40.6
−5.6 × 10
−6 Hz, the high-frequency slope is αH =
−2.6+0.6
, and the low-frequency slope is αL = −0.8
−0.5.
The errors are 90% confidence limits, an asterisk indicates
that the limit is unconstrained. For αH the best fit value
is well within the searched parameter space but the degen-
eracy produced by red-noise leak in the probability at high
values of αH , means that the upper limit is not constrained
at the 90% confidence level. The confidence contours for the
main interesting parameters are plotted in Figs. 7 and 8. Ta-
ble 2 shows the single-bend power law best fit parameters to
the data. The best fit single-bend frequency obtained here is
consistent with the value found by Markowitz et al. (2003)
3.5 Double-bend power law model
Markowitz et al. (2003) provide tentative evidence that
Figure 7. Single-bend power law model: 68, 90, and 99% confi-
dence contours for the bend frequency, νB, and the high frequency
slope, −αH , for the single-bend power law fit to the combined
RXTE and XMM-Newton PSD.
Figure 8. Single-bend power law model: 68, 90, and 99% confi-
dence contours for the bend frequency, νB, and the low frequency
slope, −αL, for the single-bending power law fit to the combined
RXTE and XMM-Newton PSD.
a second, lower, frequency break exists in the PSD of
NGC 3783. Thus, we also fitted a more complex double-bend
power law model to see if the goodness-of-fit is improved sig-
nificantly. The double-bend power law model is given by:
P (ν) =
A ναL
”αL−αI
”αI−αH
where αI is the intermediate-frequency slope and νL
and νH are the low and high bend-frequencies respectively.
We fixed the low-frequency slope to zero, to avoid making
the simulations computationally prohibitive, and because a
low-frequency slope of zero would allow the best qualitative
comparison to the low state of Cyg X-1 (Nowak et al. 1999).
Fig. 6 presents the same observed PSD as in Fig. 5,
but fitted with the double-bend power law model. A good
likelihood of acceptance is obtained (P=64 %). The best-
fitting high bend-frequency is νH = 2.6
× 10−5 Hz, the
high-frequency slope is αH = −3.2
, the intermediate-
frequency slope is αI = −1.3
, the low-frequency bend is
νL = 1.7
×10−7 Hz. As before, we use 90% confidence lim-
c© 2006 RAS, MNRAS 000, 1–8
6 D. P. Summons et al
Model Normalisation αH αI αL νH νL Acceptance
(a) (Hz) (Hz) (%)
Single-bend 1.5× 10−4 −2.6
NA −0.8
+40.6
× 10−6 NA 44.4
Double-bend 1.0× 102 −3.2
0.0 2.6
× 10−5 1.7
× 10−7 63.9
Table 2. Best fit model parameters for the examined models to the combined RXTE and XMM-Newton PSD of NGC 3783. The errors
on the single- and double-bend fits are calculated from the 90% confidence intervals. The bend-frequency for the single-bend model, νB ,
is denoted here as νH . An asterisk indicates that the limit is unconstrained.
its. The added parameters allow extra freedom to find better
fit probabilities for any given set of double-bend parameters.
For this reason, the contour levels cover larger ranges in the
parameter space and therefore, most of the 90% contours
in our double-bend fit remain unbounded over the fitted
parameter space. The high-frequency slope is subject to the
same problems as in the single-bend model. Table 2 contains
a summary of the best-fitting model parameters.
The best-fitting low-frequency bend is found close to the
lowest frequencies probed by the data and, as seen in Fig. 9,
it is essentially unbounded down to the lowest measurable
frequency at the 68% confidence level. These facts suggest
that the second, low-frequency, bend might not be required
by the data and that the improvement in the fit might be
only due to the increased complexity of the model fitted.
The likelihood of acceptance is better in the double-
bend model than in the single-bend model, 64 versus 44 %
respectively, but there are more free parameters. In order
to determine the significance of this improvement, we per-
formed the following test. Using the best-fitting single-bend
PSD parameters, we generated 300 realisations of the sets of
RXTE and XMM-Newton lightcurves. Each realisation was
then fitted with the best-fitting double-bend parameters, ex-
actly as was done with the real data, and the distribution
of their fit probabilities was constructed. We found that 121
out of the 300 single-bend simulations have a higher fit prob-
ability than the real data, when fitted with the double-bend
model. Therefore, we conclude that the improvement in fit
probability is no more than may be expected from fitting a
model which is more complicated than required by the data:
the double-bend model does not represent a significant im-
provement.
3.6 Single-bend power law with a Lorentzian
component
We finally consider whether the observed PSD might be
best-described by adding a Lorentzian component, such as
are commonly used to describe broad-band noise compo-
nents in GBHs (e.g. Nowak 2000), to the single-bend power
law. We are motivated to consider this possibility because
the PSD of the intense-sampling RXTE light curve is not
very well described by either the single- or double-bend
power law model. Visual inspection of this light curve, shown
in Fig. 2, suggests that the variability is strongly concen-
trated on time-scales of around a day, or equivalently, fre-
quencies around 10−5 Hz, which is confirmed by the peak
seen in the corresponding section of the PSD, and the drop
in the same PSD at lower frequencies (∼ 10−6Hz). The
long-term monitoring PSDs, however, do not show a dip
at 10−6Hz, creating a large discrepancy in the PSD mea-
Figure 9. Double-bend power law model: 68, and 90% confi-
dence contours for the high bend-frequency, νH , and the low bend-
frequency, νL, for the double-bend power law fit to the combined
RXTE and XMM-Newton PSD.
surements at this frequency. A strongly peaked component
in the underlying PSD, at ∼ 10−5 Hz, could produce the
observed features. Such a component would appear as a
peak in a PSD that covered frequencies above and below
its peak-frequency, but would be insufficiently sampled by
the long-term monitoring campaigns; thus, its power would
be aliased into the highest frequencies of the longer time-
scale data, making them rise above the underlying model
level and causing the apparent disparity.
The Lorentzian profile is described by:
PLor(ν) =
ν2c + 4Q
2(νc − ν)2
where the centroid frequency νc is related to the peak-
frequency νp by νp = νc
1 + 1/4Q2 and the quality factor
Q is equal to νc divided by the full width at half maximum
of the Lorentzian. The variable A parameterizes the relative
contribution of the power law and Lorentzian components
to the total rms. Fitting a Lorentzian component in addition
to a single-bend power law provides a good fit (P=52 %).
The best-fitting Lorentzian contributes 20% of the variance
in the frequency range probed and its best-fitting parame-
ters are quoted in Table 3. Fig. 10 shows the observed PSD
compared with the best-fitting single-bend power law model
plus a Lorentzian component. The Lorentzian feature in the
model can reproduce qualitatively the spurious power at the
high frequency end of the long-term monitoring data and the
turn down effect observed in the intensive-sampling data.
To determine the significance of the Lorentzian compo-
nent fit we repeated the procedure used in determining the
c© 2006 RAS, MNRAS 000, 1–8
Accretion state of NGC 3783 7
νp νB Q A αL αH Acceptance
(Hz) (Hz) (%)
× 10−6 1.1
× 10−5 5.1
Table 3. Best fit single-bend power law with Lorentzian component model parameters to the combined RXTE and XMM-Newton PSD
of NGC 3783, where νp is the Lorentzian peak frequency, Q is its quality factor, νB is the power law bend frequency and αL and αH
are the power law slopes below and above the bend, respectively. The errors are calculated from the 68% confidence intervals, and an
asterisk indicates that the limit is unconstrained.
Figure 10. The best-fitting single-bend power law with a
Lorentzian component. The fit was done using the entire data
set but here we only show the Lorentzian region. As before, solid
lines represent the real data PSD, dashed lines represent the best-
fitting model and markers with error bars represent the model
distorted by sampling effets. The Lorentzian feature in the model
can reproduce qualitatively the spurious power at the high fre-
quency end of the long-term monitoring data and the turn down
effect observed in the intensive-sampling data.
significance of the double-bend model. We found that 222 of
the 300 single-bend simulated PSDs have a higher fit proba-
bility than the data, when fitted with the single-bend power
law plus Lorentzian model. This result indicates that the
increase in fit probability could be due to the added com-
plexity of the model, and that the improvement in the fit
over a simple bending power law is not significant.
4 DISCUSSION AND CONCLUSIONS
We have combined our own new RXTE monitoring data
with archival RXTE and XMM-Newton observations to
construct a high-quality PSD of NGC 3783 spanning five
decades in frequency.
We find that a ‘soft’ state model, with a single
bend at 6.2 × 10−6 Hz, similar to that found earlier by
Markowitz et al. (2003), a power law of slope approximately
-0.8 extending over almost three decades in frequency below
the bend, and slope above the bend of approximately -2.6
is a good fit to the data. We also find that a ‘hard’ state
model, with a double bend, fits the data, as does a model
with a single bend plus an additional Lorentzian compo-
nent. However the improvement in fit is marginal and, given
the additional free parameters, is not significant. Thus we
conclude that a simple ‘soft’ state model provides the most
likely explanation of the data.
Assuming a mass of 3 × 107M⊙ for NGC 3783
(Peterson et al. 2004), and an accretion rate of 7% of
the Eddington limit (Uttley & McHardy 2005, based on
Woo & Urry 2002), then NGC 3783 is still in good agree-
ment with the scaling of PSD break timescale as ∼ M/ṁE
between AGN and GBHs found by McHardy et al. (2006).
Our new fits, show that the PSD of NGC 3783 is per-
fectly consistent with a single-bend power law with low-
frequency slope of -1, in contrast with the earlier result of
Markowitz et al. (2003), who found that a similar model
was rejected tentatively at ∼ 98% confidence. The differ-
ence can be understood in terms of the improved long-term
data. Our new RXTE monitoring observations occur every 2
days, compared to 4 days previously, thereby increasing the
long term RXTE data set by a factor 2.6 and, in particular,
providing overlap at high frequencies with the RXTE inten-
sive monitoring data. The drop in long-timescale variability
power, evident in the older long term monitoring data is not
reproduced by the new long-term monitoring data, showing
that this drop could be just a statistical fluctuation. In addi-
tion, the very high frequencies are better constrained by the
2 orbits of XMM-Newton data than by the earlier Chandra
data used by Markowitz et al. (2003).
The classification of the PSD as being ‘soft’ state means
that NGC 3783 is no longer considered unusual amongst
AGN. The fact that this AGN is radio-quiet strongly sup-
ports the analogy with GBHs in the soft state. Also the ac-
cretion rate of NGC 3783 ( ṁE =0.07) (Uttley & McHardy
2005, based on Woo & Urry 2002) is similar to that
of other AGN with soft-state PSDs (e.g. NGC 3227
Uttley & McHardy 2005, NGC 4051 McHardy et al. 2004,
MCG-6-30-15 McHardy et al. 2005). This accretion rate is
above the rate at which the persistent GBH Cyg X-1 tran-
sits between hard and soft states in either direction and at
which other GBHs transit from the soft to hard state ( ṁE
=0.02) (Maccarone et al. 2003; Maccarone 2003). We note
that other transient GBHs in outburst, where the variable
power law emission in the soft state PSD is weak, can re-
main in the hard state to much higher accretion rates (∼ 2–
50% Homan & Belloni 2005) but it is not clear whether we
should expect similar PSD shapes to AGN for such outburst-
ing sources. Thus NGC 3783 remains compatible with other
moderately accreting AGN in being analogous to Cyg X-1
in the soft state. It is, of course, possible that the transition
rate might not be independent of mass. Observations do not
yet greatly constrain the transition rate as a function of mass
but the abscence of large deviations from the so-called ‘fun-
damental’ plane of radio luminosity, X-ray luminosity and
black hole mass (Merloni et al. 2003; Falcke et al. 2004) ar-
gues against a large spread in the transistion accretion-rates
(e.g. see Körding et al. 2006). In the case of Seyfert galaxy
c© 2006 RAS, MNRAS 000, 1–8
8 D. P. Summons et al
NGC 3227, the accretion rate is ∼ 1–2% and a ‘soft’ state
PSD is measured (Uttley & McHardy 2005), which suggests
that the transition accretion-rate in AGN should be at or
below that value.
Our observations, which show that NGC 3783 does not
have a highly unusual PSD, therefore confirm the growing
similarities between AGN and Galactic black hole systems
and leave only Arakelian 564, which is probably a very high
state object, as the only AGN showing clear double breaks
(or multiple Lorentzians) in its PSD (e.g. Arévalo et al.
2006, McHardy et al. in prep.).
ACKNOWLEDGEMENTS
We would like to thank the referee, Chris Done, for use-
ful comments and suggestions. This research has made use
of the data obtained from the High Energy Astrophysics
Science Archive Research Center (HEASARC), provided by
NASA’s Goddard Space Flight Center. We would like to
thank Information Systems Services (ISS) at the Univer-
sity of Southampton for the use of their Beowulf cluster,
Iridis2. PU acknowledges support from a Marie Curie Inter-
European Research Fellowship.
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c© 2006 RAS, MNRAS 000, 1–8
	INTRODUCTION
	OBSERVATIONS AND DATA REDUCTION
	RXTE Data Reduction
	XMM-Newton Data Reduction
	Power spectral Modelling
	Combining RXTE and XMM-Newton data
	Monte Carlo simulations
	Unbroken power law model
	Single-bend power law model
	Double-bend power law model
	Single-bend power law with a Lorentzian component
	Discussion and Conclusions
