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Ranjeev Misra

Publications and source records attributed to Ranjeev Misra.

At least 19 recordsLinked to original sources

Spectral evolution of NS binary system GX 349+2 using AstroSat observations

We present a broadband spectral study of the Sco-like Z source GX 349+2 using AstroSat LAXPC and SXT observations obtained during 2019 and 2024. The X-ray light curves exhibit large variability, and the hardness-intensity diagram traces the characteristic Z-shaped track. Using hardness ratio and intensity, the Z-track is segmented into six regions comprising normal branch, soft apex, and an extended flaring branch. We perform simultaneous broadband spectral fitting in the energy range 0.7-25.0 keV using two model configurations, tbabs*(thcomp*bbodyrad+diskbb) and tbabs*(bbodyrad+thcomp*diskbb), to study the evolution of emission from the neutron-star boundary layer, accretion disk, and Comptonizing corona along the Z-track. The comparative analysis reveals that, irrespective of the adopted Comptonization geometry, the inferred inner disk radius remains large (~100 km) and exhibits no systematic inward motion as the source luminosity increases. This suggests that the accretion disk remains truncated and the disk luminosity tends to saturate, consistent with a radiation pressure influenced inner disk. The relatively small variation in the inferred mass accretion rate across the branches indicates that changes in $\dot{M}$ alone cannot account for the observed Z-track evolution. Instead, the boundary-layer component becomes progressively dominant toward the flaring branch, with both its temperature and flux increasing with total luminosity, while the relative contribution from the disk decreases. These results indicate a redistribution of accretion power toward the boundary layer and the associated Comptonizing region, suggesting that the primary energy dissipation in GX 349+2 occurs within the boundary layer region of the neutron star.

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Complex Energy-Dependent Behaviour of Quasi-Periodic Oscillation Observed in GRS 1915+105

We present complex energy-resolved properties of quasi-periodic oscillations (QPOs) in the black hole X-ray binary GRS 1915+105 using an observation from the LAXPC instrument onboard AstroSat. Power density spectra (PDSs) are constructed in multiple energy bands and modeled with multi-Lorentzian components to investigate the energy dependence of QPO properties. The QPO frequency shows a modest increase with energy. Dynamic PDS analysis does not reveal clear evidence for time-dependent evolution of the QPO frequency, suggesting that the observed frequency shift is not primarily driven by temporal variability. We perform simultaneous fitting of energy-resolved PDSs and find that a model in which the QPO feature is described by two Lorentzian components provides a better fit. The two components exhibit different evolution in fractional root mean square amplitude as a function of energy. We further examine the phase-lag properties by simultaneously modeling the PDS and the real and imaginary parts of the cross-spectrum and find distinct phase-lag behavior for the two components. Overall, these results indicate that the apparent energy-dependent evolution of the QPO feature may be a result of the presence of more than one variability component.

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Probing the High-Energy Emission of the VHE-emitting Changing-Look Blazar B2 1420+32

We present a multi-wavelength temporal and spectral study of the changing-look blazar B2~1420+32 using \emph{Fermi}-LAT, \emph{Swift}-XRT, and \emph{Swift}-UVOT data from MJD~58818--60721. The source reached a peak 0.1--300~GeV photon flux of $(4.62 \pm 0.29) \times 10^{-6}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$ around MJD~60488, about 60 times the 4FGL-DR4 average, during which the photon index hardened to $2.19 \pm 0.14$; the flux--index evolution shows only weak evidence for global harder-when-brighter behaviour. The fractional variability is strongly energy dependent, largest in $\gamma$-rays, substantial in the optical/UV, and low in X-rays. Strong $\gamma$-ray--optical/UV correlations and a moderate $\gamma$-ray--X-ray correlation indicate that the X-ray emission tracks the $\gamma$-ray variability less closely than the optical/UV emission. The X-ray spectra are best described by a log-parabola, and the negative curvature measured in four of the five states suggests that the X-ray band samples the transition between the high-energy tail of the synchrotron component and the onset of the inverse-Compton component. We identified five activity states and modelled the high-energy (X-ray and $\gamma$-ray) component of their broadband spectral energy distributions (SEDs) using synchrotron self-Compton (SSC), external Compton (EC), and SSC+EC scenarios. The SSC-only and EC-only models either require physically disfavoured parameters or fail to reproduce the VHE emission, whereas SSC+EC provides the most self-consistent description, with a seed-photon temperature of $\sim 10^{3}$~K favouring an infrared torus origin. The brighter states require larger bulk Lorentz factors and higher jet powers, while the magnetic field varies only modestly, indicating that the flux evolution is governed by a combination of Doppler boosting and jet energetics.

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Potential detection of ~ 4.2 keV emission line from GRS 1747-312

We present a broadband spectral analysis of the neutron star LMXB GRS 1747-312 using $\sim$ 40 ks AstroSat data. The source was observed during the decay phase of the 2017 outburst, with an absorbed 1.0-5.5 keV flux of 1.67$^{+0.04}_{-0.07}\times$10$^{-11}$ erg s$^{-1}$ cm$^{-2}$, corresponding to a luminosity of $\sim$(0.9-1.80)$\times$10$^{35}$ erg s$^{-1}$. The continuum is modeled with thermal Comptonization of blackbody emission and interstellar absorption. A mildly broad iron line at $\sim$6.4 keV is fitted with a disc reflection component. Narrow lines below 2 keV are described by a hot plasma using the XSPEC model APEC. Additionally, there is a potential detection of an emission line at 4.19$^{+0.12}_{-0.10}$ keV with width $\sigma$ = 0.2 $\pm$ 0.2 keV and line flux of 13$^{+10}_{-9}\times$10$^{-5}$ erg s$^{-1}$ cm$^{-2}$. Examination of several short-duration ($\sim$ few kiloseconds) Swift observations at a few times the AstroSat source flux provided upper limits to the line flux of $<$30$\times$10$^{-5}$ erg s$^{-1}$ cm$^{-2}$. The 4.2 keV line likely originates from reflection off the neutron star surface. Shifting the neutral Fe K$_\alpha$ line from its rest energy of 6.4 keV to 4.2 keV requires a redshift of z $\sim$ 0.6, consistent with that expected from the surface of a non-spinning 1.4 M$_\odot$, 10 km radius neutron star. If confirmed, this feature provides a potential direct measurement of gravitational redshift, allowing us to place strong constraints on the neutron star's mass-to-radius ratio and gain valuable insights into the equation of state (EOS) of dense matter.

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Relativistic Scattering in the Funnel of Cygnus X-3

Cygnus X-3 presents significant challenges to standard accretion models. Recent polarimetric observations by IXPE reveal high polarization degrees (PD) in the hard state ($\sim 23\%$) and unexpectedly significant polarization in the soft state ($\sim 12\%$), which are difficult to reconcile with static scattering models at low inclination ($i \approx 30^\circ$). We present a relativistic scattering model within a funnel-shaped geometry that resolves this discrepancy. We show that a single funnel-outflow configuration with variable bulk velocity $\beta$ can reproduce both polarization states, with lower velocities ($\beta \approx 0$) yielding $\sim 12\%$ polarization (soft state) and mildly relativistic velocities ($\beta \lesssim 0.4$) producing $\sim 23\%$ polarization (hard state) at $i \approx 30^\circ$ for half funnel opening angles of $\sim 13^\circ$-$16^\circ$. Relativistic aberration modifies the effective scattering angle in the comoving frame, enhancing polarization in the hard state while recovering the static limit in the soft state. The model also yields a consistent estimate of the intrinsic luminosity, of order $\sim 10^{40}$ erg s$^{-1}$, supporting a super-Eddington interpretation. This framework provides a unified explanation of the observed polarization properties of Cygnus X-3.

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Jet Power Estimates of FSRQs PKS 1441+25 and Ton 599 from Broadband SED Modeling

Flat-Spectrum Radio Quasars (FSRQs) are among the most energetic and powerful active galactic nuclei, often exhibiting jet powers comparable to or exceeding the Eddington luminosity. In this work, we performed broadband spectral energy distribution (SED) modeling of two FSRQs PKS 1441+25 and Ton 599, using Swift-XRT/UVOT, NuSTAR, Fermi-LAT and VERITAS observations during 2015 and 2021, respectively. We considered four particle distribution models: a broken power law, a log-parabola, and two energy-dependent models in which either the diffusion or acceleration timescale depends on energy. Our results show that the jet power estimates derived from models with intrinsic curvature, such as the log-parabola and energy-dependent models, are of the same order as those obtained with a broken power-law distribution. This contrasts with the case of High Synchrotron Peaked Blazars (HBLs), where the power estimates can differ by nearly two orders of magnitude between models. We attribute this difference to the lower electron break energies typically observed in FSRQs. Consequently, our findings suggest that, unlike in HBLs, the estimated jet powers in FSRQs are relatively insensitive to the assumed particle energy distribution, reflecting the dominance of external Compton processes and weaker dependence on spectral curvature.

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Correlations Between kHz QPOs and Spectral Parameters from Time-Resolved Spectro-Temporal Analysis of 4U 1728-34

We present a time-resolved analysis of the persistent emission in 4U 1728--34 using AstroSat observations from 2016 to 2019. We detect kilohertz quasi-periodic oscillations (kHz QPOs) during all epochs, with centroid frequencies ranging from $\sim 350$ to $1180~\mathrm{Hz}$, although some detections are of lower significance ($< 3\sigma$). We model the simultaneous spectra from the Soft X-ray Telescope and the Large Area X-ray Proportional Counter using a combination of an absorbed disk component (diskbb), a blackbody component (bbodyrad), a thermal Comptonization model (thcomp), and a broad Gaussian line. From the diskbb parameters, we estimate the accretion rate and find that all observations fall into two accretion regimes, namely AR1 and AR2, with accretion rates of $\sim 3 \times 10^{16}~\mathrm{g\,s^{-1}}$ and $\sim 7 \times 10^{16}~\mathrm{g\,s^{-1}}$, respectively. Interestingly, we find that for AR1, the lower kHz QPO frequency ($\nu_{\mathrm{L}}$) is always $< 500~\mathrm{Hz}$, while for AR2 it is $\gtrsim 500~\mathrm{Hz}$. We found that the spectral index showed no clear correlation with $\nu_{\mathrm{L}}$. For AR1, the coronal electron temperature ($kT_{\mathrm{e}}$) and optical depth ($\tau$) are $\sim 10~\mathrm{keV}$ and $\sim 5$, respectively. In contrast, for AR2, $kT_{\mathrm{e}}$ decreases to $\sim 3~\mathrm{keV}$ and $\tau$ increases to $\sim 12$, showing correlations with $\nu_{\mathrm{L}}$, with Spearman's rank correlation coefficients of $-0.78$ and $0.71$, respectively. The transition of the spectral parameters at $\nu_{\mathrm{L}} \sim 500~\mathrm{Hz}$ indicates the existence of a critical QPO frequency governed or influenced by the accretion state of the source.

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Constraining Spin and Inclination Angle of XTE J2012+381 using AstroSat and NICER

We present a spectral analysis of a black hole X-ray binary XTE J2012+381 during its 2022 outburst, using data from NICER and AstroSat. Combining data from NICER, LAXPC20, and SXT, we extract energy spectra covering the 0.7-10.0 keV range. We model the energy spectra using a series of physical models and find that a reflection-Comptonization model provides the best fit. Given the uncertainties in the black hole mass and source distance, we investigate the stability of the inferred spectral parameters by systematically varying the black hole mass (7.26, 11, and 16.5 M$_\odot$), source distance (3.3, 5.4, and 7.5 kpc), and spectral hardening factor (1.5, 1.7, and 1.9). We find that, across most combinations of these parameters, the spin solutions consistently lie in the high-spin regime, spanning values between $\sim$0.67 and $\sim$0.998, with only a limited subset of configurations favoring lower spins. In contrast, the disk inclination angle remains well constrained over the majority of the explored parameter space, typically ranging between $\sim$50{\deg} and $\sim$65{\deg}. Only a few parameter combinations yield higher inclination values.

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Accretion Disk Evolution in GX 339-4 Across Spectral States Using NuSTAR, NICER, and Insight-HXMT Observations

We present a broadband spectral analysis of the black hole X-ray binary GX 339-4 during its 2021 outburst, covering both hard and soft spectral states. Using simultaneous observations from NuSTAR, NICER, and Insight-HXMT, we investigate the evolution of the accretion disk with a focus on the disk normalization derived from the diskbb component, which serves as a proxy for the apparent inner disk radius. In the standard single Comptonization model, the disk normalization in the hard state is more than an order of magnitude lower than in the soft state ($\sim$0.3$\times$10$^3$ vs. $\sim$3.0$\times$10$^3$). This result contradicts the widely accepted view that the disk radius is smaller in the soft state than in the hard state. By incorporating an additional warm Comptonization component, the disk normalization in the hard state increases to values ($\gtrsim 10^4$) exceeding those in the soft state ($\sim 10^3$), yielding results consistent with a physically truncated, cooler accretion disk. The results of this work support the presence of a dual-corona geometry in the hard state, comprising both a hot, optically thin corona and a warm, optically thick corona, while the soft state spectrum is well described by a single hot Comptonization component alone. Our findings emphasize the importance of including a warm corona in hard-state spectra, as it leads to a more physically consistent picture of the accretion geometry across spectral states.

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Tracing Fe K X-ray reverberation lag in the energy-resolved spectra of Narrow-line Seyfert 1 galaxy Ton S180

We report the Fe K relativistic reverberation feature for the first time in the Narrow-line Seyfert\,1 galaxy Ton\,S180. Using a long observation from {\it XMM-Newton} we find that the Fe K emission lag peaks at $117\pm49$ s in the lag energy spectrum computed for frequencies $(0.3-8.5) \times 10^{-4}$ Hz. The lag amplitude drops to $22.85\pm14.20$ s as the frequency increases to $(8.5-30) \times 10^{-4}$ Hz. The time-averaged spectrum of the source shows a relatively narrow Fe K line at $\sim6.4$ keV, resulting in black hole spin to be low ($a=\rm 0.43_{-0.14}^{+0.10}$) found from the reflection modelling. We perform general relativistic transfer function modelling of the lag energy spectra individually. This provides an independent timing-based measure of the spin at $a=0.30_{-0.17}^{+0.34}$, and black hole mass $M_{\rm BH} = 0.29_{-0.16}^{+0.01}\times10^8M_{\odot}$, comparable to the previous measurement, and height of the corona $h = 2.59_{-0.33}^{+5.17}r_{\rm g}$. Further, we observe that the Fe K lag and the black hole mass fit well in the linear lag-mass relation shown by other Seyfert 1 galaxies.

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Neuro-Parametric Spectral Classification of Black Hole and Neutron Star X-ray Binary Systems

We perform the classification of black hole and neutron star X-ray binary systems using deep neural networks applied to archival RXTE X-ray spectral data. We first construct two neural network models: one trained using only spectral flux values and another trained using both fluxes and their associated errors. Both models achieve high classification accuracies of ~90-94 %. To gain physical interpretability of these networks, we fit all spectra with a simple phenomenological model consisting of a thermal disk component and a power-law. From this analysis, we identify the blackbody temperature, power-law index, the ratio of blackbody to power-law flux, the reduced $\chi^2$, and the variance of the data as key parameters that likely contribute to the classification. We validate this inference by designing an additional neural network trained exclusively on this reduced parameter set, without using the spectral data directly. This parameter-based model achieves a classification accuracy comparable to that of the spectral models. Our results show that deep neural networks can not only classify compact objects in X-ray binaries with high accuracy but can also be interpreted in terms of physically meaningful spectral parameters derived from conventional X-ray spectral analysis. This framework offers a promising, mission-agnostic approach for compact object classification in current and future X-ray surveys.

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Spectral State Switching in Mrk 421: Results from the AstroSat LAXPC/SXT Observations

We carried a detailed time and flux resolved X-ray spectral analysis of the high-synchrotron-peaked blazar Mrk\,421 using simultaneous LAXPC20 and SXT observations. The 100\,s binned LAXPC20 light curve obtained during 3--8 January 2017 reveals pronounced flux variability. The source exhibits a fractional variability amplitude of $F_{\mathrm{rms}} = 0.210 \pm 0.005$ in the SXT band and $F_{\mathrm{rms}} = 0.316 \pm 0.006$ in the LAXPC20 band. During this interval, the source reached a peak LAXPC20 count rate of 122.94\,counts\,s$^{-1}$, while the peak count rate in the SXT light curve is 26.79\,counts\,s$^{-1}$. This enabled us to carry out flux-resolved spectroscopy by dividing the 100\,s binned LAXPC20 light curve into ten flux states (S1--S10), each spanning a width of 8\,counts\,s$^{-1}$. For each flux state, simultaneous SXT and LAXPC20 spectra were extracted and fitted jointly. We find that the spectra in these states are well described by a synchrotron-convolved broken power-law, which provides a better fit than a log-parabola model. The low-energy particle index (index before the break) is found to cluster around two discrete values across flux states indicating two spectra states in the source. The break energy consistently moves to high energy with increase in flux level in these states. Time-resolved spectroscopy (10-ks segments) confirms that the flux histogram is best modelled as a double lognormal distribution and the index histogram is double normal. Inclusion of two additional long observations spanning 2017-2019 shows the same double-state behaviour on longer timescales. Together, the results indicate that Mrk\,421 routinely occupies two dominant spectral; in a leptonic synchrotron framework this can be explained by Gaussian-like fluctuations in acceleration conditions producing lognormal flux states.

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Evolution of the 2021 Outburst of GX 339-4 with AstroSat

We present a comprehensive study of the 2021 outburst of GX 339-4 using AstroSat observations in the hard-intermediate (HIMS) and soft-intermediate states (SIMS). Spectral and timing analyses across these states suggest that during the SIMS, unabsorbed flux (0.1-3 keV), inner disc temperature, and "apparent" inner disc radius do not change, suggesting the stability of the disc. In the SIMS, the photon index decreases from 2.1 to 1.7, indicating spectral hardening. The power density spectra (PDS) suggest the presence of quasi-periodic oscillations (QPOs) in the HIMS and SIMS. The QPO frequency evolves from 0.1 Hz to 0.2 Hz in the HIMS, and further to 5.7 Hz in the SIMS. We also observe a decrease in QPO frequency from 5.7 Hz to 4.5 Hz during the SIMS. We discuss the evolution of the QPO, fractional root mean square (rms) amplitude, and time-lag spectra. We discover that variations in disc normalization, disc temperature, and coronal heating rate can reproduce the observed rms and lag spectra with a time delay between them.

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Synchrotron radiation from NGC 470 HLX1 - a hidden hyperluminous accreting neutron star?

We present the first broadband spectral analysis of NGC 470 HLX1, a hyperluminous X-ray source that exhibits significant flux variability over different epochs. We investigate the feasibility of synchrotron radiation with varying latitude from a magnetized neutron star to explain the source's spectra. Although the statistical quality of the data does not allow us to rule out simple phenomenological models, it is adequate to constrain the parameter space for this more physically motivated model. We also shed light on the particle acceleration mechanisms and maximum Lorentz factor of electrons within the neutron star magnetospheric plasma under super-Eddington accretion conditions. In our broadband spectral modeling, the detection of a blackbody-like component suggests the presence of a disk near the corotation radius or an outflow ejected from the disk. The viability of synchrotron emission in an HLX system offers new insights about the nature of these sources, motivating further sample studies to assess whether most of these sources are powered by accreting neutron stars.

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Multiwavelength spectral and temporal analysis of VHE Blazar 1ES 1959+650: Tracing emission mechanisms across flux states

The high-synchrotron-peaked BL Lac object 1ES\,1959+650 exhibited pronounced activity between MJD~60310 -- 60603, including a very high energy (VHE) detection reported by LHAASO. To investigate the underlying emission mechanisms, we performed a comprehensive temporal and spectral analysis using multiwavelength data from \textit{Swift}-XRT/UVOT and \textit{Fermi}-LAT, covering the optical/UV to GeV $\gamma$-ray bands. The source shows strong energy-dependent variability, with the largest fractional variability in $\gamma$-rays, followed by X-rays and UV/optical, consistent with leptonic emission scenarios. Based on the variability patterns, we identified distinct flux states (F1, F2, F3, F4, F5, VHE-FX1, and VHE-FX2). The X-ray spectra exhibit a clear ``harder-when-brighter'' trend across these states. We modeled the broadband spectral energy distributions (SEDs) using a one-zone model incorporating synchrotron and synchrotron self-Compton (SSC) emission, implemented in \textsc{xspec} using $\chi^{2}$ minimization. During the VHE detection, the corresponding X-ray/optical emission likely resembled the F2 state. Modeling the VHE SED using F1-state data led to an SSC overprediction of the VHE flux, whereas all other states were well described within the one-zone framework. Systematic trends in physical parameters are observed across flux states, including spectral hardening, increasing break energy, rising bulk Lorentz factor, and decreasing magnetic field with increasing flux. These results suggest that enhanced particle acceleration efficiency and stronger Doppler boosting drive the observed flaring activity, while the decrease in magnetic field indicates conversion of magnetic energy into particle kinetic energy, consistent with shock-driven scenarios.

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The strong Fe K line and spin of the black-hole X-ray binary MAXI J1631-479

We study the transient black hole binary MAXI J1631--479 in its soft spectral state observed simultaneously by the NICER and NuSTAR instruments. Its puzzling feature is the presence of a strong and broad Fe K line, while the continuum consists of a strong disk blackbody and a very weak power-law tail. The irradiation of the disk by a power-law spectrum fitting the tail is much too weak to account for the strong line. Two solutions were proposed in the past. One invoked an intrinsic Fe K disk emission, and the other invoked disk irradiation by the returning blackbody emission. We instead find that the strong line is naturally explained by the irradiation of the disk by the spectrum from Comptonization of the disk blackbody by coronal relativistic electrons. The shape of the irradiating spectrum at $\lesssim$10 keV reflects that of the disk blackbody; it is strongly curved and has a higher flux than that of a fit with a power-law irradiation. That flux accounts for the line. While this result is independent of the physical model used for the disk intrinsic emission, the value of the fitted spin strongly depends on it. When using a Kerr disk model for a thin disk with a color correction, the fitted spin corresponds to a retrograde disk, unlikely for a Roche-lobe overflow binary. Then, a model accounting for both the disk finite thickness and radiative transfer yields a spin of $a_*\approx0.8$--0.9, which underlines the strong model-dependence of X-ray spin measurements.

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Probing the Origin of X-ray Flares in the Low-Hard State of GRS 1915+105 Using AstroSat and NuSTAR

We performed a detailed time-resolved spectral study of GRS 1915+105 during its low-flux rebrightening phase using the broadband capabilities of AstroSat and NuSTAR in May-June 2019. The AstroSat light curves revealed erratic X-ray flares with count rates rising by a factor of $\sim$5. Flares with simultaneous LAXPC and SXT coverage were segmented and fitted using two degenerate but physically motivated spectral models: a reflection-dominated model (hereafter Model A) and an absorption-dominated model (hereafter Model B). In Model A, the inner disk radius $(R_{in})$ shows a broken power-law dependence on flux, indicating rapid inward motion of the disk at higher flux levels. In contrast, Model B shows variable column density in the range of $10^{23}$ to $10^{24}$ cm$^{-2}$, displaying a strong anti-correlation with flux. Both models exhibit significant variation in the ionization parameter between low- and high-flux segments. The total unabsorbed luminosity in the 0.7--30~keV energy range ranged from $6.64 \times 10^{36}$ to $6.33 \times 10^{38}$~erg~s$^{-1}$. Across both models, several spectral parameters exhibited step-function-like behavior around flux thresholds of $5$--$10 \times 10^{-9}$ erg cm$^{-2}$ s$^{-1}$, indicating multiple spectral regimes. The disc flux contribution, more evident in Model B, increased with total flux, supporting an intrinsic origin for the variability. These findings point to a complex interplay between intrinsic disk emission, structured winds, and variable local absorption in driving the flare activity.

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Probing the energy-dependent temporal nature of MAXI J1803-298 with AstroSat and NICER

We performed the spectral and temporal analysis of MAXI J1803-298 using AstroSat/LAXPC and NICER observations taken in May 2021 during the initial phase of the outburst. We found that the source traverses through the hard, intermediate, and soft spectral states during the outburst. The spectrum in all states can be described using soft emissions from the thermal disk and hard emissions from the coronal regions. The variation in the inner disk temperature and normalization of the disk indicates the motion of the truncated disk across these different spectral states. We confirmed the presence of broad features, Type-C, and Type-B QPOs in the power spectra of different spectral states. We investigated the fractional rms and lags of all the variability features and discovered that the lag swung between positive and negative during the outburst evolution. While modeling the features with a simple model that considers variations in accretion parameters such as the accretion rate, heating rate, and inner disk radius, along with delays between them, we found a dynamic reversal in the origin of variability between the corona and the disk. Furthermore, our results are consistent with previous works and a radio study conducted on this source during its outburst.

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