X-ray binaries

Group members:

Pasi Hakala (PhD, FINCA)
Andrew Mason (PhD, FINCA)
Vitaly Neustroev (PhD, Univ. of Oulu)
Juri Poutanen (Professor, Tuorla)
Sergey Tsygankov (PhD, Tuorla)
Alexandra Veledina (PhD, Tuorla) 
Joonas Nättilä (PhD student)
Alexander Mushtukov (PhD student)
Auni Somero (PhD student)
Jere Kuuttila (bachelor student)
Juhani Mönkkönen (bachelor student)

    Recent Master and PhD theses on X-ray binaries defended in the group:

    1.      Alexandra Veledina, PhD thesis “Imprints of non-thermal particles on spectral and temporal properties of accreting black holes”, University of Oulu, 2014

    2.      Jari Kajava, PhD thesis “X-raying compact stars in the Galaxy and beyond”, University of Oulu, 2012

    3.      Indrek Vurm, PhD thesis “Time-dependent modeling of radiative processes in magnetized astrophysical plasmas”, University of Oulu, 2010

    4.      Askar Ibragimov, PhD thesis “X-ray emission from compact objects”, University of Oulu, 2009



    1. X-ray pulsars

    X-ray pulsars (XRPs) are accreting NSs which have magnetic field strength of about B=10121013G. The strong magnetic field channels the gas towards magnetic poles, where most the gravitational energy is released in the form of X-rays. Due to the misalignment of the magnetic field with the rotational axis of the NS, such an object manifests itself as an XRP.

    Understanding the physics of accretion onto strongly magnetized NS requires detailed modeling of interaction between radiation and plasma in strong B-field regime, in particular Compton scattering.  We have derived the relativistic kinetic equation for Compton scattering with no limitations on photon or electron energies and the B-field strength, accounting for polarization of both photons and electrons as well as for induced scattering and exclusion principle  (see Mushtukov et al. 2012, 2015). Using the exact scattering cross section, which has resonances around the cyclotron frequency, we recently demonstrated (Mushtukov et al. 2014) that the so called critical luminosity of the pulsar (i.e. luminosity when the accretion shock starts to rise above the NS surface) is a non-monotonic function of the luminosity. This critical luminosity separates the regimes where the correlation between the observed cyclotron energy and luminosity is replaced by the anti-correlation.

    We have recently also proposed a novel “reflection model” describing very special behavior of cyclotron line in a case of bright sources (see Poutanen et al. 2013), which was discovered earlier (see Tsygankov et al. 2006). According to the model, the cyclotron line forms when the radiation emitted by the accretion column is reflected from the neutron star surface (Figure 1). The reflection model was successfully applied to explain the observed variations of the cyclotron line energy in a bright X-ray pulsar V 0332+53 over a wide range of luminosities. Details of the XRP behavior in the subcritical regime of accretion are not understood yet, but a complete picture of radiation and matter interaction in the vicinity of a highly magnetized NS in a wide luminosity range is gradually taking shape.

    Our current investigations are focused on modeling of the accretion column as well as determination of the maximum luminosity for magnetized neutron stars in connection with a recent discovery that some ultra-luminous X-ray sources are in fact X-ray pulsars.


    Figure 1: Illustration of the “reflection model” that reproduces the anti-correlation between cyclotron line energy and the X-ray luminosity (Poutanen et al. 2013). The larger is the accretion rate, the higher the column, the larger the illuminated fraction of the stellar surface, the weaker the average magnetic field, and the smaller the cyclotron line energy.


    Selected publications:

    1.       Mushtukov A., Nagirner D.I., Poutanen J., 2015, Compton scattering S-matrix and cross section in a strong magnetic field, Phys. Rev. D, to be submitted 

    2.       Mushtukov A.A., Suleimanov V.F., Tsygankov S.S., Poutanen J., 2014,The critical accretion luminosity for magnetized neutron stars, MNRAS, in press http://arxiv.org/abs/1409.6457

    3.       Poutanen J., Mushtukov A.A., Suleimanov V.F., Tsygankov S.S., Nagirner D.I., Doroshenko V., Lutovinov A.A., 2013, A reflection model for the cyclotron lines in the spectra of X-ray pulsars, ApJ, 777, 115, http://arxiv.org/abs/1304.2633, http://dx.doi.org/10.1088/0004-637X/777/2/115

    4.       Boldin P.A., Tsygankov S.S., Lutovinov A.A., 2013, On timing and spectral characteristics of the X-ray pulsar 4U 0115+63: Evolution of the pulsation period and the cyclotron line energy, Astr. Letters, 39, 375-388, http://arxiv.org/abs/1305.6785, http://dx.doi.org/10.1134/S1063773713060029

    5.       Mushtukov A., Nagirner D.I., Poutanen J., 2012, Relativistic kinetic equation for Compton scattering of polarized radiation in a strong magnetic field, Phys. Rev. D., 85, 103002, http://arxiv.org/abs/1203.2055, http://dx.doi.org/10.1103/PhysRevD.85.103002

    6.       Lutovinov A., Tsygankov S., Chernyakova, M., 2012, Strong outburst activity of the X-ray pulsar X Persei during 2001-2011, MNRAS,  423, 1978-1984, http://arxiv.org/abs/1204.0483 , http://dx.doi.org/10.1111/j.1365-2966.2012.21036.x

    7.       Annala M., Poutanen J., 2010, Constraining compactness and magnetic field geometry of X-ray pulsars from the statistics of their pulse profiles, A&A, 520, A76, http://arxiv.org/abs/1008.2270, http://dx.doi.org/10.1051/0004-6361/200912773

    8.       Tsygankov S.S., Lutovinov A.A., Churazov E.M., Sunyaev R.A., 2006, V0332+53 in the outburst of 2004-2005: luminosity dependence of the cyclotron line and pulse profile, MNRAS, 371, 19-28, http://arxiv.org/abs/astro-ph/0511237, http://dx.doi.org/10.1111/j.1365-2966.2006.10610.x


    2. Accreting neutron stars in low-mass X-ray binaries

    The research field of accreting NS in low-mass X-ray binaries (LMXBs) has changed dramatically during the last 15 years with the launch of the Rossi X-ray Timing Explorer (RXTE). In 1996, the first evidence of millisecond periods in NS systems came with the detection of highly coherent oscillation in the 200–600 Hz range during X-ray bursts. By now about 20 NS show such oscillations. These are called nuclear-powered millisecond pulsars since the emission during the bursts is produced by thermonuclear burning at the NS surface. In 1998 RXTE also discovered coherent ms pulsations in the persistent emission of SAX J1808.4–3658. Now there are 15 such sources showing oscillations in the frequency range 180–600 Hz. These are called accreting millisecond pulsars (AMPs, see Fig.2).   In addition, a few dozen NS show kHz quasi-periodic oscillations (QPOs).


    Figure 2: Magneto-hydrodynamic simulations of the accretion onto a NS with the inclined dipole magnetic field (Romanova et al. 2004).

    AMPs are exceptional physical laboratories for studying extreme gravity effects as well as plasma physics of the interaction between the NS magnetosphere and the accretion disc. Coherent ms pulsations in the persistent emission allow us to produce highly accurate pulse profiles by folding the data over a long observational period (days or even weeks). By detailed modelling the folded pulse profiles, one is able to determine the physical parameters such as the NS mass and radius, inclination of the system, position of the emitting region (hotspot) at the NS surface as well as the emission pattern from the hotspot responsible for the observed radiation. We have developed a theory of formation of pulse profiles from rapidly spinning NS including all relativistic effects, and proposed to use pulse profiles to obtain constraints on the NS radius as a function of its mass (Poutanen & Gierlinski 2003).  Sometimes, pulse profiles of AMPs show significant deviations from a sine wave showing double-peak structure, which can be interpreted as a signature of the secondary magnetic pole (Ibragimov & Poutanen 2009, Poutanen et al. 2009). Studying the evolution of the profile with the accretion rate then gives us a possibility to geometrically constrain the inner disc radius as a function of accretion rate. The results will allow us to determine the energy dissipation profile in the region between the disc and the magnetosphere and thus use AMPs as laboratories to study the complicated plasma physics of the disc-magnetosphere interaction (Kajava et al. 2011).

    Among the projects that we are pursuing now, one can mention detailed modelling of the pulse profiles accounting for the non-sphericity of the NS also accounting for deviations of the metric from the Schwarzschild one. Determining the NS parameters such as their masses and radii from the detailed models of the AMPs’ pulse profiles is one of the primary goals of the Large Observatory For X-ray Timing (LOFT) satellite – a candidate for the ESA M4 mission.

    Majority of old NS have weak magnetic fields and the accretion disc extends to their surface forming a boundary/spreading layer (BL/SL), where the rapidly rotating gas decelerates down to the stellar angular velocity. The X-rays from these NS show quasi-periodic oscillations (QPOs) at kHz frequencies. The mechanisms responsible for QPOs are unknown (most of the proposed models are purely kinematical). The observations univocally argue in favour of the BL/SL as a source of QPOs (Gilfanov et al. 2003). Thus understanding the BL/SL physics is of foremost importance.  To describe the structure of the BL/SL, Inogamov & Sunyaev (1999) solved a 1D problem in shallow-water approximation assuming that the layer has velocity close to the Keplerian at the equator. We later included the GR effects, considered different chemical composition of the accreting material and computed the spectra.  Comparison to the observed X-ray spectra from the BL gave constraints on the NS masses and radii (Suleimanov & Poutanen 2006). In the near future, our goal is to make a significant step forward in developing the SL model by solving the time-dependent radiation-hydrodynamics equations. We start from a 1D problem and proceed to 2D models where it is possible to produce stable, non-axisymmetric surface features, which we believe are the origin of the QPOs.


    Selected publications:

    1.       Revnivtsev M.G., Suleimanov V.F., Poutanen J., 2013, On the spreading layer emission in luminous accreting neutron stars, MNRAS, 434, 2355-2361, http://arxiv.org/abs/1306.6237 , http://dx.doi.org/10.1093/mnras/stt1179

    2.       Falanga M., Kuiper L., Poutanen J., et al. 2012, Spectral and timing properties of the accreting X-ray millisecond pulsar IGR J174982921, A&A, 545, A26, http://arxiv.org/abs/1208.1384, http://dx.doi.org/10.1051/0004-6361/201219582

    3.      Feroci M. et al. (incl. Poutanen J.), 2012, LOFT: the Large Observatory For X-ray Timing, Proceedings of SPIE, 8443-85,http://arxiv.org/abs/1209.1497, http://dx.doi.org/10.1117/12.926310

    4.      Kajava J. J. E., Ibragimov A., Annala M., Patruno A., Poutanen J., 2011, Varying disc-magnetosphere coupling as the origin of pulse profile variability in SAX J1808.43658, MNRAS, 417, 1454-1465, http://arxiv.org/abs/1107.0180, http://dx.doi.org/10.1111/j.1365-2966.2011.19360.x

    5.       Ibragimov A., Kajava J. J. E., Poutanen J., 2011, The 2009 outburst of IGR J175113057 as observed by SWIFT and RXTE, MNRAS, 415, 1864-1874, http://arxiv.org/abs/1102.1909, http://dx.doi.org/10.1111/j.1365-2966.2011.18836.x

    6.       Falanga M., Kuiper L., Poutanen J., et al. 2011, Spectral and timing properties of the accreting X-ray millisecond pulsar IGR J175113057, A&A, 529, A68, http://arxiv.org/abs/1012.0229, http://dx.doi.org/10.1051/0004-6361/201016240

    7.       Poutanen J., Ibragimov A., Annala M., 2009, On the nature of pulse profile variations and timing noise in accreting millisecond pulsars, ApJL, 706, L129-L132, http://arxiv.org/abs/0910.5868, http://dx.doi.org/10.1088/0004-637X/706/1/L129

    8.       Ibragimov A., Poutanen J., 2009, Accreting millisecond pulsar SAX J1808.43658 during its 2002 outburst: evidence for a receding disc, MNRAS, 400, 492-508, http://arxiv.org/abs/0901.0073, http://dx.doi.org/10.1111/j.1365-2966.2009.15477.x 

    9.       Babkovskaia N., Brandenburg A., Poutanen J., 2008, Boundary layer on the surface of a neutron star, MNRAS, 386, 1038-1044, http://arxiv.org/abs/0802.1663, http://dx.doi.org/10.1111/j.1365-2966.2008.13099.x

    10.    Suleimanov V., Poutanen J., 2006, Spectra of the spreading layers on the neutron star surface and constraints on the neutron star equation of state, MNRAS, 369, 2036-2048, http://arxiv.org/abs/astro-ph/0601689, http://dx.doi.org/10.1111/j.1365-2966.2006.10454.x

    11.    Poutanen J., Beloborodov A.M., 2006, Pulse profiles of millisecond pulsars and their Fourier amplitudes, MNRAS, 373, 836-844,http://arxiv.org/abs/astro-ph/0608663, http://dx.doi.org/10.1111/j.1365-2966.2006.11088.x

    12.    Poutanen J., 2006, Accretion-powered millisecond pulsars, Advances in Space Research, 38, 2697-2703, http://arxiv.org/abs/astro-ph/0510038, http://dx.doi.org/10.1016/j.asr.2006.04.025 

    13.    Viironen K., Poutanen J., 2004, Light curves and polarization of accretion- and nuclear-powered millisecond pulsars, A&A, 426, 985-997, http://www.arxiv.org/abs/astro-ph/0408250, http://dx.doi.org/10.1051/0004-6361:20041084

    14.    Poutanen J., Gierlinski M., 2003, On the Nature of the X-ray Emission from the Accreting Millisecond Pulsar SAX J1808.43658, MNRAS, 343, 1301-1311, http://arxiv.org/abs/astro-ph/0303084, http://dx.doi.org/10.1046/j.1365-8711.2003.06773.x

    3. X-ray bursts

    Matter accreting to a weakly-magnetized NS can cause thermonuclear explosion on the NS surface. These X-ray bursts have been discovered already more than 40 years ago, but still there are many mysteries. One of the goals of our research is to develop tools to understand the X-ray bursts properties in order to determine NS masses and radii, which would seriously constrain the equation of stat of cold dense matter. In collaboration with the group from Univ. of Tubingen (Germany) we are developing NS atmosphere models. For the first time, we have used the exact Compton scattering kernel to construct the most accurate atmosphere models for hot NSs (Suleimanov et al. 2012).  We have proposed a novel “cooling tail” method to determine NS parameters. We have also discovered that the cooling tail properties strongly depend on the accretion rate and showed that only the low-accretion-rate, hard-state X-ray bursts can potentially be used for NS parameter determination (Kajava et al. 2014; Poutanen et al. 2014). Using the cooling tail method, we find that the NS radius in a couple of known X-ray bursters is above 12.5 km (Suleimanov et al. 2011b; Poutanen et al. 2014), which supports stiff equation of state and is consistent with the existence of 2 solar mass pulsars.

    Our current projects include development of the atmosphere model for rapidly rotating NSs and determination of the NS masses and radii for a set of bursters using the hard-state, low-accretion-rate bursts.


    Figure 3:  Mass-radius constraints from the hard-state bursts of 4U 1608–52 (Poutanen et al. 2014).

     Selected publications: 

    1.       Kajava J.J.E.,  Nättilä J.,  Latvala O.-M., Pursiainen M., Poutanen J., Suleimanov, V.F., Revnivtsev M.G., Kuulkers E.,  Galloway D.K., 2014, The influence of accretion geometry on the spectral evolution during thermonuclear (type-I) X-ray bursts, MNRAS, in press, http://arxiv.org/abs/1406.0322

    2.       Poutanen J., Nättilä J.,  Kajava J.J.E.,  Latvala O.-M., Galloway D.K., Kuulkers E.,  Suleimanov, V.F., 2014, The effect of accretion on the measurement of neutron star mass and radius in the low-mass X-ray binary 4U 160852, MNRAS, 442, 3777-3790, http://arxiv.org/abs/1405.2663, http://dx.doi.org/10.1093/mnras/stu1139

    3.       Suleimanov V., Poutanen J., Werner K., 2012, X-ray bursting neutron star atmosphere models using an exact relativistic kinetic equation for Compton scattering, A&A, 545, A120, http://arxiv.org/abs/1208.1467, http://dx.doi.org/10.1051/0004-6361/201219480 

    4.       Suleimanov V., Poutanen J., Revnivtsev M., Werner K., 2011b, Neutron star stiff equation of state derived from cooling phases of the X-ray burster 4U 1724307, ApJ, 742, 122, http://arxiv.org/abs/1004.4871, http://dx.doi.org/10.1088/0004-637X/742/2/122 

    5.       Suleimanov V., Poutanen J., Werner K.,  2011a, X-ray bursting neutron star atmosphere models: spectra and color corrections, A&A, 527, A139, http://arxiv.org/abs/1009.6147, http://dx.doi.org/10.1051/0004-6361/201015845

    4. Stellar-mass black holes

    BHs are among the Universe most enigmatic, powerful and exotic objects. One of the most challenging questions of BH astrophysics is the nature of their emission. There is a general consensus that radio emission is associated with synchrotron radiation from a jet and the X-rays are produced in the vicinity of the compact object in a hot flow by Comptonization of some seed soft photons whose nature is debated. The origin of the IR/optical/UV emission from the BH in LMXBs is less certain. The contribution from the companion star in such systems is usually too faint and the IR/optical spectra are either connected to the jet, or the accretion process onto the compact object. The main focus of our work is the comprehensive analysis of all available sources of information and a construction of physical models consistent with the data.

    Our recent studies concentrated on modeling of the broad-band spectra and temporal properties, in particular the optical-X-ray connection. We have developed the first self-consistent model for spectral formation in BH binaries where photon and electron distributions are computed simultaneously (Vurm & Poutanen 2009). We have shown that non-thermal electrons play an important role in these objects. Interestingly, the synchrotron self-Compton mechanism operating in the hot accretion flow around BHs is capable of producing their broad-band spectra in the hard state from IR to gamma-rays  (Vurm & Poutanen 2008; Poutanen & Vurm 2009; Veledina et al. 2013; see Fig. 4). 

    We also investigated the nature of variability in stellar-mass BHs: rapid flickering and complex correlation between X-ray and optical (UV, IR) radiation on sub-second time-scales, quasi-periodic signals in these energy bands and optical/IR flares during the X-ray state transitions.

    We have also measured parameters of the BH binary SWIFT J1753.5−0127 (Neustroev et al. 2014) and showed that it hosts a BH of at most 4 solar masses.   This result calls into question the recent claims that there is a gap in the mass distribution of the compact objects between 2 to 5 M¤.


    Figure 4: Broad-band spectrum of the BH GX 3394. The model spectrum includes synchrotron self-Compton emission from various zones of the hot accretion disc  (dashed lines) and the irradiated accretion disc and Compton reflection (dotted). From Poutanen & Veledina (2014).  

    Selected publications: 

    1.       Poutanen J., Veledina A., Revnivtsev M.G., 2014, Colours of black holes: infrared flares from the hot accretion disc in XTE J1550564, MNRAS, 445, 3987-3998, http://arxiv.org/abs/1409.6504, http://dx.doi.org/10.1093/mnras/stu1989

    2.       Hakala P., Muhli P., Charles P., 2014, Simultaneous optical and near-IR photometry of 4U1957+115 - a missing secondary star, MNRAS, 444, 3802-3808, http://arxiv.org/abs/1408.4025, http://dx.doi.org/10.1093/mnras/stu1687

    3.       Neustroev V.V., Veledina A., Poutanen J., Zharikov S.V., Tsygankov S.S., Sjoberg G., Kajava J.J.E., 2014, Spectroscopic evidence for a low-mass black hole in SWIFT J1753.50127, MNRAS, 445, 2424-2439, http://arxiv.org/abs/1409.4423, http://dx.doi.org/10.1093/mnras/stu1924

    4.       Poutanen J., Veledina A., 2014, Modelling spectral and timing properties of accreting black holes: the hybrid hot flow paradigm, Space Science Reviews, 183, 61-85, http://arxiv.org/abs/1312.2761, http://dx.doi.org/10.1051/0004-6361/201322520

    5.       Veledina A., Poutanen J., Ingram A., 2013, A unified Lense-Thirring precession model for optical and X-ray quasi-periodic oscillations in black hole binaries, ApJ, 778, 165, http://arxiv.org/abs/1310.3821, http://dx.doi.org/10.1088/0004-637X/778/2/165

    6.       Veledina A., Poutanen J., Vurm I., 2011, A synchrotron self-Compton - disk reprocessing model for optical/X-ray correlation in black hole X-ray binaries, ApJL, 737, L17, http://arxiv.org/abs/1105.2744 , http://dx.doi.org/10.1088/2041-8205/737/1/L17 

    7.       Poutanen J., Vurm I., 2009, On the origin of spectral states in accreting black holes, ApJL, 690, L97-L100, http://arxiv.org/abs/1105.2744 , http://dx.doi.org/10.1088/2041-8205/737/1/L17

    8.       Vurm I., Poutanen J., 2009, Time-dependent modelling of radiative processes in hot magnetized plasmas, ApJ, 690, 698, 293-316, http://arxiv.org/abs/0807.2540 , http://dx.doi.org/10.1088/0004-637X/698/1/293


     5. Ultra-luminous X-ray sources

    Ultra-luminous X-ray sources (ULX) are bright off-nuclear X-ray point sources discovered in the nearby galaxies already with Einstein observatory.  However, their nature is still debated. The main hypothesis are intermediate-mass BH or stellar-mass BHs accreting at very high rates. We have pioneered theoretical models of super-Eddington accretion discs around BH that include advection and winds (Poutanen et al. 2007) and showed that BHs in such a state can produce easily observed X-ray luminosities exceeding 1040 erg/s. On the observational side, we have studied spectral variability of 11 ULX using archival XMM-Newton and Chandra observations (Kajava & Poutanen 2009) demonstrating that the soft excess (often interpreted as a signature of a cold accretion disc around an intermediate mass BH) shows completely different trends on luminosity–temperature plane compared to the standard accretion disc. This suggests that ULX are likely stellar-mass BHs.  

    We have also been interested in the positions of ULX and found a statistically significant displacement between ULX and young (2–5 Myr) stellar clusters in the Antennae galaxies (Poutanen et al. 2013; see Fig. 5). This gives a strong support to the idea that ULXs are massive X-ray binaries that have been ejected in the process of formation of stellar clusters.

    Recently, we discussed other alternative models for ULX where the central engine is a neutron star: either a rapidly rotating pulsar (Medvedev & Poutanen 2013) or an accreting magnetar. A recent discovery with NuSTAR of 1.37 s pulsations in ULX M82 X-2  (Bachetti et al. 2014) confirmed our expectations that some fraction of ULX host a NS instead of a BH. Our future projects include detailed studies of the super-Eddington accretion onto magnetized NSs.


    Figure 5:  An HST image of the Antennae galaxies with bright point sources being mostly stellar clusters. Green (and black) circles are the positions of ULX. The insets show VIMOS/VLT images that were used to study reddening and to determine cluster ages. From Poutanen et al. (2013).   

    Selected publications: 

    1.       Farrell S. A., Servillat M., Gladstone J.C., Webb N.A., Soria R., Maccarone T.J., Wiersema K., Hau G.K.T., Pforr J., Hakala P.J., Knigge C., Barret D., Maraston C., Kong A. K. H., 2014, Combined analysis of Hubble and VLT photometry of the intermediate mass black hole ESO 243-49 HLX-1, MNRAS, 437, 1208-1215, http://arxiv.org/abs/1310.2604 , http://dx.doi.org/10.1093/mnras/stt1924

    2.       Poutanen J., Fabrika S.,  Valeev A.F., Sholukhova O., Greiner J., 2013, On the association of the ultraluminous X-ray sources in the Antennae galaxies with young stellar clusters, MNRAS, 432, 506-519, http://arxiv.org/abs/1210.1210, http://dx.doi.org/10.1093/mnras/stt487

    3.       Medvedev A.S., Poutanen J., 2013, Young rotation-powered pulsars as ultra-luminous X-ray sources, MNRAS, 431, 2690-2702, http://arxiv.org/abs/1302.6079, http://dx.doi.org/10.1093/mnras/stt369

    4.       Soria R., Hakala P.J., Hau G.K.T., Gladstone J.C., Kong A.K.H., 2012, Optical counterpart of HLX-1 during the 2010 outburst, MNRAS, 420, 3599, http://arxiv.org/abs/1111.6783, http://dx.doi.org/10.1111/j.1365-2966.2011.20281.x

    5.       Kajava J.J.E., Poutanen J., Farrell S.A., Grise F., Kaaret P., 2012, Evolution of the spectral curvature in the ULX Holmberg II X-1, MNRAS, 422, 990-996, http://arxiv.org/abs/1202.1102, http://dx.doi.org/10.1111/j.1365-2966.2012.20671.x

    6.       Kajava J.J.E., Poutanen J., 2009, Spectral variability of ultraluminous X-ray sources, MNRAS, 398, 1450-1460, http://arxiv.org/abs/0906.1485, http://dx.doi.org/10.1111/j.1365-2966.2009.15215.x

    7.       Poutanen J., Lipunova G., Fabrika S., Butkevich A.G., Abolmasov P., 2007, Supercritically accreting stellar mass black holes as ultraluminous X-ray sources, MNRAS, 377, 1187-1194, http://arxiv.org/abs/astro-ph/0609274, http://dx.doi.org/10.1111/j.1365-2966.2007.11668.x




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