Exploring the broadband spectral and timing characteristics of GRS 1915+105 with AstroSat and NICER observations

GRS 1915+105, a Black Hole X-ray Binary (BHXB), came to the fore on 15 Aug 1992 and was detected by the WATCH All-Sky monitor on the Granat observatory. This binary system has a K-M spectral type donor star and a black hole with a mass equivalent to 12.4 solar masses and is located at a distance of 8.6 kpcs (Reid et al., 2014). This source has its relativistic jets inclined at an angle of $70^{\circ}$ from our line of sight (Mirabel & Rodriguez, 1994). This source is widely renowned for its diverse X-ray variabilities (Castro-Tirado et al., 1992; Belloni et al., 2000, 1997; Yadav et al., 1999) and exhibits 14 distinct X-ray classes, differentiated based on its X-ray flux, Color-Color Diagram (CCD), and hardness ratio (Belloni et al., 2000; Klein-Wolt et al., 2002; Hannikainen et al., 2005). Since its first detection in 1992, GRS 1915+105 has primarily appeared in bright X-ray states like the High Soft State (HS) and High Hard Intermediate State (HIMS), among others. However, this source has transitioned into a diminishing phase in recent years, starting in 2018.

X-ray binary systems exhibit rapid variability over short time scales. Fourier analysis is frequently used to understand rapid variations by computing power-density spectra (PDS) (Van der Klis, 1989). Various patterns have been observed in PDS, spanning a spectrum of broadband noise patterns and more structured peaks known as Quasi-Periodic Oscillations (QPOs). For the source, GRS 1915+105, QPOs spanning frequencies from a few millihertz to up to approximately 70 Hz have been observed (Dhaka et al., 2023; Morgan et al., 1997; Belloni & Altamirano, 2013a; Yadav et al., 1999; Paul et al., 1997; Sreehari et al., 2020). QPOs are often characterized using a Lorentzian function, allowing us to assess their characteristics like centroid frequency ($f$), strength, and quality factor (defined as the ratio of the frequency of the QPO peak to its full width at half maximum). The centroid frequencies of these QPOs can be associated with physical processes occurring in these systems. Typically, two categories of QPOs exist. High-frequency QPOs (HFQPOs) have a centroid frequency of approximately 60 Hz or more (and in certain instances, up to a few hundred hertz) (Belloni et al., 2012; Belloni & Altamirano, 2013b; Belloni, 2009) while Low-frequency QPOs (LFQPOs) exhibit a centroid frequency of around 30 Hz or less. Further, the LFQPOs have been classified into Types A, B, and C QPOs based on differences in power spectral properties and phase lag behavior (Homan et al., 2001; Wijnands et al., 1999; Remillard et al., 2002; Casella et al., 2004; Ingram & Motta, 2019).

Numerous models have been proposed to explain the underlying dynamics of type-C QPOs. Some of these models center around geometric effects linked to the Lense-Thirring precession frequency, such as those discussed by Stella & Vietri (1997), Schnittman et al. (2006), Ingram et al. (2009). Other models suggest instabilities in the accretion flow (Tagger & Pellat, 1999; Cabanac et al., 2010). Misra et al. (2020), Liu et al. (2021), Dhaka et al. (2023) have reported that the QPO might be linked to the dynamic frequency (denoted as $f_{Dyn}=c(s)/r$, with $c(s)$ representing sound speed) at the truncated disk radius. Various models of hydrodynamic origin are also found in works by Chakrabarti et al. (2008) and Cabanac et al. (2010). However, the definitive understanding of the physical origin of QPOs remains a subject of ongoing debate.
The general behavior of BHXBs in terms of their spectral characteristics is typically described through a shift from a hard, less luminous state to a soft, more luminous state. This transformation is graphically represented as a q-shaped trajectory on the Hardness-Intensity Diagram (HID) (Belloni et al., 2005; Homan & Belloni, 2005). This trajectory encompasses intermediate regimes of hardness and luminosity. Notably, the frequency of type-C QPOs increases as the source makes transitions from harder to softer states. Depending on the theoretical framework, changes in hardness can be interpreted as variations in the outer radius of a hot inner flow Esin et al. (1997)

Time lags between different energy photons are an important diagnostic to understand the nature of these systems. Reverberation lags, i.e., time-lags due to light travel time effects between the continuum photons and reflected features, can provide constraints on the geometry of the accretion disc (Mastroserio et al., 2018; Ingram et al., 2019; Lucchini et al., 2023). However, time lags between continuum photons require a different explanation. For kHz QPOs in neutron star systems, the time-lag is of the order of 50 microseconds, which is the expected timescale due to Compton scattering delays in a corona of size $\sim$10 km, i.e., the size of the neutron star (Lee & Miller, 1998). However, Compton scattering is expected to produce hard lags, while the observed ones were soft. Lee et al. (2001) showed that soft lags are possible if a fraction of the comptonized photons impinge back into the soft photon source. This idea has been further developed in several works (Kumar & Misra, 2016; Karpouzas et al., 2020) for kHz QPOs in neutron star systems. This model has been extended by Bellavita et al. (2022) to study low-frequency QPOs. However, since low-frequency oscillations show significantly longer time lags ($>$ 10 milliseconds), an explanation based on Compton scattering time scales requires large coronal sizes $>10^{3}$ km (Bellavita et al., 2022; Karpouzas et al., 2021; García et al., 2021; Zhang et al., 2022).

Mastichiadis et al. (2022) describe a model where the C-type QPO is identified with the cooling time-scale of the corona. However, they invoke an accretion rate, $\dot{M}\sim 10^{-3}L_{EDD}/c^{2}$, which with an efficiency of 10% would lead to a luminosity of $\sim 10^{35}$ ergs/sec for a 10 solar mass black hole. In another interpretation, the C-type QPOs are identified as the inner hot corona precesing at the Lense-Thirring frequency (Ingram et al., 2009, 2016). The time lag will arise here since the observed spectral shape will change during different oscillation phases as the hot inner region angle with the disc varies. There is evidence that the shift in the iron line energy is a function of phase, which supports this model (Ingram et al., 2009, 2016). However, for GRS 1915+105 analysis, Nathan et al. (2022), report that the phase-resolved analysis required a rather large disk thermalization time-scale to irradiation, and spectral analysis indicated a small inner disc radius incompatible with the Lense-Thirring interpretation. These interpretations are applicable for the particular case of C-type QPOs. Low-frequency broadband noise can be generated by stochastic variation in different radii of an accretion disc, which propagates inward, causing X-ray variation from the inner regions (Lyubarskii, 1997). Such propagation can reproduce the observed frequency-dependent time-lags if the hard X-rays are preferentially produced in inner regions compared to the soft ones (Kotov et al., 2001). While for a standard accretion disc, the higher energy photons are preferentially produced at smaller radii than low energy ones; this is unclear for thermal Comptonization photons. A high-energy thermal Comptonization photon has undergone several scatterings. Since the optical depth of the corona is typically of order unity, the photon would have scattered all over the corona. Hence, it cannot be associated with a particular corona region. In other words, it is unclear whether a corona can be divided into different zones, with the higher energy photons being produced preferentially in some zones compared to others. This situation may happen if the corona has large temperature gradients. Still, again, it is not clear whether this can happen; moreover, the time-averaged spectra usually assume a single-temperature corona.

It is important to find out under what conditions a single-zone compact thermal Corona can produce energy-dependent time-lags, which are larger than the scattering or light-crossing timescales. An approach is to consider the response of the energy spectrum to small variations in spectral parameters and then quantify which set of spectral parameters and time-lag between them can reproduce the observed energy-dependent fractional r.m.s and time-lag (Maqbool et al., 2019; Garg et al., 2020). The model assumes that at each phase of an oscillation, the energy spectrum can be represented by the same model used for the time-averaged one, with changes in the spectral parameters. The observed energy-dependent time lag is the consequence of any time lag between spectral parameters. Identifying the spectral parameters (and the time lag between them) responsible for the variation may lead to a better understanding of the temporal nature of the system. Ideally, the approach requires good broadband energy spectra and measurement of energy-dependent r.m.s. and time lag.

In this study, we adopt the model proposed by Garg 2020 to understand the radiative components responsible for generating energy-dependent temporal variability in GRS 1915–105. We study the timing and spectral properties of GRS 1915+105 by using simultaneous data from AstroSat and NICER. We reviewed all the observations of GRS 1915+105 from AstroSat and NICER and selected the simultaneous observations. Our selection of simultaneous observations from AstroSat and NICER, with their broader energy coverage of 0.7–8.0 keV (SXT) and 3.0–80.0 keV (LAXPC) by AstroSat and 0.2–12 keV (XTI) by NICER, allows for better consideration of the disc emission. The high time resolution capabilities of NICER and LAXPC are especially advantageous for studying timing properties. This work utilizes the approach mentioned in Garg et al. (2020) and Garg et al. (2022) to model and characterize the energy-dependent properties of the source.

Section 2 outlines the observations used in this study, along with the data reduction methodologies employed for both NICER and AstroSat. Section 3 explains the lightcurve variation and HID. The study of spectral and temporal characteristics is reported in Section 4 and Section 5, respectively. Furthermore, in Section 5, we explain the model and the process of fitting timing characteristics, including fractional root mean square (fRMS) and time lag variability. Finally, in Section 6, we discuss the findings of this work.

The top left panel of Figure 1 displays the background-subtracted lightcurve extracted from LAXPC 20 in the energy range of 4–50 keV. The time binning of the lightcurve is 2.3775 seconds to make it consistent with the time resolution of the SXT. The middle left panel shows the SXT light curve generated within the 1-5 keV energy interval. The bottom left panel shows the combined NICER light curve of observations 2 and 3. All the light curves are barycentric corrected. The right-hand panel of Figure 1 shows the LAXPC 20 light curve, with the variation of the hardness ratio over time. The hardness ratio is the count rate observed within the energy band of 8-30 keV to that within the 4-8 keV energy range. We partitioned the light curves into two distinct zones based on their X-ray flux and hardness intensity characteristics. The light curves exhibiting a count rate surpassing $\sim$2200 counts/sec (as depicted in the right panel of Figure 1) were categorized as the high flux segment, whereas those with a flux falling below $\sim$2200 counts/sec were assigned to the low flux segment. The shaded part in Figure 1 represents the low flux regime. Throughout the manuscript, we shall consistently refer to these segments as the high and low flux regime light curves and corresponding spectra. Figure 2 illustrates the Hardness Intensity Diagram, generated using data from LAXPC 20, observation ID G08_028T01_9000001656. This diagram is made with a time binning of 10 seconds, and the X-ray intensity, presented on the X-axis, is extracted in an energy span of 4 to 30 keV. The two colors in Figure 2 correspond to low and high flux regimes.

We have used simultaneous NICER and LAXPC data fitting for the observations in Table 1. Using XSPEC 12.12.0, we performed a simultaneous spectral fitting of NICER and LAXPC 20 spectra. Then, to compare the combined analysis of NICER/LAXPC, we performed the combined fitting of SXT/LAXPC. We performed spectral fitting for the high and low flux regimes separately.

For the grouping of the spectra we used ftgrouppha⁸⁸8https://heasarc.gsfc.nasa.gov/lheasoft/ftools/headas/ftgrouppha.html tool of Ftools⁹⁹9https://heasarc.gsfc.nasa.gov/ftools/ and used the optimal binning. To ensure consistency, we used a relative normalization constant for the simultaneous fitting of NICER/LAXPC and SXT/LAXPC data. Following the recommendation of the LAXPC and SXT team, a 3$\%$ systematic error was incorporated to account for uncertainties in the response of LAXPC and SXT instruments (Antia et al., 2017). Due to inconsistencies in the effective area and response of the SXT, energies below 1 keV were not considered. Furthermore, a gain correction was applied to the SXT data, using the gain fit in XSPEC with a fixed slope of 1.

At low energies, the NICER spectrum exhibits features likely caused by calibration uncertainties and the ’shelf’ of the response from higher energy photons¹⁰¹⁰10https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/arf-rmf/. This effect becomes more pronounced for highly absorbed sources like GRS 1915+105, where there are few detected source photons at low energies. Hence, Nathan et al. (2022) and Neilsen et al. (2020) have limited their spectral analysis of NICER spectra to energies above 2.7 and 1.5 keV, respectively. Hence, We restrict the spectral fitting of NICER data to the 1.5 to 10.0 keV range. We performed a simultaneous spectral fitting of NICER and LAXPC spectra in the broad energy range of 1.5–20 keV.

The spectra of BHXBs typically exhibit two main components: a multicolor blackbody disk emission and a high-energy thermal comptonization emission. To model the thermal disk emission, we used the Diskbb model (Mitsuda et al., 1984), incorporating parameters such as inner disk temperature ($T_{in}$) and normalization ($N_{Disk}$). For the high-energy tail, we employed a Comptonization component, thcomp (Zdziarski et al., 2020), with parameters like photon index or Thomson optical depth, electron temperature, and scattering fraction. The coronal electron temperature was fixed at 100 keV, as it was not constrained, while all other parameters were allowed to vary. To account for the impact of interstellar medium (ISM) absorption, we used the TBabs model (Wilms et al., 2000). The GRS 1915+105 system exhibits complex absorption lines. Besides the broad iron line, there is evidence of a large number of narrow absorption lines. Lines corresponding to Iron K$\alpha$ at 6.4 keV, He-like Fe XXV at 6.7 keV, and H-like Fe XXVI at 6.97 keV have been observed in the spectra of this source. Additional lines are detectable at approximately 7.85 and 8.3 keV in certain intervals (Nathan et al., 2022; Neilsen et al., 2020; Wang et al., 2024). In the spectral fitting, we observed two absorption lines corresponding to Fe XXVI Ly$\alpha$ at 6.97 keV and Fe XXVI Ly$\beta$ at 8.25 keV and fitted them with Gaussian absorption models gabs. We freeze the width of the absorption lines at 0.05 keV and allow the strengths to vary. The top and bottom left panels in Figure 3 display the energy spectra of NICER/LAXPC in the high and low flux regimes, respectively. Residuals for each spectrum are presented below the corresponding spectrum.

To compare the simultaneous analysis of NICER/LAXPC, we performed the simultaneous fitting of SXT/LAXPC spectra across the energy range of 1-20 keV using the same model. Details of the spectral results of NICER/LAXPC and SXT/LAXPC are provided in Table 3, covering the parameters like hydrogen absorption, electron temperature, disc temperature, and scattering fraction. We have restricted the spectral analysis of LAXPC data to less than 20 keV since beyond that, there are slight broad systematic residuals at the 2-sigma level, which may be due to some complex spectral features or a slight underestimation of the background.

Having obtained a reasonable fit, we replaced the diskbb models with more physically motivated, namely the relativistic model kerrd (Ebisawa et al., 2003). For the kerrd model, the black hole mass, disc inclination angle, and distance to the source were kept constant at values of 12.4$M_{\odot}$, 60^∘ and 8.6 kpc, respectively (Reid et al., 2014). The spectral hardening factor was set at 1.7 (Shimura & Takahara, 1995). We note that the mass accretion rate is $1.37\pm 0.04\times 10^{18}\text{gm/s}$ for high flux and $1.12\pm 0.05\times 10^{18}\ \text{gm/s}$ for low flux in the NICER/LXP20 spectra. In the SXT/LXP20 spectra, the mass accretion rate is $1.35\pm 0.07\times 10^{18}\ \text{gm/s}$ for high flux and $1.19\pm 0.21\times 10^{18}\ \text{gm/s}$ for low flux. The inner radius is $<2.1\ R_{g}$ for high flux and $2.2\pm 0.2\ R_{g}$ for low flux in the NICER/LXP20 spectra, while in the SXT/LXP20 spectra, it is $<2.5\ R_{g}$ for high flux and $<2.7\ R_{g}$ for low flux.

In this work, we conducted a spectral and timing study of available simultaneous AstroSat and NICER observations of GRS 1915+105 made on 31 Oct and 1 Nov 2017. The exposure time of the source for AstroSat is 15.3 ks, and for NICER, it is 4.89 ks on 31 Oct and 3 ks on 1 Nov 2017. Given the temporal variability of the source during the observation period, we segmented the lightcurve into two distinct parts, corresponding to high and low flux levels. We studied the energy spectra and timing characteristics of the distinct flux levels. We fitted the spectra with an absorbed disk model with thermal comptonization and a broad iron emission line, represented by tbabs*gabs*gabs(thcomp * diskbb + gauss) and found that the model describes the spectra for energies upto 20 keV. We replaced the xspec model diskbb with the relativistic component kerrd and obtained a similar fit. Both combinations of LAXPC with SXT and LAXPC with NICER provided similar spectral parameters. The spectral fitting revealed that the primary difference between the low and high flux levels seems to be the disk component. In high flux, the temperature of the disk is higher, and its normalization is smaller compared to the low flux

The simultaneous observation by Astrosat and NICER allowed us to study the rapid temporal behavior of the source in 1.8-20 keV energy range for time-lag and RMS spectra. The PDS generated from both Astrosat and NICER data for the low and high flux levels did not reveal the presence of the QPO but instead identified a broad feature. Our analysis focused on the broad feature at $\sim$2 Hz, where the power is notably prominent compared to other features in the PDS. The fractional root mean square (fRMS) and time-lag spectra for the feature at $\sim$2 Hz were generated for each flux level, showing that for both cases, the broad feature exhibited soft lags.

To better understand the radiative mechanism behind the variability, we modeled the energy-dependent fRMS and time-lag of the feature at $\sim$2 Hz with the model put forward by Garg et al. (2020). According to the model, the energy-dependent properties of the variability can be described with correlated variations of certain spectral components with respective time delays.

Initially, we consider variations only in coronal parameters. This case includes variations in coronal parameters such as scattering fraction ($\lvert\delta f_{sc}\rvert$), heating rate ($\lvert\delta\dot{H}\rvert$), and Thomson optical depth ($\lvert\delta\tau\rvert$), with phase lags of $\lvert\delta_{sc}\rvert$ and $\lvert\delta\tau\rvert$ relative to $\dot{H}$. However, this case results in a poor match with observed fRMS and time lag, suggesting that the corona alone is insufficient to explain the fractional root mean square (fRMS) and time-lag spectra.

Next, we considered the possibility that the inner disk temperature and the heating rate vary, but this did not provide an adequate fit to the data. Finally, considering variations in three spectral parameters, namely the inner disk temperature, the inner disk radius, and the coronal heating rate, resulted in a good fit to the energy-dependent fRMS and time lag for both the low and high flux levels. The inner disk radius and temperature variations were found to be anti-correlated to each other, with no phase lag between them. In contrast, the phase lag for the coronal heating variation is negative, implying that the coronal heating variation occurs first, and then the disk reacts.

The primary results of this work are that during the simultaneous observation by NICER and AstroSat of GRS 1915+105, the source showed two flux levels, high and low. The spectra for both levels could be fitted by a model consisting of disk emission and thermal comptonization of the disk photons for energies less than 20 keV. The spectral parameters obtained from considering NICER/LAXPC were consistent with the ones obtained from SXT/LAXPC. The fractional RMS increases with energy, which implies that the variability is dominated by the corona. However, fitting the energy-dependent RMS indicates that the variability is not only due to the corona but also significant variability in the disc. A similar result was obtained for C-type QPOs for GRS 1915+105 by Garg et al. (2020) and for MAXI 1535–571 by Garg et al. (2022) using only AstroSat/LAXPC data. This work shows that it is true when considering low-energy NICER data and the broadband noise for GRS 1915+105.

The work highlights the need for longer simultaneous observations of the source with AstroSat and NICER. Such observations would have the statistics to get well-constrained time-lags, especially in the NICER energy bands, and hence would provide better estimates of model parameters. We have not included reflection components in the spectral fitting for simplicity, as the timing model does not account for reprocessing effects. Incorporating the reflection components in spectra can be vital for future studies, ensuring a more precise representation. Importantly, the timing model utilized in this study requires further enhancement to accommodate more sophisticated spectral models, ensuring a more detailed comparison with high-quality data.

We thank the referee for the useful comments, which have improved the manuscript significantly. We would like to express our gratitude for the assistance provided by the Indian Space Research Organization (ISRO) in facilitating mission operations and disseminating data via the ISSDC. The present study used data from the Soft X-ray Telescope (SXT) developed at the Tata Institute of Fundamental Research (TIFR) in Mumbai. The authors acknowledge thankfulness to the SXT Payload Operations Centre (POC) at TIFR for their valuable assistance in verifying and releasing the data via the International Space Science Data Centre (ISSDC) data repository, as well as for providing the necessary software tools required for data analysis. The LAXPC POC, TIFR, Mumbai, is also acknowledged for providing the necessary data analysis tools. This research has used data, software, and web tools obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), a service of the Astrophysics Science Division at NASA/GSFC. The author, RD, acknowledges the frequent visits to the Inter-University Centre for Astronomy and Astrophysics (IUCAA) in Pune to carry out the major part of the work.

The observational data used in this paper are publicly available at ISRO’s Science Data Archive for AstroSat Mission (https://astrobrowse.issdc.gov.in/astro_archive/archive/Home.jsp) and NASA’s High Energy Astrophysics Science Archive Research Center (HEASARC;
(https://heasarc.gsfc.nasa.gov/)) and references are mentioned.