Comparison of Relativistic Iron Line Models
Jiri Svoboda, Michal Dovciak, Rene W. Goosmann, Vladimir Karas
aa r X i v : . [ a s t r o - ph . GA ] J a n Comparison of relativistic iron line models
Jiˇr´ı Svoboda
Astronomical Institute of the Academy of Sciences, Prague, Czech RepublicCharles University, Faculty of Mathematics and Physics, Prague, Czech Republic
Michal Dovˇciak, Ren´e W. Goosmann, Vladim´ır Karas
Astronomical Institute of the Academy of Sciences, Prague, Czech Republic
Abstract.
The analysis of the broad iron line profile in the X-ray spectra ofactive galactic nuclei and black hole X-ray binaries allows us to constrain the spinparameter of the black hole. We compare the constraints on the spin value for twoX-ray sources, MCG-6-30-15 and GX 339-4, with a broad iron line using presentrelativistic line models in XSPEC — laor and kyrline . The laor model hasthe spin value set to the extremal value a = 0 . kyrline modelenables direct fitting of the spin parameter. The spin value is constrained mainlyby the lower boundary of the broad line, which depends on the inner boundaryof the disc emission where the gravitational redshift is maximal. The positionof the inner disc boundary is usually identified with the marginally stable orbitwhich is related to the spin value. In this way the laor model can be used toestimate the spin value. We investigate the consistency of the laor and kyrline models. We find that the spin values evaluated by both models agree within thegeneral uncertainties when applied on the current data. However, the results areapparently distinguishable for higher quality data, such as those simulated for theInternational X-ray Observatory (IXO) mission. We find that the laor modeltends to overestimate the spin value and furthermore, it has insufficient resolu-tion which affects the correct determination of the high-energy edge of the broad line. Introduction
The broad emission iron lines are well-known features found in about two dozens of spectra of activegalactic nuclei and black hole binaries. They are supposed to originate close to the black hole by thereflection of the primary radiation on the accretion disc. The spin of the black hole plays an importantrole in the forming of the line shape. Especially, it determines the position of the marginally stable orbitwhich is supposed to confine the inner edge of the accretion disc (see Figure 1). The innermost stableorbit occurs closer to a black hole with a higher spin value. However, the spin affects also the overallshape of the line.Over almost two decades the most widely used model of the relativistic disc spectral line has beenthe one by
Laor [1991], which includes the effects of a maximally rotating Kerr black hole. In other words,the laor model sets the dimensionless angular momentum a to the canonical value of a = 0 . Dovˇciak et al. [2004] have relaxed this limitationand allowed a to be fitted in the suite of ky models. Other numerical codes have been developedindependently by several groups ( Beckwith and Done [2004], ˇCadeˇz and Calvani [2005],
Brenneman andReynolds [2006]) and equipped with similar functionality.However, the laor model can still be used for evaluation of the spin if one identifies the inner edgeof the disc with the marginally stable orbit. In this case the spin is actually estimated from the lowerboundary of the broad line. The comparison of the laor and kyrline model is shown in the right panelof Figure 1. The other parameters of the relativistic line models are inclination angle i , rest energy ofthe line E , inner radius of the disc R in , outer radius of the disc R out , emissivity parameters q , q withthe break radius r b . The emissivity of the line is given by I ≈ r − q for r < r b and I ≈ r − q for r > r b .The angular dependence of the emissivity is characterized by limb darkening profile I ( µ e ) ∝ . µ e in the laor model. The kyrline model enables to switch between different emission laws. We usedfurther two extreme cases, the kyrline with the same limb-darkening law as in the laor model and kyrline * with the limb-brightening law I ( µ e ) ∝ ln(1 + i ).The aim of this paper is to compare the two models applied to the current data provided by the VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS
XMM-Newton satellite, and to the artificial data generated for the on-coming X-ray mission. For thispurpose we have chosen two sources, MCG-6-30-15 and GX 339-4, which exhibit an extremely skewediron line according to recently published papers (
Vaughan and Fabian [2004],
Miller et al. [2004]). a r ms . . F l u x [ c t s c m − s − k e V − ] Energy [keV] a = 0.9982laorkyrline . . . F l u x [ c t s c m − s − k e V − ] Energy [keV] a = 0.7laorkyrline
Figure 1.
Left: Relation for the spin a and marginally stable orbit r ms . Right: Comparison of the laor (black, solid) and kyrline (red, dashed) model for two values of the spin a = 0 . a = 0 . E = 6 . q = q = 3, i = 30 ◦ . Observations and data reduction
We used the SAS software version 7.1.2 (http://xmm.esac.esa.int/sas) to reduce the XMM-Newtondata of the sources. Further, we used standard tools for preparing and fitting the data available athttp://heasarc.gsfc.nasa.gov (FTOOLS, XSPEC)The galaxy MCG-6-30-15 is a nearby Seyfert 1 galaxy ( z = 0 . Fabian et al. [2002]. We joined the three spectra into one using the ftool MATHPHA.The black hole binary GX 339-4 exhibited a strong broadened line in the 76 ks observation in 2002(
Miller et al. [2004]) when the source was in the very high state (for a description of the different statessee
Remillard and McClintock [2006]). The observation was made in the burst mode due to a very highsource flux. The 97% of photons are lost during the reading cycle in this mode, which results into 2.25 kstotal exposure time. We rebinned all the data channels in order to oversample the instrumental energy resolution max-imally by a factor of 3 and to have at least 20 counts per bin. The first condition is much strongerwith respect to the total flux of the sources – 4 × − erg cm − s − in 2–10 keV (1 . × cts) forMCG-6-30-15 and 9 × − erg cm − s − in 2–10 keV (1 . × cts) for GX 339-4. VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS f l u x [ c t s s − k e V − ] MCG−6−30−15: power law model Γ = 1.91 100.5 2 5−50050 ∆ S χ Energy [keV] ∆ S χ Energy [keV]MCG−6−30−15: Fe line
Figure 2.
The X-ray spectrum of MCG-6-30-15 observed by XMM-Newton. Left: The overall view onthe spectrum as a power law with Γ = 1 . n H = 0 . × cm − . The residuals from the model are plotted in the bottom panelclearly revealing features of a local absorption and soft excess at the soft X-ray band, and a feature ataround 6 keV which can be explained by the presence of a broad iron line. Right: More detailed view ofthe iron line band. Iron line study of the MCG-6-30-15 spectrum
We used the same continuum model for the MCG-6-30-15 spectrum as presented in
Fabian etal. [2002]: the simple power law component absorbed by neutral hydrogen with the column density n H = 0 . × cm − . The overall spectrum with a detailed view of the iron line energy band is shownin Figure 2. The employed model is sufficient to fit the data above ≈ . The value of the photon index is Γ = 1 . E = 6 . E = 6 .
77 keVwhich can be explained by a blueshifted absorption originating in an outflow. The rest energy of thebroad line is E = 6 . A good fit of the broad line was found with a broken power law line emissivity with a steeperdependence on the radius in the innermost region, which suggests a centrally localized corona. Thegoodness of the fit is constrained by the least squared method. The fit results in 2.5–9.5 keV are presentedin Table 1. The χ values give comparable results for all employed models. The χ = χ /ν ≈ . ν is the number of degrees of freedom which is related to the total number of energy bins andmodel parameters. The six independent parameters of the laor and kyrline models make the globalminimum of χ rather wide with several local minima. Each model has a different tendency to convergeto a different minimum. Hence, we did not compare only best fits of both models, but also the evaluatedspin values by the kyrline and laor models when the other model parameters correspond to eachother. The equivalent width of the line is EW ≈
750 eV. The errors in brackets presented in the tablecorrespond to 90% confidence and are evaluated when the other parameters of the model are fixed. Therealistic errors are higher because the model parameters further depend on the other parameters of theline and continuum models.To catch up these relations we produce various contour graphs focusing on the determination of thespin value, taking into account the other parameters of the used model. The relations of the χ values The broad iron line was also revealed in the analysis of the two 138 ks observations in spring 2004 by
Miller et al. [2006], when the source was in the low-hard state. The EPIC pn camera was operating in the timing mode , MOS cameras inthe full-frame mode . Using epatplot tool we found that it is not possible to avoid the pile-up by excluding the central partof the image of the source as described in the forementioned paper. Therefore we use only the very high state observationfrom 2002 in our analysis. Another components are needed to be added into the model in order to fully understand the spectrum. Several workshave been done in this way, in the most recent one by
Miller L. et al. [2008] the spectrum is characterized by an absorptionin four different zones, which affects also the higher energy band where no broad line is needed any more. The spectral complexity in the line band allows an alternative explanation – the model with two narrow emission linesat energies E = 6 . E = 6 .
97 keV. This alternative model leads to the presence of the broad line component at E = 6 . VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS on value of the spin ( kyrline ) or the inner disc radius ( laor ) are shown in the left column of Figure 3.The x-axis is oppositely directed in the case of the inner disc radius as x-variable for an easier comparisonwith the kyrline results. The contour graphs for the spin and the inclination angle are shown in themiddle column of Figure 3. The underlying model was fixed in both cases. The plots in the right columnof Figure 3 show the contours for the spin and the power law index. Taking all of these into account, weobtain for the spin value: a KY = 0 . +0 . − . and a laor = 0 . +0 . − . . Table 1. Results for MCG-6-30-15 in 2.5–9.5 keV parameter kyrline kyrline * laor best laor loc . min . a/M +0 . − . +0 . − . +0 . − . +0 . − . i [deg] 26 . . . . E [keV] 6 . . . . q . . . . q . . . . r b . . . . χ /v /
148 174 /
148 170 /
148 174 / EW [eV] 761 757 764 754 S t a t i s t i c : χ inner disc radius [Rg] a = 0.94 i n c li na t i on [ deg ] inner disc radius [Rg] + min = 169.7;Levels = 172.0 174.3 178.9 . . . t on i nde x inner disc radius [Rg] + min = 169.7; Levels = 172.0 174.3 178.9 χ spin a/M [GM/c] i n c li na t i on [ deg ] spin a/M [GM/c] + min = 175.2; Levels = 177.5 179.8 184.4 . . . t on i nde x spin a/M [GM/c] + min = 175.2; Levels = 177.5 179.8 184.4 χ spin a [GM/c] i n c li na t i on [ deg ] spin a/M [GM/c] + min = 173.6; Levels = 175.9 178.2 182.8 . . . t on i nde x spin a/M [GM/c] + min = 179.4; Levels = 181.7 184.1 188.7 Figure 3.
The contour graphs show the dependence of the value of the χ , the inclination angle and thepower law index on the value of the spin ( kyrline ) or the inner disc radius ( laor ) for the MCG-6-30-15spectrum in 2.5–9.5 keV. The black, red and green contours correspond to 1 σ , 2 σ and 3 σ , respectively.Top: The results of the laor model. Middle: The results of the kyrline model with limb darkening .Bottom: The results of the kyrline model with limb brightening . VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS
Iron line study of the GX 339-4 spectrum f l u x [ c t s s − k e V − ] GX 339−4: diskbb + powerlaw1 100.5 2 5−10010 ∆ S χ Energy [keV] ∆ S χ Energy [keV]GX 339−4: Fe line
Figure 4.
The X-ray spectrum of GX 339-4. Left: The overall view on the spectrum as a power lawwith Γ = 3 and thermal multi temperature black body with 0 .
87 keV absorbed by a neutral hydrogenwith column density n H = 0 . × cm − . The residuals from the model are plotted in the bottompanel revealing wiggles at the soft X-ray band which are likely due to instrumental response. The broadexcess at around 6 keV can be explained by the presence of a broad iron line. Right: More detailed viewof the iron line band.The continuum of the X-ray spectrum of the black hole binaries is characterized by a power lawand a multi-colour disc black-body component ( powerlaw + diskbb in the XSPEC notation). Thepower law index suggested from the simultaneous RXTE measurements is Γ = 2 . Miller et al. [2004]).However, we get an unacceptable fit with χ ≥ . Miller et al. [2004] or the re-analysis by
Reis et al. [2008]. The difference of the results is likely due toa different grouping of the instrumental energy channels applied to the data. While we did not allow tooversample the instrumental energy resolution more than by factor of 3, in the previous works only thecondition to have at least 20 counts per bin was used. This condition is very weak with respect to thetotal number of counts N counts ≈ . × and the total number of energy channels N chan = 1 . × in2–10 keV and as a result, it practically does not force the data to be grouped. This leads to an excessiveoversampling of the energy resolution, to large error bars in the flux and finally to an artificial decreaseof the χ value. In the energy range 0.8–9 keV we get χ /ν = 2835 / χ /ν = 1368 /
202 for the grouping taking the energy resolutioninto account. The χ value increased from χ . = 1 .
73 to χ . = 6 . E ≈ χ /ν → / smedge model used inthe previous works). The new model has χ /ν = 350 /
202 in 0.8–9 keV and its parameter values are n H = 0 . × cm − , Γ = 3 . kT in = 0 . pexrav ( pexriv ) or refsch model, but without any improvements of the fit. Thespectrum of GX 339-4 is shown in Figure 4 with a detailed view of the iron line band in the right panel.A broadened iron line feature is still present. However, due to different adopted value for the photonindex of the power law the line is much weaker than the one presented in Miller et al. [2004].The fitting results of the line models in 3–9 keV are summarized in Table 2 and Figure 5. There aretwo minima found during the fitting procedure. We preferred the one which better corresponds to theresults obtained by the independent radio and infrared measurements which constrained the inclinationangle to be i < ◦ ( Gallo et al. [2004]). The dependence of the goodness of the fit on the spin valueis shown in the left column of Figure 5. The contour graphs for the spin and the inclination angle aredepicted in the middle column, and for the spin and the power law photon index in the right column ofFigure 5. The derived spin value is then: a KY = 0 . +0 . − . and a laor = 0 . +0 . − . . VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS χ inner disc radius [Rg] a = 0.63 a = 0.87 i n c li na t i on [ deg ] inner disc radius [Rg] + min = 145.6; Levels = 147.9 150.2 154.8 . t on i nde x inner disc radius [Rg] + min = 138.8; Levels = 141.1 143.5 148.1 χ spin a/M [GM/c] i n c li na t i on [ deg ] spin a/M [GM/c] + min = 147.2; Levels = 149.5 151.8 156.4 . t on i nde x spin a/M [GM/c] + min = 138.7; Levels = 141.0 143.3 147.9 S t a t i s t i c : χ spin a/M [GM/c] i n c li na t i on [ deg ] spin a/M [GM/c] + min = 147.9; Levels = 150.2 152.5 157.1 . t on i nde x spin a/M [GM/c] + min = 140.2; Levels = 142.5 144.8 149.4 Figure 5.
The contour graphs show the dependence of the value of the χ , the inclination angle and thepower law index on the value of the spin ( kyrline ) or the inner disc radius ( laor ) for the GX 339-4spectrum in 3–9 keV. The black, red and green contours correspond to 1 σ , 2 σ and 3 σ , respectively. Up:The results of the laor model. Middle: The results of the kyrline model with limb darkening . Down:The results of the kyrline model with limb brightening . Table 1.
Results for GX 339-4 in 3–9 keV parameter kyrline kyrline * laor a/M +0 . − . +0 . − . +0 . − . i [deg] 19(3) 19(4) 17(4) E [keV] 6 . . . q . . . χ /v /
125 148 /
125 148 / EW [eV] 175 164 164 Table 2.
Count rates of the observations
MCG-6-30-15 GX 339-4net cts/s 3 .
59 592 . .
59 592 . .
20 5 . . × . × Fitting of the simulated data of future X-ray missions
In this section we intend to apply the laor and kyrline models on the data with significantly higherquality supposed to be achieved by on-coming X-ray missions. The presently planned International X-rayObservatory (IXO) arised from the merging of the former XEUS and Constellation-X missions. Becausethe details of the IXO mission have not been fixed yet, we used a preliminary response matrix of theformer XEUS mission (
Arnaud et al. [2008]). We generated the data for a kyrline model with a restenergy of the line E = 6 . q = 3.We rebinned the data in order to have a resolution of 30 eV per bin. We then fit the data in the 1–9 keVenergy range with the laor model using the same initial values of the fitting parameters as for thedata simulation. Due to insufficient resolution of the laor model, a significant problem appears at thehigh-energy edge of the broad line. This occurs because the next generation instruments achieve muchhigher sensitivity in the corresponding energy range. Therefore, we excluded the higher-energy drop of VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS no r m a li ze d c oun t s / s ec / k e V fake XEUS data for kyrline with a/M = 0.7, theta = 60 deg fitted with the laor model no r m a li ze d c oun t s / s ec / k e V fake XEUS data for kyrline with a/M = 0.7, theta = 80 deg fitted with the laor model r a ti o r a ti o no r m a li ze d c oun t s / s ec / k e V fake XEUS data for kyrline with a/M = 0.9982, theta = 60 deg fitted with the laor model no r m a li ze d c oun t s / s ec / k e V fake XEUS data for kyrline with a/M = 0.9982, theta = 80 deg fitted with the laor model r a ti o r a ti o Figure 6.
Simulated data for two values of the spin and inclination using the preliminary responsematrix of the XEUS mission. We show the artificial data with the expected errors (black crosses) whichwere simulated by the kyrline model (black curve), and fitted by the laor model (red curve).the lines from the analysis in order to reveal the differences in the overall shape of the line. We examinedthe artificial data for a grid of values of the angular momentum and the inclination angle. The resultsfor a/M = 0 .
7, 0 . i = 60 ◦ , 80 ◦ are shown in Figure 6. It is clearly seen from the figure that theeffect of the spin on the shape of the line is sufficiently resolved by the higher quality data.Further, we produced simulated data for the Seyfert galaxy MCG-6-30-15 and the black hole binaryGX 339-4 using rather simplified models which were suitable to fit the current XMM-Newton data.For MCG-6-30-15 we used a power law model plus a kyrline model for the broad iron line, absorbedby neutral hydrogen: phabs * ( powerlaw + kyrline ). The parameters of the continuum are thecolumn density n H = 0 . × cm − , the photon index Γ = 1 . K Γ = 5 × − . The values of the line parameters are summarized in the KY value column of Table 4.The exposure time was chosen as 220 ks and the flux of the source as 1 . × − erg cm − s − in the2–10 keV energy range (i.e. 1 . × cts).For GX 339-4 we used phabs * ( diskbb + powerlaw + kyrline ) with n H = 0 . × cm − , kT in = 0 .
87 keV ( K kT = 1 . × ), and Γ = 3 ( K Γ = 5 . . × − erg cm − s − in the 2–10 keV energy range (i.e. 1 . × cts). The number of counts is two orders of magnitude higher than for the observation of the XMM-Newton satellite. Thereason is due to the loss of 97% of the photons during the burst mode of XMM-Newton observation which eliminatesthe pile-up problem. The next generation X-ray missions are supposed to have a calorimeter instead of the CCD cameraon-board which will get rid of such problems.
VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS
Prior to the spectral analysis we rebinned the data to have approximately a 5eV resolution (as itwas planned for the XEUS instrument). We tested different grouping realizing that the discrepanciesbetween the two models increase with larger grouping, but we can see apparent differences already forthe most moderate rebinning. The results of the laor fit are shown in Table 4 and in Figure 7. Thebroad iron line component of the model is plotted in the left column. The continuum components ofthe model are not displayed there in order to clearly see the deflections of the laor model. The mostprominent discrepancy appears at the higher-energy drop, which is clearly seen in the data/model ratioplot in the middle column of Figure 7. The model parameters are constrained with small error bars (seecontours a vs. i in the right column of Figure 7), which clearly reveals a difference between the kyrline and the laor models.The spin value derived from the analysis using the laor model is: a laor , MCG = 0 . +0 . − . for MCG-6-30-15, while initially the spin value was a trial , MCG = 0 . a laor , GX = 0 . +0 . − . for GX 339-4, while initially the spin value was a trial , GX = 0 . Table 4. Results of laor fit in 3–9 keV in the simulated spectraMCG-6-30-15 GX 339-4 parameter KY value fitted value KY value fitted value R in [ G ] 2 .
00 1 . +0 . − . .
39 3 . +0 . − . i [ deg ] 26 . . . E line .
70 6 . .
97 6 . q .
90 4 . .
45 3 . q .
80 2 . r b . . K line . × − . × − . × − . × − χ /ν /
873 2298 / Conclusions
We investigated the iron line band for two representative sources – MCG-6-30-15 (active galaxy)and GX 339-4 (X-ray binary). The iron line is statistically better constrained for the active galaxyMCG-6-30-15 due to a significantly longer exposure time of the available observations – for comparisonof count rates of the sources see Table 3. The spectra of both sources are well described by a continuummodel plus a broad iron line model. We compared modeling of the broad iron line by the two relativisticmodels, laor and kyrline . The kyrline model leads to a better defined minimum of χ for the best fitvalue. The confidence contour plots for a/M versus other model parameters are more regularly shaped.This indicates that the kyrline model has a smoother adjustment between the different points in theparameter space allowing for more reliable constraints on a/M . The laor model has a less accurate gridand is strictly limited to the extreme Kerr metric. The discrepancies between the kyrline and laor results are within the general uncertainties of the spin determination using the skewed line profile whenapplied to the current data. However, the results are apparently distinguishable for higher quality data,as those simulated for the XEUS mission. We find that the laor model tends to overestimate the spinvalue and furthermore, it has insufficient energy resolution which affects the correct determination of thehigh-energy edge of the broad line. The discrepancies in the overall shape of the line are more visibleespecially for lower values of the spin a/M . As a side-product, we have found that the correct re-binningof the data with respect to the instrumental energy resolution is crucial to obtain statistically the mostrelevant results. Acknowledgments.
The present work was supported by the ESA Plan for European Cooperating States(98040).VOBODA ET AL.: COMPARISON OF RELATIVISTIC IRON LINE MODELS . . . f l u x [ c t s s − k e V − ] Energy [keV] . . . t a / m ode l r a t i o Energy [keV] 1.7 1.8 1.9 . i n c li na t i on [ deg ] inner disc radius [Rg] + min = 1363.4; Levels = 1365.7 1368.0 1372.6 f l u x [ c t s s − k e V − ] Energy [keV] . . t a / m ode l r a t i o Energy [keV] 3.15 3.2 . . . i n c li na t i on [ deg ] inner disc radius [Rg] + min = 2297.9; Levels = 2300.2 2302.5 2307.1 Figure 7.
The simulated spectra for MCG-6-30-15 (top) and GX 339-4 (bottom) using the preliminaryresponse matrix of the XEUS mission. Left: The broad iron line generated by the kyrline model (blackdata) and fitted by the laor model (red curve). Middle: The data/model ratio when fitting by the laor model. Right: Contours for the inclination angle and the inner disc radius of the laor model. The trialvalues are far from the best fit results (see KY value in Table 4).
References
Arnaud, M., Barcons, X., Barret, D., Bautz, M., Bellazzini, R., XEUS: the physics of the hot evolving universe,
ExperimentalAstronomy , tmp, 24A, 2008Beckwith, K., Done, C., Iron line profiles in strong gravity,
Monthly Notices of Royal Astronomical Society , 352, 353, 2004Brenneman, L. W., Reynolds, C. S., Constraining black hole spin via X-ray spectroscopy,
Astrophysical Journal , 652, 1028,2006ˇCadeˇz, A., Calvani, M., Relativistic emission lines from accretion discs around black holes,
Monthly Notices of RoyalAstronomical Society , 363, 177, 2005Dovˇciak, M., Karas, V., Yaqoob, T., An extended scheme for fitting X-ray data with accretion disc spectra in the stronggravity regime,
Astrophysical Journal Supplements , 153, 205, 2004Fabian, A. C., Vaughan, S. Nandra, K., Iwasawa, K., Ballantyne, D. R. et al., A long hard look at MCG-6-30-15 withXMM-Newton,
Monthly Notices of Royal Astronomical Society , 335, L1, 2002Gallo E., Corbel S., Fender R. P., A transient large-scale relativistic radio jet from GX 339-4,
Monthly Notices of RoyalAstronomical Society , 347L, 52G, 2004Laor, A., Line profiles from a disk around a rotating black hole,
Astrophysical Journal , 376, 90, 1991Miller, J. M., Fabian, A. C., Reynolds, C. S., Nowak, M. A., Homan, J. et al., Evidence of Black Hole Spin in GX 339-4:XMM-Newton/EPIC-pn and RXTE Spectroscopy of the Very High State,
Astrophysical Journal , 606, L131, 2004Miller, J. M., Homan, J., Steeghs, D., Rupen, M., Hunstead, R. W. et al., A Long, Hard Look at the Low/Hard State inAccreting Black Holes,
Astrophysical Journal , 653, 525, 2006Miller, L., Turner, T. J., Reeves, J. N., An absorption origin for the X-ray spectral variability of MCG-6-30-15,
Astronomy& Astrophysics , 483, 437, 2008Reis, R. C., Fabian, A. C., Ross, R., Miniutti, G., Miller, J. M., Reynolds, C. S., A systematic look at the Very High andLow/Hard state of GX 339-4: Constraining the black hole spin with a new reflection model, arxiv:0804.0238 , 2008Remillard, R. A. and McClintock, J. E., X-ray Properties of Black Hole Binaries,
Annual Review of Astronomy & Astro-physics , 49, 2006Vaughan, S., Fabian, A. C., A long hard look at MCG-6-30-15 with XMM-Newton - II. Detailed EPIC analysis andmodelling,