Long-term X-ray spectral evolution of Ultraluminous X-ray sources: implications on the accretion flow geometry and the nature of the accretor
Andrés Gúrpide, Olivier Godet, Filippos Koliopanos, Natalie Webb, Jean-François Olive
AAstronomy & Astrophysics manuscript no. aanda © ESO 2021February 23, 2021
Long-term X-ray spectral evolution of Ultraluminous X-ray sources:implications on the accretion flow geometry and the nature of theaccretor
A. Gúrpide , O.Godet , F. Koliopanos , N.Webb , and J.-F. Olive Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, UPS / CNRS / CNES, 9 Avenue du Colonel Roche,BP44346, F-31028 Toulouse Cedex 4, France
ABSTRACT
Context.
The discovery of pulsations in several Ultraluminous X-ray sources (ULXs) has demonstrated that a fraction of ULXs arepowered by super-Eddington accretion onto neutron stars (NS). This has opened the debate as to what is the neutron star to blackhole (BH) ratio within the ULX population and what physical mechanism allows ULXs to reach luminosities well in excess of theirEddington luminosity: the presence of strong magnetic fields or rather the presence of strong outflows that collimate the emissiontowards the observer.
Aims.
In order to distinguish between these scenarios, namely, supercritically accreting BHs, weakly or strongly magnetised NSs, westudy the long-term X-ray spectral evolution of a sample of 17 ULXs with good long-term coverage, 6 of which are known to hostneutron stars. At the same time, this study serves as a baseline to identify potential new NS-ULX candidates.
Methods.
We combine archival data from
Chandra , XMM-Newton and
NuSTAR observatories in order to sample a wide range ofspectral states for each source. We track each source’s evolution in a hardness-luminosity diagram (HLD) in order to identify spectralchanges and show that these can be used to constrain the accretion flow geometry and in some cases, the nature of the accretor.
Results.
We find NS-ULXs to be among the hardest sources in our sample with highly variable high-energy emission. On this basis,we identify M81 X-6 as a strong NS-ULX candidate, whose variability is shown to be akin to that seen in NGC 1313 X-2. Formost softer sources with unknown accretor, we identify the presence of three markedly di ff erent spectral states that we interpretinvoking changes in the mass-accretion rate and obscuration by the supercritical wind / funnel structure. Finally, we report on a lack ofvariability at high-energies ( (cid:38)
10 keV) in NGC 1313 X-1 and Holmberg IX X-1, which we argue may o ff er means to di ff erentiate BHfrom NS-ULXs. Conclusions.
We support a scenario in which the hardest sources in our sample might be powered by strongly magnetised neutronstars, so that the high-energy emission is dominated by the hard direct emission from the accretion column. Instead, softer sourcesmay be explained by weakly magnetised neutron stars or black holes, in which the presence of outflows naturally explains their softerspectra through Compton down-scattering, their spectral transitions and the dilution of the pulsed-emission, should some of thesesources contain neutron stars.
Key words.
X-rays: binaries – Accretion – Stars: neutron – Stars: black holes
1. Introduction
Ultraluminous X-ray sources are defined as extragalactic o ff -nuclear point-like sources with an X-ray luminosity in excessof ∼ erg / s (see Kaaret et al. 2017, for a review), albeitthere is now evidence for a Galactic ULX (Wilson-Hodge et al.2018). Their nature remains for the most part unknown, andgiven this empirical definition they likely constitute a heteroge-neous population of objects. It was initially proposed that ULXscould be powered by accreting intermediate-mass black holes(IMBH: ∼
100 – 10 M (cid:12) ; see Mezcua 2017, for a review) in thesub-Eddington regime (Colbert & Mushotzky 1999; Matsumotoet al. 2001). The best ULX IMBH candidates may be those atthe high-end of the High-Mass X-ray binary (HMXB) luminos-ity distribution (e.g. Mineo et al. 2012), reaching L X ≥ erg / sin some cases. Some of these objects show transitions or tempo-ral properties that seem to be consistent with the expectation ofa scaled-up version of Galactic Black Hole Binaries (GBHBs)(e.g. Farrell et al. 2009; Godet et al. 2009; Pasham et al. 2014)and / or show evidence for cooler accretion disks (e.g. Feng & Kaaret 2010; Servillat et al. 2011; Godet et al. 2012; Lin et al.2020) which suggest masses in the IMBH regime.However, it was soon realised that the bulk of the ULX popu-lation (10 < L X < erg / s) did not comply with the canonicalstates seen in GBHBs (e.g. Stobbart et al. 2006; Gladstone et al.2009; Grisé et al. 2010). It was thus suggested that stellar-massblack holes fed at super-Eddington mass-transfer rates couldpower these sources (Shakura & Sunyaev 1973; King & Pounds2003; Poutanen et al. 2007), with geometrical beaming possiblyfurther enhancing the observed luminosity (King et al. 2001). Inthis scenario, the intense radiation pressure blows-o ff some ofthe excess gas in the form of a wind or outflow, which can be-come optically thick to the hard radiation emitted in the innerparts of the disk (Poutanen et al. 2007). The wind is expectedto form a conic structure around the rotational axis of the com-pact object due to angular momentum conservation, producinghighly anisotropic emission. It was thus proposed that the short-term variability and the di ff erences in spectral shape in a broadULX sample could be understood in terms of di ff erent viewingangles and mass-accretion rates (Sutton et al. 2013; Middleton Article number, page 1 of 44 a r X i v : . [ a s t r o - ph . H E ] F e b & A proofs: manuscript no. aanda et al. 2015a) with those ULXs with L x ∼ erg / s showinga behaviour more consistent with stellar-mass black holes ac-creting close to or at their Eddington limit (e.g. Middleton et al.2011). These studies were later extended to include ultralumi-nous supersoft sources (ULSs) (Urquhart & Soria 2016), whichare interpreted as sources in which either the inclination of thesystem and / or the accretion rate are so high that the inner diskemission is completely reprocessed by the optically thick wind,with some sources possibly showing transitions between a ULX-like spectrum to a ULS state (Feng et al. 2016). Indeed, numer-ical simulations of super-Eddington accretion onto black holeshave shown extensively that the viewing angle has a strong im-pact on the observed spectrum (e.g. Ohsuga & Mineshige 2007;S ˛adowski et al. 2015; Ogawa et al. 2017). For this reason, ithas been suggested that overall ULXs belong to a homogeneousclass of objects, including stellar-mass black holes or lowly mag-netised neutron stars, being fed at super-Eddington mass-transferrates (King & Lasota 2016; King et al. 2017; Pinto et al. 2020a).Observational evidence supporting winds associated with super-Eddington accretion comes from high-resolution X-ray spec-troscopy studies, that revealed absorption and emission featuressuggesting the presence of strong ionised winds colliding withthe circumstellar medium (Pinto et al. 2016, 2017, 2020b).However, while it was generally accepted that accretingstellar-mass black holes were the engines behind ULXs below10 erg / s (e.g. Poutanen et al. 2007; Gladstone et al. 2009;Pintore et al. 2014), the discovery of X-ray pulsations in oneULX (Bachetti et al. 2014) showed that NS can also attainsuper-Eddington luminosities. Motivated by the discovery of(now) 5 more pulsating ULXs (PULXs) (Fürst et al. 2016; Israelet al. 2017b,a; Carpano et al. 2018; Sathyaprakash et al. 2019;Rodríguez-Castillo et al. 2020) and the possible confirmation ofanother NS-ULX through the identification of a cyclotron line(Brightman et al. 2018), several authors have highlighted the re-markable X-ray spectral similarity of the ULX sample with thosewith detected pulsations (Pintore et al. 2017; Koliopanos et al.2017; Walton et al. 2018c), suggesting that NS-ULX may dom-inate the ULX population. Yet, there is still some debate as towhat is the driving mechanism responsible for their extreme lu-minosities.Pintore et al. (2017) suggested that the accretion columncould be responsible for the hard emission in ULXs, as their X-ray emission could be described with a model commonly used tofit galactic X-ray pulsars. Instead, based on the theoretical calcu-lations carried out by Mushtukov et al. (2017), Koliopanos et al.(2017) argued that the ULX spectra are consistent with accretinghighly-magnetised NS (B > G), as the 0.3 – 10 keV band canbe described by two thermal components. In this scenario, thesoft thermal component arises from a truncated accretion diskat the magnetospheric radius (Ghosh & Lamb 1978) while thehard emission is produced in an optically thick envelope as theaccreting material is forced to follow the magnetic field lines,creating a closed envelope around the NS. The rotation of theenvelope, due to the coupling with the NS through the magneticfield lines, and its latitudinal temperature gradient could explainthe sinusoidal profiles seen in PULXs (e.g Fürst et al. 2018),provided that the NS rotational axis is misaligned with the mag-netic field axis. Alternatively, Walton et al. (2018c) followingthe arguments from King & Lasota (2016); King et al. (2017)showed that the interplay between the mass-accretion rate andmagnetic field strength could explain the lack / presence of pulsa-tions in ULXs, suggesting that ULXs might instead be poweredby weakly magnetised neutron stars. This in turn may explain the di ff erent spectral shape of those ULXs for which broadbandspectroscopy data is available, compared to the PULXs.However, the long-term evolution of PULXs is marked byhigh levels of variability of 2 orders of magnitude or more influx (Israel et al. 2017a,b) while other ULXs show variationsof a factor 5 or less throughout year-time scales (Grisé et al.2013; Luangtip et al. 2016; Pinto et al. 2020b) with PULXs be-ing also somewhat harder than the rest of the population (Pin-tore et al. 2017). Whether these represent di ff erences in the na-ture of the accretor or are due to a disfavourable viewing an-gle (e.g. King & Lasota 2020) is still not fully understood (e.g.Walton et al. 2018c). If beaming is a natural consequence ofsuper-Eddington mass transfer (King 2009), theoretical studiesshow that the fraction of observed BH-ULX could be higher thanNS-ULX (Middleton & King 2017). Similarly, binary popula-tion synthesis studies suggest that BH-ULX could even domi-nate the observed ULX population (Wiktorowicz et al. 2019),as NSs need stronger beaming factors to reach L X > erg / s.However, the evidence for supercritically accreting stellar-massblack holes remains elusive. The best observational evidence forsuch BH-ULX systems might be M101 ULX-1, which was esti-mated to host a ∼
20 M (cid:12)
BH, although its dynamical mass deter-mination was challenged by Laycock et al. (2015). Constrainingthe BH to NS ratio in ULXs can lead to important clues aboutthe formation path leading to such systems and their connectionwith HMXBs (e.g. Mineo et al. 2012) and the formation of BH-BH and BH-NS systems.Thus, while the spectral resemblance of the ULX populationis undeniable, tracing their long-term evolution can be the key inunderstanding the geometry of the accretion flow and discrimi-nating between super-Eddington accretion models and the natureof the accretor. Therefore, in this paper, we perform a compre-hensive study of the long-term spectral evolution of a representa-tive sample of 17 ULXs (including 6 NS-ULXs) in the 10 < L x < erg / s range, in an e ff ort to gain insights into the accretionflow geometry as well as the nature of the accretor. More specif-ically, we focus on studying each source spectral evolution in anattempt to assess which scenario best describes the variabilityobserved: super-Eddington accretion onto a highly magnetisedNS, a weakly magnetised NS or a black hole. This in turn givesclues about the nature of the accretor and by comparing its evo-lution with the known PULXs, we can identify potential strongNS-ULX candidates. To do so, we build a phenomenologicalmodel taking into account the new insights gained on the ULXbroadband emission with NuSTAR (Bachetti et al. 2014; Waltonet al. 2015; Mukherjee et al. 2015; Walton et al. 2020) and tracktheir spectral changes in a hardness-luminosity diagram.We describe the sample of sources selected for this work andthe data reduction in Section 2. In Section 3 we describe thedata analysis and results. We discuss our results in Section 4 andpresent our conclusions in Section 5.
2. Sample selection and data reduction
In order to have a representative sample of the possible range ofspectral variability of each source, we searched in the literaturefor sources that have been observed on at least 5 occasions, wellspaced in time, by either
XMM-Newton (Jansen et al. 2001) or
Chandra (Weisskopf et al. 2000). We further required that theyhave either: high-quality
XMM-Newton data (with (cid:38)
NuS-TAR (Harrison et al. 2013) in at least one epoch. We were less
Article number, page 2 of 44. Gúrpide et al.: Long term evolution of ULXs stringent with the data constraints on the PULXs, since they arethe only sources for which the nature of the accretor is knownand thus they will be crucial for our study. From the currentPULXs sample (NGC 7793 P13, NGC 5907 ULX1, NGC 300ULX1, M51 ULX–7, NGC 1313 X–2 and M82 X–2), we dis-carded M82 X–2 as this source is only resolved by
Chandra andits spectra are frequently a ff ected by pile-up. Its emission is alsooften contaminated with nearby sources and di ff use emission ofunknown origin (Brightman et al. 2016), precluding a clean de-tailed spectral analysis of the source. Another source of interestis M51 ULX–8, which was identified as harbouring an accret-ing NS through the detection of a cyclotron resonance feature(Brightman et al. 2018), although no pulsations have been re-ported to date. We therefore included this source in our sampleto further investigate its spectral properties with respect to thePULXs.For those ULXs for which the accretor is unknown, we in-cluded at least two sources from each of the di ff erent spectralregimes proposed by Sutton et al. (2013) in order to have a repre-sentative characterisation of the ULX population. We also madesure to include those showing evidence for super-Eddington out-flows with 3 σ detections (Pinto et al. 2016, 2017). Thus, we alsoincluded NGC 55 ULX1, even if it does not meet our criterionof having more than three epochs. The final sample selected forthis study is presented in Table 1.Finally, note that the luminosities reported for NGC 5907ULX1 in this work are subject to an additional source of uncer-tainty, as there is a large discrepancy in the distance measure-ments to the host galaxy. The distance measurements range from ∼
17 (Tully et al. 2016) to ∼ ∼ XMM-Newton data reduction was carried out using SAS ver-sion 17.0.0. We produced calibrated event files from EPIC-pn(Strüder et al. 2001) and MOS (Turner et al. 2001) cameraswith the latest calibration files as of March 2018 using the tasks epproc and emproc (version 2.24.1), respectively. We selectedevents from patterns 0 to 4 for pn and patterns ≤
12 for the MOScameras. The standard filters were used to remove pixels flaggedas bad and those close to the CCD gaps. We created high-energy(10 −
12 keV) lightcurves from single pattern events from thefull field of view to assess the presence of high-background par-ticle flaring periods that could contaminate our spectra. We fil-tered these periods by removing times where the count-rate wasabove a certain threshold by visually inspecting the lightcurves.These thresholds varied for each observation, and ranged from ∼ − to 1.2 cts s − and from ∼ − to 0.5 cts s − forthe pn and MOS respectively.Generally, we extracted source events from circular regionswith a radius of 40" and 30" for pn and MOS respectivelyowing to their di ff erent angular resolution, rejecting observa-tions in which the source fell on a chip gap. We reduced thesource regions to avoid contamination from nearby sources,chip-gaps, or in cases where the source was faint in order toincrease the S / N, but always ensuring that at lest 50% of thePSF was enclosed. We used elliptical regions in cases wherethe source was placed at large o ff -axis angles, resulting ina distorted PSF. This was the case, for example, for the pnobservations 0657801601 and 0657802001 of Holmberg IXX-1, observations 0112521001, 0112521101, 0657801801,0657802001, 0657802201, 0693850801, 0693850901, 0693851001, 0693851101 of M81 X-6 and observation0656580601 for Circinus ULX 5. The background region wasselected from a larger circular source-free region and on thesame chip as the source when possible. For the pn we also triedto select the background region from a distance to the readoutnode as close as possible as for the source region. Finally, forM51 ULX-7 we used regions of ∼
20" and ∼
25" for pn andMOS detectors respectively, to reduce contamination from thedi ff use emission the source is immersed in (Rodríguez-Castilloet al. 2020). We discuss possible contamination by the di ff useemission and its treatment in Section 3.1.1.We noted also that Holmberg IX X-1 and Holmberg II X-1were bright enough in some occasions to cause pile-up in the XMM-Newton detectors. We assessed the importance of pile-upusing the tool epatplot (version 1.22) when the source count ratewas above the recommended values . In order to mitigate its ef-fects, we excised the inner core of the PSF by using an annu-lar extraction region. The inner excised radius was never below10.25" and 2.75" for the pn and the MOS cameras respectively,to avoid introducing inaccuracies in the flux estimation, as rec-ommended .We finally used the tasks rmfgen (version 2.8.1) and arfgen (version 1.98.3) to generate redistribution matrices and auxiliaryresponse files, respectively. We regrouped our spectra to have aminimum of 20 counts per bin to allow the use of χ minimisa-tion and also avoiding oversampling the instrumental resolutionby setting a minimum channel width of 1 / Chandra data using the script chan-dra_repro with calibration files from
CALDB wavdetect to extract sourceevents. Background regions were selected from roughly 3 timeslarger, circular, nearby, source-free regions. The level of pile-up was assessed by inspecting the images created using the pileup_map tool. We rejected observations with a pile-up frac-tion (cid:38) ≥ ff erent mod-els. All data were also rebinned to a minimum of 20 counts perbin. NuSTAR data was processed using the
NuSTAR
Data Anal-ysis Software version 1.8.0 with
CALDB version 1.0.2. We ex-tracted source and background spectra using nuproducts with thestandard filters. Source events were selected from a circular re-gion of ∼ NuSTAR spectra to 40 counts per bin, owing tothe lower energy resolution compared to the
EPIC cameras. Forthis work, we only considered
NuSTAR observations for whichsimultaneous soft X-ray coverage with
XMM-Newton was avail-able. A summary of all observations considered can be found inTable 1. https://xmm-tools.cosmos.esa.int/external/xmm_user_support/documentation/uhb/epicmode.html https://cxc.harvard.edu/ciao/ahelp/pileup_map.html Article number, page 3 of 44 & A proofs: manuscript no. aanda
3. Data analysis and results
We used the X-ray spectral fitting package XSPEC (Arnaud1996) version 12.10.1f for spectral fitting and quote uncertain-ties on spectral parameters at the 90% confidence level for a sin-gle parameter of interest, unless stated otherwise. All fluxes wereestimated using the pseudo-model cflux in XSPEC.In general, we fitted EPIC data and the ACIS data in the0.3 – 10 keV range. For the sources with the highest absorptioncolumns (NGC 5907 ULX1, IC 342 X-1 and Circinus ULX5),we inspected the epatplot to choose the most suitable energyrange to perform spectral fitting on the EPIC data. For IC 342X-1 and Circinus ULX5, we noticed strong deviations from theobserved pattern distributions with respect to the epatplot modelbelow ∼ NuS-TAR , we typically considered the 3 – 35 keV range, although toavoid including bins with negative number of counts in the χ minimisation we restricted the high-end of the energy range tothose bins where the net number of counts was positive.When simultaneously fitting spectra from di ff erent instru-ments from the same epoch, we attempted to compensate forcalibration uncertainties by introducing a multiplicative cross-normalisation factor that was allowed to vary between the dif-ferent instruments. This factor was frozen to unity for the pn (orthe two MOS detectors if no pn data was available). We usedthe same factor for the MOS detectors as we found them to begenerally in good agreement, while FPMA and FPMB had eachtheir own separate constant, as recommended . The agreementbetween the pn and the MOS cameras was usually within errors,with a few cases in M81 X–6 where the disagreement reached upto 10%, due to the highly elliptical distorted PSF because of theo ff -axis position of the source on the detectors. The value of thecross-normalisation factor between EPIC data and
NuSTAR de-tectors was typically in agreement within the errors, reaching insome cases a 5-20% disagreement, with the largest values foundwhen the source was highly o ff -axis on the NuSTAR detectors.Finally, we fitted together i.e. we assumed the same spec-tral model for two or more datasets if they were close in time( ∼ few days) and, if after inspecting each observation separately,we found no significant variation in flux and spectral parame-ters. This is also noted in Table 1 where we quote the di ff er-ent datasets that have been fitted together based on the above.Throughout this work, we use the word epoch to refer to alldatasets that have been fitted together assuming the same model. Our first aim was to characterise the long-term spectral evolu-tion of our sample in a simple and coherent manner, by study-ing variations of the spectral components (i.e. luminosity, radius,temperature, etc). As the latest studies have revealed that the 0.3– 10 keV band can be modelled by two thermal components(e.g. Mukherjee et al. 2015; Koliopanos et al. 2017, 2019; Wal-ton et al. 2020) that can reproduce the curvature seen at high-energies, we first considered a phenomenological model basedon two multi-colour blackbody disks ( diskbb in XSPEC; Mit-suda et al. 1984) to fit the data in this band, taking into account https://heasarc.gsfc.nasa.gov/docs/nustar/nustar_faq.html interstellar absorption by neutral hydrogen with two absorbingcomponents tbabs in XSPEC. One was frozen at the Galacticvalue along the source line of sight (see Table 1), and the otherone was left free to vary to take into account possible absorptionfrom the host galaxy and the system itself. We adopted abun-dances given by Wilms et al. (2000) and cross-sections given byVerner et al. (1996) as recommended.While other models have been commonly adopted to re-produce the hard emission ( ∼ diskbb over these for various reasons. First of all, a warmoptically thick corona up-scattering photons from the disk ismerely a proxy to reproduce the curvature seen at high-energies,as its physical interpretation is subject to several caveats (seeKoliopanos et al. 2017, and references therein). Additionally,broadband spectroscopic studies have shown how this modelfails to reproduce the spectral shape of ULXs (Walton et al.2015; Mukherjee et al. 2015). Therefore, for the purpose of re-producing the spectral curvature in (at least) the XMM-Newton band, the diskbb has been shown to be equally valid with onlytwo parameters. The power-law (or a power-law with a cuto ff for the same matter) unphysically diverges towards low-energies,thus taking up flux from the soft component and causing the ab-sorption column to be overestimated.Another advantage of the dual thermal component is thatthanks to its simplicity, it can be used as a proxy to representmore complex models. For instance, in the context of super-Eddington accretion, the soft black body has been frequentlyassociated with an outflow, while the hard one has been asso-ciated with emission from the inner parts of the accretion flow(e.g. Walton et al. 2014). Alternatively, Koliopanos et al. (2017)associated the soft component with an accretion disk truncated atthe magnetospheric radius, and the hard component to the emis-sion from the magnetospheric envelope (Mushtukov et al. 2017).The diskbb also allows to test easily theoretical predictions bystudying the evolution of its temperature with its luminosity aswe show in Sections 3.4 and 3.5.However, visual inspection of the fit residuals revealedstrong residuals at high energies in the 0.3 – 10 keV band in someepochs, indicating that our phenomenological model is not ableto reproduce the emission at high energies. We show this for twohigh quality observations of Holmberg II X-1 and NGC 5408X-1 in Fig 1. This is perhaps not surprising, as broadband stud-ies using NuSTAR data have revealed the presence of a faint hardpower-law like excess dominating above ∼
10 keV (e.g. Mukher-jee et al. 2015; Walton et al. 2015, 2017). We found that for thoseepochs for which we had broadband coverage with
NuSTAR , thisexcess can be well modelled as Comptonisation of the hard / hotthermal component as noted by previous studies. Since the na-ture of this Comptonisation component is still poorly understood(Walton et al. 2017) and given the lack of broadband coveragefor most of the observations considered here, we decided to usethe simpl model (Steiner et al. 2009) to reproduce it, as it doesnot assume any geometry but simply scatters a fraction of pho-tons ( f scat ) of the seed component towards high energies emulat-ing a power-law component with a certain Γ , with the advantagethat it does not diverge towards low energies.In order to identify those epochs for which the simpl model component is required, we would ideally rely on Monte-Carlo simulations. However, given the large number of datasetsconsidered here this is not feasible. Instead, to have an es-timate as to when the data quality allows to constrain thiscomponent we performed an F-test between the dual-thermal Article number, page 4 of 44. Gúrpide et al.: Long term evolution of ULXs −5 −4 −3 P ho t on s c m − s − k e V − σ Energy (keV) −6 −5 −4 −3 P ho t on s c m − s − k e V − σ Energy (keV)
Fig. 1.
Unfolded pn (blue), MOS1(red) and MO2 (green) spectra fitted with an absorbed dual thermal component ( tbabs ⊗ tbabs ⊗ ( diskbb + diskbb ) on left observation 0200470101 of Holmberg II X-1 ( χ r ∼ right observations 0723130301 and 0723130401 of NGC 5408 X-1( χ r ∼ σ significance and aminimum of 35 counts per bin. Some clear residuals are seen at high energies indicating that the model is inadequate. model described above and the model tbabs ⊗ tbabs ⊗ ( diskbb + simpl ⊗ diskbb ) and decided to include the simpl model onlyif the probability of rejecting ( P rej ) the simpler model was ∼ σ . We also included the simpl model for observations with P rej slightly below this value if we were able to constrain its parame-ters using near-in-time observations with P rej > σ (see below).Similarly, we excluded the simpl component in some cases with P rej > σ if its parameters are largely unconstrained. We areaware that this is not an appropriate use of the F-test, however,the presence of this component was already shown to be sig-nificant by Walton et al. (2018c) and indeed we found that thiscomponent was required to fit the highest quality datasets. Weare not claiming whether this component is present or not, butinstead we used these values to have a reference as to when thedata quality allows to constrain this component. We present theresult of this F-test in Table 7 where we also indicate for whichobservations we finally included this component.For NGC 7793 P13 we found that this component is largelyunconstrained even in the broadband datasets, resulting in nofit improvement when adding this component. The broadbanddatasets yield fits with χ r ∼ simpl model is mostly responsible forthe emission above ∼ Chandra or XMM-Newton data areconsidered alone, and only in long
XMM-Newton exposures with > f scat and Γ simulta-neously. We also found good consistency between the Γ -valuesin several epochs and that most sources are found recurrently atsimilar fluxes and hardness ratios (see Section 4). We thus tied Γ across epochs where the source is found at similar flux andhardness ratio, while leaving f scat and the rest of the parame-ters free to vary. By doing so we were able to use the broadbandinformation provided by NuSTAR to have some constraints onthose epochs where this information is not available. For NGC1313 X-1, after checking the consistency of Γ across epochs andbearing in mind that its variability above 10 keV has been shownto be small (Walton et al. 2020), we tied Γ for all observationswhere the simpl model is used. For NGC 5408 X-1 and NGC6946 X-1, we also found very little variability at high-energiesand thus we again tied Γ across all observations where we addedthe simpl model. Finally, for NGC 1313 X-2, we also found that the same Γ -value can be tied for the four epochs for which weincluded the simpl model, albeit in this case the source showscertain variability at high energies (see Section 3.3).For M81 X-6, M51 ULX-7, M51 ULX-8 and M83 ULX1,given the lack of broadband coverage and that the dual-thermalmodel gave an acceptable fit to the data, we found no need to tryto improve the fit by adding the simpl model and thus we didnot explore this option. As stated in Section 2, the XMM-Newton observations of M51 ULX-7 might be contaminated by some dif-fuse emission. To quantify the possible contamination from thisdi ff use emission, we extracted two MOS1 and MOS2 spectra(from obs id 0824450901) from two circular (25" in radius) re-gions located 34" from the source in two di ff erent directions. Wefitted both emission spectra with a powerlaw and a mekal modelsubject to Galactic absorption only. The spectral parameters ofboth spectra are consistent within errors, with Γ = + . − . and2.8 ± = ± + . − . keV, for region 1 and 2 respectively. We thus ruled out strongspatial variations and computed the luminosity of region 1. Wefound a total unabsorbed luminosity of (4.9 + . − . ) × erg / s inthe 0.3 – 10 keV band, with the soft band (0.3 – 1.5 keV) being ∼ ff use emission can make the source appear ∼
25% softer in the
XMM-Newton observations, given that M51 ULX-7 has a typi-cal luminosity of 4 × erg / s. We therefore added this di ff useemission model as a fixed additive component to the M51 ULX-7 continuum in all XMM-Newton observations and decided todiscard obsids 0677980701, 0677980801 and 0830191401 whenthe source was at its lowest.Finally, some sources showed strong residuals at soft en-ergies that have been associated with unresolved emission andabsorption lines produced in an outflow colliding with the cir-cumstellar gas (Pinto et al. 2016, 2017, 2020b). In most cases,we ignored them, as we are interested in the continuum emis-sion and this will not a ff ect our results. There are two exceptionsto this: for NGC 5408 X-1, including a Gaussian emission lineat ∼ ∆ χ improvement that ranges from ∼
50 to122 (for 3 extra degrees of freedom) depending on the observa-tion. We thus decided to also determine the parameters of thisGaussian in the joint fit of the high-quality datasets, by tying to-gether all its parameter. We obtained E = ± σ = ± = + . − . × − photons / cm / s. For Article number, page 5 of 44 & A proofs: manuscript no. aanda
NGC 5204 X-1, we also included a Gaussian emission line forthe
Chandra obsid 3933 following Roberts et al. (2006) as weagain noted similar strong residuals. In this case we obtained E = ± σ = + − eV and normalisation = ± × − photons / cm / s, consistent with the values reported by Robertset al. (2006). There is still no consensus as to whether the local absorptioncolumn in ULXs is variable (e.g. Kajava & Poutanen 2009) ornot (e.g. Miller et al. 2013). The main argument for variabilityof the absorption column in ULXs is the contribution from out-flows (e.g. Kajava & Poutanen 2009; Middleton et al. 2015b),which could imprint stochastic variability in n H due to windclumps crossing our line of sight (Takeuchi et al. 2013; Mid-dleton et al. 2015a) depending on their column density and ion-isation state. Alternatively, Middleton et al. (2015b) argued thatsome expelled gas could cool down far from the source and con-tribute to the neutral absorption column. If this was the case, itis then not clear over which timescale n H would react to instan-taneous changes in the mass-accretion rate.To make matters more complicated, Miller et al. (2009)showed by studying absorption edges at high spectral resolutionin X-rays that the absorption column remains stable throughoutspectral changes in a set of X-ray binaries, and that changes inthe soft component must come from changes in the source spec-trum and not from the absorption column itself.In view of these complications, we attempted to study vari-ations of n H by fitting individually all epochs for each sourceusing the dual-thermal component over the 0.3 – 8 keV band, soas to use the same model for all epochs and avoid introducingartificial changes in n H due to the di ff erent energy ranges con-sidered when using NuSTAR data. We found that in general, thevalues of the absorption column for a given source were con-sistent within 3 σ errors throughout epochs, which we show inFigure 2 for four sources in our sample. Small discrepanciescan be attributed to low data quality (e.g. short exposure Chan-dra observations and / or calibration uncertainties) rather than realphysical- n H changes. For NGC 5408 X-1, when fitting the 0.3– 8 keV band with the dual-thermal model we still saw strongresiduals at high-energies, which may indicate that the dual-thermal model cannot adequately fit the 0.3 – 8 keV band. Wethus repeated the study of the n H variations replacing the hard diskbb with a power-law with a high-energy cuto ff ( cutoffpl in XSPEC) to ensure that the lack of mismodelling of the high-energy emission does not a ff ect the n H variations (or lack of)found before. With this model we again found all n H values con-sistent at the 3 σ level.Conversely, we did find evidence for variability in the ab-sorption column of NGC 1313 X-1 and NGC 55 ULX1 when fol-lowing the same approach, where variations above the 3 σ con-fidence level were seen (see the arrows in Figure 3). However,given the phenomenological nature of our model, we cannot ruleout that these discrepancies are due to a change of the underlyingcontinuum, changing therefore the parameter degeneracies.For the other sources not discussed, we did not find as strongevidence for variability in the absorption column as for thesources discussed above, although in some cases this could bedue to poorly constrained model parameters. Thus, in view ofthe above considerations, we considered that the absorption col-umn can be assumed to be constant for the most part, with theexception of epoch 2004-08-23 of NGC 1313 X-1 and epoch Fig. 2.
Evolution of the local absorption column over time for NGC5408 X-1 (green), NGC 7793 P13 (blue), Holmberg IX X-1 (red) andNGC 1313 X-2 (black) shifted by 0.2 10 cm − for clarity. All spectrahave been fitted with a model consisting of an absorbed dual diskbb model in the 0.3 – 8 keV band. Errors are shown at 3 σ confidence level.Circles and squares correspond to XMM-Newton and
Chandra data re-spectively.
Fig. 3.
As for Figure 2 but for NGC 1313 X-1 (black) and NGC 55ULX1 (red). Arrows indicate epochs where a 3 σ significant changes isseen with respect to some other epochs (see text for details). n H tovary together with the continuum parameters as this is preferredby the fit. We found a ∆ χ improvement of ∼
25 and 15 for NGC1313 X-1 and NGC 55 ULX1 respectively when leaving n H free,compared to the case where n H is frozen to the average value(see next Section). We discuss this in more detail in Section 4.4. Ideally, we would jointly fit all datasets for each source, tying the n H and Γ across certain datasets as explained above. However,such a procedure would be computationally prohibitive. Sincethe joint fit will mostly be driven by those datasets with higherdata quality, in order to reduce the computational burden of thisapproach we decided to do our spectral fitting in two steps: we Article number, page 6 of 44. Gúrpide et al.: Long term evolution of ULXs first jointly fitted those datasets with better statistics, tying to-gether Γ across those epochs where the source is found at sim-ilar flux / hardness ratio and n H across all epochs, while the restof the parameters are free to vary. We typically consider 3 to 8datasets for each source that include those observations with thelongest XMM-Newton exposures when the three EPIC camerasare operational, those for which simultaneous
NuSTAR coverageis available and in some rare cases, the longest
Chandra obser-vations. We next fitted individually the remaining observationsof lower data quality with n H and Γ frozen at the values found inthe joint fit. The results of the joint and the subsequent individualfits are reported in Table 2.For Circinus ULX5, the joint fit approach resulted in largelyunconstrained parameters for the low-energy components at softenergies. This is likely due to a combination of the calibrationuncertainties at low energies (see Section 3) and the high ab-sorption column along the line of sight ( n HGal = × cm − ;HI4PI Collaboration et al. 2016). We thus considered only epoch2013-02-03 to constrain n H as it o ff ers the best constrains on thebroadband emission. As a first source classification and in order to highlight the dif-ferences and similarities between the sources in our sample, westarted by building a hardness ratio luminosity diagram (HLD),similar to that often used for X-ray binaries (Done & Gierli´nski2003) and also for ULXs (e.g. Sutton et al. 2013). We did this bycomputing unabsorbed fluxes rather than counts since given thedi ff erent instruments employed for this work, relying on countrates is not feasible. Furthermore, fluxes have the advantage thatcan be corrected for absorption column. To do this, we retrievedthe total unabsorbed luminosity in the 0.3 – 10 keV band fromthe tbabs ⊗ tbabs ⊗ ( diskbb + simpl ⊗ diskbb or diskbb ), de-pending on the epoch. The hardness ratio is computed as the ratioof unabsorbed fluxes in a soft band (0.3 – 1.5 keV) and a hardband (1.5 – 10 keV). This is motivated by the fact that the pul-sating component in PULX has been shown to dominate at highenergies (e.g. Israel et al. 2017a; Walton et al. 2018b) and thuswe may expect to highlight the di ff erences between pulsatingand non-pulsating sources, while the soft component in ULXsusually stops dominating above ∼ ∼ × erg / s, with just Holmberg IX X-1 andNGC 5907 ULX1 above this value. This is also highlighted inFigure 5, where a drop in sources reaching a maximum luminos-ity ∼ × erg / s is clearly seen.Lastly, we note that as we have rejected observations below ∼ ff states below ∼ erg / slike those seen for NGC 5907 ULX-1 (Israel et al. 2017a), NGC7793 P13 (Israel et al. 2017b) or M51 ULX-7 (Brightman et al.2019) are not reflected in this diagram. We also present the temporal evolution of each individual sourcein the HLD in Figure 6, along with the unfolded spectra of someselected epochs. For this, we selected 2 to 4 clearly distinct spec-tral states based on the HLD, in order to highlight the possible range of spectral variability of each source. When possible, weselected observations for which
NuSTAR data is available so thebroadband variability can be observed. We caution that giventhe sparse monitoring o ff ered by XMM-Newton and
Chandra insome cases, care must be taken when looking at the source varia-tions in the HLD. Arrows indicate the chronological order but inmany cases we cannot guarantee that the source did not evolvedi ff erently between the epochs considered here. Several authors have attempted to study the nature of the softcomponent in ULX spectra by investigating its evolution on theluminosity–temperature (L–T) plane (e.g Kajava & Poutanen2009; Miller et al. 2013). However, these studies have frequentlyyielded contradictory results and thus there is still no consen-sus on its true nature. We thus investigated the correlation of thebolometric luminosity of the cool diskbb component with itstemperature. We did this by retrieving unabsorbed luminositiesof the diskbb component in the 0.01 – 100 keV . All fluxes arereported in Table 3. We did not attempt to derive any correla-tion for NGC 55 ULX1 and NGC 300 ULX1, due to the limitednumber of observations available for these sources.We next assessed whether L-T are correlated by running aSpearman correlation test . The results are reported in Table4. Five of our sources show a strong positive L–T correlation(Spearman correlation ≥ p -value of (cid:46) python routine odr , that takesinto account both errors on x and y variables (see Figure 7 andTable 4 for the results). In order to investigate whether these cor-relations were driven by the degeneracy between T soft and itsnormalisation, we derived 99% χ confidence contours aroundthe best-fit T soft and its normalisation for those sources showinga positive L–T correlation. Given the extensive computationaltime required by the steppar command in XSPEC, we did thisonly for some selected epochs, ensuring that at least one wasfrom the joint fit. The results are shown in Figure 8 for NGC1313 X-1, Holmberg IX X-1, Holmberg II X-1 and NGC 5204X-1, where we also overlaid the best-fit T soft and normalisationfrom all epochs. In all cases where a positive L–T correlation isobserved, including IC 342 X-1 that we did not show for brevity,a strong degeneracy between the T soft and its normalisation isobserved, highly correlated with the datapoints from the individ-ual observations, indicating that the L–T correlations are simplydue to a degeneracy between these two parameters.For M81 X-6, while the correlation test could indicate a pos-itive correlation, visual inspection of the data clearly reveals thatthere is no apparent trend (see Figure 9). We recall that the Spear-man’s test coe ffi cient does not take into account errors on the pa-rameters and hence these values need to be treated with caution.In fact, the fit with the powerlaw yields a large error on the index α = ± Similarly, we studied the hard thermal component evolution inthe L–T plane. In cases where we have employed the simpl For the jointly fitted data, this flux calculation is done taking intoaccount errors associated with all tied parameters. https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.spearmanr.html https: // docs.scipy.org / doc / scipy / reference / odr.htmlArticle number, page 7 of 44 & A proofs: manuscript no. aanda
Fig. 4.
Hardness-luminosity diagram for the ULX sample selected for this study. All fluxes and luminosities are unabsorbed. Pulsating ULXs areshown in shades of orange and the epochs were pulsations have been reported in the literature (Israel et al. 2017a; Fürst et al. 2018; Carpano et al.2018; Vasilopoulos et al. 2018; Sathyaprakash et al. 2019; Rodríguez-Castillo et al. 2020) are highlighted by a black edge around the marker. Thedashed black lines indicate respectively 10 and 100 times the Eddington limit for a neutron star ( ∼ × erg / s). Fig. 5.
Histogram of the maximum unabsorbed luminosity in the 0.3 –10 keV band attained by each source considered in this work. A cleardrop of sources with L ≥ × erg / s is seen. model on this component, we retrieved the intrinsic flux of thehard diskbb by using cflux as simpl ⊗ cflux ⊗ diskbb andfreezing the normalisation of the diskbb . Derived fluxes arepresented in Table 3 and the results from the L–T correlationin Table 5.Most of the sources show no clear correlation in the hardthermal component. The only exception is M83 ULX1, which Table 4.
Results of the L-T correlation for the soft thermal component.We quote the Spearman’s rank correlation coe ffi cient, the false alarmprobability ( p -value) and the index ( α ) of the L ∝ T α relationship withits 90% confidence level uncertainty. Source Spearman p -value α NGC 7793 P13 –0.13 0.73 - a NGC 5907 ULX1 0.57 0.14 - a NGC 5408 X-1 –0.14 0.65 - a Circinus ULX5 0.32 0.5 - a HoIX X-1 0.87 0.0005 1.31 ± b IC342 X-1 0.67 0.05 1.27 ± ± ± ± a NGC 6946 X-1 0.45 0.26 - a M83 ULX1 0.71 0.11 - a M51 ULX-7 –0.22 0.52 - a M51 ULX-8 0.54 0.108 - a Notes. ( a ) Non-correlated source. ( b ) Not considered correlated due touncertainties. shows a strong positive correlation (Spearman correlation of0.94 with a p -value = χ contours around the best-fit temperature and normalisation for Article number, page 8 of 44. Gúrpide et al.: Long term evolution of ULXs
Fig. 6.
Left: Temporal tracks on the hardness-luminosity diagram. Filled coloured markers indicate fluxes obtained from
XMM-Newton data,unfilled markers indicate fluxes obtained from joint
XMM-Newton - NuSTAR data and black-filled markers indicate fluxes obtained from
Chandra data. The legend indicates the date of the epoch in each case. Right: Unfolded spectra for selected epochs in which the source has experiencedstrong changes, following the same colour-code as for the left panels. Selected epochs are indicated in the legend. For the EPIC data, only pnis shown (circles) or MOS1 if pn is not available (as triangles up). In cases where we have used
NuSTAR data, FPMA is shown, represented assquares and with the same colour as pn.
Chandra data is shown with triangles down. The soft and hard diskbb model components are shown witha dashed line and dotted line respectively, while the total model is shown with a solid line. For epochs where the simpl model has been used seeTable 2. Data has been rebinned for clarity. Article number, page 9 of 44 & A proofs: manuscript no. aanda
Fig. 6.
Continued some selected epochs and overlaid the results from the spectralfitting on them as shown in Figure 10. In this case, it seems thatthe degeneracy between these two parameters is not driving theexisting correlation.While NGC 6946 X-1 might seem positively correlatedbased on the Spearman test alone, examination of the data clearlyrevealed that there is an overall lack of strong variation of thehard component in most observations (see Figure 11). Further-more, we noted a certain bias in those observations for which wehave not included the simpl model, as the temperature of thehard diskbb appears to be systematically higher, as the diskbb is pushed towards high-energies due to the lack of an additionalhigh-energy component.
4. Discussion
We have examined the long-term spectral evolution of a sampleof sources containing known pulsating and ULXs for which theaccretor is unknown, in order to gain insights on their nature andthe accretion processes driving their extreme luminosities. Whileour spectral fitting approach is phenomenological, we have at-tempted to understand the nature of the soft and the hard com-ponents by means of L–T correlations. The positive L–T corre-lations for the soft component found in Section 3.4 are broadlyconsistent with previous results reported by Miller et al. (2013), who studied a similar sample of sources and also assumed a con-stant absorption column, albeit using a di ff erent model based onan accretion disk whose photons are Compton-up scattered by anoptically thick corona of hot ( T e > diskbb and apowerlaw. These correlations have frequently been used to arguein favour of an accretion disk as the nature of the soft componentin ULXs. However, our analysis reveals that these are driven bythe existing degeneracy (see Figure 8) between the temperatureof the soft component and its normalisation and thus these rela-tionships cannot be used reliably to support this scenario. Indeed,it has been shown that depending on the assumption of the un-derlying model, the correlation can disappear entirely (see e.g.Luangtip et al. 2016; Walton et al. 2020) (see also Gonçalves& Soria (2006) for a discussion on the weaknesses of associ-ating the soft component with an accretion disk). Nevertheless,these correlations might be useful to identify sources evolving ina similar fashion.Conversely, the positive L–T correlation found for the hardthermal component of M83 ULX1 might have a physical ori-gin as we argue in Section 4.6, given that this correlation is notdriven by the existing degeneracy between the parameters (seeFigure 10). Article number, page 10 of 44. Gúrpide et al.: Long term evolution of ULXs
Fig. 6.
Continued
Similarly, Kajava & Poutanen (2009) used the found nega-tive L–T correlation for the soft component to argue in favour ofan outflow as the nature of the soft component. However, this re-sult was likely artificially created by employing a powerlaw forthe high-energy emission while leaving the absorption columnfree to vary. We thus suggest that the beaming formalism de- rived by King (2009) using the results from Kajava & Poutanen(2009), linking the mass-transfer rate ( ˙ m ) with the beaming fac-tor ( b ) for super-Eddington accretion onto BHs or weakly mag-netised NSs, should be revisited in view of these new results.Overall, our study suggests that given the limitation from us-ing phenomenological models to describe the ULX continuum, Article number, page 11 of 44 & A proofs: manuscript no. aanda
Fig. 6.
Continued the observed changes in the best-fit spectral parameters may notbe the most appropriate way to build a physical picture for oursources. For this reason, most of our discussion will be basedon the variability observed in terms of luminosity and hardnessratios (see Figures 4 and 6).Figures 4 and 5 show that most sources seem to have a max-imum luminosity of roughly 2 × erg / s. M51 ULX-7 andM82 X-2 (the other PULX not analysed in this work) also reachluminosities of a few × erg / s (Brightman et al. 2016, 2019).While the sample presented here is rather small in a statisticalsense, it has the advantage that we have taken into account thelong-term variability of each source, it is also free of contami-nants and the absorption column has been carefully estimated.On this basis, our work seems to support larger sample studies(Swartz et al. 2011), where a possible cuto ff at around 2 × erg / s was observed in the luminosity function of a sample of 107ULX candidates. Mineo et al. (2012) showed that ULXs seem toextend the X-ray luminosity function of HMXBs up to a possibleenergy cuto ff also at around 2 × erg / s, supporting ULXs asbeing an evolutionary stage of HMXBs. Thus, ULXs might berelated to systems where the companion star expands and startsto fill its Roche Lobe as suggested by King & Lasota (2020). AsNS accretors are more numerous among HMXBs (e.g. Casareset al. 2017), it is possible that a substantial fraction of ULXswith L x ∼ − erg / s could host NS. However, we stress that given the limited sample studied here, we may be running intosmall numbers when distinguishing a cuto ff distribution from apowerlaw one (Walton et al. 2011).A luminosity cuto ff around 2 × erg / s would be consis-tent with the maximum accretion luminosity NSs can attain ac-cording to Mushtukov et al. (2015). The authors considered theaccretion column model proposed by Basko & Sunyaev (1976)and the reduction of the electron scattering cross-section in thepresence of high-magnetic fields, that allows to overcome theEddington limit. Mushtukov et al. (2015) suggest that NSs couldreach ∼ erg / s for a reasonable parameter space of magneticfields and spin periods. Indeed, the hard component (the diskbb or the more complex simpl ⊗ diskbb when applicable), that wewould associate with the accretion column (e.g. Walton et al.2018a), reaches a maximum luminosity of ∼ erg / s in NGC7793 P13, M51 ULX-7 and NGC 1313 X-2. However, the factthat we find a PULX (NGC 5907 ULX1) also above the break isproblematic. The hard component is a factor ∼ Article number, page 12 of 44. Gúrpide et al.: Long term evolution of ULXs
Fig. 6.
Continued the maximum luminosity with the mass-accretion rate (Narayanet al. 2017), as their models start to become radiatively ine ffi cientabove ∼
10 ˙ M Edd . Their simulations show that the observed lumi-nosity saturates at 2 × erg / s for a 10 M (cid:12) black hole viewedclose to face-on, which might be supported by our observations. The mass-transfer rate ( ˙ m ) in ULXs is generally acceptedto be super-Eddington, even if the sustainability of such processat such extremes over long timescales (sometimes over severaldecades) has still to be understood. Models put forward to ex-plain the emission of super-Eddington accretion onto black holespredict that as the mass-transfer rate increases beyond the classi- Article number, page 13 of 44 & A proofs: manuscript no. aanda
Fig. 6.
Continued cal Eddington limit, a radiatively driven outflow will be launchedfrom within the spherisation radius (R sph ), the radius at whichthe disk reaches the local Eddington limit (Shakura & Sunyaev1973; Poutanen et al. 2007). The outflow leaves an optically thinfunnel around the rotational axis of the compact object, so that atlow inclinations we see a hard spectrum dominated by the inner parts of the disk (Hard ULXs: Sutton et al. 2013). At higher in-clinations the outflow becomes optically thick to Thomson scat-tering (Poutanen et al. 2007) and thus an observer at such in-clinations should see a softer and fainter spectrum (soft ULXs:Sutton et al. 2013) as most of the emission will be Comptondown-scattered in the wind before reaching the observer (Mid-
Article number, page 14 of 44. Gúrpide et al.: Long term evolution of ULXs
Fig. 7.
Examples of sources showing a positive correlation between the soft diskbb component unabsorbed bolometric luminosity and its tem-perature. Black line shows the best fit power-law with grey shaded areas indicating the 90% confidence interval on the exponent. Symbols arecoloured as per Figure 6. The data have been fitted with the model tbabs ⊗ tbabs ⊗ ( diskbb + simpl ⊗ diskbb or tbabs ⊗ tbabs ⊗ ( diskbb + diskbb ) (see text for details). Table 5.
Results of the L–T correlation for the hard thermal component.Columns as per Table 4.
Source Spearman p-value α NGC 7793 P13 0.45 0.19 - a NGC 5907 ULX1 0.52 0.18 - a NGC 5408 X-1 0.49 0.01 - a Circinus ULX5 –0.46 0.29 - a Ho IX X-1 0.31 0.38 - a M81 X-6 –0.08 0.83 - a IC342 X-1 0.05 0.91 - a NGC 1313 X-1 0.3 0.2 - a NGC 5204 X-1 0.15 0.58 - a Ho II X-1 –0.37 0.47 - a NGC 1313 X-2 –0.07 0.73 - a NGC 6946 X-1 0.90 0.002 - b M83 ULX1 0.94 0.005 4.36 ± a M51 ULX-8 –0.17 0.67 - a Notes. ( a ) Non-correlated source. ( b ) Not considered correlated due touncertainties (see text for details) dleton et al. 2015a; Kawashima et al. 2012). A corollary of thisscenario is that as the wind funnel narrows as the mass-accretionrate increases (King 2009; Kawashima et al. 2012) and the windstarts to enter our line of sight, the contribution from the softcomponent will dominate the emission, as the wind starts todown-scatter out of the line of sight part of the hard emission.Therefore, a source with a hard ULX aspect could shift to a softULX aspect under certain conditions. A similar e ff ect can occurif the source precesses (Abolmasov et al. 2009; Middleton et al.2015a), but we may see di ff erences in the long-term variabilitybetween these two scenarios. The increase in the mass-accretionis also expected to increase the Thomson optical thickness ofthe gas within the funnel, preventing high-energy photons fromescaping to the observer without being scattered (Narayan et al.2017; Kawashima et al. 2012). It is argued that, in extreme cases,either due to a high-mass accretion rate or / and higher inclina-tion angle, a source may appear as a super-soft ultraluminoussource (ULS) (Urquhart & Soria 2016), where most of the emis-sion comes from the wind photosphere.One key observational property of the presence of the funnel-like structure created by strong outflows is highly anisotropicemission. While a relationship between anisotropy and super-Eddington mass-transfer rates may be a natural consequence of Article number, page 15 of 44 & A proofs: manuscript no. aanda
Fig. 8. χ contours (solid black lines) between T soft and its normalisation for sources showing a positive L–T correlation. For each source, 2to 4 di ff erent epochs are represented with the epoch indicated next to the contour. A clear anti-correlation is seen in all cases that closely followsthe best fit values from all the epochs (blue datapoints, 90% confidence level error bars), which indicates that the L–T positive correlation is dueto the degeneracy between these two parameters. For the sake of readability, we have ignored epoch 2004-06-05 in the panel of NGC 1313 X-1 asit had a much higher normalisation ( ∼
51) compared to the other observations. super-Eddington accretion onto black holes (King 2009), NSmay have means to circumnavigate this relationship. Crucially,in the presence of a strong magnetic field, the disk might be trun-cated before radiation pressure starts to be significant to inflatethe disk and drive strong outflows (e.g. Chashkina et al. 2019).This occurs when the magnetospheric radius, given by: R m = ξ R B GM NS ˙ M / (1)where R NS is the radius of the neutron star, B is its magnetic field,M NS is the mass of the neutron star, ˙ M is the mass accretion rateat R m and ξ is a dimensionless parameter that takes into accountthe geometry of the accretion flow and is usually assumed to be0.5 for an accretion disk (Ghosh et al. 1977), is larger than thespherisation radius (R sph ). R sph in turn has a linear dependenceon ˙ m . This o ff ers means for a NS to be fed at high-mass trans-fer rates, while largely reducing anisotropy. On the other hand,we may expect that for weakly magnetised NSs, the disk willbecome super-critical given the dependency of R m on B . In thiscase the emission will be collimated by the outflow in a similarfashion as for super-critically accreting black holes (e.g. Kinget al. 2017; Takahashi & Ohsuga 2017). Additionally, we mayexpect a NS with strong outflows to appear softer, as outflowswill Compton down-scatter the emission from the accretion col-umn. We therefore can make use of the long-term variability ob-served in the HLD to discuss which scenario best describes thevariability observed in each source: super-Eddington accretiononto BHs, weakly magnetised NSs or highly magnetised NSs.At the same time, the wealth of data analysed in this work al-lows us to identify groups of sources showing common evolutionand similar spectral states, while identifying new NS-ULX can-didates based on their similarity with the PULXs. Given that ouranalysis focuses on discussing the spectral transitions observedin the HLD (see Figure 6), our study is less constraining for NGC6946 X-1 and NGC 5408 X-1 , given the lack of marked spectralstates. We therefore do not attempt to o ff er any interpretation forthese two sources.Finally, a common characteristic of the PULXs seems to bea hard spectrum accompanied with high-levels of variability athigh-energies ( (cid:38) and its high spectral variabilityat high energies as we discuss in Section 4.3. This high-energycomponent is likely associated with emission from the accretion Note that the increase of luminosity of NGC 5408 X-1 in 2001 isless certain given the short exposure of the 2001 observations and ourassumption of constant n H .Article number, page 16 of 44. Gúrpide et al.: Long term evolution of ULXs Fig. 9.
As for Figure 7 but for sources showing no correlation between the soft diskbb bolometric luminosity and its temperature.
Fig. 10.
Left: As for Figure 7 for M83 ULX1 for the hard diskbb . Right: As for Figure 8 for the countours around the best-fit T hard and itsnormalisation for three selected epochs of M83 ULX1. The degeneracy between these two parameters can be ruled out as the cause of the positiveL–T correlation. column in the case of PULXs (Walton et al. 2018b,c) and may of-fer means to distinguish NS- and BH-ULXs (which we discuss inSection 4.5). While IC 342 X-1 and Circinus ULX5 also show ahard spectra with high-levels of variability at high-energies, theyboth show a soft and dim state that we argue is akin to that seenin NGC 1313 X-1, a much softer source with relatively stablehigh-energy emission (see Figure 6) and thus we discuss themin Section 4.4.1. Nevertheless, we stress that the spectral simi-larity across the sample is undeniable as also noticed in previousstudies (e.g. Pintore et al. 2017; Walton et al. 2018c).
Remarkably, our analysis shows (Figure 4) that PULXs areamong the hardest sources in our sample, something also notedby Pintore et al. (2017) employing a colour-colour diagram. In-terestingly, PULXs with higher pulse-fractions, e.g. NGC 7793P13 (PF ∼ ∼ ∼ ∼
5% Sathyaprakash et al. 2019). Figure 6shows that harder PULXs show little variability in the HLD (seethe case of NGC 7793 P13 and M51 ULX-7 ), while in contrastNGC 1313 X-2 shows strong changes in hardness by a factor of ∼
3, without undergoing to the propeller regime. Below we dis-cuss whether these di ff erences in the long-term evolution couldbe explained due to the di ff erent interplay between R m and R sph .We note that in the super-Eddington regime, the interaction be-tween the magnetic field and the disk is likely to be more com-plex than as predicted by Equation 1 as radiation pressure candominate over the gas ram pressure (Takahashi & Ohsuga 2017;Chashkina et al. 2019) but for the qualitative picture discussedhere we neglect these facts. For NGC 300 ULX1, given the lim-ited number of observations we cannot o ff er a detailed discus-sion as for the other sources and thus we will not consider thissource further. Note that epochs 2003-01-15 and 2013-11-25 of NGC 7793 P13and M51 ULX-7, where the sources are found in a softer and dimmerstate, are likely associated with the sources resuming from the propellerregime. Article number, page 17 of 44 & A proofs: manuscript no. aanda
Fig. 11.
Bolometric luminosity of the hard diskbb component as afunction of its temperature for NGC 6946 X-1. Due to the uncertaintiesassociated with the parameters, we do not consider these two quantitiesto be correlated (see text for details). Symbols as per Figure 6.
NGC 1313 X-2 : R m < R sph – This source shows a strong bi-modal behaviour in the HLD (see Figure 6 and also Feng &Kaaret 2006; Pintore & Zampieri 2012) that is likely associ-ated with the 158 day quasi-periodicity reported by Weng &Feng (2018) using Swift -XRT data, although an association isnot straightforward since several periodicities are found in theperiodogram presented by the authors. Our analysis reveals thatthis bi-modal behaviour is driven by a highly variable hard com-ponent while the soft emission is rather stable (the soft diskbb varies by a factor (cid:46) (cid:46)
5, see Figure 9). This bi-modal be-haviour is confirmed by
Swift -XRT long-term monitoring (Weng& Feng 2018).This variability is unlikely to be produced by the propellere ff ect, where the centrifugal barrier of the magnetosphere pre-vents further infalling of gas onto the NS (Illarionov & Sunyaev1975), as for a period of ∼ ∼
220 (see forinstance equation 5 from Tsygankov et al. 2016) assuming a NSradius of 10 km and a mass of 1.4 M (cid:12) , whereas the observed dropin luminosity from brightest to dimmest is only about a factor ∼ al-ways smaller than the co-rotation radius, the radius at which theKeplerian disk velocity equals the rotation of the NS. We thusrequire that at the minimum luminosity observed in the source,R m < R C . We can rearrange equation (37) from Mushtukov et al.(2015) to derive an upper limit on the magnetic field strength: B (cid:46) . × ξ − / m / R − / P / L / intr (2)where L intr is the minimum intrinsic luminosity in units of 10 erg / s, B is the magnetic field in units of 10 G, R is the NSradius in units of 10 cm, m is the NS mass in M (cid:12) , P is theperiod in seconds and ξ is the same dimensionless parameter asfor Equation 1 which we take again to be 0.5. We can express theintrinsic luminosity in terms of the observed luminosity takinginto account a beaming factor ( b ) (e.g. King & Lasota 2020) sothat L intr = b L observed with b ≤
1. Setting L observed = ± = m = P = B = ( b / ± × G.Thus, this suggests that we can rule out extreme magnetic fields( B ≥ G) for moderate values of b ( (cid:46) ∼ sph > R m and therefore outflows andprecession cause the emission to be highly anisotropic. This isalso supported by the recent ray tracing Monte-Carlo simulationsof Mushtukov et al. (2021), showing that larger scale-heightflows lead to lower pulse-fraction due to the increased numberof scatterings. NGC 7793 P13 and
M51 ULX-7 : R m > R sph – Conversely,both the long-term evolution of NGC 7793 P13 and M51 ULX-7show little variability in terms of hardness ratio, albeit also be-ing associated with super-orbital periodicities, of 66.9 days (seeFürst et al. 2018, Figure 5) in the case of NGC 7793P13 and of39 days in the case of M51 ULX-7 (Vasilopoulos et al. 2020). In-deed, long-term Swift -XRT monitoring shows no clear bi-modalbehaviour (Weng & Feng 2018) in a hardness-intensity diagramin the case of NGC 7793 P13. Both sources also show very hothard component (T hard ∼ ∼ ∼ m is similar to that of supercritically accreting black holes, our soft diskbb could represent the emission from the outer regions ofthe accretion disk, with partial reprocessing by the wind if R m > R sph (Kitaki et al. 2017). If we consider that this model com-ponent can give us a rough estimate of the size of this emittingregion, a larger emitting area compared to NGC 1313 X-2, forwhich we have argued that outflows are important, could indi-cate that the disk is being truncated further from the accretor inthe case of NGC 7793 P13 and M51 ULX-7. To illustrate this,we compute the mean radius of the inner disk given by the soft diskbb normalisation ( N ) from all epochs. Using: R in = (cid:112) N / cos i × D × f (3) Article number, page 18 of 44. Gúrpide et al.: Long term evolution of ULXs −5 −4 −3 E F E ( k e V c m − s − k e V − ) NGC 1313 X−210.5 2 5−202 σ Energy (keV)
Fig. 12.
Unfolded spectra of NGC 1313 X-2 of epoch 2017-06-20 (onlypn is shown for clarity) fitted with an absorbed dual thermal-component.The soft and hard diskbb components are shown with dashed line andthe dotted line respectively, while the total model is shown with a solidline. Strong residuals are seen at soft energies at around 1 keV. where i is the inclination of the system, D is its distance inunits of 10 kpc and f col is the colour correction factor (Shimura& Takahara 1995) which we take as 1.8 (e.g. Gierli´nski & Done2004) throughout this paper. This gives 1637 + − (cos i ) − / km,1975 + − and 2257 + − (cos i ) − / km for NGC 1313 X-2, M51ULX-7 and NGC 7793 P13, respectively. Naively assuming thisradius gives a rough estimate of the size of the magnetosphericradius (R m ), it may indicate a higher-mass accretion rate forNGC 1313 X-2 (and / or a lower magnetic field strength) and thusa scenario in which the disk becomes thick and outflows causeanisotropic emission. Instead, the larger radius of NGC 7793 P13and M51 ULX-7 may suggest that either the mass-accretion rateis lower or the magnetic field strength is higher, which can re-sult in the disk remaining geometrically thin (see also Chashk-ina et al. 2017) and therefore in reduced anisotropy. We notethat these would support previous studies by Koliopanos et al.(2017), where the same relationships for R m and R sph were foundfor NGC 7793 P13 and NGC 1313 X-2 (see their Table 2 and 4).Assuming the mass-accretion rate varies within a similarrange in the three sources, a stronger magnetic field in NGC7793 P13 and M51 ULX-7 is also supported by the fact bothsources undergo periods of inactivity to (cid:46) erg / s, likelyassociated with the propeller regime (e.g. Fürst et al. 2016;Vasilopoulos et al. 2021), indicating that the condition R m > R C is more easily achieved. Furthermore, the lower pulse-fractionof NGC 1313 X-2 compared to that of NGC 7793 P13 and M51ULX-7 is consistent with less material reaching the magneto-sphere and thus the accretion column, as a result of the mass lossin the disk. Therefore, the emission at high-energies is not onlyintrinsically diminished but also down-scattered in the outflow(Mushtukov et al. 2021), which might explain why NGC 1313X-2 is generally softer than NGC 7793 P13 and M51 ULX-7.We thus suggest that the magnetic field in NGC 7793 P13and M51 ULX-7 is likely to be higher than that of NGC 1313X-2 so that R m > R sph . The low degree of beaming and high-magnetic field implied by this solution is in agreement withprevious magnetic field estimates (Vasilopoulos et al. 2020;Rodríguez-Castillo et al. 2020), that suggested a magnetic fieldof ∼ G in M51 ULX-7.
NGC 5907 ULX1 : R m ∼ R sph – Contrary to the rest of PULXsin our sample, the luminosity of NGC 5907 ULX1 clearly ex-ceeds 10 erg / s. The variability between the observations clus-tered at L X ∼ (6–8) × erg / s (epochs 2003 and 2014) andepoch 2012 was shown to be associated with di ff erent phasesof the 78-day super-orbital period (Walton et al. 2016a) of thesource by Fürst et al. (2017). This suggests that these changesare not due to a change in the mass-accretion rate and suggestsinstead changes in the viewing angle as the sources precesses.It has been speculated that the extreme luminosity of the sourcecould be due to a high-degree of beaming (e.g. King et al. 2017;King & Lasota 2019), in which the super-orbital modulation wasdue to a conical outflow beaming the emission into and out ofour line of sight (e.g. Dauser et al. 2017). However, our Figure6 shows that the source is harder when it becomes dimmer inepoch 2012-02-09 (see also Figure 3 from Sutton et al. 2013)compared to epochs 2003 / sph ≤ R m is likely in the case of NGC 5907ULX1.We note that other mechanisms could also cause the lumi-nosity to be overestimated under the assumption of isotropicemission. In fact, the emission from the accretion column isnot expected to be emitted isotropically. Instead, radiation-hydrodynamic simulations of super-Eddington accretion ontomagnetised NSs by Kawashima et al. (2016) show that the ac-cretion column is expected to have a flat emission profile alongits sides, as the emission is only able to escape through the lateralsides of the confined material in it. This naturally creates highlyanisotropic emission and can cause the observed emission to begreatly in excess of the Eddington limit.A high ˙ m is still likely required to produce the observedluminosities. This may require the presence of a strong magneticfield so that the disk is truncated roughly at the point where itbecomes supercritically. Thus, as suggested previously (Waltonet al. 2018c; King & Lasota 2019) R sph ∼ R m seems a plausiblecondition to explain the high-luminosity of NGC 5907 ULX1. This source was identified as a NS through the identification ofa possible cyclotron resonance feature (Brightman et al. 2018) . We note that its position in the HLD (see Figure 4) maybe consistent with a lack of pulsations (Brightman et al. 2018),as this source is markedly dimmer and softer than the overallPULX sample, and sources with higher pulse fractions tend tosit in the harder end of the diagram, as stated before. However,given the apparent lack of variability, it is hard to give a com-parison between this source and other PULXs in our sample.Strong variability is only observed in epoch 2018-05-25, wherethe hard component increased by a factor of 2 in luminosity. Itsbehaviour is somewhat similar to NGC 1313 X-2 and M81 X-6, that we argue is a good PULX candidate (see Section 4.3),although we lack enough observations of the source at higher lu-minosities to confirm this similarity. The soft component showsalso little variability and no clear correlation, suggesting again alink between these three sources, which would favour a weaklymagnetised NS in M51 ULX8 in agreement with the study pre- Chandra obs id 13813, where the putative line was identified byBrightman et al. (2018) was not considered in this work due to a certaindegree of pile-up a ff ecting the observation.Article number, page 19 of 44 & A proofs: manuscript no. aanda sented by Middleton et al. (2019). Should this be the case, thenlong-term monitoring of the source will be crucial to attempt toidentify any quasi-periodicity similar to those seen in NGC 1313X-2 and M81 X-6.
M81 X-6 – As stated above, M81 X-6 constitutes our best NS-ULX candidate. The spectral evolution and the track in the HLDfor this source is strikingly similar to that of NGC 1313 X-2(Figure 6). Both sources transit back and forth from a soft (HR (cid:46) (cid:46) × erg / s) to a hard (HR ∼ diskbb changes by afactor (cid:46) (cid:46) tingray (Huppenkothen et al. 2019). Unfortunately, all of theobservations except one have less than 5000 counts in pn, andtypically 10000 counts seem to be required in order to detectpulsations (Rodríguez-Castillo et al. 2020). We thus searched inthe observation with the longest exposure ( ∼
73 ks in pn, seeTable 1 and Figure 6 epoch 2001-04-23, HR ∼ L ∼ × erg / s) suitable for pulse searches, assuming M81 X-6 has a pe-riod and period derivative similar to the other PULXs. We usedthe Chandra coordinates given by Swartz et al. (2003) to extractbarycentred corrected events in the 0.2 – 12 keV band. We ranHENDRICS on the unbinned event file searching for coherentpulsations in the 0.2 – 8 Hz range, based on previous PULXdetections, using the Z statistic (Buccheri et al. 1983) suitablefor sinusoidal pulses. The search was performed using the op-tion fast , that optimises the search in the f – ˙ f space and reducesthe computational time 10–fold compared to a classical search.We found no detection above the 3 σ level. We ran the samesearch in the 4 longest GTI intervals, ranging from 20 ks to 40ks, as pulsations in PULXs have been shown to vary during thecourse of an observation (e.g. Bachetti et al. 2020), but again wedid not find any significant detections. Overall there is no peakthat can be robustly identified as several peaks with similar Z power are found, well below the 3 σ level. We also looked in thepn data of the individual observations with shorter exposures,but found no significant detections. We performed a last searchlooking into the 0.02 – 0.2 Hz range to look for longer periodsas those seen in NGC 300 ULX1 (see e.g. Vasilopoulos et al.2018), with similar results. This could indicate that pulsations inthis source are as elusive and faint as those found in NGC 1313X-2 (Sathyaprakash et al. 2019) and that deep exposures withthe source on-axis or deeper searches correcting for the orbitalparameters will be required to detect pulsations.Alternatively, the source spectral state may play a role inthe detectability of the pulsations. Considering the case ofNGC 1313 X-2, the epochs when pulsations were detected bySathyaprakash et al. (2019) are 2017-09-02 and 2017-12-09 (i.e.the last two epochs in Figure 6). The authors also found that the pulse fraction (and hardness, as shown in this work, Figure 4)decreases with the source luminosity. As argued before, we un-derstand the hardening of the source as a decrease in the view-ing angle as the system precesses. Considering the pulse-fractioncalculations for super-critical accretion columns proposed by In-oue et al. (2020), this might imply that the angle between the ro-tational axis and the magnetic field axis ( Θ B ) is greater than theangle between the observer’s line of sight and the rotational axis( Θ obs ) (e.g. Θ B > ◦ and Θ obs < ◦ , see Figure 5 from Inoueet al. (2020)). Assuming the same applies to M81-X6, this couldimply that pulsations are more likely to be found in softer anddimmer states (HR ∼ ∼ × erg / s) where we expectthe pulse fraction to be higher.If instead, the dilution of the pulsed emission is mainly dueto a stochastic process such as multiple scatterings through thewind, then it may be possible to find a PULX in similar spec-tral states, with and without pulsations. Nevertheless, studyingthe dependence of the appearance of pulsations on the sourcespectral states seems a promising tool to put constraints on theaccretion flow geometry in PULXs. Several of the softer sources for which the accretor is unknownshow a common pattern in their long-term evolution: three dis-tinct spectral states, two of them at similar low luminosities butdistinct hardness and a third one at a higher luminosity (see forinstance NGC 1313 X-1, Circinus ULX5 and IC342 X-1 in Fig-ure 6). Two other sources that show also three marked spectralstates are Holmberg II X-1 and NGC 5204 X-1, albeit the lumi-nosity of the dimmer states di ff er in this case by a factor of ∼ ff erence in luminosity between one of the two dim statesand the bright state might be naturally explained by changes in˙ m . However, the presence of an additional dim state requiresanother explanation. A super-critical funnel, as we discuss be-low, may o ff er an explanation to these three states either throughobscuration as ˙ m increases (sources in Section 4.4.1) or dueto changes in the inclination of the system (sources in Section4.4.2). Given some of the common transitions and other spectralproperties as we show below, we discuss together NGC 1313 X-1, Holmberg IX X-1, NGC 55 ULX1, Circinus ULX5 and IC342 X-1 in Section 4.4.1 and Holmberg II X-1 and NGC 5204X-1 in Section 4.4.2.For the discussion, we will use NGC 1313 X-1 as our bench-mark to discuss some of the transitions observed to the soft anddim states. In some cases, the timescale between these transi-tions and the duration of each state are poorly constrained due tothe sparsity of our data. However, in a few cases, like for NGC5204 X-1 and NGC 1313 X-1, the sampling rate is high enoughso that we do observe the source switching from one state toanother and thus we refer to these changes as transitions. NGC 1313 X-1 and
Holmberg IX X-1 – As we show later, NGC1313 X-1 undergoes a transition similar to that observed in thesuper-soft ULXs in NGC 247 Feng et al. (2016) and M101 (So-ria & Kong 2016), which are seen to transit from ULSs to a softULXs spectra. A similar transition is also seen in NGC 55 ULX1(Pinto et al. 2017) (and in this work as we argue later), althoughthe source would still classify as a ULX when in this dim-state.These transitions are all marked by an increase in the size of theemitting region of the soft component and a decrease in tem-
Article number, page 20 of 44. Gúrpide et al.: Long term evolution of ULXs perature, interpreted as an expansion of the wind photosphereas the spherisation radius increases with the corresponding de-crease in temperature (Poutanen et al. 2007). While the ULXs inM101 and NGC 247 are frequently thought to be viewed at highinclinations (e.g. Ogawa et al. 2017), NGC 1313 X-1 is likelyviewed down the optically thin funnel (e.g. Poutanen et al. 2007;Narayan et al. 2017), so that the hard component dominates theemission (epoch 2012-12-16 in Figure 6).The spectral transitions of NGC 1313 X-1 between the lowstate (L ∼ × erg / s, epoch 2012-12-06) and the high-state(L ∼ × erg / s, epoch 2004-06-05) have been frequentlyinterpreted as the wind entering our line due to a narrowingof the funnel as the mass-accretion rate increases (e.g. Suttonet al. 2013). However, the fact that the high-energy emission( (cid:38)
10 keV) remains relatively stable may be at odds with thisinterpretation, as we should expect the wind to down-scatter(Kawashima et al. 2012; Middleton et al. 2015a) or even absorb(Abolmasov et al. 2009) the high-energy emission from the innerparts of the accretion flow. We should also expect the increase inthe mass-transfer rate to lead to an increase in the Thomson scat-tering optical depth of the funnel (Kawashima et al. 2012), alsocausing the high-energy emission to drop.The physical processes at play to produce these high-energyphotons are still poorly understood (e.g. Walton et al. 2020) but itis generally accepted that this emission is produced in the vicin-ity of the accretor (e.g. Kawashima et al. 2012; Takahashi et al.2016; Walton et al. 2020). For the remainder of this part, we as-sume that this high-energy component is indeed produced in theinner regions of the accretion flow and focus on the influence ofthe wind / funnel structure on the spectra, rather than on the originof this emission, which will be discussed in Section 4.5.The fact that the high-energy component remains stable,could therefore imply that the gas within the funnel has remainedoptically thin over a certain range of mass-transfer rate, and thatthe inclination of the system ( i ) remains well below the half-opening angle of the funnel ( θ f ). The second condition is re-quired so that the higher degree of beaming caused by the re-duction of θ f , will only result in an increase in the amount ofphotons that are down-scattered o ff the wind walls into the ob-server’s line of sight, with the wind remaining out of the line ofsight. Since the optical depth of the wind is lowest near the ro-tational axis of the compact object (Poutanen et al. 2007), theemission from the innermost regions are more likely to reachthe observer without su ff ering severe energy loses (Kawashimaet al. 2012). This may support previous works suggesting thatNGC 1313 X-1 is seen at low viewing angles (e.g. Middletonet al. 2015a).The lack of obscuration of the high-energy emission suggeststhat the mass-accretion rate has to be moderate ( ˙ M (cid:46)
10 ˙ M Edd ) as for higher mass-transfer rates the gas within the funnel isexpected to become optically thick (Narayan et al. 2017). There-fore, regardless of the exact nature of this high-energy powerlawtail, we argue that albeit the increase in mass-accretion rate inNGC 1313 X-1 up to epoch 2004-06-05, the physical conditionswithin the funnel have remained stable. The similar persistenthigh-energy emission seen in Holmberg IX X–1 and the simi-lar L–T positive correlation, suggests a similar evolution in bothsources, albeit NGC 1313 X–1 is seen in an obscured state (seebelow) not seen in Holmberg IX X–1. We discuss in more detailthe possible di ff erences between these two sources focussing onthe nature of the high-energy tail in Section 4.5. Here we adopt the definition of ˙ M of (Narayan et al. 2017) where ˙ M = L Edd η c where η depends on the black hole spin. Interestingly, after NGC 1313 X–1 reaches its maximum lu-minosity (epoch 2004-06-05), it becomes extremely soft andits luminosity decreases (epoch 2004-08-23 – obscured state ).This spectral transition (note that these two observations are justtwo months apart) can be understood if a further increase in themass-accretion rate leads to a narrowing of the opening angle ofthe funnel as the wind becomes more mass-loaded, to the pointwhere the gas within the funnel becomes optically thick to thehigh-energy radiation. This implies that now θ f < i and thus thewind e ff ectively enters the line of sight and starts obscuring theinner accretion flow. The optical depth of the wind in the direc-tion parallel to the disk is also expected to be an order of magni-tude higher than in the perpendicular direction (Poutanen et al.2007). High-energy photons are now heavily down-scattered orabsorbed and therefore we mostly observe the soft emission fromthe expanded wind photosphere, as supported by the increase inthe normalisation of the soft component (from ∼ ∼
50 beforeand after the obscuration respectively).This transition is also in good agreement with the GR-RMHD simulations presented by Narayan et al. (2017) of super-Eddington accretion onto black holes. The authors observe atransition from a hard spectrum to a very soft one, as the mass ac-cretion rate increases ( ˙ M ∼
23 ˙ M Edd from their simulations) andthe gas within the funnel becomes optically thick (see their Fig-ure 9). Furthermore, their simulations also show that the lumi-nosity for an observer with a line of sight close to the rotationalaxis of the accretor ( i ∼ ◦ ) is capped at around 2 × erg / s,which is in very good agreement with the maximum luminos-ity observed in NGC 1313 X-1. Their simulations also predictan increase in the spectral emission at low energies ( (cid:46) (cid:38)
23 ˙ M Edd ), do not observe an in-crease in luminosity at low energies. It is also possible that due tothe expansion of the photosphere, the soft component peaks nowin the extreme UV and thus given our limited bandpass, we can-not reliable assess whether the luminosity of the soft componenthas increased.Numerical simulations by Ogawa et al. (2017) also predict asteep decline of the high-energy emission as the outflow photo-sphere enters the line of sight. We find that the temperature ofthe hard diskbb diminishes from 1.6 ± + . − . keV in epoch 2004-08-23 and its unabsorbedbolometric luminosity decays from (11.2 ± × erg / s to(2.9 ± × erg / s, which seems to support this interpreta-tion. NGC 55 ULX1 – Similarly, we argue that the soft and dimspectral state observed in NGC 55 ULX1 is analogue to theobscured state observed in NGC 1313 X-1. In both cases, weobserve a possible increase in the neutral absorption column(see Section 3.1.2). Albeit this might be model dependent (thisis discussed further below), it suggests that their spectrum hasevolved in a similar manner. The ratio of unabsorbed bolometricfluxes in the obscured state are F harddiskbb / F softdiskbb = + . − . and 0.29 + . − . in NGC 1313 X-1 (epoch 2004-08-23) and NGC55 ULX1 (epoch 2010-05-24), respectively. This is a factor of ∼ diskbb (see also Pintore et al.2015), akin to the transitions seen in the ULXs in M101 and Article number, page 21 of 44 & A proofs: manuscript no. aanda
NGC 247 (Feng et al. 2016; Soria & Kong 2016). The increasein the neutral absorption column may indicate that now we seeparts of the wind less exposed to the central source (Pinto et al.2020a), where self-absorption could start to be important, albeitmore physically motivated models are needed to address this.The presence of outflows is supported by studies using high-resolution spectroscopy (Pinto et al. 2017, 2020b) which mighthave revealed the presence of soft residuals associated with out-flowing winds in NGC 1313 X-1 and NGC 55 ULX1. Theirsimilar transitions highlighted here support therefore the unifi-cation scenario proposed by (Middleton et al. 2015a; Pinto et al.2020a).
IC 342 X-1 and
Circinus ULX5 – As shown in Figure 6, IC342 X-1 and Circinus ULX5, not only share a very similar evo-lution in the HLD, but are also found in a soft and dim state(epochs 2012-10-29 and 2016-08-23 for IC 342 X-1 and Circi-nus ULX5 respectively), reminiscent again of the obscured stateseen in NGC 1313 X-1. When both sources are hard and dim(e.g. epochs 2012-08-07 and 2001-08-06 for IC 342 X-1 andCircinus ULX5 respectively) the mass-transfer rate is likely tobe low, similar to NGC 1313 X-1 in epoch 2012-12-16. Thebrighter and harder states (epochs 2005-02-10 and 2013-02-30for IC 342 X-1 and Circinus ULX5 respectively) might corre-spond to an increase in the mass-transfer rate while the softestand dimmest states are likely again due to the central sourcebeing obscured by the funnel becoming optically thick at high-transfer rates. This is supported by the diminishing of the hardcomponent in both temperature and luminosity. In this case, wedo not see an increase in the local n H -value as for NGC 1313 X-1or NGC 55 ULX1, that could strengthen the similarities of theseobscured states, but we note that these are the two sources withthe largest n HGal -values ( (cid:38) × cm − ) in our sample andthat we noted some calibration uncertainties at low energies (seeSection 2.2). Nevertheless, these sources show that both archety-pal soft ULXs (e.g. NGC 55 ULX1) and hard ULXs (e.g. IC 342X-1) undergo similar type of transitions. Holmberg II X-1 and
NGC 5204 X-1 – The similarities betweenHolmberg II X-1 and NGC 5204 X-1 are clear when lookingat their long-term evolution in the HLD (see also the similaritybetween the three spectra shown in Figure 6) and are further sup-ported by the similar L–T correlations found for the soft diskbb ( α NGC5204X-1 = ± α HolmbergIIX-1 = ± / or accretion flow (see also Gúrpide etal. in prep ).In epochs 2004-04-15 and 2006-11-16 of Holmberg II X-1 and NGC 5204 X-1 respectively, both sources are foundwith a hard spectrum and an intermediate luminosity – hard / intermediate state. Again, we favour a low viewing angle asfor NGC 1313 X-1 as the hard component dominates the emis-sion, although the inclination in this case may be higher than forNGC 1313 X-1, given their softer spectra. As both these sourcesmove in the HLD (see 2003 XMM-Newton epochs for NGC 5204X-1 for the transition) from these epochs to softer spectra andbrightest luminosities – bright / soft state (e.g. epochs 2004-04-15 and 2006-11-16 for Holmberg II X-1 and NGC 5204 X-1respectively), the temperature of the hard component decreases as seen in NGC 1313 X-1 , while the soft component increasesin temperature and luminosity (see Table 2). Similarly, most ofthe variability between these two epochs is seen at mid to softenergies ( ∼ (cid:38) (cid:38)
10 keV, see especiallyspectra for Holmberg II X-1) may be due to the fact that our lineof sight may be now grazing the optically thick walls of the wind,and thus some of the high-energy photons from the inner partsof the accretion flow are now being Compton down-scattered bythe wind. The transitions from hard / intermediate to soft / brightin NGC 5204 X-1 were also reported by Sutton et al. (2013) interms of hard and soft ULX transitions.Our study shows that these sources are also seen to transitfrom bright / soft to another state that we term dim / soft (epochs2002-09-18 and 2001-05-02 for Holmberg II X-1 and NGC 5204X-1 respectively) and vice-versa. For NGC 5204 X-1, this is alsoseen in the Chandra observations of 2003 (see also the full setof
Chandra observations presented by Roberts et al. (2006) ).For Holmberg II X-1, this is also seen in 2010 (see also the2009 / Swift -XRT monitoring of Holmberg II X-1 in Griséet al. (2010)).While there are certain similarities between these transitionsand that seen in NGC 1313 X-1 in the obscured state, namely asoftening and dimming of the source, we found also certain dif-ferences that may indicate that these transitions are not due to thesame phenomenon as for NGC 1313 X-1. From the bright / softstate to the dim / soft state, the entire spectrum seems to havediminished in luminosity in the case of Holmberg II X-1 andNGC 5204 X-1 (see the spectra from Figure 6), while for NGC1313 X-1 we showed that it was the hard component that wasmostly responsible for the dimming. Indeed, the soft diskbb isthe faintest in the dim / soft state, while the temperature of thehard diskbb remains consistent within errors with respect to thebright / soft state (for both Holmberg II X-1 and NGC 5204 X-1).If the funnel has become optically thick due to an increase in themass-transfer rate and is now obscuring the hard emission, weshould expect the soft component to be relatively stable as seenin NGC 1313 X-1. Therefore, the dimming of this componentmay be at odds with this interpretation.It is worth noting that the spectral evolution of NGC 5204 X-1 and Holmberg II X-1 from bright / soft to dim / soft bears someresemblance with how the inclination a ff ects the spectral shape(see for example Kawashima et al. 2012; Kitaki et al. 2017;Narayan et al. 2017), which could suggest that changes in the in-clination are responsible for these spectral changes. Indeed, nu-merical simulations by Narayan et al. (2017) predict a decreasein about one order of magnitude in luminosity between a sourcewith a face-on aspect and a source viewed at high inclinations( i > ◦ ), which is consistent with our observations of the tran-sitions from bright / soft to dim / soft. However, if the inclinationof the system is indeed changing due to precession of the super-critical funnel, we should expect these changes to be associated For NGC 5204 X-1, see those epochs of higher quality as the epochswhen simpl was not included tend to appear with artificially hotter tem-peratures for the hard diskbb . Albeit these transitions were well sampled by
Chandra at the end of2003, we were not able to use the short exposure ( ∼ with some periodicity. Thus, the fact that these transitions do notseem to be periodic (Grisé et al. 2010) may be at odds with thee ff ects of a precessing funnel (albeit see Gúrpide et al. in prep ).These transitions were also shown to occur rapidly, in somecases in timescales shorter than half a day (Grisé et al. 2010).This short-term variability may be expected if dense clumps ofthe wind are intersecting our line of sight (Takeuchi et al. 2013;Middleton et al. 2015a) or if our line of sight is rapidly changingbetween seeing down the funnel and seeing through the windwalls, expected if our line of sight grazes the wind as arguedbefore. More information and monitoring is needed about thetimescale of these transitions to address this issue and thus thiswill be further studied in a forthcoming publication. As stated above, NGC 1313 X-1 and Holmberg IX X-1 showa remarkably stable emission above ∼ ff ers an explanation for the presence of a stable emissioncomponent: advection and photon trapping e ff ects (Abramowiczet al. 1988; Ohsuga & Mineshige 2007). In the super-Eddingtonregime, the di ff usion photon time in the vicinity of the black holeis expected to be greater than the accretion timescale, while partof the excess energy will go into powering the outflow, so that theluminosity only increases logarithmically with the mass-transferrate (Poutanen et al. 2007): L ∼ L Edd (1 + x ln ˙ m ) (4)where x = x = ff erentiating BH- from NS-ULXs, as NS have no meansof swallowing any excess energy. Therefore, if we assume thehigh-energy emission is rather insensitive to ˙ m as suggested bythe stability of the high-energy component in Holmberg IX X-1and NGC 1313 X-1, we suggest that the former might harbour aheavier black hole than the latter given its brighter high-energycomponent (around a factor ∼ ∼ ff ected by Compton down-scattering and will beobserved as a high-energy powerlaw tail in the spectrum. Ki-taki et al. (2017) argued that the temperature of this region isindependent on the black hole mass, resulting in a similar spec-tral shape for the high-energy tail regardless of the black holemass. Therefore, provided that the mass-transfer rate betweentwo given sources is similar, the luminosity of this high-energycomponent may provide means to estimate the black hole mass ratio between two given sources. The two sources for which thisstability is best observed, NGC 1313 X-1 and Holmberg IX X-1,have indeed similar slope of the hard tail Γ NGC1313X-1 = + . − . and Γ = + . − . and Γ = + . − . where 1and 2 indicate the two di ff erent Γ values we have used for thelow and high flux epochs respectively. If we instead refit all thehigh data quality sets of Holmberg IX X-1 assuming one sin-gle value for Γ tied between all epochs, we obtain Γ= ± χ r = ff erence in terms of stability between PULXs and sources likeNGC 1313 X-1 and Holmberg IX X-1. This source sits at the lower end of the ULX luminosity distri-bution. We found the maximum unabsorbed luminosity of M83ULX1 to be ∼ × erg / s, close to the maximum observedluminosity of ∼ × erg / s by Soria et al. (2015), althoughthis was computed using a powerlaw which could have boostedthe unabsorbed luminosity. This maximum luminosity, using Ed-dington mass scaling, suggests an accretor of ∼
25 M (cid:12) . We alsofound that the hard diskbb component follows L hard ∝ T . ± . ,which as suggested by Figure 10, does not seem to be spuri-ously created by existing degeneracies. This may suggest thatthis component arises from an accretion disk with constant innerradius. This fact together with its low maximum luminosity, maysuggest that we are witnessing a black hole accreting close to theEddington-limit, as binary synthesis population studies predictthat BH-ULXs tend to emit isotropically, since super-Eddingtonmass-transfer rates (a factor ∼ p ) of –0.75 for a standard thin accre- Article number, page 23 of 44 & A proofs: manuscript no. aanda
Fig. 13.
Dependency of the p radial index of the diskpbb with its tem-perature for M83 ULX1 (see text for details). This dependency is similarto that seen in stellar-mass black holes in the standard regime (Kubota& Makishima 2004). Symbols are as per Figure 7. Table 6.
Results from jointly fitting all datasets of M83 ULX1 with anabsorbed diskpbb model.
Epoch n H T in p norm10 cm − keV 10 −
1X 3.2 ± ± ± + −
2X 1.3 ± ± + −
3X 1.9 + . − . ± + −
4X 1.5 ± + . − . + −
5X 1.65 ± ± + −
6X 1.8 ± ± + − χ r diskbb model. In order to explore such deviations, we refittedall our data with an absorbed broadened disk model ( diskpbb inXSPEC). As in Section 3, we assumed again constant absorptioncolumn and we jointly fitted our data tying n H across all datasetswith the diskpbb model. We obtained an excellent fit with χ ∼ ∼
10 M (cid:12) black hole XTE J1550–564 (Kubota & Mak-ishima 2004). Our hard diskbb when using the dual-thermalcomponent shows constant inner-disk radius, closely followingthe L ∝ T relationship as XTE J1550–564 in the standard regime(i.e. when L disk ∝ T ) (e.g. period 3 in Kubota & Makishima2004) . Additionally, when using the diskpbb model, the tem-perature increases with the radial index p of the diskpbb (Fig-ure 13) as seen in XTE J1550–564 and LMC X-3 when fittedwith the same model (see their Figure 9). Kubota & Makishima(2004) argued that this increase in p with temperature is an arte-fact caused by the limited bandpass and the fact that the radialdependency is flatter near the innermost disk radius than the –0.75 given by the diskbb approximation. Our diskpbb L–T re- Note that Kubota & Makishima (2004) uses RXTE that covers the3–20 keV range and thus their soft component corresponds roughly toour hard component. lationship follows α = ± ffi cient of 0.94, again with roughly constantnormalisation, suggesting we are witnessing the inner-most sta-ble orbit as in XTE J1550–564 and LMC X-3 in the standardregime. A typical value of the normalisation N ∼ in ∼
95 (cos i ) − / km, assuming f col = in = R isco = S , and we obtain a BH mass estimateof ∼
10 (cos i ) − / M (cid:12) . This mass estimate would be a factor 6larger if we consider instead a maximally spinning Kerr blackhole.A further constraint on the mass of the black hole comesfrom the fact that Kubota & Makishima (2004) argued that asource enters the anomalous regime when L diskb / L Edd ∼ disk ∼ × erg / s, then the mass of theM83 ULX1 could be of the order of 60 M (cid:12) , which could easilybe accounted for with reasonable values of inclination and spinof the black hole. We note that it is unlikely that the source is inthe anomalous state as we should expect p to decrease with tem-perature, as this parameter starts to deviate from standard valuefor a thin disk of –0.75 (Kubota & Makishima 2004; Shakura &Sunyaev 1973), at odds with our observations (Figure 13).Albeit the exact mass estimate is rather uncertain, we con-clude that the behaviour of this source is consistent with a mas-sive stellar-mass black hole accreting close to the Eddingtonlimit, in the high / soft state, given its similar evolution with ac-creting black holes in the standard regime. This conclusion is inagreement with previous studies by Soria et al. (2015) and otherstudies suggesting that sources below 3 × erg / s could beconsistent with massive black holes accreting close to the Ed-dington limit (Middleton et al. 2013; Sutton et al. 2013). Suchmassive black holes might not be rare given the black holemasses estimated from gravitational wave events (Abbott et al.2019).
5. Conclusions
We have presented a thorough study of the long-term spectralevolution of a representative sample of ULXs and PULXs usingdata from
XMM-Newton , Chandra , and
NuSTAR . By studyingtheir spectral states and transitions, we have been able to explainthe main sources of variability in these sources which can besummarised as: changes in the mass-transfer rate, changes in thedegree of beaming, precession and obscuration by the opticallythick parts of the wind as this becomes more mass-loaded.We have shown that PULXs are among the hardest sourcesin the sample and discussed their evolution in terms of the in-terplay between the magnetospheric radius and the spherisationradius. We favour a scenario in which the softest PULX, NGC1313 X-2, is consistent with being a weakly magnetised NS sothat R sph > R m and the wind / funnel structure is responsible forimprinting highly anisotropic emission as the source precesses,given the wide HR variability the source spans. This interpre-tation can explain the significantly softer spectra of NGC 1313X-2 and its lower pulsed-fraction, as the primary emission fromthe accretion column is expected to be downscattered in the coolelectrons of the outflow. Additionally, the lack of transitions tothe propeller regime in NGC 1313 X-2 supports this interpre-tation, as the weak magnetic field (or high-mass transfer rate)implied by the condition R sph > R m , will naturally lead to smallermagnetospheric radii and thus transitions to the propeller regimeare less likely to occur. Instead, the hardest PULXs, NGC 7793P13 and M51-ULX7, are consistent with being strongly magne- Article number, page 24 of 44. Gúrpide et al.: Long term evolution of ULXs tised, so that R m > R sph given the lack of HR variability whichwe interpret as lack of strong anisotropy. In this scenario, the ac-cretion disk is being truncated before it becomes supercritical,suppressing the anisotropy that the funnel / wind structure wouldotherwise imprint. For NGC 5907 ULX1, we have shown thatin those epochs associated with the super-orbital variability, thesource appears harder when dimmer. This is hard to reconcilewith the anisotropy expected from the funnel / wind structure inwhich we expect the source to become harder when brighter (asfor NGC 1313 X-2). Still, a high-mass transfer rate is required toexplain its high luminosity and therefore we conclude that R sph ∼ R m is a plausible condition to explain the source variability.By comparing the evolution of PULXs with the sources inour sample, we have been able to identify a strong NS candidatewith very similar evolution to that seen in NGC 1313 X-2: M81X-6. Albeit we were not able to detect pulsations in the source, itis possible that longer exposures sampling the source in di ff erentspectral states may be needed to detect pulsations. Additionally,deeper pulse searches taking into account orbital parameters cor-rections may be needed.Most of the softer sources for which the accretor is unknown,show three markedly di ff erent spectral states: one at highest lu-minosity and two at similar low luminosities but di ff erent hard-ness ratio. A super-critical funnel can o ff er an explanation ofsuch degeneracy between luminosity and hardness, because asource is expected to be dim at both low mass-transfer rates andwhen the gas within the funnel becomes optically thick at high-mass transfer rates, so that the hard radiation from the innerregions of the accretion flow becomes abruptly obscured. Thiscould explain the evolution seen in NGC 1313 X-1, NGC 55ULX1, IC 342 X-1 and Circinus ULX5. For Holmberg II X-1and NGC 5204 X-1, these transitions may be better explainedif our line of sight is grazing the half-opening angle of the fun-nel, so that our view of the accretion flow rapidly transits be-tween seeing down the funnel and seeing through the opticallythick wind walls as the source precesses. Future higher cadencemonitoring of these transitions will be key in order to deter-mine the exact nature of these transitions, by studying both theirtimescale and the source evolution prior and after them. Never-theless, these transitions are suggestive of strong winds in thesesources, which together with their softer appearance comparedto most PULXs supports a scenario in which the sources consid-ered here are powered by weakly magnetised NSs or BHs.Finally we have reported on the stability of the high-energyemission ( (cid:38)
10 keV) in some of the sources in our sample.Notably, none of the PULXs show such stability, albeit furtherhigh-quality
NuSTAR observations are needed to probe the dif-ferent spectral states of both PULXs and those sources for whichthe accretor is unknown. Black holes are favoured candidates toexplain this stability, as they naturally o ff er means to swallowany excess radiation, stabilising the output radiation even as themass-transfer rate increases. Should this be the case, this high-energy emission may be the smoking gun to identify BH-ULXs.On the other hand, should some of this sources host NS, thenthis stability may o ff er interesting clues about the accretion flowgeometry around NSs in the super-Eddington regime. Neverthe-less, we stress the importance of obtaining future NuSTAR ob-servations as we may expect to see most of the observationaldi ff erences between BH- and NS-ULXs at high-energies, wherethe mechanism responsible for the emission is expected to dif-fer (i.e. an accretion column compared to the case of the innerregions of the accretion disk around a black hole). Acknowledgements.
The authors would like to thank the anonymous referee forhis comments and suggestions that helped improve the quality of the manuscript. A. Gúrpide would like to thank M. Bachetti for his help and assistance during thesearch of pulsations and to I. Pastor-Marazuela for the computational resourcesprovided. NW acknowledges support by the CNES. This work made used of thefree software Veusz developed by J. Sanders to produce some of the plots.
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Article number, page 27 of 44 & A proofs: manuscript no. aanda
Table 1.
Sample of sources selected for this study with their respective distance, Galactic absorption (Kalberla et al. 2005; HI4PI Collaborationet al. 2016) and log of observations considered. For each particular epoch, the number of Xs,Ns or Cs indicate the number
XMM-Newton , NuSTAR and
Chandra observations respectively, that have been fitted together.
Epoch Telescope Instrument Date Obs. ID Good Exp(ks)Holmberg II X − D = a , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2002-04-10 0112520601 4.6 / / XMM-Newton pn / MOS1 / MOS2 2002-04-16 0112520701 3.7 / / XMM-Newton pn / MOS1 / MOS2 2002-09-18 0112520901 3.8 / / XMM-Newton pn / MOS1 / MOS2 2004-04-15 0200470101 35.0 / / XMM-Newton pn / MOS1 / MOS2 2010-03-26 0561580401 21.7 / / XMM-Newton pn / MOS1 / MOS2 2013-09-09 0724810101 4.6 / / NuSTAR
FPMA / FPMB 2013-09-09 30001031002 31.4 / NuSTAR
FPMA / FPMB 2013-09-09 30001031003 79.4 / XMM-Newton pn / MOS1 / MOS2 2013-09-17 0724810301 5.8 / / NuSTAR
FPMA / FPMB 2013-09-17 30001031005 111.1 / − D = a , n H = × cm − )1X XMM-Newton - / MOS1 / MOS2 2001-04-23 0111800101 - / / XMM-Newton pn / MOS1 / MOS2 2002-04-10 0112521001 7.0 / / XMM-Newton pn / MOS1 / MOS2 2002-04-16 0112521101 7.6 / / XMM-Newton pn / MOS1 / MOS2 2004-09-26 0200980101 64.2 / / XMM-Newton pn / - / - 2011-03-24 0657802001 2.9 / - / -6X XMM-Newton pn / MOS1 / MOS2 2011-09-26 0657801801 10.3 / / XMM-Newton pn / MOS1 / MOS2 2011-11-23 0657802201 13.1 / / XMM-Newton pn / MOS1 / MOS2 2012-10-23 0693850801 5.9 / / XMM-Newton pn / MOS1 / MOS2 2012-10-25 0693850901 5.5 / / XMM-Newton pn / MOS1 / MOS2 2012-10-27 0693851001 3.9 / / NuSTAR
FPMA / FPMB 2012-10-26 30002033003 88.1 / NuSTAR
FPMA / FPMB 2012-10-26 30002033002 31.2 / XMM-Newton pn / MOS1 / MOS2 2012-11-12 0693851701 7.1 / / NuSTAR
FPMA / FPMB 2012-11-11 30002033005 40.7 / NuSTAR
FPMA / FPMB 2012-11-11 30002033006 35.2 / XMM-Newton pn / MOS1 / MOS2 2012-11-14 0693851801 6.8 / / XMM-Newton pn / MOS1 / MOS2 2012-11-16 0693851101 2.9 / / NuSTAR
FPMA / FPMB 2012-11-14 30002033008 14.5 / NuSTAR
FPMA / FPMB 2012-11-15 30002033010 49.0 / − D = a , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2001-02-11 0093640901 4.8 / / XMM-Newton pn / MOS1 / MOS2 2004-02-20 0206890101 10.2 / / XMM-Newton pn / MOS1 / MOS2 2004-08-17 0206890201 17.0 / / XMM-Newton pn / MOS1 / MOS2 2005-02-10 0206890401 6.2 / / XMM-Newton pn / MOS1 / MOS2 2012-08-11 0693850601 37.5 / / NuSTAR
FPMA / FPMB 2012-08-10 30002032002 21.0 / NuSTAR
FPMA / FPMB 2012-08-10 30002032003 98.6 / XMM-Newton pn / MOS1 / MOS2 2012-08-17 0693851301 33.3 / / NuSTAR
FPMA / FPMB 2012-08-16 30002032005 127.4 / Chandra
ACIS 2002-04-29 2916 9.32C
Chandra
ACIS 2002-08-26 2917 9.93C
Chandra
ACIS 2012-10-29 13686 9.1NGC 5204 X − D = c , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2003-01-06 0142770101 15.3 / / XMM-Newton pn / MOS1 / MOS2 2003-04-25 0142770301 3.5 / / XMM-Newton pn / MOS1 / MOS2 2003-05-01 0150650301 4.8 / / XMM-Newton pn / MOS1 / MOS2 2006-11-16 0405690101 7.8 / / XMM-Newton pn / MOS1 / MOS2 2006-11-19 0405690201 30.9 / / XMM-Newton pn / MOS1 / MOS2 2006-11-25 0405690501 20.4 / / XMM-Newton pn / MOS1 / MOS2 2013-04-21 0693851401 13.4 / / XMM-Newton pn / MOS1 / MOS2 2013-04-29 0693850701 10.0 / / NuSTAR
FPMA / FPMB 2013-04-19 30002037002 96.0 / Article number, page 28 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 1.
Continued.
NuSTAR
FPMA / FPMB 2013-04-29 30002037004 89.0 / XMM-Newton pn / MOS1 / MOS2 2014-06-27 0741960101 19.0 / / Chandra
ACIS 2001-05-02 2029 9.02C
Chandra
ACIS 2003-08-06 3933 46.23CC
Chandra
ACIS 2003-08-14 3936 4.6
Chandra
ACIS 2003-08-17 3937 4.64C
Chandra
ACIS 2003-09-05 3940 4.85C
Chandra
ACIS 2003-09-14 3941 4.96C
Chandra
ACIS 2003-09-23 3942 5.27C
Chandra
ACIS 2003-10-03 3943 4.9M83 ULX1 ( D = a , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2013-08-07 0723450101 44.7 / / XMM-Newton pn / MOS1 / MOS2 2014-01-11 0723450201 37.7 / / XMM-Newton pn / MOS1 / MOS2 2014-07-06 0729561201 24.0 / / XMM-Newton pn / MOS1 / MOS2 2015-02-02 0729561001 15.4 / / XMM-Newton pn / MOS1 / MOS2 2015-08-07 0761620101 53.1 / / XMM-Newton pn / MOS1 / MOS2 2016-01-20 0761620201 31.9 / / − D = e , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2001-07-31 0112290501 3.5 / / XMM-Newton pn / MOS1 / MOS2 2001-08-08 0112290601 4.5 / / XMM-Newton - / MOS1 / MOS2 2001-08-24 0112290701 - / / XMM-Newton pn / MOS1 / MOS2 2003-01-28 0112291201 2.7 / / XMM-Newton pn / MOS1 / MOS2 2006-01-13 0302900101 90.6 / / XMM-Newton pn / MOS1 / MOS2 2008-01-13 0500750101 45.2 / / XMM-Newton pn / MOS1 / MOS2 2010-07-17 0653380201 76.6 / / XMM-Newton pn / MOS1 / MOS2 2010-07-19 0653380301 96.3 / / XMM-Newton pn / MOS1 / MOS2 2011-01-26 0653380401 79.7 / / XMM-Newton pn / MOS1 / MOS2 2011-01-28 0653380501 83.5 / / XMM-Newton pn / MOS1 / MOS2 2014-02-11 0723130301 30.4 / / XMM-Newton pn / MOS1 / MOS2 2014-02-13 0723130401 29.5 / / Chandra
ACIS 2010-05-02 11032 11.0
Chandra
ACIS 2010-05-15 11033 11.12C
Chandra
ACIS 2010-05-28 11034 10.9NGC 1313 X − D = a , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2000-10-17 0106860101 18.3 / / XMM-Newton pn / - / - 2003-12-21 0150280301 7.4 / - / - XMM-Newton pn / - / - 2003-12-23 0150280401 3.2 / - / -3XX XMM-Newton pn / MOS1 / - 2004-01-08 0150280601 7.1 / / - XMM-Newton pn / MOS1 / MOS2 2004-01-17 0150281101 3.1 / / XMM-Newton pn / MOS1 / MOS2 2004-05-01 0205230201 0.6 / / XMM-Newton pn / MOS1 / MOS2 2004-06-05 0205230301 8.7 / / XMM-Newton pn / MOS1 / MOS2 2004-08-23 0205230401 4.4 / / XMM-Newton - / MOS1 / MOS2 2004-11-23 0205230501 - / / XMM-Newton pn / MOS1 / MOS2 2005-02-07 0205230601 8.9 / / XMM-Newton pn / MOS1 / MOS2 2006-10-16 0405090101 81.1 / / XMM-Newton pn / MOS1 / MOS2 2012-12-16 0693850501 90.9 / / NuSTAR
FPMA / FPMB 2012-12-16 30002035002 100.9 / XMM-Newton pn / MOS1 / MOS2 2012-12-22 0693851201 85.4 / / NuSTAR
FPMA / FPMB 2012-12-21 30002035004 127.0 / XMM-Newton pn / MOS1 / MOS2 2014-07-05 0742590301 53.7 / / NuSTAR
FPMA / FPMB 2014-07-05 80001032002 63.5 / XMM-Newton - / MOS1 / MOS2 2015-12-05 0764770101 - / / XMM-Newton pn / MOS1 / MOS2 2017-03-29 0794580601 26.1 / / NuSTAR
FPMA / FPMB 2017-03-29 90201050002 72.8 / XMM-Newton pn / MOS1 / MOS2 2017-06-14 0803990101 110.8 / / NuSTAR
FPMA / FPMB 2017-06-14 30302016002 94.2 / XMM-Newton pn / MOS1 / MOS2 2017-06-20 0803990201 110.9 / / XMM-Newton pn / MOS1 / MOS2 2017-08-31 0803990301 47.2 / / XMM-Newton pn / MOS1 / MOS2 2017-09-02 0803990401 30.1 / / NuSTAR
FPMA / FPMB 2017-09-03 30302016006 73.0 / Article number, page 29 of 44 & A proofs: manuscript no. aanda
Table 1.
Continued.
XMM-Newton pn / MOS1 / MOS2 2017-12-07 0803990501 60.1 / / XMM-Newton pn / MOS1 / MOS2 2017-12-09 0803990601 71.8 / / NuSTAR
FPMA / FPMB 2017-12-09 30302016010 79.3 / D = d , n H = × cm − )1X XMM-Newton - / MOS1 / - 2001-08-06 0111240101 - / / -2XNN XMM-Newton pn / MOS1 / MOS2 2013-02-03 0701981001 33.0 / / NuSTAR
FPMA / FPMB 2013-02-03 30002038004 40.3 / NuSTAR
FPMA / FPMB 2013-02-02 30002038002 18.3 / XMM-Newton pn / MOS1 / MOS2 2014-03-01 0656580601 23.8 / / XMM-Newton pn / MOS1 / MOS2 2016-08-23 0792382701 17.2 / / NuSTAR
FPMA / FPMB 2016-08-23 90201034002 49.8 / XMM-Newton pn / MOS1 / MOS2 2018-02-07 0780950201 5.0 / / XMM-Newton pn / MOS1 / MOS2 2018-09-16 0824450301 88.8 / / Chandra
ACIS 2010-12-24 12824 38.9M81 X − D = a , n H = × cm − )1X XMM-Newton pn / - / MOS2 2001-04-22 0111800101 73.6 / - / XMM-Newton pn / MOS1 / MOS2 2002-04-10 0112521001 7.0 / / XMM-Newton pn / MOS1 / MOS2 2002-04-16 0112521101 7.6 / / XMM-Newton - / MOS1 / MOS2 2004-09-26 0200980101 - / / XMM-Newton pn / - / MOS2 2011-03-24 0657802001 2.9 / - / XMM-Newton pn / MOS1 / MOS2 2011-09-26 0657801801 5.8 / / XMM-Newton pn / - / - 2011-11-23 0657802201 13.0 / - / -8X XMM-Newton pn / MOS1 / MOS2 2012-10-23 0693850801 5.8 / / XMM-Newton pn / MOS1 / MOS2 2012-10-27 0693851001 3.9 / / XMM-Newton pn / MOS1 / MOS2 2012-10-25 0693850901 2.2 / / XMM-Newton - / MOS1 / - 2012-11-12 0693851701 - / / - XMM-Newton - / MOS1 / - 2012-11-14 0693851801 - / / - XMM-Newton pn / MOS1 / - 2012-11-16 0693851101 2.8 / / -NGC 55 ULX1 ( D = b , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2001-11-14 0028740201 27.3 / / XMM-Newton - / MOS1 / MOS2 2001-11-15 0028740101 - / / XMM-Newton pn / MOS1 / MOS2 2010-05-24 0655050101 98.9 / / − D = b , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2004-06-13 0200670301 7.9 / / XMM-Newton - / MOS1 / MOS2 2007-11-02 0500730201 - / / XMM-Newton pn / MOS1 / MOS2 2007-11-08 0500730101 19.5 / / XMM-Newton pn / MOS1 / MOS2 2012-10-21 0691570101 88.0 / / XMM-Newton pn / MOS1 / MOS2 2017-06-01 0794581201 35.5 / / NuSTAR
FPMA / FPMB 2017-05-21 90302004002 66.8 / NuSTAR
FPMA / FPMB 2017-06-01 90302004004 47.8 / Chandra
ACIS 2001-09-07 1043 58.32C
Chandra
ACIS 2004-10-22 4631 29.73CC
Chandra
ACIS 2004-11-06 4632 28.0
Chandra
ACIS 2004-12-03 4633 26.64C
Chandra
ACIS 2016-09-28 17878 40.0NGC 1313 X − D = a , n H = × cm − )1X XMM-Newton pn / - / MOS2 2000-10-17 0106860101 18.2 / - / XMM-Newton pn / MOS1 / MOS2 2003-12-21 0150280301 7.4 / / XMM-Newton pn / MOS1 / MOS2 2003-12-23 0150280401 3.2 / / XMM-Newton pn / MOS1 / MOS2 2003-12-25 0150280501 5.8 / / XMM-Newton pn / MOS1 / MOS2 2004-01-08 0150280601 7.1 / / XMM-Newton pn / MOS1 / MOS2 2004-01-17 0150281101 3.1 / / XMM-Newton pn / MOS1 / MOS2 2004-06-05 0205230301 8.7 / / XMM-Newton - / MOS1 / MOS2 2004-08-23 0205230401 - / / XMM-Newton pn / MOS1 / MOS2 2004-11-23 0205230501 12.5 / / XMM-Newton pn / MOS1 / MOS2 2005-02-07 0205230601 8.9 / / XMM-Newton pn / - / - 2006-03-06 0301860101 17.3 / - / -12X XMM-Newton pn / - / - 2006-10-16 0405090101 80.4 / - / - Article number, page 30 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 1.
Continued.
XMM-Newton pn / MOS1 / MOS2 2012-12-16 0693850501 90.9 / / NuSTAR
FPMA / FPMB 2012-12-16 30002035002 100.9 / XMM-Newton pn / MOS1 / MOS2 2012-12-22 0693851201 85.4 / / NuSTAR
FPMA / FPMB 2012-12-21 30002035004 127.0 / XMM-Newton pn / - / - 2013-06-08 0722650101 12.2 / - / -16X XMM-Newton pn / - / - 2014-07-05 0742590301 53.5 / - / -17X XMM-Newton pn / - / - 2015-03-30 0742490101 78.9 / - / -18X XMM-Newton pn / MOS1 / MOS2 2015-12-05 0764770101 53.5 / / XMM-Newton pn / MOS1 / MOS2 2016-03-23 0764770401 16.7 / / XMM-Newton pn / MOS1 / MOS2 2016-10-08 0782310101 76.2 / / XMM-Newton pn / - / - 2017-03-29 0794580601 26.0 / - / - NuSTAR
FPMA / FPMB 2017-03-29 90201050002 72.8 / XMM-Newton - / MOS1 / MOS2 2017-06-14 0803990101 - / / XMM-Newton pn / - / - 2017-06-20 0803990201 110.4 / - / -24X XMM-Newton - / - / MOS2 2017-08-31 0803990301 - / - / XMM-Newton - / - / MOS2 2017-09-02 0803990401 - / - / XMM-Newton pn / MOS1 / MOS2 2017-12-07 0803990501 60.1 / / XMM-Newton pn / MOS1 / MOS2 2017-12-09 0803990601 71.8 / / NuSTAR
FPMA / FPMB 2017-12-09 30302016010 79.3 / D = b , n H = × cm − )1XN XMM-Newton pn / MOS1 / MOS2 2016-12-17 0791010101 96.4 / / NuSTAR
FPMA / FPMB 2016-12-16 30202035002 163.1 / XMM-Newton pn / MOS1 / MOS2 2016-12-19 0791010301 46.1 / / Chandra
ACIS 2018-02-11 20966 9.1
Chandra
ACIS 2018-02-08 20965 9.1NGC 5907 ULX1 (P) ( D = a , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2003-02-20 0145190201 10.1 / / XMM-Newton pn / MOS1 / MOS2 2003-02-28 0145190101 10.9 / / XMM-Newton pn / MOS1 / MOS2 2012-02-09 0673920301 12.8 / / XMM-Newton pn / MOS1 / MOS2 2012-02-05 0673920201 5.3 / / Chandra
ACIS 2012-02-11 12987 16.0
Chandra
ACIS 2012-02-11 14391 13.14XN
XMM-Newton pn / MOS1 / MOS2 2013-11-12 0724810401 18.9 / / NuSTAR
FPMA / FPMB 2013-11-12 30002039005 112.9 / XMM-Newton pn / MOS1 / MOS2 2014-07-09 0729561301 37.6 / / NuSTAR
FPMA / FPMB 2014-07-09 80001042002 57.1 / NuSTAR
FPMA / FPMB 2014-07-12 80001042004 56.3 / XMM-Newton pn / MOS1 / MOS2 2017-07-02 0804090301 21.3 / / XMM-Newton pn / MOS1 / MOS2 2017-07-05 0804090401 31.3 / / XMM-Newton pn / MOS1 / MOS2 2017-07-08 0804090501 34.1 / / XMM-Newton pn / MOS1 / MOS2 2017-07-15 0804090601 32.5 / / D = c , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2013-11-25 0693760401 41.1 / / XMM-Newton pn / MOS1 / MOS2 2014-12-10 0748390901 42.0 / / XMM-Newton pn / MOS1 / MOS2 2016-05-20 0781800101 23.1 / / NuSTAR
FPMA / FPMB 2016-05-20 80201010002 106.3 / XMM-Newton pn / - / MOS2 2017-05-13 0804670201 5.2 / - / XMM-Newton pn / MOS1 / MOS2 2017-05-20 0804670301 44.9 / / NuSTAR
FPMA / FPMB 2017-05-19 30302005002 83.6 / XMM-Newton pn / MOS1 / MOS2 2017-05-31 0804670401 25.0 / / XMM-Newton pn / MOS1 / MOS2 2017-06-12 0804670501 19.9 / / XMM-Newton pn / MOS1 / MOS2 2017-06-20 0804670601 23.0 / / XMM-Newton pn / MOS1 / MOS2 2017-11-25 0804670701 41.8 / / NuSTAR
FPMA / FPMB 2017-11-25 30302005004 76.7 / Chandra
ACIS 2003-09-06 3954 48.9M51 ULX − D = f , n H = × cm − )1X XMM-Newton pn / MOS1 / MOS2 2003-01-15 0112840201 17.1 / / XMM-Newton pn / MOS1 / MOS2 2005-07-01 0212480801 24.0 / / XMM-Newton pn / MOS1 / MOS2 2006-05-20 0303420101 29.4 / / Article number, page 31 of 44 & A proofs: manuscript no. aanda
Table 1.
Continued. XMM-Newton pn / MOS1 / MOS2 2006-05-24 0303420201 20.2 / / XMM-Newton pn / MOS1 / MOS2 2018-05-13 0824450901 64.7 / / XMM-Newton pn / MOS1 / MOS2 2018-06-13 0830191501 51.6 / / XMM-Newton pn / MOS1 / MOS2 2018-06-15 0830191601 51.7 / / Chandra
ACIS 2003-08-07 3932 48.02C
Chandra
ACIS 2012-09-09 13813 179.23C
Chandra
ACIS 2012-09-12 13812 157.54CC
Chandra
ACIS 2012-09-19 15496 41.0
Chandra
ACIS 2012-09-20 13814 189.95C
Chandra
ACIS 2012-09-23 13815 67.2M51 ULX − g ) ( D = f , n H = × cm − )1X XMM-Newton - / MOS1 / MOS2 2005-07-01 0212480801 - / / XMM-Newton pn / MOS1 / MOS2 2006-05-20 0303420101 29.4 / / XMM-Newton pn / MOS1 / MOS2 2006-05-24 0303420201 20.2 / / XMM-Newton pn / MOS1 / MOS2 2018-05-13 0824450901 64.5 / / XMM-Newton pn / - / - 2018-05-25 0830191401 80.1 / - / -6XX XMM-Newton pn / - / - 2018-06-13 0830191501 51.4 / - / - XMM-Newton pn / - / - 2018-06-15 0830191601 51.4 / - / -1C Chandra
ACIS 2003-08-07 3932 48.02C
Chandra
ACIS 2012-09-12 13812 157.53CCC
Chandra
ACIS 2012-09-19 15496 41.0
Chandra
ACIS 2012-09-20 13814 189.9
Chandra
ACIS 2012-09-23 13815 67.24C
Chandra
ACIS 2012-09-26 13816 73.1
Notes.
Observations for which an instrument was not available because it was not active or because the source was not in the field of view aremarked with "-". (P) indicates a source for which pulsations have been identified. Distances from: ( a ) Tully et al. (2016) , ( b ) Lelli et al. (2015) , ( c ) Karachentsev et al. (2017) , ( d ) Tully et al. (2008) , ( e ) Karachentsev et al. (2002) and ( f ) Cappellari et al. (2011) . ( g ) No pulsations have beendetected in this source but it was identified as a NS through the detection of a cyclotron line (Brightman et al. 2018).Article number, page 32 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 2.
Best fit spectral fit parameters. Errors are quoted at a 90% confidence level. The first epochs in each source correspond to the high-qualitydatasets, that were jointly fitted and from which we determine Γ and n H . The rest of the data were fitted individually by freezing n H and / or Γ to thebest fit value found in the joint fit of the high-quality data. Epoch n H kT soft norm kT hard norm Γ f scat χ r / dof10 cm − keV keV 10 − %Holmberg II X-11X 4.3 ± + . − . + − + . − . + − + . − . + a − / ± + − + . − . + − + a −
4X 0.29 ± + − + . − . + − + −
5X 0.23 ± + − + . − . + − ± ± + − + . − . + − ± + a − ± + − + . − . + − + a −
3X 4.3 b ± + − + . − . + − - - 1.07 / + . − . ± ± + . − . + . − . + . − . + a − / ± + . − . ± + . − . + − ± + . − . ± + − + . − . + − + . − . + − + . − . + − + −
1X 9.8 b ± + . − . ± ± / b ± ± + . − . + − b + a − / b ± + . − . + . − . + − b + a − / b ± ± + a − . + . − . - - 0.80 / b ± + . − . + . − . + − b + a − / b ± + . − . ± + . − . - - 0.97 / b ± ± ± + . − . - - 1.047 / ± + . − . + . − . ± + . − . - - 1.03 / + . − . + . − . + . − . ± ± + . − . + . − . + . − . - -5XNN 0.39 ± + . − . + . − . + . − . ± + a − ± + . − . + . − . + . − . + a −
1X 55 b + . − . + . − . + . − . + . − . - - 0.89 / b + . − . + − + . − . + . − . - - 0.80 / b ± + . − . + a − . + . − . - - 1.08 / b + . − . + − + . − . + − - - 1.01 / ± + . − . + − ± + − + . − . + − / ± + . − . ± + − + −
6X 0.28 + . − . ± + . − . + − + a − + . − . + − + . − . + . − . + . − . + a −
1X 3.0 b ± ± ± + . − . - - 1.05 / b ± ± ± + . − . - - 1.21 / b ± ± ± + . − . - - 1.08 / b ± ± ± ± / b ± + − + . − . + − - - 0.86 / b ± ± + . − . + − - - 1.05 / b ± + − + . − . + − - - 0.95 / b + . − . + − + . − . + − - - 0.98 / b + . − . + − + . − . + − - - 1.15 / b ± + − + . − . + . − . - - 1.05 / b + . − . + − + . − . + − - - 0.75 / Article number, page 33 of 44 & A proofs: manuscript no. aanda
Table 2.
Continued.
Epoch n H kT soft norm kT hard norm Γ f scat χ r / dof10 cm − keV keV 10 − %M83 ULX11X 4 ± + . − . + . − . ± ± / ± + . − . + . − . ± + . − . + . − . + . − . ± + . − . + − + . − . ± + . − . + . − . + . − . ± + . − . + . − . + . − . + . − . - -NGC 5408 X-15X 5.0 ± ± + − + . − . + − + . − . + − / + . − . + − + . − . + − + −
7X 0.176 + . − . + − ± + − + a −
8X 0.173 ± + − + . − . + − + a −
9X 0.176 ± + − + . − . + − + a −
10X 0.178 ± + − + . − . + − + a − a ± + − ± + − + a −
1X 5.0 b ± + − + . − . + − - - 1.34 / b ± + − + . − . ± / b ± + − + . − . + − - - 1.16 / b ± + − ± + . − . - - 0.96 / b ± + − + . − . + − - - 1.15 / b ± + − ± + − - - 1.07 / + . − . ± + . − . + . − . + . − . + . − . + a − / ± ± + . − . + . − . + a − ± ± + . − . + − + a − ± + . − . + . − . + . − . + a − ± + . − . + . − . + − + a − ± ± + . − . + . − . + a − ± + . − . + . − . + − + a −
1X 22.1 b ± ± ± + . − . - - 1.19 / b ± + − ± + − - - 0.87 / b ± ± + . − . + − b + a − / b ± .
04 7 + − + . − . + . − . - - 0.91 / b + . − . ± ± ± / ± ± + − + . − . + − - - 1.18 / b ± .
02 8 + − + . − . + . − . - - 1.01 / b ± .
02 12 ± + . − . ± b + a − / b ± .
01 14 ± + . − . + . − . b + a − / b ± .
01 8 ± ± + . − . - - 0.99 / b ± .
01 8.0 ± + . − . + . − . b + a − / b ± .
01 8.8 + . − . + . − . + . − . b + a − / ±
12 0.26 + . − . + − + . − . + . − . ± + − / b + . − . + . − . + . − . + . − . - - 0.82 / b ± + . − . + . − . + . − . - - 1.06 / b + . − . + . − . + . − . + . − . - - 1.00 / b ± + − + . − . + . − . - - 0.99 / b ± + − ± ± / b + . − . + . − . + a − + . − . - - 0.80 / Article number, page 34 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 2.
Continued.
Epoch n H kT soft norm kT hard norm Γ f scat χ r / dof10 cm − keV keV 10 − %M81 X-61X 11.7 + . − . + . − . + . − . + . − . + . − . - - 1.18 / ± + . − . + . − . + . − . - -2X 11.7 b + a − . + . − . + . − . + . − . - - 1.08 / b + . − . + . − . + . − . + . − . - - 1.02 / b + . − . + . − . + a − + . − . - - 0.60 / b + . − . + . − . + . − . + . − . - - 0.87 / b + . − . + . − . + . − . + . − . - - 0.75 / b + . − . + − + . − . ± / b + . − . + . − . + . − . + . − . - - 1.12 / b + . − . + − + . − . ± / + . − . ± + − + . − . + − + . − . ± / ± + − + . − . + − + −
3X 32.5 + . − . + . − . + − + . − . + . − . + . − . ± / ± ± + − + . − . + − + . − . + a − / ± + − + . − . + − + a −
2C 0.24 ± + − + . − . + − + a − a ± + − + . − . + − + a −
3X 0.24 ± + − + . − . + − + a − ± + − + . − . + . − . + a − b ± + − ± + . − . - - 1.15 / b ± + − + . − . + . − . - - 0.94 / + . − . ± + . − . + . − . + − + . − . + a − / ± + . − . ± + . − . + −
20X 0.37 + . − . + . − . + . − . + − + − + . − . + − + . − . + − + a − ± ± + . − . + . − . - -26XXN 0.37 ± + . − . ± ± b ± + . − . + . − . + . − . - - 0.97 / b ± + . − . ± + . − . - - 0.89 / b + . − . + . − . ± ± / b + . − . + . − . ± + . − . - - 0.91 / b ± + . − . + . − . + . − . - - 0.93 / b + . − . + . − . + . − . + . − . - - 1.00 / b + . − . + . − . ± ± / b ± + − + . − . + . − . - - 1.07 / b ± + . − . + . − . + . − . - - 1.17 / b + . − . + . − . ± ± / b ± + . − . + . − . + . − . - - 1.05 / b ± + − + . − . + . − . - - 1.07 / b ± + . − . + . − . + . − . - - 1.30 / b ± + . − . + . − . + . − . - - 1.10 / b ± + . − . ± ± / b ± + . − . + . − . + . − . - - 1.12 / b ± + . − . + . − . + . − . - - 1.07 / b ± + . − . + . − . ± / Article number, page 35 of 44 & A proofs: manuscript no. aanda
Table 2.
Continued.
Epoch n H kT soft norm kT hard norm Γ f scat χ r / dof10 cm − keV keV 10 − %24X 17.4 b ± + . − . + . − . + . − . - - 1.05 / b + . − . + . − . + . − . + . − . - - 0.94 / ± ± + . − . ± ± ± + − / ± ± + . − . + . − . + − a b + a − . + . − . + a − + . − . - - 1.08 / + − + . − . + . − . + . − . ± / + . − . + . − . ± ± + . − . + . − . ± + . − . - -5XNN 0.41 + . − . + . − . ± + . − . + . − . + a − b + . − . + . − . + . − . + . − . - - 0.91 / b + a − . + . − . + a − + . − . - - 0.87 / b + . − . + . − . + . − . ± / b ± + − ± ± / b + . − . + − ± + . − . - - 1.25 / ± + . − . + . − . + . − . + . − . - - 1.12 / + . − . + . − . + . − . ± ± + . − . ± ± ± ± + . − . ± + . − . + − + . − . + . − . - -5XN 0.27 + . − . + . − . + . − . + . − . - -6X 0.30 ± + . − . ± + . − . - -7X 0.29 ± + − ± ± ± ± ± ± ± + . − . + . − . ± ± + . − . + . − . + − + . − . - - 1.06 / + . − . + . − . + . − . + . − . - -2X 0.37 ± + . − . + . − . + . − . - -3X 0.36 ± + . − . + . − . ± + . − . + . − . + . − . ± + . − . + . − . + . − . ± + . − . + . − . + . − . + . − . - -4CC 0.35 + . − . ± + . − . ± + . − . + . − . + a − . + . − . - -5X 0.34 ± + . − . + . − . + . − . - -6XX 0.32 ± + . − . + . − . ± + . − . ± + . − . + . − . + . − . - - 1.00 / + . − . + . − . + . − . + . − . - -2X 0.35 + . − . + . − . + . − . + . − . - -3X 0.40 ± + . − . + a − . + . − . - -2C 0.41 + . − . + . − . ± ± ± + . − . + . − . + . − . - -4C 0.33 + . − . + . − . + . − . + . − . - -4X 0.30 + . − . + . − . + . − . ± + . − . + . − . + . − . ± ± + . − . + . − . + . − . - - Article number, page 36 of 44. Gúrpide et al.: Long term evolution of ULXs
Notes. ( a ) Parameter frozen at the value determined in the joint fits. ( b ) Unbound parameter. Article number, page 37 of 44 & A proofs: manuscript no. aanda
Table 3.
Estimated unabsorbed luminosities in units of 10 erg / s for each epoch using the distances from Table 1 and models from Table 2.For jointly fit data, the error estimation takes into account the errors on the joint parameters. Uncertainties are quoted at 90% confidence level.First column indicates the epoch given in Table 1 sorted chronologically. The simpl flux luminosity corresponds to the entire diskbb ⊗ simpl component. Epoch L soft L hard L tot L soft diskbb L hard diskbb L simpl (0.3-1.5 keV) (1.5-10 keV) (0.3 – 10 keV) (0.01 – 100 keV) (0.01 – 100 keV) (0.01 – 100 keV)Holmberg II X-11X 6.1 ± ± ± + − + − + −
2X 5.5 ± ± ± + . − . ± ±
13X 1.87 ± ± ± ± ± ± ± ± + . − . + . − . + . − .
5X 2.87 + . − . ± + . − . ± + . − . + . − . + . − . ± + . − . ± + . − . + . − . + . − . ± ± ± + . − . ± + . − . ± ± + − ± + . − . + . − . ± ± + . − . + . − .
3X 5.11 + . − . ± + . − . ± + . − . + . − .
4X 3.70 + . − . + . − . + . − . ± + . − . + . − .
5X 4.7 ± ± ± + . − . + − -6X 6.95 + . − . + . − . + . − . ± + . − . + . − .
7X 7.3 ± ± ± + . − . ± ± ± ± ± ± + . − . ± ± ± + . − . ± ± ± ± ± + − ± ± ± ± + . − . + − ± ± ± ± ± + . − . -1C 1.82 ± + . − . ± ± + . − . -2C 1.61 ± ± + . − . + . − . + . − . -2X 2.9 ± ± ± + . − . + . − . -3X 1.8 ± ± ± ± ± + . − . ± ± + . − . ± ± ± ± + . − . + . − . ± + . − . ± + . − . ± + . − . ± + . − . ± ± + . − . + . − . -NGC 5204 X-11C 1.54 ± ± ± + . − . + . − . -1X 2.08 ± ± ± ± ± ± + . − . ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± + . − . -5C 4.7 ± ± ± + . − . + . − . -6C 2.8 ± + . − . ± ± + . − . -7C 4.4 ± ± ± + . − . + . − . -4X 4.5 + . − . ± + . − . + . − . + . − . + . − .
5X 3.61 ± ± ± ± + . − . + . − .
6X 2.65 + . − . ± ± + . − . + . − . + − + . − . + . − . + . − . + . − . + . − . ± ± ± ± ± ± ± ± ± + . − . ± ± ± ± + . − . ± ± ± ± + . − . ± Article number, page 38 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 3.
Continued.
Epoch L soft L hard L tot L soft disk L hard disk L simpl (0.3-1.5 keV) (1.5-10 keV) (0.3 – 10 keV) (0.01 – 100 keV) (0.01 – 100 keV) (0.01 – 100 keV)4X 0.55 ± ± ± + . − . ± ± ± ± + . − . ± ± ± ± + . − . ± ± ± ± ± ± ± ± ± + . − . ± ± ± ± ± ± ± ± ± ± ± + . − . ± + . − . + . − . + . − . + . − .
6X 5.20 ± + . − . ± ± + . − . ± ± ± ± ± ± ± + . − . ± + . − . ± ± ± ± + . − . + . − . + . − .
8X 6.10 + . − . ± ± + . − . + . − . + . − .
9X 5.81 + . − . ± + . − . + . − . + . − . ± + . − . + . − . + . − . ± + . − . ± + . − . ± + . − . ± + . − . + . − . NGC 1313 X-11X 3.65 + . − . ± ± ± ± ± ± ± ± ± ± ± ± ± + . − . + . − .
4X 4.1 ± ± ± ± + . − . -5X 8.0 ± ± ± ± ± ± ± ± + − ± ± ± ± ± ± + . − . + . − . ± ± + . − . + . − .
9X 3.37 ± + . − . + . − . ± + . − . ± + . − . + . − . ± + . − . + . − . ± + . − . ± ± + . − . + . − . + . − . ± ± ± ± + . − . + . − .
13X 4.16 ± ± ± ± + . − . -14XN 4.48 ± ± + . − . ± + . − . ± + . − . + . − . + . − . ± + . − . + . − .
16X 5.62 ± + . − . + . − . + . − . + . − . ± ± + . − . + . − . + . − . + . − . + . − .
18X 5.12 + . − . + . − . + . − . ± + . − . ± + . − . ± + . − . ± + . − . + . − . Circinus ULX51X 2.2 ± ± ± ± + . − . -1C 1.62 + . − . ± ± ± + . − . -2XNN 4.5 + . − . ± ± + − + . − . + . − .
3X 2.3 ± ± ± ± + . − . -4XN 2.94 ± ± ± ± ± ± ± ± + . − . + . − . -6X 4.63 ± + . − . ± ± ± ± ± ± + . − . + . − . -2X 1.35 ± + . − . ± + . − . ± ± ± ± + . − . ± + . − . ± ± + . − . ± ± ± ± + . − . + . − . -6X 1.53 ± ± ± + . − . + . − . -7X 1.01 ± ± ± ± + . − . - Article number, page 39 of 44 & A proofs: manuscript no. aanda
Table 3.
Continued.
Epoch L soft L hard L tot L soft disk L hard disk L simpl (0.3-1.5 keV) (1.5-10 keV) (0.3 – 10 keV) (0.01 – 100 keV) (0.01 – 100 keV) (0.01 – 100 keV)8X 1.69 ± ± ± + . − . ± + . − . ± ± + . − . + . − . -10XXX 1.81 + . − . + . − . + . − . + . − . + . − . -NGC 55 ULX11X 2.5 ± ± ± + . − . ± + . − .
2X 2.7 + . − . ± ± ± + . − . + −
3X 1.98 + . − . ± + . − . + . − . + . − . + . − . NGC 6946 X-11C 3.8 + . − . + . − . ± ± + . − . + . − .
1X 3.8 ± + . − . ± + . − . + . − . + . − .
2C 3.3 + . − . ± ± + . − . + . − . + . − . ± ± ± ± ± ± + . − . + . − . ± + . − . + . − .
3X 4.5 + . − . ± + . − . ± ± + . − .
4C 4.3 ± ± ± + . − . ± + . − . ± ± + . − . + . − . + . − . NGC 1313 X-21X 1.43 ± + . − . ± + . − . ± + . − . ± ± + . − . ± ± ± ± + . − . ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± + . − . + . − . -8X 1.34 ± ± ± ± + . − . -9X 1.40 ± ± ± ± ± ± ± ± + . − . ± ± ± ± + . − . ± + . − . ± ± ± + . − . + − ± ± ± ± ± + . − . ± ± ± ± ± ± ± ± ± ± ± ± ± + . − . + . − . -17X 1.09 ± ± ± + . − . + . − . -18X 1.10 ± ± ± ± ± ± ± ± ± + . − . -20X 2.15 ± ± + . − . ± + . − . + − + . − . ± ± + . − . + . − . + . − .
22X 1.63 ± ± ± ± ± ± ± ± + . − . + . − . -24X 1.59 + . − . ± ± ± + . − . -25X 2.16 ± ± ± + . − . ± ± ± ± ± ± ± ± ± + . − . + . − . + . − .
2X 0.92 + . − . ± + . − . + . − . + . − . + . − . ± ± ± ± ± ± ± ± + − ± ± ± ± + − ± ± ± ± + . − . + − ± ± ± + − ± + − ± + − + − + − + − Article number, page 40 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 3.
Continued.
Epoch L soft L hard L tot L soft disk L hard disk L simpl (0.3-1.5 keV) (1.5-10 keV) (0.3 – 10 keV) (0.01 – 100 keV) (0.01 – 100 keV) (0.01 – 100 keV)6X 9.9 + . − . ± ± ± ± ± ± ± + − ± + . − . ± ± + − ± ± ± ± ± + . − . -1X 0.58 ± ± ± ± + . − . -2X 0.98 ± ± ± + . − . ± ± + . − . ± + . − . ± ± ± ± ± + . − . -5XN 0.88 ± ± ± ± ± ± ± ± ± ± ± ± ± + . − . ± ± ± ± + . − . + . − . -9XN 1.31 ± ± ± ± ± ± ± ± ± + . − . -1C 1.04 ± ± ± ± + . − . -2X 1.7 ± ± ± ± + . − . -3X 1.36 + . − . + . − . ± ± + . − . -4X 1.8 ± ± ± ± + . − . -2C 1.76 + . − . ± ± ± + . − . -3C 1.51 ± ± ± ± + . − . -4CC 1.13 ± ± ± ± + . − . -5C 0.77 ± + . − . ± ± + . − . -5X 1.55 ± ± ± ± + . − . -6XX 2.11 ± ± ± + . − . ± ± ± ± ± + . − . -1X 0.91 + . − . ± ± ± + . − . -2X 0.78 ± ± ± ± ± ± ± ± ± + . − . -2C 1.20 ± ± ± + . − . + . − . -3CCC 1.04 ± ± ± ± ± ± + . − . ± + . − . + . − . -4X 0.99 ± ± ± + . − . ± ± + . − . ± + . − . + . − . -6XX 0.97 ± ± ± ± + . − . - Article number, page 41 of 44 & A proofs: manuscript no. aanda
Table 7.
Results of the F-test between tbabs ⊗ tbabs ⊗ ( diskbb + diskbb ) (1) and tbabs ⊗ tbabs ⊗ ( diskbb + simpl ⊗ diskbb ) (2) models. Epochsare sorted chronologically and the nomenclature indicate the number XMM-Newton , Chandra and
NuSTAR observations fit together. (see Table 1).
Epoch χ r / dof a χ r / dof b ∆ χ [1-Prob(F-test)] ×
100 (%) simpl ?Holmberg II X–11X 1.01 /
281 0.90 /
279 32.8 100.0 yes2X 1.06 /
246 1.02 /
244 10.7 99.40 yes3X 1.07 /
124 1.08 /
122 1.3 45.02 no4X 1.32 /
392 1.15 /
390 70.9 100.0 yes5X 1.12 /
316 1.06 /
314 22.6 100.0 yes6XNN 1.31 /
490 0.99 /
488 159.2 100.0 yes7XN 1.17 /
467 0.91 /
465 125.5 100.0 yesHolmberg IX X–11X 1.19 /
198 1.20 /
196 0.9 31.29 no2X 1.08 /
342 1.04 /
340 13.2 99.80 yes3X 1.05 /
353 0.98 /
351 25.4 100.0 yes4X 1.25 /
502 1.20 /
500 30.0 100.0 yes5X 0.82 /
81 0.80 /
79 3.1 85.00 no6X 1.19 /
398 1.09 /
396 40.3 100.0 yes7X 0.97 /
372 0.97 /
370 3.6 84.24 no8X 1.05 /
301 1.05 /
299 2.6 70.80 no9XXNN 1.24 / / /
956 1.04 /
954 175.8 100.0 yes11XXNN 1.18 / / /
156 0.90 /
154 - 0.00 no1C 0.80 /
84 0.82 /
82 0.0 0.00 no2C 1.07 /
77 1.10 /
75 0.0 0.00 no2X 1.00 /
336 1.00 /
334 1.9 61.32 no3X 1.11 /
286 1.11 /
284 1.2 41.54 no4X 0.98 /
288 0.97 /
286 4.0 87.06 no5XNN 1.09 /
775 0.95 /
773 111.0 100.0 yes6XN 1.29 /
802 1.10 /
800 154.5 100.0 yes3C 1.04 /
74 1.01 /
72 4.4 87.94 noNGC 5204 X–11C 0.86 /
50 0.89 /
48 0.1 5.46 no1X 1.04 /
249 1.04 /
247 2.34 67.45 no2X 1.22 /
157 1.21 /
155 4.0 80.66 no3X 1.08 /
180 1.08 /
178 2.0 60.09 no2C 1.27 /
151 1.27 /
149 1.7 48.59 no3CC 0.94 /
152 0.95 /
150 0.1 5.12 no4C 0.97 /
47 1.01 /
45 0.0 0.00 no5C 1.06 /
78 1.09 /
76 0.4 16.77 no6C 1.08 /
47 1.04 /
45 3.9 83.55 no7C 0.66 /
68 0.68 /
66 0.0 0.00 no4X 0.97 /
185 0.94 /
183 7.8 98.28 yes5X 1.01 /
339 0.97 /
337 15.3 99.96 yes6X 1.03 /
307 1.00 /
305 12.1 99.74 yes7XXNN 1.13 /
625 1.02 /
623 72.5 100.0 yes8X 1.07 /
260 1.06 /
258 4.7 88.84 noNGC5408X–11X 1.18 /
138 1.16 /
136 4.7 86.41 no2X 1.01 /
139 1.01 /
137 1.2 44.48 no3X 1.13 /
97 1.12 /
95 2.9 71.99 no4X 0.97 /
106 0.97 /
104 2.4 70.65 no5X 1.86 /
352 1.57 /
350 106.4 100.0 yes6X 1.56 /
314 1.41 /
312 48.9 100.0 yes1CC 1.15 /
201 1.15 /
199 3.9 81.52 no2C 1.07 /
99 1.04 /
97 5.5 92.42 no7X 1.65 /
379 1.45 /
377 79.9 100.0 yes
Article number, page 42 of 44. Gúrpide et al.: Long term evolution of ULXs
Table 7.
Continued.
Epoch χ r / dof a χ r / dof b ∆ χ [1-Prob(F-test)] ×
100 (%) simpl ?8X 1.85 /
382 1.58 /
380 105.4 100.0 yes9X 1.79 /
366 1.40 /
364 145.8 100.0 yes10X 1.75 /
377 1.42 /
375 129.1 100.0 yes11XX 1.51 /
568 1.36 /
566 86.3 100.0 yesNGC 1313 X–11X 1.16 /
338 1.15 /
336 4.8 87.49 no2XX 0.85 /
150 0.84 /
148 3.7 88.67 no3XX 1.00 /
343 0.98 /
341 6.9 99.05 yes c
4X 0.91 /
109 0.86 /
107 7.8 98.73 no5X 1.01 /
286 1.01 /
284 0.7 29.23 no6X 1.18 /
166 1.19 /
164 - 0.00 no7X 1.01 /
157 1.02 /
155 - 0.00 no8X 1.09 /
218 1.06 /
216 9.3 98.67 yes c
9X 1.27 /
457 1.21 /
455 30.0 100.0 yes10XN 1.43 /
649 1.20 /
647 157.3 100.0 yes11XN 1.43 /
678 1.15 /
676 189.5 100.0 yes12XN 1.61 /
558 1.18 /
556 244.2 100.0 yes13X 0.98 /
256 0.98 /
254 1.8 60.07 no14XN 1.38 /
512 1.11 /
510 142.6 100.0 yes15XN 1.71 /
759 1.16 /
757 415.8 100.0 yes16X 1.58 /
487 1.30 /
485 139.2 100.0 yes17XXN 1.39 /
983 1.24 /
981 148.8 100.0 yes18X 1.31 /
457 1.12 /
455 87.3 100.0 yes19XN 1.82 /
655 1.26 /
653 368.1 100.0 yesCircinus ULX51X 0.78 /
119 0.80 /
117 0.0 64.12 no1C 0.78 /
84 0.77 /
82 1.9 70.14 no2XNN 1.30 /
678 1.21 /
676 67.9 100.0 yes3X 1.04 /
271 1.01 /
269 12.2 99.73 no d /
305 0.98 /
303 3.6 83.73 no5X 0.99 /
201 0.99 /
199 2.0 63.55 no6X 1.30 /
486 1.30 /
484 5.4 87.40 noNGC 55 ULX11X 1.11 /
293 1.06 /
291 17.5 99.97 yes2X 1.36 /
178 1.32 /
176 11.2 98.44 yes c
3X 1.43 /
317 1.36 /
315 26.9 99.99 yesNGC 6946 X–11C 1.1 /
162 1.0 /
160 19.1 100.0 yes1X 1.1 /
130 1.0 /
128 8.6 98.7 yes c
2C 1.1 /
97 1.0 /
95 11.5 99.5 yes3CC 1.0 /
103 0.9 /
101 6.2 95.9 no2XX 1.1 /
329 1.1 /
327 19.0 100.0 yes3X 1.4 /
357 1.2 /
355 72.0 100.0 yes4C 1.0 /
102 0.9 /
100 3.6 84.82 no4XNN 1.3 /
328 1.2 /
326 29.6 100.0 yesNGC 1313 X–21X 0.98 /
135 0.97 /
133 3.3 81.43 no2X 0.89 /
279 0.89 /
277 0.0 0.00 no3X 1.06 /
199 1.06 /
197 2.7 71.91 no4X 0.91 /
170 0.92 /
168 0.0 0.00 no5X 0.91 /
175 0.90 /
173 3.8 87.53 no6X 1.00 /
110 0.97 /
108 5.6 93.99 no7X 0.78 /
293 0.79 /
291 0.4 22.49 no8X 1.22 /
95 1.21 /
93 3.6 76.86 no9X 1.18 /
181 1.18 /
179 2.1 58.75 no10X 0.93 /
302 0.93 /
300 1.1 44.53 no11X 1.05 /
118 1.05 /
116 2.0 61.00 no
Article number, page 43 of 44 & A proofs: manuscript no. aanda
Table 7.
Continued.
Epoch χ r / dof a χ r / dof b ∆ χ [1-Prob(F-test)] ×
100 (%) simpl ?12X 1.10 /
154 0.92 /
152 29.7 100.0 yes13XN 1.11 /
484 1.09 /
482 8.3 97.69 yes14XN 1.15 /
393 1.15 /
391 4.8 87.56 no15X 1.09 /
59 1.12 /
57 0.0 0.00 no16X 1.30 /
127 1.29 /
125 3.1 69.48 no17X 1.11 /
85 1.14 /
83 0.0 0.00 no18X 0.88 /
335 0.88 /
333 2.0 67.96 no19X 1.11 /
232 1.12 /
230 0.0 0.00 no20X 1.09 /
433 1.03 /
431 26.2 100.0 yes21XN 1.14 /
160 1.04 /
158 17.4 99.96 yes22X 1.06 /
246 1.07 /
244 0.0 0.00 no23X 1.51 /
135 1.48 /
133 0.0 87.02 no24X 1.02 /
100 1.01 /
98 2.8 74.54 no25X 0.90 /
108 0.91 /
106 1.1 45.26 no26XXN 1.23 /
625 1.23 /
623 1.3 66 noNGC 300 ULX11XN 1.59 /
857 1.34 /
855 221.3 100.0 yes2X 1.1 /
450 1.1 /
448 12.1 99.6 yes1CC 1.05 /
165 1.06 /
163 - 0.00 noNGC 5907 ULX-11X 0.80 /
215 0.81 /
213 0.0 0.00 no2X 1.11 /
187 1.12 /
185 0.0 0.00 no3XXCC 0.91 /
239 0.92 /
237 0.0 - no4XN 1.12 /
232 1.11 /
230 5.2 90.13 no5XNN 1.03 /
491 0.94 /
489 47.7 100.0 yes6X 1.06 /
151 1.03 /
149 6.4 95.19 no7X 0.93 /
122 0.94 /
120 0.0 0.00 no8XX 1.14 /
125 1.15 /
123 2.2 61.46 noNGC 7793 P131C 1.05 /
221 1.06 /
219 0.2 8.98 no1X 1.07 /
336 1.08 /
334 0.0 0.00 no2X 1.25 /
401 1.25 /
399 1.3 40.56 no3XN 1.13 /
812 1.12 /
810 6.8 95.10 no4X 0.90 /
168 0.91 /
166 0.6 28.11 no5XN 1.17 /
579 1.18 /
577 -0.5 - no6X 1.23 /
403 1.23 /
401 4.6 84.56 no7X 1.04 /
423 1.05 /
421 -3.0 - no8X 1.09 /
422 1.09 /
420 3.6 80.70 no9XN 1.10 /
661 1.10 /
659 2.9 73.12 no
Notes: a χ r and degrees of freedom of the tbabs ⊗ tbabs ⊗ ( diskbb + diskbb ) model. b Similarly for model tbabs ⊗ tbabs ⊗ ( diskbb + simpl ⊗ diskbb ). c simpl model included as we could constrain it with another observations wherethe source was similar in flux and hardness-ratio. d simpl model not included as we could not constrain its parameters with anotherobservations where the source was similar in flux and hardness-ratio.model not included as we could not constrain its parameters with anotherobservations where the source was similar in flux and hardness-ratio.