# Comparing Reflection and Absorption Models for the Soft X-ray Variability in
the NLS1 AGN UGC 11763

Jiachen Jiang,1 Luigi C. Gallo,2 Dirk Grupe,3,4 Michael L. Parker1
1Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge
CB3 0HA, UK
2Department of Astronomy and Physics, Saint Mary’s University, 923 Robie
Street, Halifax, NS, B3H 3C3, Canada
3blackDepartment of Physics, Geology and Engineering Technology, Northern
Kentucky University, Nunn Drive, Highland Heights, KY 41099, USA
4Department of Physics, Earth Science, and Space System Engineering, Morehead
State University, 235 Martindale Dr, Morehead, KY 40351, USA
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present a spectral analysis of two XMM-Newton observations of the narrow-
line Seyfert 1 galaxy UGC 11763. UGC 11763 shows very different soft X-ray
spectral shapes in the two observations separated by 12 years. Three spectral
models are considered to explain the multi-epoch X-ray variability of UGC
11763, blackone based on the relativistic disc reflection model, one based on
multiple partially-covering absorbers combined with the warm corona model, and
a hybrid model. In the first model, the X-ray variability of UGC 11763 is
caused by the emission from a compact coronal region with a variable size. The
resulting disc reflection component changes accordingly. A warm absorption
model with a modest column density is required in this model too. In the
blackpartially-covering absorption scenario, the X-ray variability of UGC
11763 is caused by the variable covering factors of two absorbers located
within a region of $r<\approx 100r_{\rm g}$. Moreover, the temperature and
strength of the warm corona have to change significantly too to explain the
variable underlying soft X-ray emission. Lastly, we investigate the
possibility of variable blackintrinsic power-law emission from the hot corona
combined with variable absorption in UGC 11763 blackwithout changing the
geometry of the corona in the third model. This hybrid model provides a
slightly better fit than the blackpartially-covering absorption model with
improvements in fitting the iron emission band. Current CCD-resolution data
cannot distinguish these spectral models for UGC 11763. Future high-resolution
X-ray missions, e.g. Athena and XRISM, will test them by resolving different
spectral components.

###### keywords:

accretion, accretion discs - black hole physics, X-ray: galaxies, galaxies:
Seyfert

††pubyear: 2022††pagerange: Comparing Reflection and Absorption Models for the
Soft X-ray Variability in the NLS1 AGN UGC 11763–Comparing Reflection and
Absorption Models for the Soft X-ray Variability in the NLS1 AGN UGC 11763

##  1 Introduction

Narrow-line Seyfert 1 galaxies (NLS1s) are a class of peculiar Seyfert 1
galaxies (Sy1s) with strong Fe ii emission, narrow H$\beta$ emission and weak
[O iii] emission in the optical band in comparison with other Sy1s (Goodrich,
1989). It is believed that NLS1s host low-mass supermassive black holes (BHs)
that are accreting near or around the Eddington limit (e.g. Boroson, 2002;
Grupe & Mathur, 2004), although some studies point out that the BH mass
measurements of NLS1s might be biased towards low values when radiation
pressure is ignored in the broad line region model for the H$\beta$ emission
of NLS1s (Marconi et al., 2008).

In the X-ray band, the nuclei of NLS1s often show rapid, large-amplitude X-ray
variability (e.g. McHardy et al., 1995; Boller et al., 2003; Smith & Vaughan,
2007; Jin et al., 2017; Alston et al., 2019) and steep X-ray continuum
emission (Puchnarewicz et al., 1992; Boller et al., 1996; Grupe et al., 1998).
Gallo (2006) finds that NLS1s show complex spectral features in the X-ray
band, especially during their low flux state. In particular, NLS1s often show
strong excess emission below 2–3 keV in addition to the hard X-ray continuum
extrapolated to the soft X-ray band (Boller et al., 1996; Piconcelli et al.,
2005).

Different models have been proposed to explain the broad-band X-ray spectra of
NLS1s (see a review of this topic in Gallo, 2018). One of them is the disc
reflection model (e.g. Fabian et al., 2004; Larsson et al., 2008; Miniutti et
al., 2009; Brenneman et al., 2011; Reis et al., 2012; Tan et al., 2012;
Risaliti et al., 2013; Gallo et al., 2013; Walton et al., 2013; Parker et al.,
2014a; Marinucci et al., 2014; Jiang et al., 2019b; Jiang et al., 2020). The
surface of the optically thick disc produces reprocessed emission of the
illuminating coronal emission in the soft X-ray band and the Compton-
scattering hump in the hard X-ray band. They are often referred to as the disc
‘reflection’ component (Fabian et al., 1989). The most prominent feature of a
disc reflection component is the Fe K$\alpha$ emission line around 6.4 keV,
which is broadened by relativistic effects in the vicinity of the BH (Tanaka
et al., 1995). The disc reflection model of Seyfert active galactic nuclei
(AGNs) is also supported by the discoveries of X-ray reverberation lags in the
soft X-ray band (e.g. Fabian et al., 2009; De Marco et al., 2013), the Fe K
band (e.g. Kara et al., 2016) and the hard X-ray band (e.g. Zoghbi et al.,
2014; Kara et al., 2015)

Another model used to explain X-ray spectra of Sy1s is the double partially-
covering absorption model (Tanaka et al., 2004). In this model, multiple high-
column density absorbers crosses our line of sight towards the X-ray emission
region. The absorbers require a tricky geometry to partially cover the compact
X-ray emission region as suggested by X-ray data (Reynolds et al., 2009). In
this model, the absorbers produce strong Fe K edge in the spectrum, which is
used to explain the steep spectra of some NLS1s (e.g. Gallo et al., 2015).

An additional component is still required to fit the soft excess emission when
one uses the absorption model to fit the data in the Fe K band. For instance,
a soft power-law model was used to explain the soft excess emission of the
NLS1 1H 0707$-$495 in combination with the absorption model in Tanaka et al.
(2004). Such a soft power-law component is proposed to originate in a warm
coronal region with a high optical depth of $\tau_{\rm T}=10-20$ and a low
temperature of $kT_{\rm e}<1$ keV (Magdziarz et al., 1998; Petrucci et al.,
2001; Czerny et al., 2003; Jin et al., 2017; Ursini et al., 2020). At such a
low temperature, atomic opacity dominates over the Thomson opacity. Strong
emission and absorption features could be shown in the spectrum of the warm
corona in contradiction to the data of Sy1s (Garcia et al., 2018). Simulations
by Petrucci et al. (2020), however, suggest that the warm corona has to be
heated by hard X-ray continuum from the hot corona and the disc emission from
below, where the ions in the upper layer of the warm corona can be completely
ionised showing no or weak emission and absorption lines. Photoionisation
models also find that a higher accretion rate in the accretion disc leads to a
warm corona producing stronger soft excess emission, similar to what is
suggested by the X-ray data of Sy1s (Ballantyne, 2020).

In this work, we investigate how the models introduced above may explain the
XMM-Newton observations of the blackactive galaxy UGC 11763 at $z=0.063$ (23
32 27.8, +10 08 19, Clements, 1981; Huchra et al., 1999). blackUGC 11763 was
classified as a NLS1 galaxy by Boroson & Green (1992); Constantin & Shields
(2003). The H$\beta$ emission of this NLS1 has a width of 2250–2800 km s-1
(Boroson & Green, 1992; Grupe et al., 2004a; Mullaney & Ward, 2008), which is
higher than the values of typical NLS1s. The mass of the central BH in UGC
11763 is estimated to be around $4.57\times 10^{8}M_{\odot}$ (Peterson et al.,
2004) blackusing broad emission-line reverberation-mapping data. Ho et al.
(2008) further lowered this mass measurement by a factor of 1.8 to $2.5\times
10^{8}M_{\odot}$ for consistency with the virial mass zero point111blackSee
Footnote 4 in Greene & Ho (2005). adopted by (Greene & Ho, 2005). These
measurements are near the upper limit of the BH mass distribution of NLS1s
(Grupe et al., 2004a). Peterson et al. (2004) estimated the luminosity of UGC
11763 at 5100Å to be $\log(\lambda L_{\lambda})=44.46\pm 0.04$. Assuming
$L_{\rm Bol}=9\lambda L_{\lambda}$ (Kaspi et al., 2000) and a BH mass of
$4.6\times 10^{8}$ $M_{\odot}$ (Peterson et al., 2004), the Eddington ratio of
UGC 11763 is around 5%.

In the X-ray band, Cardaci et al. (2009) reported a steep X-ray emission from
UGC 11763 and strong soft excess emission as well as the EXOSAT data of the
same source (Singh et al., 1991). Cardaci et al. (2009) also found Fe
‘Unresolved Transition Array’ (UTA) absorption in the soft X-ray band of UGC
11763, which indicates the existence of photoionised absorbers, e.g. warm
absorption commonly seen in AGNs (e.g. Reynolds, 1997; George et al., 1998).
Large-amplitude X-ray variability of UGC 11763 has been realised for decades
and was first discovered by Singh et al. (1991); Grupe et al. (2001). For
instance, the X-ray flux of this source measured by ROSAT varies by 50% in the
0.1–2 keV band in only one year.

In this paper, we present spectral analysis of the XMM-Newton data of UGC
11763 using two archival observations. We consider both the reflection-based
and the absorption-based model. In Section 2, we introduce our data reduction
processes; in Section 4, we present three models for the spectra of UGC 11763;
in Section 5, we discuss our results; in Section 6, we conclude our work.

##  2 Data Reduction

Table 1: The list of XMM-Newton observations analysed in this work. $F_{\rm 0.3-3keV}$ and $F_{\rm 3-10keV}$ are the observed flux of UGC 11763 measured by pn in corresponding energy bands. Name | Obs ID | Date | Time | $\log(F_{\rm 0.3-3keV})$ | $\log(F_{\rm 3-10keV})$
---|---|---|---|---|---
|  |  | ks | erg cm-2 s-1 | erg cm-2 s-1
obs1 | 0150470701 | 2003-05-16 | 38 | $-11.467\pm 0.002$ | $-11.535^{+0.009}_{-0.007}$
obs2 | 0744370201 | 2015-05-01 | 33 | $-11.141\pm 0.005$ | $-11.483\pm 0.019$
Figure 1: Long-term X-ray lightcurves of UGC 11763 in units of $10^{-12}$ erg
cm-2 s-1 (top: 0.5–2 keV; bottom: 2–10 keV; black circles: Swift XRT observed
flux; red squares: XMM-Newton pn observed flux). The error bars of the red
squares are smaller than the sizes of points. The dashed lines show the
average flux of UGC 11763 in the two energy bands.

We use the European Photon Imaging Camera (EPIC) observations for X-ray
continuum modelling. A full list of observations used in our work is in Table
1.

The EPIC data are reduced using blackV20.0 of the XMM-Newton Science Analysis
System (SAS) software package. The version of the calibration files is
v.black20220407. We first generate a clean event file by running EMPROC (for
EPIC-MOS data) and EPPROC (for EPIC-pn data). Then, we select good time
intervals by filtering out the intervals that are dominated by flaring
particle background. These high-background intervals are where the single
event (PATTERN=0) count rate in the >10 keV band is larger than 0.35 counts
s-1 (0.4 counts s-1) for MOS (pn) data. By running the EVSELECT task, we
select single and double events for EPIC-MOS (PATTERN<=12) and EPIC-pn
(PATTERN<=4, FLAG==0) source event lists from a circular source region of 35
arcsec. Background spectra are extracted from a nearby circular region of 60
arcsec. No obvious evidence of pile-up effects has been found in obs1 in 2003.
The pn and MOS instruments were operated in the full frame mode in 2015. Some
evidence of pile-up effects were found. An annulus region with an inner radius
of 10 arcsec and an outer radius of 35 arcsec is used to extract source
spectra. The inner radius is chosen according to the EPATPLOT tool in
SAS222blackWe use EPATPLOT to estimate the full-band observed-to-model ratios
for single and double events based on expected pattern distribution functions
from the latest calibration data. This ratio is $0.96\pm 0.01$ for singles and
$1.12\pm 0.02$ for doubles when a circular region is used to extract source
products from the pn observation, suggesting evidence of pile-up. Singles and
doubles ratios are respectively $0.99\pm 0.02$ and $1.03\pm 0.04$ when an
annulus region with an inner radius of 10 arcsec is used. Similar conclusions
are found for MOS observations.. Last, we create redistribution matrix files
and ancillary response files by running RMFGEN and ARFGEN. In this work, we
consider the full 0.3–10 keV band of EPIC data. The spectra are grouped to
have a minimum of 20 counts per bin and oversample by a factor of 3.

##  3 Soft X-ray Variability of UGC 11763

Figure 2: XMM-Newton pn lightcurves of UGC 11763 in the 3–10 keV and 0.3–3 keV
bands (left: obs1; right: obs2). Note that the y-axes are in log scale. The
bottom panels show the hardness ratio defined as the count rate ratio between
3–10 keV and 0.3–3 keV bands. Unlike typical NLS1s, UGC 11763 does not show
extreme X-ray variability on timescales of kiloseconds.

Fig. 1 shows the long-term X-ray lightcurves of UGC 11763 in the 0.5–2 keV and
2–10 keV bands. In particular, the XMM-Newton observations analysed in this
work are marked with the red squares in the figure. The X-ray flux of UGC
11763 shows variability on timescales of months and years . For instance, the
0.5–2 keV flux of this source increased from the reported minimum flux of
$1.6\times 10^{-12}$ erg cm-2 s-1 in April 2011 to the maximum flux $8.3\times
10^{-12}$ erg cm-2 s-1 in April 2014. X-ray variability with a similar
amplitude was realised in previous observations (Singh et al., 1991; Grupe et
al., 2001).

In this work, we focus on the XMM-Newton observations of this source. The
first observation was taken during a low flux state and the second was taken
during a higher flux state in the soft X-ray band. In comparison with the soft
X-ray band, the 2–10 keV flux of UGC 11763 does not show large amplitude
variability. This leads to the question–what may cause the X-ray variability
of UGC 11763 confined below 2 keV.

We show EPIC-pn lightcurves extracted from the two XMM-Newton observations in
Fig. 2. Unlike other extreme NLS1s (e.g. McHardy et al., 1995; Boller et al.,
2003; Smith & Vaughan, 2007; Jin et al., 2017; Alston et al., 2019), UGC 11763
does not show rapid and large-amplitude variability on timescales of
kiloseconds in the X-ray band. The lack of rapid variability on kilosecond
timescales and the evidence of large-amplitude variability on longer
timescales might be related to the relatively higher BH mass of UGC 11763 (a
few times $10^{8}M_{\odot}$, Peterson et al., 2004; Ho et al., 2008) in
comparison with other NLS1s.

##  4 Spectral Analysis

Figure 3: Top: folded EPIC-pn spectra of UGC 11763 corrected for effective
area. Two observations, separate by 12 years, show significantly different
soft X-ray emission below 1 keV. Bottom: data/model ratio plots of the pn
spectra of UGC 11763 using the best-fit absorbed power-law model for the 1–10
keV band of each observation. The smaller panel zooms in on the 4–9 keV band.
Both observations show evidence of Fe K$\alpha$ emissions.

We use the XSPEC software (v.12.12.1) for spectral analysis (Arnaud, 1996). We
start our analysis by fitting the spectra above 2 keV with an absorbed power
law. The tbnew model is used to account for Galactic absorption (Wilms et al.,
2000), which is estimated to be $N_{\rm H}=4.6\times 10^{20}$ cm-2 (Willingale
et al., 2013). Corresponding data/model ratio plots are shown in Fig. 3. A
zoom-in of the 3–10 keV band is shown in the lower panel. Both epochs show
evidence of Fe K$\alpha$ emission in the Fe K band. Meanwhile, two epochs show
different spectral shape in the soft X-ray band.

In the rest of the section, we focus on modelling the spectra of UGC 11763
using the absorption, disc reflection and hybrid models.

###  4.1 Relativistic Disc Reflection Model (blackModel 1)

####  4.1.1 Model set-up

In the disc reflection scenario, the soft excess is interpreted as part of the
reprocessed emission from the inner accretion disc (e.g. Crummy et al., 2006;
Jiang et al., 2020). To model the disc reflection component, we use the
relxilld model (blackModel 1, García et al., 2016). A broken power-law
emissivity profile parameterised by q1, q2 and $R_{\rm b}$ is considered.
Other free parameters include the spin of the BH, the inclination angle, the
iron abundance and the electron number density of the disc. The reflection
fraction parameter of relxilld is set to be a free, positive number, so the
model returns both the hot coronal emission and the corresponding disc
reflection spectrum.

Figure 4: Data/model ratio of the EPIC pn (black), MOS1 (blue crosses) and
MOS2 (green squares) spectra of UGC 11763 in 2003 (obs1) using relxilld (top).
Absorption features at 0.8 keV (16–17Å) are shown in the data. They are a
blend of Fe M-shell absorption lines (Fe ‘Unresolved Transition Array’),
suggesting the existence of ionised absorbing gas in UGC 11763. Similar
results were found in the grating data of UGC 11763 (Cardaci et al., 2009). An
additional low-ionisation absorption model improves the fit by
$\Delta\chi^{2}=46$ with two more free parameters (bottom).

By applying relxilld to obs1, we find evidence of absorption features at 0.8
keV. See Fig. 4 for corresponding data/model ratio plots. The goodness of this
fit is $\chi^{2}/\nu=$black551.62/424. The absorption features correspond to
Fe UTA, suggesting the existence of photoionised absorbers in a low ionisation
state, e.g. warm absorbers commonly seen in AGNs (e.g. Lee et al., 2001;
Ebrero et al., 2016). Cardaci et al. (2009) pointed out similar residuals in
the spectra of UGC 11763 extracted from obs1 when applying a simple model
including Galactic absorption, a power law, a black body and Fe K$\alpha$
emission line.

To fit the absorption features, we use a tabulated version of the xabs
photoionised absorption model (Steenbrugge et al., 2003) from SPEX (Kaastra et
al., 1996), implemented as an XSPEC table model by Parker et al. (2019) and
available from www.michaelparker.space/xspec_models. The version used here
assumes the photoionisation is driven by a $\Gamma=2$ power-law input
spectrum, and covers ionisations from $\log(\xi)=-4$ to 5, with parameters for
the column density, velocity broadening, and covering fraction.

When fitting the warm absorption features in the data, we assume low velocity
broadening of 100 km s-1 and a full-covering geometry. The assumption for this
geometry is based on the long distance between warm absorbers and the X-ray
emission region: typical warm absorbers are estimated to be near the broad
line region (e.g. Reynolds & Fabian, 1995).

By including the xabs model, the fit is significantly improved, e.g.
$\Delta\chi^{2}=45$ and two more free parameters. We, therefore, conclude that
our best-fit model is tbnew * xabs * relxilld (blackModel 1). We only obtain
an upper limit of the Galactic column density ($N_{\rm H}<6\times 10^{20}$
cm-2). This parameter is thus fixed at the nominal value calculated by
Willingale et al. (2013) ($4.6\times 10^{20}$ cm-2). Similar conclusions are
found for obs2.

####  4.1.2 Multi-epoch analysis

blackWe fit the two observations of UGC 11763 simultaneously with Model 1 to
better understand the spectral variability in this object. Best-fit parameters
are shown in the first two columns of Table 2.

Some of the parameters for the two observations are consistent within their
uncertainty ranges. For instance, we only obtain an upper limit of the density
of the reflection surface of the disk for each observation. Both values are
consistent with a low density of $10^{15}$ cm-3, which was commonly assumed in
the disc reflection modelling of AGN data (e.g. Ross & Fabian, 2005). In
addition, the spin of the central BH, the inclination angle and iron
abundances of the accretion disc are not expected to change on observable
timescales. We obtain consistent measurements of these parameters for two
observations, which increases our confidence in the choice of our reflection
model. Lastly, the ionisation state of the warm absorber also remains
consistent in these two observations.

We conduct multi-epoch spectral analysis with all the parameters mentioned
above linked between two observations. By doing so, we obtain a good fit for
both observations with $\chi^{2}/\nu=$black867.37/721. The best-fit parameters
are shown in Table 2 and the best-fit models are shown in the upper panel of
Fig. 5. Corresponding data/model ratio plots are shown in the lower panels of
Fig. 5.

####  4.1.3 Results

By comparing the best-fit parameters of blackModel 1 for the two XMM-Newton
observations of UGC 11763, we find that the coronal emission shows a softer-
when-brighter pattern–the photon index of the coronal emission increases from
2.26 to 2.41. This is commonly seen in other AGN too (e.g. Jiang et al., 2018;
Wu et al., 2020).

The fit of the disc reflection spectrum in obs2 requires a flatter disc
emissivity profile, i.e. a lower q1 and a higher $R_{\rm b}$, suggesting a
change in the coronal geometry, e.g. a more extended corona in UGC 11763
during obs2 than obs1 (Dauser et al., 2013). The anti-correlation between the
X-ray flux and the reflection fraction parameter suggests a similar
conclusion. When the coronal region is more compact, more coronal photons are
lost to the event horizon. On the other hand, disc reflected photons from a
more extended emission region is less affected by light-bending effects,
resulting in a higher reflection fraction in the spectrum (e.g. Miniutti et
al., 2003).

In summary, the spectral difference between obs1 and obs2 is explained by the
variable coronal emission in blackModel 1. The disc reflection component
changes accordingly. During the low flux state (obs1), the coronal region is
more compact as suggested by the steeper emissivity profile and the higher
reflection fraction parameter. Meanwhile, the variable column density of the
warm absorber also contributes to the soft X-ray variability while the
ionisation state of the warm absorber remains consistent.

The spin of the BH, the inclination angle of the inner disc and the iron
abundances of the disc are not expected to change on observable timescales. By
linking these parameters of two observations, we obtain $i=32\pm 2^{\circ}$,
$a_{*}>0.97$ and $Z_{\rm Fe}=4.8\pm 1.2Z_{\odot}$.

Figure 5: Best-fit models for two XMM-Newton observations using Model 1 and corresponding data/model ratio plots (red: obs1 pn; black: obs2 pn; blue squares: MOS1; green circles: MOS2). Spectra extracted from two observations are fit together. See text for more details. Model | Parameter | Unit | obs1 & 2
---|---|---|---
xabs | $N_{\rm H}$ |  $10^{20}$ cm-2 | $25\pm 4$ | $7\pm 3$
| $\log(\xi)$ | erg cm s-1 | $1.7\pm 0.2$
relxilld | q1 | - | $8.0\pm 0.3$ | $4.0\pm 0.4$
| q2 | - | $2.9\pm 0.2$ | $3.1^{+0.7}_{-0.6}$
| $R_{\rm b}$ | $r_{\rm g}$ | $3.4^{+0.2}_{-0.4}$ | $5\pm 2$
| $a_{*}$ | - | >0.97
| $i$ | deg | $32\pm 2$
| $Z_{\rm Fe}$ | $Z_{\odot}$ | $4.8\pm 1.2$
| $\log(n_{\rm e})$ | cm-3 | $<15.7$
| $\log(\xi)$ | erg cm s-1 | $1.20\pm 0.15$ | $1.3^{+0.3}_{-0.2}$
| $\Gamma$ | - | $2.26\pm 0.02$ | $2.49\pm 0.06$
| $f_{\rm refl}$ | - | $10\pm 4$ | $3.0\pm 1.5$
| $\log(F_{\rm X})$ | erg cm-2 s-1 | $-11.105\pm 0.008$ | $-10.865\pm 0.015$
| $\chi^{2}/\nu$ | - | 867.37/721
Table 2: Best-fit parameters obtained by using Model 1. $F_{\rm X}$ is the
unabsorbed flux of the model in the 0.3–10 keV band.

The best-fit blackModel 1 of UGC 11763 suggests that the column density of the
warm absorber decreases from $2.5\pm 0.4\times 10^{21}$ cm-3 in obs1 to
$1.0\pm 0.3\times 10^{21}$ cm-3 in obs2 while its ionisation state remains
consistent. We investigate whether it is possible to explain the X-ray
spectral variability of UGC 11763 by varying only the intrinsic continuum
emission. By linking the column density parameters of two observations, the
fit is significant worse below 1 keV with $\chi^{2}/\nu=$black910.63/723.
Therefore, although the X-ray variability is dominated by the variable
intrinsic continuum emission in blackModel 1, the contribution of the variable
line-of-sight column density of the warm absorber in UGC 11763 cannot be
ignored.

###  4.2 Partially-Covering Absorption Model (blackModel 2)

####  4.2.1 Model set-Up

In this section, we blackconsider a model based on multiple partially-covering
absorbers (e.g. Tanaka et al., 2004). In this model, the residuals between 4–8
keV as shown in Fig. 3 are explained by the Fe K absorption edge of two
high-$N_{\rm H}$ absorbers (e.g. Waddell et al., 2019).

Figure 6: Data/model ratio plots of the obs1 spectra of UGC 11763 fit to
different models (red: pn; blue squares: MOS1; green circles: MOS2). See text
for more details.

We first fit the soft excess emission of UGC 11763 to a soft Comptonisation
model, similar to the model for another NLS1 Mrk 335 in Gallo et al. (2015).
The comptt model (Titarchuk, 1994; Marshall et al., 2003) is used for this
purpose. The combination of warm and hot corona models provides a fit to the
obs1 data, for example, with $\chi^{2}/\nu=$black630.42/430. See the first
panel of Fig. 6 for the corresponding data/model ratio plot. Residuals are
seen at 6.4 keV and <1 keV, suggesting the existence of Fe K$\alpha$ emission
and low-ionisation absorption.

Similar to the absorption model in Tanaka et al. (2004); Gallo et al. (2015),
we consider a low-ionisation partially-covering model to fit the negative
residuals at 7 keV and the absorption features below 1 keV. The same xabs
model as in blackModel 1 is used to model the photoionisation absorption in
the data.

One additional xabs component improves the fit by $\Delta\chi^{2}=$black30
with three more free parameters ($N_{\rm H}$, $\log(\xi)$ and $f_{\rm cov}$).
See the second panel of Fig. 6 for the corresponding data/model ratio plot.
The fit of Fe UTA at 0.8 keV is improved by adding xabs. To further improve
the fit below 1 keV, we add a second xabs model, which decreases $\chi^{2}$ by
black65 with three more free parameters.

We then add an additional xillver model (García & Kallman, 2010) with the
ionisation parameter fixed at $\log(\xi)=0$ to account for narrow Fe K$\alpha$
emission from a distant reflector. The additional reflection component
improves the fit by $\Delta\chi^{2}=$black20 with one more free parameter. The
final best-fit model is tbnew * xabs1 * xabs2 * (comptt + powerlaw + xillver)
(blackModel 2) in XSPEC notations. Similar conclusions are found for obs2. In
summary, blackModel 2 needs two layers of low-ionisation absorption in
combination with the warm corona model.

Note that some positive residuals are still seen at 6 keV of obs1 using
blackModel 2 (see the last panel of Fig. 6). The combination of narrow Fe
K$\alpha$ emission from the distant reflection model and the Fe K absorption
from partially-covering absorbers is unable to fit the spectra in the iron
emission band perfectly. Relativistic correction for the reflection component
is still required, although blackModel 2 is able to provide an acceptable fit
to the X-ray continuum emission of UGC 11763. In Section 4.3, we will further
improve the fit in the iron emission band by considering a hybrid model
including both absorption and disc reflection.

Lastly, blackModel 1 offers obs1 a better fit than blackModel 2 with
$\Delta\chi^{2}=$black9. The difference of two fits are in not only the iron
emission band as described above but also the 8–10 keV band in the observed
frame. Positive residuals are seen when fitting the spectra of obs1 with
blackModel 2. In comparison, blackModel 1 fits the spectra better near the
upper limit of the EPIC energy range. Future hard X-ray observations, e.g.
from NuSTAR (Harrison et al., 2013) or HEX-P (Madsen et al., 2019), may help
distinguishing two models in the >10 keV band.

####  4.2.2 Multi-epoch analysis

By applying blackModel 2 to two observations, we also obtain reasonably good
fits for the continuum emission. The best-fit parameters are shown in Table 3.
blackBy doing so, we find a good fit for both observations with
$\chi^{2}/\nu=880.46/721$. Best-fit parameters are shown in Table 3 and the
best-fit models are shown in the upper panel of Fig. 7. Corresponding
data/model ratio plots are shown in the lower panels of Fig. 7.

In blackModel 2, the ionisation states of the two absorbers are consistent in
two epochs: the first absorber has an ionisation state of $\log(\xi)\approx
2.5$; the second absorber has an ionisation state of $\log(\xi)\approx 0.7$.
The covering factor of the first absorber decreases from 0.5 during obs1 to
0.3 during obs2; the same parameter of the second absorber decreases from 0.76
during obs1 to 0.6 during obs2. Furthermore, the optical depth of the warm
corona remains consistent with 20 while its temperature increases from
black0.15 keV to black0.26 keV.

####  4.2.3 Results

In blackModel 2, the soft X-ray variability of UGC 11763 is explained by
variable line-of-sight absorption and intrinsic continuum emission including
the soft excess emission and the hot coronal emission.

Two partially-covering absorbers in a low-ionisation state, xabs1 and xabs2,
are needed in blackModel 2. The first absorber xabs1 has a higher column
density, a higher ionisation state and a lower covering factor than xabs2. For
instance, xabs1 has a column density of black2.8$\times 10^{23}$ cm-2, which
is approximately black18 times the column density of xabs2. The ionisation
parameter of xabs1 is around black64 times the same parameter333Note that the
ionisation parameter is reported in log in Table 3. of xabs2. The covering
factor of xabs1 is lower than that of xabs2.

The column density and covering factor of the first absorber xabs1 increase
from the high flux state during obs2 to the low flux state during obs1. The
best-fit value of the column density changes by a factor of black3. The
covering factor of xabs1 increases by a factor of black1.6. The column density
of the second absorber xabs2 decreases by a factor of 2 from obs2 to obs1
while the covering factor increases by a factor black1.3.

In addition to variable absorption, blackModel 2 also requires the intrinsic
emission to be variable to fit the data. The photon index of the hot coronal
emission increases dramatically from black1.8 in obs1 to black2.5 in obs2. The
temperature and the strength of the warm corona also increase from obs1 to
obs2. In particular, the unabsorbed flux of the warm coronal emission
increases by a factor of 13 in the XMM-Newton energy band.

We investigate the possibility of fitting the spectra of UGC 11763 using
blackModel 2 without the need of changing the intrinsic emission. The
following additional parameters are linked between two epochs: $F_{\rm w}$,
$kT$, $F_{\rm h}$, $\Gamma$ and $F_{\rm x}$. By doing so, we obtain a worse
fit with $\chi^{2}/\nu=$black927.46/726 than the fit presented in Table 3 and
Fig. 7 ($\chi^{2}/\nu=$black880.46/721). This model requires intermediate
values of the parameters for the linked components: for instance, the flux of
the warm corona and the hot corona is $\log(F_{\rm w})=-11.40^{+0.12}_{-0.19}$
and $\log(F_{\rm h})=-10.87^{+0.06}_{-0.07}$; the temperature of the warm
corona is $0.21^{+0.03}_{-0.02}$ keV. Based on the high value of $\chi^{2}$ of
this fit, we argue that blackModel 2 requires both the intrinsic emission and
the absorption to be variable to explain the data.

Figure 7: Best-fit models for two XMM-Newton observations using Model 2 and corresponding data/model ratio plots (red: obs1 pn; black: obs2 pn; blue squares: MOS1; green circles: MOS2). Solid lines: total models; shaded regions: soft Comptonisation models; dash-dotted lines: power-law components; dotted lines: distant reflectors. Spectra of two observations are fit together. See text for more details. Model | Parameter | Unit | obs1 & obs2
---|---|---|---
xabs1 | $N_{\rm H}$ |  $10^{22}$ cm-2 | $28^{+9}_{-6}$ | $10\pm 7$
| $\log(\xi)$ | erg cm s-1 | $2.5\pm 0.2$
| $f_{\rm cov}$ | - | $0.50\pm 0.04$ | $0.31^{+0.17}_{-0.11}$
xabs2 | $N_{\rm H}$ |  $10^{22}$ cm-2 | $1.6\pm 0.3$ | $3.4^{+0.7}_{-0.2}$
| $\log(\xi)$ | erg cm s-1 | $0.7\pm 0.2$
| $f_{\rm cov}$ | - | $0.76\pm 0.04$ | $0.60\pm 0.05$
comptt | $\tau$ | - | $20\pm 3$
| kT | keV | $0.145^{+0.015}_{-0.012}$ | $0.26\pm 0.02$
| $\log(F_{\rm w})$ | erg cm-2 s-1 | $-11.72\pm 0.02$ | $-10.6^{+0.3}_{-0.4}$
powerlaw | $\Gamma$ | - | $1.81\pm 0.07$ | $2.50^{+0.13}_{-0.15}$
| $\log(F_{\rm h})$ | erg cm-2 s-1 | $-11.16^{+0.03}_{-0.02}$ | $-10.72^{+0.26}_{-0.12}$
xillver | $\log(F_{\rm x})$ | erg cm-2 s-1 | $-12.49^{+0.15}_{-0.12}$ | $-11.8\pm 0.3$
| $\chi^{2}/\nu$ | - | 880.46/721
Table 3: Best-fit parameters obtained by using Model 2.

###  4.3 Hybrid Model

In previous two sections, we introduce two spectral models to fit the XMM-
Newton spectra of UGC 11763: one is based on the relativistic disc reflection
model (blackModel 1) and the other is based on double partially-covering
absorption model (blackModel 2). The evidence of Fe K$\alpha$ emission and
soft excess in the spectra of UGC 11763 motivates the choice of blackModel 1.
An additional warm absorption model with a modest column density of
1–$2.5\times 10^{21}$ cm-2 is required to fit the Fe UTA at 0.8 keV.
Alternatively, one may fit the soft excess of UGC 11763 with the warm corona
model which is included in blackModel 2.

In this section, we first compare blackModel 1 and blackModel 2 and summarise
the interpretations of the soft X-ray variability of UGC 11763 based on two
models. We then introduce a hybrid model where the intrinsic emission is
described by the relativistic disc reflection model and additional absorption
models are used to explain the variability. Such a model can improve the fit
in the iron emission and 8–10 keV bands in comparison to blackModel 2.

####  4.3.1 blackVariable reflection or/and absorption?

UGC 11763 shows significant long-term variability in the <2 keV band on
timescales of months and years (see Fig. 1). We conduct multi-epoch spectral
analysis for the two XMM-Newton observations of this object based on
blackModel 1 and blackModel 2 to study the origin of such variability.

In blackModel 1, the soft X-ray variability is dominated by the intrinsic
emission from the hot corona and the reflected emission from the inner
accretion disc. The best-fit unabsorbed blackModel 1 for two XMM-Newton
observations is shown in the top panel of Fig. 8. The X-ray continuum emission
is softer during obs2 when the flux is high. The variable disc emissivity
profile and reflection fraction of the disc reflection model agrees with the
light-bending model (Miniutti et al., 2003), where the size of the coronal
region plays an important role. Variability in the column density of the warm
absorption, which shows a consistent ionisation state, contribute to the soft
X-ray variability too.

In blackModel 2, both absorption and intrinsic emission contribute to the soft
X-ray variability of UGC 11763. Two low-ionisation partially-covering
absorbers are required to fit the broad band spectra. They show a higher
covering factor when the observed soft X-ray flux of UGC 11763 is low during
obs1. Meanwhile, they remain consistent ionisation states. The unabsorbed
intrinsic emission of blackModel 2 is shown in the lower panel of Fig. 8.
Emission from both hot and warm corona changes: the hot coronal emission
becomes softer and the temperature and strength of the warm corona increase.
In comparison with blackModel 1, blackModel 2 requires the photon index of the
hot coronal emission to increase by a larger amplitude: $\Gamma$ in blackModel
1 increases from 2.26 in obs1 to black2.49 in obs2; $\Gamma$ in blackModel 2
increases from black1.81 to black2.50.

Figure 8: The unabsorbed intrinsic X-ray emission from UGC 11763 during obs1
(black solid lines) and obs2 (red solid lines) suggested by Model 1 (top) and
Model 2 (bottom). All low-ionisation absorption in the AGN and Galactic
absorption in the foreground are removed in this figure. Dash-dotted lines:
hot coronal emission; shaded regions: warm coronal emission; dotted lines:
distant reflection components.

Furthermore, blackModel 1 provides a slightly better fit to the spectra of two
observations than blackModel 2 by $\Delta\chi^{2}=$black13 with the same
number of parameters. The difference in the goodness of their fits is in the
6–10 keV band, where the Fe K emission line is not well fit by blackModel 2
and some positive residuals are still seen above 8 keV (see Fig. 6 and 4).

In addition to blackModel 2 and blackModel 1, we propose a hybrid model where
the disc reflection model is used to fit the intrinsic emission and absorption
models are still needed to explain the variability. Such a model can improve
the fit in the 6–10 keV band by modelling the broad Fe K$\alpha$ emission with
a relativistic disc model. We also investigate whether the spectral
variability can be explained by variable absorption and power-law emission
without the need for changes in the size of the corona in this hybrid model.

####  4.3.2 Model set-up

In this section, we present a multi-epoch analysis of the XMM-Newton spectra
of UGC 11763 based on a hybrid model. The relativistic disc reflection model
relxilld is used to model the intrinsic emission. The same model is used in
Section 4.1.2. Two xabs models as in Section 4.2.2 are included to account for
absorption.

In blackModel 1, one xabs model is included to fit the Fe UTA of the full-
covering warm absorber in UGC 11763. Although the variability is dominated by
the varying intrinsic emission, the variable column density of the warm
absorber cannot be ignored (see Section 4.1.2). In particular, blackModel 1
also suggests that the size of the coronal region has to change to explain the
variable disc emissivity profiles and reflection fractions. In this hybrid
model, we study whether it is possible to keep the geometry of the coronal
region consistent and interpret the soft X-ray variability with absorption
together with changes in the illuminating coronal emission.

To achieve the goals above, we link most of the parameters in relxilld between
two observations. They include the emissivity profile, density, ionisation and
reflection fraction of the disc. Besides, the spin of the central BH, the
inclination angle and iron abundances of the disc are not expected to change
on observable timescales. So, they are linked too. We try to fit the data with
linked photon index, but the fit is significantly worse. We, therefore, allow
the photon index and normalisation of relxilld to be different in two
observations. These two parameters describe the illuminating spectrum of the
disc.

The first absorption model xabs1 is required to fit the spectrum of obs1 but
not necessary for obs2 when flux is high. We, therefore, link the column
density and ionisation parameter of xabs1 for two observations. Only an upper
limit of the covering factor is found for obs2 ($f_{\rm cov}<0.09$). The
second absorption model xabs2 remains a consistent ionisation state. The
ionisation parameter is thus linked too. We obtain only a lower limit of the
covering factor for xabs2 at 0.97, suggesting a full-covering geometry. The
best-fit ionisation parameter is around 0.9, which is lower than the value of
blackModel 1 but still consistent with typical values in most AGN (Reynolds &
Fabian, 1995; Laha et al., 2014). Similar to blackModel 1, the column density
of xabs2 increases from $6\times 10^{20}$ cm-2 during the high flux state
(obs2) to $1.1\times 10^{21}$ cm-2 during the low flux state (obs1).

####  4.3.3 Results

Figure 9: Best-fit models for two XMM-Newton observations using a hybrid model and corresponding data/model ratio plots (red: obs1 pn; black: obs2 pn; blue squares: MOS1; green circles: MOS2). Spectra of two observations are fit together. In this scenario, the intrinsic emission is modelled by the relativistic disc reflection model. We assume that the geometry of the coronal region remains consistent. Variable absorption and primary emission from the corona are responsible for the spectral variability. Model | Parameter | Unit | obs1 & 2
---|---|---|---
xabs1 | $N_{\rm H}$ |  $10^{22}$ cm-2 | $1.7^{+0.7}_{-0.6}$
| $\log(\xi)$ | erg cm s-1 | $1.52^{+0.20}_{-0.15}$
| $f_{\rm cov}$ | - | $0.47\pm 0.07$ | <0.09
xabs2 | $N_{\rm H}$ |  $10^{21}$ cm-2 | $1.1^{+0.2}_{-0.3}$ | $0.6^{+0.2}_{-0.3}$
| $\log(\xi)$ | erg cm s-1 | $0.9\pm 0.2$
| $f_{\rm cov}$ | - | >0.97
relxilld | q1 | - | $5.6^{+0.4}_{-0.5}$
| q2 | - | $2.6\pm 0.6$
| $R_{\rm b}$ | $r_{\rm g}$ | $5.5^{+2.0}_{-1.4}$
| $a_{*}$ | - | >0.95
| $i$ | deg | $32\pm 3$
| $Z_{\rm Fe}$ | $Z_{\odot}$ | $4\pm 2$
| $\log(n_{\rm e})$ | cm-3 | $16.6^{+0.8}_{-1.0}$
| $\log(\xi)$ | erg cm s-1 | $1.06\pm 0.02$
| $\Gamma$ | - | $2.29\pm 0.02$ | $2.51\pm 0.03$
| $f_{\rm refl}$ | - | $3.2\pm 0.3$
| $\log(F_{\rm X})$ | erg cm-2 s-1 | $-11.01\pm 0.02$ | $-10.82^{+0.03}_{-0.02}$
| $\chi^{2}/\nu$ | - | 872.41/721
Table 4: Best-fit parameters obtained by using a hybrid model. $F_{\rm X}$ is
the unabsorbed flux of the model in the 0.3–10 keV band.

The hybrid model introduced above provides a good fit to both observations
with $\chi^{2}/\nu=$black872.41/721. The fit is slightly worse than blackModel
1 by $\Delta\chi^{2}=5$ with the same number of free parameters, and better
than blackModel 2 by $\Delta\chi^{2}=$black8 also with the same number of
parameters. Best-fit models are shown in Fig. 9 and best-fit parameters are
shown in Table 4. The fit in the iron emission band is improved compared to
blackModel 2. Some residuals are still seen above 8 keV in obs1 but reduced
from the fit of blackModel 2.

Assuming the geometry of the coronal region remains consistent, we obtain an
intermediate value of reflection fraction for the disc (black3.2$\pm 0.3$),
which lies between the values for two observations inferred by blackModel 1.
Similar conclusion is found for the emissivity profile of the disc, which is
flatter than the one for obs1 in blackModel 1 but steeper than the one for
obs2. Consistent measurements for the spin of the BH, the inclination and iron
abundances of the disc are achieved. Tentative evidence shows that a higher
disc density is required when fitting two spectra with the same reflection
model. The 90% confidence range of the density parameter is $\log(n_{\rm
e}/{\rm cm}^{-3})=16.6^{+0.8}_{-1.0}$. Considering a 3-$\sigma$ uncertainty
range444The hard lower limit of $n_{\rm e}$ in relxilld is $10^{15}$ cm-3., we
obtain only an upper limit at $10^{18}$ cm-3.

In this hybrid model, the strength and shape of the coronal emission are
allowed to be different in two epochs. The resulting reflection spectrum
changes accordingly with a consistent flux fraction. We show the best-fit
unabsorbed models in Fig. 10. The intrinsic emission is softer during obs2
than obs1. The photon index of the power-law emission increases from
black$2.29$ to black$2.51$. The unabsorbed flux of the relxilld, however, does
not change a lot ($\log(F)=$black-11.01 in obs1 and $\log(F)=$black-10.82 in
obs2).

Additional variable absorption is needed in the hybrid model. The first
absorber xabs1 is in a higher ionisation state than the second absorber xabs2.
xabs1 has a covering factor of 0.47 during obs1 when the soft X-ray flux of
UGC 11763 is low. During the high flux state, obs2 requires no xabs1. We
estimate the upper limit of its covering factor to be at 0.09. The second
absorber is similar to typical warm absorbers seen in other AGN. The covering
factor is consistent with 1 (>0.97). The column density of xabs2 decreases by
a factor of 2 from obs1 to obs2.

In summary, the hybrid model is also able to explain to the multi-epoch
variability of UGC 11763. This model provides a slightly worse fit than
blackModel 1 but a better fit than blackModel 2 with improvements of fitting
the data in the 6–10 keV band. In this hybrid model, the soft X-ray
variability of UGC 11763 is explained by variable power-law emission from the
corona. The reflected emission from the accretion disc changes accordingly
without changing the geometry of the corona. During the low flux state, a
partially-covering absorber of $\log(\xi)=$black1.5 crosses our line of sight
to the source with a covering factor of around 47%. During the high soft X-ray
flux state, this absorber moves out of our line of sight. Additional full-
covering warm absorber similar to those in other AGN is needed to fit the
data. The warm absorber shows a slightly higher column density in obs1 than
obs2.

blackThe hybrid model improves the fit in the iron emission band compared to
Model 2 by including the relativistic disc reflection model. No additional
component is required to fit the soft excess emission. We investigate whether
an additional soft Comptonisation component as in Model 2 is able to further
improve the fit. The comptt model is used for this purpose. We find that the
fit is not significantly improved as the disc reflection component accounts
for both the iron emission and the soft excess of UGC 11763. We fix the
parameters of the comptt model at the best-fit values in Model 2 (see Table 3)
and then obtain an upper limit for the contribution of the soft Comptonisation
component in the 0.3–10 keV band, $F_{\rm w}<1.6\times 10^{-13}$ erg cm-2 s-1
and $<4\times 10^{-13}$ erg cm-2 s-1 respectively for obs1 and obs2.

Figure 10: Same as Fig. 8 but for the hybrid model.

##  5 Discussion

We present different spectral models for the XMM-Newton observations of UGC
11763. blackThe first model is based on the relativistic disc reflection model
and requires a variable size in the coronal region to explain the data. The
second model is based on multiple partially-covering absorbers in combination
with the warm corona model. The observed soft X-ray variability is interpreted
by variable line-of-sight absorption and soft Comptonisation emission. We also
propose a third hybrid model, where both multiple absorption and disc
reflection models are included. In this scenario, the size of the corona
remains consistent while intrinsic variability in its emission is expected.
The soft X-ray variability is dominated by one partially-covering absorber in
the low X-ray flux state, which leaves our line of sight during the high X-ray
flux state.

###  5.1 Variable Disc Reflection (blackModel 1)

In blackModel 1, the spectral variability is dominated by the Comptonisation
emission from the hot corona. The photon index of the coronal continuum
emission is higher when the X-ray luminosity is higher, which was often seen
in many other Sy1s (e.g. Jiang et al., 2018; Wu et al., 2020).

The resulting disc reflection component changes according to the variable
illuminating coronal emission. In particular, the lower flux state observation
(obs1) has a higher reflection fraction than the higher flux state observation
(obs2). This can be explained by the light-bending effects of the variable
size of the corona in UGC 11763 (e.g. Miniutti et al., 2003; Reis et al.,
2013; Jiang et al., 2018).

The reflection fraction parameter in relxilld is defined as the ratio between
the intensity of the coronal component that reaches the disc and the one seen
by the observer, and the value of this parameter can easily exceed unity when
the corona is compact (Dauser et al., 2016). The best-fit reflection fraction
parameters for obs1 and obs2 are respectively black10 and black3. Such a large
amplitude change of the reflection fraction parameter was also seen in the
multi-epoch variability of other AGNs (Jiang et al., 2019a). The high values
of reflection fraction parameters suggest that the corona is within a region
of <3 $r_{\rm g}$ assuming a simple ‘lamp-post’ geometry555The ‘lamp-post’
model assumes a point-like, isotropic geometry of the corona located on the
rotating axis of the BH. (Dauser et al., 2016). The flatter disc emissivity
profile also suggests the existence of a more extended coronal region in UGC
11763 in obs2 than obs1. Because the outer region of the accretion disc is
more illuminated when the coronal region is larger (e.g. Gonzalez et al.,
2017). blackThe corona is known to be very compact within a few gravitational
radii in many AGN as well as UGC 11763 according to advanced timing analyses
in the X-ray band (e.g. Fabian et al., 2009; Reis & Miller, 2013). Similar
conclusions were found in microlensing events of AGN (Morgan et al., 2008;
Chartas et al., 2017). The compact corona also agrees with the predictions of
some coronal models, such as magnetic reconnection where the magnetic field
increases strength towards smaller radii (Merloni & Fabian, 2001), the base of
the jet (Ghisellini et al., 2004) and pair productions in the magnetosphere
around the central BH (Hirotani & Okamoto, 1998; Chen & Yuan, 2020).

We estimate the distance of the warm absorber in blackModel 1 from the central
BH using the best-fit ionisation parameter $\xi=$black50 erg cm s-1. The
bolometric luminosity is estimated to be $9\times L_{\rm 5100}\approx
3.6\times 10^{45}$ erg s-1 (Peterson et al., 2004). Assuming a density of
$n=10^{9}$ cm-3 (Reynolds & Fabian, 1995) and an isotropic illuminating
source, we estimate the location of the warm absorber in UGC 11763 to be
around $d=\sqrt{\frac{L_{\rm Bol}}{4\pi
n\xi}}\approx\textcolor{black}{6}\times 10^{17}$ cm.

In our calculation, the assumption of $n=10^{9}$ cm-3 for the warm absorber is
based on the agreement of recombination timescale and the variability
timescale of the illuminating emission in MCG-6-30-15 (Reynolds & Fabian,
1995). If the recombination timescale is larger than the variability
timescale, photoionization equilibrium would not apply. The primary emission
of MCG-6-30-15 is much more variable than UGC 11763 on timescales of
kiloseconds. So, the density of the warm absorber in UGC 11763 is allowed to
be lower than $n=10^{9}$ cm-3 as the recombination timescale is approximately
proportional to $n^{-1}$ (Reynolds & Fabian, 1995). Furthermore, we also
assume an isotropic illuminating source and apply a factor of $4\pi$ in the
calculation, which can also be lower. So, the estimated distance of
$\textcolor{black}{6}\times 10^{17}$ cm is only the lower limit.

Lastly, blackModel 1 also provides an estimation of the BH spin of UGC 11763.
By fitting two epochs simultaneously and linking their spin parameters, we
achieve a high BH spin of $a_{*}>0.97$ in Section 4.1.2. Previously, Reynolds
(2014) noted the tentative evidence that the most massive black holes ($M_{\rm
BH}>10^{8}M_{\odot}$) and the least massive black holes ($M_{\rm
BH}<10^{6}M_{\odot}$) may have more modest spins by compiling a number of
measurements in previous work. The properties of the host galaxy may play an
important role in the evolution of the BH spin (Sesana et al., 2014). UGC
11763 may host one of the few massive BHs (Peterson et al., 2004; Ho et al.,
2008) which have a high BH spin. Future reflection studies of AGN with similar
high BH masses enable us to better understand the spin distribution in a wider
range of BH masses.

###  5.2 Variable Absorption and Intrinsic Soft X-ray Emission (blackModel 2)

blackModel 2 provides multi-epoch spectra of UGC 11763 a slightly worse fit
than blackModel 1 by $\Delta\chi^{2}=\textcolor{black}{13}$ with the same
number of parameters. In blackModel 2, the ionisation states and the column
densities of two absorbers are also consistent within their 90% confidence
ranges between two observations. The soft X-ray variability is mainly caused
by the variable covering factors of the absorbers: the covering factor of the
first absorber increases from 0.34 in obs2 to 0.50 in obs1. We estimate the
location of the absorbers according to the X-ray variability assuming the
absorbers are orbiting around the central BH: the observed soft X-ray flux of
UGC 11763 increases from $\log(F)=-11.47$ in the 0.3–3 keV band in 2003 to
$\log(F)=-11.14$ in 2015 (see Table 1) by a factor of more than 2 in 12 years.
Meanwhile, the X-ray flux of UGC 11763 does not show large-amplitude
variability on kilosecond timescales as many other NLS1s.

We extract long-term lightcurves of UGC 11763 based on Swift observations in
the archive to investigate how rapidly the soft X-ray emission of UGC 11763
varies. The first two panels of Fig. 1 show the X-ray lightcurves. The X-ray
flux of UGC 11763 can amplify by a factor of up to 5 during this long-term
period of Swift observations. The fifth and sixth Swift observations are
separated by 6 months in 2010. The soft X-ray flux changes by a factor of 2.7.
Similar large-amplitude variability on timescales of months is also seen in
other intervals. Assuming a BH mass of $4\times 10^{8}M_{\odot}$, the orbital
period at $r=6.8\times 10^{13}$ m$\approx 100r_{\rm g}$ is approximately 6
months. So, if the soft X-ray variability observed by Swift results from
variable absorption only as inferred by blackModel 2, the absorbers need to be
located less than $\approx 100r_{\rm g}$ from the central BH of UGC 11763 to
explain the observed large-amplitude X-ray variability on timescales of
months.

In addition to the variability in absorption, dramatic changes in the
intrinsic emission are also required by blackModel 2 to explain the spectral
variability. The unabsorbed flux of the warm coronal emission increases by a
factor of 13 in the XMM-Newton energy range. The temperature of the corona
increases from 0.18 keV to 0.23 keV.

blackIn the warm corona model, the soft Comptonisation emission from the warm
corona is often found to dominate the extreme-UV band (e.g. Jin et al., 2017).
We extend our best-fit models to the extreme-UV band and calculate their
predicted flux in the 0.01–0.1 keV band where the soft Comptonisation emission
peaks. The warm corona model suggests that the unabsorbed extreme-UV flux of
the non-thermal emission in UGC 11763 increase by a factor of 9 from $4\times
10^{-12}$ erg cm-2 s-1 to $3.6\times 10^{-11}$ erg cm-2 s-1. A significant
change in the bolometric luminosity is thus expected in Model 2. It is
interesting to note that the Eddington ratio of UGC 11763 is estimated to be
around 5% based on the observed 5100Å luminosity (see Section 1). The soft
excess emission plays an important role in the estimation of bolometric
luminosities for AGN at a few percent of Eddington when the warm corona model
is used (Noda & Done, 2018).

blackIn comparison, the relativistic disc reflection model in Model 1 suggests
that the unabsorbed flux of the non-thermal emission in UGC 11763 increases by
a factor of only 2.9 from $2\times 10^{-12}$ erg cm-2 s-1 to $5.7\times
10^{-12}$ erg cm-2 s-1 in the 0.01–0.1 keV band. A much smaller increase in
the extreme-UV luminosity is required in the disc reflection model.
Unfortunately, due to Galactic absorption, it is not possible to measure the
luminosity of UGC 11763 in this energy band and test each model.

blackThe Optical Monitor on XMM-Newton provides complementary optical and UV
views of UGC 11763 at longer wavelengths, although we are unable to measure
the extreme-UV flux of this object. The observed magnitude of UGC 11763
increases by a factor of 2 from $13.597\pm 0.008$ during obs1 to $13.307\pm
0.007$ during obs2 in the UVW1 band and a factor of 2.3 from $13.692\pm 0.008$
to $13.337\pm 0.007$ in the UVM2 band. Photometric observations with only two
filters are not able to constrain the thermal emission from the disc and thus
the spectral energy distribution of this object. But we find that the observed
UV flux at longer wavelengths varies by a similar factor as the extreme-UV
flux predicted by the disc reflection model rather than the warm corona model.

###  5.3 Hybrid Model

Based on the fits of blackModel 1 and blackModel 2, we propose for a hybrid
model, where the intrinsic emission is modelled by disc reflection and
absorption is still required to explain the spectral variability in UGC 11763.
This hybrid model also provides a good fit to the data. Such a model improves
the fit in the iron emission band in comparison with the absorption model,
blackModel 2.

In the hybrid model, the variability of the intrinsic X-ray emission from UGC
11763 is caused by the variable intrinsic power-law emission from the corona.
The flux of the coronal emission increases by a small amplitude from
$9.5\times 10^{-12}$ erg cm-2 s-1 to $1.4\times 10^{-11}$ erg cm-2 s-1 while
its photon index increases from $2.29$ to $2.51$. We assume the coronal region
remains the same geometry during the two observations in this model. The
resulting disc reflection spectrum changes according to the variable power-law
emission with a consistent reflection fraction.

Furthermore, two layers of absorption are needed to explain the spectral
variability of UGC 11763: one full-covering warm absorption with a modest
column density of approximately $10^{21}$ cm-3 and one partially-covering
absorber in a higher ionisation state of $\log(\xi)\approx 1.7$. The
partially-covering absorber has a covering factor of 47% in obs1 when the flux
is low and disappear on the line of sight during obs2. Assuming this
partially-covering absorber contributes to the variability of UGC 11763 on
timescales of months observed by Swift, this absorber needs to be located in
the region of $<100$ $r_{\rm g}$. Variable absorption at a large distance
along the line of sight has been seen in other AGN too (e.g. Grupe et al.,
2004b; Parker et al., 2014b; Kaastra et al., 2018; Miller et al., 2021).
Objects like NGC 6814 require both disc reflection and absorption models to
fit the X-ray data (Gallo et al., 2021). Variable absorption at a large
distance from the innermost X-ray emission region plays an important role in
the observed variability of these sources.

##  6 Conclusion

In this work, we investigate the nature of the soft X-ray variability of the
NLS1 AGN UGC 11763 based on two XMM-Newton observations in the archive. The
soft excess emission of UGC 11763 shows a very different spectral shape in
these two observations. We apply two models to the EPIC data of the source,
one based on relativistic disc reflection (blackModel 1) and the other based
on partially-covering absorption in combination with the warm corona model
(blackModel 2).

In the reflection scenario, the X-ray variability of UGC 11763 is dominated by
the variable emission from the hot corona. The disc reflection component
changes accordingly. The anti-correlation between the reflection fraction
parameter and the X-ray flux suggests a variable coronal geometry in UGC
11763. The flatter disc emissivity profile also supports the conclusion that
the coronal region of UGC 11763 is more extended during the high X-ray flux
state than the low X-ray flux state. The variable modest column density of the
line-of-sight warm absorption also contributes to the soft X-ray variability.

In the absorption scenario, the two high-$N_{\rm H}$ absorbers produce strong
Fe K edges in the Fe K band. An additional low-ionisation reflection component
is required to fit the Fe K$\alpha$ emission of UGC 11763. The variability of
UGC 11763 is caused by the variable covering factor of the line-of-sight
absorbers in this model, while they remain in a consistent low-ionisation
state. Swift observations suggest that the absorbers have to be located within
a region of $r<\approx 100r_{g}$ to explain the large-amplitude X-ray
variability of UGC 11763 on timescales of months. In addition, the intrinsic
emission from the AGN also needs to be variable: the temperature and strength
of the warm corona increases.

To further improve the fit in the iron band based on blackModel 2, we
investigate the possibility of a hybrid model, where 1) we assume that the
geometry of the coronal region remains the same during the two observations;
2) the intrinsic power-law emission from the corona is allowed to vary; 3)
variable absorption is used to explain the soft X-ray variability. Such a
hybrid model offers a slightly better fit than blackModel 2. The variable
absorbers in the hybrid model have two component, one full-covering warm
absorber as those commonly seen in typical AGN (Reynolds & Fabian, 1995) and
one partially-covering absorber. The partially-covering absorber has a
covering factor of 47% during obs1 when the observed soft X-ray flux of UGC
11763 is low and completely moves out of our line of sight during obs2 when
the observed flux is high.

blackModel 1, 2 and the hybrid model provide CCD-resolution data of UGC 11763
with a similarly good fit. However, a different number of absorbers in
different ionisation states is needed in them. Unfortunately, archival EPIC
data of XMM-Newton do not have high enough spectral resolutions to distinguish
these models. The RGS observation of obs2 is off-axis. No high-resolution soft
X-ray spectrum during obs2 is available for comparison. But future high-
resolution X-ray observations, e.g. from Athena (Barcons et al., 2017) and
XRISM (XRISM Science Team, 2020), might provide us with a unique opportunity
to constrain any of the models for UGC 11763 by resolving multiple spectral
components, blacke.g., from disc reflection (Parker et al., 2022a) and warm
absorption (Parker et al., 2022b).

## Acknowledgements

This paper was written during the worldwide COVID-19 pandemic in 2022. We
acknowledge the hard work of all the health care workers around the world. We
would not be able to finish this paper without their protection. J.J.
acknowledges support from the Leverhulme Trust, the Isaac Newton Trust and St
Edmund’s College, University of Cambridge. blackThis work is based on
observations obtained with XMM-Newton, an ESA science mission with instruments
and contributions directly funded by ESA Member States and NASA. This project
has made use of the Science Analysis Software (SAS), an extensive suite to
process the data collected by the XMM-Newton observatory.

## Data Availability

All the data can be downloaded from the HEASARC website at
https://heasarc.gsfc.nasa.gov. blackThe relxill package can be downloaded at
https://www.sternwarte.uni-erlangen.de/dauser/research/relxill/index.html.

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