Astronomy & Astrophysics manuscript no. 6713 c© ESO 2018
October 31, 2018
Correlated modulation between the redshifted Fe Kα line
and the continuum emission in NGC 3783
F. Tombesi1,2, B. De Marco3, K. Iwasawa4, M. Cappi1, M. Dadina1, G. Ponti1,2, G. Miniutti5, and G.G.C. Palumbo2
1 INAF-IASF Bologna, Via Gobetti 101, I-40129 Bologna, Italy
2 Dipartimento di Astronomia, Università degli Studi di Bologna, Via Ranzani 1, I-40127 Bologna, Italy
3 International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste, Italy
4 Max-Planck-Institut fur Extraterrestrische Physik, Giessenbachstrasse, D-85748 Garching, Germany
5 Institute of Astronomy, Madingley Road, Cambridge CB3 OHA, United Kingdom
Received 8 November 2006 / Accepted 20 March 2007
ABSTRACT
Aims. It has been suggested that X-ray observations of rapidly variable Seyfert galaxies may hold the key to probe the gas orbital motions in
the innermost regions of accretion discs around black holes and, thus, trace flow patterns under the effect of the hole strong gravitational field.
Methods. We explore this possibility by re-analyzing the multiple XMM-Newton observations of the Seyfert 1 galaxy NGC 3783. A detailed
time-resolved spectral analysis is performed down to the shortest possible time-scales (few ks) using “excess maps” and cross-correlating light
curves in different energy bands.
Results. In addition to a constant core of the Fe Kα line, we detected a variable and redshifted Fe Kα emission feature between 5.3–6.1 keV.
The line exhibits a modulation on a time-scale of ∼27 ks that is similar to and in phase with a modulation of the 0.3–10 keV source continuum.
The two components show a good correlation.
Conclusions. The time-scale of the correlated variability of the redshifted Fe line and continuum agrees with the local dynamical time-scale of
the accretion disc at ∼10 rg around a black hole with the optical reverberation mass ∼10
7M⊙. Given the shape of the redshifted line emission
and the overall X-ray variability pattern, the line is likely to arise from the relativistic region near the black hole, although the source of the few
cycles of coherent variation remains unclear.
Key words. Line: profiles – Relativity – Galaxies: active – X-rays: galaxies – Galaxies: individual: NGC 3783
1. Introduction
The fluorescent iron K (Fe Kα) emission line is considered to
be a useful probe of the accretion flow around the central black
hole of an active galaxy. In particular, due to the high orbital
velocity and strong gravitational field in the innermost regions
of an accretion disc, its profile shall be deformed by the con-
currence of Doppler and relativistic shifts. The resulting line is
therefore broadened, with a red-wing extending towards lower
energies (e.g. Fabian et al. 2000; Reynolds & Nowak 2003).
Detailed modelling of time-averaged spectra have been used to
obtain important estimates of the disc ionization state, its cover-
ing factor and, at least for the brightest and best cases, its emis-
sivity law, inner radius and BH spin (Brenneman & Reynolds
2006; Miniutti et al. 2006; Guainazzi et al. 2006; Nandra et
al. 2006). It is also well established that time-resolved spec-
tral analysis is a fundamental tool if we want to understand
not only the geometry and kinematics of the inner accretion
flow but also its dynamics. Early attempts (i.e. Iwasawa et al.
Send offprint requests to: F. Tombesi
e-mail: tombesi@iasfbo.inaf.it
1996; Vaughan & Edelson 2001; Ponti et al. 2004; Miniutti et
al. 2004) have clearly shown that the redshifted component of
the Fe Kα line is indeed variable and that complex geometrical
and relativistic effects should be taken into account (Miniutti et
al. 2004).
More recently, results of iron line variability have been reported
(Iwasawa, Miniutti & Fabian 2004; Turner et al. 2006; Miller et
al. 2006). These are consistent with theoretical studies on the
dynamical behaviour of the iron emission arising from local-
ized hot spots on the surface of an accretion disc (e.g. Dovčiak
et al. 2004). Iwasawa, Miniutti & Fabian (2004), for example,
measured a ∼25 ks modulation in the redshifted Fe Kα line flux
in NGC 3516, which suggests that the emitting region is very
close to the central black hole. However, these are likely to be
transient phenomena, since such spots are not expected to sur-
vive more than a few orbital revolutions. For this reason, it is
inherently difficult to establish the observational robustness of
these type of models, if not by accumulating further observa-
tional data.
Here we present results on the iron line variability in the
bright Seyfert galaxy NGC 3783 (z≃0.01) based on XMM-
http://arxiv.org/abs/0704.0226v1
2 F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783
Fig. 1. The X-ray light curves of NGC 3783 in the 0.3–10 keV band. Left panel: light curve of the 2000 observation. Right panel:
light curves of the 2001a and 2001b observations.
Newton data. This object has been taken as an example in
which multiple warm absorbers can mimic the broad iron line
feature (Reeves et al. 2004), contrary to the initial claim of
the presence of a broad iron line emission using ASCA data
(Nandra et al. 1997). However, the recent study by De Marco
et al. (2006) found evidence for a transient excess feature in the
5–6 keV energy band, interpreted as a redshifted component
of the Fe K line. This result is also supported by a variability
study by O’Neill & Nandra (2006), who examined rms vari-
ability spectra of a sample of bright active galaxies observed
with XMM-Newton. Given the above considerations, we re-
examined all the XMM-Newton observations of NGC 3783 to
perform a comprehensive study of the iron line temporal evo-
lution, on the shortest possible time-scale.
2. XMM-Newton observations
XMM-Newton observed NGC 3783 on 2000 December 28–
29 and on 2001 December 17–21. The first observation (ID
0112210101) has a duration of ∼40 ks while the second (ID
0112210201 and ID 0112210501, hereafter observation 2001a
and 2001b respectively) lasts over two complete orbits for a
total duration of ∼270 ks. Only the EPIC pn data are used in
the following analysis because of the high sensitivity in the
Fe K band. The EPIC pn camera was operated in the “Small
Window” mode with the Medium filter both during the 2000
and the 2001 observations. The live time fraction is thus 0.7.
The data were reduced using the XMM-SAS v. 6.5.0 software
while the analysis was carried on using the lheasoft v. 5.0 pack-
age. High background time intervals were excluded from the
analysis. The useful exposure time intervals are listed in Tab. 1,
together with the mean 0.3–10 keV count rate for each obser-
vation. Only single and double events were selected. Source
photons were collected from a circular region of 56 arcsec ra-
dius, while the background data were extracted from rectangu-
Table 1. Date, duration, useful exposure and mean EPIC pn
0.3–10 keV count rate for each XMM-Newton observation of
NGC 3783.
Obs. ID Date Duration Exposure 〈CR〉
(ks) (ks) (c/s)
0112210101 2000 Dec 28–29 40.412 35 8.5
0112210201 2001 Dec 17–19 137.818 115 6.5
0112210501 2001 Dec 19–21 137.815 120 8.5
lar, nearly source-free regions on the detector. The background
is assumed to be constant throughout the useful exposure. The
0.3–10 keV light curves are shown in Fig. 1 for each observa-
tion.
3. Data analysis
3.1. Spectral features of interest and selection of the
energy resolution
The time-averaged spectrum was analyzed using the XSPEC
v. 11.2 software package. For simplicity, we limited the anal-
ysis to the 4–9 keV band. In this energy band, we checked
that the complex and highly ionized warm absorber (with logξ
and NH up to ∼2.9 erg cm s
−1 and 5×1022 cm−2, Reeves et
al. 2004) shall not affect our conclusions below. The resid-
uals against a simple power-law plus cold absorption contin-
uum model for the 2001b observation, the longest continuous
dataset available, are shown in Fig. 2. In this fit we excluded
the Fe K energy band (i.e. 5–7 keV) and the best fit parameters
are (2.5 ± 0.6) × 1022 cm−2 and 1.81 ± 0.04, for the absorber
column density and power-law slope respectively.
Identified are four excess emission features: the main
Fe Kα core at ∼6.4 keV, a wing to the line core at around 6
keV, a peak at ∼7 keV (possibly Fe Kβ) and a narrow peak at
F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783 3
Fig. 2. The 4–9 keV residuals against a simple power-law
plus cold absorption continuum model for the spectrum of
NGC 3783 during the 2001b observation. The data are obtained
from EPIC pn.
∼5.4 keV. Moreover we identified two absorption features at
∼6.7 keV and ∼7.6 keV. When fitted with Gaussian emission
and absorption lines, all these features are significant at more
than ∼99% confidence level. Similar results were also obtained
by a detailed analysis with more complex models (Reeves et al.
2004). We will focus here on the analysis of the features vari-
ability properties. The application of the excess map technique
to the identified absorption features did not give significant re-
sults, thus, in the following, we will focus on the analysis of
emission features variability only. The 2001a observation has
been divided into two parts because of the gap in the data be-
tween t∼5×104 s and t∼6×104 s. Since all the selected spec-
tral features are comparable to the CCD spectral resolution, we
chose 100 eV for the energy resolution of the excess maps.
3.2. Selection of the time resolution
In choosing the time resolution for the excess maps we looked
for the best trade-off between getting a sufficiently short time-
scale, in order to oversample variability, and keeping enough
counts in each energy resolution bin. We first considered the
2001b observation, having the longest and continuous expo-
sure. Spectra were extracted during different time intervals (1
ks, 2.5 ks and 5 ks) around the local minimum flux state at
t∼215 ks. The required condition is that each 100 eV energy
bin in the 4–9 keV band has to contain at least 50 counts. At
the time resolution of 2.5 ks we got ∼90 counts per energy
bin at the energies of the “red” feature (5.3–5.4 keV), and ∼80
counts per energy bin in the “wing” feature energy band (5.8–
6.1 keV). Moreover, for a 107 M⊙ black hole we expect the
Keplerian orbital period to be ∼104 s at a radius of 10 rg. Thus,
selecting 2.5 ks as the excess maps time resolution, enables us
to completely oversample this typical time-scale. This choice
of time resolution, optimized for the 2001b observation, was
extended to the 2000 and 2001a data.
4. Excess emission maps
Energy spectra for a duration of the chosen exposure time (2.5
ks) are extracted in time sequence. 14 spectra are obtained
Table 2. Spectral features of interest in the 4–9 keV band with
the selected band-passes and mean intensity.
Feature Energy band 〈I〉
(keV) (10−5 ph s−1cm−2)
red 5.3–5.4 0.6
wing 5.8–6.1 2
core (Kα) 6.2–6.5 5.3
Kβ 6.8–7.1 1.2
Red+Wing 5.3–6.1 3.2
from the 2000 observation, 46 and 48 spectra are obtained from
2001a and 2001b observations respectively. For each spectrum
the continuum is determined and subtracted. The residuals in
counts unit are corrected for the detector response and put
together in time sequence to construct an image in the time-
energy plane.
4.1. Continuum subtraction
The continuum model is assumed to be always a simple ab-
sorbed power-law, throughout all the observations. For each
spectrum the energy band of the observed spectral features (i.e.
5–7 keV) is excluded during the continuum fit. The 4–5 keV
and 7–9 keV data are rebinned so that each channel contains
more than 50 counts to enable the use of the χ2 minimization
process when performing spectral fitting and to ensure that the
high energy end of the data (7–9 keV) have enough statistical
weight. Because of the chosen low energy bound (4 keV), the
fit is not sensitive to cold absorption. Thus the cold absorption
column density is fixed to the time-averaged spectrum value
(NH ≃ 2.5× 10
22 cm−2). Each 4–9 keV spectrum at 100 eV en-
ergy resolution is then fitted with its best-fit continuum model
and residuals are used to construct the excess emission map in
the time-energy plane.
Once all the continuum spectral fits have been done, we
checked if continuum changes could affect our measurements
of the line fluxes. The mean power-law slopes during the three
observations are 1.85, 1.75 and 1.79 respectively, with stan-
dard deviations of 0.08, 0.1 and 0.09. The power-law slopes
are indeed quite constant, consistent with values obtained from
the mean spectrum (§3.1), which result in a very marginal ef-
fect (< 0.1%) in the flux measurement of the narrow features
we found here. These power-law continuum slopes are also
in agreement with those previously found in observations us-
ing other instruments with overlapping spectral coverage, like
BeppoSAX (De Rosa et al. 2002), ASCA, RXTE and Chandra
(Kaspi et al. 2001).
4.2. Image smoothing
As discussed in Iwasawa, Miniutti & Fabian (2004), if the data
are acquired continuously and the characteristic time-scale of
any variation in a feature of interest is longer than the sam-
pling time (i.e. the time resolution), it is possible to suppress
random noise between neighboring pixels by applying a low-
pass filter. A circular Gaussian filter is used with σ=0.85 pixel
4 F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783
Time (ks)
Energy (keV)
0 0.05
 Excess (ph/2500s/cm^2)
0 50 100 150 200 250
Time (ks)
Energy (keV)
0 0.02 0.04 0.06
 Excess (ph/2500s/cm^2)
Fig. 3. The excess emission maps of the 4–9 keV band in the time-energy plane at 2.5 ks time resolution. The images have been
smoothed. Since the 6.4 keV line core is very strong and stable, the color map is adjusted to saturate the line core and allow
lower surface brightness features to be visible. Left panel: excess emission map from the 2000 observation. Right panel: excess
emission map from the 2001a and 2001b observations.
(200 eV in energy and 5 ks in time, FWHM). The excess map
Gaussian-filtered images for each observation are shown in
Fig. 3. Systematic variations are observed in the 5.3–5.4 keV
and in the 5.8–6.1 keV energy bands of the 2001b observation.
However, the image filtering can slightly smear these narrow
features and reduce their intensity.
5. Results
5.1. Light curves of the individual spectral features
Light curves of the four emission features are extracted from
the excess map filtered images. The selected band-passes are
listed in Tab. 2. During the image filtering process individ-
ual pixels lose their independence to the neighbouring ones.
This means that a simple counting statistics may be inappro-
priate for estimating the features light curves errors. For this
reason the estimation of the errors has been done by exten-
sive Monte Carlo simulations. We implemented 1000 simula-
tions following the same procedure in making the excess map
images. In the simulations all the spectral features parameters
and the power-law slope are assumed to be constant, while let-
ting the power-law normalization vary according to the 0.3–10
keV light curve. Light curves of individual spectral features
have been extracted from each simulation and their mean val-
ues and variances recorded. The square root of the mean of the
variances (i.e. the dispersion) has been regarded as the light
curves error. In Fig. 4 the emission features light curves for the
2001a and 2001b observations are shown. The 2000 observa-
tion light curves are not reported because they do not show any
sign of variability. The most intense variations are registered
in the light curves of the “red” (E=5.3–5.4 keV) and “wing”
(E=5.8–6.1 keV) features during the 2001b observation. The
observed peaks seem to follow the same kind of variability
pattern and, as shown in more details below, appear to be in
phase with the continuum emission. In order to check the sig-
nificance of the observed variability we extracted both real and
simulated data light curves in the entire 5.3–6.1 keV band, i.e.
of the “red+wing” structure. Then we compared the χ2 values
against a constant hypothesis for the real data and the 1000
simulations; equivalent results can be derived comparing the
variances directly. Only 73 of the simulations show variability
at the same level or greater than the real data, therefore we get
a variability confidence level of 93%.
The light curves of the excess emission features in the 5–6 keV
energy band (red, wing and red+wing) seem to show a variabil-
ity pattern with a recurrence of the flux peaks on time-scales
of 27 ks. We further investigated how it is likely to occur by
chance applying a method that makes use of the 1000 Monte
Carlo simulations. We folded the real data light curve with the
interval of 27 ks and we fitted it with a constant. We obtained a
χ2r = 88 for 19 degrees of freedom. We did the same to the simu-
lated red+wing light curves but, this time, folding in n = 9 trial
periods, from 17 to 37 ks at intervals of 2.5 ks, and recorded
the χ2i values. If N is the total number of simulated red+wing
light curves for which χ2i ≥ χ
r , the confidence level can be de-
F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783 5
/s Continuum
8 Core
0 105 2×105
Time (s)
Kbeta
Fig. 4. The light curves of the total 0.3–10 keV continuum
flux and of the four spectral features (Tab. 2) extracted from
the excess maps of the 2001a and 2001b observations (Fig. 3,
Right panel), with errors computed from simulations. The time
resolution is 2.5 ks.
rived as (1 − N1000·n ). Only N = 54 of the simulated red+wing
light curves folded at the trial periods show chi-square values
greater than the real one. Therefore, we could derive a confi-
dence level for the recurrence pattern on the 27 ks time scale of
99.4%.
Finally, we checked that the continuum above 7 keV (which
carries the photons eventually responsible for the Fe line pro-
duction) varies following the same pattern of the 0.3–10 keV
band (Fig. 4, Top panel).
5.2. Correlation with the continuum light curve
In the 0.3–10 keV light curve of observation 2001b (Fig. 5,
Upper panel) flux variations of ∼30% are visible with four
peaks separated by approximately equal time intervals. Given
such peculiar time series shape, we focused on this observa-
tion and searched for some typical time-scale in the variability
pattern. Thus, we applied the efsearch task (in Xronos), which
searches for periodicities in a time series calculating the maxi-
mum chi-square of the folded light curve over a range of peri-
ods. We found a typical time-scale for variability of 26.6±2.2
ks. We then removed the underlying long-term variability trend
by subtracting a 4th degree polynomial to the 0.3–10 keV con-
tinuum light curve (see Fig. 5, Middle panel). The polynomial
has been determined using the lcurve task (in Xronos), which
makes use of the least-square technique. Applying again the
efsearch task we found a typical time-scale for short-term vari-
ability of ∼27.4 ks1. The peaks observed in the continuum light
curve seem to appear at the same times at which those ob-
served in the “wing” and “red” light curves do. In order to look
1 It should be noted that the variability PSD study of this XMM-
Newton dataset by Markowitz (2005) suggests an excess of power
around 4×10−5 Hz (corresponding to about 25 ks) during the 2001b
observation (square symbols in his Fig. 3).
0.3−10 keV
0.3−10 keV
0 5×104 105
Time (s)
Red+Wing
Fig. 5. Upper panel: The 0.3–10 keV light curve of NGC 3783
during 2001b observation at 2.5 ks time resolution. Middle
panel: The 0.3–10 keV light curve of NGC 3783 during the
2001b observation after subtraction of a 4th degree polynomial
(long-term variations) at 2.5 ks time resolution. Lower panel:
The 5.3–6.1 keV (“red+wing” energy band) light curve ex-
tracted from the excess emission map of the 2001b observation
(Fig. 3, Right panel) at 2.5 ks time resolution.
for some correlation between the continuum and the 5.3–6.1
keV (“red+wing”) feature flux we computed the cross corre-
lation function (CCF) between the two time series, where the
input continuum light curve is the “de-trended” one. It is re-
ported in Fig. 6 as a function of time delay, measured with
respect to the continuum flux variations. No delay is evident,
with an estimated error at the peak of 2.5 ks. The continuum
and “red+wing” fluxes seem to show a correlation, with peak
value 0.7. To estimate the significance of the correlation we
computed the CCFs between the continuum and the simulated
“red+wing” light curves. If N is the number of simulated light
curves which have a higher cross correlation than the real one,
the significance of the correlation is (1 − N/1000). Applying
this method we found a confidence level greater than 99.9%.
5.3. High/Low flux state line profiles
Looking at the “red+wing” light curve (Fig. 5, Lower panel)
we constructed two spectra from the integrated high and low
flux intervals to verify the variability in this energy band. The
line profiles are shown in Fig. 7 where the ratio between the
data and a simple power-law plus cold absorption model is
shown. While the 6.4 keV and 6.9 keV features remain the
same, a small increase of counts is visible in the 5.3–5.4 keV
and 5.8–6.1 keV bands in the high flux state. Adding an emis-
sion Gaussian model to the simple power law plus Gaussian
line (at the Fe Kα energy) model in the high flux state inte-
grated spectra improves the χ2 of 18. Thus the significance of
the excess is ∼99.9%.
6 F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783
−104 0 104−
Time Delay (s)
Fig. 6. The cross correlation function calculated between the
de-trended 0.3–10 keV continuum light curve and the 5.3–6.1
keV feature (“red+wing”) light curve.
.4 HIGH
6 7 8
Energy (keV)
Fig. 7. The Fe K line profile during the High flux (open
squares) and the Low flux (solid circles) phases of the 5.3–6.1
keV feature. The ratios are computed against the best-fitting
continuum model. The energies are in the observer frame.
6. Discussion
In the 2001b observation, NGC 3783 clearly exhibits contin-
uum emission with two different time-scales: a long-term mod-
ulation with variations up to a factor 2 on intervals greater than
60 ks is superimposed to a shorter one on a time-scale of 27
ks, with modulations of 30% of the average value. According
to an estimated black hole mass of MBH = (3.0±0.5)×10
(Peterson et al. 2004), the latter modulation occurs with a
characteristic time-scale corresponding to the orbital period at
∼9–10 rg (e.g. Bardeen, Press & Teukolsky (1972)). It should
be noted, however, that a previous mass estimate by Onken &
Peterson (2002) gave the value of MBH = (8.7± 1.1)× 10
6 M⊙,
that would correspond to ∼20 rg. These mass discrepancies are
mainly due to a different scaling of the virial relation in per-
forming reverberation mapping measurements. However, the
former estimate is more accurate because it has been calibrated
to the MBH −σ relation and thus we will adopt this value in the
following discussion. The power spectral density of the source
is consistent with a red-noise shape (Markowitz 2005) where
variability mainly occurs on intervals of the order of days. Here
we identify an additional (additive) shorter time-scale compo-
nent (see the footnote 1), most likely produced within the in-
nermost accretion flow/corona system.
The most remarkable result of our analysis is the detec-
tion of redshifted (5.3–6.1 keV) Fe K emission and of its vari-
ability. The redshifted emission appears to respond only to the
shorter ∼27 ks time-scale modulation and shows a good cor-
relation with the continuum with a time-lag consistent with
zero within the errors (∆τ ∼ 1.25 ks). This indicates that the
continuum modulation on this time interval is likely to induce
Fe K emission from dense material close to the black hole
(which explains the observed redshift of the emission feature);
moreover the lack of time-lags implies that the distance be-
tween the sites of continuum and line production is smaller than
c∆τ ∼ 4×1013 cm ∼ 8 rg (for the black hole mass given above).
We are therefore most likely observing emission from the in-
nermost accretion flow in both the continuum and line emission
(corona and disc).
As discussed above, the variability time-scale suggests we
are looking at emission from around ∼9–10 rg. As a consis-
tency check, we fitted the time-averaged spectrum by including
a diskline component to account for the redshifted features. We
forced the emission region to be an annulus of ∆r= 0.5 rg with
uniform emissivity because the purpose of this test is to as-
sess the approximate location of the line-emitting region. We
obtain good fits with an almost face-on disc (i = 11 ± 4◦)
and an annulus at 9–15 rg depending on the assumed Fe line
rest-frame energy (from neutral at 6.4 keV to highly ionized
at 6.97 keV). For all cases we tested, the statistical improve-
ment is of ∆χ2 ∼ 16 for 3 additional degrees of freedom, cor-
responding to a confidence level of 99.7%. This fit shows that
the redshifted Fe line emission we detected is indeed consistent
in shape with being produced around 10 rg, where the disc or-
bital period is of the order of 27 ks, which agrees well with the
correlated (and zero-lag) variability of the two components.
The interpretation of our results is however not straightfor-
ward. The quasi-sinusoidal modulations of the continuum and
line emission (see Fig. 5) would suggest the presence of a local-
ized co-rotating flare above the accretion disc which irradiates
a small spot on its surface. The intensity modulations we see
(Fig. 5) would then be produced by Doppler beaming effects
(acting on both the flare and spot emission, i.e. on both contin-
uum and line) and the characteristic time-scale of 27 ks would
be identified with the orbital period (because of gravitational
time dilation, the period measured by an observer on the disc
at 10 rg would be shorter by ∼10%). As demonstrated above, a
flare/spot system orbiting the black hole at ∼10 rg would also
produce a time-averaged line profile in agreement with the ob-
servations. However, such a model makes definite prediction
on the Fe line energy modulation within one orbital period. In
this framework, the orbiting spot on the accretion disc would
also give rise to energy modulations of the Fe line due to the
Doppler effect and such energy modulation is barely seen in
the data (see Fig. 3). We stress that the adopted time resolu-
tion (2.5 ks) is good enough to detect energy modulations with
a characteristic 27 ks time-scale. This has been demonstrated
with XMM-Newton in the case of NGC 3516, where the modu-
lation occurs on a very similar time-scale (Iwasawa et al. 2004;
F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783 7
see also Dovčiak et al. 2004 for theoretical models). Therefore,
the lack of Fe line energy modulation disfavours the orbiting
flare/spot interpretation for NGC 3783.
However, a variability time-scale of the order of the orbital
one at a given radius does not necessarily imply the motion of
a point-like X-ray source. In fact, since the orbital time-scale is
the fastest at a given disc radius, and since the observed time-
scale of ∼27 ks corresponds to the orbital period at ∼10 rg, one
could argue that the data only imply that the X-ray variability
likely originates from within ∼10 rg. The apparent recurrence
in the X-ray continuum modulation may not necessarily be re-
lated to a real physical periodicity, especially considering the
limited length of the observation (only four putative cycles are
detected).
A possible explanation for the observed behaviour is that
the X-ray continuum source(s) (located within ∼10 rg from
the center) irradiates the whole accretion disc, but only a ring-
like structure around 10 rg is responsible for the fluorescent Fe
emission. This is possible if the bulk of the accretion disc is
so highly ionized that little Fe line is produced, while an over-
dense (and therefore lower ionization) structure is responsible
for the fluorescent emission. Such an over-dense region could
have an approximate ring-like geometry if it is for instance as-
sociated with a spiral-wave density perturbation. In this case,
the Fe emitting region is extended in the azimuthal direction
and we do not expect strong energy modulation with time,
whatever the origin of the continuum modulation. We point out
that spiral density distributions could result from the ordered
magnetic fields in the inner region of the disc and that the en-
ergy dissipation (via e.g. magnetic reconnection) could be en-
hanced there, thereby providing a common site for the produc-
tion of the X-ray continuum and the Fe line (e.g. Machida &
Matsumoto 2003).
On the other hand, if the apparent recurrence is in fact
real, it is worth noting that the continuous theoretical effort in
understanding the origin of quasi-periodic oscillations (QPO)
in neutron star and black hole systems provides a wealth of
mechanisms inducing quasi-periodic variability, although none
is firmly established (Psaltis 2001; Kato 2001; Rezzolla et al.
2003; Lee et al. 2004; Zycki & Sobolewska 2005 and many
others). A connection between QPO phase and Fe line inten-
sity has been previously claimed in the Galactic black hole
GRS 1915+105 (Miller & Homan 2005). Although in our case,
the presence of a QPO cannot be claimed because of the very
small number of detected cycles, the analogy is suggestive. In
the case of GRS 1915+105, Miller & Homan consider that a
warp in the inner disc, possibly due to Lense-Thirring preces-
sion, may produce the observed QPO-Fe line connection (e.g.
Markovic & Lamb 1998). However, to produce the observed
∼15% rms variability in the X-ray lightcurve, the black hole
spin axis should be inclined with respect to the line of sight by
at least 60◦ (which is at odds with our inclination estimate of
11±4◦ and with the Seyfert 1 nature of NGC 3783), and the tilt
precession angle should be larger than 20◦–30◦ (Schnittman,
Homan, Miller 2006). Both requirements make it highly un-
likely that Lense-Thirring precession can successfully account
for the observed modulations in NGC 3783.
While the origin of the coherent intensity modulation still
remains unclear, the correlated variation of the continuum and
line emission and the Fe line shape are consistent with an emis-
sion site at ∼10 rg. Moreover, the fact that the iron line variabil-
ity responds to the 27 ks time-scale modulation only implies
that this short time-scale variation is somehow detached from
the long-term variability. The latter may be associated with per-
turbations in the accretion disc propagating inwards from outer
radii and modulating the X-ray emitting region (Lyubarskii
1997), while the former seems to genuinely originate in the
inner disc.
Further observational data may help to clarify the complex
phenomena related to the relativistic Fe line temporal evolu-
tion in Seyfert 1 galaxies. Our work makes it clear that higher
quality data in the Fe band will be able to probe the inner-
most regions of accretion flows with high accuracy. Next gen-
eration of large collecting area X-ray missions such as XEUS
and Constellation-X or even very long observations with XMM-
Newton will be crucial to fully exploit such potential.
Acknowledgements. This paper is based on observations obtained
with the XMM-Newton satellite, an ESA funded mission with con-
tributions by ESA Member States and USA. We thank A. Müller, K.
Nandra, L. Nicastro, P. O’Neill and M. Orlandini for useful discus-
sions. MC, MD and GP acknowledge financial support from ASI un-
der contract ASI/INAF I/023/05/0. The authors thank the anonymous
referee for suggestions that led to improvements in the paper.
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	Introduction
	XMM-Newton observations
	Data analysis
	Spectral features of interest and selection of the energy resolution
	Selection of the time resolution
	Excess emission maps
	Continuum subtraction
	Image smoothing
	Results
	Light curves of the individual spectral features
	Correlation with the continuum light curve
	High/Low flux state line profiles
	Discussion

  It has been suggested that X-ray observations of rapidly variable Seyfert
galaxies may hold the key to probe the gas orbital motions in the innermost
regions of accretion discs around black holes and, thus, trace flow patterns
under the effect of the hole strong gravitational field. We explore this
possibility analizing XMM-Newton observations of the seyfert 1 galaxy NGC 3783.
A detiled time-resolved spectral analysis is performed down to the shortest
possible time-scales (few ks) using "excess maps" and cross-correlating light
curves in different energy bands. In addition to a constant core of the Fe K
alpha line, we detected a variable and redshifted Fe K alpha emission feature
between 5.3-6.1 keV. The line exhibits a modulation on a time-scale of 27 ks
that is similar to and in phase with a modulation of the 0.3-10 keV source
continuum. The time-scale of the correlated variability of the redshifted Fe
line and continuum agrees with the local dynamical time-scale of the accretion
disc at 10 r_g around a black hole of 10^7 M_sun. Given the shape of the
redshfted line emission and the overall X-ray variability pattern, the line is
likely to arise from the relativistic region near the black hole.

Introduction
The fluorescent iron K (Fe Kα) emission line is considered to
be a useful probe of the accretion flow around the central black
hole of an active galaxy. In particular, due to the high orbital
velocity and strong gravitational field in the innermost regions
of an accretion disc, its profile shall be deformed by the con-
currence of Doppler and relativistic shifts. The resulting line is
therefore broadened, with a red-wing extending towards lower
energies (e.g. Fabian et al. 2000; Reynolds & Nowak 2003).
Detailed modelling of time-averaged spectra have been used to
obtain important estimates of the disc ionization state, its cover-
ing factor and, at least for the brightest and best cases, its emis-
sivity law, inner radius and BH spin (Brenneman & Reynolds
2006; Miniutti et al. 2006; Guainazzi et al. 2006; Nandra et
al. 2006). It is also well established that time-resolved spec-
tral analysis is a fundamental tool if we want to understand
not only the geometry and kinematics of the inner accretion
flow but also its dynamics. Early attempts (i.e. Iwasawa et al.
Send offprint requests to: F. Tombesi
e-mail: tombesi@iasfbo.inaf.it
1996; Vaughan & Edelson 2001; Ponti et al. 2004; Miniutti et
al. 2004) have clearly shown that the redshifted component of
the Fe Kα line is indeed variable and that complex geometrical
and relativistic effects should be taken into account (Miniutti et
al. 2004).
More recently, results of iron line variability have been reported
(Iwasawa, Miniutti & Fabian 2004; Turner et al. 2006; Miller et
al. 2006). These are consistent with theoretical studies on the
dynamical behaviour of the iron emission arising from local-
ized hot spots on the surface of an accretion disc (e.g. Dovčiak
et al. 2004). Iwasawa, Miniutti & Fabian (2004), for example,
measured a ∼25 ks modulation in the redshifted Fe Kα line flux
in NGC 3516, which suggests that the emitting region is very
close to the central black hole. However, these are likely to be
transient phenomena, since such spots are not expected to sur-
vive more than a few orbital revolutions. For this reason, it is
inherently difficult to establish the observational robustness of
these type of models, if not by accumulating further observa-
tional data.
Here we present results on the iron line variability in the
bright Seyfert galaxy NGC 3783 (z≃0.01) based on XMM-
http://arxiv.org/abs/0704.0226v1
2 F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783
Fig. 1. The X-ray light curves of NGC 3783 in the 0.3–10 keV band. Left panel: light curve of the 2000 observation. Right panel:
light curves of the 2001a and 2001b observations.
Newton data. This object has been taken as an example in
which multiple warm absorbers can mimic the broad iron line
feature (Reeves et al. 2004), contrary to the initial claim of
the presence of a broad iron line emission using ASCA data
(Nandra et al. 1997). However, the recent study by De Marco
et al. (2006) found evidence for a transient excess feature in the
5–6 keV energy band, interpreted as a redshifted component
of the Fe K line. This result is also supported by a variability
study by O’Neill & Nandra (2006), who examined rms vari-
ability spectra of a sample of bright active galaxies observed
with XMM-Newton. Given the above considerations, we re-
examined all the XMM-Newton observations of NGC 3783 to
perform a comprehensive study of the iron line temporal evo-
lution, on the shortest possible time-scale.
2. XMM-Newton observations
XMM-Newton observed NGC 3783 on 2000 December 28–
29 and on 2001 December 17–21. The first observation (ID
0112210101) has a duration of ∼40 ks while the second (ID
0112210201 and ID 0112210501, hereafter observation 2001a
and 2001b respectively) lasts over two complete orbits for a
total duration of ∼270 ks. Only the EPIC pn data are used in
the following analysis because of the high sensitivity in the
Fe K band. The EPIC pn camera was operated in the “Small
Window” mode with the Medium filter both during the 2000
and the 2001 observations. The live time fraction is thus 0.7.
The data were reduced using the XMM-SAS v. 6.5.0 software
while the analysis was carried on using the lheasoft v. 5.0 pack-
age. High background time intervals were excluded from the
analysis. The useful exposure time intervals are listed in Tab. 1,
together with the mean 0.3–10 keV count rate for each obser-
vation. Only single and double events were selected. Source
photons were collected from a circular region of 56 arcsec ra-
dius, while the background data were extracted from rectangu-
Table 1. Date, duration, useful exposure and mean EPIC pn
0.3–10 keV count rate for each XMM-Newton observation of
NGC 3783.
Obs. ID Date Duration Exposure 〈CR〉
(ks) (ks) (c/s)
0112210101 2000 Dec 28–29 40.412 35 8.5
0112210201 2001 Dec 17–19 137.818 115 6.5
0112210501 2001 Dec 19–21 137.815 120 8.5
lar, nearly source-free regions on the detector. The background
is assumed to be constant throughout the useful exposure. The
0.3–10 keV light curves are shown in Fig. 1 for each observa-
tion.
3. Data analysis
3.1. Spectral features of interest and selection of the
energy resolution
The time-averaged spectrum was analyzed using the XSPEC
v. 11.2 software package. For simplicity, we limited the anal-
ysis to the 4–9 keV band. In this energy band, we checked
that the complex and highly ionized warm absorber (with logξ
and NH up to ∼2.9 erg cm s
−1 and 5×1022 cm−2, Reeves et
al. 2004) shall not affect our conclusions below. The resid-
uals against a simple power-law plus cold absorption contin-
uum model for the 2001b observation, the longest continuous
dataset available, are shown in Fig. 2. In this fit we excluded
the Fe K energy band (i.e. 5–7 keV) and the best fit parameters
are (2.5 ± 0.6) × 1022 cm−2 and 1.81 ± 0.04, for the absorber
column density and power-law slope respectively.
Identified are four excess emission features: the main
Fe Kα core at ∼6.4 keV, a wing to the line core at around 6
keV, a peak at ∼7 keV (possibly Fe Kβ) and a narrow peak at
F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783 3
Fig. 2. The 4–9 keV residuals against a simple power-law
plus cold absorption continuum model for the spectrum of
NGC 3783 during the 2001b observation. The data are obtained
from EPIC pn.
∼5.4 keV. Moreover we identified two absorption features at
∼6.7 keV and ∼7.6 keV. When fitted with Gaussian emission
and absorption lines, all these features are significant at more
than ∼99% confidence level. Similar results were also obtained
by a detailed analysis with more complex models (Reeves et al.
2004). We will focus here on the analysis of the features vari-
ability properties. The application of the excess map technique
to the identified absorption features did not give significant re-
sults, thus, in the following, we will focus on the analysis of
emission features variability only. The 2001a observation has
been divided into two parts because of the gap in the data be-
tween t∼5×104 s and t∼6×104 s. Since all the selected spec-
tral features are comparable to the CCD spectral resolution, we
chose 100 eV for the energy resolution of the excess maps.
3.2. Selection of the time resolution
In choosing the time resolution for the excess maps we looked
for the best trade-off between getting a sufficiently short time-
scale, in order to oversample variability, and keeping enough
counts in each energy resolution bin. We first considered the
2001b observation, having the longest and continuous expo-
sure. Spectra were extracted during different time intervals (1
ks, 2.5 ks and 5 ks) around the local minimum flux state at
t∼215 ks. The required condition is that each 100 eV energy
bin in the 4–9 keV band has to contain at least 50 counts. At
the time resolution of 2.5 ks we got ∼90 counts per energy
bin at the energies of the “red” feature (5.3–5.4 keV), and ∼80
counts per energy bin in the “wing” feature energy band (5.8–
6.1 keV). Moreover, for a 107 M⊙ black hole we expect the
Keplerian orbital period to be ∼104 s at a radius of 10 rg. Thus,
selecting 2.5 ks as the excess maps time resolution, enables us
to completely oversample this typical time-scale. This choice
of time resolution, optimized for the 2001b observation, was
extended to the 2000 and 2001a data.
4. Excess emission maps
Energy spectra for a duration of the chosen exposure time (2.5
ks) are extracted in time sequence. 14 spectra are obtained
Table 2. Spectral features of interest in the 4–9 keV band with
the selected band-passes and mean intensity.
Feature Energy band 〈I〉
(keV) (10−5 ph s−1cm−2)
red 5.3–5.4 0.6
wing 5.8–6.1 2
core (Kα) 6.2–6.5 5.3
Kβ 6.8–7.1 1.2
Red+Wing 5.3–6.1 3.2
from the 2000 observation, 46 and 48 spectra are obtained from
2001a and 2001b observations respectively. For each spectrum
the continuum is determined and subtracted. The residuals in
counts unit are corrected for the detector response and put
together in time sequence to construct an image in the time-
energy plane.
4.1. Continuum subtraction
The continuum model is assumed to be always a simple ab-
sorbed power-law, throughout all the observations. For each
spectrum the energy band of the observed spectral features (i.e.
5–7 keV) is excluded during the continuum fit. The 4–5 keV
and 7–9 keV data are rebinned so that each channel contains
more than 50 counts to enable the use of the χ2 minimization
process when performing spectral fitting and to ensure that the
high energy end of the data (7–9 keV) have enough statistical
weight. Because of the chosen low energy bound (4 keV), the
fit is not sensitive to cold absorption. Thus the cold absorption
column density is fixed to the time-averaged spectrum value
(NH ≃ 2.5× 10
22 cm−2). Each 4–9 keV spectrum at 100 eV en-
ergy resolution is then fitted with its best-fit continuum model
and residuals are used to construct the excess emission map in
the time-energy plane.
Once all the continuum spectral fits have been done, we
checked if continuum changes could affect our measurements
of the line fluxes. The mean power-law slopes during the three
observations are 1.85, 1.75 and 1.79 respectively, with stan-
dard deviations of 0.08, 0.1 and 0.09. The power-law slopes
are indeed quite constant, consistent with values obtained from
the mean spectrum (§3.1), which result in a very marginal ef-
fect (< 0.1%) in the flux measurement of the narrow features
we found here. These power-law continuum slopes are also
in agreement with those previously found in observations us-
ing other instruments with overlapping spectral coverage, like
BeppoSAX (De Rosa et al. 2002), ASCA, RXTE and Chandra
(Kaspi et al. 2001).
4.2. Image smoothing
As discussed in Iwasawa, Miniutti & Fabian (2004), if the data
are acquired continuously and the characteristic time-scale of
any variation in a feature of interest is longer than the sam-
pling time (i.e. the time resolution), it is possible to suppress
random noise between neighboring pixels by applying a low-
pass filter. A circular Gaussian filter is used with σ=0.85 pixel
4 F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783
Time (ks)
Energy (keV)
0 0.05
 Excess (ph/2500s/cm^2)
0 50 100 150 200 250
Time (ks)
Energy (keV)
0 0.02 0.04 0.06
 Excess (ph/2500s/cm^2)
Fig. 3. The excess emission maps of the 4–9 keV band in the time-energy plane at 2.5 ks time resolution. The images have been
smoothed. Since the 6.4 keV line core is very strong and stable, the color map is adjusted to saturate the line core and allow
lower surface brightness features to be visible. Left panel: excess emission map from the 2000 observation. Right panel: excess
emission map from the 2001a and 2001b observations.
(200 eV in energy and 5 ks in time, FWHM). The excess map
Gaussian-filtered images for each observation are shown in
Fig. 3. Systematic variations are observed in the 5.3–5.4 keV
and in the 5.8–6.1 keV energy bands of the 2001b observation.
However, the image filtering can slightly smear these narrow
features and reduce their intensity.
5. Results
5.1. Light curves of the individual spectral features
Light curves of the four emission features are extracted from
the excess map filtered images. The selected band-passes are
listed in Tab. 2. During the image filtering process individ-
ual pixels lose their independence to the neighbouring ones.
This means that a simple counting statistics may be inappro-
priate for estimating the features light curves errors. For this
reason the estimation of the errors has been done by exten-
sive Monte Carlo simulations. We implemented 1000 simula-
tions following the same procedure in making the excess map
images. In the simulations all the spectral features parameters
and the power-law slope are assumed to be constant, while let-
ting the power-law normalization vary according to the 0.3–10
keV light curve. Light curves of individual spectral features
have been extracted from each simulation and their mean val-
ues and variances recorded. The square root of the mean of the
variances (i.e. the dispersion) has been regarded as the light
curves error. In Fig. 4 the emission features light curves for the
2001a and 2001b observations are shown. The 2000 observa-
tion light curves are not reported because they do not show any
sign of variability. The most intense variations are registered
in the light curves of the “red” (E=5.3–5.4 keV) and “wing”
(E=5.8–6.1 keV) features during the 2001b observation. The
observed peaks seem to follow the same kind of variability
pattern and, as shown in more details below, appear to be in
phase with the continuum emission. In order to check the sig-
nificance of the observed variability we extracted both real and
simulated data light curves in the entire 5.3–6.1 keV band, i.e.
of the “red+wing” structure. Then we compared the χ2 values
against a constant hypothesis for the real data and the 1000
simulations; equivalent results can be derived comparing the
variances directly. Only 73 of the simulations show variability
at the same level or greater than the real data, therefore we get
a variability confidence level of 93%.
The light curves of the excess emission features in the 5–6 keV
energy band (red, wing and red+wing) seem to show a variabil-
ity pattern with a recurrence of the flux peaks on time-scales
of 27 ks. We further investigated how it is likely to occur by
chance applying a method that makes use of the 1000 Monte
Carlo simulations. We folded the real data light curve with the
interval of 27 ks and we fitted it with a constant. We obtained a
χ2r = 88 for 19 degrees of freedom. We did the same to the simu-
lated red+wing light curves but, this time, folding in n = 9 trial
periods, from 17 to 37 ks at intervals of 2.5 ks, and recorded
the χ2i values. If N is the total number of simulated red+wing
light curves for which χ2i ≥ χ
r , the confidence level can be de-
F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783 5
/s Continuum
8 Core
0 105 2×105
Time (s)
Kbeta
Fig. 4. The light curves of the total 0.3–10 keV continuum
flux and of the four spectral features (Tab. 2) extracted from
the excess maps of the 2001a and 2001b observations (Fig. 3,
Right panel), with errors computed from simulations. The time
resolution is 2.5 ks.
rived as (1 − N1000·n ). Only N = 54 of the simulated red+wing
light curves folded at the trial periods show chi-square values
greater than the real one. Therefore, we could derive a confi-
dence level for the recurrence pattern on the 27 ks time scale of
99.4%.
Finally, we checked that the continuum above 7 keV (which
carries the photons eventually responsible for the Fe line pro-
duction) varies following the same pattern of the 0.3–10 keV
band (Fig. 4, Top panel).
5.2. Correlation with the continuum light curve
In the 0.3–10 keV light curve of observation 2001b (Fig. 5,
Upper panel) flux variations of ∼30% are visible with four
peaks separated by approximately equal time intervals. Given
such peculiar time series shape, we focused on this observa-
tion and searched for some typical time-scale in the variability
pattern. Thus, we applied the efsearch task (in Xronos), which
searches for periodicities in a time series calculating the maxi-
mum chi-square of the folded light curve over a range of peri-
ods. We found a typical time-scale for variability of 26.6±2.2
ks. We then removed the underlying long-term variability trend
by subtracting a 4th degree polynomial to the 0.3–10 keV con-
tinuum light curve (see Fig. 5, Middle panel). The polynomial
has been determined using the lcurve task (in Xronos), which
makes use of the least-square technique. Applying again the
efsearch task we found a typical time-scale for short-term vari-
ability of ∼27.4 ks1. The peaks observed in the continuum light
curve seem to appear at the same times at which those ob-
served in the “wing” and “red” light curves do. In order to look
1 It should be noted that the variability PSD study of this XMM-
Newton dataset by Markowitz (2005) suggests an excess of power
around 4×10−5 Hz (corresponding to about 25 ks) during the 2001b
observation (square symbols in his Fig. 3).
0.3−10 keV
0.3−10 keV
0 5×104 105
Time (s)
Red+Wing
Fig. 5. Upper panel: The 0.3–10 keV light curve of NGC 3783
during 2001b observation at 2.5 ks time resolution. Middle
panel: The 0.3–10 keV light curve of NGC 3783 during the
2001b observation after subtraction of a 4th degree polynomial
(long-term variations) at 2.5 ks time resolution. Lower panel:
The 5.3–6.1 keV (“red+wing” energy band) light curve ex-
tracted from the excess emission map of the 2001b observation
(Fig. 3, Right panel) at 2.5 ks time resolution.
for some correlation between the continuum and the 5.3–6.1
keV (“red+wing”) feature flux we computed the cross corre-
lation function (CCF) between the two time series, where the
input continuum light curve is the “de-trended” one. It is re-
ported in Fig. 6 as a function of time delay, measured with
respect to the continuum flux variations. No delay is evident,
with an estimated error at the peak of 2.5 ks. The continuum
and “red+wing” fluxes seem to show a correlation, with peak
value 0.7. To estimate the significance of the correlation we
computed the CCFs between the continuum and the simulated
“red+wing” light curves. If N is the number of simulated light
curves which have a higher cross correlation than the real one,
the significance of the correlation is (1 − N/1000). Applying
this method we found a confidence level greater than 99.9%.
5.3. High/Low flux state line profiles
Looking at the “red+wing” light curve (Fig. 5, Lower panel)
we constructed two spectra from the integrated high and low
flux intervals to verify the variability in this energy band. The
line profiles are shown in Fig. 7 where the ratio between the
data and a simple power-law plus cold absorption model is
shown. While the 6.4 keV and 6.9 keV features remain the
same, a small increase of counts is visible in the 5.3–5.4 keV
and 5.8–6.1 keV bands in the high flux state. Adding an emis-
sion Gaussian model to the simple power law plus Gaussian
line (at the Fe Kα energy) model in the high flux state inte-
grated spectra improves the χ2 of 18. Thus the significance of
the excess is ∼99.9%.
6 F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783
−104 0 104−
Time Delay (s)
Fig. 6. The cross correlation function calculated between the
de-trended 0.3–10 keV continuum light curve and the 5.3–6.1
keV feature (“red+wing”) light curve.
.4 HIGH
6 7 8
Energy (keV)
Fig. 7. The Fe K line profile during the High flux (open
squares) and the Low flux (solid circles) phases of the 5.3–6.1
keV feature. The ratios are computed against the best-fitting
continuum model. The energies are in the observer frame.
6. Discussion
In the 2001b observation, NGC 3783 clearly exhibits contin-
uum emission with two different time-scales: a long-term mod-
ulation with variations up to a factor 2 on intervals greater than
60 ks is superimposed to a shorter one on a time-scale of 27
ks, with modulations of 30% of the average value. According
to an estimated black hole mass of MBH = (3.0±0.5)×10
(Peterson et al. 2004), the latter modulation occurs with a
characteristic time-scale corresponding to the orbital period at
∼9–10 rg (e.g. Bardeen, Press & Teukolsky (1972)). It should
be noted, however, that a previous mass estimate by Onken &
Peterson (2002) gave the value of MBH = (8.7± 1.1)× 10
6 M⊙,
that would correspond to ∼20 rg. These mass discrepancies are
mainly due to a different scaling of the virial relation in per-
forming reverberation mapping measurements. However, the
former estimate is more accurate because it has been calibrated
to the MBH −σ relation and thus we will adopt this value in the
following discussion. The power spectral density of the source
is consistent with a red-noise shape (Markowitz 2005) where
variability mainly occurs on intervals of the order of days. Here
we identify an additional (additive) shorter time-scale compo-
nent (see the footnote 1), most likely produced within the in-
nermost accretion flow/corona system.
The most remarkable result of our analysis is the detec-
tion of redshifted (5.3–6.1 keV) Fe K emission and of its vari-
ability. The redshifted emission appears to respond only to the
shorter ∼27 ks time-scale modulation and shows a good cor-
relation with the continuum with a time-lag consistent with
zero within the errors (∆τ ∼ 1.25 ks). This indicates that the
continuum modulation on this time interval is likely to induce
Fe K emission from dense material close to the black hole
(which explains the observed redshift of the emission feature);
moreover the lack of time-lags implies that the distance be-
tween the sites of continuum and line production is smaller than
c∆τ ∼ 4×1013 cm ∼ 8 rg (for the black hole mass given above).
We are therefore most likely observing emission from the in-
nermost accretion flow in both the continuum and line emission
(corona and disc).
As discussed above, the variability time-scale suggests we
are looking at emission from around ∼9–10 rg. As a consis-
tency check, we fitted the time-averaged spectrum by including
a diskline component to account for the redshifted features. We
forced the emission region to be an annulus of ∆r= 0.5 rg with
uniform emissivity because the purpose of this test is to as-
sess the approximate location of the line-emitting region. We
obtain good fits with an almost face-on disc (i = 11 ± 4◦)
and an annulus at 9–15 rg depending on the assumed Fe line
rest-frame energy (from neutral at 6.4 keV to highly ionized
at 6.97 keV). For all cases we tested, the statistical improve-
ment is of ∆χ2 ∼ 16 for 3 additional degrees of freedom, cor-
responding to a confidence level of 99.7%. This fit shows that
the redshifted Fe line emission we detected is indeed consistent
in shape with being produced around 10 rg, where the disc or-
bital period is of the order of 27 ks, which agrees well with the
correlated (and zero-lag) variability of the two components.
The interpretation of our results is however not straightfor-
ward. The quasi-sinusoidal modulations of the continuum and
line emission (see Fig. 5) would suggest the presence of a local-
ized co-rotating flare above the accretion disc which irradiates
a small spot on its surface. The intensity modulations we see
(Fig. 5) would then be produced by Doppler beaming effects
(acting on both the flare and spot emission, i.e. on both contin-
uum and line) and the characteristic time-scale of 27 ks would
be identified with the orbital period (because of gravitational
time dilation, the period measured by an observer on the disc
at 10 rg would be shorter by ∼10%). As demonstrated above, a
flare/spot system orbiting the black hole at ∼10 rg would also
produce a time-averaged line profile in agreement with the ob-
servations. However, such a model makes definite prediction
on the Fe line energy modulation within one orbital period. In
this framework, the orbiting spot on the accretion disc would
also give rise to energy modulations of the Fe line due to the
Doppler effect and such energy modulation is barely seen in
the data (see Fig. 3). We stress that the adopted time resolu-
tion (2.5 ks) is good enough to detect energy modulations with
a characteristic 27 ks time-scale. This has been demonstrated
with XMM-Newton in the case of NGC 3516, where the modu-
lation occurs on a very similar time-scale (Iwasawa et al. 2004;
F. Tombesi et al.: Correlated modulation between the redshifted Fe Kα line and the continuum emission in NGC 3783 7
see also Dovčiak et al. 2004 for theoretical models). Therefore,
the lack of Fe line energy modulation disfavours the orbiting
flare/spot interpretation for NGC 3783.
However, a variability time-scale of the order of the orbital
one at a given radius does not necessarily imply the motion of
a point-like X-ray source. In fact, since the orbital time-scale is
the fastest at a given disc radius, and since the observed time-
scale of ∼27 ks corresponds to the orbital period at ∼10 rg, one
could argue that the data only imply that the X-ray variability
likely originates from within ∼10 rg. The apparent recurrence
in the X-ray continuum modulation may not necessarily be re-
lated to a real physical periodicity, especially considering the
limited length of the observation (only four putative cycles are
detected).
A possible explanation for the observed behaviour is that
the X-ray continuum source(s) (located within ∼10 rg from
the center) irradiates the whole accretion disc, but only a ring-
like structure around 10 rg is responsible for the fluorescent Fe
emission. This is possible if the bulk of the accretion disc is
so highly ionized that little Fe line is produced, while an over-
dense (and therefore lower ionization) structure is responsible
for the fluorescent emission. Such an over-dense region could
have an approximate ring-like geometry if it is for instance as-
sociated with a spiral-wave density perturbation. In this case,
the Fe emitting region is extended in the azimuthal direction
and we do not expect strong energy modulation with time,
whatever the origin of the continuum modulation. We point out
that spiral density distributions could result from the ordered
magnetic fields in the inner region of the disc and that the en-
ergy dissipation (via e.g. magnetic reconnection) could be en-
hanced there, thereby providing a common site for the produc-
tion of the X-ray continuum and the Fe line (e.g. Machida &
Matsumoto 2003).
On the other hand, if the apparent recurrence is in fact
real, it is worth noting that the continuous theoretical effort in
understanding the origin of quasi-periodic oscillations (QPO)
in neutron star and black hole systems provides a wealth of
mechanisms inducing quasi-periodic variability, although none
is firmly established (Psaltis 2001; Kato 2001; Rezzolla et al.
2003; Lee et al. 2004; Zycki & Sobolewska 2005 and many
others). A connection between QPO phase and Fe line inten-
sity has been previously claimed in the Galactic black hole
GRS 1915+105 (Miller & Homan 2005). Although in our case,
the presence of a QPO cannot be claimed because of the very
small number of detected cycles, the analogy is suggestive. In
the case of GRS 1915+105, Miller & Homan consider that a
warp in the inner disc, possibly due to Lense-Thirring preces-
sion, may produce the observed QPO-Fe line connection (e.g.
Markovic & Lamb 1998). However, to produce the observed
∼15% rms variability in the X-ray lightcurve, the black hole
spin axis should be inclined with respect to the line of sight by
at least 60◦ (which is at odds with our inclination estimate of
11±4◦ and with the Seyfert 1 nature of NGC 3783), and the tilt
precession angle should be larger than 20◦–30◦ (Schnittman,
Homan, Miller 2006). Both requirements make it highly un-
likely that Lense-Thirring precession can successfully account
for the observed modulations in NGC 3783.
While the origin of the coherent intensity modulation still
remains unclear, the correlated variation of the continuum and
line emission and the Fe line shape are consistent with an emis-
sion site at ∼10 rg. Moreover, the fact that the iron line variabil-
ity responds to the 27 ks time-scale modulation only implies
that this short time-scale variation is somehow detached from
the long-term variability. The latter may be associated with per-
turbations in the accretion disc propagating inwards from outer
radii and modulating the X-ray emitting region (Lyubarskii
1997), while the former seems to genuinely originate in the
inner disc.
Further observational data may help to clarify the complex
phenomena related to the relativistic Fe line temporal evolu-
tion in Seyfert 1 galaxies. Our work makes it clear that higher
quality data in the Fe band will be able to probe the inner-
most regions of accretion flows with high accuracy. Next gen-
eration of large collecting area X-ray missions such as XEUS
and Constellation-X or even very long observations with XMM-
Newton will be crucial to fully exploit such potential.
Acknowledgements. This paper is based on observations obtained
with the XMM-Newton satellite, an ESA funded mission with con-
tributions by ESA Member States and USA. We thank A. Müller, K.
Nandra, L. Nicastro, P. O’Neill and M. Orlandini for useful discus-
sions. MC, MD and GP acknowledge financial support from ASI un-
der contract ASI/INAF I/023/05/0. The authors thank the anonymous
referee for suggestions that led to improvements in the paper.
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	Introduction
	XMM-Newton observations
	Data analysis
	Spectral features of interest and selection of the energy resolution
	Selection of the time resolution
	Excess emission maps
	Continuum subtraction
	Image smoothing
	Results
	Light curves of the individual spectral features
	Correlation with the continuum light curve
	High/Low flux state line profiles
	Discussion
