Evolution of the temporal and the spectral properties in 2010 and 2011 outbursts of H 1743-322
aa r X i v : . [ a s t r o - ph . H E ] S e p Evolution of the temporal and the spectral properties in 2010 and 2011 outbursts ofH 1743-322
Dipak Debnath ∗ Indian Centre For Space Physics, 43 Chalantika, Garia Station Road, Kolkata, 700084, India
Sandip K. Chakrabarti S. N. Bose National Center for Basic Sciences, JD-Block, Salt Lake, Kolkata, 700098, India
Anuj Nandi
Space Astronomy Group, SSIF / ISITE Campus, ISRO Satellite Centre, Outer Ring Road, Marathahalli, Bangalore, 560037, India
Abstract
The Galactic black hole candidate H 1743-322 exhibited two X-ray outbursts in rapid succession: one in August 2010 and theother in April 2011. We analyze archival data of this object from the PCA instrument on board RXTE (2-25 keV energy band) tostudy the evolution of its temporal and spectral characteristics during both the outbursts, and hence to understand the behavioralchange of the accretion flow dynamics associated with the evolution of the various X-ray features. We study the evolution of QPOfrequencies during the rising and the declining phases of both the outbursts. We successfully fit the variation of QPO frequencyusing the Propagating Oscillatory Shock (POS) model in each of the outbursts and obtain the accretion flow parameters such asthe instantaneous shock locations, the shock velocity and the shock strength. Based on the degree of importance of the thermal(disk black body) and the non-thermal (power-law) components of the spectral fit and properties of the QPO (if present), the entireprofiles of the 2010 and 2011 outbursts are subdivided into four di ff erent spectral states: hard, hard-intermediate, soft-intermediateand soft. We attempt to explain the nature of the outburst profile (i.e., hardness-intensity diagram) with two di ff erent types of massaccretion flow. Keywords:
X-Rays:binaries, Black Holes, shock waves, accretion disks, Stars:individual (H 1743-322)
1. Introduction
Galactic transient black hole candidates (BHCs) are the mostfascinating objects to study in X-ray domain since these sourcesexhibit evolutions in their timing and spectral properties dur-ing their outbursts. Several attempts (McClintock & Remil-lard, 2006; Belloni et al., 2005; Remillard & McClintock, 2006;Debnath et al., 2008; Nandi et al., 2012) were made for a thor-ough study on the temporal and spectral evolutions of the tran-sient black hole (BH) binaries during their outbursts. Variousspectral states were identified during di ff erent phases of the out-burst. In general, four basic spectral states ( Hard , Hard − Intermediate , S o f t − Intermediate , S o f t ) are observed dur-ing the outburst of a transient BHC (McClintock & Remillard,2006; Belloni et al., 2005; Nandi et al., 2012). One can find ∗ Corresponding author
Email addresses: [email protected] (Dipak Debnath), [email protected] (Sandip K. Chakrabarti), [email protected] (Anuj Nandi) Tel.: +
91 33 24366003 / +
91 3324366003 / Also a ffi liated to Indian Centre For Space Physics, 43 Chalantika, GariaStation Road, Kolkata, 700084, India detailed discussions about these spectral states and their transi-tions in the literature (Homan & Belloni, 2005a; Belloni, 2010c;Dunn et al., 2010; Nandi et al., 2012). It was also reported byseveral authors (Fender et al., 2004; Homan & Belloni, 2005a;Belloni, 2010c; Nandi et al., 2012) that the observed spectralstates form a hysteresis loop during their outbursts. Also, thesedi ff erent spectral states of the hysteresis-loop are found to be as-sociated with di ff erent branches of a q-like plot of X-ray colorvs intensity i.e., the hardness-intensity diagram (HID) (Mac-carone & Coppi, 2003; Homan & Belloni, 2005a).The transient low-mass Galactic X-ray binary H 1743-322was first discovered (Kaluzienski & Holt, 1977) with the Ariel-V All-Sky Monitor and subsequently observed with the HEAO-1 satellite (Doxsey et al., 1977) in X-rays during the period ofAug-Sep, 1977. During the 1977-78 outburst, the source wasobserved several times in the hard X-ray band of 12 −
180 keVenergy range with the HEAO-1 satellite (Cooke et al., 1984).The observation revealed that the soft X-ray transient (basedon the 1 −
10 keV spectral properties) also emits X-rays in theenergy range of 10 −
100 keV (Cooke et al., 1984). White &Marshall (1984) categorized the source as a potential black holecandidate (BHC) based on the ‘color-color’ diagram using thespectral data of the HEAO-1 satellite.
Preprint submitted to Advances in Space Research October 2, 2018 fter almost two decades, in 2003, the INTEGRAL satel-lite discovered signatures of renewed activity in hard X-rays(Revnivtsev et al., 2003) and later, RXTE also verified the pres-ence of such an activity (Markwardt & Swank, 2003). Duringthe 2003 outburst, the source was continuously and extensivelymonitored in X-rays (Parmar et al., 2003; Homan et al., 2005b;Remillard et al., 2006; McClintock et al., 2009), IR (Steeghset al., 2003), and in Radio bands (Rupen et al., 2003) to re-veal the multi-wavelength properties of the source. The multi-wavelength campaign on this source during its 2003 and 2009outbursts were also carried out by McClintock et al. (2009);Miller-Jones et al. (2012) respectively.The low-frequency as well as high frequency quasi-periodicoscillations (QPOs) along with a strong spectral variability areobserved in the 2003 and other outbursts of the source in RXTEPCA data (Capitanio et al., 2005; Homan et al., 2005b; Remil-lard et al., 2006; Kalemci et al., 2006; Prat et al., 2009; McClin-tock et al., 2009; Stiele et al., 2013). These have resemblancewith several other typical Galactic black hole candidates (e.g.,GRO J1655-40, XTE J1550-564, GX 339-4 etc.). Another im-portant discovery of large-scale relativistic X-ray and radio jetsassociated with the 2003 outburst (Rupen et al., 2004; Corbel etal., 2005) put the source in the category of ‘micro-quasar’. Thiswas also reconfirmed by McClintock et al. (2009), from theircomparative study on the timing and the spectral properties ofthis source with XTE J1550-564.Recently in 2010 and 2011, the transient black hole can-didate H 1743-322 again exhibited outbursts (Yamaoka et al.,2010; Kuulkers et al., 2011) with similar characteristics of statetransitions (Shaposhnikov & Tomsick, 2010a; Shaposhnikov,2010b; Belloni et al., 2010a,b, 2011) as observed in other out-burst sources (Homan & Belloni, 2005a; Nandi et al., 2012).Recently, Altamirano & Strohmayer (2012) reported a new classof accretion state dependent 11 mHz QPO frequency during theearly initial phase of both the outbursts under study.RXTE has observed both these outbursts on a daily basis,which continued for a time period of around two months. Wemade a detailed study on the temporal and the spectral prop-erties of H 1743-322 during these two outbursts using archivaldata of PCA instrument on board RXTE satellite. Altogether49 observations starting from 2010 August 9 (MJD = = = = = M ⊙ to 13 M ⊙ .The evolution of QPO frequency during the outburst phasesof the transient BHCs has been well reported for a long time(Belloni & Hasinger, 1990; Belloni et al., 2005; Debnath etal., 2008; Nandi et al., 2012). Same type of QPO evolutionswere observed during both the rising and the declining phasesof these two outbursts as of other black hole candidates, suchas, 2005 outburst of GRO J1655-40 (Chakrabarti et al., 2005,2008), 1998 outburst of XTE J1550-564 (Chakrabarti et al.,2009) and 2010-11 outburst of GX 339-4 (Debnath et al., 2010;Nandi et al., 2012). The successful interpretation of these QPOevolutions with the Propagating Oscillatory Shock (POS) model(Chakrabarti et al., 2005, 2008) motivated us to fit the QPOevolutions of the recent outbursts of H 1743-322 with the samemodel. From the model fit, accretion flow parameters are cal-culated (see, Table 1 below).This Paper is organized in the following way: In the nextSection, we discuss about the observation and data analysisprocedures using HEASARC’s HEASoft software package. In §
3, we present temporal and spectral results of our observation.In § § § § §
4, wepresent the brief discussion and concluding remarks.
2. Observation and Data Analysis
The campaigns carried out with RXTE cover the entire 2010and 2011 outbursts of H 1743-322 starting from 2010 August 9(MJD = = = = µ s . To generate thepower-density spectra (PDS), we use the “powspec” task ofXRONOS package with a normalization factor of ‘-2’ to havethe expected ‘white’ noise subtracted rms fractional variabilityon 2-15 keV (0-35 channels of PCU2) light curves of 0 .
01 sectime bins. The power obtained has the unit of rms / Hz. Ob-served QPOs are generally of Lorentzian type (Nowak, 2000;van der Klis, 2005). So, to find centroid frequency of QPOs,power density spectra(PDS) are fitted with Lorentzian profilesand fit error limits are obtained by using “fit err” command.For the selection of QPOs in PDS, we use the standard method(see Nowak, 2000; van der Klis, 2005) based on the coherenceparameter Q ( = ν /∆ ν ) and amplitudes ( = % rms), where ν , ∆ ν are the centroid QPO frequency and full-width at half maxi-mum respectively as discussed in Debnath et al. (2008). Here,for these two outbursts, observed Q values and amplitudes arevaried from ∼ −
15 and ∼ −
16 respectively. In the entirePCA data analysis, we include the dead-time corrections andalso PCA break down corrections (arising due to the leakage ofpropane layers of PCUs).For the spectral analysis, the standard data reduction proce-dure for extracting RXTE PCA (PCU2) spectral data are used.The HEASARC’s software package XSPEC (version 12.5) isused for analyzing and modeling the spectral data. A fixedvalue of 1% systematic error and the hydrogen column den-sity ( N H ) of 1 . × (Capitanio et al., 2009) for absorptionmodel wabs , are used to fit the spectra. 2 . −
25 keV back-ground subtracted PCA spectra are fitted with a combination ofstandard thermal (diskbb) and non-thermal (power-law) modelsor with only power-law component, where thermal photon con-tribution was much less (mainly in spectra from the hard andhard-intermediate spectral states). To achieve best fit, a singleGaussian Iron line ∼ . ff er-ent model components of the spectra are calculated using cflux calculation method.
3. Results
The accretion flow properties during the outburst phases ofthe transient BHCs can be understood in a better manner bystudying X-ray properties of these sources both in temporal andspectral domains. It is pointed out by Debnath et al. (2010)that depending upon the outburst light curve profiles, there aremainly two types of outbursting BHCs: one is ‘fast-rise slow-decay’ (FRSD) type and the other is ‘slow-rise slow-decay’(SRSD) type. The source, H 1743-322 belongs to the first cat-egory. Although the general nature of the transient X-ray bina-ries is more complex (see for example, Chen et al., 1997).
For studying X-ray intensity variations of the 2010 and 2011outbursts of H 1743-322, we extract light curves from PCU2data of RXTE / PCA instrument in di ff erent energy bands: 2 − − −
25 keV (9 −
58 channels), and 2 − −
58 channels). We have divided the 2 −
25 keV energy - k e V C oun t R a t e ( c t s / s ) Day (MJD) H a r dn e ss ( - k e V / - k e V ) (a)(b) HardHard SoftSoft-IntermediateHard-Intermediate - k e V C oun t R a t e ( c t s / s ) Day (MJD) H a r dn e ss ( - k e V / - k e V ) (a)(b) HardHard Hard-IntermediateSoftSoft-Intermediate
Figure 1: (a) 2-25 keV PCA light curves and (b) hardness ratios (4-25 keVversus 2-4 keV count ratio) as a function of the MJD of 2010 (top panel) and2011 (bottom panel) outbursts of H 1743-322 are shown. The vertical dashedlines indicate the transitions between di ff erent spectral states. band in the above two bands because 2 − −
25 keV) come from theComptonized sub-Keplerian disk (Compton corona). This factmay not be true always because the contributions for di ff erentspectral components also depend on accretion states. Variationsof PCA count rates in 2 −
25 keV energy band and hardness ra-tios between 4 −
25 keV and 2 − In Fig. 2, we plot a combined 2 −
25 keV PCA count ratesof the 2010 and 2011 outbursts against X-ray color (PCA countratio between 4 −
25 keV and 2 − A , B , C , D , E , F , G ,and H are on MJD = = = = = = = = A and H respectively are the indicators of the start andthe end of RXTE observations for the outburst and the points B , C , D , E , F , G are the points on the days where the state transi-tions from hard → hard intermediate, hard-intermediate → soft-intermediate, soft-intermediate → soft, soft → soft-intermediate,soft-intermediate → hard-intermediate, and hard-intermediate → hard, respectively occurred. Similarly, the points a , b , c , d ,3 .69 2.197 2.8561 3.7129 4.8268 6.2749 8.1573 Hardness Ratio (4-25 keV/2-4 keV) P C A - k e V C oun t R a t e ( c t s / s ) A aB bC cD dEe F f Gg H h
Figure 2: Hardness Intensity Diagram of the 2010 (solid curve) and 2011 (dot-ted curve) outbursts as observed with RXTE / PCA are shown. Here A − H and a − h indicate the start / state transitions / end of our observations from the 2010and 2011 outbursts respectively. e , f , g , and h indicate MJD = = = = = = = = ff erent branches of the HIDs with di ff erentspectral states (see, Figs. 2, 6, 7). In the subsequent subsec-tions, the variations of the spectral properties during the out-bursts along with the POS model fitted evolutions of QPO fre-quency during the rising and the declining phases of the out-bursts are discussed. Studying temporal variability and finding QPOs in powerdensity spectra (PDS) is an important aspect for any black holecandidate (BHC). It is observed (mainly at hard and hard-int-ermediate spectral states) that the frequency of QPOs are seento evolve with time. LFQPOs are reported extensively in theliterature, although there is some uncertainty about the originof these QPOs. So far, many models are introduced to explainthe origin of this important temporal feature of BHCs, such astrapped oscillations and disko-seismology (Kato & Manmoto,2000), oscillations of warped disks (Shirakawa & Lai, 2002),accretion-ejection instability at the inner radius of the Kepleriandisk (Rodriguez et al., 2002), global disk oscillations (Titarchuk& Osherovich, 2000), and perturbations inside a Keplerian disk(Trudolyubov et al., 1999), propagating mass accretion rate fluc-tuations in hotter inner disk flow (Ingram & Done, 2011), andoscillations from a transition layer in between the disk and hot Comptonized flow (Stiele et al., 2013). However, none of thesemodels attempt to explain long duration continuous observa-tions and the evolutions of QPOs during the outburst phasesof transient BHCs. One satisfactory model namely shock os-cillation model (SOM) by Chakrabarti and his collaborators(Molteni et al., 1996), shows that the oscillation of X-ray inten-sity could be due to the oscillation of the post-shock (Comp-tonizing) region. According to SOM, shock wave oscillateseither because of resonance (where the cooling time scale ofthe flow is comparable to the infall time scale; (Molteni et al.,1996)) or because the Rankine-Hugoniot condition is not satis-fied (Ryu et al., 1997) to form a steady shock. The QPO fre-quency is inversely proportional to the infall time ( t in fall ) in thepost-shock region. The Propagating Oscillatory Shock (POS)model, which can successfully explain the evolutions of QPOfrequency, is nothing but a special case (time varying form) ofSOM.As explained in our earlier papers on POS model (Chakrabartiet al., 2005, 2008, 2009; Debnath et al., 2010; Nandi et al.,2012) during the rising phase, the shock moves towards theblack hole and during the declining phase it moves away fromthe black hole. This movement of the shock wave depends onthe non-satisfaction of Rankine-Hugoniot condition which isdue to the temperature and energy di ff erences between pre- andpost- shock regions. Moreover, sometimes in soft-intermediatestates, QPOs are observed sporadically (for e.g., during the2010-11 outburst of GX 339-4; see Nandi et al., 2012) andvanishes in soft spectral states and reappears in declining in-termediate / hard states. This disappearance and appearance ofQPO frequency depends on the compression ratio ( R ) due tothe velocity / density di ff erence in pre- and post- shock regionsor could be due to the ejection of Jets (see Radhika & Nandi,2013; Nandi et al., 2013).When R =
1, i.e., density of pre-and post- shock region more or less becomes the same, a shockwave vanishes, and so does the QPO.We now present the results of the evolution of QPO fre-quency observed in both rising and declining phases of boththe outbursts. So far in the literature, there is no consensuson the origin of QPOs despite its long term discovery (Belloni& Hasinger, 1990; Belloni et al., 2005), other than our group(Chakrabarti et al., 2005, 2008, 2009; Debnath et al., 2010;Nandi et al., 2012). In this work, we have tried to connect thenature of the observed QPOs and their evolutions during therising and the declining phases of the current outbursts with thesame POS model and find their implications on accretion diskdynamics. From the fits, physical flow parameters, such as in-stantaneous location, velocity, and strengths of the propagatingshock wave are extracted. Detailed modeling and comparativestudy between QPO evolutions observed in the rising and thedeclining phases of the outbursts of transient BHCs will be pre-sented in our follow-up works, where we will compare the POSmodel fit parameters with the spectral / temporal properties (suchas count rates, hardness ratios, spectral fluxes, photon indicesetc.) of the BHCs. This study can predict the mass of the BHCs,whose masses are not measured dynamically till now (for e.g.,H 1743-322). Similarly, our study can predict the properties ofQPOs in subsequent days, once the data for the first few days is4vailable.The monotonically increasing nature of QPO frequency (from0 .
919 Hz to 4 .
796 Hz for the 2010 outburst and from 0 .
428 Hzto 3 .
614 Hz for the 2011 outburst) during the rising phases andthe monotonically decreasing nature of QPO frequency (from6 .
417 Hz to 0 .
079 Hz for the 2010 outburst and from 2 .
936 Hzto 0 .
382 Hz for the 2011 outburst) during the declining phasesof the recent successive two outbursts of H 1743-322 are verysimilar to what is observed in the 2005 outburst of GRO J1655-40 (Chakrabarti et al., 2005, 2008), 1998 outburst of XTE J1550-564 (Chakrabarti et al., 2009), and 2010 outburst of GX 339-4(Debnath et al., 2010; Nandi et al., 2012). This motivated us tostudy and compare these evolutions with the same POS modelsolution. We found that during the rising and the decliningphases of these two outbursts of H 1743-322, QPO evolutionsalso fit well with the POS model. The POS model fitted param-eters (for e.g., shock location, strength, velocity etc.) are con-sistent with the QPO evolutions of GRO J1655-40, XTE J1550-564, and GX 339-4. The POS model fitted accretion flow pa-rameters of the 2010 and 2011 outbursts of H 1743-322 aregiven in Table 1. Only noticeable di ff erence observed duringthe present QPO frequency evolutions of H 1743-322 with thatof the 2005 outburst of GRO J1655-40 and 2010-11 outburst ofGX 339-4 is that during both the rising phases of GRO J1655-40 and GX 339-4 outbursts, the shock was found to move inwith a constant speed of ∼ cm s − , and ∼ cm s − respectively, whereas during the same phases of the currenttwo outbursts of H 1743-322, the shock was found to move inwith an acceleration. On the other hand, during the decliningphase for all these outbursts of GRO J1655-40, GX 339-4, andH 1743-322, the shock was found to be moved away with con-stant acceleration. It is also noticed that during both the risingand the declining phases of the 2010 outburst, the shock movedaway with an acceleration twice as compared to that of 2011outburst. It seems to be an interesting result, which may oc-cur due to the lack of supply of matter (mostly Keplerian) intothe disk from the companion that could have created a sudden‘void’ in the disk for the shock to move away rapidly outward.According to the POS solution (Chakrabarti et al., 2008,2009; Debnath et al., 2010; Nandi et al., 2012), one can ob-tain the QPO frequency if one knows the instantaneous shocklocation or vise-versa and the compression ratio ( R = ρ + / ρ − ,where ρ + and ρ − are the densities in the post- and the pre- shockflows) at the shock. According to POS model in the presenceof a shock (Chakrabarti & Manickam, 2000; Chakrabarti et al.,2008), the infall time in the post-shock region is given by, t in fall ∼ r s / v ∼ Rr s ( r s − / , (1)where, r s is the shock location in units of the Schwarzschildradius r g = GM / c , v is the velocity of propagating shockwave in cm s − .The QPO frequency happens to be inversely proportionalto the in-fall time scale from the post-shock region. Accord-ing to the shock oscillation model (Molteni et al., 1996), os-cillations of the X-ray intensity are generated due to the os-cillation of the post-shock region. This is also the centrifu-gal pressure supported boundary layer (or, CENBOL) which behaves as a Compton cloud in the Chakrabarti & Titarchuk(1995) model of two component accretion flow (TCAF). Ac-cording to the numerical simulations of the sub-Keplerian (low-angular momentum) accretion which includes the dynamicalcooling (Ryu et al., 1997) or the thermal cooling (Molteni etal., 1996; Chakrabarti et al., 2004), the frequency of the shockoscillation is similar to the observed QPO frequency for BHCs.Thus, the instantaneous QPO frequency ν QPO (in s − ) is ex-pected to be ν QPO = ν s / t in fall = ν s / [ Rr s ( r s − / ] . (2)Here, ν s = c / r g = c / GM is the inverse of the light crossingtime of the black hole of mass M in unit of s − and c is thevelocity of light. In a drifting shock scenario, r s = r s ( t ) is thetime-dependent shock location given by r s ( t ) = r s ± v t / r g , (3)where, r s is the shock location at time t = v is the corresponding shock velocity in thelaboratory frame. The ‘ + ’ ve sign in the second term is to beused for an outgoing shock in the declining phase and the ‘-’ve sign is to be used for the in-falling shock in the rising phase.When the velocity of the shock wave (as in the rising phase ofthe 2005 GRO J1655-40 outburst) is constant, v = v . For theaccelerating case (as in the rising and declining phases of the2010 and 2011 outbursts of H 1743-322) v is time-dependentand can be defined as v ( t ) = v + at , where a is the accelerationof the shock front.Since in the presence of cooling, the shock moves close tothe black hole, at the rising phase of the outburst, where thecooling gradually increases due to rise of the Keplerian rate,the shock wave moves towards the black hole and thus the QPOfrequency rises on a daily basis. The reverse is true in the de-clining phases. The POS model fitted results of the QPO evolu-tions during rising and declining phases of the 2010 and 2011outbursts are presented in the following sub-sections. The QPOs are observed in 23 observations out of total 49observations starting from 2010 August 9 (MJD = = • Rising Phase:On the very first observation day (2010 August 9, MJD = .
919 Hz andits first harmonics of 1 .
842 Hz were observed. On subsequentdays, QPO frequencies are observed to be increased till 2010August 16 (MJD = .
796 Hz QPO is observed).From the next day, the frequency of the observed QPO (type‘B’) is decreased (3 .
558 Hz). We have fitted this evolution ofthe QPO frequency with the POS model (Fig. 3a) and we foundthat the shock wave started moving towards the black hole from ∼
428 Schwarzschild radii ( r g ) and reached at ∼ r g (Fig.5 Time (day) Q P O F r e qu e n c y ( H z ) Time (day) (a) (b) th day = 55417.25 MJD 0 th day = 55663.68 MJD Figure 3: (a) Variations of the QPO frequency with time (in day) of the ris-ing phase of the (a) 2010 outburst and (b) 2011 outburst which are fitted withthe POS model solution (dashed curve). The diamond indicates the last eventwhen the QPO was observed on (a) 2010 August 17 and (b) 2011 April 23, notincluded in the fits.
Time (day) Q P O F r e qu e n c y ( H z ) Time (day) (a) (b) th day = 55455.45 MJD 0 th day = 55690.14 MJD Figure 4: Variations of the QPO frequency with time (in day) of the decliningphase of the (a) 2010 outburst and (b) 2011 outburst with the fitted POS model(dotted curve). Here, initial soft-intermediate state QPOs (as indicated by dia-mond points in Fig. 3) are not shown in the plot and also not included in thefit.
Time (day) S ho c k L o ca ti on (r g ) Time (day) (a) (b) (0, 550)(9.16, 217)(0, 428) (6.81, 181)(13.57, 751)(0, 65) r i s i ng d ec li n i ng (0, 118) (10.05, 411) r i s i ng d ec li n i n g Figure 5: Variation of the shock locations (in r g ) during the rising and thedeclining phases of the (a) 2010 and (b) 2011 outbursts of BHC H 1743-322(see text for details). ∼ ∼
180 cm s − to ∼ − with an acceleration of ∼
140 cm s − d − and the shock com-pression ratio R , which is inverse of the shock strength β , ischanged from 1 .
39 to 1 .
00. Unlike 2005 GRO J1655-40 or2010 GX 339-4, we did not start with the strongest possibleshock ( R =
4) in the present case. This is because RXTEmissed this object in the first few days of observation. In thefirst ’observed’ day, the shock has already moved in and theQPO frequency is already too high ( ∼ R decreased with time by the relation1 / R → / R + α ( t d ) , where R is the initial compression ra-tio (here R = . t d is the time in days (assuming first ob-servation day as 0 th day). Here, α is a constant ( = . R = ff ects are supplied(Chakrabarti, 1990). • Declining PhaseThe source is seen to move to this phase on 2010 Septem-ber 16 (MJD = .
417 Hz frequency isobserved. On subsequent days, the observed frequency of theQPO decreases, and it reaches to its lowest detectable value of79 mHz on the 2010 September 30 (MJD = ∼ . − . = ∼ r g till ∼ r g (Fig. 5a). The shock compression ratio R appearsto remain constant at 3 .
33. Also, during this phase, the shockvelocity varies from ∼
560 cm s − to ∼ cm s − due to anacceleration of 75 cm s − d − .6 able 1: POS model fit of QPO Evolutions Outburst Period ν i ν f r si r sf v i v f a R α Phase (day) (Hz) (Hz) ( r g ) ( r g ) (cm / s) (cm / s) (cm / s / d)Ris.’10 6.81 0.919 4.796 428 181 180 1133 140 1.39 0.0060Dec.’10 13.57 6.417 0.079 65 751 560 1578 75 3.33 ......Ris.’11 9.16 0.428 3.614 550 217 340 1137 87 2.00 0.0055Dec.’11 10.05 2.936 0.382 118 411 460 912 45 2.78 ......Here, ν i & ν f are the initial and the final POS model QPO frequenciesrespectively. r si & r sf are the initial and the final shock locationsrespectively. v i & v f & a are the initial and the final velocitiesand the acceleration of the shock wave respectively. R isthe initial value of the shock compression ratio and α is a constant. The QPOs are observed in 19 observations out of a total of27 observations spread over the entire outburst. Out of these19 observations, 11 are observed in the rising phase and theremaining 8 are in the declining phase of the outburst. • Rising PhaseDuring this phase of the outburst, a QPO of frequency 0 .
428 Hzis observed on the first RXTE PCA observation day (2011 April12, MJD = .
614 Hz (as observedby RXTE) on 2011 April 21 (MJD = = = .
562 Hz and3 .
306 Hz respectively. The evolutionary track of the QPO fre-quency is fitted with the POS model (Fig. 3b) with the methodsame as that used for 2010 data and here also it is found thatthe shock wave moved towards the black hole starting from thelaunching of shock location at ∼ r g (Fig. 5b). This reachedat ∼ r g within a period of ∼ ∼
340 cm s − to ∼ − withthe e ff ect of the acceleration of ∼
87 cm s − d − and the shockcompression ratio R varies from 2 .
00 to 1 . R followed the same equation as the rising phase ofthe 2010 outburst with di ff erent constant values of R = . α = . ff erent days after the onsets of these two outbursts.It is di ffi cult to predict the acceleration of the shock front with-out knowing how the matter is supplied at the outer boundary,these are treated as parameters in the present solution. • Declining PhaseThe source is observed to reach at this phase of the QPOevolution on the 2011 May 9 (MJD = .
936 Hz is observed. Subsequently, as in the 2010outburst, the frequency of the observed QPO decreased withtime and reached to its lowest detectable value of 0 .
382 Hz on2011 May 19 (MJD = .
215 Hz is observed on2011 May 6 (MJD = Table 2: Spectral Evolutions of H 1743-322 during the 2010 and 2011 outbursts.
Spec. Obs. Id UT T in ( keV ) Γ DBB Flux PL Flux χ / DOFStates 2010 OutburstHS X-01-00 10 / − − − . + . − . − − − . + . − . / / − − − . + . − . − − − . + . − . / /
08 1 . + . − . . + . − . . + . − . . + . − . / /
08 0 . + . − . . + . − . . + . − . . + . − . / /
09 0 . + . − . . + . − . . + . − . . + . − . / / − − − . + . − . − − − . + . − . / / − − − . + . − . − − − . + . − . / / − − − . + . − . − − − . + . − . / / − − − . + . − . − − − . + . − . / /
04 0 . + . − . . + . − . . + . − . . + . − . / /
04 0 . + . − . . + . − . . + . − . . + . − . / /
05 0 . + . − . . + . − . . + . − . . + . − . / / − − − . + . − . − − − . + . − . / / − − − . + . − . − − − . + . − . / T in & Γ represent the values of disk black body temperaturesand power-law photon indices respectively, and corresponding modelfluxes (in 10 − ergs cm − s − ) in 2 . −
25 keV energy range are enlistedin DBB & PL Flux columns. The errors are calculated with 90%confidence. Here, X = = / mm format. and found that the shock moved away from the black hole withaccelerating velocity and constant shock strength ( β ∼ .
36 i.e., R ∼ . ∼
10 days, the shockwave was found to move from ∼ r g to ∼ r g (Fig. 5b)with a change of velocity from ∼
460 cm s − to ∼
912 cm s − due to an acceleration of 45 cm s − d − . In the previous Section, we showed that the QPO frequen-cies increased in the first few days and then decreased (declin-ing phase) systematically in both the outbursts and indeed simi-lar to the other outbursts studied by the same group. The move-ments of the shock location is related to the spectral evolutionand thus it is worthwhile to check if the spectral evolution ofH 1743-322 is also similar to those studied earlier. For study-ing the spectral properties, we fit the RXTE PCA spectra of2 . −
25 keV energy band with the combination of the thermal(disk black body) and the non-thermal (power-law) componentsor with only non-thermal (power-law) component. To achievethe best fit, a single Gaussian line ∼ . ffi -cient to fit the initial rising and final declining phases of thePCA spectra in 2 . −
25 keV energy range. A similar kind ofthe spectral behavior also observed in GX 339-4, as studied byMotta et al. (2009). For all observations, we kept hydrogencolumn density ( N H ) for absorption model wabs to be fixed at1 . × (Capitanio et al., 2009).Based on the degree of importance of the disk black bodyand power-law components (according to fitted component valueand their individual flux) and nature (shape, frequency, Q value,rms% etc.) of QPO (if present), the entire outburst periods of2010 and 2011 are divided into four di ff erent spectral states:hard (HS), hard-intermediate (HIMS), soft-intermediate (SIMS)7 .30.60.91.21.5 d i s kbb ( T i n ) P L I nd . ( Γ ) d i s kbb f l ux P L f l ux Q P O ( H z ) (a)(b)(c)(d)(e)Hard SoftSoft-IntermediateHard-Intermediate Hard Figure 6: Variation of (a) disk black body temperature ( T in in keV), (b) power-law photon index ( Γ ), and 2 . −
25 keV fluxes (in 10 − ergs cm − s − ) of (c)diskbb, and (d) power-law models with day, observed in the 2010 outburst ofH 1743-322, are shown. The parameters T in & Γ are obtained from the XSPECmodel fit (using diskbb and power-law) of RXTE PCA spectra in 2 . −
25 keVenergy band. In bottom panel (e), observed QPO frequency (in Hz) with day(MJD) are shown. The vertical dashed lines indicate spectral state transitions. and soft (SS) (see, Homan & Belloni (2005a) for the definitionsof these basic spectral states). Out of these four spectral states,the low frequency quasi-periodic oscillations (LFQPOs) are ob-served during hard, hard-intermediate and soft-intermediate spec-tral states while according to POS, the QPO evolutions are ob-served only during the hard and hard-intermediate spectral states.In soft-intermediate states, QPOs are observed sporadically. Ingeneral, observed QPOs during the hard and hard-intermediatespectral states are of ‘C’ type (van der Klis, 2004) with Q-value ≥ ≥
10% and during soft-intermediate spectral stateare of ‘B’ type with lesser Q and rms value. During both theoutbursts, these four spectral states are observed in the samesequence and completed a hysteresis-type loop, with hard spec-tral state in both the start and the end phases while other threespectral states in between. It is to be noted that during the spec-tral evolution, the soft state is observed only once, during themid-region of the outburst (see, Fig. 1(a-b), Fig. 2, Fig. 6, andFig. 7). In Table 2, the model fitted values of the disk blackbody temperature ( T in in keV) and power-law photon index ( Γ )and their flux contribution to the spectra in 2 . −
25 keV en-ergy range for seven observations, selected from seven di ff erentspectral states of the 2010 and 2011 outbursts are enlisted.Daily variations of the model fitted parameters and their fluxcontribution in 2 . −
25 keV spectra of the 2010 and 2011 out-bursts are plotted in Figs. 6 & 7 respectively. The variations ofthe black body temperature ( T in ), the power-law photon index( Γ ) and their flux contributions in 2 . −
25 keV energy rangeare shown in these Figures. These variations justify the spectralclassifications. The Figures also show clearly that the evolu-tions of the spectral parameters and model fluxes are similarduring the same spectral states of the two consecutive outburstsof H 1743-322.
Initial ∼ = .
919 Hz to 1 .
045 Hz. (ii) Rising Hard-Intermediate State:
In the following ∼ = .
045 Hz to 4 .
796 Hz. (iii) Rising Soft-Intermediate State:
On the following day (MJD = . (iv) Soft State: The source is observed at this spectral statefor the next ∼
24 days (up to MJD = (v) Declining Soft-Intermediate State: For the following ∼ = T in and Γ values are observed to be al-most constant at ∼ .
70 keV and ∼ .
20 respectively. Duringthis phase, disk black body flux is observed to be constant at ∼ . × − ergs cm − s − , although there is an initial riseand then steady fall in the PL flux. Sporadic QPOs of ∼ (vi) Declining Hard-Intermediate State: The source is ob-served to be in this spectral state for the next ∼ . = .
417 Hz to 2 . (vii) Declining Hard State: This spectral state completes thehysteresis-like loop of the spectral state evolution (see Fig. 2).The source has been observed during this spectral state till theend of RXTE PCA observation of the 2010 outburst. In thisphase of evolution, the spectra are dominated by the non-thermal(power-law) flux. So, we fitted 2 . −
25 keV spectra with onlyPL model component. Similar to the previous spectral state, the8 .60.91.21.5 d i s kbb ( T i n ) P L I nd . ( Γ ) d i s kbb f l ux P L f l ux Q P O ( H z ) (a)(b)(c)(d)(e)Hard SoftSoft-IntermediateHard-Intermediate Hard Figure 7: Same variations as in Fig. 6, except for the 2011 outburst of H 1743-322.
QPO frequency is found to be monotonically decreasing from1 .
761 Hz to 79 mHz during this phase.
Initial ∼ = . −
25 keV) are mostly dominated by non-thermal photons with-out any signatures of thermal photons. The observed QPO fre-quency is found to be monotonically increased from 0 .
428 Hzto 0 .
807 Hz. (ii) Rising Hard-Intermediate State:
In the next 3 observations(up to MJD = .
885 Hz to 3 .
614 Hz. (iii) Rising Soft-Intermediate State:
The source is observed tobe in this spectral state for the next ∼ . = T in and Γ values are observed to be almostconstant at ∼ .
90 keV and ∼ .
20 respectively. A sharp rise in2 . −
25 keV DBB flux over the previous state value is observed,where as the PL flux in the same energy range is observed to benearly constant. As in the 2010 outburst, here also sporadicQPOs of frequency ∼ . (iv) Soft State: Next ∼ = T in and Γ values are varied from ∼ .
90 to ∼ .
80 keV and from ∼ . ∼ .
20 respectively. During this phase, the spectra are mostlydominated by low energy DBB flux (i.e., thermal emission)with decreasing in nature. QPOs are not observed during this state, which are also missing during the soft state of the 2010outburst (see Figs. 6 & 7). (v) Declining Soft-Intermediate State:
On the next day (MJD = .
215 Hz. (vi) Declining Hard-Intermediate State:
After that up to MJD = .
94 Hz to 2 .
01 Hz. (vii) Declining Hard State:
At the final phase of the outburst,the source is found to be in the hard state again, which com-pletes the hysteresis-like loop of the spectral state evolutions(see Fig. 2). Similar to the ‘canonical’ hard state in the risingphase, here we also found that diskbb component is not essen-tial to fit the PCA spectra in 2 . −
25 keV range, only PL compo-nent is su ffi cient to fit the spectra along with an Gaussian line at ∼ . . .
382 Hz.
4. Discussions and concluding remarks
We carried out the temporal and the spectral analysis of thedata of the 2010 and 2011 outbursts of the black hole candidateH 1743-322. We studied the evolution of quasi-periodic oscilla-tion frequency during the rising as well as the declining phases.We also studied the evolution of spectral states during both theoutbursts. The variations of QPO frequencies can be fitted as-suming that an oscillating shock wave progressively moves to-wards the black hole during the rising phase and moves awayfrom the black hole in the declining phase. Fundamentally, itis possible that a sudden rise in viscosity not only causes theKeplerian rate to rise but also causes the inner edge to movetowards the black hole. Initially, the higher angular momentumflow forms the shock far away, but as the viscosity transportsthe angular momentum, the shock moves in, especially so dueto enhanced cooling e ff ects in the post-shock region. The Kep-lerian disk moves in along with the shock.This scenario accomplishes all that we observe in an out-bursting source: (a) The QPO frequency rises / decreases withtime in the rising / declining phase, mainly observed during thehard and hard-intermediate spectral states and during the soft-intermediate spectral state QPOs are seen sporadically (see Nandiet al., 2013). It is to be noted that shocks exist only in thesestates. (b) The spectrum softens as the Keplerian disk movesin with a higher rate. (c) At the intermediate state(s), the Ke-plerian and the sub-Keplerian rates are similar. (d) During thedeclining phase, when the viscosity is reduced, the shock andthe Keplerian disk moves back to a larger distance and the QPOfrequency is also reduced. (e) The outflows can form only fromthe post-shock region (CENBOL), namely, the subsonic regionbetween the shock and the inner sonic point. In softer states,9he CENBOL disappears and the outflows also disappear. Ourmodel predicts that since the QPOs could be due to the oscil-lation of the shocks, whose frequency is roughly the inverseof the infall time scale, the frequency gives the location of theshock when the compression ratio is provided. In our scenario,a strong shock ( R ∼
4) starts at ∼ r g , but by the time itcomes closer to the black hole, it becomes weaker due to therapid cooling by enhanced Keplerian disk rate. QPO ceases toexist when the compression ratio is unity. These constraintsallowed us to compute the shock strength as a function of time.As far as the evolution of the spectral states during the twooutbursts of the transient BHC H 1743-322 is concerned, thiscan be well understood by the detailed study of the spectralproperties. During both the outbursts, it has been observedthat the source starts from the hard state and finally return backto hard state again after passing through the hard-intermediate,soft-intermediate and soft spectral states. It completes hystere-sis loop of hard → hard − intermediate → so f t − intermediate → so f t → so f t − intermediate → hard − intermediate → hard .Several attempts have already been made to understand thesetype of hysteresis spectral state transitions in black hole sourcesand to find their correlations with HIDs (Meyer et al., 2007;Meyer-Hofmeister et al., 2009), but one can easily explain thistype of evolution of spectral states with the TCAF model(Chakrabarti & Titarchuk, 1995), where the low-angular mo-mentum sub-Keplerian matter flows in nearly free-fall time scale,while the high angular momentum Keplerian matter flows inthe slow viscous time scale (Mandal & Chakrabarti, 2010). Ini-tially the spectra are dominated by the sub-Keplerian flow andas a result, the spectra are hard. As the day progresses, moreand more sub-Keplerian matter is converted to Keplerian mat-ter (through viscous transport of angular momentum) and thespectra become softer, progressively through hard-intermediate(Keplerian rate slightly less than the sub-Keplerian rate), soft-intermediate (Keplerian rate comparable to the sub-Keplerianrate) and soft state (dominating Keplerian rate). When viscos-ity is turned o ff at the outer edge, the declining phase begins.At the declining phase of the outburst, the Keplerian rate startsdecreasing, and the spectra start to become harder again. How-ever, the spectrum need not be retrace itself, since the informa-tion about the decrease of viscosity had to arrive at the viscoustime scale. This causes a hysteresis e ff ect. But the spectra stillfollows the declining soft-intermediate, hard-intermediate andhard states.In this work, we successfully applied the POS model fit evo-lutions of QPO frequency during both the rising and declin-ing phases of two (2010 and 2011) outbursts of H 1743-322and shock wave parameters related to the evolutions are ex-tracted. Earlier, the same POS model was also applied to ex-plain the evolution of QPO frequency of other black hole can-didates (e.g., GRO J1655-40, XTE J1550-564, GX 339-4, etc.)very successfully (Chakrabarti et al., 2005, 2008, 2009; Deb-nath et al., 2010; Nandi et al., 2012). All these objects seem toexhibit a similar behaviour as far as the QPO and spectral evo-lutions are concerned. In future, we will carry out detailed mod-eling and comparative study between QPO evolutions observedin other outbursts of H 1743-322 and other transient BHCs with this POS model and hence to understand accretion flow be-haviours during the outburst phases more precisely. However,the basic questions still remain: (a) What are the sources of en-hanced viscosity? (b) Does it scale with the mass of the blackhole or the mass of the donor? (c) Is the duration of the highviscosity phase (i.e., the duration between the end of the risingphase and the beginning of the declining phase) predictable, orit is totally random and depends mostly on the physical condi-tions of the donor? (d) Which processes decide the total timeinterval for which an outburst may last? And finally, (e) Whatdetermines the interval between two outbursts? If the cause isthe enhancement of viscosity, then clearly it may be also ran-dom. We are in the process of exploring these aspects throughcomparison of all the known candidates. Recently, we havebeen able to include TCAF model in XSPEC as a local additivemodel, and from the spectral fit using this model directly weobtain instantaneous location of the shock ( r s ) and compres-sion ratio ( R ) other than two component (Keplerian and sub-Keplerian) accretion rates (see Debnath et al., 2013a). As weknow from the POS model, one can determine the QPO fre-quency if the values of r s and R are known or vise-versa (see,Eqn. 2). So, from the spectral fit, we will be able to predict theobserved QPO frequency. The preliminary result on this workis already presented in a Conference Proceeding (Debnath etal., 2013b). References
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