# Long term X-Ray Observations of Seyfert 1 Galaxy Ark 120: On the origin of
soft-excess

Prantik Nandi1, Arka Chatterjee1, Sandip K. Chakrabarti2, Broja G. Dutta2,3
1Department of Astrophysics & Cosmology, S. N. Bose National Centre for Basic
Science, Salt lake, Sector III, Kolkata 700091, India
2Indian Centre for Space Science, Garia Station Road, Kolkata 700084, India
3Department of Physics, Rishi Bankim Chandra College, Naihati, West Bengal,
743165, India E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the long-term X-ray spectral and temporal analysis of a ‘bare-type
AGN’ Ark 120. We consider the observations from XMM-Newton, Suzaku, Swift, and
NuSTAR from 2003 to 2018. The spectral properties of this source are studied
using various phenomenological and physical models present in the literature.
We report (a) the variations of several physical parameters, such as the
temperature and optical depth of the electron cloud, the size of the Compton
cloud, and accretion rate for the last fifteen years. The spectral variations
are explained from the change in the accretion dynamics; (b) the X-ray time
delay between 0.2-2 keV and 3-10 keV light-curves exhibited zero-delay in
2003, positive delay of $4.71\pm 2.1$ ks in 2013, and negative delay of
$4.15\pm 1.5$ ks in 2014. The delays are explained considering Comptonization,
reflection, and light-crossing time; (c) the long term intrinsic luminosities,
obtained using nthcomp, of the soft-excess and the primary continuum show a
correlation with a Pearson Correlation Co-efficient of $0.922$. This indicates
that the soft-excess and the primary continuum are originated from the same
physical process. From a physical model fitting, we infer that the soft excess
for Ark 120 could be due to a small number of scatterings in the Compton
cloud. Using Monte-Carlo simulations, we show that indeed the spectra
corresponding to fewer scatterings could provide a steeper soft-excess power-
law in the 0.2-3 keV range. Simulated luminosities are found to be in
agreement with the observed values.

###### keywords:

galaxies: active – galaxies: Seyfert – X-rays: galaxies – X-rays: individual:
Ark 120

††pubyear: 2020††pagerange: Long term X-Ray Observations of Seyfert 1 Galaxy
Ark 120: On the origin of soft-excess–References

##  1 Introduction

Active Galactic Nuclei (AGNs) are the most energetic phenomena in the
universe. The emitted radiation is observed over the entire range of the
electromagnetic spectrum. The high energy X-rays are believed to be emitted
from the innermost region of an accretion disc which surrounds the central
black hole (Shakura & Sunyaev, 1973; Pringle et al., 1973). The X-ray spectra
of Seyfert 1 galaxies, a subclass of AGNs, is mostly fitted by a power-law
component with photon index in the range $\Gamma=1.6-2.2$ (Bianchi et al.,
2009; Sobolewska & Papadakis, 2009) and a high energy cut-off. The spectral
contribution which deviates from the power-law at lower energy (below $\sim 2$
keV) is known as ‘soft excess’ (Halpern, 1984; Arnaud et al., 1985; Singh et
al., 1985). The X-ray spectra are often associated with a Fe K$\alpha$ line,
which is observed near 6.4 keV, and a Compton hump in the energy range of 20.0
to 40.0 keV. It has been observed that the primary power-law emission is
produced by the Comptonization of low energy seed photons (Sunyaev &
Titarchuk, 1980; Titarchuk, 1994) emitted from the standard Keplerian disc.
The seed photons are processed from the accretion mechanism, and the peak
emission arises at optical/ultraviolet (UV) wavelengths (Pringle et al., 1973)
for a supermassive black hole (SMBH). However, the location, as well as the
geometry of the Compton reprocessing region, are still a matter of debate.
This Compton cloud can be situated above the accretion disc (Haardt &
Maraschi, 1991, 1993; Poutanen & Svensson, 1996) or at the base of the
relativistic jet (Chakrabarti & Titarchuk, 1995; Fender et al., 1999, 2004;
Markoff et al., 2005). The region could be a hot, radiatively inefficient and
behave like a quasi-Bondi flow as discussed initially by Ichimaru (1977). This
region could originate the thermal Comptonization of soft photons produced in
the optical/UV range from an optically thick Keplerian disc (Magdziarz et al.,
1998; Dewangan et al., 2007; Done et al., 2012; Lohfink et al., 2012) or a
blurred reflection from ionized disc (Fabian et al., 2002; Ross & Fabian,
2005; Crummy et al., 2006; García et al., 2014). The iron line is thought to
be originated by the photoelectric absorption followed by the fluorescence
line emission from a dense and relatively cold accretion disc. Moreover, it is
believed that the Compton hump could be due to the Compton scattering
dominated above 10 keV in a relatively cold dense medium. Nevertheless, the
complex broad-band spectrum of AGNs requires a proper physical explanation of
the flow dynamics and radiative properties around the central engine across
the soft and hard energy regime of the X-ray.

In this scenario, the Two-Component Advective Flow (TCAF) (Chakrabarti &
Titarchuk, 1995) model, which combines the essence of all the salient features
of a viscous transonic flow (Chakrabarti, 1989, 1990, 1995) around black holes
is worth exploring. It is a physical solution encompassing hydrodynamics and
radiative processes. The transonic flow solution allows two types of accretion
flows depending on how efficiently angular momentum is being transported: a
viscous, geometrically thin, optically thick standard Keplerian component
(Shakura & Sunyaev, 1973) and a weakly viscous, geometrically thick, optically
thin sub-Keplerian halo component (Chakrabarti & Titarchuk, 1995). The latter
is basically an inefficiently radiating generalized Bondi flow with high
radial velocity till it forms the centrifugal barrier after which it becomes
efficient in radiating at higher energies. The Keplerian disc is formally
truncated at the centrifugal barrier, the outer boundary of which is the shock
location (Chakrabarti, 1989). The post-shock region (i.e., the region between
the shock and the innermost sonic point) is known as CENtrifugal barrier
supported BOundary Layer or CENBOL and it acts as the Compton cloud. The soft
photons from the Keplerian disc are upscattered by Comptonization process in
the post-shock region and produce the high energy X-ray photons. TCAF, a self-
consistent model, is quantified by four flow parameters: two types of
accretion rates, namely, the disc rate ($\dot{m}_{d}$) and halo rate
($\dot{m}_{h}$), size and density of the Compton cloud, through the shock
location ($X_{s}$) and the compression ratio ($R$), ratio of the post-shock
and the pre-shock flow densities ($\frac{\rho_{+}}{\rho_{-}}$). It also
requires an intrinsic parameter, namely, the mass of the central black hole
(in the units of $M_{\odot}$), and an extrinsic parameter, namely, the
normalization which is required to place the observed spectrum over the
theoretical spectrum of TCAF. The broadband spectra of M87 was explained with
this model by fitting the data from multi-wavelength observations(Mandal &
Chakrabarti, 2008). Later, TCAF has been implemented in the xspec as a local
table model and has been successful to fit the data of the Galactic black
holes (Debnath et al., 2014) and has also been able to estimate the mass of
nearby Seyfert 1 galaxy NGC 4151 using NuSTAR data (Nandi et al., 2019).

Arakelian 120 (Ark 120) is a nearby ($z=0.03271$111The redshift is taken from
the NASA/Infrared Process and Analysis center (IPAC) Extragalactic Database.
https://ned.ipac.caltech.edu) radio-quiet Seyfert 1 AGN with radio-loudness
$R\approx 0.1$ (Condon et al., 1998; Ho, 2002). This source was intensely
monitored nearly in all wavelengths: optical/UV (Kollatschny et al., 1981,
1981; Schulz & Rafanelli, 1981; Alloin et al., 1988; Marziani et al., 1992;
Peterson et al., 1998; Stanic et al., 2000; Popović et al., 2001; Doroshenko
et al., 2008; Kuehn et al., 2008) and X-ray (Vaughan et al., 2004; Nardini et
al., 2016; Reeves et al., 2016; Gliozzi et al., 2017; Lobban et al., 2018) and
was found to be consistently bright in optical, UV, and X-rays displaying
substantial wavelength-dependent variability (Gliozzi et al., 2017; Lobban et
al., 2018). From the simultaneous UV/X-ray measurements, it was reported that
the observations are neither ‘contaminated’ by absorption signatures along the
line of sight (Vaughan et al., 2004; Reeves et al., 2016; Crenshaw et al.,
1999) nor by neutral intrinsic absorbers (Reeves et al., 2016) around the
central engine. Furthermore, Ark 120 is nearly free from intrinsic reddening
in the IR-optical-UV continuum (Ward et al., 1987; Vasudevan et al., 2009).
Therefore, it provides one of the cleanest views ($N_{H}\sim 3\times 10^{19}$
cm-2; (Vaughan et al., 2004)) of the central region. This type of AGNs are
called “bare nucleus” Seyferts or bare AGNs. The estimated mass of the central
black hole of Ark 120 is M${}_{BH}=1.50\pm 0.19\times 10^{8}$ M⊙ (Peterson et
al., 2004) which was measured using the reverberation-mapping technique. From
the spectroscopic monitoring data of Ark 120 during 1976 to 2013 using a 70 cm
telescope, Denissyuk et al. (2015) estimated the mass of the central SMBH to
be M${}_{BH}=1.675\pm 0.028\times 10^{8}$ M⊙. This source has a low Eddington
ratio of $L_{bol}/L_{E}\sim 0.05$ (Vasudevan & Fabian, 2007) with a strong
soft-excess (Matt et al., 2014; Porquet et al., 2004, 2019) and a significant
broad Fe Kα line (Vaughan et al., 2004; Nardini et al., 2011). Nardini et al.
(2011) analyzed Ark 120 spectra, where, in the absence of absorber of complex
morphology, soft-excess was explained by reflection from the centrally located
hot and cold medium located at a distance. Marinucci et al. (2019) used the
Monte-Carlo technique to investigate the favourable shape of the Compton cloud
considering the future polarimetric missions such as IXPE (Weisskopf et al.,
2016).

Although Ark 120 is a widely studied source, the evolution of the X-ray
spectra over the last two decades is yet to be understood. However, a
steepening of the X-ray spectrum was observed during six-month monitoring in
2014 with Swift. The observed spectral variability was attributed to the
possible existence of a large disc reprocessing region (Gliozzi et al., 2017).
Again during 2017-18, a longer time delay was observed (Lobban et al., 2018)
between longer wavelength difference (i.e., optical and X-ray). They predicted
that the accretion disc could exist in a longer scale as predicted by standard
accretion disc theory. The soft-excess part of Ark 120 could be originated due
to the Comptonization within the hot electron cloud of various shape
(Marinucci et al., 2019), reflection from a cold medium (Nardini et al., 2011)
or the shock heating near the inner edge of the disc (Fukumura et al., 2016).
We analyzed the long term X-ray archival data of Ark 120 which provides an
ideal testbed to understand the soft-excess as well as its interaction with
the harder (>2 keV) photons. Along with the observations, we perform Monte-
Carlo simulations to find the effect of Comptonizaton within the energy range
of soft-excess. We also study the X-ray variability of the source over a
longer period and to calculate the approximate time-delays in X-ray bands. For
the first time, we also find the flow and system parameters by fitting of the
X-ray data. The paper is structured in the following way: in Sec 2, we provide
the details of the observational data and their reduction procedure. The
results of the spectral and temporal analysis are presented in Sec 3 and 4. We
discuss our findings in Sec 5 and finally, draw our conclusions in Sec 6.

##  2 Observation and Data Reduction

We use the publicly available archival data of XMM-Newton, NuSTAR, Chandra,
and Suzaku using HEASARC222http://heasarc.gsfc.nasa.gov/. We reprocessed all
data using HEAsoft v6.26.1 (Arnaud, 1996), which includes XSPEC v12.10.1f.

Table 1: Observation Log ID | Date | Obs. ID | Instrument | Exposures
---|---|---|---|---
| (yyyy-mm-dd) |  |  | (ks)
XMM1 | 2003-08-24 | 0147190101 |  XMM-Newton/EPIC-pn | 112.15
S1 | 2007-04-01 | 702014010 |  Suzaku/XIS-HXD | 100.86
XRT1 | 2008-07-24 | 00037593001 |  Swift/XRT | 10.86
| -2008-08-03 | -00037593003 |  |
XMM2 | 2013-02-18 | 0693781501 |  XMM-Newton/EPIC-pn | 130.46
N1 | 2013-02-18 | 60001044004 |  NuSTAR/FPMA | 65.46
XMM3 | 2014-03-22 | 0721600401 |  XMM-Newton/EPIC-pn | 124.0
N2 | 2014-03-22 | 60001044002 |  NuSTAR/FPMA | 55.33
XRT2 | 2014-09-04 | 00091909002 |  Swift/XRT | 22.81
| -2014-10-19 | -00091909022 |  |
XRT3 | 2014-10-22 | 00091909023 |  Swift/XRT | 20.18
| -2014-12-05 | -00091909044 |  |
XRT4 | 2014-12-09 | 00091909045 |  Swift/XRT | 23.48
| -2015-01-26 | -00091909068 |  |
XRT5 | 2015-01-26 | 00091909069 |  Swift/XRT | 21.66
| -2015-03-15 | -00091909090 |  |
XRT6 | 2017-12-07 | 00010379001 |  Swift/XRT | 44.14
| -2018-01-24 | -00010379048 |  |

###  2.1 XMM-Newton

Ark 120 has been observed by XMM-Newton (Jansen et al., 2001) during three
epochs from 2003 to 2014. In 2003 and 2013, it has made $\sim$ 112 ks (XMM1)
and $\sim$ 130 ks (XMM2) observations respectively. The XMM1 data is used by
(Vaughan et al., 2004) and reported that the source Ark 120 is one of the
cleanest Sy1 type AGN. In 2014, XMM-Newton observed Ark 120 four times between
March 18 and March 24. Out of these, one (XMM3) was simultaneous with NuSTAR
observation. The details of the observation log are presented in Table 1. It
was observed that the X-ray flux of this source was about a factor of two
higher in 2014 than the XMM2 observation (Matt et al., 2014; Marinucci et al.,
2019) made in 2013. A similar trend of flux variation was also reported in
optical/UV (Lobban et al., 2018) band.

Due to the high brightness of the source, the European Photon Imaging Camera
(EPIC-pn (Strüder et al., 2001)) operated in Small Window (SW) mode to prevent
any pile-up. The details of the XMM-Newton/EPIC-pn observations of this source
are listed in Table-1. We reprocessed the raw data to level 1 data for EPIC-pn
by Scientific Analysis System (SAS
v16.1.0333https://www.cosmos.esa.int/web/xmm-newton/sas-threads) with
calibration files dated February 2, 2018. We have used only the unflagged
(FLAG == 0) events for excluding the edge of CCD and the edge of the bad
pixel. Besides this, we also use PATTERN $\leq 4$ for single and double pixel.
We exclude the photon flares by proper GTI files to acquire the maximum signal
to noise ratio. After that, we use an annular area of 30″ outer radii and 5″
inner radii centered at the source to extract the source event. For the
background, we use a circle of 60″ in the lower part of the window that
contains no (or negligible) source photons. The response files (arf and rmf
files) for each EPIC-pn spectral data set were produced with SAS tasks ARFGEN
and RMFGEN, respectively. The GRPPHA task is used with 100 counts per bin for
0.3 - 10.0 keV EPIC-pn spectra.

###  2.2 Suzaku

Suzaku observed Ark 120 on 2007 April 1 (Obs ID: 702014010) in HXD normal
position with exposure of $\sim$ 101 ks using X-ray imaging spectrometer
(Koyama et al., 2007) and $\sim$ 89 ks for Hard X-ray Detector (Takahashi et
al., 2007). The photons were collected in both $3\times 3$ and $5\times 5$
editing modes. From this observation, a presence of soft-excess emission in
soft X-ray was reported by (Nardini et al., 2011). Also, Fe K$\alpha$ emission
line with full-width at half maximum of $4700^{+2700}_{-1500}$ km s-1 was
previously reported by (Nardini et al., 2016) by using Suzaku observation
along with XMM-Newton, Chandrai, and NuSTAR.

We use the standard data reduction technique for Suzaku data analysis
illustrated in Suzaku Data Reduction
Guide444http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/abc/ and followed
the recommended screening criteria while extracting Suzaku/XIS spectrum and
light-curves. The latest calibration
files555http://www.astro.isas.jaxa.jp/suzaku/caldb/ available (2014-02-03)
using FTOOLS 6.25 is used to reprocess the event files. The source spectra and
lightcurves are extracted from a circular region of radius 200″centered on the
Ark 120 and the background region is selected on the same slit with a circular
region 250″. Finally, we merge the two front illuminated detectors (XIS0 and
XIS3) to produce the final spectra and lightcurves for Ark 120. We generated
the response files through XISRESP script.

As Suzaku has a high energy X-ray detector (HXD), we use the HXD/PIN data for
our analysis. We reprocessed the unfiltered event files using the standard
tools. The output spectrum and lightcurves are extracted by using the
hxdpinxbpi and hxdpinxblc, respectively. Further, we correct the spectrum to
take into account both the non-X-ray and the cosmic X-ray backgrounds and the
dead time correction.

###  2.3 NuSTAR

NuSTAR (Harrison et al., 2013) observed Ark 120 simultaneously with XMM-Newton
with FPMA and FPMB on 2013 February 18 (N1) and 2014 March 22 (N2) for the
exposure of $\sim$166 ks and $\sim$ 131 ks respectively. The details of the
observation log are given in Table 1. We consider both N1 and N2 observations
for our analysis. (Porquet et al., 2018, 2019) used this data along with XMM-
Newton and determined the spin $0.83^{+0.05}_{-0.03}$ and comment on the
dimension of the corona and temperature by analyzing these X-ray data.

The level 1 data is produced from the raw data by using the NuSTAR data
analysis software (NuSTARDAS v1.8.0). The cleaned event files are produced
with standard NUPIPELINE task and calibrated with the latest calibration files
available in the NuSTAR calibration database
(CALDB)666http://heasarc.gsfc.nasa.gov/FTP/caldb/data/nustar/fpm/. We chose
90″ radii for source and 180″ radii for the background region on the same
detector to avoid contamination and detector edges. For the final background-
subtracted lightcurves, we use 100s bin for both FPMA and FPMB. As both
detectors are identical, here we present the results of FPMA only. The
response files (arf and rmf files) are generated by using the numkrmf and
numkarf modules, respectively.

###  2.4 Swift data

Swift X-ray telescope (XRT; Burrows et al. (2005)), working in the energy
range of 0.2 to 10.0 keV, is an X-ray focusing telescope. XRT observed this
source in both WT (windowed timing) and pc (photon count) modes depending on
the brightness of the source. Ark 120 was observed over $\sim 130$ times from
2008-07-24 to 2018-01-24. In 2008, Swift observed three times, July 24, July
31 and August 3. We stack the spectra to produce a combined spectrum (XRT1).
Then, it again observed on 2014-03-22, which has a simultaneous observation
with XMM and NuSTAR. We consider the XMM3 observation over this particular XRT
observation. Swift observed Ark 120 from 2014-09-06 to 2015-03-15 on a nearly
daily basis. Further, we stack these observations into four observations
(XRT2, XRT3, XRT4, XRT5) with each observations spanning around 50 days. In
the last epoch, Swift observed Ark 120 from 2017-12-05 to 24-01-2018 over
$\sim$ 50 days. We stack the observations to produce the spectra of XRT6. The
details of the observation log are stated in Table 1. We use the online tool
“XRT product builder”777http://swift.ac.uk/user_objects/ Evans et al. (2009)
to extract the spectrum and light curves. This product builder performs all
necessary processing and calibration and produces the final spectra and
lightcurves of Ark 120 in WT and PC mode.

##  3 Spectral Analysis

We use XMM-Newton, Suzaku, NuSTAR, and Swift data for the spectral analysis
and explore the spectral variation over $\sim$15 years (2003-2018) period
using XSPEC v12.10.1f (Arnaud, 1996). We explore the broad spectral properties
with nthcomp model (Zdziarski, Johnson & Magdziarz, 1996). Later, we apply Two
Component Advective Flow (TCAF) model (Chakrabarti & Titarchuk, 1995) to
extract the physical flow parameters such as the accretion rates and size of
the Compton cloud.

Along with these models, we use a Gaussian component for the Fe fluorescent
emission line. While fitting the data, we use two absorption components,
namely TBabs and zTBabs (Wilms et al., 2000). The component, TBabs is used for
the Galactic absorption, where hydrogen column density ($N_{H,gal}$) is fixed
at $9.78\times 20^{20}$ cm-2 (Kalberla et al., 2005). To calculate the error
for each parameter in spectral fitting with 90% confidence level, we use
‘error’ command in XSPEC.

We use following cosmological parameters in this work: $H_{0}$ = 70 km s-1 Mpc
-1, $\Lambda_{0}$ = 0.73, $\Omega_{M}$ = 0.27 (Bennett et al., 2003). With the
assumed cosmological parameters, the luminosity distance of Ark 120 is 142
Mpc.

Table 2:  nthcomp fitting result for the spectrum above 3.0 keV. The optical depth $\tau$ is calculated from equation-1. ID | MJD | $\Gamma^{nth}$ | $kT_{e}$ | Fe $K_{\alpha}$ | EW | $\chi/dof$ | $\tau^{*}$
---|---|---|---|---|---|---|---
|  |  | (keV) | (keV) | (eV) |  |
XMM1 | $52875$ | $1.90^{+0.01}_{-0.01}$ | $159.45^{+81.68}_{-81.69}$ | $6.40^{+0.016}_{-0.017}$ | $116^{+3}_{-4}$ | 312.33/300 | $0.733\pm 0.003$
S1 | $54191$ | $2.08^{+0.03}_{-0.03}$ | $124.65^{+35.54}_{-35.21}$ | $6.38^{+0.052}_{-0.052}$ | $710^{+10}_{-10}$ | 1117.31/1093 | $0.726\pm 0.008$
XRT1 | $54676$ | $1.76^{+0.02}_{-0.08}$ | $217.72^{+105.6}_{-112.5}$ | - | - | 75.68/74 | $0.671\pm 0.030$
XMM2+N1 | $56341$ | $1.75^{+0.01}_{-0.02}$ | $221.56^{+105.3}_{-107.5}$ | $6.42^{+0.061}_{-0.062}$ | $136^{+8}_{-9}$ | 644.55/641 | $0.670\pm 0.074$
XMM3+N2 | $56738$ | $1.87^{+0.01}_{-0.01}$ | $205.95^{+100.6}_{-99.87}$ | $6.37^{+0.052}_{-0.052}$ | $227^{+12}_{-11}$ | 508.07/469 | $0.612\pm 0.003$
XRT2 | $56926$ | $1.60^{+0.01}_{-0.02}$ | $274.40^{+136.5}_{-130.8}$ | $-$ | - | 306.65/290 | $0.700\pm 0.008$
XRT3 | $56974$ | $1.84^{+0.02}_{-0.02}$ | $215.72^{+105.5}_{-105.8}$ | $-$ | - | 319.98/320 | $0.610\pm 0.006$
XRT4 | $57024$ | $1.72^{+0.02}_{-0.03}$ | $225.57^{+109.7}_{-109.9}$ | $-$ | - | 269.17/280 | $0.688\pm 0.011$
XRT5 | $57073$ | $1.88^{+0.02}_{-0.02}$ | $201.58^{+99.78}_{-99.20}$ | $-$ | - | 246.53/261 | $0.616\pm 0.006$
XRT6 | $58118$ | $1.65^{+0.02}_{-0.02}$ | $246.87^{+120.9}_{-122.8}$ | $-$ | - | 327.78/318 | $0.708\pm 0.008$
Table 3:  Soft-excess spectral indices are generated while keeping the spectral slope of nthcomp ($\Gamma^{nth}$) frozen. Intrinsic luminosities are calculated for both of the components using clum in the energy energy 0.5 to 10.0 kev. ID | $\Gamma^{PC}$ | $Norm^{PC}$ | $L^{PC}$ | $\Gamma^{SE}$ | $Norm^{SE}$ | $L^{SE}$
---|---|---|---|---|---|---
| $=\Gamma^{nth}$ | $(10^{-2})$ |  |  | $(10^{-2})$ |
XMM1 | $1.90$ | $1.16^{+0.04}_{-0.05}$ | $44.18^{+0.06}_{-0.07}$ | $3.15^{+0.07}_{-0.06}$ | $0.58^{+0.02}_{-0.02}$ | $43.66^{+0.05}_{-0.04}$
S1 | $2.08$ | $18^{+20.3}_{-25.6}$ | $45.35^{+0.05}_{-0.05}$ | $2.52^{+0.02}_{-0.02}$ | $2105^{+10.6}_{-16.5}$ | $45.58^{+0.04}_{-0.04}$
XRT1 | $1.76$ | $0.66^{+0.03}_{-0.03}$ | $43.99^{+0.04}_{-0.04}$ | $4.11^{+0.22}_{-0.20}$ | $0.84^{+0.10}_{-0.10}$ | $43.87^{+0.02}_{-0.03}$
XMM2+N1 | $1.75$ | $0.57^{+0.03}_{-0.03}$ | $43.93^{+0.05}_{-0.05}$ | $3.03^{+0.03}_{-0.02}$ | $0.19^{+0.03}_{-0.05}$ | $43.16^{+0.03}_{-0.03}$
XMM3+N2 | $1.86$ | $1.21^{+0.01}_{-0.01}$ | $44.90^{+0.04}_{-0.04}$ | $4.23^{+0.02}_{-0.02}$ | $0.88^{+0.10}_{-0.10}$ | $43.19^{+0.04}_{-0.04}$
XRT2 | $1.60$ | $0.48^{+0.03}_{-0.03}$ | $44.92^{+0.04}_{-0.04}$ | $2.92^{+0.19}_{-0.20}$ | $0.57^{+0.03}_{-0.04}$ | $43.66^{+0.04}_{-0.04}$
XRT3 | $1.84$ | $0.79^{+0.03}_{-0.04}$ | $44.04^{+0.05}_{-0.05}$ | $3.27^{+0.27}_{-0.27}$ | $0.47^{+0.06}_{-0.06}$ | $43.57^{+0.05}_{-0.05}$
XRT4 | $1.72$ | $0.57^{+0.04}_{-0.05}$ | $43.94^{+0.04}_{-0.04}$ | $2.53^{+0.10}_{-0.12}$ | $0.39^{+0.05}_{-0.06}$ | $43.54^{+0.04}_{-0.04}$
XRT5 | $1.88$ | $0.76^{+0.03}_{-0.03}$ | $44.00^{+0.04}_{-0.04}$ | $3.17^{+0.34}_{-0.34}$ | $0.31^{+0.05}_{-0.05}$ | $43.37^{+0.05}_{-0.05}$
XRT6 | $1.65$ | $0.42^{+0.02}_{-0.03}$ | $43.84^{+0.03}_{-0.03}$ | $2.96^{+0.28}_{-0.29}$ | $0.23^{+0.02}_{-0.03}$ | $43.27^{+0.06}_{-0.05}$
Table 4:  The TCAF parameter space is defined in the file lmod.dat.

Model parameters | Parameter units | Default value | Min. | Min. | Max. | Max. | Increment
---|---|---|---|---|---|---|---
$\rm M_{BH}$ | $\rm M_{Sun}$ | $\rm 1.0\times 10^{8}$ | $2\times 10^{6}$ | $2\times 10^{6}$ | $5.5\times 10^{9}$ | $5.5\times 10^{9}$ | $10.0$
$\dot{m}_{d}$ | $\rm Edd$ | $\rm 0.001$ | $0.0001$ | $0.0001$ | $1.0$ | $2.0$ | $0.0001$
$\dot{m}_{h}$ | $\rm Edd$ | $\rm 0.01$ | $0.0001$ | $0.0001$ | $2.0$ | $3.0$ | $0.0001$
$\rm X_{s}$ | $\rm r_{g}$ | $\rm 100.0$ | $10.0$ | $10.0$ | $1000.0$ | $1000.0$ | $2.0$
$\rm R$ |  | $\rm 1.5$ | $1.1$ | $1.1$ | $6.8$ | $6.8$ | $0.1$

###  3.1  Nthcomp

We have started the spectral fitting with nthcomp model, and the model in
XSPEC reads as:

TBabs*zTBabs*(nthcomp+zGaussian)

nthcomp is a thermally Comptonized continuum model proposed by Zdziarski,
Johnson & Magdziarz (1996) and later extended by Zycki, Done & Smith (1999).
We fit all X-ray spectrum above 3.0 keV by this baseline model. The model
depends on the seed photon energy ($kT_{bb}$), which we consider at 3 eV for
all spectrum. Although, Marinucci et al. (2019) considered $kT_{bb}$ at 15 eV.
It is to be noted that, we vary $kT_{bb}$ from 1 eV to 50 eV, and failed to
notice any deviation in the residuals of the fitted spectra. We consider these
seed photons to be disc-blackbody type. For that, we have opted for the inp-
type is 1 for all fit. For the spectral fitting, first, we consider the energy
range 3.0 to 10.0 keV. The fitted asymptotic power-law photon index
$\Gamma=1.90$, electron temperature $kT_{e}=159.45$ keV and an iron K$\alpha$
line at 6.40 keV with equivalent width (EW) of $116^{+3}_{-4}$ eV with reduced
chi-square ($\chi^{2}/dof$)=1.04 for degrees of freedom (dof) = 300 is
obtained. Next, we analyse the data from the 2007 Suzaku observation. We have
combined the Suzaku/XIS observation with Suzaku/HXD and make a spectrum from
0.5 to 40.0 keV. But, we fit 3.0 to 40.0 keV spectrum using the baseline
model. The fitted parameters are $\Gamma=2.08$, $kT_{e}=124.65$ keV and iron
K$\alpha$ line at 6.38 keV with equivalent width (EW) of $710^{+10}_{-10}$ eV.
We are also in need of an additional powerlaw and Gaussian to take care of
high energy (above 10.0 keV) spectrum and emission lines. We have obtained the
reduced chi-square ($\chi^{2}/dof$)=1.02 for degrees of freedom (dof) = 1093
for this fitting. We have fitted the combined spectrum of XMM2+N1 (MJD-56341)
and XMM3+N2 (MJD-56738) spectrum using this model for the energy range 3.0 to
79.0 keV with the model parameters such as $\Gamma=1.75$ & $1.87$ and
corresponding $kT_{e}=221.56$ & $205.95$ respectively. We have applied a
zGaussian for a Fe K$\alpha$ line at $6.42^{+0.061}_{-0.062}$ &
$6.37^{+0.052}_{-0.052}$ keV with equivalent widths (EW) of $136^{+8}_{-9}$ &
$227^{+12}_{-11}$ eV for these combined spectra and the
($\chi^{2}/dof$)=644.55/641 & ($\chi^{2}/dof$)= 508.07/469 respectively. Next,
we analyse the data obtained from Swift/XRT observation for the energy range
of 3.0 to 10.0 keV. Fe K$\alpha$ line is not detected for all the six XRT
spectra. We have fitted the Swift/XRT spectra by removing Gaussian component
from the baseline model. The power-law index $\Gamma$ vary from 1.60 to 1.88
and the corresponding electron temperature $kT_{e}$ vary from 274.40 to 201.58
keV respectively. The nthcomp model fitted spectral analysis result is
presented in Table 2. Furthermore, we calculate the optical depth for each
observation using the formula:

$\tau=\sqrt{\frac{9}{4}+\frac{3}{\theta_{e}(\Gamma+2)(\Gamma-1)}}-\frac{3}{2},$
(1)

by inverting the relation A1 is presented in Zdziarski, Johnson & Magdziarz
(1996). Here, $\theta_{e}=\frac{kT_{e}}{m_{e}c^{2}}$ is the electron energy
with respect to the rest mass energy. The value of optical depth $\tau$ for
each observation is provided in Table 2. The maximum error in optical depth is
obtained from
$\Delta\tau\sim(\frac{1}{2}\frac{\Delta\theta_{e}}{\theta_{e}}+\frac{\Delta\Gamma}{\Gamma})\times\tau$,
where $\Delta\theta_{e}$ and $\Delta\Gamma$ are considered from the fitted
errors presented in Table 2.

We address the soft-excess (< 3 keV) part by adding another powerlaw
component. We freeze the $\Gamma$ obtained earlier while fitting the primary
continuum alone. The second power-law fits the soft-excess, and the results
are presented in Table 3. It should be noted that the spectral index of soft-
excess ($\Gamma^{SE}$) is higher than the spectral index of the primary
continuum ($\Gamma^{PC}$) for every observation.

Figure 1: Variation of $\chi_{red}$ is shown for each model components on
broadband spectra of Ark 120 during 2014 epoch. Primarily, we have started
with TCAF, and then added zGaussian and Pexrav upon necessity.

Figure 2: TCAF model fitted spectra of Ark 120 from the XMM-Newton, Suzaku,
NuSTAR and Swift observations along with the residuals obtained from the
spectral fitting. Table 5:  TBabs*zTBabs*(TCAF+zGaussian) model fitted
Parameters in 0.2-79.0 keV energy band for Ark 120. The TBabs is fixed at
$N_{H_{gal}}$= $9.78\times 10^{20}$ cm-2. The second column shows the
variation of zTBabs for z = 0.033.

ID | MJD | $N_{H}$ | $M_{BH}$ | $\dot{m}_{d}$ | $\dot{m}_{h}$ | $X_{s}$ | $R$ | $N_{TCAF}$ | $\Gamma_{pexrav}$ | $R_{ref}$ | $N_{pexrav}$ | $\chi^{2}/dof$
---|---|---|---|---|---|---|---|---|---|---|---|---
|  | $(10^{20}cm^{-2})$ | $\rm(10^{8}M_{\odot})$ | $(\dot{m}_{Edd})$ | $(\dot{m}_{Edd})$ | $(r_{g})$ |  | $(10^{-3})$ |  |  |  ($10^{-3}$) |
XMM1 | $\rm 52875$ | $1.0^{+0.2}_{-0.2}$ | $1.50^{+0.03}_{-0.03}$ | $\rm 0.063^{+0.002}_{-0.002}$ | $\rm 0.112^{+0.001}_{-0.001}$ | $20.36^{+4.46}_{-4.55}$ | $1.95^{+0.34}_{-0.33}$ | $0.16^{+0.05}_{-0.05}$ | $0.14^{+0.10}_{-0.08}$ | $1.96^{+0.05}_{-0.09}$ | $0.14^{+0.04}_{-0.05}$ | $1026.20/842$
|  |  |  |  |  |  |  |  |  |  |  |
S1 | $\rm 54191$ | $1.4^{+0.1}_{-0.2}$ | $1.49^{+0.04}_{-0.04}$ | $\rm 0.126^{+0.002}_{-0.001}$ | $\rm 0.191^{+0.001}_{-0.001}$ | $21.44^{+4.96}_{-4.85}$ | $1.66^{+0.54}_{-0.57}$ | $233.6^{+54.26}_{-58.65}$ | $1.46^{+0.15}_{-0.41}$ | $0.642^{+0.71}_{-0.51}$ | $5.09^{+1.05}_{-1.03}$ | $1869.89/1673$
|  |  |  |  |  |  |  |  |  |  |  |
XRT1 | $\rm 54675$ | $1.6^{+0.6}_{-0.4}$ | $1.49^{+0.19}_{-0.15}$ | $\rm 0.064^{+0.005}_{-0.005}$ | $\rm 0.110^{+0.004}_{-0.003}$ | $30.08^{+5.36}_{-6.24}$ | $2.80^{+0.54}_{-0.56}$ | $0.54^{+0.01}_{-0.02}$ | $-$ | $-$ | $-$ | $307.78/283$
|  |  |  |  |  |  |  |  |  |  |  |
XMM2+N1 | $\rm 54341$ | $1.9^{+0.3}_{-0.2}$ | $1.50^{+0.08}_{-0.07}$ | $\rm 0.068^{+0.006}_{-0.005}$ | $\rm 0.111^{+0.004}_{-0.004}$ | $52.83^{+8.65}_{-8.56}$ | $2.83^{+0.55}_{-0.52}$ | $0.57^{+0.02}_{-0.02}$ | $0.90^{+0.09}_{-0.10}$ | $0.254^{+0.47}_{-0.06}$ | $0.25^{+0.06}_{-0.05}$ | $1230.15/1112$
|  |  |  |  |  |  |  |  |  |  |  |
XMM3+N2 | $\rm 54738$ | $2.3^{+0.3}_{-0.3}$ | $1.51^{+0.09}_{-0.10}$ | $\rm 0.103^{+0.006}_{-0.005}$ | $\rm 0.126^{+0.004}_{-0.004}$ | $28.24^{+5.04}_{-5.25}$ | $2.43^{+0.55}_{-0.58}$ | $0.31^{+0.01}_{-0.01}$ | $1.66^{+0.19}_{-0.19}$ | $0.96^{+0.05}_{-0.56}$ | $0.12^{+0.06}_{-0.06}$ | $1578.92/1359$
|  |  |  |  |  |  |  |  |  |  |  |
XRT2 | $\rm 56926$ | $2.5^{+0.1}_{-0.1}$ | $1.49^{+0.18}_{-0.20}$ | $\rm 0.068^{+0.005}_{-0.006}$ | $\rm 0.110^{+0.003}_{-0.003}$ | $53.56^{+8.27}_{-8.87}$ | $2.73^{+0.51}_{-0.47}$ | $0.36^{+0.01}_{-0.02}$ | $-$ | $-$ | $-$ | $579.89/555$
|  |  |  |  |  |  |  |  |  |  |  |
XRT3 | $\rm 56974$ | $1.9^{+0.5}_{-0.5}$ | $1.51^{+0.19}_{-0.20}$ | $\rm 0.068^{+0.006}_{-0.006}$ | $\rm 0.110^{+0.004}_{-0.005}$ | $55.16^{+8.57}_{-8.80}$ | $2.74^{+0.45}_{-0.41}$ | $0.25^{+0.01}_{-0.01}$ | $-$ | $-$ | $-$ | $630.08/594$
|  |  |  |  |  |  |  |  |  |  |  |
XRT4 | $\rm 57024$ | $1.1^{+0.2}_{-0.3}$ | $1.50^{+0.15}_{-0.18}$ | $\rm 0.061^{+0.006}_{-0.006}$ | $\rm 0.110^{+0.005}_{-0.003}$ | $56.86^{+10.97}_{-10.89}$ | $2.69^{+0.48}_{-0.47}$ | $0.11^{+0.01}_{-0.01}$ | $-$ | $-$ | $-$ | $702.39/548$
|  |  |  |  |  |  |  |  |  |  |  |
XRT5 | $\rm 57073$ | $1.4^{+0.4}_{-0.3}$ | $1.49^{+0.16}_{-0.15}$ | $\rm 0.069^{+0.006}_{-0.007}$ | $\rm 0.110^{+0.005}_{-0.005}$ | $57.87^{+12.99}_{-12.08}$ | $2.77^{+0.52}_{-0.54}$ | $0.28^{+0.02}_{-0.01}$ | $-$ | $-$ | $-$ | $551.49/531$
|  |  |  |  |  |  |  |  |  |  |  |
XRT6 | $\rm 58118$ | $2.0^{+0.4}_{-0.4}$ | $1.51^{+0.16}_{-0.15}$ | $\rm 0.081^{+0.006}_{-0.005}$ | $\rm 0.140^{+0.006}_{-0.007}$ | $42.95^{+8.98}_{-8.20}$ | $2.69^{+0.59}_{-0.61}$ | $0.22^{+0.01}_{-0.01}$ | $-$ | $-$ | $-$ | $612.9/589$
|  |  |  |  |  |  |  |  |  |  |  |

Figure 3: Variation of different model parameters with time are presented.

###  3.2 TCAF

From the nthcomp model fitting, we have extracted several valuable information
on the spectral hardness and electron temperature of the emitting system in a
time duration of $\sim$ 15 years. We have also calculated the optical depths
from these parameters, which are shown in Table 2. However, the fundamental
properties, such as the central black hole mass, accretion rates, the size of
the Compton cloud radius could provide a deeper physical understanding of the
system. To estimate these quantities, we use the Two-Component Advective Flow
(TCAF) model (Chakrabarti & Titarchuk, 1995) for our spectral analysis. For
the spectral fitting, the model in XSPEC reads as:

TBabs*zTBabs*(TCAF+zGaussian)

TCAF is based on one black hole parameter and four flow parameters: (i) black
hole mass in units of the solar mass ($M_{\odot}$); (ii) Keplerian disc
accretion rate ($\dot{m}_{d}$) in the unit of the Eddington rate
($\dot{M}_{EDD}$); (iii) Sub-Keplerian halo accretion rate ($\dot{m}_{h}$) in
units of Eddington rate ($\dot{M}_{EDD}$); (iv) shock compression ratio (R)
and (v) shock location ($X_{s}$) in units of the Schwarzschild radius
($r_{g}=2GM/c^{2}$). The upper and lower limits of all the parameters are put
in a data file called lmodel.dat provided in Table-4 as an input to run the
source code using initpackage and lmod task in XSPEC. For the final spectral
fitting of a specified observation, we run the source code for a vast number
of times and select the best spectrum from many spectra using minimization of
$\chi$ method. First, we have started fitting by the baseline model described
as above. Some spectra, like XMM1, S1, XMM2+N1, XMM3+N2 have high reduced
$\chi^{2}$ ($\chi^{2}_{red}>2$) value. We noticed that the model has deviated
from the actual data at the high energy end. To compensate for that, we have
added a powerlaw/pexrav with the baseline model. Thus the model became:

TBabs*zTBabs*(TCAF+powerlaw/pexrav+zGaussian).

We have fitted the spectra with this model and found $\chi^{2}_{red}\approx
1$. Further, to investigate the source of this power-law (whether it is from
reflection or not), we have replaced the powerlaw component by pexrav
(Magdziarz & Zdziarski, 1995). The pexrav model has a power-law continuum with
a reflected component from an infinite neutral slab. We have estimated the
relative reflection coefficient ($R_{ref}$) with photon index
($\Gamma_{pexrav}$) and cosine of inclination angle $\cos\theta$ from the
model fitting. We find $\theta$ to vary from $40\degree$ to $72\degree$. We
fix abundances for heavy elements, such as iron at the Solar value (i.e., 1).
For the photon index ($\Gamma_{pexrav}$), first, we freeze its value to the
value of $\Gamma$ obtained from nthcomp. For this, we have found
$\chi^{2}_{red}>2$. Thereafter, we thaw this parameter and fit it again which
have resulted $\chi^{2}_{red}\approx 1$ with new value of $\Gamma_{pexrav}$.

We first fit the XMM-Newton observation (XMM1) during 2003 (MJD-52875) in the
energy range of 0.2 to 10.0 keV with TBabs*zTBabs*(TCAF+zGaussian) model.
However, we found a high $\chi^{2}_{red}$. The model has deviated after 9.2
keV from the actual data. As mentioned above, we then add a powerlaw with the
baseline model, and then the powerlaw is replaced by pexrav. The fitted
parameters are, $M_{BH}=1.5\times 10^{8}M_{\odot}$, $\dot{m}_{d}=0.063$,
$\dot{m}_{h}=0.112$, $X_{s}=20.36$, $R=1.95$ with $\Gamma_{pexrav}=0.14$,
$R_{ref}=1.96$, and $E_{fold}=16.08$ keV and the corresponding
$\chi^{2}=1026.20$ with degrees of freedom (dof)= 842. The Fe line is found at
$6.4$ keV with an equivalent width of $116$ eV.

Next, we consider the Suzaku observation (S1) of 2007 (MJD-54191). We combine
the Suzaku/XIS and Suzaku/HXD spectra and make a broadband spectrum in the
energy range of 0.5 to 40 keV. We follow the similar steps as described in
XMM1 fitting and the fitted parameters are $M_{BH}=1.49\times
10^{8}M_{\odot}$, $\dot{m}_{d}=0.126$, $\dot{m}_{h}=0.191$, $X_{s}=21.44$,
$R=1.66$ with $\Gamma_{pexrav}=1.46$, $R_{ref}=0.642$, and the corresponding
$\chi^{2}_{red}/dof=1869.89/1673$. The position of Fe line is $6.38$ keV with
an equivalent width of $710$ eV. It is to be noted that, within $6-7$ keV
range, Nardini et al. (2011) reported the possibility of three lines for XMM1
and two lines for S1 observation respectively.

Following a similar procedure, we fit the broadband spectra of Ark 120 for the
observations during 2013 XMM2+N1 (MJD-56341) and 2014 XMM3+N2 (MJD-56738). For
these, we have obtained $M_{BH}=1.50$ & $1.51\times 10^{8}M_{\odot}$,
$\dot{m}_{d}=0.068$ & $0.103$, $\dot{m}_{h}=0.111$ & $0.126$, $X_{s}=52.83$ &
$28.24$, $R=2.83$ & $2.43$ with $\Gamma_{pexrav}=0.96$ & $1.66$ respectively.
The details of data fitting are given in Table-5.

We fit all the six Swift/XRT spectra using the baseline model. Here, we do not
find any Fe line in all these spectra. From the fitting, it is noticed that
the mass of the central black hole $M_{BH}$ =$1.5\times 10^{8}M_{\odot}$, the
disc $\dot{m}_{d}\sim 0.065$ and halo accretion rates $\dot{m}_{h}$$\sim
0.110$ are more or less constant except XRT6 observation. Here, we find
$\dot{m}_{d}=0.081$ & $\dot{m}_{h}=0.14$ and the corresponding shock location
has moved inward from 57.87 to 42.95 $r_{g}$. Therefore, the shock location
($X_{s}$) has varied in between $30.0$ to $57.87~{}r_{g}$, and the
corresponding variation of the compression ratio (R) is in between $2.6$ to
$2.8$ within September 2014 to January 2018. Here, we do not require any
additional powerlaw to fit the high energy spectra. The details of the
parameter variations are presented in Table-5. In Figure 2, we plot the model
fitted spectrum with the variation of $\chi$. Detailed discussions on spectral
properties are demonstrated in Sec 5.1.

Table 6: Variability statistics in various energy ranges are shown in this Table. We have opted for 100s time bins for variability analysis. In some cases, the average error of observational data exceeds the limit of $1\sigma$, resulting negative excess variance. In such cases, we have imaginary $F_{var}$, which are not shown in the table. ID | Energy band | $N$ | $x_{max}$ | $x_{min}$ | $\frac{x_{max}}{x_{min}}$ | $\sigma^{2}_{NXS}$ | $F_{var}$
---|---|---|---|---|---|---|---
| keV |  | Count/s | Count/s |  | $(10^{-2})$ | $(10^{-2})$
XMM1 | 0.2-2.0 | 1117 | 21.95 | 19.58 | 1.12 | $0.57\pm 0.003$ | $1.6\pm 0.14$
XMM2 | 0.2-2.0 | 1294 | 10.24 | 8.40 | 1.21 | $2.9\pm 0.015$ | $5.6\pm 0.40$
XMM3 | 0.2-2.0 | 1309 | 21.37 | 17.11 | 1.25 | $8.22\pm 0.011$ | $6.4\pm 0.41$
XMM1 | 3-10.0 | 1117 | 1.95 | 1.53 | 1.79 | $0.18\pm 0.023$ | $3.2\pm 0.04$
XMM2 | 3-10.0 | 1294 | 1.22 | 0.94 | 1.30 | $0.137\pm 0.035$ | $3.5\pm 0.55$
XMM3 | 3-10.0 | 1309 | 3.64 | 2.92 | 1.24 | $0.56\pm 0.0011$ | $4.1\pm 0.34$
N1 | 10.0-78.0 | 722 | 0.711 | 0.105 | 6.748 | $0.093\pm 0.007$ | $7.5\pm 1.6$
N2 | 10.0-78.0 | 667 | 1.712 | 0.239 | 7.143 | $0.147\pm 0.024$ | $3.5\pm 3.6$
XMM1 | 0.5-10.0 | 1117 | 20.46 | 15.26 | 1.341 | $10.11\pm 0.06$ | $2.36\pm 0.14$
S1 | 0.5-10.0 | 586 | 9.80 | 5.58 | 1.76 | $5.64\pm 0.31$ | $8.62\pm 0.31$
XRT1 | 0.5-10.0 | 8 | 3.22 | 1.67 | 3.01 | -$22.3\pm 5.6$ | $-$
XMM2 | 0.5-10.0 | 1294 | 10.36 | 6.73 | 1.54 | $2.93\pm 0.02$ | $5.85\pm 0.19$
XMM3 | 0.5-10.0 | 1309 | 20.13 | 13.67 | 1.47 | $5.80\pm 0.01$ | $5.79\pm 0.15$
XRT2 | 0.5-10.0 | 50 | 2.13 | 0.70 | 3.02 | $5.50\pm 0.44$ | $20.70\pm 2.3$
XRT3 | 0.5-10.0 | 43 | 2.79 | 1.52 | 2.79 | $3.61\pm 0.42$ | $15.31\pm 2.1$
XRT4 | 0.5-10.0 | 43 | 1.90 | 0.88 | 2.16 | $4.50\pm 0.46$ | $18.01\pm 2.3$
XRT5 | 0.5-10.0 | 42 | 1.77 | 0.81 | 2.18 | $2.72\pm 0.25$ | $14.03\pm 1.8$
XRT6 | 0.5-10.0 | 72 | 1.63 | 0.52 | 3.09 | $6.02\pm 0.49$ | $23.40\pm 2.2$
Figure 4: Top panel: The light-curves of the energy ranges of $0.2$ to $2.0$
keV and $3.0$ to $10.0$ keV observed by XMM-Newton are plotted for three
epochs. The high energy count always remained a fraction of low energy
counterpart. In 2013, the low-energy count dropped to nearly 50% as compared
to 2003. Again in 2014, the $0.2-2$ keV count doubled from its value observed
in 2013. Middle panel: Corresponding discrete cross-correlations between
light-curves of $0.2-2$ keV and $3-10$ keV are plotted. All three epochs
exhibited different patterns where zero, positive, and negative delays are
observed in 2003, 2013, and 2014 respectively. We have also presented the ICF
(solid-blue line) for XMM3 observation. Lower panel: $\zeta$-discrete cross-
correlations (light-green) are plotted for light-curves of $0.2-2$ keV and
$3-10$ keV. While 2003 and 2013 patterns remain similar to what have been
observed from DCF, the pattern obtained from 2014 data develops twin peak. The
likelihoods (dark-green), simulated using 12000 points, are plotted along with
the ZDCF.

##  4 Timing Analysis

###  4.1 Variability

X-ray variability of an AGN provides a powerful probe of the nearby regions of
the central black hole. Since Ark 120 has a ‘bare-type nucleus’, the X-ray
comes from the Compton cloud and is not intercepted by any clouds such as BLR,
NLR or molecular torus. Thus, the X-ray variability is originated from the
varying Compton cloud and the central accretion disc. To analyze the temporal
variability in X-ray of Ark 120 in different energy bands, we have estimated
different parameters for the duration of 2003 (MJD-52875) to 2018 (MJD-58118).
The fractional variability $F_{var}$ ((Edelson et al., 1996); (Nandra et al.,
1997); (Edelson et al., 2001); (Edelson et al., 2012); (Vaughan et al., 2003);
(Rodríguez-Pascual et al., 1997)) of lightcurves of $x_{i}$ count/s with
finite measurement error $\sigma_{i}$ of length $N$ with a mean $\mu$ and
standard deviation $\sigma$ is given by:

$F_{var}=\sqrt{\frac{\sigma^{2}_{XS}}{\mu^{2}}}$ (2)

where, $\sigma^{2}_{XS}$ is excess variance (Nandra et al. (1997); Edelson et
al. (2002)), an estimator of the intrinsic source variance and is given by:

$\sigma^{2}_{XS}=\sigma^{2}-\frac{1}{N}\sum_{i=1}^{N}\sigma^{2}_{i}.$ (3)

The normalized excess variance is given by
$\sigma^{2}_{NXS}=\sigma^{2}_{XS}/\mu^{2}$. The uncertainties in
$\sigma^{2}_{NXS}$ and $F_{var}$ are taken from Vaughan et al. (2003) and
Edelson et al. (2012).

The X-ray variability of Ark 120 in different energy bands ($0.5-10.0$ keV;
$0.2-2.0$ keV; $3.0-10.0$ keV) have demonstrated different degrees of
variabilities (Table 6) while the time binsize is kept constant at $100$s.
From XMM1, the lower energy ($0.2-2.0$ keV) count rate was initially high
($X_{max}=21.95$) in 2003 observation. Then, in 2013 (XMM2), it became half
($X_{max}=10.24$) from its initial value. In 2014 (XMM3), the count increased
($X_{max}=21.37$). The fractional variability in this energy range increased
from $0.016$ to $0.064$ from 2003 to 2014 observations. A similar trend is
shown by $\sigma^{2}_{NXS}$ ($0.006$ to $0.082$) in this energy band for each
observation of XMM (Table 6). Like low energy part, the high energy
($3.0-10.0$ keV) follow the similar type of trend for the count rate and
fractional variability. The average value of $\sigma^{2}_{NXS}$ is $0.003$,
with a range from $0.0014$ to $0.0056$.

We calculate the variability in $0.5-10.0$ keV range from the Suzaku data. We
find higher variability $F_{var}=8.62\pm 0.31$ in the 2007 Suzaku data as
compared to the previous XMM observations. The variability for XRT
observations in $0.5-10.0$ keV range is shown in Table 6. Due to the lack of
data points, XRT1 observation yields an imaginary value of $F_{var}$, and is
not shown in Table 6. From the other observations of Swift/XRT, we observe
high fractional variability ($F_{var}$) from $0.14$ to $0.23$ with
$<F_{var}>=18.22$. The average value of $x_{max}/x_{min}$ and
$\sigma^{2}_{NXS}$ for these observations are $2.65$ and $0.045$ with a range
from $2.16$ to $3.09$ and $0.027$ to $0.060$ respectively.

###  4.2 Delay Estimation

For temporal analysis of the long term archival data of Ark 120, we stress
three epochs of XMM-Newton, 2003, 2013, and 2014 out of which the latter two
have high energy (3-80 keV) counterparts observed by NuSTAR. We have performed
cross-correlation analysis using DCF (Edelson & Krolik, 1988) and
$\zeta$-discrete cross-correlation function (ZDCF888ZDCF:
http://www.weizmann.ac.il/particle/tal/research-activities/software,
Alexzander (1997)) for comparison. The likelihood is calculated using 12000
simulation points in the ZDCF code for the lightcurves obtained by XMM-Newton.
The peak error is calculated using the formula provided by Gaskell & Peterson
(1987). We have followed a similar procedure as in Chatterjee et al. (2020).
The time resolution of each light curve is $1000$s. The $0.2-2$ keV lightcurve
obtained from 2003 data yields an acceptable $\chi^{2}_{red}<1.5$ when fit
with a straight line. However, data procured in 2013 and 2014 in a similar
energy band have a high residual and are not suitable for linear fitting. All
three high energy lightcurves (3-10 keV) have $\chi^{2}_{red}<1.5$ when fitted
with straight lines. We have carried out the delay estimation using the XMM-
Newton/Epic-pn data to ensure the simultaneity in their procurements.

Table 7: Parameters used in delay estimations are presented. The error in measurement of delay is considered as the larger between binsize and $\epsilon_{\tau}$. $\epsilon^{d}_{\tau}$ and $\epsilon^{z}_{\tau}$ represents errors for DCF and ZDCF patterns. Id | Epochs | Bin size | $\epsilon^{d}_{\tau}$ | $\Delta\tau^{dcf}_{d}$ | $\epsilon^{z}_{\tau}$ | $\Delta\tau^{zdcf}_{d}$
---|---|---|---|---|---|---
| Year | (ks) | (ks) | (ks) | (ks) | (ks)
blackXMM1 | 2003 | 1 | 0.388 | $0.16\pm 1$ | 0.936 | $-0.057\pm 1$
blackXMM2 | 2013 | 1 | 0.862 | $4.71\pm 1$ | 2.11 | $6.76\pm 2.11$
blackXMM3 | 2014 | 1 | 0.622 | $-4.15\pm 1$ | 1.54 | $-4.56\pm 1.54$
blackXMM3 | 2014 | 1 | $-do-$ | $-do-$ | 1.58 | $-49.2\pm 1.58$

The DCF (Edelson & Krolik, 1988), performed using the lightcurves, have
generated three distinct patterns. The 2003 data has produced $2.78\pm 16.67$
minutes or $\sim 0.16$ ks delay. We have fitted the peak using a Gaussian
model (dotted line in Fig. 4). Considering the error, no delay can be seen
between two bands of X-ray. Similar delay pattern is also observed from ZDCF,
and the likelihood density also maximizes around zero. Likewise, we have
performed Gaussian fitting for 2013 data where a positive delay of $78.51\pm
35.17$ minutes or $\sim 4.7$ ks has been seen between soft and hard X-ray
photons using DCF. But, the ZDCF peak maximizes around $112.68\pm 35.22$
minutes or 6.7 ks and likelihood peak coincides with that (see Fig. 4). In
2014, the delay sign have switched, and we find a negative delay of $-69.19\pm
25.67$ minutes or $\sim-4.1$ ks between the soft and hard band from DCF
analysis. However, ZDCF peaks maximize around two positions, $-76.19\pm 25.67$
($-4.56\pm 1.54$ ks) and $-820.19\pm 26.46$ ($-49.2\pm 1.58$ ks) minutes
having peak values of 0.664 and 0.722 respectively. Between these two, the
former coincides with the DCF pattern (see, Table 7 for details). For all
three cases, we find the peak values of ZDCF patterns are lesser than the
corresponding peak values obtained from DCF patterns.

##  5 Discussions

We have studied the central region of Ark 120 through X-ray (above 0.2 keV)
using the data of XMM, Suzaku, NuSTAR and Swift/XRT in the period 2003
(MJD-52875) to 2018 (MJD-58118). As it is a bare type AGN, the X-ray spectra
mainly generated from the nearby region of the central engine.

###  5.1 Evolution of the Source: Primary Continuum

The ‘bare-type AGN’ Ark 120 was observed for a period of fifteen years, 2003
to 2018 using various X-ray satellites. During these observations, the source
has exhibited variabilities in both spectral and temporal domain. The
luminosity of the source in the energy range of 2.0 to 10.0 keV varied within
$\sim 10^{43.5}-10^{45.5}$ erg/s throughout these observations. From the
nthcomp model, we report the variation of the spectral index
(1.6<$\Gamma$<2.08) where the harder spectra were observed after 2014.
Following Vaughan et al. (2004), we have fitted the 2003 spectrum of Ark 120
with (nthcomp + Gaussian) model. The fitted $\Gamma=1.90^{+0.01}_{-0.01}$
agrees with the spectral index previously observed (Table 4 of Vaughan et al.
(2004)). Corresponding temperature of the Compton cloud is
$kT_{e}=159.45^{+81.68}_{-81.69}$ keV. The (TCAF + Gaussian) model provided a
few previously unknown parameters like accretion rates, disc rate
$\dot{m}_{d}=0.063\pm 0.002$ and halo rate $\dot{m}_{h}=0.112\pm 0.001$. This
suggests that the the source was initially halo dominated. This is normal for
an AGN. The shock location or the size of the CENBOL ($X_{s}$), estimated from
the fits, is $20.36\pm 4.4~{}r_{g}$. The shock is found to be moderately
strong with a compression ratio of $R=1.95\pm 0.05$.

The softest spectrum, having $\Gamma=2.08^{+0.03}_{-0.03}$ is seen during the
Suzaku observation in 2007. It is to be noted that, Nardini et al. (2011)
found the spectral index to be $\Gamma=2.03^{+0.01}_{-0.04}$ for the Suzaku
data using blurred reflection model. We have estimated the temperature of the
Compton cloud to be $kT_{e}=124.65^{+35.54}_{-35.21}$ keV. This is the least
of all temperatures obtained from all the observations. Using a single
Gaussian, we find the presence of a broad iron line ($6.38^{+0.052}_{-0.052}$)
keV having an equivalent width of $EW=710^{+10}_{-10}$ eV. The derived optical
depth is $\tau=0.726^{+0.008}_{-0.008}$. This suggests an optically thin
Compton cloud. From the TCAF fits, we find that the size of the Compton cloud
has slightly increased to $X_{s}=21.44\pm 4.9~{}r_{g}$ from the earlier
observation. Corresponding disc rate, which enhances the soft seed photons,
has increased to $\dot{m}_{d}=0.126$. Also, the halo rate has increased to
$\dot{m}_{h}=0.191$. However, shock strength has decreased (see Table 5). The
drop in the $kT_{e}$ could be understood easily from TCAF, where the increase
in disc rate leads to an enhanced cooling fraction. Thus, within the epochs of
2003 and 2007, the temperature of the Compton cloud was varied from 159.45 to
124.65 and as a result the spectrum softened.

Figure 5: Correlation of fitted parameters are plotted. Fig. (a) represents
the correlation between $\Gamma$ vs $kT_{e}$ and the corresponding PCC is
-0.95. It is also noted that the $kT_{e}$ is losely bound with $\Gamma$. Fig.
(b) is the correlation between $\tau$ and R. The PCC for these parameters is
-0.72. In Fig. (c) represents the correlation between $\tau$ vs $X_{s}$ and
the corresponding PCC is -0.45. Fig. (d) provides the correlation of $\Gamma$
vs $X_{s}$ with PCC -0.53.

Later, in 2008, Swift observed the source where the spectrum hardened from the
previous observation having $\Gamma=1.76^{+0.02}_{-0.08}$,
$kT_{e}=217.72^{+105.6}_{-112.5}$ keV, and optical depth
$\tau=0.671^{+0.030}_{-0.030}$. The iron line could not be detected from the
XRT spectrum. Corresponding TCAF fitted parameters, such as the shock location
$30.08~{}r_{g}$ and $R=2.80$ while $\dot{m}_{d}$ and $\dot{m}_{h}$ have
changed to $0.064$ and $0.11$ respectively.

Significant variation of spectral properties is also noted during 2013 and
2014. The broad-band spectra (3-78) keV are fitted with (nthcomp + Gaussian)
having the spectral indices $1.75^{+0.01}_{-0.02}$ and $1.87^{+0.01}_{-0.01}$
and are in good agreement with parameters obtained by Porquet et al. (2018);
Marinucci et al. (2019). The optical depth is reduced from $\tau=0.670\pm
0.074$ to $\tau=0.612\pm 0.003$. The flux in 2-10 keV band has doubled within
a year. The spectral softening could be explained by the drop of temperature
of the Compton cloud. However, the decrease in the optical depth for March
2014 data with respect to 2013 has also been seen from Monte-Carlo simulations
(Marinucci et al., 2019). From TCAF fitting, we find a distinct variation of
the flow parameters. The $\dot{m}_{d}$ changed from $0.068$ to $0.103$,
$\dot{m}_{h}$ changed from $0.111$ to $0.126$, and $X_{s}$ changed from
$52.83$ to $28.24$ within 2013 and 2014 observations respectively. As the disc
accretion rate increases, Compton cooling increases, and this lead to the
decrease in the $X_{s}$ which finally softens the spectrum. Considering TCAF,
the lower optical depth for softer spectrum could be explained by the
weakening of the shock ($R=2.43$ as compared to $R=2.83$ in February 2013) for
this observation. The stronger shock creates a distinct boundary between the
halo and CENBOL region where the majority of the hard photons are produced.
However, for the weaker shock, the CENBOL boundary is less sharp and a
fraction of inverse Comptonization could occur within the halo component.
Thus, the effective optical depth of the medium could become lower even though
the spectrum has softened.

Ark 120 has shown significant variabilities after February 2014 and is
monitored by Swift. We have tabulated the spectral and temporal variabilities
in Table 2 and 5. During September-October of 2014, we find that the spectral
slope was $\Gamma=1.60^{+0.01}_{-0.02}$ and the corresponding temperature was
$274.40\pm 130.0$ keV, which was maximum within the duration of our
observation. From the TCAF fitting, we find $\dot{m}_{d}$ and $\dot{m}_{h}$
has changed to $0.068$ and $0.11$ respectively and the corresponding shock
location has changed to $53.56\pm 8.2~{}r_{g}$ and the shock strength has
increased from $2.43$ to $2.73\pm 0.5$ as observed during February 2014\.
Later, in December 2014, the spectrum has softened with $\Gamma=1.84\pm 0.02$
with the temperature of Compton cloud $215.72\pm 105.5$ keV. The corresponding
shock has moved outward and observed at $55.16~{}r_{g}$ and $R=2.74$. Like
previous observations, we see the halo rate and disc rates are fixed at $0.11$
and $0.068$, respectively.

XRT4 and XRT5 observations were made starting from the end of December 2014 to
March of 2015. During this time, the spectral indices are $1.74$ and $1.88$
respectively. The temperature and optical depths have also varied during this
time. From TCAF fitting, we find the halo rate has decreased to $0.061$ in the
XRT4 observation. However, the disc rate was constant. Again in XRT5
observation, halo rate has increased to $0.069$ while the disc rate remained
the same. The shock location and the compression ratio remained constant
(considering the errors) within this period. Thus, we can see that Ark 120
exhibited spectral variability (see Fig. 3) within $\sim$200 days (since
September 2014-March 2015).

In XRT6, which was observed from December 2017 to January 2018, the spectrum
of Ark 120 has hardened with respect to the earlier observations during
January 2015. The spectral index and temperature of Compton cloud are $1.65\pm
0.02$ and $246.87\pm 121$ keV respectively. From TCAF fitting, we find the
disc and halo rates have increased to $\dot{m}_{d}=0.081$ & $\dot{m}_{d}=0.14$
respectively and the corresponding shock location settled at $42.95\pm
8.0~{}r_{g}$.

In Figure 5, we have plotted the correlations of a few spectral parameters. We
find the spectral index and the temperature of the Compton cloud is anti-
correlated (Fig. 5a with Pearson Correlation Co-efficient (PCC) = -0.9542) for
the long term observation. However, the values of $kT_{e}$ are poorly
constrained with respect to spectral indices. This is a well-established
relation and is generally found in case of AGNs and Galactic black holes. In
Fig. 5b, we have presented the correlation between shock compression ratio and
optical depth. We find $R-\tau$ produces anti-correlation having PCC=-0.721.
In general, stronger shocks are associated with the harder spectra where the
optical depth is expected to be less (Chatterjee et al., 2016) and the
corresponding shock location is also expected to be bigger. Keeping that
argument, we also show the $X_{s}-\tau$ correlation where an anti-correlation
(PCC=-0.457) has been observed from the long term data and presented in Fig.
5c. As a consequence, the spectral softens due to the reduction of the shock
location $X_{s}$ i.e., the size of the Compton cloud, we find a global trend
of anti-correlation (PCC=-0.562) between $X_{s}-\Gamma$ (see Fig. 5) for Ark
120.

From the nthcomp fitting, it can be found that the Compton cloud of the source
was optically thin for the entire period of observation. Overall, we also
noticed that the disc and halo rate is nearly constant and they are $\sim
0.07$ and $\sim 0.11$ respectively for the majority of observations. But, we
find a higher disc and halo rate in 2007 and 2014 observation. The shock
location and the compression ratio have varied with time. The variation of
these parameters is shown in Figure 3. First, the shock location increases
with time from 20 to 52 $r_{g}$ in the first $\sim 10$ years. Then the shock
location falls to 26.7$r_{g}$ within the next $\sim$ 13 months. Later, we find
that the shock location again moves outward from 26.7 to 57.8 $r_{g}$ before
moving inward again, and finally settling at 42.95$r_{g}$ in January 2018. The
Compression ratio (R) also varies as the shock location ($X_{s}$). First, the
compression ratio increased from 1.95 to 2.83 in $\sim 10$ years. Then, the
value of $R$ decreased to $1.67$ within next 1 year. After that, it increased
to 2.73 within less than six months and finally reached 2.69 at the end of
January 2018.

###  5.2 Evolution of the Source: Delay patterns

The Compton delay (Payne, 1980; Sunyaev & Titarchuk, 1980) for an electron
cloud of size $\mathcal{R}$ having an optical depth $\tau$ and temperature
$\theta_{e}=kT_{e}/m_{e}c^{2}$ can be described by,

$t_{c}=\frac{\mathcal{R}}{c(1+\tau)}\frac{ln(E_{h}/E_{ss})}{ln[1+4\theta_{e}(1+4\theta_{e})]},$

where, $c$ is the velocity of light, $E_{h}$ and $E_{ss}$ are the energy of
hard photons and soft seed photons respectively. For AGNs having a central
black hole mass of $1.5\times 10^{8}$ (Peterson et al., 2004), the seed
temperature of the photons remains in the 1-10 eV range. The maximum of the
hard and soft energy band is considered to be $10$ keV and $1$ keV and the
seed photon temperature is $E_{ss}=3$ eV. The light-crossing time for 1$r_{g}$
is $r_{g}/c=$1.5 ks for Ark 120. We calculated the delays for the combined
parameters obtained from nthcomp and TCAF model.

We have calculated the Compton delay for XMM1 observation where the size of
the Compton cloud is $\sim 20~{}r_{g}$, optical depth $0.733$, and
$\theta_{e}=0.311$. Substituting the values, we find $t^{h}_{c}=105.3$ ks and
$t^{s}_{c}=75.3$ ks which produces a positive theoretical delay of
$\Delta\tau=t^{h}_{c}-t^{s}_{c}=30$ ks. However, from the observed DCF
pattern, we fail to notice any such delay for this case. Here, we find light
crossing delay ($\tau_{lc}$) of 30 ks for a $\sim 20~{}r_{g}$ Compton cloud.
The observed zero-delay could be a combined result of $\tau_{c}$ and
$\tau_{lc}$. In that case, it is to be noted that $\tau_{lc}$ becomes crucial
in presence of a significant contribution of reflection component
($R_{ref}=1.96$, see Table 5).

Figure 6: Correlation of intrinsic luminosities of 0.5-10.0 keV obtained using
nthcomp. Left: shows a correlation (PCC=0.92) between the observed intrinsic
luminosities of primary continuum and soft-excess (blue-circle). Monte-Carlo
simulated luminosities for both energy ranges are presented with red-diamond
points. Right: No correlation between intrinsic luminosities and $N_{H}$ from
long term observations.

For the broadband observation (XMM2+N1), the size of the Compton cloud is
$\mathcal{R}\sim 50$ $r_{g}$, having an optical depth of $0.67$ and
temperature $\theta_{e}=0.434$. Combining all these, the maximum hard and soft
energy delay which can be generated via Compton scatterings are
$t^{h}_{c}=208$ ks and $t^{s}_{c}=148$ ks respectively. Thus, the maximum
delay between hard and soft bands of X-ray can be
$\Delta\tau=t^{h}_{c}-t^{s}_{c}=60$ ks. The light crossing delay is around
$\tau_{lc}=75$ ks. The combined effects of $\Delta\tau$ and $\tau_{lc}$ should
yield a negative delay of 15 ks. However, as discussed previously, $\tau_{lc}$
could dominate if reflection becomes dominating (here $R_{ref}=0.25$). Also,
the size of the Compton cloud is much bigger than the what should be the
‘transition radius’ (see, Dutta & Chakrabarti (2016); Dutta, Pal & Chakrabarti
(2018) for details) of an AGN having mass $1.5\times 10^{8}~{}M_{\odot}$.
Being an intermediate inclination angle source (Nardini et al., 2011;
Marinucci et al., 2019), Comptonization dominates the time delay when the size
of the Compton cloud is bigger. The theoretical structure of Compton cloud is
somewhat deviated from the sphere (see, Chakrabarti & Titarchuk (1995)) and
the thermodynamical fluctuations within the inhomogeneous Compton cloud (see,
Chatterjee et al. (2017b)) contributes to the delay patterns. Considering
this, the effect of light crossing delay would be much less and Comptonization
could be considered as the core process, which generates $0.2-2$ keV photons
during 2013 observations.

In a similar way, we calculate the Compton delay for broadband observation in
2014 (XMM3+N2). For that, the size of the Compton cloud
$\mathcal{R}=28~{}r_{g}$, the optical depth is $\tau=0.612$, and
$\theta_{e}=0.403$. We have obtained $t^{h}_{c}=123.4$ ks and $t^{s}_{c}=88.2$
ks which produces $\Delta\tau=t^{h}_{c}-t^{s}_{c}=35$ ks. Contrary to that,
the observed delay is $-69.19\pm 16.67$. Clearly, the Comptonization may not
be the dominating radiative process for this observation. From Table 5, we see
that the reflection co-efficient $R_{ref}=0.96$, which refers to a stronger
reflection. It is also to be noted that Lobban et al. (2018) found the X-ray
to be leading the U-band by $2.4\pm 1.8$ days which they have explained with
the light crossing delay. Considering the Compton cloud only, $\tau_{lc}$
becomes 42 ks, which is comparable to compensate for the positive lag obtained
from Comptonization. In this particular case, the maximum possible negative
delay would be $\Delta\tau-\tau_{lc}\sim-7$ ks or -116 minutes. However, as
the size of the Compton cloud has become bigger and $R_{ref}$ is much less
than the XMM1 observation. Thus, the contribution from $\tau_{lc}$ could be
less effective and we observe a negative delay much less than the maximum
allowed delay.

Thus, along with the spectral variations, we find the delay patterns have
varied over the three epochs (2003, 2013, and 2014) in which XMM-Newton
observed Ark 120. A significant change in the delay pattern is observed within
a year (2013-2014) where the positive delay changed sign and becomes negative
with a similar magnitude.

###  5.3 Soft Excess

The origin of ubiquitous soft-excess (Arnaud et al., 1985; Singh et al., 1985;
Brandt et al., 1993; Fabian et al., 2002; Gierliński & Done, 2004) remains
debated. A plausible cause of soft-excess was given using reflection
Sobolewska & Done (2007). The multi-wavelength campaign of Mrk 509 (Mehdipour
et al., 2011) revealed the correlation of soft-excess with the optical-UV part
both in the spectral and temporal domains where they concluded that the soft-
excess was generated due to Comptonization by a warm optically thick region
surrounding the accretion disc. Done et al. (2012) proposed that the high mass
accretion rate of the disc could generate the soft-excess. For lower
$L/L_{EDD}$, the energy dependent variability in the soft-excess part was
found to be less in case of Narrow line Seyfert 1 galaxies. Lohfink et al.
(2012) studied Seyfert 1 galaxy Fairfall 9 where the origin of the soft-excess
component was found to be connected with source which generates the broad iron
line. However, they implied that another source of Comptonization might be
responsible for the formation of the soft-excess.

Figure 7: Monte-Carlo simulated spectra for Ark 120 are presented. We have
considered $M_{BH}=1.5\times 10^{8}~{}M_{\odot}$ for Ark 120. Simulation
boundary extends up to $100~{}r_{g}$. For left panel $\dot{m}_{d}$ = 0.06;
$\dot{m}_{h}$ = 0.1, $X_{s}=60~{}r_{g}$, and maximum $kT_{e}=270$ keV. For
right panel $\dot{m}_{d}$ = 0.1; $\dot{m}_{h}$ = 0.1, $X_{s}=40~{}r_{g}$, and
maximum $kT_{e}=100$ keV. Notice the spectral contributions due to increasing
number of scatterings. $L_{\nu}$ has been normalized with respect to the
observed spectrum.

A strong soft-excess present in the X-ray spectrum of Ark 120 was reported by
Brandt et al. (1993); Matt et al. (2014); Porquet et al. (2004). This soft-
excess is also free from the absorbers and was reported by Nardini et al.
(2011). As a first step, we investigate the spectral slopes and the relative
contribution of the soft-excess from 2003 to 2018 using the
nthcomp+zGaussian+powerlaw model and the results are presented in Table 3.
Subsequently, we freeze the $\Gamma^{nth}$ obtained from nthcomp while fitting
the soft excess below 3 keV. The $\Gamma^{pl}$ fits the soft-excess < 3 keV.
For every observation, we find a soft-excess steeper than the primary
continuum (see, Table 3) which is a characteristic associated with the Narrow
line Seyfert 1 galaxies. Apart from the steeper power law, the variation of
soft-excess luminosity and spectral index can be observed from long term
observations presented in Table 3. We have calculated the intrinsic
luminosities of nthcomp and powerlaw within the energy range 0.5 to 10.0 keV.
In Fig. 6a, we see a strong correlation (PCC=0.9227) between the intrinsic
luminosities of soft-excess ($L^{SE}_{int}$) and primary continuum
($L^{PC}_{int}$). However, as a “bare” type AGN, Ark 120 has not shown any
correlation (Fig. 6b) among the intrinsic luminosities and the line of sight
hydrogen column density ($N_{H}$).

While nthcomp provides a good fit in the high energy range, we have used
TCAF+zGaussian+pexrav model (presented in Table 5) in the entire range. We
find that the TCAF fits well in the range of $0.2-10$ and requires no other
additional model for the soft-excess part with the range of $0.2-3$ keV. The
fitted results and residuals are presented in Fig. 2. From the spectral
fitting using TCAF, one recognizes that the soft-excess could be originated
from the photons which are rarely scattered in the Compton cloud. The
surrounding halo will contribute to this energy band (0.2 - 2 keV). Also, some
high energy photons from the Compton cloud which could be reflected from the
disc will appear in this energy range after losing their energy through
reflection from the cold disc. We have performed Monte-Carlo simulations to
show the spectral variations with $N_{s}$. This is briefly discussed in Sec.
5.3.1.

####  5.3.1 Simulated spectra

Radiative and hydrodynamic origin of soft-excess has been investigated in
Fukumura et al. (2016) where they proposed that the shock heating near the
ISCO could produce the soft-excess. The model reproduced the spectra of “bare”
Seyfert 1 galaxy, Ark 120. We have inspected the possibility of scattering
dependent spectral contribution from the pre-shock and the post-shock regions
(Chakrabarti & Titarchuk, 1995). We extend the work of Ghosh et al. (2011);
Chatterjee et al. (2018) in case of AGNs considering Ark 120. Using the Total
Variation Diminishing (TVD) scheme (Ryu et al., 1997), we inject matter having
a halo rate of $0.1$ from the outer boundary at $200~{}r_{g}$. TCAF fitted
parameters are used for the simulation setup and are mentioned in the Fig. 7.
Considering the Keplerian disc in the equatorial plane ($z=0$), we construct
the profile of the accretion disc following Shakura & Sunyaev (1973). The
Monte-Carlo simulation ($0<r<100~{}r_{g}$) has followed the process provided
by Pozdnyakov et al. (1983) and later extended by Ghosh et al. (2009);
Chatterjee et al. (2017a). The simulations are performed using $10^{7}$
injected photons for each case. The emergent Comptonized spectra are plotted
in Fig. 7. We show the variation of spectral components with respect to the
number of scatterings (see also Ghosh et al. (2011)) within the region. From
Fig. 7, we find that the spectra harden as the number of scatterings increase.
The spectra of the primary component within the energy range 2.0 to 10.0 keV
is dominated by the photons where the number of scatterings are $\geq 10$.
However, the soft-excess, the red long-dashed line within 0.2-2 keV, is
dominated by the contribution from photons which have suffered $\leq 10$
scatterings. A steeper spectral slope ($\Gamma^{SE}$) for soft-excess is
achieved with respect to the primary component ($\Gamma^{PC}$) for both of the
spectrum. This is similar to what has been observed for Ark 120 (Table 3). It
is to be noted that, Boissay et al. (2016) studied the AGN 102 Sy1 and found
that there is no link between the reflection and the soft excess. Instead,
they indicated that the soft-excess could be related to the thermodynamical
properties of Compton cloud and associated medium.

##  6 Conclusions

We have studied $\sim 15$ years of X-ray data of Ark 120. We find the source
varied considerably within that time span. This source was previously reported
to be a ‘bare-type AGN’ and we also find a similar nature of this source from
the long term analysis. The X-ray count rate has increased by a factor of two
in a few years, and it is not found to be related to the Hydrogen column
density ($N_{H}$) since it is a ‘bare-type AGN’. Following are the major
findings from our work.

  1. 1.

The spectral slopes of the primary continuum ($\Gamma^{PC}$) and the soft-
excess ($\Gamma^{SE}$) are not constant throughout our observational time
span. $\Gamma^{PC}$ has varied between 1.60 and 2.08 whereas $\Gamma^{SE}$
between 2.52 and 4.23 from 2003 to 2018.

  2. 2.

The variation is reflected in fitted parameters of TCAF, namely, the accretion
rates and properties of the Compton cloud. From the spectral fitting using
TCAF, we find that the disc rate ($\dot{m}_{d}$) and the halo rate
($\dot{m}_{h}$) have varied between $0.061$ and $0.126$ and between $0.108$
and $0.191$ respectively. The shock location ($X_{s}$) or the size of the
Compton cloud and compression ratio ($R$) vary correspondingly. $X_{s}$ varies
between $20.36$ and $57.87$, whereas $R$ varies between $1.66$ and $2.73$.

  3. 3.

We focussed on the simultaneous observations in low ($0.2-2.0$ keV) and high
($3.0-10.0$ keV) energy X-ray band from XMM-Newton to calculate the time delay
between them. We find that in XMM1 observation, there is no delay between the
low and high energy band, while a positive delay of $4.71\pm 1$ ks is detected
in XMM2 observation and a negative delay of $4.15\pm 1$ ks is seen in XMM3
observation. A correlated variability among the optical, UV, and X-ray bands
have already been reported Lobban et al. (2020). Also, (Dutta & Chakrabarti,
2016; Chatterjee et al., 2017b) reported in a different context that the X-ray
lag has a strong dependency on the geometric structure of the Comptonization
region and orientation of the Keplerian disc. The net delay is a resultant
effect of different physical mechanisms, e.g., Comptonization, reflection,
focusing, and jet/outflow emission (Chatterjee et al., 2019; Patra et al.,
2019). For the lower inclination and radio-quiet nature of Ark 120, the
positive delay could be attributed to the Compton delay while reflection and
light-crossing delay could contribute to the negative delay.

  4. 4.

From the analysis of the long term data, we report that the luminosity is
independent of Hydrogen column density ($N_{H}$). This is expected as the
source has a negligible line-of-sight hydrogen column density ($N_{H}<5\times
10^{20}$). The luminosity of the primary continuum is highly correlated
(PCC$\sim 0.92$) with the soft excess emission. From TCAF fitting and Monte-
Carlo simulations using TCAF flow configurations, we show that the soft-excess
spectral slope ($\Gamma^{SE}$) is the result of a fewer Compton scatterings in
the Compton cloud and the primary continuum ($\Gamma^{PC}$) is the result of
the higher number of Compton scatterings. Corresponding intrinsic luminosities
obtained from simulations corroborate with the observed pattern.

## Acknowledgements

PN acknowledges CSIR fellowship for this work. AC acknowledges Post-doctoral
fellowship of S. N. Bose National Centre for Basic Sciences, Kolkata India,
funded by Department of Science and Technology (DST), India. BGD acknowledges
Inter-University Centre for Astronomy and Astrophysics (IUCAA) for the
Visiting Associateship Programme. This research has made use of data and/or
software provided by the High Energy Astrophysics Science Archive Research
Center (HEASARC), which is a service of the Astrophysics Science Division at
NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian
Astrophysical Observatory. This work has made use of data obtained from the
Suzaku, a collaborative mission between the space agencies of Japan (JAXA) and
the USA (NASA). This work made use of data supplied by the UK Swift Science
Data Centre at the University of Leicester. This work has made use of data
obtained from the NuSTAR mission, a project led by Caltech, funded by NASA and
managed by NASA/JPL, and has utilized the NuSTARDAS software package, jointly
developed by the ASDC, Italy and Caltech, USA. This research has made use of
the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This research has made use
of the SIMBAD database, operated at CDS, Strasbourg, France.

## Data Availability

We have used archival data for our analysis in this manuscript. All the
softwares used in this manuscript are publicly available. Appropriate links
are given in the manuscript.

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