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Comptonizing Efficiencies of IGR 17091-3624 and its similarity to GRS 1915+105

Variability classes in the enigmatic black hole candidate GRS 1915+105 are known to be correlated with the variation of the Comptonizing Efficiency (CE) which is defined to be the ratio between the number of power-law (hard) photons and seed (soft) photons injected into the Compton cloud. Similarities of light curves of several variability classes of GRS 1915+105 and IGR 17091-3624, some of which are already reported in the literature, motivated us to compute CE for IGR 17091-3624 as well. We find that they are similar to what were reported earlier for GRS 1915+105, even though masses of these objects could be different. The reason is that the both the sizes of the sources of the seed photons and of the Comptonizing corona scale in the same way as the mass of the black hole. This indicates that characterization of variability classes based on CE is likely to be black hole mass independent, in general.


Introduction
Classifications of spectral states of neutron stars are made on the basis of color-color diagrams (CCDs) from their energetic radiations (Hasinger 1987;Hasinger & van der Klis 1989;Schulz et al. 1989). Since the masses of neutron stars fall within a narrow range, CCDs drawn using fixed sets of energy bands, can be used to classify all the neutron stars easily. However, stellar mass black holes are known to have masses in the range of 3 − 20M ⊙ (Remillard & McClintock 2006) and CCDs drawn using a particular set of energy bands, may not be similar for a given spectral state. Assuming that a spectrum is fitted with multicolor black body (BB) radiation and a power-law (PL) component, the range of energy in the BB component and in PL component will change with the mass of the black hole. Energy range of BB photons for low mass blackhole could be the energy range of Comptonized photons for a high mass black hole. As a result, the same spectral state may produce different types of CCDs and just by observing CCDs one may not be able to make a statement about the spectral state (Chakrabarti 2008).
A useful hardness ratio (we hereafter call it 'the dynamic hardness ratio') has been defined recently Pal et al. (2011Pal et al. ( , 2013; Pal & Chakrabarti (2014). This is the Comptonizing Efficiency (CE) which is the ratio of the photon counts under the PL component and the injected BB seed photons. Of course, unlike conventional CCDs, which can be drawn without any knowledge about the spectra, CE requires the knowledge of the spectra. The added benefit is that CE provides us with the fraction of injected seed photons which are Comptonized by the hot electron cloud (Sunyaev & Titarchuk 1980, 1985. Thus, it contains information about the geometry of the Compton cloud. Its evolution with time implies the evolution of the geometry of the Compton cloud. It has been shown recently that the variability classes of GRS 1915+105 could be characterized by average CE values which suggests that the geometry of the Compton -4cloud changes systematically during variability class transitions (Pal et al. 2013). CE is very small for softer classes and larger for harder classes. Earlier, these classes were characterized by conventional CCDs for GRS 1915+105 (Morgan et al. 1997;Belloni et al. 1997a,b;Taam et al. 1997;Muno et al. 1999;Belloni et al. 2000). Since CCDs may 'look' different when a black hole of another mass is chosen, one may require to adjust energy ranges suitably to have similar looking CCDs for the same type of variability class. This happens while comparing IGR 17091-3624 and GRS 1915+105 (Altamirano et al. 2011a,b,c;Pahari et al. 2012). Such adjustments are arbitrary. It is thus necessary to use a mass independent concept, such as CE, i.e., a spectral state dependent dynamical hardness ratio, to check whether the two objects pass through the same spectral states while having similar variability class. Moreover, since the sequence of CE also gives the sequence in which the class transitions would occur, it is clearly a powerful tool to understand X-ray active black hole candidates.

IGR J17091-3624 was first observed by an INTEGRAL Galactic Center Deep
Exposure Coverage (Kuulkers et al. 2003). Later, the position was confirmed through Swift observation leaving two nearby blended candidates (Kennea & Capitanio 2007;Chaty et al. 2008). In early 2011, Swift-BAT detected an outburst from IGR J17091-3624 ). Optical/IR observations of the compact object was performed before and during the outburst (Torres et al. 2011). In this outburst observations, radio emission was detected which confirmed the presence of an accreting black hole candidate in its low-hard state (Corbel et al. 2011;Rodriguez et al. 2011). RXTE Observations detected low-frequency quasi-periodic oscillations (Rodriguez et al. 2011) and milli-Hertz and highfrequency QPOs (Altamirano et al. 2011d;Altamirano & Belloni 2012). Again some variability classes of the light curve that were seen in GRS 1915+105 were detected for IGR 17091-3624 (Altamirano et al. 2011a,b,c;Pahari et al. 2012). As IGR J17091-3624 has lower luminosity than GRS 1915+105 (Rodriguez et al. 2011), it is assumed that IGR J17091-3624 either -5consists of a very low mass black hole (Altamirano et al. 2011c) and/or it is located far away in the Galaxy with distance of around 17 − 20 kpc (Rodriguez et al. 2011;Altamirano et al. 2011c).
In the present paper, we show that similar variability classes of the two objects yield similar dynamical hardness ratios or CEs despite the fact that their masses could be totally different. Thus we are one step ahead of characterizing each variability class by a unique CE value, independent of the mass of the black hole. Since CEs of both IGR J17091-3624 and GRS 1915+105 are similar, the sequence in which the class transitions would take place for IGR J17091-3624 also becomes predictable. Since CE carries the information about geometry of the Compton cloud, we find that the geometry in IGR J17091-3624 evolves in the same way as that in GRS 1915+105 Pal et al. (2011, 2013; Pal & Chakrabarti (2014).
In the next Section, we present our analysis procedure and computation of Comptonizing Efficiency or CE for the IGR 17091-3624. We then present analysis results for IGR 17091-3624. Then we compare CE values of IGR 17091-3624 with CE values of GRS 1915+105 and we draw our conclusions.

Spectral Analysis
We analyze RXTE-PCA and Swift-XRT data given in Table. 1. We chose data sets by common MJDs of the outbursts observation, obtained from the NASA archive for both instruments. These data are downloaded from HEASARC, NASA Archive. RXTE and Swift data are reduced with HEASOFTv6.12 software.
For RXTE data reduction, we exclude data collected for elevation angles less than 10 • , for offset greater than 0.02 • and those acquired during the South Atlantic Anomaly (SAA) -6passage. We selected RXTE PCU2 data as it was active during the time of observation.
The light curve was drawn with 2 − 40keV photons. The RXTE-PCA spectra are extracted using "standard2" mode data which have 16 sec time resolution and energy selection from 3.0 keV to 25 keV.
For Swift data reduction, the level 2 cleaned event files of SWIFT-XRT are obtained from window grade 0 events of timing (WT) mode data with xrtpipeline. From a 40 × 10 pixel region in best source position spectra are extracted. The background is estimated from an off-axis region of the same size. The ancillary response files (arfs) are extracted with xrtmkarf. The WT redistribution matrix file (rmf) version (v.12) is used in the spectral fits. The Swift-XRT spectra are extracted with 16 sec time resolution and energy selection from 0.5 keV to 10 keV.
The combined 0.5 keV to 25 keV spectrum, consists of 0.5 keV to 10 keV Swift-XRT spectrum and 3.0 keV to 25 keV RXTE-PCA spectrum of the same good time interval and the same spectral resolution, are analysed for using software package XSPEC 12.8.2. Here each combined spectrum is averaged for 16 sec. Each 16 sec averaged spectra are analysed to obtain the parameters. We have used a systematic error of 0.5% for model fitting. All spectra are fitted with diskbb and power-law model along with hydrogen column density for absorption nH 1.1 × 10 22 cm −2 (Krimm & Kennea 2011). During fitting of all spectra we have used the technique introduced by Sobczak et al. (1999); Pal et al. (2011Pal et al. ( , 2013 to obtain spectral parameters to calculate the number of seed photons and comptonized photons. We have considered error-bars at 90% confidence level in each case.

Calculation of Comptonizing Efficiency (CE)
The fitting parameters are used to calculate the black body photons from the Keplerian disk and the power-law photons from the hot electron cloud. The number of black body photons are obtained from the fitted parameters of the multi-color disk black body model (Makishima et al. 1986). This is given by, (exp E/T −1) and r in can be calculated from, where, K is the normalization of the blackbody spectrum obtained after fitting, r in is the inner radius of the accretion disk in km, T in is the temperature at r in in keV, D is the distance of the compact object in kpc and i is the inclination angle of the accretion disk. Here, both the energy and the temperature are in keV. The black body flux, f (E) in photons/s/keV is integrated between 0.1 keV to the maximum energy dbb e . dbb e is the highest energy up to which the spectrum is fitted with diskbb model alone (Sobczak et al. 1999;Pal et al. 2011Pal et al. , 2013. This gives us N BB , the rate of the number of the emitted black body photons.
The Comptonized photons N P L that are produced due to inverse-Comptonization of the soft black body photons by 'hot' electrons in the Compton cloud are calculated by fitting with the power-law given below, where, α is the power-law index and N is the total photons/s/cm 2 /keV at 1keV. It is already reported in Titarchuk (1994), that the Comptonization spectrum will have a peak at around 3 × T in . The power law equation is integrated from 3 × T in to 40keV to obtain the -8rate of emitted Comptonized photons. In Table. 2 we give parameters of spectral analysis of XRT and PCA spectrum.
At any given instant, the ratio N P L /N BB is the Comptonizing Efficiency (CE). This is a 'hardness ratio' but the ranges of the hard and the soft photons are automatically determined by the fitting process as described above. Thus CE is actually a dynamic hardness ratio where energy ranges were not kept fixed a priory. This way the influence

Results
We have analysed data in the common good time intervals in which IGR 17091-3624 was observed on days mentioned in Table. 1. We compute CE for each observation. Note that in no occasion, transition from one variability class to another was observed during a single observation dwell.

Discussion & Conclusion
In order to show the necessity of using CE, we first show that conventional CCDs do not look alike even when the variability class is the same for both the objects. As an example, in Fig. 2(a), we show the 2 − 40 keV data of 04/08/2011 PCA observation of IGR 17091-3624 which look similar to the so-called ρ class data of GRS 1915+105 in Fig. 2(b). In Fig. 2(d), we draw the color-color diagram of GRS 1915+105 (Fig. 2b) following Belloni et al. (2000) with 2 − 5keV, 5 − 13keV, and 13 − 60keV energy bands.
When we repeat the exercise for IGR 17091-3624 ( Fig. 2a) in Fig. 2(c), the CCD looks different, more like that of the φ class. With suitable adjustment one can try to make them look similar, but this exercise this difficult to justify. in these two objects leads us to believe that average CE in a given class may characterize variability classes uniquely for any stellar mass black holes. Furthermore, the combined geometry of the Compton cloud and the Keplerian disk for any given variability class as given in Chakrabarti & Titarchuk (1995) should also be similarly independent of its mass. Conventional color-color diagrams with fixed energy bands, though useful to classify spectral states of neutron stars (because of very narrow range in which the mass varies) will look different for different black holes even for the same variability class of wide range of masses which they may have. This is primarily because the physical origin of photons of a given energy band is different when the mass changes.
Massive and super-massive black holes do have spectral states similar to stellar mass -13black holes. They also show short and long term variabilities (e.g., Cameron et al. (2012); Emmanoulopoulos et al. (2013) and references therein). It is not unlikely that the CE defined in our method will have similar values in these objects as well. This interesting aspect will be explored separately elsewhere.