Abstract
The nature of ultraluminous X-ray sources (ULXs) – off-nuclear extragalactic sources with luminosity, assumed isotropic, ≳1039 erg s−1 – is still debated. One possibility is that ULXs are stellar black holes (BHs) accreting beyond the Eddington limit. This view has been recently reinforced by the discovery of ultrafast outflows at ∼0.1–0.2c in the high-resolution spectra of a handful of ULXs, as predicted by models of supercritical accretion discs. Under the assumption that ULXs are powered by super-Eddington accretion on to BHs, we use the properties of the observed outflows to self-consistently constrain their masses and accretion rates. We find masses ≲100 M⊙ and typical accretion rates ∼10−5 M⊙ yr−1, i.e. ≈10 times larger than the Eddington limit calculated with a radiative efficiency of 0.1. However, the emitted luminosity is only ≈10 per cent beyond the Eddington luminosity, because most of the energy released in the inner part of the accretion disc is used to accelerate the wind, which implies radiative efficiency ∼0.01. Our results are consistent with a formation model where ULXs are BH remnants of massive stars evolved in low-metallicity environments.
1 INTRODUCTION
Ultraluminous X-ray sources (ULXs) are non-nuclear, point-like, extragalactic sources with X-ray luminosity, assumed isotropic, LX ≳ 1039 erg s−1; they are preferentially hosted by star-forming galaxies (see Feng & Soria 2011 for a review). There is no consensus yet on the nature of ULXs. Indeed, their luminosities are larger than the Eddington luminosity of ∼10 M⊙ black holes (BHs) in Galactic binaries, suggesting that they could represent a different class of objects, unless various combinations of significant beaming (e.g. King et al. 2001) and super-Eddington accretion (e.g. Begelman 2002; Poutanen et al. 2007; King 2008) are advocated. On the other hand, ULXs could also be powered by sub-Eddington accretion on to intermediate-mass black holes (IMBHs) with masses 100 ≲ M•/M⊙ ≲ 105; however, IMBHs might be required only to explain the most luminous ULXs (e.g. Farrell et al. 2009) and perhaps some of those showing quasi-periodic oscillations (e.g. Earnshaw et al. 2016; but see also Middleton et al. 2011), but they are unlikely to account for the majority of the ULX population (e.g. Stobbart, Roberts & Wilms 2006; Mapelli et al. 2008; Gladstone, Roberts & Done 2009). An intermediate possibility is represented by massive stellar BHs (20 ≲ M•/M⊙ ≲ 80) produced by low metallicity (Z ≲ 0.4 Z⊙), massive (≳40 M⊙) stars (Mapelli, Colpi & Zampieri 2009; Mapelli et al. 2010), which are expected in ULX host galaxies owing to their low metallicity and high star formation rate (Pakull & Mirioni 2002; Zampieri & Roberts 2009). Moreover, some ULXs are powered by accretion on to neutron stars (Bachetti et al. 2014; Fürst et al. 2016; Israel et al. 2017); therefore, ULXs likely represent an heterogeneous class of objects.
Unfortunately, dynamical masses are not available for most ULXs. Recently, Liu et al. (2013) claimed the detection of the orbital modulation in M101 ULX-1, inferring a mass >5 M⊙ and likely ∼30 M⊙. However, the putative companion is likely a Wolf–Rayet star, which makes this dynamical measurement uncertain (Laycock, Maccarone & Christodoulou 2015). In addition to that, hard X-ray observations with NuSTAR of a few ULXs show a downturn in the spectra at energies ≳10 keV, which excludes sub-Eddington accretion on to IMBHs, whereas it favours super-Eddington accretion on lighter accretors (Bachetti et al. 2013; Walton et al. 2014). If super-Eddington accretion is common among ULXs with luminosities ∼1040 erg s−1, an expected feature is the presence of optically thick outflows from the inner, geometrically thick, radiation-dominated regions of the accretion disc (Poutanen et al. 2007; Takeuchi, Ohsuga & Mineshige 2013). Remarkably, recent work on high-resolution soft (∼0.4–1.8 keV) X-ray spectra revealed for the first time blueshifted, high-excitation absorption lines compatible with velocity offsets as high as ∼0.25c in three ULXs (Pinto et al. 2017; Pinto, Middleton & Fabian 2016). These results were strengthened by the high-energy counterpart of the NGC 1313 X-1 outflow observed in moderate-resolution broad-band (∼3–20 keV) X-ray spectra (Walton et al. 2016). The discovery of ultrafast outflows from ULXs strongly hints that at least a fraction of them may be powered by super-Eddington accretion. However, as the nature of ULXs remains mostly unknown, it is unclear whether this would make them a peculiar class of accretors or an evolutionary phase of more common sources (e.g. high-mass X-ray binaries).
In this Letter, we assume that ULXs are BHs accreting beyond the Eddington limit and therefore that they are able to launch radiation-driven outflows from the inner part of the accretion disc. We neglect here the case of ULXs powered by accreting neutron stars. We use the observed properties of the outflows to self-consistently constrain the expected mass and accretion rate of the powering BH within such a framework. Our results suggest that the few ULXs with observed outflows could be associated with BHs with masses between ∼10 and ∼100 M⊙, and typical accretion rates ∼10−5 M⊙ yr−1. If some ULXs are powered by BHs and ultrafast outflows caused by super-Eddington accretion are common, then our results suggest that their origin could be consistent with being the remnant of massive metal-poor stars.
2 SUPERCRITICAL ACCRETION DISCS WITH OUTFLOWS
3 CONSTRAINING THE BLACK HOLE MASS
Recent observations have discovered fast outflows in the deepest X-ray spectra of ULXs (e.g. Pinto et al. 2016; Walton et al. 2016). They are identified through high ionization Fe, O and Ne absorption lines produced by gas outflowing at ≈0.1–0.2c with photoionization parameters ξ = Lion/(nr2) ranging from ∼102 to ≳104 erg cm s−1, where n is the density of the absorbing gas at radial distance r from the source emitting the ionizing luminosity Lion in the energy band 1–1000 Ry. We can use these results to constrain the parameters of a supercritical accretion disc potentially able to produce such winds and eventually the mass of the central BH as follows.
Fig. 1 summarizes the results of our calculations, showing the values of εw, |$\dot{m}$|, Γ and η in the ξ–β∞ plane. We adopt fiducial values for the parameters Ωw = 0.5, Cw = 0.3 and f = 1. For values of β∞ above ≈0.05–0.1, the lines of constant εw roughly scale as β∞ ∝ [εwξ/(1 − εw)]1/3. Mildly relativistic winds (β∞ ≳ 0.05) typically require ≳90 per cent of the energy produced within Rsp to accelerate the outflows, unless log ξ ≫ 4 and εw can reduce to ∼50 per cent. The remaining energy is released in photons and it contributes to bolometric luminosities ∼10 per cent in excess of LEdd, as shown by the isocontours of Γ. εw can even exceed 99 per cent for fast outflows ∼0.2c at log ξ < 3, locking the bolometric luminosity at about LEdd. On the other hand, the accretion rate |$\dot{m}$| mainly depends on the outflow velocity because ξ enters only weakly in equation (3) through εw and |$\dot{m} \sim r_{\rm sp} \sim \beta _{\infty }^{-2}$|. Fast winds with β∞ ≳ 0.1 are typically associated with |$\dot{m} \sim 10$|, where ∼50 per cent reaches the central BH while the remaining is accelerated in the outflows. The differences between the isocontours of |$\dot{m}$| and Γ determines the actual radiative efficiency of the disc, |$\eta = \tilde{\eta } \Gamma / \dot{m}$|, which is typically ∼0.001 and increases up to ∼0.01 for winds as fast as ∼0.2c. This trend is in qualitative agreement with numerical simulations of supercritical accretion discs with radiation-driven outflows that show η ∼ 0.04, larger than the equivalent slim disc (Jiang, Stone & Davis 2014; Sa̧dowski et al. 2015); however, we also infer η’s slightly lower than what numerical simulations predict.
Results of the model shown in the ξ–β∞ plane. From left to right: fraction εw of the released energy within Rsp that is converted in kinetic luminosity of the wind, accretion rate |$\dot{m}$| in the outer part of the disc in units of |$\dot{M}_{\rm Edd}$| (see equation 1), bolometric luminosity Γ in units of LEdd and radiative efficiency |$\eta = \tilde{\eta } \Gamma /\dot{m}$|. We adopt the fiducial values for the model parameters: Ωw = 0.5, Cw = 0.3 and f = 1. The symbols with error bars refer to the sources listed in Table 1: the white circles are the observations of NGC 1313 X-1 by Pinto et al. (2016); the black circles with red and cyan edges are the observations of NGC 1313 X-1 by Walton et al. (2016) where the absorption feature is respectively attributed to Fe xxv and Fe xxvi; the triangle is the highest significance absorber in NGC 55 ULX detected by Pinto et al. (2017) and the square is the observation of NGC 5408 X-1 by Pinto et al. (2016).
Fig. 2 shows the corresponding BH mass in the ξ–β∞ plane for a source scaled to Lγ = lγ,40 × 1040 erg s−1. ULXs associated with outflows faster than ∼0.1c are expected to be powered by BHs with masses M• ∼ 40–70lγ,40 M⊙. In fact, the isocontours follow those of the luminosity Eddington ratio Γ and the mass asymptotically tends to the limiting mass M•, Edd when β∞ increases at constant ξ (i.e. faster wind with higher Pw), while it decreases when ξ increases at constant β∞ (i.e. less dense wind with lower Pw). These trends arise because, for a given Lγ, a wind that has a larger Pw requires a higher fraction εw of the energy produced within Rsp, which implies that η reduces and Γ → 1+, i.e. the emitted luminosity mostly comes from the outer, thinner disc. We note that, for high β∞ and low ξ, our mass estimates tend to saturate at about M•, Edd.
The colour-coded map shows the mass of the central BH scaled to a bolometric luminosity Lγ = lγ,40 × 1040 erg s−1. We adopt the fiducial values for the model parameters: Ωw = 0.5, Cw = 0.3 and f = 1. Observations are overplotted with the same symbols as in Fig. 1.
Both Figs 1 and 2 show the positions in the ξ–β∞ of different observations of ULX outflows detected in three nearby star-forming low-metallicity spiral/dwarf galaxies. The observations are summarized in Table 1; the table also shows the inferred radiative efficiency η, BH mass M• and accretion rate |$\dot{M}$|. All these quantities have been derived by assuming Lγ = LX, which could introduce a systematic error in the mass estimates. However, if we take the results with caution as order of magnitude estimates, we see that our calculations constrain the BH masses for those ULXs grossly to range between ∼10 and ∼100 M⊙, with accretion rates ∼10−5 M⊙ yr−1 (corresponding to |$\dot{m} \sim 10$|) and η ∼ 0.01.
Summary of the observational properties of ULXs with outflows and the model results. From left to right: outflow velocity β∞, photoionization parameter ξ, X-ray luminosity LX (assumed isotropic), estimated radiative efficiency η, estimated BH mass M• (upper limits excluding beaming) and estimated accretion rate |$\dot{M}$|. The inferred M• and |$\dot{M}$| assume LX as a proxy for Lγ.
| Source | β∞ | log ξ (erg cm s−1) | L X (erg s−1) | η | M • (M⊙) | |$\dot{M}$| (10−5 M⊙ yr−1) |
|---|---|---|---|---|---|---|
| NGC 1313 X-1a | 0.217 ± 0.007 | 2.20 ± 0.04 | 1.04 × 1040 | 0.011 | 75.0 | 1.7 |
| NGC 1313 X-1b | 0.25 ± 0.05 | 4.55 ± 0.22 | 1.04 × 1040 | 0.015 | 71.8 | 1.2 |
| NGC 1313 X-1c | 0.236 ± 0.005 | |$3.3^{+0.3}_{-0.5}$| | 1.04 × 1040 | 0.013 | 74.8 | 1.5 |
| NGC 1313 X-1d | ∼0.2 | ∼4.5 | 1.04 × 1040 | 0.011 | 68.4 | 1.7 |
| NGC 55 ULXe | 0.199 ± 0.003 | 3.35 ± 0.20 | 1.3–2.1 × 1039 | 0.009 | 12.2 | 0.3 |
| NGC 5408 X-1f | 0.22 ± 0.01 | 1.70 ± 0.26 | 2.01 × 1040 | 0.012 | 145.0 | 3.1 |
| Source | β∞ | log ξ (erg cm s−1) | L X (erg s−1) | η | M • (M⊙) | |$\dot{M}$| (10−5 M⊙ yr−1) |
|---|---|---|---|---|---|---|
| NGC 1313 X-1a | 0.217 ± 0.007 | 2.20 ± 0.04 | 1.04 × 1040 | 0.011 | 75.0 | 1.7 |
| NGC 1313 X-1b | 0.25 ± 0.05 | 4.55 ± 0.22 | 1.04 × 1040 | 0.015 | 71.8 | 1.2 |
| NGC 1313 X-1c | 0.236 ± 0.005 | |$3.3^{+0.3}_{-0.5}$| | 1.04 × 1040 | 0.013 | 74.8 | 1.5 |
| NGC 1313 X-1d | ∼0.2 | ∼4.5 | 1.04 × 1040 | 0.011 | 68.4 | 1.7 |
| NGC 55 ULXe | 0.199 ± 0.003 | 3.35 ± 0.20 | 1.3–2.1 × 1039 | 0.009 | 12.2 | 0.3 |
| NGC 5408 X-1f | 0.22 ± 0.01 | 1.70 ± 0.26 | 2.01 × 1040 | 0.012 | 145.0 | 3.1 |
Notes. aXABS 2 of Model 1 from Pinto et al. (2016).
bXABS 3 of Model 2 from Pinto et al. (2016).
cAbsorption feature at ≈8.8 keV attributed to Fe xxv (Walton et al. 2016).
dAbsorption feature at ≈8.8 keV attributed to Fe xxvi (Walton et al. 2016).
eData for the most significant absorber at ≈3.5σ from Pinto et al. (2017).
fData from Pinto et al. (2016).
Summary of the observational properties of ULXs with outflows and the model results. From left to right: outflow velocity β∞, photoionization parameter ξ, X-ray luminosity LX (assumed isotropic), estimated radiative efficiency η, estimated BH mass M• (upper limits excluding beaming) and estimated accretion rate |$\dot{M}$|. The inferred M• and |$\dot{M}$| assume LX as a proxy for Lγ.
| Source | β∞ | log ξ (erg cm s−1) | L X (erg s−1) | η | M • (M⊙) | |$\dot{M}$| (10−5 M⊙ yr−1) |
|---|---|---|---|---|---|---|
| NGC 1313 X-1a | 0.217 ± 0.007 | 2.20 ± 0.04 | 1.04 × 1040 | 0.011 | 75.0 | 1.7 |
| NGC 1313 X-1b | 0.25 ± 0.05 | 4.55 ± 0.22 | 1.04 × 1040 | 0.015 | 71.8 | 1.2 |
| NGC 1313 X-1c | 0.236 ± 0.005 | |$3.3^{+0.3}_{-0.5}$| | 1.04 × 1040 | 0.013 | 74.8 | 1.5 |
| NGC 1313 X-1d | ∼0.2 | ∼4.5 | 1.04 × 1040 | 0.011 | 68.4 | 1.7 |
| NGC 55 ULXe | 0.199 ± 0.003 | 3.35 ± 0.20 | 1.3–2.1 × 1039 | 0.009 | 12.2 | 0.3 |
| NGC 5408 X-1f | 0.22 ± 0.01 | 1.70 ± 0.26 | 2.01 × 1040 | 0.012 | 145.0 | 3.1 |
| Source | β∞ | log ξ (erg cm s−1) | L X (erg s−1) | η | M • (M⊙) | |$\dot{M}$| (10−5 M⊙ yr−1) |
|---|---|---|---|---|---|---|
| NGC 1313 X-1a | 0.217 ± 0.007 | 2.20 ± 0.04 | 1.04 × 1040 | 0.011 | 75.0 | 1.7 |
| NGC 1313 X-1b | 0.25 ± 0.05 | 4.55 ± 0.22 | 1.04 × 1040 | 0.015 | 71.8 | 1.2 |
| NGC 1313 X-1c | 0.236 ± 0.005 | |$3.3^{+0.3}_{-0.5}$| | 1.04 × 1040 | 0.013 | 74.8 | 1.5 |
| NGC 1313 X-1d | ∼0.2 | ∼4.5 | 1.04 × 1040 | 0.011 | 68.4 | 1.7 |
| NGC 55 ULXe | 0.199 ± 0.003 | 3.35 ± 0.20 | 1.3–2.1 × 1039 | 0.009 | 12.2 | 0.3 |
| NGC 5408 X-1f | 0.22 ± 0.01 | 1.70 ± 0.26 | 2.01 × 1040 | 0.012 | 145.0 | 3.1 |
Notes. aXABS 2 of Model 1 from Pinto et al. (2016).
bXABS 3 of Model 2 from Pinto et al. (2016).
cAbsorption feature at ≈8.8 keV attributed to Fe xxv (Walton et al. 2016).
dAbsorption feature at ≈8.8 keV attributed to Fe xxvi (Walton et al. 2016).
eData for the most significant absorber at ≈3.5σ from Pinto et al. (2017).
fData from Pinto et al. (2016).
Finally, we note that the derived masses depend on three free parameters, namely Ωw, Cw and f. The fiducial values that we adopt for Cw and Ωw, the latter corresponding to 60° from the rotation axes of the disc, are grossly expected from theoretical and numerical models (King 2008; Takeuchi et al. 2013). The fudge factor f is more uncertain, as it may account for different effects. We tested the sensitivity of our results to these parameters by varying Cw and Ωw between 0.2 and 0.8, and f between 0.2 and 3. As they always appear together as CwΩwf in equation (7) and (8), changing each of them independently has the same effect. We find that M• and |$\dot{M}$| change by up to ≈15–20 per cent, i.e. they do not significantly affect our estimates.
4 DISCUSSION AND CONCLUSIONS
In this Letter, we attempted to constrain the mass and the accretion rate of three ULXs through the properties of their observed ultrafast outflows, under the assumption that the latter are caused by super-Eddington accretion on to BHs. We find masses between ∼10 and ∼100 M⊙ and accretion rates ∼10−5 M⊙ yr−1, about 10 times larger than |$\dot{M}_{\rm Edd}$| in equation (1). However, the bolometric luminosity results to be only up to ∼10 per cent in excess of LEdd, implying a typical radiative efficiency η ∼ 0.01, because ≳90 per cent of the luminosity produced within Rsp is required to accelerate the outflow.
Bearing in mind that our small sample may not be representative of the whole population of ULXs, it is none the less interesting to note that the inferred masses lie between typical Galactic binaries and the presumed low-mass tail of IMBHs (e.g. Casares & Jonker 2014). However, they should not be regarded as exotic; they are well consistent with the expected remnants of low-metallicity massive stars. Indeed, Mapelli et al. (2009, 2010) have shown that such massive stellar BHs may statistically account for a large fraction of ULXs as well as for the correlation between the number of ULXs and the star formation rate of their host. Therefore, this might support the speculation that many ULXs could be powered by super-Eddington accretion on ∼10–100 M⊙ BHs (e.g. Gladstone et al. 2009; Middleton et al. 2015). However, a future larger sample of ultrafast outflows in ULX spectra as well as more robust dynamical mass estimates are necessary to eventually confirm this scenario.
Our investigation represents a tentative new approach to exploit recent observations of ultrafast outflows to constrain the mass of a few ULXs under the plausible assumption of super-Eddington accreting BHs. However, we emphasize again that the derived masses should be taken as indicative. Indeed, a factor of ∼2–3 to reduce the derived masses may still be accommodated, because we have effectively neglected geometric beaming effects when we associate the bolometric luminosity to the observed one. They might be particularly relevant for the radiation produced within Rsp that is mainly released in a rather narrow funnel along the disc rotation axis (Poutanen et al. 2007; Takeuchi et al. 2013). As a consequence, our masses should be considered as upper limits because the true Lγ, and therefore M•, could be lower by the beaming factor b ≲ 0.5–0.7 (King 2008, 2009). Moreover, we assumed Lγ = LX for the sake of simplicity, but in fact the bolometric correction of the inferred X-ray luminosity might vary from system to system. This might depend e.g. on the line of sight through the outflow, as hinted by the change in spectral hardness among the ULXs considered in Table 1, as well as by the conjectured connection with ultraluminous supersoft sources (Middleton et al. 2011, 2015; Pinto et al. 2017). According to this scenario, NGC 1313 X-1 is likely to be seen more face-on because of the harder spectrum, and therefore Lγ ≈ LX is a reasonable assumption (but it is more likely to suffer from beaming though), while NGC 55 ULX and NGC 5408 X-1 have softer spectra that may come from the reprocessing of the harder radiation from the inner edge of the disc (and perhaps by a close hot corona) by the optically thick wind, for which LX ≲ Lγ. This latter correction might partially compensate the effect of beaming, but note that LX as well is assumed isotropic and neglects beaming effects. None the less, even when reduced by a factor ∼2–3, our inferred masses are consistent with previous estimates of similar systems as well as with the aforementioned scenario of ULX formation.
Our calculations also neglect general relativistic effects, such as spinning BHs, and magnetic fields. We explored the impact of a spinning BH by changing the inner boundary condition and the normalizing radiative efficiency |$\tilde{\eta }$|. We find values of M• up to ≈20 per cent lower than in the no spin cases, owing to larger values of Γ and η at similar accretion rates. Magnetic fields might also contribute to accelerate the outflow (Blandford & Payne 1982), effectively lowering εw and increasing Lγ for the same accretion rate. This might also lower the value of the inferred central mass.
Regardless of their masses, BHs are not the only possible accretors powering ULXs. Indeed, the light curves of three ULXs show sinusoidal pulses with a period ≈1 s that are a distinctive signature of neutron stars (Bachetti et al. 2014; Fürst et al. 2016; Israel et al. 2017). Recently, King & Lasota (2016) and King, Lasota & Kluzniak (2017) argued that neutron stars may actually power a fraction of ULXs larger than previously expected. According to their analysis, pulsations may only be observed during a rather short phase of the ULX evolution, preventing an easy detection. However, the variability of the optical spectrum has revealed the existence of a massive stellar BH, likely ∼20–30 M⊙, in M101 ULX-1 (Liu et al. 2013) and perhaps also in X-ray binaries associated with Wolf–Rayet stars (Prestwich et al. 2007; Crowther et al. 2010; but see also Laycock et al. 2015). Therefore, it appears evident that ULXs comprise a diverse variety of accreting objects, and whether the majority is represented by BHs or neutron stars must be scrutinized further. Clearly, our analysis can be applied only to the subset of ULXs with outflows that probably host an accreting BH; none the less, it would be possible to extend this treatment to neutron stars by modifying the inner boundary conditions in modelling the accretion disc owing to the magnetic fields.
Finally, we step on to more speculative grounds by noting that the BH masses we infer, when considered as upper limits as discussed above, are not too dissimilar from those of the binary BHs detected by Advanced LIGO (Abbott et al. 2016a,b). While this might be just a coincidence, it is none the less worth to stress that such observations at least unambiguously demonstrate the existence in nature of rather heavy stellar BHs. According to stellar evolution models, the most natural pathway to form ≳30 M⊙ stellar BH is the evolution of massive stars in Z < 0.1–0.5 Z⊙ environments (Belczynski et al. 2010; Spera, Mapelli & Bressan 2015). Despite the evolution of binary stars is complicated by several physical processes that make difficult to predict the final outcome (Dominik et al. 2012), it is still conceivable to imagine an evolutionary connection between binary massive stars, whose fraction can be as high as 70 per cent (Sana et al. 2008), an intermediate phase when the binary turns into an ULX, and finally the merger of heavy stellar BH binaries (see also Pavlovskii et al. 2017). While this may sound attractive, further observations are required to better assess the puzzle of the nature of ULXs and consequently this potential connection.
Acknowledgments
We acknowledge useful discussions with Massimo Dotti, Michela Mapelli and Elena M. Rossi. DF acknowledges support by European Research Council (ERC) Starting Grant 638707 ‘Black holes and their host galaxies: coevolution across cosmic time’. CP and ACF acknowledge support by ERC Advanced Grant 340442 ‘Accreting black holes and cosmic feedback’.
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