The ultraluminous X-ray sources NGC 1313 X-1 and X-2: a broadband study with NuSTAR and XMM-Newton
Matteo Bachetti, Vikram Rana, Dominic J. Walton, Didier Barret, Fiona A. Harrison, Steven E. Boggs, Finn E. Christensen, William W. Craig, Andrew C. Fabian, Felix Fürst, Brian W. Grefenstette, Charles J. Hailey, Ann Hornschemeier, Kristin K. Madsen, Jon M. Miller, Andrew F. Ptak, Daniel Stern, Natalie A. Webb, William W. Zhang
aa r X i v : . [ a s t r o - ph . H E ] N ov Draft version October 30, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE ULTRALUMINOUS X-RAY SOURCES NGC 1313 X-1 AND X-2:A BROADBAND STUDY WITH
NuSTAR
AND
XMM–Newton
Matteo Bachetti , Vikram Rana , Dominic J. Walton , Didier Barret , Fiona A. Harrison , Steven E.Boggs , Finn E. Christensen , William W. Craig , Andrew C. Fabian , Felix F¨urst , Brian W. Grefenstette ,Charles J. Hailey , Ann Hornschemeier , Kristin K. Madsen , Jon M. Miller , Andrew F. Ptak , DanielStern , Natalie A. Webb , and William W. Zhang Draft version October 30, 2018
ABSTRACTWe present the results of
NuSTAR and
XMM–Newton observations of the two ultraluminous X-raysources NGC 1313 X-1 and X-2. The combined spectral bandpass of the two satellites enables usto produce the first spectrum of X-1 between 0.3 and 30 keV, while X-2 is not significantly detectedby
NuSTAR above 10 keV. The
NuSTAR data demonstrate that X-1 has a clear cutoff above 10 keV,whose presence was only marginally detectable with previous X-ray observations. This cutoff rules outthe interpretation of X-1 as a black hole in a standard low/hard state, and it is deeper than predictedfor the downturn of a broadened iron line in a reflection-dominated regime. The cutoff differs fromthe prediction of a single-temperature Comptonization model. Further, a cold disk-like black bodycomponent at ∼ . XMM–Newton only. We observe a spectral transition in X-2, from a state with high luminosity and strong variabilityto a lower-luminosity state with no detectable variability, and we link this behavior to a transitionfrom a super-Eddington to a sub-Eddington regime.
Subject headings: accretion, accretion disks — black hole physics — stars: black holes — X-rays:individual (NGC 1313 X-1, NGC 1313 X-2) — X-rays: stars INTRODUCTION
Ultraluminous X-ray sources (ULXs) are off-nuclearpoint-like sources with apparent X-ray luminosities ex-ceeding the Eddington limit for stellar-mass black holes(StMBHs). Their high luminosity can be due to yet-unknown mechanisms of super-Eddington accretion ona StMBH (or beamed emission from it), or the pres-ence of a black hole (BH) with a high mass, suchas an intermediate-mass black hole (IMBH). While forluminosities > erg s − the identification with anIMBH is most probable, as was shown for the sourceHLX-1 (Farrell et al. 2009), for lower luminosities bothmechanisms can apply. Convincing evidence for super-Eddington accretion has been reported for two ULXs inM31 (Middleton et al. 2012, 2013). See Roberts (2007) [email protected] Universit´e de Toulouse; UPS-OMP; IRAP; Toulouse, France CNRS; Institut de Recherche en Astrophysique etPlan´etologie; 9 Av. colonel Roche, BP 44346, F-31028 Toulousecedex 4, France Cahill Center for Astronomy and Astrophysics, Caltech,Pasadena, CA 91125 Space Sciences Laboratory, University of California, Berke-ley, CA 94720, USA DTU Space, National Space Institute, Technical Universityof Denmark, Elektrovej 327, DK-2800 Lyngby, Denmark Lawrence Livermore National Laboratory, Livermore, CA94550, USA Institute of Astronomy, University of Cambridge, MadingleyRoad, Cambridge CB3 0HA, UK Columbia Astrophysics Laboratory, Columbia University,New York, NY 10027, USA NASA Goddard Space Flight Center, Greenbelt, MD 20771,USA Department of Astronomy, University of Michigan, 500Church Street, Ann Arbor, MI 48109-1042, USA Jet Propulsion Laboratory, California Institute of Technol-ogy, Pasadena, CA 91109, USA and Feng & Soria (2011) for reviews.ULX spectra below 10 keV have been thoroughly in-vestigated (see, e.g., Gladstone et al. 2009) with
XMM–Newton (Jansen et al. 2001),
Suzaku (Mitsuda et al.2007) and
Chandra (Weisskopf et al. 2002). Their X-ray spectral shape does not match that of known BHs,in the mass range from 10 to millions of solar masses(see Done et al. 2007 for a review of standard BHs). Aspectral break below 10 keV has been observed in mostULXs (Stobbart et al. 2006; Gladstone et al. 2011), to-gether with a disk-like black body component at lowtemperatures ( . . ∼ M ⊙ , and thus thepresence of an IMBH (Miller et al. 2003, 2004). Butthe temperature-luminosity relation for this componentdoes not match that expected in standard accretion disksin the soft state, where the disks extend to the inner-most stable circular orbit (see, e.g., Kajava & Poutanen2009, Feng & Soria 2011 for a review). This relationcan be partially recovered in some cases by assuminga constant absorption column between the observations(Miller et al. 2013) or using non-standard disk models(Vierdayanti et al. 2006). Also, the cutoff is at muchlower temperature than is expected in standard BH hardstates (Done et al. 2007). Some authors associate thelow-temperature disk-like component with the presenceof an optically thick corona that blocks the inner part ofthe disk, so that the visible part of the disk has a muchlower temperature (Gladstone et al. 2009). Others sug-gest that it might come from a strong outflow (e.g. King2004) or be the result of blurred line emission from highlyionized, fast-moving gas (Gon¸calves & Soria 2006).From X-ray data below 10 keV it is impossible todistinguish between a cutoff and a downturn pro- Bachetti et al.duced by the imperfect fit of the continuum dueto the presence of a broadened iron complex in areflection-dominated regime (Caballero-Garcia & Fabian2010; Gladstone et al. 2011). The difference becomesclear above 10 keV (see, e.g., Walton et al. 2011a), in aregion of the spectrum that past sensitive satellites couldnot explore.The Nuclear Spectroscopic Telescope Array ( NuSTAR ;Harrison et al. 2013), launched in 2012 June, with its fo-cusing capabilities, large bandpass between 3 and 80 keVand large effective area, represents the ideal complementto
XMM–Newton (given the similar effective area be-tween 5 and 10 keV and spectral capabilities). X-raysare focused by multilayer-coated grazing incidence opticsonto two independent focal plane modules, called FocalPlane Module A and B (hear after FPMA and FPMB).Each focal plane contains four cadmium zinc telluridedetectors. The spatial resolution is 58 ′′ half-power diam-eter and 18 ′′ FWHM. NuSTAR is therefore a powerfultool for studying ULX broad band X-ray spectra. Sincethe launch of the satellite, we have observed a sampleof luminous ( L x ∼ erg s − ), close-by ( d .
10 Mpc)and hard (showing X-ray power law photon index Γ . NuSTAR and
Suzaku or XMM–Newton , producing the first ULX spec-tra extending over the range 0.3 and 30 keV.In this paper, we describe the results obtained for thetwo ULXs in the spiral galaxy NGC 1313, ( d ∼ .
13 Mpc,M´endez et al. 2002). These two ULXs are amongthe brightest, hardest and closest ULXs (Swartz et al.2004; Walton et al. 2011b), and therefore they are idealtargets for our program. They are known to showspectral variability below 10 keV (Feng & Kaaret 2006;Dewangan et al. 2010; Pintore & Zampieri 2012). Sig-nificant variability at high fluxes has also been observedin both sources (Heil et al. 2009).In Section 2 we describe the observations done, in Sec-tion 3 we provide some details on data reduction, thenin Section 4 and Section 5 we discuss the spectral andtiming analysis of the two sources, and finally we discussthe results. THE OBSERVATIONS
During this campaign, we observed NGC 1313 with
XMM–Newton and
NuSTAR two times, as summarizedin Table 1. Observations were executed with a separa-tion of about a week, to search for variability. The twoULXs are separated by about 7 ′ and can be observed si-multaneously by XMM–Newton and
NuSTAR . We choseto place X-1 close to the optical axis. It was not possibleto keep both ULXs close to the optical axis of
NuSTAR ,so we chose to obtain the best spectral quality for atleast one of them rather than reducing the quality forboth. X-1 is historically brighter and harder than X-2 (Pintore & Zampieri 2011), and we estimated that theaddition of
NuSTAR data would yield more valuable newinformation for this source. DATA REDUCTION
NuSTAR
DataNuSTAR data were processed using the version 1.0.1 ofthe
NuSTAR data analysis system, (
NuSTAR DAS ). The
NuSTAR DAS tools are divided in two main parts: thepreprocessing pipeline ( nupipeline ) that produces the
Table 1
Summary of the Data used in This PaperCamera Exposure (ks) X-1 Counts X-2 CountsEpoch 1 – 2012 Dec 16FPMA 100.9 3314 (386.2) 2336 (1074.2)FPMB 100.8 3444 (473.0) 2504 (1076.3)EPIC-pn 93.8 74002 (1523.4) 52603 (1029.1)EPIC-MOS1 Note . — Values in parentheses are background counts, scaled to thesource region size. X-1 on detector edge; X-2 on detector edge
L1 filtered files, and the products pipeline ( nuproducts )that is used to extract spectra, lightcurves and otherhigh-level products.We ran nupipeline on all observations with the de-fault options for good time interval filtering, and pro-duced cleaned event files. We then ran nuproducts usinga 30 ′′ extraction region around X-1 (see Section 3.1 forthe details) and a 60 ′′ extraction region around X-2, anda for background an 80 ′′ extraction region in the samedetector as the source, further than 1’ away to avoid con-tributions from the point-spread function (PSF) wings.We applied standard PSF, alignment and vignetting cor-rections. Spectra were rebinned in order to have at least20 counts bin − to ensure the applicability of the χ statistics, and in some cases to 50 counts bin − in orderto reduce computation times in particularly complicatedmodels.As it turned out, NuSTAR data of X-2 produced verypoor spectral information above ∼
10 keV. Besides beingvery faint, the
NuSTAR data were likely to be affectedby response degradation due to the off-axis position ofthe source, and a very uncertain background level due tothe
NuSTAR sloping aperture background. We decidednot to use them for the next steps of the analysis.As can be seen in Figure 1, NGC 1313 X-1 has a nearbycontaminating source separated by ∼ ′′ that is notclearly resolved by NuSTAR . While the source is outsidethe
XMM–Newton
PSF of X-1 and it is quite easy toavoid it through the choice of a small extraction region,the evaluation of its possible effect on
NuSTAR data isless straightforward, due to the larger PSF. The contam-inating source has a flux ∼
10 times lower than X-1 inthe
XMM–Newton band, but the
NuSTAR
PSF of X-1appears elongated towards the contaminating source. Toevaluate the effects of this source, we produced
NuSTAR spectra with two different extraction regions, one includ-ing the nearby source (radius 80 ′′ ) and one not includingit (radius 30 ′′ ). As shown in Figure 2, the two spectrado not differ substantially between 10 keV and the in-tersection of source and background levels, while thereis some minor deviation at lower energy, in the XMM–Newton band. The best-fit power laws below 10 keV inthe two datasets are marginally compatible (spectral in-GC 1313 X-1 and X-2 with NuSTAR and XMM-Newton 3 : . : : . . : . : . : . : . - : : . : . . : : . . . : . : . : . : . - : : . X - X-1
Figure 1. (Left)
NuSTAR and (right) EPIC-pn images of the two ULXs, produced with DS9 (Joye & Mandel 2003). Data are from thewhole energy bands of the detectors.
Chandra contours corresponding to the ULXs and possible contaminants are shown in red. Yellowdashed regions are the extraction regions used for analysis. The radius of the region around X-1 is 30 ′′ in both cases in order to avoid thecontaminating source about 50 ′′ SE of the source. For X-2, instead, it is 60 ′′ in NuSTAR and 30 ′′ for XMM–Newton .
105 20 − − − − Energy (keV) P ho t on s c m − s − k e V − Figure 2.
NuSTAR spectrum of X-1, rebinned to 30 counts bin − ;black corresponds to an 80 ′′ extraction region, red to 30 ′′ (whichexcludes the contaminating region 53 ′′ SE of X-1). Circles labelthe source spectra, while “x”s mark the background spectra. Thereis no significant change in the spectrum between 10 and 30 keV, butthe larger extraction region is much more affected by background.Also, below 10 keV there is some very small deviation. dex 2 . ± .
08 in the first and 1 . ± . ′′ extraction region is used. In the following analysis,we only consider spectra below 30 keV where the sourceis stronger than, or compatible with, the background. XMM–Newton
Data
The
XMM–Newton data reduction was carried outwith the
XMM–Newton
Science Analysis System (SASv12.0.1). We produced calibrated event files with epproc and emproc , created custom good time inter-val files to filter out periods of high background accord-ing to the prescription in the SAS manual, and selectedonly events for EPIC-pn and events for EPIC-MOS cam-eras. We also filtered the events along detector gapsthrough
FLAG==0 . The resulting event files were thenfiltered with a 30 ′′ region around the two ULXs. Back- ground events were selected in each detector in regionswith no detector edges, bad pixels or visible sources.Spectra were extracted for all three cameras, unlessthe source was in a detector gap (see Table 1). We used fselect for spectral extraction, and ancillary responsesand redistribution matrices were created with arfgen and rmfgen , with the new ELLBETA PSF correctionenabled. Spectra were finally rebinned with grppha inorder to have at least 20 counts bin − . SPECTRAL ANALYSIS
Software Tools and General Procedure
Spectral analysis was carried out with the Interac-tive Spectral Analysis System (ISIS; Houck & Denicola2000). We chose this software over the more commonlyused X-ray spectral fitting package XSPEC (Arnaud1996) because of its scriptability and the transparentuse (in multicore computers) of parallel processing dur-ing confidence region calculation and parameter spacesearching, while being able to use all XSPEC models,table and local models .To model neutral absorption we used the tbnew model , the new version of tbabs (Wilms et al. 2000)featuring higher spectral resolution and, also impor-tantly, much faster computation due to caching tech-niques (see linked Web site for the details). This modelcan be used in different ways, by including custom abun-dances of a large number of elements. We use the sim-plest version, tbnew feo , including only the abundancesof iron and oxygen besides the usual hydrogen column n H , and fixing the abundances of all elements to the stan-dard values from Wilms et al. (2000). We use the cross In the following sections we will show several unfolded spectra(i.e. spectra corrected for the response and thus ideally equal tothe “real” spectrum of the source). In ISIS, the calculation ofunfolded spectra is done in a model-independent way by using theresponse matrices, as opposed to XSPEC where the calculationof these spectra is performed through the distance of data pointsfrom the model. This calculation is less statistically robust, andis used only for display purposes. Model fitting and residuals arecalculated in the usual way, by applying the response matrix tothe model and comparing to the uncorrected detector counts. Seemore details in Nowak (2005). http://pulsar.sternwarte.uni-erlangen.de/wilms/research/tbabs/ Bachetti et al. − − × − × − × − × − k e V P ho t on s c m − s − k e V − − χ Energy (keV)
Figure 3.
EPIC-pn and
NuSTAR unfolded spectrum ofNGC 1313 X-1 during the two observations, and residuals withrespect to the best-fit absorbed power law in the
XMM–Newton band. Black and red points are EPIC-pn data, and blue and cyanFPMA data. Circles indicate the first observation, crosses indicatethe second. The spectrum shows a soft excess and a cutoff, as ob-served in this source when in its low-flux state. The archival 2006October
XMM–Newton observation is also plotted (grey squares)for comparison. Data are rebinned to 200 counts bin − (EPIC-pn)and 30 counts bin − (FPMA) for visual purposes. The spectralshape does not change significantly between the two observationsand is qualitatively similar to the archival spectrum, with a slightlyhigher flux. The slight misalignment between NuSTAR and
XMM–Newton data is due to residual cross-calibration and possibly thenon perfect simultaneity of the observations. sections from Verner et al. (1996). The hydrogen columnwe measure from our fits is at least ∼ NuSTAR and
XMM–Newton data,we first fit a constant*cutoffpl model between 5 and10 keV, with the constant for EPIC detectors fixed to 1and the others left free , to determine a cross-calibrationconstant that we fix for the subsequent fits. This takesinto account residual cross-calibration between XMM–Newton and
NuSTAR and the possible mismatches dueto non-strictly simultaneous observations.
NGC 1313 X-1
Figure 3 shows an overview of the spectral featuresof X-1. As can be seen in this plot, the spectrum didnot change significantly between the two observations,either in the
XMM–Newton or in the
NuSTAR bands.We determined the cross-normalization constant between
NuSTAR and
XMM–Newton data to be 1 . ± .
06 forFPMA and 1 . ± .
07 for FPMB in the first observa-tion, and 1 . ± .
06 FPMA and 1 . ± .
07 FPMB inthe second. We measure an absorbed (0.3–10) keV lu-minosity of (6 . ± . × erg s − in the first obser-vation ( ∼ . × unabsorbed, assuming the best-fit diskbb+cutoffpl model below) and (6 . ± . × The cross-calibration between pn and MOS { } is negligiblewith respect to the one between pn and FPM in our data. erg s − in the second ( ∼ × unabsorbed).The corresponding absorbed 0.3–30 keV luminosities are(8 . ± . × and (7 . ± . × erg s − , respec-tively. The spectral residuals with respect to the best-fitpower law in the XMM–Newton band are qualitativelysimilar to the one reported from the 2006 October
XMM–Newton observation (Dewangan et al. 2010), associatedwith the low-flux state of this source, as opposed to thehigher states where the soft excess is less prominent, asalso shown in Figure 3.
Cutoff versus Reflection
The first thing that becomes evident thanks to the
NuSTAR data is that the spectrum shows a clear cut-off above 10 keV. As we mentioned earlier, hints of thiscutoff are present in
XMM–Newton archival data of manyULXs, but this feature could be produced by a real cut-off or by relativistically smeared iron features. Withthe addition of
NuSTAR data this degeneracy is broken.We fitted the data with three models: (1) a power lawwith exponential cutoff (XSPEC model cutoffpl ), withand without an additional disk component modeled asa multicolor disk (MCD; diskbb ; Mitsuda et al. 1984); (2) diskbb plus a Comptonization model ( comptt ;Titarchuk 1994) with the Comptonization seed photontemperature linked to the inner disk temperature for con-sistency; (3) a blurred reflection model obtained by con-volving the reflionx table (Ross & Fabian 2005) witha Laor profile (Laor 1991), provided by the convolutionmodel kdblur2 to account for general relativistic effects,following the method used by Walton et al. (2011a) andCaballero-Garcia & Fabian (2010). See Table 2 for de-tails.While blurred reflection models and Comptoniza-tion/cutoff models yield similarly good fits in the
XMM–Newton band alone, they predict a completely differentbehavior around and above 10 keV, as shown in Figure 4.In reflection models, by adding
NuSTAR data we canfind a decent nominal fit ( χ / d . o . f . ∼ .
08 in the firstobservation, 1.18 in the second, see Table 2), but it ismostly due to the large number of
XMM–Newton spec-tral bins below 10 keV. From the residuals in Figure 4it is clear that the description of the spectrum is inade-quate around and above 10 keV. Even in the reflection-dominated regime where the power law normalization iszero and the downturn produced by the broadened ironline is maximum, the downturn is not sufficient to ac-count for the very deep cutoff seen in
NuSTAR data,and the Compton “hump” produced by reflection clearlyover predicts the spectrum above 10 keV.
Comparison of Comptonization Models
NuSTAR data enable us to obtain a much better con-straint on the cutoff. This is shown in Figure 5, wherethe contour levels between kT e and τ are shown withand without NuSTAR data. It is clear from the contourplots that the addition of
NuSTAR data improves theconstraint considerably. An alternative way to show thepoor constraint given by
XMM–Newton data alone is tofix the electron temperature of comptt ( kT e ) to 50 keV,and fit the data. If we take XMM–Newton data only,the fit deteriorates (∆ χ ∼
20 in the first observation, ∼
30 in the second for ∆d . o . f . = 1) but we can still re-cover an overall acceptable fit ( χ / d . o . f . ∼ .
08 in theGC 1313 X-1 and X-2 with NuSTAR and XMM-Newton 5 − − χ DISKBB + CUTOFFPL − − χ DISKBB + COMPTT − − χ OPTXAGNF 1 10 − − χ Energy (keV)
KDBLUR2(REFLIONX)
Figure 4. (Left) The unfolded spectrum of the second observation of X-1. Black circles represent EPIC–pn data, and blue squaresrepresent FPMA data normalized with the cross-normalization constant. We superimpose the best-fit diskbb+cutoffpl model (red, solid),its single components (dashed), and the best-fit reflection model (green, dash-dotted). (Right) residuals from a selection of models listed inTables 2 and 3. Black is EPIC–pn, blue FPMA and light blue FPMB. The models are calculated with all available detectors, but for clarityonly pn data are plotted for
XMM–Newton . Also for clarity, data have been rebinned to 30 counts bin − . The red model overplotted to thedata in the spectrum shows the best fit with a reflection-dominated spectrum. Note that this model works very well in the XMM–Newton band, and the downturn produced by the iron line around 10 keV is able to fit the cutoff below 10 keV, but the addition of
NuSTAR dataclearly rules it out.
Electron temperature (keV) O p t. T h i ck ne ss Figure 5.
Confidence contours for the kT e and τ parameters inthe diskbb + comptt model fit for X-1, using only XMM–Newton data (dashed) and
XMM–Newton and
NuSTAR data (solid) of thesecond observation. The added value of NuSTAR data when itcomes to constraining the electron temperature is evident. first, 1.06 in the second) and even obtain a compatiblevalue of the disk temperature (Table 2).
XMM–Newton response drops and data have only a few points around10 keV, where the constraint on the cutoff is set, andsmall systematic errors in the instrument response caninfluence the fit. The difference between the two modelsdisappears if one discards the last 20 bins of the spec-trum. With the addition of
NuSTAR data this is nottrue anymore, and in fact the fit deteriorates further( χ / d . o . f . > .
2) and the disk temperature assumes in-compatible values (see Table 2).From Table 2 and Figure 4 it is also clear that the comptt model gives a slightly worse fit than the sim-ple cutoffpl model, with a high-energy slope visiblysteeper than what
NuSTAR data show. This fact in-dicates that a single-temperature Comptonization modelis probably not sufficient to describe the data. We makeuse of the optxagnf model (Done et al. 2012), whichis a phenomenological model that represents the evolu- tion of the dkbbfth model (Done & Kubota 2006) oftenused for ULXs in the past (e.g. Gladstone et al. 2009;Walton et al. 2011a). optxagnf , originally developed foractive galactic nuclei (AGN), tries to balance in a self-consistent way the optically thick emission from the disk,a low-temperature Comptonization component originat-ing from the inner part of the disk, and a second, hotComptonization component with cutoff above 100 keVproduced by a hot corona. With respect to the dkbbfth model, optxagnf adds a second Comptonizing compo-nent while maintaining the possibility of hiding the un-derlying disk emission below a corona that covers thedisk and is powered by it. The latter was the reason dkbbfth was used in the past. Moreover, optxagnf hassuperior computational stability and a more convenientchoice of parameters, using the expected mass, spin andluminosity of the BH instead of a generic normalizationparameter linked to the position of the inner disk (in fact,in this model the normalization factor should normallybe frozen to 1, but see below).This model, however, has nine free parameters (mass,spin, luminosity, photon index and normalization of thehot Comptonizing component, optical thickness and tem-perature of the cold Comptonizing component, radius ofthis cold component, and outer radius of the disk), andtherefore it is able to yield many different solutions fora given spectrum. We therefore restrict the parameterspace by fixing some of them to reasonable values anddiscuss the results obtained with this approach, with theobvious associated caveats. A discussion of the full rangeof scenarios that this model can describe is beyond thescope of this work and will be discussed in a future paper.Our
NuSTAR data show an excess with respect to asingle-temperature Comptonization model, but do notshow the plateau at high energies that has been observedfor example in the bright AGN (Done et al. 2012). Wetherefore fix the power law index of the hot electrons, Γ,to 2, a typical value observed in BH power law spectra,and we free only its normalization factor, f PL . We alsofix the outer disk to 10 R g , the spin parameter a to 0 Bachetti et al. Table 2X-1 : Best-fit Parameters for Some Common Spectral ModelsEPIC–pn only pn, MOS2, FPM { A,B } Parameter Unit Epoch 1 Epoch 2 Epoch 1 Epoch 2 tbnew feo*(cutoffpl) n H cm − . ± .
006 0 . ± .
006 0 . ± .
006 0 . ± . N cut (7 . ± . × − (8 . ± . × − (7 . ± . × − (8 . ± . × − Γ 2 . ± .
02 2 . ± .
02 1 . ± .
03 1 . ± . E cut keV 500 ∗− ∗− +62 − +9 − χ / dof 1399/987 1379/968 2699/1952 2707/1939 tbnew feo*(diskbb+cutoffpl) n H cm − . ± .
02 0 . ± .
02 0 . ± .
01 0 . ± . N dbb +4 − +5 − +3 − ± T in keV 0 . ± .
02 0 . ± .
02 0 . ± .
01 0 . ± . N cut (4 . ± . × − (4 . ± . × − (4 . ± . × − (4 . ± . × − Γ 1 . +0 . − . . ± . . ± . . ± . E cut keV 6 +3 − +5 − . +0 . − . . ± . χ / dof 1037/985 1010/966 1998/1950 1986/1937 tbnew feo*(diskbb+comptt) n H cm − . ± .
02 0 . ± .
02 0 . ± .
01 0 . ± . N dbb +9 − +10 − +7 − +7 − T in keV 0 . ± .
02 0 . ± .
02 0 . ± .
01 0 . ± . N comp (4 . ± . × − (4 . ± . × − (4 . ± . × − (4 . ± . × − kT e keV 2 . +0 . − . . +0 . − . . +0 . − . . ± . τ . ± . . ± . . ± . . ± . χ / dof 1033/985 1011/966 2020/1950 2013/1937 tbnew feo*(diskbb+comptt) ( kT e = 50 keV) n H cm − . ± .
02 0 . ± .
02 0 . ± .
02 0 . ± . N dbb +14 − . +13 − +25 − +40 − T in keV 0 . ± .
01 0 . ± .
01 0 . +0 . − . . ± . N comp (2 . ± . × − (2 . ± . × − (3 . ± . × − (3 . ± . × − τ . +0 . − . . ± .
05 0 . ± .
02 0 . ± . χ / dof 1069/986 1028/967 2357/1951 2482/1938 tbnew feo*(powerlaw+kdblur2(1,reflionx)) n H cm − . +0 . − . . ± .
009 0 . ± .
007 0 . +0 . − . N pow . ∗− . × − (6 . ± . × − ∗ ∗ N ref . +0 . − . × − +2 − × − (4 . ± . × − . +0 . − . × − A Fe ∗− +8 − . +0 . − . . +0 . − . Γ 1 . +0 . − . . +0 . − . . ± .
04 1 . +0 . − . X i (3 ± × (0 . +0 . − . ) × . +0 . − . × . +0 . − . × q +3 − +5 − ± . +0 . − . R in +7 ∗ +6 ∗ . +0 . − . . ± . i deg 71 ± +5 − +8 − +1 − χ / dof 1011/973 973/953 2110/1877 2281/1934 Note . — All uncertainties refer to single-parameter 90% confidence limits. ∗ Values were fixed, or the parameter was unconstrained and, as is prescribed in the documentation, the normal-ization factor to 1. Because this model does not take intoaccount the inclination and assumes an observing angleof 60 o , and the norm is proportional to cos i/ cos 60 o , wealso fitted the data with the norm fixed to 2 (source seenface-on) to evaluate whether a change in this parametercould dramatically affect the results.We summarize the best fit in this reduced parame-ter space in Table 3. In both observations this modelyields an intriguing result: under the above assumptions( a =0, Γ = 2), and with both normalizations, the spec-trum seems to be well described by a quite massive ( ∼
70– 90 M ⊙ ) BH, accreting close to (or slightly above) Edding-ton, with a large corona reaching ∼ R g . The fractionof energy that is reprocessed from the hot part of thecorona is about 60%, while the rest is reprocessed by thecold and optically thick part. As expected, fixing thenorm to 2 has the effect of lowering both the mass of theBH and the luminosity, but the rest of parameters do notchange significantly.All of the above models leave some residuals around1 keV and below. They appear very similar in allfits, indicating that they are independent from theparticular continuum model used. Similar residu-GC 1313 X-1 and X-2 with NuSTAR and XMM-Newton 7 Table 3X-1 : Best-fit Parameters for optxagnf , with theData from All Instruments.Parameter Unit Epoch 1 Epoch 2 tbnew feo*optxagnf (norm fixed to 1) n H . +0 . − . . ± . M solar 93 +17 − +19 − log L/L
Edd − . +0 . − . − . +0 . − . R cor rg 66 +6 − ± kT e keV 2 . +0 . − . . ± . τ +2 − +1 . − . f PL . ± . . +0 . − . χ / dof 1178/1190 1327/1220 tbnew feo*optxagnf (norm fixed to 2) n H . +0 . − . . ± . M solar 63 +14 − +13 − log L/L
Edd − . +0 . − . − . ± . R cor rg 67 +5 − +5 − kT e keV 2 . ± . . ± . τ +3 − +1 . − . f PL . +0 . − . . ± . χ / dof 1178/1190 1327/1220 Note . — All uncertainties refer to single-parameter 90% confidence limits. Note that for thismodel data were rebinned to 50 counts bin − for XMM–Newton , in order to reduce computation timesduring error bar calculations. als are often observed in ULXs (see, e.g., Soria et al.2004; Gon¸calves & Soria 2006; Gladstone et al. 2009;Caballero-Garcia & Fabian 2010). We tested the im-provement of the fit with the addition of a MEKAL com-ponent (Mewe & Gronenschild 1981) to the cutoffpl and diskbb+cutoffpl models. We failed to obtain agood fit in the first case, while in the second we founda general improvement of the fit(∆ χ ∼ NGC 1313 X-2
As described in Section 3.1, we did not use
NuSTAR data for the analysis of X-2. Figure 6 shows the shapeof the
XMM–Newton spectrum of X-2 in the two epochs.The flux and overall shape of the spectrum changed con-siderably between the two observations, as also did thetiming behavior (see Section 5.4). We measure a 0.3–10 keV absorbed luminosity of (4 . ± . × erg s − in the first epoch and (2 . ± . × erg s − in thesecond epoch.Spectral fits with several models are presented in Ta-ble 4. The spectrum is reasonably well described by anabsorbed cutoff power law in both epochs, but the val-ues of the spectral index (down to 0.9 in one case) arevery different from what would be expected by Comp-tonization, the main process known to produce this kindof spectral shape, that instead yields spectral indices be-tween 1.5 and 3. The addition of a disk component tothe cutoff power law barely improves the fit (∆ χ ∼ − − k e V P ho t on s c m − s − k e V − − − χ Energy (keV)
Figure 6.
XMM–Newton unfolded spectra of NGC 1313 X-2 dur-ing the two observations. Black points are EPIC-pn and red pointsare EPIC-MOS1 data, due to the source being in the gap of pn inthe second observation. The best-fit slim-disk model for the twoobservations with modelID set to 4 is superimposed.. the first observation, and ∼ diskbb+comptt model does not improve the fit with respect to the cutoffpl model.The spectral shape is clearly not well describedby a standard MCD (XSPEC model diskbb ), but itis well modeled by a so-called p -free disk ( diskpbb ,Mineshige et al. 1994; Kubota et al. 2005). When theaccretion rate is high, it is expected that the struc-ture of the disk deviates considerably from the standardShakura & Sunyaev (1973) thin disk. In this model, theradial dependency of the disk temperature is parameter-ized with T ∝ r − p , where p is different from the 3 / p -disk would recoverthe standard thin disk if p = 0 .
75. For p < .
75 thetemperature profile is affected by advection. At p =0.5,advection dominates and the disk is a so-called slim disk (Abramowicz et al. 1988; Watarai & Fukue 1999).The p -free model seems to yield a very good fit for bothepochs, with values of p very close to the slim disk regime.The amount of advection is closer to the slim disk regimein the fainter observation. This behavior has been re-ported for this and other ULXs in the past (Mizuno et al.2007; Middleton et al. 2011b; Straub et al. 2013). Thedeviation of p from 0.5 in the brightest observation mightimply some reprocessing of the disk emission, for exampleby a corona.The fact that these two observations have such differ-ent fluxes and spectral shapes gives us the opportunityto jointly fit the data with more physically-motivatedmodels that would be difficult to constrain with singleobservations, and try to obtain an estimate on the massof the source.With this goal in mind, we used an advanced slimdisk model, implemented by Kawaguchi (2003, hereafter slimdisk ). In this local XSPEC table model (used in thepast for fitting ULX spectra, see, e.g. Vierdayanti et al.2006; Godet et al. 2012), mass M (in M ⊙ ) and accre-tion rate ˙ M are the only physical parameters. ˙ M iscalculated in units of L Edd /c , where L Edd is the Ed-dington luminosity. Since L ≃ η ˙ M c , where η is theefficiency, then the value of ˙ M corresponding to the Bachetti et al. Table 4X-2 : Best-fit Parameters for Some Models, with the Data from
XMM–Newton
Only.Parameter Unit Epoch 1 Epoch 2 tbnew feo*(cutoffpl) n H cm − . ± .
02 0 . ± . N cut (7 . ± . × − (5 . ± . × − Γ 0 . ± . . ± . E cut keV 2 . ± . . +0 . − . χ / dof 776/833 613/528 tbnew feo*(diskbb) n H cm − . +0 . − . . ± . N dbb . ± .
003 0 . ± . T in keV 1 . ± .
02 0 . ± . χ / dof 959/834 833/529 tbnew feo*(diskpbb) n H cm − . ± .
02 0 . +0 . − . N dbb . ± .
002 0 . +0 . − . T in keV 1 . ± .
06 1 . ± . p . ± .
01 0 . +0 . ∗ χ / dof 776/833 611/528 tbnew feo*(diskbb+cutoffpl) n H cm − . +0 . − . . +0 . − . N dbb . . +1 . − . T in keV 0 . +0 . − . . +0 . − . N cut +2 − × − +3 − × − Γ 0 . +1 . − − . +1 . − . E cut keV 2 . ± . . +2 . − . χ / dof 773/831 607/526 tbnew feo*(diskbb+comptt) n H . ± .
008 0 . +0 . − . N dbb . +0 . − . +12 − × T in keV 0 . ± . . ± . N comp (1 . ± . × − (2 . +0 . − . ) × − kT e keV 2 . +0 . ∗ . +0 . ∗ τ . +1 . − . . +0 . − . χ / dof 811/831 661/526 tbnew feo*optxagnf n H cm − . ± .
01 0 . +0 . − . M M ⊙ +4 − +27 − log L/L
Edd . +0 . − . − . +0 . − . R cor rg 39 +61 − +8 − kT e keV 1 . +0 . − . . +0 . − . τ +4 − +7 − χ / dof 559/599 443/422 Note . — All uncertainties refer to single-parameter 90% confidencelimits.
Eddington luminosity is 1 /η ∼
16, assuming the ef-ficiency for a Schwarzschild BH calculated by usinga pseudo-Newtonian potential (see, e.g., Ebisawa et al.2003). Comptonization from a corona, gravitationalredshift and transverse Doppler effect are included self-consistently, but there is no observing angle dependence,as the source is assumed to be face-on. Ideally, this modelprovide a unique value of the mass given the mass accre-tion rate, or vice versa. The choice of the spectral model (slim disk alone, with an additional thermal componentor Comptonization, with or without relativistic effects)to include in the computation is done by switching thevalues of the modelID parameter. For our purposes, weare interested in the treatment of a slim disk with Comp-tonization, and with or without relativistic effects (i.e.using modelID equal to 4 or 7). The disk viscosity pa-rameter α , the only non-observable quantity, can also beset.We tied almost all parameters of the model in thetwo epochs, leaving only the mass accretion rate ˙ M freeto vary between them; we fixed the normalization to(10kpc /d ) = 5 . × − , assuming d = 4 .
13 Mpc.We initially fixed the modelID to 7, meaning that weused all corrections for gravity and Comptonization. Wetried different values for the α parameter, and found thatthe spectral shape was best described by α ∼ .
01, i.e.,the lower limit of this table for the viscosity parameter.Even with these very restrictive assumptions, the modelwas able to fit the data quite well (see Table 5).By taking out the relativistic corrections, namelychanging the modelID to 4, we were again able to fitthe data fairly well. In this case, there was need for ahigher viscosity in order to reproduce the curvature ofthe spectrum. As a result the measured values of themass are higher, but always in the range of StMBHs.In addition to the slimdisk model, we used the afore-mentioned optxagnf . We started by fitting the modelto the single observations, similarly to what was donefor X-1 (best-fit results in Table 4), this time fixing thepower law index to 2.2 (by analogy with high-accretionrate Seyfert galaxies) and the fraction of emission in thehot corona to 0.3. Then we fitted together the two ob-servations. Given the complexity of this model, we usedit to obtain estimates on the most likely source param-eters by fixing the mass, the photon index of the hotelectrons Γ and the spin a to discrete values (10, 30, 60,90 M ⊙ for M , 1.8, 2 and 2.2 for Γ, 0 and 0.998 for a )and freeing the fraction of hot power law emission, theoptical thickness and the cold corona temperature. Thenorm was fixed to 1 and then to 2, because of the ar-guments considered in Section 4.2.2. For norm =1, wefound the best fit ( χ / dof = 1 . M = 30 M ⊙ andΓ = 2 .
2. The fit with M = 10 M ⊙ was always unaccept-able ( χ / dof & . M = 60 M ⊙ we could obtainan acceptable fit ( χ / dof . .
05) only for Γ = 2. Inall other cases either the fit was worse, or one or moreparameters reached their hard limits, implying a non-ideal regime of the model. Varying the spin from 0 to0.998 did not change the results dramatically, with τ , kT e and f PL compensating for most of the change in spectralshape. As before, fixing the norm to 2 lowered the esti-mate on the mass, permitting to obtain decent fit values( χ / dof = 1 .
06) also for M = 10 M ⊙ and Γ =1.8–2.As a bottom line, the favored interpretation, from both optxagnf and slimdisk , seems to be a StMBH (up to ∼ M ⊙ ) accreting around Eddington, or transitioningbetween a super-Eddington and a sub-Eddington regime.The emission from the cold and thick corona given by optxagnf , extending over a large region of the inner disk,does not differ substantially from the bloated disk de-scribed in the slimdisk model, and it is thus not sur-prising that the two models produce similar results.GC 1313 X-1 and X-2 with NuSTAR and XMM-Newton 9 Table 5X-2 : Best-fit parameters for X-2, with the slimdisk model, and the mass tied between the two observations.Subscripts 1 and 2 refer to the two observations. modelID α n H , (cm − ) n H , (cm − ) M ( M ⊙ ) ˙ M ( L Edd /c ) ˙ M ( L Edd /c ) χ / dof7 0 . +0 . ∗ . ± .
006 0 . ± .
01 21 . ± . ± . +0 . − . . +0 . − . . +0 . − . . ± .
01 36 +2 − . +0 . − . . ± . Note . — The mass was tied in the two observations. All uncertainties refer to single-parameter 90% confidence limits. modelID =4 means that we are modeling a slim disk plus Comptonization. With modelID =7, we are also adding relativisticcorrections. Being the grid of the slimdisk model quite sparse, the errors on the parameters are typically inside the rangebetween a value and the following in the grid. For this reason, one should use these uncertainties with some caution.
The same caveats discussed for X-1 apply here: thisresult is model-dependent and based on the assump-tions we made about the parameters; only further inves-tigation using more observations with different spectralstates will tell if the constraints on the mass are robust. TIMING ANALYSIS
We extracted filtered event lists for both ULXs fromall datasets and produced lightcurves cleaned from gapsand periods of increased background activity. These datawere then processed with the following timing analysistechniques. rms variability
The first variability test we used on our data is thenormalized excess variance test (Edelson et al. 1990;Vaughan et al. 2003). Let S be the intrinsic variance ofthe source signal (as calculated from the lightcurve), σ i the standard error on the i th bin of the lightcurve (cal-culated from Poissonian statistics) and ¯ σ the mean stan-dard error, ¯ I the mean counts per bin in the lightcurve.The excess variance is then simply S − ¯ σ ; we normalizeit as follows: F var = s S − ¯ σ ¯ I . (1) F var has the advantage of being a linear quantity, andthus yields a measure of the intrinsic root mean square(rms) variability of the source. The error we quote is theone derived in Vaughan et al. (2003). Power Density Spectrum
For each lightcurve, we extracted a power densityspectrum (PDS), the normalized square modulus of theFourier Transform (see van der Klis 1989 for an exten-sive review of the methods used in the following). Weused the Leahy et al. (1983) normalization, so that thePDS has a white noise level of 2. Dead time effects cansafely be ignored due to the very low count rates of thesources analyzed.This timing analysis is very sensitive to data gapsin lightcurves, which produce low-frequency noise andspikes in the PDS.
NuSTAR data, because of the veryshort orbital period of the satellite ( ∼
90 minutes) andthe position of the source, have about ∼
30 minutes ofoccultation every orbit. Moreover, both
XMM–Newton and
NuSTAR data have other gaps due to, for example,the filtering of periods of high background activity. Asa strategy in our analysis, we decided to fill gaps of veryshort length (several seconds) with white noise at the av-erage count rate in the nearby 4000s of data. We verified that, due to the very low count rate, this did not pro-duce any spurious features in the spectrum. Data chunkswith longer gaps, such as occultation periods, were sim-ply ignored. This also limits the maximum length ofsingle fast Fourier Transoforms for
NuSTAR data to lessthan ∼ XMM–Newton .We used different rebinning factors in order to lookfor features with different spectral width. FollowingBarret & Vaughan (2012), we used maximum-likelihoodfitting to evaluate features in cases where the rebin-ning was not sufficient to attain the Gaussian regime.The maximum frequency investigated was 512 Hz, toinclude possible high-frequency quasi-periodic oscilla-tions (QPOs) as often observed in BH sources (seeRemillard & McClintock 2006; Belloni et al. 2012, for re-views). The minimum frequency was the inverse of thelength of each analyzed chunk with no gaps. For
NuS-TAR this was limited to ∼ . XMM–Newton data ∼ . NGC 1313 X-1
The PDS of NGC 1313 X-1 is almost featureless. TheKolmogorov-Smirnov test, calculated from the lightcurveat different bin times, does not detect any variabilityand we find no significant detections of QPOs or low-frequency noise in the PDS. F var is consistent with 0.This source historically showed variability only in itsbrighter states. Dewangan et al. (2010) studied the re-lation between variability and spectral states in X-1 andour timing results are, together with our spectral results(Section 4.2) compatible with what they call the “low-flux” state. NGC 1313 X-2
The behavior of this source is quite interesting from thetiming point of view. The results of the timing analysisare shown in Figure 7. The change in spectral shape ob-served in this source (Section 4.3) is also reflected in thetiming properties. As Figure 7 shows, in the observationwith higher flux the power spectrum shows low-frequencyvariability. The overall rms `a la Vaughan et al. (2003) is F var = 13 . closest to the BH, where variability timescales should be faster ,0 Bachetti et al.surely well above 1 Hz. But the PDS shows that thisvariability is mostly at low frequencies ( < DISCUSSION
In this paper we present the first
NuSTAR + XMM–Newton results on the two ULXs in NGC 1313.
NuSTAR data have proven particularly useful for X-1, where thedata above 10 keV clearly show a cutoff that was notwell constrained by
XMM–Newton (see Figure 5). In X-2, due to the soft spectrum and the unfavorable positionin the field of view,
NuSTAR data are not as decisive, but
XMM–Newton data are sufficient to perform high-qualityspectral and timing analysis below 10 keV.
X-1
The results obtained for this source thanks to
NuS-TAR data represent a new landmark in the understand-ing of ULX physics. Before
NuSTAR was launched, ULXspectra had been studied in detail only below 10 keV.At least two different models were previously able todescribe the spectral energy distribution: a reflection-dominated regime where the downturn is produced by avery strong and broadened iron line, and several combi-nations of MCDs (or other kinds of soft excess models)and low-temperature Comptonized emission cutting offslightly below 10 keV.We show also in this paper that, even with a ∼
100 kspointing, the
XMM–Newton spectrum alone is not suf-ficient to constrain the cutoff. Also using a reflectionmodel gives a very nice description of the spectrum withlow residuals and good χ in the XMM–Newton band.With
XMM–Newton alone, the spectrum might describea standard low-hard state of a quite massive BH witha strong Comptonized component from a hot and opti-cally thin medium, a reflection dominated state wherethe underlying power law is not observable, or a softdisk component and a reprocessed component that cutsoff around 10 keV.The addition of
NuSTAR data removes this degener-acy. In the
NuSTAR band, the spectrum shows a veryclear cutoff around 10 keV, similar in character to thatexpected from Comptonization by a cold, thick medium,but slightly less steep. The quality of
NuSTAR datais such that we can put tight constraints on the cut-off energy as shown in Figure 5 and Table 2, and, as aresult, the significance of a low-temperature disk com-ponent detected by
XMM–Newton . The presence of alow-temperature, optically thick Comptonized compo-nent suggests that we are observing accretion at highEddington fractions that make the geometry of the sys-tem deviate substantially from the standard picture validfor lower luminosity BHs and confirms previous, albeitmuch less constraining, observations (e.g. Stobbart et al.2006).By going into more detail and fitting the optxagnf phenomenological model that includes a color-correctedMCD plus a two-component corona composed of a cold,optically thick medium and a second, hot and opticallythin one, we obtain an interesting result: X-1 would bea quite massive StMBH of about 70–100 M ⊙ , accreting close to Eddington, with a large, cold corona coveringa significant part of the inner disk. This is in agree-ment with the lack of signatures of strong outflows thatshould be associated with highly super-Eddington ac-cretion (see, e.g., Poutanen et al. 2007), such as photo-ionized bubbles (that are seen instead for other sources,e.g., in Pakull & Mirioni 2002; Ramsey et al. 2006) ordiscrete atomic features in their high-energy spectra thatcould be associated with either iron emission or absorp-tion from a wind (Walton et al. 2012). An alternativeexplanation is that these winds are not pointing towardsthe observer, and the source is observed almost face-on(this would also agree with the lack of variability; see,e.g., Middleton et al. 2011a; Sutton et al. 2013).To summarize, this source is clearly not accreting ina standard BH hard or soft state, as is shown by theabsence of a power law and a spectrum not dominatedby disk emission, and hence the high luminosity and thecold inner disk are not indicative of the mass. The spec-tral shape is instead well described by what is generallyassociated with accretion close to Eddington, that is anoptically thick corona covering the inner part of the disk,and the energetics of the system points towards the high-end of the StMBH population. X-2
We caught a large spectral variation in X-2 that is ex-tremely interesting both for the rapidity (one week) ofthe change and for its characteristics. The higher stateis the one with the higher variability. This spectral be-havior is reminiscent of the hard state of known BHs,where there is a linear correlation between rms variabil-ity and flux (see, e.g., Uttley & McHardy 2001; McHardy2010 for a review). Nonetheless, the shape of the spec-tra do not match the general picture of spectra in thehard state, where a prominent power law component isusually present (Done et al. 2007). In our spectra thehigh-energy component drops off very quickly below oraround 10 keV.The spectrum of the source is instead well describedby a StMBH with an advection-dominated disk, or slimdisk , accreting around the Eddington limit. By link-ing the mass between the two observations and fittingthe slimdisk model, and independently by using the optxagnf model, we are able to obtain an estimate ofthe mass of the BH around 25 M ⊙ and a luminosity thatis shifting from super-to sub-Eddington.Even if Comptonization were not required by the spec-trum, the fact that the most variability comes fromhigher energies, as shown in Figure 7, gives support tomodels including this component. A simple slim diskwould be able to yield this variation of rms with energybut we would expect the highest energies to be producedin the region of the disk closer to the BH, where vari-ability is faster. This is in contradiction to the very lowfrequencies we observe in the PDS, and makes us favoran interpretation where variability comes instead fromthe corona, whose relative contribution to the spectrumis more important at high energies. ACKNOWLEDGEMENTS
M.B. wishes to acknowledge the support from the Cen-tre National d’´Etudes Spatiales (CNES). This work wassupported under NASA Contract No. NNG08FD60C,GC 1313 X-1 and X-2 with NuSTAR and XMM-Newton 11
Figure 7.
NGC 1313 X-2, from top to bottom: PDS with geometric rebinning (bin factor 1.03), and rms spectrum calculated from thenormalized excess variance F var (see Section 5.4 for details). From left to right, first and second observations. We did not include the fullrange of frequencies investigated for clarity. Dotted lines in the PDS show the white noise level of 2. Errors in the PDS are calculated as2 / √ MW , with M the number of averaged PDSs and W the number of averaged nearby bins. We only use XMM–Newton data due to thepoor quality of
NuSTAR data for this source (see Section 3.1). In the rms spectrum we only plot points where F var >
0. According to thePDS and the rms spectrum significant variability is only present in the first observation. and made use of data from the
NuSTAR mission, aproject led by the California Institute of Technology,managed by the Jet Propulsion Laboratory, and fundedby the National Aeronautics and Space Administration.We thank the
NuSTAR
Operations, Software and Cali-bration teams for support with the execution and anal-ysis of these observations. This research has madeuse of the
NuSTAR
Data Analysis Software (NuSTAR-DAS) jointly developed by the ASI Science Data Center(ASDC, Italy) and the California Institute of Technol-ogy (USA). This work also makes use of observations ob-tained with
XMM–Newton , an ESA science mission withinstruments and contributions directly funded by ESAMember States and NASA, and of observations made bythe
Chandra X-ray Observatory . For timing analysis andplotting, a set of Python codes making use of the NumPyand Scipy libraries was used. For some plots, we used theVeusz software. The authors wish to thank Olivier Godetand Chris Done for interesting discussions, and the ref-eree Matt Middleton, whose comments and suggestionssubstantively improved the quality of the manuscript.
REFERENCESAbramowicz, M. A., Czerny, B., Lasota, J. P., & Szuszkiewicz, E.1988, ApJ, 332, 646 Arnaud, K. A. 1996, ADASS, 101, 17Barret, D., & Vaughan, S. 2012, ApJ, 746, 131Belloni, T. M., Sanna, A., & Mendez, M. 2012, MNRAS, 426,1701Caballero-Garcia, M. D., & Fabian, A. C. 2010, MNRAS, 402,2559Dewangan, G. C., Misra, R., Rao, A. R., & Griffiths, R. E. 2010,MNRAS, 407, 291Done, C., Davis, S. W., Jin, C., Blaes, O., & Ward, M. 2012,MNRAS, 420, 1848Done, C., Gierli´nski, M., & Kubota, A. 2007, Astron AstrophysRev, 15, 1Done, C., & Kubota, A. 2006, MNRAS, 371, 1216Ebisawa, K., ˙Zycki, P., Kubota, A., Mizuno, T., & Watarai, K.-y.2003, ApJ, 597, 780Edelson, R. A., Krolik, J. H., & Pike, G. F. 1990, ApJ, 359, 86Farrell, S. A., Webb, N. A., Barret, D., Godet, O., & Rodrigues,J. M. 2009, Nat., 460, 73Feng, H., & Kaaret, P. 2006, ApJ, 650, L75Feng, H., & Soria, R. 2011, New Astronomy Reviews, 55, 166Gladstone, J. C., Roberts, T. P., & Done, C. 2009, MNRAS, 397,1836—. 2011, Astron. Nachr., 332, 345Godet, O., Plazolles, B., Kawaguchi, T., et al. 2012, ApJ, 752, 34Gon¸calves, A. C., & Soria, R. 2006, MNRAS, 371, 673Harrison, F. A., Craig, W. W., Christensen, F. E., et al. 2013,ApJ, 770, 103Heil, L. M., Vaughan, S., & Roberts, T. P. 2009, MNRAS, 397,1061Houck, J. C., & Denicola, L. A. 2000, ADASS, 216, 591Jansen, F., Lumb, D., Altieri, B., et al. 2001, A&A, 365, L12 Bachetti et al.