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Measuring Spin Parameters of Stellar-Mass Black Holes

Ramesh Narayan. Measuring Spin Parameters of Stellar-Mass Black Holes. Spin: Fundamental Property of a Black Hole. Mass: M Spin: a * (J=a * GM 2 /c) Charge: Q ( ~ 0) From the point of view of BH physics, the spin of a BH is very fundamental. Importance in Astrophysics.

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Measuring Spin Parameters of Stellar-Mass Black Holes

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  1. Ramesh Narayan Measuring Spin Parameters of Stellar-Mass Black Holes

  2. Spin: Fundamental Property of a Black Hole • Mass:M • Spin:a* (J=a*GM2/c) • Charge:Q (~0) From the point of view of BH physics, the spin of a BH is very fundamental

  3. Importance in Astrophysics • Free energy associated with BH spin may be responsible for relativistic jets • BH spin values give a handle on angular momenta of progenitor stars • Gamma-ray bursts and BH spin? • SMBH spin and galaxy merger history • BH spin affects gravitational wave signals

  4. Mass is Easy, Spin is Hard • Mass can be measured in the Newtonian limit using test particles (e.g., stellar companion) at large radii • Spin has no Newtonian effect • To measure spin we must be in the regime of strong gravity, where General Relativityoperates • Need test particles at small radii • So we must use the gas in the accretion disk…

  5. Estimating Black Hole Spin • X-Ray Continuum Spectrum  • Relativistically Broadened Iron Line – • Quasi-Periodic Oscillations

  6. Our Team Jeff McClintock Ramesh Narayan Charles Bailyn, Shane Davis, Lijun Gou, Akshay Kulkarni, Li-Xin Li, Jifeng Liu, Jon McKinney, Jerry Orosz, Bob Penna, Mark Reid, Ron Remillard, Rebecca Shafee, Danny Steeghs, Manuel Torres, Jack Steiner, Sasha Tchekhovskoy, Yucong Zhu

  7. Innermost Stable Circular Orbit (ISCO) • RISCO/M depends on the value of a* • If we can measure RISCO, we will obtaina* • Note factor of 6variation in RISCO • Especially sensitive as a*1

  8. The Basic Idea Accretion disk has a dark central “hole” with no radiation Measure radius of hole by estimating area of the bright inner disk

  9. Measuring the Radius of a Star • Measure the flux Freceived from the star • Measure the temperature T*(from spectrum) R*

  10. Measuring the Radius of the Disk Inner Edge • We want the radius of the “hole” in the disk emission • Same principle as for a star • From X-ray data we obtain FXand TX  (bright) • Knowing distance D and inclination i we get RISCO(some (geometrical factors) • From RISCO/M we get a* • Need to be careful: focus on Thermal Dominant (TD) data Zhang et al. (1997); Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007); Gou et al. (2009,2010); Steiner et al. (2010)… RISCO RISCO

  11. Shakura-Sunyaev model Rin=6M Note that the result does not depend on the details of the ‘viscous’ stress (parameter)

  12. H1743-322 A Test of the Blackbody Assumption • For a blackbody, L scales asT4 (Stefan-Boltzmann Law) • BHaccretion disks vary a lot in their luminosity • If a disk is a perfect blackbody, Lshould exactly as T4 • Good, but not perfect… Kubota, Done et al. (2002,…) McClintock et al. (2008)

  13. Tin4 f = Tcol/Teff Davis et al. (2005, 2006) H1743-322 After including the color correction, we get an excellent L-T4 trend f Spectral hardening factor f Conclusion: Thermal State is very good for quantitative modeling Teff4

  14. General Relativistic Disk Model: Novikov & Thorne (1973) L(r) peaks at a different radius for each value of the dimensionless BH spin parameter a* Therefore, the observed spectrum depends on a* This is what enables us to estimate a* from observations

  15. Summary of the Method • We fit the X-ray continuum spectrum • We include all relativistic effects • We focus on “good data” (TD),where the emission is mostly blackbody so that we can model the spectrum reliably   • To convert “solid angle” measurement to an estimate of RISCO, we measure independently D, i • Then, knowing M, we calculate RISCO/M, and thus obtain an estimate of a*

  16. LMC X-3: 1983 - 2009 L / LEdd LMC X-3

  17. LMC X-3: 1983 - 2009 Thick Disk L / LEdd Hard State LMC X-3

  18. LMC X-3: 1983 - 2009 L / LEdd LMC X-3 Rin Steiner et al. (2010) 403 spectra (assuming M=10M, i=67o)

  19. New Result: XTE J1550-564 (Steiner, Reis et al. 2010) • M=9.100.61, D=4.380.5, i=74.73.8 (Orosz et al. 2010) • Spin estimate from continuum fitting: a* ~ 0.35 (90% cl: -0.11, +0.71) • Spin estimate from iron line fitting: a* ~ 0.55 (1 limits: 0.33, 0.70) • Combined spin estimate: a* = 0.49 (1 limits: 0.29, 0.62)

  20. XTE J1550-564: Outburst Light Curve 1998-1999

  21. X-ray continuum spectral fits and residuals for aTD (“gold”) and anSPL (“silver”) observation

  22. Estimates of disk inner edge Rinand BH spin parameter a*from all suitable TD (“gold”) and SPL/Intermediate (“silver”) observations

  23. Combined CF Method: Includes errors in M, D, I Fe line method Probability distribution of spin of J1550(Steiner et al. 2010)

  24. BH Spin Measurements via Continuum-Fitting Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010); Steiner et al. (2010)

  25. A Major Issue • NT model assumes that the torque vanishes at the ISCO (Shakura & Sunyaev 1973) • But magnetic fields could produce significant torque at and inside the ISCO (Krolik 1999; Gammie 1999) • Afshordi & Paczynski (2003), Shafee et al. (2008) showed that the effect is not important for a THIN hydrodynamic disk • But what about an MHD disk?

  26. 3D GRMHD Simulations of Thin Accretion Disks • Shafee et al. (2008), Penna et al. (2010) • Self-consistent MHD simulations (HARM: Gammie, McKinney & Toth 2003) • All GR effects included • h/r ~ 0.05 — 0.08 (thin!!) • Very few other thin disk simulations: Reynolds & Fabian (2008); Noble, Krolik & Hawley (2009, 2010) a*=0 a*=0, 0.7, 0.9, 0.98 Kulkarni et al. (2010)

  27. a*=0.9; i=15o, 45o, 75o a*=0, 0.7, 0.9; i=75o

  28. Modeling Error Due to Deviations From the Novikov-Thorne Model • The systematic error due to assuming the NT model is less than the statistical error due to measurement uncertainties • The simulated disks correspond to L/LEdd ~ 0.5 • Measurements are, however, made using data at L  0.3 LEdd • True systematic errors will be less than the above values Kulkarni et al. (2010)

  29. BH Spin Measurements via Continuum-Fitting Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010); Steiner et al. (2010)

  30. Disk Inclination Is BH spin aligned with orbit vector? We assume this in order to estimate i X-ray polarimetry will help: GEMS Population synthesis studies look hopeful (Fragos et al. 2010) Li, Narayan & McClintock (2009)

  31. Importance of BH Spin • Of the two parameters, mass and spin, spin is more fundamental • Mass is merely a scale – just tells us how big the BH is • Spin fundamentally affects the basic properties of space-time around a BH • More than simple re-scaling • BH spin may power relativistic jets…

  32. Relativistic Jets in GRS 1915+105 GRS 1915+105 has an extreme value of spin: a*=0.98-1 Also spectacular relativistic jets Blobs of material are seen to flow out with v = 0.92c Could the relativistic ejections be connected to the BH spin? GRS 1915+105

  33. BH Spin Values vs Relativistic Jets Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010); Steiner et al. (2010)

  34. Summary • BH spin measurement by continuum fitting is now a well-developed technique • Measurement errors are quantifiable (except for disk inclination) • Systematic model errors are under control • XTE J1550-564: Consistent spin estimates from continuum-fitting & Fe-line methods • BH spin is perhaps not very important for relativistic jets…

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