20 research outputs found
Simultaneous spectral and reverberation modelling of relativistic reflection in Mrk 335
We present an X-ray spectral and timing model to investigate the broad and
variable iron line seen in the high flux state of Mrk 335. The model consists
of a variable X-ray source positioned along the rotation axis of the black hole
that illuminates the accretion disc producing a back-scattered, ionized
reflection spectrum. We compute time lags including full dilution effects and
perform simultaneous fitting of the 2-10 keV spectrum and the
frequency-dependent time lags of 2.5-4 vs. 4-6.5 keV bands. The best-fitting
parameters are consistent with a black hole mass of approximately 1.3 x 10^7
M_sun, disc inclination of 45 degrees and the photon index of the direct
continuum of 2.4. The iron abundance is 0.5 and the ionization parameter is
10^3 erg cm / s at the innermost part of the disc and decreases further out.
The X-ray source height is very small, approximately 2 r_g. Furthermore, we fit
the Fe L lags simultaneously with the 0.3-10 keV spectrum. The key parameters
are comparable to those previously obtained. We also report the differences
below 2 keV using the xillver and reflionx models which could affect the
interpretation of the soft excess. While simultaneously fitting spectroscopic
and timing data can break the degeneracy between the source height and the
black hole mass, we find that the measurements of the source height and the
central mass significantly depend on the ionization state of the disc and are
possibly model-dependent.Comment: 11 pages, 8 figures, accepted for publication in MNRA
X-ray time lags in AGN: inverse-Compton scattering and spherical corona model
We develop a physically motivated, spherical corona model to investigate the
frequency-dependent time lags in AGN. The model includes the effects of Compton
up-scattering between the disc UV photons and coronal electrons, and the
subsequent X-ray reverberation from the disc. The time lags are associated with
the time required for multiple scatterings to boost UV photons up to soft and
hard X-ray energies, and the light crossing time the photons take to reach the
observer. This model can reproduce not only low-frequency hard and
high-frequency soft lags, but also the clear bumps and wiggles in reverberation
profiles which should explain the wavy-residuals currently observed in some
AGN. Our model supports an anti-correlation between the optical depth and
coronal temperatures. In case of an optically thin corona, time delays due to
propagating fluctuations may be required to reproduce observed time lags. We
fit the model to the lag-frequency data of 1H0707-495, Ark 564, NGC 4051 and
IRAS 13224-3809 estimated using the minimal bias technique so that the observed
lags here are highest-possible quality. We find their corona size is ~7-15 r_g
having the constrained optical depth ~2-10. The coronal temperature is ~150-300
keV. Finally, we note that the reverberation wiggles may be signatures of
repeating scatters inside the corona that control the distribution of X-ray
sources.Comment: 15 pages, 10 figures, accepted for publication in MNRA
Investigating scaling relations in X-ray reverberating AGN using symbolic regression
Symbolic regression (SR) is a regression analysis based on genetic algorithms
to search for mathematical expressions that best fit a given data set, by
allowing the expressions themselves to mutate. We use the SR to analyze the
parameter relations of the X-ray reverberating Active Galactic Nuclei (AGN)
where the soft Fe-L lags were observed by XMM-Newton. Firstly, we revisit the
lag-mass scaling relations by using the SR to derive all possible mathematical
expressions and test them in terms of accuracy, simplicity and robustness. We
find that the correlation between the lags, , and the black hole mass,
, is certain, but the relation should be written in the form of
, where
. Moreover, incorporating more parameters such as
the reflection fraction () and the Eddington ratio () to
the lag-mass scaling relation is made possible by the SR. It reveals that
, rather than being a constant, can be or , with the fine-tuned different and . These
further support the relativistic disc-reflection framework in which such
functional dependencies can be straightforwardly explained. Furthermore, we
derive their host-galaxy mass, , by fitting the spectral energy
distribution (SED). We find that the SR model supports a non-linear -- relationship, while varies
between and , with an average value of . No significant
correlation between and is confirmed in these
samples.Comment: 14 pages, 7 figures, 2 tables, accepted for publication in MNRA
Coronal height constraint in IRAS 13224-3809 and 1H 0707-495 by the random forest regressor
We develop a random forest regressor (RFR) machine learning model to trace
the coronal evolution in two highly variable active galactic nuclei (AGNs) IRAS
13224-3809 and 1H 0707-495 observed with XMM-Newton, by probing the X-ray
reverberation features imprinted on their power spectral density (PSD)
profiles. Simulated PSDs in the form of a power-law, with similar frequency
range and bins to the observed data, are produced. Then, they are convolved
with relativistic disc-response functions from a lamp-post source before being
used to train and test the model to predict the coronal height. We remove some
bins that are dominated by Poisson noise and find that the model can tolerate
the frequency-bin removal up to bins to maintain a prediction
accuracy of . The black hole mass and inclination should be fixed
so that the accuracy in predicting the source height is still . The
accuracy also increases with the reflection fraction. The corona heights for
both AGN are then predicted using the RFR model developed from the simulated
PSDs whose frequency range and bins are specifically adjusted to match those
from each individual observation. The model suggests that their corona varies
between , with for all observations. Such
high accuracy can still be obtained if the difference between the true mass and
the trained value is . Finally, the model supports the
height-changing corona under the light-bending scenario where the height is
correlated to source luminosity in both IRAS 13224-3809 and 1H 0707-495.Comment: 9 Figures, 1 Table, Accepted for publication in MNRA
Simultaneous spectral and reverberation modelling of relativistic reflection in Mrk 335
Extended Corona Models of X-ray Reverberation in the AGN 1HΒ 0707-495 and IRAS 13224-3809
Predicting the black hole mass and correlations in X-ray reverberating AGNs using neural networks
We develop neural network models to predict the black hole mass using 22
reverberating AGN samples in the XMM-Newton archive. The model features include
the fractional excess variance () in 2-10 keV band, Fe-K lag
amplitude, 2-10 keV photon counts and redshift. We find that the prediction
accuracy of the neural network model is significantly higher than what is
obtained from the traditional linear regression method. Our predicted mass can
be confined within -5) per cent of the true value, suggesting that the
neural network technique is a promising and independent way to constrain the
black hole mass. We also apply the model to 21 non-reverberating AGN to rule
out their possibility to exhibit the lags (some have too small mass and , while some have too large mass and that contradict the
-lag-mass relation in reverberating AGN). We also simulate 3200
reverberating AGN samples using the multi-feature parameter space from the
neural network model to investigate the global relations if the number of
reverberating AGN increases. We find that the -mass
anti-correlation is likely stronger with increasing number of newly-discovered
reverberating AGN. Contrarily, to maintain the lag-mass scaling relation, the
tight anti-correlation between the lag and must preserve. In an
extreme case, the lag-mass correlation coefficient can significantly decrease
and, if observed, may suggest the extended corona framework where their
observed lags are more driven by the coronal property rather than geometry.Comment: 15 pages, 12 figures, 4 tables, accepted for publication in MNRA
Effects of the refractive index of the X-ray corona on the emission lines in AGNs
X-ray reflection from an accretion disc produces characteristic emission
lines allowing us to probe the innermost regions in AGN. We investigate these
emission lines under a framework of Riemannian geometrical optics where the
corona has a refractive index of . The empty space outside is a
vacuum with . The Kerr metric is modified to trace the light rays that
are bent due to not only the gravity of the black hole, but also the effects of
coronal plasma dependent on . The choice of alters the null geodesics,
producing the effect which is analogous to the light deflection. For the corona
with , the disc on the far side within the corona covers a larger area
on the observer' sky, enhancing the blue wing of the line and producing more
flux difference between the blue peak and extended red tail. The inverse
effects are seen when and
could induce extra shifts in the blue wing () to higher and
lower energy, respectively. These effects are more prominent when the
inclination angle is and the corona extends to . To obtain the deviation of the line shift of , the difference between the refractive index of the corona and that of
the empty space must be . Finally, the lensing corona
can influence the arrival time of photons that may affect the observed
variability of these emission linesComment: 12 pages, 11 figures, accepted for publication in MNRA