# Magnetic field strength of a neutron-star-powered ultraluminous X-ray source

M. Brightman, F.A. Harrison, F. Fürst, M.J. Middleton, D.J. Walton, D.

Stern, A.C. Fabian, M. Heida, D. Barret, M. Bachetti

► To cite this version:

M. Brightman, F.A. Harrison, F. Fürst, M.J. Middleton, D.J. Walton, et al., Magnetic field strength of a neutron-star-powered ultraluminous X-ray source. Nature Astronomy, 2018, 2 (4), pp.312-316.
10.1038/s41550-018-0391-6 . hal-01768083

HAL Id: hal-01768083

https://hal.science/hal-01768083v1

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# Magnetic field strength of a neutron-star-powered ultraluminous X-ray source

M. Brightman<sup>1*</sup>, F. A. Harrison<sup>1</sup>, F. Fürst<sup>2</sup>, M. J. Middleton<sup>3</sup>, D. J. Walton<sup>4</sup>, D. Stern<sup>5</sup>, A. C. Fabian<sup>4</sup>, M. Heida<sup>1</sup>, D. Barret<sup>6,7</sup> and M. Bachetti<sup>1,8</sup>

Ultraluminous X-ray sources (ULXs) are bright X-ray sources in nearby galaxies not associated with the central supermassive black hole. Their luminosities imply they are powered by either an extreme accretion rate onto a compact stellar remnant, or an intermediate mass (~100–10⁵ M<sub>☉</sub>) black hole<fnref n="1" />. Recently detected coherent pulsations coming from three bright ULXs<sup>2–5</sup> demonstrate that some of these sources are powered by accretion onto a neutron star, implying accretion rates significantly in excess of the Eddington limit, a high degree of geometric beaming, or both. The physical challenges associated with the high implied accretion rates can be mitigated if the neutron star surface field is very high (10<sup>14</sup> G)⁶, since this suppresses the electron scattering cross-section, reducing the radiation pressure that chokes off accretion for high luminosities. Surface magnetic field strengths can be determined through cyclotron resonance scattering features<sup>7,8</sup> produced by the transition of charged particles between quantized Landau levels. Here, we present the detection at a significance of 3.8σ of an absorption line at 4.5 keV in the Chandra spectrum of a ULX in M51. This feature is likely to be a cyclotron resonance scattering feature produced by the strong magnetic field of a neutron star. Assuming scattering off electrons, the magnetic field strength is implied to be ~10<sup>11</sup> G, while protons would imply a magnetic field of B ~10<sup>15</sup> G.

The interacting galaxies of M51 have a large population of ultraluminous X-rays sources (ULXs), which were first discovered by the Einstein X-ray Observatory⁹. Since the galaxies are nearby (8.58 Mpc)¹⁰ and face on, their ULXs have been well studied and characterized by many X-ray telescopes including the X-ray Multi-Mirror Mission (XMM) Newton and Chandra observatories. RX J133007+47110, otherwise known as NGC5194/5 ULX8 (ref. ¹¹) is located at 13 h 30 m 07.55 s, +47° 11′ 06.1 on the sky (J2000 coordinates) and is ~2.6 arcmin east of the nucleus of M51a (NGC 5194) in one of the spiral arms (Fig. 1a). It is one of the brightest ULXs in M51 with an X-ray luminosity of ~2 × 10<sup>39</sup> erg s<sup>-1</sup> (assuming isotropic emission)¹².

On 2012 September 09, the Chandra X-ray observatory conducted a deep 181 ks observation of M51 with its Advanced CCD Imaging Spectrometer, during which ULX8 was brighter than previously observed and exhibited several ~10 ks duration bursts of X-rays up to 10<sup>40</sup> erg s<sup>-1</sup> that occurred throughout the observation (Fig. 1b). We extracted and fitted the Advanced CCD

Imaging Spectrometer spectrum of ULX8 from the entire observation, which revealed a strong absorption line feature at rest-frame 4.52 ± 0.05 keV, with a Gaussian width, σ = 0.11<sup>+0.07</sup><sub>-0.05</sub> keV, and an equivalent width, EW = -0.19<sup>+0.06</sup><sub>-0.09</sub> keV. The continuum is well described by a power-law spectrum (Γ = 1.3 ± 0.3) with an exponential cut-off (E<sub>C</sub> = 3.7<sup>+2.2</sup><sub>-1.0</sub> keV; Fig. 1c) or a multi-colour disk model with temperature T = 1.87<sup>+0.54</sup><sub>-0.28</sub> keV and a radial temperature profile with index p = 0.54 ± 0.03, typical of other ULXs observed below 10 keV (ref. ¹³). The goodness of fit values for these models are χ² = 252.4 and 253.2, respectively, both with 204 degrees of freedom. The addition of a Gaussian absorption line improves the cut-off power-law fit by Δχ² = -44.3, which we find to be highly significant from simulations (~3.8σ).

The absorption line is also present throughout the observation and does not appear to change during the bursting episodes. We also searched through all other long archival XMM-Newton and Chandra observations of M51 (all X-ray observations used in this paper are listed in Table 1) to determine whether the absorption line is transient or a permanent feature of the source. We modelled the spectra in the same way as described above (all X-ray spectral fitting results are given in Table 2), but with the line width fixed to 0.1 keV and the energy allowed to vary by ±1 keV from 4.5 keV. We did not find that the addition of the Gaussian absorption line was significant in any other observation, but the statistical lower limits on the EW afforded by the lower signal-to-noise ratio of these observations are such that we cannot rule out its presence.

There are no absorption features related to the Chandra mirrors or detectors around 4.5 keV and the count rate is low enough that pileup effects that could potentially distort the spectrum are small (the pileup fraction is <10%). Therefore, we rule out an instrumental origin of the absorption line. While several atomic absorption and emission lines from iron, oxygen and neon have recently been detected from stacked XMM-Newton and Nuclear Spectroscopic Telescope Array observations of three other ULXs<sup>14,15</sup>, the energy of the line we find in the Chandra spectrum of ULX8 is not consistent with any known bound-bound atomic transition. Highly blue-shifted features from lower energies caused by an ultra-fast outflow are unlikely since the line observed is isolated, whereas the low-energy lines are usually accompanied by lines from other elements. The large EW of the line makes absorption by iron, with its high cosmological abundance, the most likely atomic solution. However, the nearest strong iron absorption line is the Fe xxv Kα transition at

<footnote n="1">¹Cahill Center for Astrophysics, California Institute of Technology, Pasadena, CA, USA. ²Science Operations Department, European Space Astronomy Centre, Madrid, Spain. ³Department of Physics and Astronomy, University of Southampton, Southampton, UK. ⁴Institute of Astronomy, University of Cambridge, Cambridge, UK. ⁵Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA. ⁶Centre National de la Recherche Scientifique, Centre d'Etude Spatiale des Rayonnements, Toulouse, France. ⁷Université Toulouse III—Paul Sabatier-Observatoire Midi-Pyrénées, Centre d'Etude Spatiale des Rayonnements, Toulouse, France. ⁸Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Cagliari, Selargius, Italy.
*e-mail: murray@srl.caltech.edu</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1** | Observational information on ULX8. **a,** The position of ULX8 in M51. The grey-scale image is a near-infrared (3.6 µm Infrared Array Camera on the Spitzer Space Telescope) image of the galaxy, and the red circles are Chandra contours showing the brightest X-ray sources (>2 counts pixel⁻¹). The nuclei of the two galaxies and the ULXs are labelled. **b,** 0.5–8 keV Chandra light curve from observation 13813 with time bins of 1,000 s and 1σ error bars. **c,** Top: Chandra spectrum (black data points; 1σ error bars) from the same observation fitted with an absorbed cut-off power-law model (red line). Middle: residuals to the fit, clearly showing the absorption line at 4.5 keV. Bottom: residuals after the addition of a Gaussian absorption line. The horizontal red line again represents the fitted model. **d,** Results from the significance simulations showing a histogram of Δχ² values obtained from adding a line to 10,000 simulated spectra. The dashed line shows the observed change in χ².</figcaption></figure>

6.67 keV, an association with which would require a redshift of ~0.5. At the flux of ULX8, less than 0.15 galactic and extragalactic sources are expected in the region of M51 (ref. ⁹). Given this expected rate, the probability that ULX8 is a background active galactic nuclei or a foreground source based on a Poisson distribution is <0.13. Furthermore, the near infrared fluxes of active galactic nuclei are as high as, or higher than, their X-ray fluxes¹⁶, even considering a redshift of 0.5, but the upper limit on the near infrared emission at the position of the ULX is an order of magnitude lower than the observed X-ray flux¹⁷.

The best remaining possibility is that this line is produced by a cyclotron resonance scattering feature (CRSF), since these lines can theoretically occur over a wide range of energies depending mostly on the strength of the magnetic field that causes them. Most CRSF features that have been observed in Galactic neutron star binaries are associated with transitions of electrons, such as SMC X-2 (ref. ¹⁸) and V0332+53 (ref. ¹⁹). Alternatively, some CRSF features have been ascribed to the transitions of protons, most notably in the spectra of soft γ-ray repeaters, such as SGR 1806−20 (ref. ²⁰) and SGR 0418+5729 (ref. ²¹). SGRs are sources that emit large bursts of X-rays and γ-rays and have been shown to be powered by magnetars²².

However, association with either electrons or protons gives significantly different measurements of the magnetic field strength. For electrons, the transition energy, ΔE, is 11.6(1+z)⁻¹(Β/10¹² G) keV, where z=(1−2GM/r_cyc²)⁻¹/²−1 is the gravitational redshift and is ~0.25 for the emission from the surface of a typical neutron star. The 4.5 keV line that we have detected would therefore imply Β=4(1+z)×10¹¹ G. For protons, ΔE=6.3(1+z)⁻¹(Β/10¹⁵ G) keV; thus, interpreting our observed line as a proton CRSF would imply a very high magnetic field strength of 7(1+z)×10¹⁴ G.

One piece of observational evidence that could serve to discriminate between these two scenarios is the width of the absorption feature, which is thought to be caused by the Doppler effect produced by the thermal energy of the charged particles. Electrons, which are much lighter than protons, produce broader lines. For Galactic pulsars with known electron CRSFs, the features have Gaussian line widths of the order ~1 keV, and are seen mostly at energies above 10 keV, giving broadening ratios, σ/Ε ~ 0.1 (refs ¹⁸,¹⁹). The broadening ratio of the line we have observed is 0.02. In contrast, protons are more massive and should produce narrower lines. The few proton CRSFs observed to date were indeed narrow (σ<0.4 keV) and at energies below 10 keV (refs ²⁰,²¹), giving broadening ratios of
<table><caption>**Table 1 | Observational data used for analysis**</caption><thead><tr><th>Observatory</th><th>Identification</th><th>Start date (UT)</th><th>Exposure (ks)</th></tr></thead><tbody><tr><td>XMM-Newton</td><td>0112840201</td><td>2003 January 15, 13 h 12 min 55 s</td><td>20.9</td></tr><tr><td>XMM-Newton</td><td>0212480801</td><td>2005 July 01, 6 h 38 min 0 s</td><td>49.2</td></tr><tr><td>XMM-Newton</td><td>0303420101</td><td>2006 May 20, 6 h 31 min 1 s</td><td>54.1</td></tr><tr><td>XMM-Newton</td><td>0303420201</td><td>2006 May 24, 11 h 12 min 5 s</td><td>36.8</td></tr><tr><td>Chandra</td><td>13813</td><td>2012 September 09, 17 h 47 min 30 s</td><td>181.6</td></tr><tr><td>Chandra</td><td>13812</td><td>2012 September 12, 18 h 23 min 50 s</td><td>159.5</td></tr><tr><td>Chandra</td><td>13814</td><td>2012 September 20, 7 h 21 min 42 s</td><td>192.4</td></tr><tr><td>Chandra</td><td>13815</td><td>2012 September 23, 8 h 12 min 8 s</td><td>68.1</td></tr><tr><td>Chandra</td><td>13816</td><td>2012 September 26, 5 h 11 min 40 s</td><td>74.1</td></tr></tbody></table>

$\sigma/E < 0.1$. Furthermore, theoretical work has been carried out concerning the X-ray emission of highly magnetized neutron stars$^{23-26}$, and radiative transfer calculations$^{24}$ predict that proton CRSFs should have EWs of 0.03–1 keV with $\sigma/E \sim 0.05-0.2$, which is very similar to the characteristics of the line that we detected. However, these calculations were carried out assuming much lower luminosities than those observed from ULX8. ULX8 is the most luminous CRSF source identified so far, so drawing a connection to lower-luminosity neutron star systems may be tenuous.

The velocity dispersion, $v$, associated with the line width we observed is $0.02c = 6 \times 10^6 \text{ m s}^{-1} (\sigma_E = v_c)$. For electrons, the implied thermal energy ($\frac{1}{2}m_e v^2$) is $1.6 \times 10^{-17} \text{ J}$ (0.1 keV), whereas the implied thermal energy when considering protons is ~200 keV. The temperature of the accretion disk, which we measured from the continuum, is 2 keV and is not consistent with either scenario. However, it is not known where the CRSF is formed in this system. This may occur in a hotter region of the system, or indeed a cooler one. Furthermore, the thermal motion of charged particles in the presence of an intense magnetic field is constrained by the direction of the magnetic field, thus the width of any absorption feature is probably highly dependent on our viewing angle and the magnetic geometry of ULX8, which is currently unknown. Therefore, it is not possible to draw

definitive conclusions regarding the type of charged particle producing the CRSF from the width of the line alone.

An additional key piece of evidence for CRSFs is the detection of harmonic features caused by transitions to higher Landau levels and expected at integer multiples of the energy of the fundamental line. Assuming the 4.5 keV line is the fundamental, the first harmonic should lie at 9.0 keV. However, the effective area of the Chandra detectors is very low at this energy (~10% of the area at 4.5 keV) so no constraints can be placed on the presence of a harmonic line here. Nevertheless, we can investigate whether the 4.5 keV line is in fact a harmonic by testing the presence of a fundamental line at 2.25 keV. Adding an absorption line at this energy with the same width as the 4.5 keV line does not improve the fit ($\Delta\chi^2 < 0.1$). If it were present, it would have an equivalent width of $-5 \times 10^{-5} \text{ keV}$ (a 90% confidence lower limit of $-0.03 \text{ keV}$) and thus several factors smaller than the line at 4.5 keV. If there is indeed a fundamental line at 2.25 keV, it has suffered from a large amount of photon spawning, caused by transitions from high to low Landau levels that produce photons at the energy of the fundamental line$^{27}$. This effect is strongest for electrons and hard X-ray spectra, whereas the spectrum of ULX8 is relatively soft ($\Gamma = 1.3 \pm 0.3$ with an exponential cut-off at 4 keV). We therefore conclude that the 4.5 keV line is the probable fundamental. The detection of a harmonic line at 9 keV and measuring its strength with respect to the fundamental could provide the key observational evidence in favour of an electron or proton CRSF. This could be done with the Nuclear Spectroscopic Telescope Array, XMM-Newton or the Neutron star Interior Composition Explorer when the ULX exhibits similar bursting behaviour to when the CRSF was detected by Chandra.

While the unambiguous detection of the CRSF determines that the compact object that powers ULX8 is a neutron star, we do not detect pulsations from this source. If the neutron star is spinning, and the rotation period is 1 s, we find that the pulse fraction would need to be at least 45% to be detected at $3\sigma$ significance in the short XMM-Newton observations. This is higher than the pulsed fractions below 10 keV of the other ULX pulsars discovered to date, which are <30% (refs $^{2-5}$). Although the Chandra observations are longer, the time resolution of the Advanced CCD Imaging Spectrometer detectors is not good enough to detect the ~1 s pulsation periods typical of the other ULX pulsars.

To date, the only observational constraints on the magnetic field strengths of neutron-star-powered ULXs have come from the observed spin up of the neutron star caused by the transfer of angular momentum from the accretion disk to the star. The accretion torque is applied at the inner edge of the accretion disk,

<table><caption>**Table 2 | Parameters of the cut-off power-law model used to fit the continuum, without the absorption line**</caption><thead><tr><th>Identification<sup>a</sup></th><th>N<sub>H</sub> (10<sup>20</sup> cm<sup>-2</sup>)<sup>b</sup></th><th>Γ<sup>c</sup></th><th>E<sub>c</sub> (keV)<sup>d</sup></th><th>χ<sup>2</sup>, d.f.<sup>e</sup></th><th>F<sub>X</sub> (10<sup>-13</sup> erg cm<sup>-2</sup> s<sup>-1</sup>)<sup>f</sup></th><th>L<sub>X</sub> (10<sup>39</sup> erg s<sup>-1</sup>)<sup>g</sup></th></tr></thead><tbody><tr><td>112840201</td><td>11.2<sup>+3.3</sup><sub>-4.5</sub></td><td>2.27<sup>+0.08</sup><sub>-0.44</sub></td><td>-</td><td>72.1, 58</td><td>2.99<sup>+0.28</sup><sub>-0.52</sub></td><td>2.6<sup>+0.2</sup><sub>-0.5</sub></td></tr><tr><td>212480801</td><td>6.0<sup>+2.8</sup><sub>-2.5</sub></td><td>1.99<sup>+0.15</sup><sub>-0.19</sub></td><td>-</td><td>82.7, 66</td><td>2.49<sup>+0.16</sup><sub>-0.16</sub></td><td>2.2<sup>+0.1</sup><sub>-0.1</sub></td></tr><tr><td>303420101</td><td>9.9<sup>+2.8</sup><sub>-2.6</sub></td><td>2.19<sup>+0.16</sup><sub>-0.21</sub></td><td>-</td><td>78.1, 79</td><td>2.20<sup>+0.14</sup><sub>-0.14</sub></td><td>1.9<sup>+0.1</sup><sub>-0.1</sub></td></tr><tr><td>303420201</td><td>13.2<sup>+3.3</sup><sub>-3.4</sub></td><td>2.25<sup>+0.15</sup><sub>-0.28</sub></td><td>-</td><td>65.8, 62</td><td>2.69<sup>+0.21</sup><sub>-0.22</sub></td><td>2.4<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>13812</td><td>4.7<sup>+4.8</sup><sub>-4.7</sub></td><td>1.12<sup>+0.40</sup><sub>-0.40</sub></td><td>2.1<sup>+0.9</sup><sub>-0.5</sub></td><td>170.2, 153</td><td>3.30<sup>+0.31</sup><sub>-0.26</sub></td><td>2.9<sup>+0.3</sup><sub>-0.2</sub></td></tr><tr><td>13813</td><td>7.7<sup>+3.7</sup><sub>-3.7</sub></td><td>1.26<sup>+0.29</sup><sub>-0.30</sub></td><td>3.7<sup>+2.2</sup><sub>-1.0</sub></td><td>252.4, 204</td><td>5.43<sup>+0.35</sup><sub>-0.32</sub></td><td>4.8<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>13814</td><td>10.5<sup>+5.4</sup><sub>-5.3</sub></td><td>1.70<sup>+0.46</sup><sub>-0.47</sub></td><td>2.5<sup>+2.0</sup><sub>-0.8</sub></td><td>145.6, 141</td><td>2.64<sup>+0.37</sup><sub>-0.30</sub></td><td>2.3<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>13815</td><td>16.7<sup>+8.4</sup><sub>-9.7</sub></td><td>2.30<sup>+0.52</sup><sub>-0.92</sub></td><td>&gt;1.8</td><td>69.6, 73</td><td>3.13<sup>+0.65</sup><sub>-0.70</sub></td><td>2.8<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td>13816</td><td>4.4<sup>+8.1</sup><sub>-4.4</sub></td><td>1.12<sup>+0.71</sup><sub>-0.50</sub></td><td>2.1<sup>+2.4</sup><sub>-0.8</sub></td><td>112.2, 99</td><td>2.98<sup>+0.54</sup><sub>-0.32</sub></td><td>2.6<sup>+0.5</sup><sub>-0.3</sub></td></tr></tbody></table>

<footnote><sup>a</sup>Observation identification number. <sup>b</sup>Neutral column density intrinsic to the source. <sup>c</sup>Power-law index of the continuum model. <sup>d</sup>High-energy cut-off. No data indicates that the parameter was unconstrained. <sup>e</sup>χ<sup>2</sup> of the fit and the number of degrees of freedom. <sup>f</sup>0.5–8 keV flux, corrected for absorption. <sup>g</sup>Intrinsic luminosity of the source, assuming isotropic emission and a distance of 8.58 Mpc.</footnote>
which is located where the magnetic field disrupts the accretion flow. This radius depends on the magnetic field strength, so knowledge of the spin up combined with the accretion rate gives a magnetic field strength estimate. These estimates have generally yielded strengths of B ~ 10¹² G for the known ULX pulsars²,³ and are thus consistent with the magnetic field strength inferred for ULX8 when assuming an electron CRSF. Other theoretical arguments have hypothesized strengths that vary over five orders of magnitude, from 10⁹⁻¹⁰¹⁴ G, depending on the model. The proton scenario yields a magnetic field strength of B ~ 10¹⁵ G and supports models that invoke such strong magnetic fields that are needed to reduce the electron scattering cross-section and allow super-critical accretion⁶.

## Methods

**Observations and data reduction.** Chandra has observed M51 on 13 separate occasions between 2000 and 2017. The majority of the exposure time resulted from a large 750 ks programme studying the interstellar medium, supernova remnants and X-ray binaries in the galaxy²⁰. We considered only five of all 13 observations where the exposure was longer than 50 ks, such that the signal-to-noise ratio was large enough for detailed spectral fitting. We used CIAO version 4.7 to analyse these data. We extracted events from a circular region with a 1 arcsec radius centred on the source, as well as background events from a nearby source-free region using the tool specextract.

XMM-Newton observed M51 nine times between 2003 and 2011. We analysed only four of these, which had exposures longer than 20 ks, using xmsms version 15.0 software. Events were extracted from a 15 arcsec circular region, and background from a larger region located on the same chip. We only considered European Photon Imaging Camera (EPIC)-pn data due to the larger effective area than the EPIC-MOS (Metal Oxide Semi-conductor) instruments, and filtered out periods of high background from the XMM-Newton data. The observational data are listed in Table 1.

**Spectral fitting.** We grouped all spectra with a minimum of 20 counts per bin with the HEAsoft tool grppha. Spectral fitting was carried out using XSPEC version 12.9.1 to fit background-subtracted spectra using $\chi^2$ as the fit statistic. For the Chandra spectra, we fit in the 0.5–8 keV range, and for XMM-Newton we fit in the 0.2–10 keV range.

We fit the Chandra and XMM-Newton data with a power-law model with a high-energy cut-off, where $F_γ = AE^{-Γ_e(E/E_C)}$, a phenomenological model that reproduces the spectral curvature typical of ULXs below 10 keV. We also applied photoelectric absorption caused by the interstellar medium of our own Galaxy, fixed at $N_{it} = 1.5 \times 10^{20} \text{cm}^{-2}$, as well as absorption intrinsic to the source at the redshift of M51 ($z=0.002$), which was left as a free parameter in the fit.

Table 2 lists the results from the spectral fitting. We found that the absorbed cut-off power-law model describes the data well in general. The yielded parameters varied from observation to observation, with $N_{it} = 4–16 \times 10^{20} \text{cm}^{-2}$ and power-law index $Γ = 1.1–2.3$. $E_C$ was not well constrained in many observations, but when it was, it varied from 2–5 keV. The absorption-corrected luminosity ranged from $2–5 \times 10^{39} \text{ erg s}^{-1}$. Inspecting the residuals of the fits, we discovered a strong absorption-line feature at 4.5 keV in Chandra observation 13813.

**Significance simulations.** To determine the statistical significance of the absorption line, we carried out simulations. We took the best-fit absorbed cut-off power-law model from the Chandra observation and simulated $10^5$ spectra in XSPEC using the fakeit command. We conducted these simulations based on the response matrix files and auxiliary response files for this observation. We simulated source and background spectra with the same exposure time as the real observation.

We then refit the spectrum with the same continuum model and noted the $\chi^2$ of the fit. We then added the Gaussian absorption line with an initial trial energy of 4.5 keV and the Gaussian width fixed to 0.1 keV. The equivalent width was allowed to take any negative value. The energy of the line was allowed to vary between 0.5 and 8 keV. We then noted the $\Delta\chi^2$ of the fit after the addition of this line. A histogram of the $\Delta\chi^2$ values produced by the simulated data is presented in Fig. 1d, where the real $\Delta\chi^2$ is plotted as a dashed line. From the $10^5$ simulated spectra, 18 produced a $\Delta\chi^2$ as large as the real observation. Varying the initial energy of the line in the fit did not change the result. The false alarm rate of $2 \times 10^{-4}$ corresponds to a significance of ~3.8$\sigma$.

**Absorption line characteristics.** While the absorption line featured at 4.5 keV was not visually evident in the other datasets, we added the absorption line to these spectral fits to determine a lower limit to the EW to assess whether the line was a transient feature. As for the significance simulations, we fixed the width of the line to 0.1 keV. We allowed the energy of the line to vary by $\pm 1$ keV from 4.5 keV to allow for energy dependence; for example, on luminosity¹⁹. We found only two out

of nine observations where the 68% confidence interval on the EW of the line was not consistent with the EW width of the strongly detected line ($-0.18^{+0.04}_{-0.09}$ keV). If we stacked the Chandra observations where the line was not detected and the ULX was at low fluxes, we could place a tighter constraint on the lower limit of the EW of -0.1 keV at 90% confidence. Doing the same with the XMM-Newton observations yielded a lower limit of -0.2 keV. This indicated that the line is not necessarily transient, but may be weaker at lower fluxes and require high signal-to-noise spectra to detect.

During Chandra observation 13813, the flux from ULX8 was highly variable, ranging from $5 \times 10^{-13} \text{ erg cm}^{-2} \text{s}^{-1}$ to $10^{-12} \text{ erg cm}^{-2} \text{s}^{-1}$. We tested whether the properties of the absorption line changed during the flaring episodes by splitting the observation into two flux regimes—a low-flux regime where $F_γ < 6 \times 10^{-13} \text{ erg cm}^{-2} \text{s}^{-1}$ and a high-flux regime where $F_γ > 6 \times 10^{-13} \text{ erg cm}^{-2} \text{s}^{-1}$. We found the continuum parameters in the low flux regime to be $Γ = 1.31^{+0.34}_{-0.35}$ and $E_C = 3.2^{+2.2}_{-1.0}$ keV, and the line parameters to be $E = 4.54^{+0.07}_{-0.17}$ keV, $\sigma < 0.48$ keV and EW = -0.16$^{+0.08}_{-0.34}$ keV. During the high-flux state, the continuum parameters were $Γ = 1.46^{+0.35}_{-0.37}$ and $E_C = 4.5^{+5.3}_{-3.6}$ keV and the line parameters were $E = 4.46^{+0.22}_{-0.13}$ keV, $\sigma = 0.21^{+0.48}_{-0.13}$ keV and EW = -0.21$^{+0.11}_{-0.35}$ keV. We found no evidence for any spectral changes in either the line or continuum during the flaring episodes.

**Timing analysis.** For each of the observations where we conducted line searches, we also searched for pulsations expected from a neutron star accretor. We applied barycentric corrections to each events file, using the CIAO tool axbary on the Chandra data and the xmsms tool barycen on the XMM-Newton data. Unbinned source+background light curves for the ULX were constructed and fast-Fourier transform analysis was carried out on the light curves using the IDL tool ft. However, no evidence for coherent pulsations was found.

Finally, we proceeded to determine the upper limit on the putative pulsed fraction by simulating light curves with the same statistical properties as the measured ones, but with an additional sinusoid with a 1 s period that had some pulsed fraction on top of it. From this theoretical light curve, we drew Poisson-distributed measurements and calculated a fast-Fourier transform on each of the randomized light curves. We then determined whether any power in these fast-Fourier transforms was higher than the $3\sigma$ limit for white noise, taking the number of trials (that is, frequencies in the power spectrum density) into account. We ran this 500 times for four pulsed fractions—30, 35, 40 and 45%—finding that 20.4, 62, 92 and 99.8% of these light curves showed pulsations at $>3\sigma$, respectively. Therefore, this ULX would require a high pulsed fraction for the pulsations to be detected at high confidence with the current observations.

**Data availability.** The data that support the plots within this paper and other findings of this study are available from public archives or the corresponding author upon reasonable request.

Received: 5 December 2017; Accepted: 16 January 2018;
Published online: 26 February 2018

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## Acknowledgements

M.J.M. and D.J.W. appreciate support from Ernest Rutherford Science and Technology Facilities Council fellowships. The work of D.S. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

## Author contributions

M. Brightman reduced and analysed the Chandra and XMM-Newton data. F.F. performed timing analysis of the Chandra and XMM-Newton data. M.H. analysed the ULX multiwavelength counterpart. M. Brightman, F.A.H., F.F., M.J.M., D.J.W., A.C.F., D.B. and M. Bachetti interpreted the results. M. Brightman, F.A.H., D.J.W. and D.S. prepared the manuscript.

## Competing interests

The authors declare no competing interests.

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