The accretion properties of a low-mass Active Galactic Nucleus: UGC 6728

We present a comprehensive analysis of approximately $15$ years ($2006-2021$) of X-ray observations of UGC~6728, a low-mass bare AGN, for the first time. Our study encompasses both spectral and temporal aspects of this source. The spectral properties of this source are studied using various phenomenological and physical models. We conclude that (a) the observed variability in X-ray luminosity is not attributed to the Hydrogen column density ($N_H$) as UGC~6728 exhibits a bare nucleus, implying a negligible $N_H$ contribution along the line of sight, and (b) the spectral slope in the X-ray band demonstrates a systematic variation over time, indicating a transition from a relatively hard state to a comparatively soft state. We propose that the underlying accretion dynamics around the central object account for this behavior. By performing X-ray spectral fitting, we estimate the mass of the central supermassive black hole (SMBH) in UGC~6728 to be $M_{BH}=(7.13\pm1.23)\times10^5$ M$_\odot$ with spin $a=0.97^{+0.20}_{-0.27}$ and inclination angle $i=49.5\pm14.5$ degree. Based on our spectral and temporal analysis, we suggest that UGC~6728 lacks a prominent Compton hump or exhibits a very subtle hump that remains undetectable in our analysis. Furthermore, the high-energy X-ray photons in this source are likely to originate from the low-energy X-ray photons through inverse Compton scattering in a Compton cloud, highlighting a connection between the emission in two energy ranges. We notice a strong soft excess component in the initial part of our observations, which later reduced substantially. This variation of soft excess is explained in view of accretion dynamics.


INTRODUCTION
Active galactic nuclei (AGNs) are among the most luminous sources which are powered by the process of accretion of matter from the host galaxy (Storchi-Bergmann & Schnorr-Müller 2019) onto the supermassive black holes (SMBHs) (Lynden-Bell 1969;Rees 1984) located at their center.The mass of an SMBH ranges from 10 5 to 10 9 M ⊙ (Kormendy & Richstone 1995;Peterson et al. 2004;Event Horizon Telescope Collaboration et al. 2019).The AGNs are generally characterized by their complex spatial and temporal variabilities (McHardy et al. 1999;Nandra 2001;Webb & Malkan 2000;Ballantyne et al. 2014;Zoghbi et al. 2017) over the entire range of the electromagnetic spectrum, starting from radio to very high energy −rays.The X-ray photons are believed to be originated from a region closer to the central SMBH (Fabian et al. 1989;Wilkins et al. 2021).Thus, X-ray spectroscopy is a powerful tool to probe the innermost regions of the accretion disc around the SMBHs.It allows us to determine the physical conditions of the plasma surrounding the central X-ray source.By observing these X-ray photons, we can characterize the fundamental parameters of the black hole, such as its mass, spin, etc.These parameters play a crucial role in understanding ★ E-mail: prantiknandi007@gmail.com the physical nature of the central engine and its cosmological evolution (Fabian 2012;Kormendy & Ho 2013).However, our knowledge of the physical processes in AGNs is mostly based on the galaxies which harbour a SMBH of mass greater than 10 6 M ⊙ .However, the low mass AGNs ( < 10 6 ⊙ ) are yet to be explored.One can explore the missing link to probe whether the accretion mechanism is independent of the mass of the black hole.
According to standard accretion disc theory (Pringle et al. 1973;Shakura & Sunyaev 1973), X-ray photons are thought to be originated from the innermost region of the accretion disc, which surrounds the central black hole.Observationally, the X-ray spectra of AGNs are explained by the power-law continuum (Bianchi et al. 2009;Sobolewska & Papadakis 2009) with high-energy cut-off (Fabian et al. 2015(Fabian et al. , 2017;;Tortosa et al. 2018;Middei et al. 2019;Baloković et al. 2020).The power-law continuum is thought to be generated by inverse Comptonization (Sunyaev & Titarchuk 1980a) of thermal optical/UV photons in a hot corona or Compton cloud located close to the accretion disc (Haardt & Maraschi 1991).However, the geometry and location of the Compton reprocessing region are still not well understood.This cloud can be located above the disc (Haardt & Maraschi 1991, 1993;Poutanen & Svensson 1996) or at the base of the jet (Chakrabarti & Titarchuk 1995;Fender et al. 1999;Markoff et al. 2005).This region is formed by the hot ( ∼ 10 9 K) and radiatively inefficient plasma (Sunyaev & Titarchuk 1980a), which behaves like a quasi-Bondi flow (Ichimaru 1977).
In this scenario, X-ray observations play a crucial role in constraining the geometry, such as the size and location, of the emitting region with a proper understanding of its formation.A common characteristic observed in X-ray studies of nearby bright Seyfert galaxies is the detection of X-ray reverberation lags.This phenomenon suggests that the X-ray emitting region is compact and lies within a few tens of the gravitational radii of the black hole (Fabian et al. 2009;De Marco et al. 2013;Cackett et al. 2014;Emmanoulopoulos et al. 2014;Uttley et al. 2014;Kara et al. 2016).The spectral modelling of optical to X-ray spectra from AGNs also yields a similar size of Xray emitting region (Petrucci et al. 2013;Done et al. 2013;Kara et al. 2013;Nandi et al. 2019Nandi et al. , 2021)).From a physical perspective, the twocomponent advective flow (TCAF) (Chakrabarti & Titarchuk 1995) model may provide a self-consistent picture of the accretion dynamics around the central SMBHs.This model is quantified by four flow parameters: two types of accretion flow rates, namely, disc rate ( ) (Shakura & Sunyaev 1973) and halo rate ( ℎ ) (Chakrabarti 1989(Chakrabarti , 1990(Chakrabarti , 1995) ) in the unit of Eddington rate ( ), the dimension of the Compton cloud or CENBOL through shock location ( ) in the unit of Schwarzschild radius ( = 2 /2 ), and the density of this cloud by the shock compression ratio ( ) (Chakrabarti 1989), which is defined as the ratio of the post-shock and the pre-shock flow densities.Along with these parameters, we also need an intrinsic parameter, namely, the mass of the central black hole (in the unit of M ⊙ ) and an extensive parameter, called normalization, which is used to match the observed spectrum with the theoretical one, and essentially a function of the distance of the source and the collecting area of the instrument.This model is used to constrain the geometry around the black hole mass from few solar mass (Chakrabarti 1997;Dutta & Chakrabarti 2010;Debnath et al. 2014) to supermassive AGNs (Mandal & Chakrabarti 2008;Nandi et al. 2019Nandi et al. , 2021)).However, for the reflection-dominated AGN spectra, various geometries for the Compton cloud have been proposed for the X-ray spectra fitting (Dauser et al. 2013;García et al. 2014;Niedźwiecki et al. 2016;Ingram et al. 2019;Mastroserio et al. 2021;Dovčiak et al. 2022).It is to be noted that the TCAF model includes the reflection component in the very process of obtaining the solution (Chakrabarti & Titarchuk 1995).
UGC 6728 is a relatively less explored nearby ( =0.00651 (Kalberla et al. 2005)) Seyfert 1 AGN, which shows broad emission lines in the optical band (Bentz et al. 2016).This AGN is a late-type galaxy and contains an SMBH of mass M = (7.1 ± 4.0) × 105 M ⊙ (Bentz et al. 2016).The X-ray observation of UGC 6728 reported that it has a 'bare nucleus,' i.e., little or no obscuration along the line of sight to the nucleus (Walton et al. 2013).
We organize the paper as follows.In Section 2, we describe the details of the data selection and reduction techniques for different observatories.Then in Section 3, we perform our analysis of X-ray data from various observations and present the corresponding results.We further divide our analysis into two sub-sections.In Section 3.2, we analyze and discuss the timing properties of corresponding observations.Section 3.1 describes the various phenomenological and physical models to extract different physical properties of this source.Later, we discuss our findings from the X-ray data analysis of this source in Section 4. Finally, we draw our conclusions based on our results in Section 5.

OBSERVATIONS AND DATA REDUCTION
In the present work, we use publicly available archival data of the low mass, bare AGN UGC 6728 from XMM-Newton, Swift, and NuS-TAR using HEASARC 2 .We reprocessed all the data using HEAsoft v6.26.1 (Arnaud 1996), which includes Xspec v12.10.1f.

NuSTAR
NuSTAR is a hard X-ray focusing telescope that operates in the energy range from 3.0 to 79.0 keV using two identical moduli, FPMA and FPMB (Harrison et al. 2013).This telescope observed UGC 6728 in two phases in 2016 and 2017.The details of the observations are listed in Table 1.We obtained the observational data from NASA's HEASARC archive3 and used standard data reduction technique4 to reprocess the data.The data were reprocessed by NuSTAR Data Analysis Software NUSTARDASv1.4.1.We used standard filtering criteria to generate clean event files using the nupipeline task.We used the latest calibration data (20230918) from the NuSTAR database 5 to calibrate the data.The source and the background products were extracted by considering circular regions of 60 arcsec and 120 arcsec radii, respectively.We considered the centre of the source region to be at the source coordinates.The background region was considered far from the source region to avoid any contamination.Later, we used the nuproduct task to extract the source spectra and rebinned them by ensuring at least 50 counts per bin by using the GRPPHA task.

XMM-Newton
UGC 6728 was observed with XMM-Newton (Jansen et al. 2001) only once on 23 February 2006.The XMM-Newton observation of the source was carried out in Full Window Mode.The details of the observation are given in Table 1.We used the Science Analysis System (SAS v16.1.06) to reprocess the raw data of EPIC-pn (Strüder et al. 2001) with calibration data files dated 2 February 2018.To prevent the edge of CCD and the bad pixels, we used only the unflagged events using FLAG == 0. Along with this, we also used PATTERN ≤ 4 for single and double pixels.We exclude the photon flares by considering appropriate Good Time Interval (GTI) files to acquire the maximum signal-to-noise ratio.For the spectrum, initially, we used circular regions of 30 arcsec and 60 arcsec radii for the source and background, respectively.Then we apply the SAS task especget for spectrum extraction.After that, we inspected the spectrum for photon pile-up using SAS task epaplot.To remove the pile-up effect, we considered numerous values of the inner radii for the source and investigated the presence of pile-up7 .Finally, we found that in an annular region with inner and outer radii of 10 arcsec and 30 arcsec, respectively, the source spectrum became free from the pile-up effect.We use this annular region to extract the final source spectrum and use it to fit various spectral models.The response files (arf and rmf files) were generated with the SAS task arfgen and rmfgen, respectively.Finally, we rebinned the data by ensuring at least 100 counts per bin using GRPPHA on the final 0.2 to 10.0 keV EPIC-pn spectrum.

Swift
Swift/XRT (Burrows et al. 2005) is an X-ray focusing telescope sensitive in the energy range of 0.3 to 10.0 keV.UGC 6728 was monitored with this telescope in three epochs from 2006 to 2021.Between them, this source was observed simultaneously with NuSTAR in 2016 and 2017 (see Table 1 for details).To generate X-ray spectra between 0.3 to 10.0 keV, we used standard online tools provided by the UK Swift Science Data Centre8 (Evans et al. 2009).In the case of 2021 observations, we combined all the spectra into a single spectrum to achieve enough exposure time.We also considered these observations individually in our spectral fitting using a simple power-law model.However, we did not observe any significant difference in the model parameters.Finally, we used GRPPHA task to rebin the XRT spectra, ensuring a minimum of 10 counts per bin.

Suzaku
Suzaku observed UGC 6728 on 6 June 2009, with the X-ray imaging spectrometer (XIS) (Koyama et al. 2007) and the Hard X-ray Detector (HXD) (Takahashi et al. 2007) for effective exposures of approximately ∼ 46 ks and ∼ 39 ks, respectively.The XIS observations were carried out in STANDARD mode, whereas the HXD observation was carried out in WELL mode.This observation was previously used by Walton et al. (2013) in their study, where they reported the presence of narrow and broad iron emission features.However, they encountered challenges in constraining the reflection parameters and consequently, fixed the inclination angle for this source at 45 degrees.
For the data reduction, we followed the standard procedures as described in the Suzaku Data Reduction Guide9 and applied recommended screening criteria to generate the final spectra and light curves.We used calibration files10 (dated 2016-16-06) in FTOOLS v6.25 to reprocess the event files.Circular regions of radii 200 arcsecs and 250 arcsecs with center at the source coordinates were considered for the source and background products, respectively.The final spectrum and light curve were obtained by merging data from the two front-illuminated detectors (XIS0 and XIS3).The response files were generated using XISRESP task.In our analysis, we excluded the data in the 1.6-2.0keV range to avoid the effect of known Si Kedge.The XIS spectrum was subsequently binned using the GRPPHA task, with a minimum of 100 counts per bin.For the HXD/PIN data reduction, we applied hxdpinxbpi and hxdpinxblc tasks on the event file to produce the spectrum and light curves.Furthermore, the HXD spectrum was corrected for the non-X-ray background, cosmic X-ray background and dead time.

Spectral Analysis
We performed X-ray spectral analysis using data from Swift/XRT, XMM-Newton/EPIC-pn, Suzaku/XIS-HXD and NuSTAR/FPMA-FPMB instruments, covering a duration of approximately 15 years (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021).The spectral analysis was carried out using 2 statistics onto the observational data in Xspec v12.10.1f(Arnaud 1996) software package.The details of the observations from multiple observatories used in the current work are presented in Table 1.For the Suzaku observation, data in the range of 0.5-30 keV are used in the spectral analysis.In 2016 and 2017, the source was observed with Swift/XRT and NuSATR simultaneously.For these observations, data in the energy ranges of 0.3-10 keV and 3-79 keV are used from XRT and NuSTAR, respectively.Apart from these simultaneous broadband observations, UGC 6728 was also observed with XMM-Newton in 2006 and Swift/XRT in 2020 and 2021 in the soft X-ray energy band (below 10 keV).Data from these observations are fitted using multiple spectral models, and the error associated with each parameter of the model is determined at a 90% confidence level (or 1.6 ) using the 'error' 11 task in Xspec.The unabsorbed luminosity is calculated using the 'clumin' 12 task on the composite model.The Eddington luminosity for UGC 6728 is computed as = 8.91 × 10 43 erg/s, based on a mass of 7.1×10 5 ⊙ (Bentz et al. 2016).In this work, we adopted the following cosmological parameters: 0 = 70 km s −1 Mpc −1 ; Λ 0 = 0.73, and Ω = 0.27 (Bennett et al. 2003).

Model Construction
As the X-ray spectral properties of UGC 6728 are not well understood to date, our motivation was to characterize the X-ray spectrum of this source.For this purpose, at first, we parameterize the X-ray spectrum across a broad energy range, from 0.3 to 79.0 keV, using various simple models (Power law, Gaussian, etc.).Then, we focus on the primary continuum within the energy range of 3.0 to 10.0 keV.According to current understanding, the X-ray continuum photons are produced mainly by the inverse Compton scattering of thermal photons from the accretion disc in a hot electron cloud.This process, being non-thermal, often leads to a power-law-type spectrum with a high-energy cut-off.Therefore, we begin our analysis by employing the power law (powerlaw 13 ) and cut-off power law (cutoffpl 14 ) models to characterize the primary continuum.The equivalent hydrogen column density along the line of sight of the source modifies the shape of the power law component.To account for this, we consider the Galactic hydrogen column density as , at 4.42× 10 20 cm −215 using a multiplicative model TBabs 16 (Verner et al. 1996) in Xspec.Along with this, we introduce another multiplicative model component zTBabs (Wilms et al. 2000) to incorporate the extragalactic hydrogen column density ( ) with redshift (z) = 0.0065.So, our base model to fit the X-ray continuum is expressed as TBabs*zTBabs*constant*(powerlaw/cutoffpl), where constant is used for cross-normalisation for different instruments.
We fit each spectrum by this baseline model, and the corresponding variation of for the 2017 XRT2+N2 observation is shown in the top panel of Figure 1.During the spectral fitting, a distinctive line-like feature emerged in the energy range of 6-7 keV for the SU (MJD-54988), XRT1+N1 (MJD-57579), and XRT2+N2 (MJD-58093) observations.To account this feature, we introduce a Gaussian model, zGauss 17 with z=0.0065 in Xspec and the corresponding variation of for the 2017 XRT2+N2 observation is shown in the second panel of Figure 1.
After successfully fitting the primary continuum with the Fe-line, we extend the X-ray spectrum into the high-energy regime (above 10.0 keV) and observe no significant deviations.This suggests that the reflection component in the X-ray spectra above 10.0 keV is either absent or not significant within a 90% confidence level.Next, we extend the X-ray spectra into the low energy regime (below 3.0 keV) and observe a significant deviation of the model from the observed spectra.Given that UGC 6728 is a Seyfert 1 AGN, it is expected to exhibit a soft-excess component below 2.0 keV.We initially model this component by powerlaw (Nandi et al. 2021(Nandi et al. , 2023)).Subsequently, we fit the broadband spectra (0.3-79.0 keV) using physical models, such as TCAF, relxill.We present the variation of for the 2017 XRT2+N2 observation in the last panel of Figure 1 using TCAF model fitting.

Power-law
We start the spectral fitting using the power-law model to characterize the primary continuum within the energy range of 3.0-10.0keV.This model, represented in Xspec as tbabs*zTbabs*(powerlaw+zGauss), is used as the baseline for our analysis.The zGauss component is used to compensate for the Fe-line at 6.4 keV.Later, we substitute the power law model with a cut-off power law model, represented as cutoffpl.The spectral fitting results are presented in Table 2.It is to be noted that there are no significant variations in the spectral index (Γ) observed in either case.
For the spectral analysis of XMM-Newton (MJD-53789) data in the 3.0-10.0keV range, we employ tbabs*tbabs*cutoffpl model in our fitting.This model provided a satisfactory fit with a spectral index of Γ = 1.39 +0.10 −0.11 and cut-off energy of = 489.54+258.54   −254.62   keV, resulting in a 2 value of 42.71 for 37 degrees of freedom (dof).The continuum luminosity in the 2.0-10.0keV range is calculated as log( ) = 41.85 ± 0.28.No Fe-line was detected during this observation.
In the subsequent analysis, we employ the combined observations from XRT2+N2 (MJD-58093) to conduct spectral analysis using the cut-off power-law model.The results indicate a spectral index (Γ) of 1.69 +0.03  −0.02 and a cut-off energy ( ) of 344.89 +100.15−157.83keV.The goodness of fit is evaluated by a 2 value of 685.54 for 665 .During this analysis, an Fe-line was detected at 6.41 +0.01  −0.01 keV with equivalent width = 80 +7 −8 eV and the result is listed in Table 2.The continuum luminosity in the energy range of 2.0-10.0keV is estimated to be log( ) = 42.14 ± 0.37.

Nthcomp
In order to understand the physical processes leading to the primary continuum X-ray emission from UGC 6728, we fit the broadband energy spectrum with the thermal Comptonization model, Nthcomp 18 (Zdziarski et al. 1996;Życki et al. 1999).The model depends on the seed photon energy ( ), which we consider to be 200 eV, corresponding to the Wien's temperature of the disc for this source.It is worth mentioning that we tested a range of values of ( ) from 150 to 250 eV and found no significant deviations in the spectral fitting.For our analysis, we opted _ = 1, which is the case when the seed photons are of a multicolour blackbody nature.The composite model we used in Xspec reads as TBabs*zTBabs*constant*(Nthcomp+zGauss).
For the spectral fitting, we initially focus on the 3.0 to 10.0 keV range spectra and apply the asymptotic power law model.Subsequently, we extend the spectra above 10.0 keV and below 3.0 keV, keeping the photon index constant.Then, we apply the Nthcomp model replacing the power-law component in the broadband spectral fitting.Interestingly, we observe positive residuals below 2.0 keV, indicating the presence of soft-excess emission in this source.Additionally, we provide annotations for the model components of the broadband spectral fitting (0.3 − 79.0 keV range) during the 2017 (XRT2+N2) observation in the respective panels.We illustrate the variation of 2 for the Nthcomp model in Figure 1.
Subsequently, we carry out spectral analysis of the Swift/XRT observations from 2020 (XRT3) and 2021 (XRT4) using Nthcomp model.No iron lines are detected in the spectra from these observations.The power-law indices (Γ) from the spectral fitting are 1.66 ± 0.10 and 1.85 ± 0.05 for XRT3 and XRT4, respectively and the corresponding electron temperatures ( ) are 248.78± 124.36 and 178.32 ± 126.32 keV, respectively.
Through the comprehensive spectral fitting of X-ray broadband data from all observations using the Nthcomp model, we determine that the hydrogen column density ( ) along the line of sight is negligible and remains relatively constant throughout our observations.This parameter, ( ) varies from 0.09 +0.13 −0.09 × 10 20 cm −2 to 0.12 +0.15 −0.12 × 10 20 cm −2 , where the Galactic hydrogen column density ( , ) is fixed at 4.42×10 20 cm −2 .Additionally, we observe an increase in the photon index (Γ) from 1.38±0.4 to 1.85±0.5, while the electron temperature ( ) exhibited a decrease from 475.89±250.35keV to 178.32 ± 126.32 keV.Furthermore, we calculate the optical depth ( ) for each observation using the formula (Zdziarski et al. 1996): Here, = 2 is the thermal energy of electrons with respect to the rest mass energy.The values of for each observation are given in Table 3.The maximum possible error in is calculated using the formula ∼ ( 1 2 Δ + ΔΓ Γ ) × , where Δ and ΔΓ are taken from the estimated errors presented in Table 3.The variation of is presented in Table 3 as well as in Figure 2 (second panel from top).We find the values of optical depth to be always below 1.0.This suggests  3.
that the Compton cloud of the source was optically thin for the entire observation period.

CompTT
From the thermal Comptonization model (Nthcomp), we derive the temperature of the Compton cloud and spectral index from the model fitting.We also estimate the optical depth using Equation 1.However, it is important to note that for most of the observations covering energies up to 10.0 keV, constraining the electron temperature from spectral fitting is challenging, resulting in relatively large errors in optical depth calculations.To validate the derived values of these fundamental parameters, we employ another physical model called CompTT 19 on the X-ray spectra of UGC 6728.The CompTT (Sunyaev & Titarchuk 1980b;Titarchuk 1994;Hua & Titarchuk 1995;Titarchuk & Lyubarskĳ 1995) model is characterized by the input soft photons with a temperature ( 0 ) determined from the Wien's law.This model incorporates the plasma 19 https://heasarc.gsfc.nasa.gov/xanadu/Xspec/manual/node158.htmltemperature of the Compton cloud ( ), optical depth ( ), and the assumed geometry (disc, sphere, analytical approximation).In our analysis, we adopt a spherical geometry.The default input value for the soft photon temperature is set at 200 eV (0.2 keV) in the fitting.It is to be noted that the parameter 0 is treated as a free parameter in the fitting.The composite model we used in Xspec reads as, TBabs*zTBabs*constant(CompTT+zGauss).
We begin our spectral fitting of data above 3.0 keV from the XMM-Newton observation in 2006 using this model, and the corresponding results are presented in Table 4.For this observation, we find the soft photon temperature ( 0 ) at 0.21 ± 0.14 keV with Compton cloud temperature ( ) at 470.54 +145.62  −148.26keV.The optical depth ( ) for spherical cloud is estimated as 0.75 +0.42  −0.35 and the model normalization is found to be 8.95 +2.85  −0.86 × 10 −6 photons/keV/sec/cm 2 .During the model fitting, we did not observe any significant deviations of the observational data from the continuum model around ∼ 6.4 keV.Therefore, we discard the model component zGauss for this particular spectral fitting of XMM-Newton data.
We follow a similar methodology for fitting the data from the Suzaku observation (MJD-54988) within the energy range of 3.0 to 30.0 keV.As with the Nthcomp model fitting (see 3.1.3),we initially consider the 3.0 keV to 10.0 keV spectrum for this observation when employing the CompTT model.Then, we extend the observed spectrum to higher-energy regions and perform fitting accordingly.However, we are unable to distinguish the reflection component above 10.0 keV due to poor data quality.It is plausible that the reflection was either absent or barely present during this observation.While conducting the spectral fitting, we identify the presence of Fe-line at 6.54 +0.10  −0.09 keV with an equivalent width of 290 +15 −17 eV.From the continuum fitting, using the composite model described above, we determine the following parameters: soft photon temperature 0 = 0.20 +0.15  −0.18 keV, temperature of the Compton cloud = 386.87+103.08  −098.65 keV and optical depth = 0.61 +0.32 −0.31 .We then attempt to fit two broadband X-ray spectra from 2016 and 2017 observations of UGC 6728 obtained from the simultaneous Swift/XRT and NuSTAR observations, covering the energy band of 3.0 to 79.0 keV.In both the observations, we detect a narrow Feline at 6.4 ± 0.02 keV with an equivalent width of 104 +8 −9 eV and 80 +7 −8 eV for XRT1+N1 (MJD-57579) and XRT2+N2 (MJD-58093) observations, respectively.The disc temperature ( 0 ) is found to be In the subsequent analysis, we perform spectral fitting using Swift/XRT data.The disc temperature ( 0 ) is found to be consistent at 0.14 +0.17 −0.19 for the observations XRT3 and XRT4.The temperature of the Compton cloud ( ) is found to be 248.78+126.35−146.24keV and 215.06 +104.63  −151.21keV for XRT3 and XRT4, respectively.The optical depth is found to vary accordingly.The estimated values of are found to be 0.74 +0.32  −0.24 for XRT3 and 0.39 +0.41 −0.28 for XRT4.The Feline is found to be absent in these two observations, leading us to exclude the zGauss component from the composite model.The normalizations for the continuum of these observations using the CompTT model are estimated to be 16.0 +3.76  −4.19 × 10 −6 photons/keV/sec/cm 2 for XRT3 and 52.1 +7.47  −8.15 × 10 −6 photons/keV/sec/cm 2 for XRT4.The parameters obtained from the CompTT model fitting are presented in Table 4.
Throughout the long-term (2006-2021) X-ray spectral fitting of the continuum of UGC 6728 using CompTT model, we find that the extra-galactic hydrogen column density ( ) was nearly constant and insignificant.This is attributed to the 'bare' nature of the nucleus of this AGN.The disc temperature ( 0 ) vary between 0.14 ± 0.2 to 0.21 ± 0.14 keV.The Compton cloud temperature ( ) and the optical depth ( ) also exhibit variations between 215.06 +104.63  −151.21 to 470.54 +145.62  −148.26keV and 0.87 +0.21 −0.23 to 0.39 +0.41 −0.28 , respectively.These variations of and closely resemble that observed from the thermal Comptonization model (Nthcomp) fitting.The optical depth is found to be consistently below 1.0, suggesting that the cloud was optically thin throughout the observational period.

TCAF
By conducting Nthcomp model fitting of X-ray spectra spanning over approximately 15 years (2006 − 2021), we derive several valuable physical parameters related to the spectral hardness and electron temperature of the Compton cloud or corona in UGC 6728.The calculated value of optical depth consistently indicated an optically thin Compton cloud.Nevertheless, fundamental properties such as the mass of the central object, accretion flow rates, and size of the Compton cloud for this accreting supermassive black hole are still not derived from the above analysis.Knowledge of these parameters would contribute to a deeper comprehension of this massive accreting system.To address this, we employ the Two Component Advective Flow (TCAF) model (Chakrabarti & Titarchuk 1995) to analyze the X-ray spectrum of this object.For the spectral fitting, the model used is TBabs*zTBabs*constant(TCAF+zGauss).
The TCAF model is based on four accretion flow parameters: (i) Keplerian disc accretion rate ( ) in units of the Eddington rate ( ), (ii) Sub-Keplerian halo accretion rate ( ℎ ) in units of the Eddington rate ( ), (iii) shock compression ratio (R), and (iv) shock location ( ) in units of the Schwarzschild radius ( = 2 / 2 ) with an intrinsic parameter which is the mass of the central black hole in units of the solar mass ( ⊙ ).The upper limit, lower limit, and default values of each parameter are kept in a file called lmodel.dat.These values are provided in Table 5.We use initpackage and lmod task in Xspec to run this table to fit the X-ray spectrum of UGC 6728 with the TCAF model.We run the source code about ∼ 10 5 times and select the best spectrum by minimizing .
We begin the spectral fitting process of X-ray data from the XMM-Newton observation ( 2006) using the baseline model as described above.During model fitting, any significant deviation in spectral fit near ∼ 6.4 keV is not seen.Therefore, the Gaussian component zGauss is excluded from the fitting procedure.The fitted parameters obtained from the TCAF model for this specific observation are presented in Table 6 and the model fitted spectrum with the variation of is presented in Figure 3.For this observation, we obtain = 7.28 +1.09 −1.08 × 10 5 M ⊙ for the central SMBH with disc and halo mass accretion rates ( ) and ( ℎ ), of 0.05 +0.01 −0.01 and 0.07 +0.01 −0.01 , respectively.Furthermore, we determine the shock location or the boundary of the Compton cloud ( ) to be at 31.58 +4.65   −3.56   with a shock strength of ( ) = 1.92 +0.99  −0.91 for this XMM-Newton observation.
Using a similar approach, we fit the broadband (0.5 − 30.0 keV) Xray spectra from Suzaku (MJD-54988), and the corresponding result is shown in Table 5 and the spectra are presented in Figure 3.The estimated values of model parameters are : = 7.09 +0.59 −0.57× 10 5 M ⊙ ,  , and = 1.34 +0.06 −0.05 .We observe that the normalization for XRT1+N1 (2016) observation is 1.51 +0.37  −0.38 × 10 −5 photons/keV/sec/cm 2 , which is increased to 1.81 +0.80  −0.78 × 10 −5 photons/keV/sec/cm 2 during the XRT2+N2 (2017) observation.We observe a change in X-ray luminosity from ∼ 6.0 × 10 41 (XRT1+N1: 2016) to ∼ 1.5 × 10 42 erg/s (XRT2+N2: 2017) in about 500 days.It is to be noted that this type of spectral variability in a short timescale is commonly seen in AGNs (Ballantyne et al. 2014;Zoghbi et al. 2017).The details of the parameter space are presented in Table 6, and corresponding TCAF fitted spectra from these two observations are shown in Figure 3 along with the variation of .It is to be noted that, for these broadband spectra, we find the Fe K line at 6.4 ± 0.02 and 6.41 ± 0.01 keV for XRT1+N1 and XRT2+N2 observations with equivalent width (EW) of 104 +8 −9 and 80.9 +7 −8 eV, respectively.We then proceed to fit the data from the last two Swift/XRT obser-vations, XRT3 and XRT4, using the baseline model.No Fe-line is observed in these spectra.From the TCAF model fitting, we estimate the mass of the central black hole to be = 7.07 +2.05 −2.10 × 10 5 and = 7.03 +1.15  −1.19 × 10 5 M ⊙ , disc accretion rates = 0.07 ± 0.02 and 0.08 ± 0.01 , sub-Keplerian halo accretion rates ℎ = 0.10 +0.02 −0.02 and ℎ = 0.09 ).The estimated mass of the central black hole is 7.13±1.23× 10 5 M⊙, which closely aligns with the mass estimated from the reverberation mapping method conducted by Bentz et al. (2016).Furthermore, this model provides valuable insights into the dynamics of accretion flow surrounding the central black hole.
We observe variations in the disc accretion rate ( ), ranging from 0.05 ± 0.01 to 0.08 ± 0.01 , which has an increasing trend over time, reaching its maximum during the 2021 observation.The shock location, representing the boundary of the Compton cloud, moves accordingly.The Compton cloud is found to be the largest (31.58 +4.65   −3.56   ) during the 2006 XMM-Newton observation.Subsequently, the location of the shock gradually shifts inward.The halo accretion rate ( ℎ ) displays variations from 0.09 ± 0.01 to 0.11 ± 0.01 , peaking during the 2017 (XRT2+N2) observation.Consequently, this observation exhibits a high X-ray luminosity for that time of observation.We also detect a narrow Fe K line at ∼ 6.41 keV with an equivalent width (EW) of approximately 100 eV in the XRT1+N1 (2016) and XRT2+N2 (2017) observations.
The variations of accretion flow parameters of TCAF model, namely , ℎ , , and , are presented in Table 6 and potted in Figure 2, with other parameters.The unabsorbed X-ray luminosity in the 0.5 − 10.0 keV range, determined using the 'clumin' task in Xspec for all the observations, is provided in Table 6.It is observed that the source remained in the sub-Eddington luminosity regime throughout the observation period.The long-term variations of the X-ray spectral parameters are also illustrated in Figure 2.

relxillCp
From the power-law fitting above 10.0 keV, we observed that the high-energy spectra of UGC 6728 lacked a reflection component in the high-energy domain above 10 keV.However, the presence of Feline (see Table 2) suggests the existence of a reflection component over the primary continuum above 10.0 keV.Despite the considerable uncertainty in the temperature estimation, we also observed a correlation between the equivalent width of the Fe-line and the temperature of the Compton cloud.It is anticipated that the equivalent width decreases as the temperature of the Compton cloud decreases unless the photons from outflows excite the Fe atoms (Chakrabarti & Titarchuk 1995).To investigate the presence of reflection in the X-ray spectra of UGC 6728, we employ the relativistic reflection model RELXILL (García et al. 2013(García et al. , 2014;;Dauser et al. 2013Dauser et al. , 2014Dauser et al. , 2016) ) on the broadband spectra.This model assumes a broken power-law emission profile with the broken radius .The emissivity is expressed as ( ) ∼ − 1 for < and ( ) ∼ − 2 for > , where 1 and 2 are the inner and outer emissivity index, respectively.The model parameter provides information about the ratio of intensity emitted towards the disc compared to escaping to infinity (Dauser et al. 2016).Other parameters, such as the ionization parameter ( ), iron abundance ( ), inclination angle ( 0 ), inner radius of the accretion disc ( ), and the spin of the black hole ( ), are allowed to vary during the fitting process.
For the broadband X-ray spectral fitting, we use relxillCp flavour with the final model specified in Xspec as Tbabs*zTbabs*constant*relxillCp.The relxillCp flavour does not assume any particular geometry, and the primary continuum emission is given by the thermal Comptonized model depending on the spectral index (Γ) and cut-off energy ( ).We do not use additional Gaussian components to fit the Fe-line as this model incorporates Fe abundance as a free parameter.We fix the values of the outer radius of the accretion disc at = 1000 and redshift = 0.0065 and the corresponding results are represented in Table 7.We apply the relxillCp model to SU observation (MJD-54988), and this model provided a satisfactory fit of the X-ray spectrum with 2 / = 621.96/563.The parameters for the primary continuum are estimated as Γ = 1.50 , respectively.The Fe abundance for this observation was estimated as 1.05 +0.70 −0.74 ⊙ with ionisation parameter log( ) = 3.71 +0.32  −0.33 and reflection fraction = 0.74 +0.11  −0.10 .The intrinsic parameters of this source were estimated as the black hole spin = 0.99 +0.12 −0.34 and inclination angle = 48.20 +14.2  −15.4 degrees.The spectrum is plotted on the left panel of Figure 4.
We followed a similar procedure for XRT1+N1 (MJD-57579) and XRT2+N2 (MJD-58093) observations for the broadband, and the corresponding estimated values from the X-ray spectral fitting is given in Table 7.For these observations, the parameters for the primary continuum were obtained as follows: the spectral index Γ are 1.65 and = 15.0 , respectively.We fixed at its default value (15.0 ) for XRT2+N2 observation as this parameter was not well constrained during fitting.The emissivity indices are found at 1 = 2.85 +0.47  −0.61 and 1 = 3.00 +0.63 −0.58 respectively for inner region where < and 2 = 3.01 +0.52 −0.51 and 2 = 3.00 +0.50 −0.59 respectively for outer region of these observations.The Fe abundance and the ionization parameters are nearly same and the values are = 0.51 +0.20 −0.21 ⊙ and 0.50 +0.20 −0.23 ⊙ with log( ) = 3.45 +0.63 −0.62 and 3.37 +0.22 −0.23 , respectively.The reflection fraction is determined to be = 0.11 +0.05 −0.07 and 0.12 +0.08 −0.05 for these observations.It is expected that the intrinsic parameters would be constant for all observations and the estimated values for black hole spin and inclination angles are = 0.98 +0.20  −0.18 and = 0.96 +0.29 −0.30 with = 53.59+15.7 −16.1 and = 46.62 +13.6  −12.3 degrees, respectively.The spectra are plotted on the middle and right panels of Figure 4.

Timing Analysis
We conducted a comprehensive timing analysis of the light curves with time binsize=500s obtained from the XMM-Newton, Swift, and NuSTAR observations of UGC 6728 (see Table 1).To investigate the variability, we partitioned the X-ray light curves from the XMM-Newton and Swift observations in the 0.3-10 keV energy range into two segments: the soft excess component (0.3-2.0 keV range) and the primary continuum component (3.0-10.0keV range).The light curves in the 0.3-10 keV range are illustrated in the top panels of Figure 5.The bottom panels in the figure show the light curves of the source in the soft and hard X-ray ranges.The left panels represent the light curves from the XMM-Newton observation, whereas the other panels represent the light curves from the Swift/XRT observations of UGC 6728.In this figure, it becomes apparent that the source count rates during the XMM-Newton observation significantly exceed the count rates observed during the XRT observations.This discrepancy may be attributed to the use of different instruments for the respective observations.
To explore the variability in the high-energy regime, we considered light curves from NuSTAR observations.For the correlation study in the broad energy range, we considered the NuSTAR observations in 2016 (N1) and 2017 (N2) due to their substantial exposure times (above 20 ks; see Table 1).The light curves obtained from the NuS-TAR observations in the 3.0 − 79.0 keV energy range were divided into two energy bands: 3.0 − 6.0 keV and 7.0 − 79.0 keV ranges and were utilized for the correlation study (see Figure 6).Notably, we excluded the light curve in the 6.0 − 7.0 keV band as it predominantly comprises photons associated with the Fe K emission line, while our primary interest lies in investigating the continuum emission.

Variability
X-ray variability is a powerful tool to probe the nearby regions of the central supermassive black bole of an AGN.Since UGC 6728 has a 'bare-nucleus' (see Table 3 and Table 6), the X-ray photons originated at the Compton cloud are not intercepted by any other    medium such as BLR, NLR or molecular torus.As a result, the variability in the X-ray emission of this source is very likely produced by the Compton cloud itself or the very inner edge of the accretion disc.To study the temporal variability of UGC 6728, we estimated different variability parameters for all the X-ray observations used in the present work.The results are presented in Table 1.The fractional variability (Edelson et al. 1996;Nandra et al. 1997;Rodríguez-Pascual et al. 1997;Edelson et al. 2001;Vaughan et al. 2003;Edelson & Malkan 2012) for a light curve of counts/s with error for number of data points, with a mean count rate and  standard deviation is given by, where, is the excess variance (Nandra et al. 1997;Edelson et al. 2002) which is defined as, We defined the normalized excess variance as 2 = 2 / 2 and the uncertainties on corresponding parameters ( 2 , and ) are calculated as described by (Vaughan et al. 2003;Edelson & Malkan 2012).To investigate the variability in the X-ray light curves, we calculated peak-to-peak amplitude as = / , where and are the maximum and minimum flux, respectively.
The X-ray light curves from different energy bands exhibit different magnitudes of variability.The results from the variability analysis are presented in Table 8.During 2006 XMM-Newton observation, the highest count rates were observed in all energy bands ranging from 0.3 to 10.0 keV.For this entire energy range (0.3-10.0 keV), the maximum count rate ( ), the minimum count rate ( ) and the mean count rate ( ) were 8.44 counts/s, 3.47 counts/s, and 5.60 counts/s, respectively.For this observation, the soft band (0.3-3.0 keV range) mean count rate ( ) was determined to be 2.58 counts/s, with a maximum count rate ( ) and minimum count rate ( ) of 3.95 counts/s and 1.55 counts/s, respectively.Along with this, the primary continuum (3.0-10.0keV) exhibited a similar trend with , and of 3.02 counts/s, 4.50 counts/s, and 1.92 counts/s, respectively.The variability parameters such as the peak-to-peak amplitude ( ), normalized excess variance 2 , and fractional variability ( ) are found to be comparable for the light curves in the low (0.3 − 2.0 keV), high (3.0−10.0keV) and total (0.3−10.0 keV) energy ranges of this observation.We found that varies in the range of 2.32 to 2.56, whereas 2  and are approximately the same at 0.04 ± 0.004 and ∼ 20%, respectively, for the low-energy, high energy, and the entire energy bands.The detailed results are given in Table 8.
In the case of Swift/XRT observations, the exposure time is comparatively lower with respect to other observations (see Table 1).As a result, we have a smaller number of data points for these observations (see Table 8 and Figure 5).In the soft energy band (0.3 − 2.0 keV), we found that the maximum count rates ranged from 0.35 count/s to 1.05 count/s, with corresponding minimum count rates varying from 0.09 count/s to 0.17 count/s.The mean count rates ranged from 0.16 count/s to 0.48 count/s.We observe a similar trend in the high energy band (3.0 − 10.0 keV), with maximum count rates ranging from 0.40 count/s to 0.61 count/s, minimum count rates varying from 0.01 count/s to 0.18 count/s, and mean count rates ranging from 0.19 count/s to 0.30 count/s.For the entire energy range (0.3 − 10.0 keV) of the Swift/XRT observations, the maximum count rates varied from 0.22 count/s to 1.16 count/s, minimum count rates ranged from 0.1 count/s to 0.23 count/s, and the mean count rates varied from 0.20 count/s to 0.58 count/s.In all the Swift/XRT observations, we observed that XRT2 had comparatively higher counts compared to other observations, as shown in Figure 5 and presented in Table 8.Due to the low count rate and high error associated with each data point, we encountered negative values for normalized excess variance ( 2 ), resulting in imaginary fractional variability ( ) for most of the XRT observations.However, for observations with positive 2 , we observed fractional variability ( ) ranging from 35.4% to 43.5%, with an average of 39.5% for the low energy band, and from 30.1% to 38.8%, with a mean of 35.0% for the entire energy band.In the energy range from 3.0 to 10.0 keV, only XRT3 showed a positive 2 = (0.35 ± 0.07) with = 18.7 ± 2.1%.The detailed results are presented in Table 8.The soft X-ray variability studies could be improved with future missions, such as Colibrí (Heyl et al. 2019;Caiazzo et al. 2019;Heyl et al. 2020).
We have only two NuSTAR observations of UGC 6728 in 2016 (N1) and 2017 (N2).The entire energy band (3.0 − 79.0 keV) is divided into several sub-energy bands, namely, 3.0 − 6.0 keV for the primary continuum, 6.0 − 7.0 keV for the Fe K line and 7.0 − 79.0 keV for the high energy counter-part.Figure 6 displays the temporal variation of the X-ray photons in the energy bands of 3.0 − 6.0 keV and 7.0−79.0keV for the 2016 (N1) and 2017 (N2) observations.The results of the variability analysis for different energy bands of these observations can be found in Table 8.For the N1 observation, we observed a maximum count rate of 0.20 count/s and a minimum count rate of 0.04 count/s in the 3.0 − 6.0 keV energy band.The average count rate ( ) in this band was 0.10 count/s.A similar count rate pattern was observed in the high-energy counterpart (7.0−79.0keV), with maximum, minimum and average count rates of 0.35 count/s, 0.09 count/s, and 0.18 count/s, respectively.The Fe K energy band (6.0 − 7.0 keV) exhibited lower count rates, with maximum count rates of 0.08 count/s, minimum count rates of 0.01 count/s, and an average count rate of 0.04 count/s.For the entire X-ray energy band (3.0 − 79.0 keV), the count rates ranged from a maximum value of 0.53 count/s to a minimum value of 0.17 count/s, with a mean value of 0.32 count/s.The variability parameter ( ) ranged from 11.6 ± 5.2% to 31.6 ± 2.6%, indicating higher variability in the lower energy band compared to the higher energy band for this observation.In the entire energy range, the average variability was = 22.9 ± 5.6%.Please refer to Table 8 for detailed results.In the case of the 2017 NuSTAR observation (N2), we observed a similar trend to N1.For the lower energy band (3.0 − 6.0 keV), the maximum, minimum and average count rates were 0.37 count/s, 0.07 count/s, and 0.22 count/s, respectively.In the Fe K energy band (6.0 − 7.0 keV), the photon counts varied from a maximum value of 0.12 count/s to a minimum value of 0.02 count/s, with an average count rate of = 0.07 count/s.However, for the high-energy counterpart (7.0 − 79.0 keV), the errors associated with each photon count were higher than the standard deviation of the light curve.Consequently, the fractional variability became imaginary, and those values are not presented in Table 8.For this light curve, we found that the = 0.05 count/s and = 0.02 count/s with = 0.03 count/s.For the entire energy range (3.0 − 79.0 keV), the maximum count rate was 1.17 count/s, the minimum count rate was 0.24 count/s, and the average count rate was = 0.62 count/s.We found that the variability parameter remained nearly constant for all energy bands as well as for the entire energy range, ranging from 21.8 ± 4.1% to 26.5 ± 2.0%.The detailed results are presented in Table 8.

Correlation
For the temporal analysis of the long-term X-ray observation of UGC 6728, we concentrated on two epochs of NuSTAR observations: 2016 and 2017 which were accompanied by low energy (0.3 − 10.0 keV) observations from Swift/XRT.To study the correlation between the light curves, we have chosen the simultaneous observations from NuSTAR (N1 and N2) in two energy bands: (i) 3.0 − 6.0 keV and (ii) 7.0 − 79.0 keV.We excluded the light curve in 6.0 − 7.0 keV band as it contains primarily photons from the Fe K line, which appears at ∼ 6.4 keV (see Section 3.1).
The −discreate cross-correlation function (ZDCF20 , (Alexander 1997)) was utilized for this analysis.The likelihood of the correlation function was calculated for the same DCF function using 15000 simulated points in the ZDCF code for the light curves obtained from the NuSTAR observations.We fitted a Gaussian function to estimate the peak and the error on the peak is obtained using the formula provided by Gaskell & Peterson (1987).Our approach followed a similar procedure as described in Nandi et al. (2021).Initially, we fitted all the light curves with a straight line and found the 2 < 1.5 with different slopes and intercepts.However, these data points are not suitable for linear fitting.Next, we performed the correlation analysis of these light curves to ensure the simultaneity of their observations (see the upper panel of Figure 6).
The ZDCF obtained from both NuSTAR observations (N1 and N2) show a similar type of delay pattern.In the case of 2016 NuSTAR observation (N1), a delay of 66.8 ± 500s is observed.We fitted a Gaussian function (indicated by the dotted black line in the lower panel of Figure 6).The uncertainty of the position of the peak is obtained as Δ = 162.5s,which is smaller than the time bin size (500s) of the light curves.Hence, we considered 500s as the error of the position of the peak.The detailed results are given in Table 9.We calculated the likelihood function, represented by deep-green bars in the lower panel of Figure 6, to accurately determine the position of the peak.A similar procedure was followed for the 2017 observation (N2).In this case, we found that the delay between the two given energy bands is = 66.8s.The uncertainty of the position of the peak, obtained from the prescription provided by (Gaskell & Peterson 1987) is Δ = 46.5s, is much smaller than the time bin size.As with the N1 observation, we considered the time bin size (500s) as the uncertainty for the parameter .The results are summarized in Table 9.Table 9.The parameters used for estimating the time delay are presented.The peak value of the correlation function is denoted by , and the corresponding time delay is represented by .The uncertainty of the position of the peak of the correlation function is calculated using the procedure described in Gaskell & Peterson (1987) and is given by Δ .To ensure the reliability of the results, we compared this error with the time bin size and selected the larger one for our analysis.Further details can be found in Section 3.2.2.

DISCUSSIONS
In this study, we investigated the X-ray observations of UGC 6728 utilizing data from XMM-Newton, NuSTAR and Swift/XRT spanning from 2006 (MJD-53789) to 2021 (MJD-59414) (see Table 1).We observed that UGC 6728 is a highly spinning ( = 0.98 ± 0.3) black hole with an inclination angle around ∼ 50 degrees.The results of our spectral and temporal analysis are presented in Section 3. In this section, we will discuss the key findings derived from our data analysis.

Evolution of Primary Continuum
The 'bare-nucleus' (Walton et al. 2013) of UGC 6728 was observed over the period of 2006 to 2021 by various X-ray observatories, revealing both spectral and temporal variabilities.Throughout the long-term X-ray observations, the X-ray luminosity of UGC 6728 is found to vary in the range of ∼ 10 41.8 − 10 44.2 erg/s.The spectral index of the primary continuum (3.0 − 10.0 keV) also displayed variations ranging from 1.38 ± 0.14 to 1.85 ± 0.05, during this observational period.Correspondingly, the electron temperature of the Compton cloud varied from 475.89 ± 250.35 keV to 178.32 ± 126.32 keV.The hardest spectrum was observed in 2006 XMM-Newton observation, with a spectral index of Γ = 1.38 ± 0.14 and an electron temperature of 475.9 ± 250.4 keV according to the Nthcomp model.This is the highest temperature of the electron cloud obtained from all the observations.It is worth noting that the spectral index Γ is lower than that of other sources mentioned in the literature.This could be attributed to the relatively poor data quality, as the exposure time was limited for this observation.If we take into consideration the uncertainty of this parameter, its value falls within the range of 1.14 to 1.52, which is consistent with the observed Γ values reported in the literature (Kriss et al. 1980).The corresponding temperature of the electron also appears to be high, with a large uncertainty for this observation.It is important to mention that the parameter, , is estimated using various models such as cut-off power-law, Nthcomp, and CompTT.The significant uncertainties in the estimation of might be due to the absence of high-energy data beyond 10.0 keV.The model TCAF provides insights into the accretion flow dynamics around the central object for this observation.By fitting the 0.2 to 10.0 keV spectra with the TCAF model, we found that the sub-Keplerian halo accretion rate ( ℎ = 0.07 ± 0.01) was higher than the disc accretion rate ( = 0.05 ± 0.01) during that time.This suggests that the flow was sub-Keplerian-dominated for that observational period.This behavior is commonly observed in AGNs (Nandi et al. 2019(Nandi et al. , 2021)).We found that the boundary of the Compton cloud or the shock location ( ) was estimated to be ∼ 31.6 with a relatively weak shock strength of ∼ 1.92 based on spectral fitting.This is the highest shock strength when all the X-ray observations of this source are considered.A higher value of indicates the higher temperature of the Compton cloud, which is consistent with the results obtained from the Nthcomp model fitting, implying an outward push of the boundary of the Compton cloud.
In the next Suzaku observation in 2009, we observe that the X-ray luminosity of UGC 6728 is maximum.This increase in luminosity can be attributed to the high normalization of the primary continuum during this observation.It is noted that the spectral index changed from 1.38 ± 0.14 to 1.50 ± 0.07, and the corresponding electron temperature decreased from 475.9 ± 250.4 to 350.42 ± 151.74 keV.This variation in spectral index and electron temperature could be explained by the variation in accretion dynamics.During this observation, we found that the accretion rates remained constant with those of the previous observation.However, the shock strength decreased from 1.92 to 1.40.As a result, the electrons in the Compton cloud could not gain energy from the shock, leading to a decrease in temperature.Moreover, we observed a prominent Fe-line at 6.54 ± 0.1 keV with an equivalent width of 188 ± 17 eV.The presence of the Fe-line suggests the existence of either reflection or a high abundance of iron in the accreting medium.To distinguish between these possibilities, we applied the relxillCp model to this observation and found that the high abundance ( = 1.05 ± 0.72) of iron with a relatively small amount of reflection ( = 0.74 ± 0.11).We conducted a broadband (0.3 − 79.0 keV) spectral analysis of UGC 6728 using combined data from the 2016 Swift/XRT (XRT1) and NuSTAR (N1) observations.For this particular observation, we observed a relatively softer spectrum (Γ = 1.64 ± 0.03) for the primary continuum (3.0 − 79.0 keV) compared to the 2006 (XMM) observation.The corresponding temperature of the electron cloud in the Compton cloud also changed from 475.9 ± 250.35 keV to 254.4 ± 86.21 keV.We determined the optical depth of the Compton cloud to be 0.69 ± 0.02, indicating an optically thin cloud.The disc accretion rate ( ) and the halo accretion rate ( ℎ ), changed from 0.05 ± 0.01 to 0.06 ± 0.01 and 0.07 ± 0.01 to 0.09 ± 0.01 , respectively, with respect to the XMM observation.The increase in implies an increased supply of soft photons, which interact with the Compton cloud or corona, resulting in a relatively softer spectrum.Consequently, the shock location moved inward, with shifting from 31.58 +4.65   −3.56   to 23.62 ± 2.55 .The strength of the shock also increased from 1.40 ± 0.08 to 1.68 ± 0.09.These changes contributed to the observation of a relatively softer spectrum during this particular observation.By fitting a single Gaussian, we detected a narrow Fe K line at 6.40 ± 0.02 keV with an equivalent width (EW) of 104 ± 9 eV.The detection of Fe-line suggests the presence of reprocessed emission.To investigate this, we applied the relxillCp model on the broadband spectra.The model output indicated a reflection fraction of = 0.11 ± 0.06 along with an Fe abundance of = 0.51 ± 0.20 ⊙ .In the 2017 observation, which was carried out by Swift/XRT (XRT2) and NuSTAR (N2) simultaneously, we obtained another broadband spectrum (0.3 − 79.0 keV) with a higher X-ray luminosity compared to the previous broadband observation in 2016 (see the first panel of Figure 5).By fitting the primary continuum (3.0 − 10.0 keV) of this broadband spectrum with the Nthcomp model, we found a marginal increase in the spectral index from 1.64 to 1.69, along with a decrease in the electron temperature ( ) of the Compton cloud from 256.40 ± 86.21 keV to 249.18 ± 41.95 keV, with large uncertainties in .We also found the presence of an optically thin Compton cloud with optical depth 0.66 ± 0.02 during this observation.Additionally, we detected a narrow Fe line near 6.41 keV with an equivalent width (EW) of 80.9 ± 8 eV.To investigate the presence of reflection component beyond 10.0 keV, we used relxillCp model to fit the broadband spectra and found that = 0.50 ± 0.2 ⊙ and = 0.11 ± 0.6.The low values of these parameters indicate the high energy spectrum is barely dominated by reflection above 10.0 keV.
The increase in X-ray luminosity suggests a change in the accretion flow, which can be quantified through TCAF model fitting.We observed the accretion rates, and ℎ , increase from 0.06 ± 0.01 to 0.07 ± 0.01 and 0.09 ± 0.01 to 0.11 ± 0.01 , respectively.As a result, the luminosity of UGC 6728 increased by ∼ 2.4 times from the previous (2016) observation.Moreover, the shock location shifted inward from 23.62 ± 2.56 to 21.23 ± 2.07 , accompanied by a corresponding decrease in the shock strength from 1.68 ± 0.038 to 1.34 ± 0.80.
In the 2020 observation carried out by Swift/XRT (XRT3), we encountered a spectrum similar to that of the previous observation in 2017.The flow parameters, as well as the spectral index (Γ) and electron temperature ( ), remained unchanged compared to the parameters obtained from the 2017 observation.Specifically, we found Γ = 1.66 with = 249.18keV and corresponding optical depth ( ) is 0.69 ± 0.02.We also estimated the X-ray luminosity in 0.5 − 10.0 keV range and found that this is nearly the same as in the case of the 2017 observation (see Table 3).
The accretion dynamics exhibited minimal changes in this observation.The TCAF fitting suggests the accretion rates for 2020 observation to be = 0.07 ± 0.02 and ℎ = 0.11 ± 0.01 which are similar to those during the 2017 observation.The shock location is located near 18.38 ± 5.6 with a shock strength of 1.77 ± 0.56 for this observation.
In the 2021 observation from Swift/XRT (XRT4), we found the softest X-ray spectrum for UGC 6728.The spectral index was determined to be Γ = 1.85 ± 0.05, with an electron temperature of = 178.32 ± 126.32 keV.The corresponding optical depth was measured to be = 0.71 ± 0.02.During this observation, we estimated the maximum disc accretion rate as = 0.08 ± 0.01 .Additionally, the halo accretion rate decreased from 0.109 ± 0.01 to 0.09 ± 0.01 .The increase in the disc accretion rate leads to the cooling of the Compton cloud due to the presence of soft photons generated in the disc.As a result, the Compton cloud cannot maintain its size and gradually shrinks.This causes the shock location to move inward, eventually settling at 11.03 ± 4.65 , with a shock strength of = 1.68 ± 0.2.The reduction in the size of the Compton cloud affects the production of hard photons, resulting in the observed soft spectrum.
Throughout the X-ray observation period (2006-2021), we found that the Compton cloud remained optically thin.However, the spectral index (Γ) exhibited systematic variations.The hardest spectra were observed in the 2006 (XMM) observation, followed by a transition to a softer state.The softest state was observed in the 2021 (XRT4) observation.The variations in Γ are summarized in Table 3 and visualized in Figure 2.
As the source transitioned from one state to another state, the other spectral parameters, such as the accretion rates, the size of the Compton cloud, the temperature of the Compton cloud etc, changed accordingly.We found that the disc accretion rate ( ) increased from 0.051 ± 0.01 (in Table 6) to 0.08 ± 0.01 as the spectra became softer.On the other hand, the halo accretion rate ( ℎ ) increased from 0.07 ± 0.01 to 0.09 ± 0.01 before reaching a relatively constant value of ∼ 0.1 ± 0.01 .The change in also influenced the position of the shock location ( ).As the disc rate increased and the source transitioned from a harder to a softer state, the shock location moved inward.This resulted in a decrease in the size of the Compton cloud, a behavior commonly observed in AGNs and Galactic black holes (Chakrabarti & Titarchuk 1995;Nandi et al. 2019Nandi et al. , 2021)).The shock strength ( ) showed relatively minor variations, ranging from 1.34 ± 0.06 to 1.92 ± 0.99, with an average value of 1.69 ± 0.59.
In addition, We also estimated the hydrogen column densities ( ) along the line of sight, while assuming a constant galactic hydrogen column density.The results showed that the extragalactic hydrogen column densities varied within a range of approximately (10 19 − 10 20 )/cm 2 .This result supports that the source has a 'bare-nucleus', as previously reported by Walton et al. (2013).Furthermore, we conducted an estimation of the mass of the central supermassive black hole (SMBH) using TCAF fitting.The obtained value for the SMBH mass was (7.13 ± 1.23) × 10 5 M ⊙ .This measurement aligns with the results obtained by (Bentz et al. 2016) ) using an independent method, further confirming the consistency of our findings.

Evolution of Soft Excess
The soft excess (Arnaud et al. 1985;Singh et al. 1985;Fabian et al. 2002;Gierliński & Done 2004), characterized by an excess emission below 2.0 keV, is an extraordinary feature in the X-ray spectra of most Seyfert 1 AGNs.Despite its common occurrence, the origin of this excess emission remains unclear.However, multiple explanations are proposed to explain this feature in literature (Miniutti & Fabian 2004;Crummy et al. 2006;Sobolewska & Done 2007;Done et al. 2007;Mehdipour et al. 2011;Done et al. 2012;Lohfink et al. 2012;Walton et al. 2013;Liebmann et al. 2018).In this context, a longterm X-ray observation of UGC 6728 showed a strong correlation between the primary continuum and the soft excess (Nandi et al. 2023).In this study, we also observe the presence of the soft excess.However, the strength of this component exhibited variability throughout our analysis.
The presence of a strong soft excess is observed in 2006 (XMM) and 2009 (SU) observations as presented in the top two panels of Figure 7.During these observations, the spectra appear relatively harder with (Γ = 1.39 +0.10 −0.11 and Γ = 1.50 , respectively.The disc and halo accretion rates are estimated to be 0.05± and 0.07 ± 0.01 , respectively, for these two observations.The increased size of the Compton cloud could produce a relatively cooler electron region near the outer boundary of CENBOL or Compton cloud, leading to the enhanced production of photons in the soft energy band (below 3.0 keV), as described in Nandi et al. (2021).As a result, a strong presence of soft excess could be observed during the initial epochs.
The soft excess component exhibited a diminished presence in the 2016 (XRT1+N1) and 2017 (XRT2+N2) observations, as illustrated in the bottom panels of respectively.The reduction in the size of the Compton cloud led to a decreased number of photons being generated in the primary continuum as well as a weaker soft excess component in these observations.On the other hand, we also observed weaker reflection fraction ( ) for weaker soft-excess (Fabian et al. 2002).It would be interesting to observe UGC 6728 in the future to see whether the soft excess diminishes or re-brightens, preserving the primary continuum Mehdipour et al. (2023).

Correlation between Spectral Parameters
The spectral analysis using Nthcomp and TCAF models reveals the nature of the region where the X-ray photons are generated.For UGC 6728, we found that the Compton cloud remains optically thin throughout the entire observation period (see Figure 3).However, we observe a transition of the source from a comparatively hard state (Γ = 1.38) to a comparatively soft state (Γ = 1.85) between 2006 and 2021.The X-ray luminosities (0.5 − 10.0 keV) remain relatively constant, around ∼ 10 42.15 erg/s.We examined the correlation among various spectral parameters and the corresponding result is presented in Table 10  PCC value of −0.97.This anti-correlation is commonly observed in AGNs (Nandi et al. 2021), and it is displayed in the upper left panel of Figure 8 with linear interpolation.However, due to the inability to constrain accurately with the available spectra up to 79.0 keV, we obtained high -values during the calculation of the correlation coefficient.Consequently, correlations involving are not presented in Table 10.
Next, we found a strong correlation between Γ and the disc accretion rate ( ) with a PCC of 0.88 ( -value = 0.051).As the disc rate increases, more disc (seed) photons are generated, leading to interactions with the Compton cloud and a subsequent decrease in cloud temperature.Consequently, a smaller number of hard photons are produced, resulting in the transition of the source from a hard to a soft state, as indicated by an increase in Γ.We also plotted the variation of Γ and with linear interpolation in the upper left panel of Figure 8.The parameter Γ is also loosely correlated with the halo accretion rate ℎ with PCC=0.66.However, the high - value ( -value = 0.15) makes it challenging to draw any definitive conclusions based on this correlation coefficient.Furthermore, we calculated the correlation between Γ and the total accretion rate , and the corresponding PCC is estimated to be 0.88 with -value=< 0.05.This correlation is well-established and commonly observed in AGNs and Galactic black holes.We observed a strong global anti-correlation trend between Γ and , with a Pearson Correlation Coefficient (PCC) value of −0.96 and corresponding -value of < 0.05.This finding suggests that as the shock location or the boundary of the Compton cloud ( ) decreases, the spectrum tends to soften, aligning with the concept described by Chakrabarti & Titarchuk (1995).In line with this understanding, we can also anticipate an anti-correlation between and , as illustrated in the lower left panel of Figure 8.
In our investigation of the accretion flow parameters estimated from the spectral fitting using TCAF model, we explored correlations among , ℎ , , and .It is generally anticipated that the shock location moves inward as the disc accretion rate increases (Chakrabarti & Titarchuk 1995;Chakrabarti 1995).We discovered a similar correlation between and , exhibiting an anti-correlation with a Pearson Correlation Coefficient (PCC) of −0.94 and a corresponding -value of < 0.05.The relationship between and is depicted with linear interpolation in the right panel of Figure 8.As for the other parameters, we observed weak correlations or anticorrelations among them.This outcome is expected since these parameters are intrinsic to TCAF and act independently during X-ray spectral fitting.

CONCLUSIONS
We conducted a comprehensive analysis of X-ray observations spanning approximately 15 (2006-2021) years for UGC 6728, a low-mass Seyfert 1 AGN which has a highly spinning black hole at the centre with the inclination angle nearly ∼ 50 degrees.Throughout this period, we observed significant variations in the X-ray luminosity of the source.The X-ray luminosity exhibited fluctuations on a yearly timescale, with a factor of approximately 2.4 variations observed in the 2016-2017 observations.Our investigation focused on the broadband X-ray spectra covering the energy range of 0.3-79.0keV.We find this source is retaining its 'bare'-nature throughout the obser-vational period.In this section, we present a summary of our major findings.
3. The observed variation of Γ can be attributed to the accretion flow dynamics surrounding the central supermassive black hole and the characteristics of the Compton cloud.Our analysis reveals that the disc rate ( ) increases from 0.05 ± 0.01 to 0.08 ± 0.01 , while Γ changes from 1.38 ± 0.14 to 1.85 ± .0.05, indicating a transition of this source from a hard state to a soft state.Correspondingly, the shock location ( ) or the size of the Compton cloud and compression ratio ( ) exhibit variations.Notably, the Compton cloud is optically thin ( < 1.0) throughout the entire observation period.
4. The intensity of the soft excess component varied over the duration of our observational period.The 2006 and 2009 observations displayed profound soft excess, compared with the diminished presence of soft excess observed in 2016 and 2017 epochs.The variation in the strength of soft excess could be explained by the variation of the accretion dynamics.
5. In our timing study, we observed a similar order of variability in the high energy band (above 3.0 keV).Furthermore, correlation analysis between two high energy bands, specifically 3.0 − 6.0 keV and 7.0 − 79.0 keV, does not reveal any time delays, suggesting that the photons in both energy ranges may have originated from a similar mechanism.Since the high energy spectra (above 3.0 keV) of UGC 6728 can be adequately described by a single power-law model, we can infer that this source exhibits either no reflection hump or a very minimal hump in relation to the primary continuum above 10.0 to 15.0 keV.6.By performing X-ray spectral fitting using TCAF model, we determined the mass of the central supermassive black hole (SMBH) to be = (7.13± 1.23) × 10 5 M ⊙ with a high spin at = 0.97 +0.20  −0.27 and inclination angle of 49.5 ± 14.5 degree.

Figure 1 .
Figure 1.Variation of is shown for each model component while fitting the broadband spectrum of UGC 6728 during the 2017 XRT2+N2 observation.Initially, we fitted the data above 3.0 keV with the Nthcomp model.Then we added zGaussian for the Fe-line at ∼ 6.41 keV.Later, we replaced Nthcomp by TCAF for the broadband spectrum (0.3 − 79.0 keV).

Figure 3 .
Figure 3. TCAF model fitted X-ray spectra of UGC 6728 from various observations from 2009-2021, along with the residuals obtained from the spectral fitting.

Figure 4 .
Figure 4. relxillCp model fitted X-ray spectra of UGC 6728 from various observations from 2009-2021, along with the residuals obtained from the spectral fitting.

Figure 5 .
Figure 5. Variation of photon counts with respect to time from XMM-Newton and Swift/XRT observations of UGC 6728 at different epochs (see Table1).The light curves in the 0.3−10.0keV range are shown in the top panels, whereas the bottom panels show the light curves in the soft X-ray band (represented by red dots/line) and hard X-ray band (represented by blue dots/line), plotted together for comparison.The top and bottom left panels represent light curves from the XMM-Newton observation, whereas the other panels are from the Swift/XRT observations of UGC 6728.

Figure 6 .
Figure6.Top panel: The light curves of UGC 6728 in the energy bands of 3.0 to 6.0 keV (red) and 7.0 to 79.0 keV (blue) are presented for two epochs of NuSTAR observations in 2016 and 2017.The high energy band have higher count rates in comparison to the low energy band for these two observations.Lower Panel: -discrete cross-correlation functions (light-green) are plotted for the light curves in 3.0 − 6.0 keV and 7.0 − 79.0 keV ranges.The likelihood functions (dark-green), simulated using 15000 points, are plotted along with the ZDCF.

Figure 7 .
In comparison to the preceding XMM and SU observations, these spectra appeared softer.From the spectral fitting by the TCAF model, we estimated the size of the Compton cloud for these observations were = 23

Figure 7 .
Figure 7.The variation of the strength of soft excess with respect to the primary continuum is plotted for the observations from 2006 to 2017.The trend indicates a decline in the strength of the soft excess as the source moved from a relatively softer state to a comparatively harder state.

Figure 8 .
Figure 8. Correlation between different spectral parameters estimated from the spectral fitting of X-ray spectra.
† exposure time for XIS and HXD, respectively.

Table 2 .
cutoffpl fitting result for all spectra.The unabsorbed luminosity is calculated for the energy range from 2.0 to 10.0 keV.
x Figure 2. Variation of different parameters of powerlaw fitting with time for all spectra.The corresponding parameters are given in Table

Table 3 .
Results obtained from the spectral fitting above 3.0 keV spectra with Nthcomp model.The optical depth is calculated using Equation 1.

Table 4 .
Results obtained from the spectral fitting of 3.0-10.0keV data with CompTT model.

Table 5 .
The TCAF parameter space is defined in the file lmod.dat.The two columns for minima and maxima are provided for the range of iterations.Between them, the 1st column indicates the soft bound and the 2nd column gives the hardbound of the parameters.
TCAF model fitting are presented in Table6and the model fitted spectra with the variation of are presented in the bottom middle and bottom right panels of Figure3.Through the comprehensive spectral fitting of the long-term (2006 − 2021) X-ray observations of UGC 6728 using TCAF model, we encounter a negligible amount of extra-galactic hydrogen column density (

Table 6 .
Parameters obtained from the TCAF model fitting with all the spectra.The unabsorbed X-ray luminosity is calculated for the energy range from 0.5 to 10.0 keV.

Table 7 .
Parameters obtained from the relxillCp model fitting with all the spectra.
indicates the parameter that was fixed during X-ray spectrum fitting.

Table 8 .
The table presents the variability statistics in different energy ranges for various observations for 500s time bins.It is important to note that in some cases, the average error of the observational data exceeds the 1 limit, leading to negative excess variance.Consequently, these cases have imaginary values for , which are not included in the table.

Table 10 .
Correlation among different spectral parameters estimated from the spectral fitting of long term (∼ 15 years) X-ray observations with various satellites.The correlation analysis involved Parameter-1 and Parameter-2, which are displayed in the first and second columns, respectively.The third column represents the Pearson Correlation Coefficient (PCC), while the corresponding -values are presented in the final column.A positive PCC value indicates a positive correlation between the two parameters, whereas a negative value indicates an anti-correlation.