Black Holes in X-ray Binary Systems.

1. Black Holes in X-ray Binary Systems. A.M.Cherepashchuk (Sternberg Astronomical Institute of Moscow University)

2. Overview. • Introduction: 40 years of optical and X-ray investigations of BH candidates. • Modern methods of mass determination. • Masses of BH in X-ray binaries. • Stellar mass BH demography. • Conclusion. • Future investigations.

3. 1. Introduction. • 40 years ago first Black Hole candidate (Cyg X-1) has been discovered in X-ray binary system. • X-ray binary: optical star – donor of matter and accreting relativistic object – neutron star (NS) or black hole (BH).

4. X-ray and optical investigations of X-ray binary systems are very important: • X-ray: Luminosity, spectrum and variability (Δt ≤ 10-3 sec.) allow to make the conclusion about existence of compact (r ≤ cΔt ≈ 300 km) relativistic object (NS or BH). • Optical: photometric and spectral observations of X-ray binary system allow to study the motion of optical star (“probe body” in the gravitational field of relativistic object) and to estimate the mass of NS or BH.

5. According to modern theory of stellar evolution taking into account Einstein General Relativity: if Mstar core > 3M => BH, if Mstar core < 3M => NS or WD. • Dimensions of the orbit radii of optical star in X-ray binaries are much more (~ 106) than the value of gravitational (Schwarzschild) radius of the compact object rg = 2GM/c2 ≈ 10 km for M = 10 M.

6. Therefore Newton gravitational law can be applied for determination of the masses of relativistic objects in X-ray binary systems. • Because asymptotic for any gravitational theory is the Newton gravitation, masses of relativistic objects, obtained from investigations of X-ray binaries are independent of the specific gravitational theory.

7. Possibilities to observe BH • Zeldovich (1964) and Salpeter (1964) – strong energy release from non-spherical accretion onto BH. • Zeldovich and Guseinov (1966) – binary systems as a tool for determination of masses of relativistic objects. • Pringle and Rees (1972) • Shakura and Sunyaev (1973) – theory of disk accretion • Novikov and Thorne (1973) onto BH.

8. Giaccony et al. (1971) – UHURU epoch. ~100 compact X-ray sources, first X-ray binaries: Cyg X-1, Her X-1, Cen X-3, Vela X-1, SMC X-1 etc. • Optical identifications and investigations of optical appearances of X-ray binaries: • Kurochkin (1972 – identification of HZ Her = Her X-1 • Cherepashchuk, Efremov, – interpretation of optical Kurochkin, Shakura, Sunyaev (1972), variability of HZ Her • Bahcall and Bahcall (1972) as X-ray heating effect (“reflection” effect).

10. Webster and Murdin (1972): measuring of mass function for Cyg X-1 by spectroscopic observations. • Lyutyi, Sunyaev, Cherepashchuk (1973): discovery of regular optical variability of Cyg X-1 (ellipticity effect of optical star), estimation of inclination of the orbit plane i ≈ 35° and mass of BH Mx > 5.6 M.

11. Margon et al (1979), Vittone et al. (1979): discovery of the moving emission lines in SS 433. • Milgrom (1979), Martin and Rees (1979) – model of precessing jets in SS 433.

12. Crampton, Cowley, Hutchings (1980) – SS 433 – a spectroscopic binary system with p ≈ 13.1 days. • Cherepashchuk (1981) – discovery of optical eclipses in SS 433. Model of SS 433 as a massive X-ray binary at advanced evolutionary stage with precessing optically bright supercritical accretion disk around relativistic object. • SS 433 first example of Microquasar. • Up to now ~20 microquasars in The Galaxy are known.

13. SS 433 optical light curve

14. Ellipticity and “reflection” effects are typical optical appearances of X-ray binaries. These effects allow us to make optical identifications of X-ray binaries as well as to estimate the inclination of the orbit plane i for them.

15. Up to now from the borders of many special X-ray space observatories (Einstein, Rosat, XMM Newton, Integral etc.) several thousands of X-ray binaries were discovered. • Optical investigations made by many scientific groups (USA, England, Germany, Russia etc.) allowed to estimate the masses of 26 stellar mass BH in X-ray binary systems. • Up to now masses of ~50 NS in binary systems are measured.

16. New branch of astrophysics is developed: BH demography (birth, growth of BHs and their relationship with the other objects: stars, galaxies etc.)

17. 2. Modern methods of the mass determination. • In the framework of the model of X-ray binary system as the system of two point-like companions on the Keplerian orbits the mass of the BH can be estimated: • , (1) • where q = mx/mv – mass ratio (mx, mv – masses of BH and optical star respectively), i – inclination of the orbit plane, fv(m) mass function of optical star – observed value: • . (2) • Here Kv – observed semi amplitude of the radial velocity curve (in km/s), p – orbital period (in days), e – eccentricity of the orbit.

19. Value of i is determined from the analysis of the optical or near infrared light curve of the X-ray binary (Lyutyi, Sunyaev, Cherepashchuk, 1973).

20. Value of q is determined from observations of rotational broadening of absorption lines in the spectrum of optical star in X-ray binary system: • , (3) • where vrotsini and Kv are determined from spectroscopic observations.

21. For high value of mass ratio q = mx/mv>>1 the model of point-like source for the optical star can be considered as satisfactory because the dimension of the Roshe Lobe for the optical star is relatively small.

22. For small value of q ≤ 1 center of gravity of the binary system is located inside the body of optical star and this star can not be considered as a point-like source

23. Recently new methods of interpretation of the light curves, line profiles and radial velocity curves have been developed in our group. In these methods tidal and rotational deformations of the optical star are taken into account. X-ray heating effect as well as the eclipsing effects are taken into account too.

24. The surface of the star is divided on several thousands of elementary area. For each elementary area by solving the differential equation for transfer of radiation the intensity of radiation going to the observer is calculated. Than contribution from all visible area is integrated taking into account Doppler Effect. As a result, integrated line profile for each phase of the orbital period can be calculated and realistic theoretical radial velocity curve is calculated too. In these calculations Local Thermodynamical Equilibrium (LTE) model as well as non-LTE model of stellar atmosphere were used (Antokhina and Cherepashchuk, 1996; Antokhina et al., 2005).

26. Some new results obtained with new methods of interpretation of radial velocity curves of X-ray binaries. • It is shown that the masses of X-ray pulsars in binaries with OB supergiants, obtained in the framework of the simple model of two point-like sources are underestimated on 5 – 10% (Abubekerov, Antokhina, Cherepashchuk, 2004a). This result is important for better understanding of the equation of state of matter of NS.

27. From the analysis of high precision radial velocity curve of the system Cyg X-1 (502 observational nights) inclination of orbit plane i is constrained i <45° and independent estimate of the mass of BH is obtained: mx = (8.5 – 13.6) M (Abubekerov, Antokhina, Cherepashchuk, 2004b).

28. Taking into account strong X-ray heating effect in X-ray binary system 2S0921-63 allowed us to decrease the mass of the relativistic object by ~1 M. So, we have shown that the relativistic object in this X-ray binary system is a NS but not low-mass BH.

29. 3. Masses of BH in X-ray binary systems. • Up to now masses of 26 stellar mass BH and ~50 NS are measured in binary systems. • Masses of 50 NS lie in the range (1 – 2) M. Mean mass of the NS is ~1.4 M.

30. NS with measured masses are X-ray pulsars, radiopulsars or X-ray bursters of the first kind. All these properties are the evidences of the observed surface of NS. • Therefore, in all 50 cases when the relativistic object shows evidences of the observed surface its mass does not exceed the value 3 M – absolute upper limit of the mass of NS predicted by the Einstein General Relativity (!).

31. Masses of 26 BH lie in the range (4 - 25) M. Mean mass of the BH is ~9 M. None of this 26 BH candidates is X-ray pulsars, radiopulsars or X-ray bursters of the first kind. Therefore none of these massive (mx > 3 M) compact objects show the evidence of observed surface in agreement with the predictions of the Einstein General Relativity (!).

32. So, basic conclusion based on the 40 years of investigations of the relativistic objects in binary systems can be formulated as follows: NS and BH are different from each other not only by the masses, but also by the observational evidences in full agreement with the Einstein General Relativity.

33. It should be stressed however, that some NS can not show direct evidences of the observed surfaces. In particular, if rotational axes of the NS coincides with the axes of magnetic dipole, the phenomenon of the X-ray pulsar or radiopulsar can not be observed for NS. Therefore all observational evidences for the BH described above are only necessary but not sufficient. However, big number of BH candidates (26) allows us to believe in real existence of stellar mass BH in The Universe.

34. Recently, due to operation of new generation optical 8 – 10 meter telescopes, the optical investigations of X-ray binary systems in many other galaxies have been realized (e.g., Orosz et al., 2009). Due to these investigations the many new mass determinations for stellar mass BH in X-ray binaries will be obtained.

35. 4. Stellar mass BH demography. • There is no correlation between masses of relativistic objects and those of companion stars in binary systems.

36. Number of BH does not increase with decreasing of their masses. • It seems to be strange because the number of stars in The Galaxy – progenitors of BHs (M > 30 M) is strongly increasing with decreasing of their masses: N ~ M-5.

37. It can be shown (e.g., Cherepashchuk, 2003) that this peculiarity in the mass distribution for BH is not due to observational selection effects (disruption of binary system after supernova explosion, strong mass loss by the star due to stellar wind etc).

38. The gap in the range (2 – 4) M in the mass distribution of NS and BH can be suggested (Bailyn et al., 1998; Cherepashchuk, 1998). In this range (2 – 4) M the number of NS and BH discovered in binary systems up to now is close to zero. It can be shown that this gap is not due to observational selection effects (Cherepashchuk, 2001, 2003; Özel at al., 2010).

39. Therefore, there are grounds to suggest that stellar mass BH formation is determined not only by mass of the progenitor star, but also by other parameters: rotation, magnetic field etc. (e.g. Fryer and Kalogera, 2001; Postnov and Prokhorov, 2001; Cherepashchuk, 2001).

40. Some new possibility to explain peculiarities in the mass distribution of BHs has been considered by Postnov and Cherepashchuk (2003). Deficit of low-mass BH and the gap in the range (2 – 4) M may be due to enhanced quantum evaporation of BH which have been suggested in some multidimensional models of gravity (e.g. Randall and Sundrom, 1999). In these models of gravity the characteristic time of quantum evaporation of BH is much less than that in the Hawking (1974) mechanism.

41. Characteristic time of quantum evaporation of BH in RS model of gravity can be estimated by the formula: • , (4) • where M – the mass of BH, L – characteristic scale of additional space dimension (in the bulk). For MBH≈ 10 M and L ≤ 0.01 mm value of τ ≤ 108 years which is close to the time of nuclear evolution of the stars.

42. Because τ strongly decreases with MBH it can be suggested that deficit of low-mass BH is due to their enhanced quantum evaporation.

43. Change of orbital periods of X-ray binary systems caused by enhanced quantum evaporation of BH may be suggested. From such investigations independent estimate of the value of L has been obtained recently (Johansen, Psaltis and McClintock, 2009): L < 0.1 mm (3σ upper limit).

44. Model of rapidly rotating, Kerr BH and relativistic jets is applied recently for the interpretation of cosmic γ-ray bursts. • As was pointed out by Tutukov and Cherepashchuk (2003, 2004), in very close binary system orbital motion of the companion star due to tidal interactions can stimulate rapid rotation of the core of massive star despite considerable loss of angular momentum of the star due to supernova explosion.

45. Therefore, observations of cosmic γ-ray bursts allow us to investigate the processes of formation of rapidly rotating BH in very close binary systems.

46. 5. Conclusion. • A big progress in the problem of investigations of the stellar mass BH in X-ray binary systems is achieved during last 40 years. 26 reliable BH candidates with measured masses have been discovered and investigated.

47. All observational data about NS and BH candidates are in good agreement with the Einstein General Relativity. In particular, NS and BH candidates (mx> 3 M) are different from each other not only by the masses, but also by observational appearances in full agreement with General Relativity. • It gives us a ground to believe in the real existence of stellar mass BH in The Universe.

48. 6. Future investigations. • Optical observations of X-ray binaries in other galaxies using modern new generation 8 – 10 meter optical telescopes will increase the number of BH with measured masses. • Realization of space astrometric project GAIA will allow to measure the distances for many X-ray binary systems in The Galaxy. Knowledge of the distances will allow us to increase the reliability of the mass determination for stellar mass BH. It is important for further investigations of peculiar bimodal distribution of masses of relativistic objects. • X-ray investigations of Low-frequency and High-frequency QPOs in X-ray binary systems seems to be very important. High-frequency QPOs are related to the physical processes in strong gravity near the event horizon of BH.