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Estimating the Spin of Stellar-Mass Black Holes Jeffrey McClintock Harvard-Smithsonian CfA STScI Black Hole Symposium April 25, 2007.

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Presentation on theme: "Estimating the Spin of Stellar-Mass Black Holes Jeffrey McClintock Harvard-Smithsonian CfA STScI Black Hole Symposium April 25, 2007."— Presentation transcript:

1 Estimating the Spin of Stellar-Mass Black Holes Jeffrey McClintock Harvard-Smithsonian CfA STScI Black Hole Symposium April 25, 2007

2 Chronological List of Team Members NameYear Jeffrey McClintock Ramesh Narayan Li-Xin Li Rebecca Shafee Ronald Remillard Shane Davis Jerome Orosz Danny Steeghs Charles Bailyn Michael Muno Thomas Megeath NameYear Wolfgang Pietsch Mark Reid Vik Dhillon Stuart Littlefair Vivek Dhawan Joel Hartman Manuel Torres Jack Steiner Lucas Macri Jifeng Liu This effort to measure spin requires a mix of theory & observation.

3 Introduction

4 The Essentials Objects: Stellar-mass BHs in X-ray binaries Objects: Stellar-mass BHs in X-ray binaries Method: Spin via fitting the X-ray continuum Method: Spin via fitting the X-ray continuum  Absolute Requirements: Accurate values of BH mass, i & D Accurate values of BH mass, i & D “Thermal-Dominant” X-ray data “Thermal-Dominant” X-ray data State-of-the-art relativistic models State-of-the-art relativistic models Li, Zimmerman, Narayan & McClintock 2005 Li, Zimmerman, Narayan & McClintock 2005 Shaffee, McClintock, Narayan, Davis, Li & Remillard 2006 Shaffee, McClintock, Narayan, Davis, Li & Remillard 2006 McClintock, Shafee, Narayan, Remillard, Davis & Li 2006 McClintock, Shafee, Narayan, Remillard, Davis & Li 2006

5 Number of BH binaries known = 21 Courtesy J. Orosz Ii M ~ 10 Msun

6 Number of BH binaries known = 21 Courtesy J. Orosz Ii M ~ 10 Msun

7 Black Holes are Extremely Simple Mass: M Mass: M Spin: J = a * GM 2 /c (0 < a * < 1) Spin: J = a * GM 2 /c (0 < a * < 1) (Electric Charge: Q) (Electric Charge: Q) 21 BH masses M have been measured Obvious next frontier: Measure BH spin a * (much harder)

8 f T ~ 2 keV 42% T ~ 1 keV 6% a * = 1 a * = 0 R ISCO = 15 km R ISCO = 90 km R ISCO : Extreme-Kerr vs. Schwarzschild

9 Two Foundations 1. ISCO 2. Thermal Dominant State

10   A disk terminates at R ISCO and gas falls freely onto the BH inside this radius.   Thus, disk emission has a “hole” of radius R ISCO at center.   If we measure the size of the hole, we will obtain a *  90 km 15 km  R ISCO  a * First Foundation Innermost Stable Circular Orbit (ISCO)

11 Typical X-ray nova 2-20 keV light curve 170 RXTE/PCA observations over 9 months Fit spectra with MCD model (diskbb) + power law Non-relat. MCD model has 2 params: T in & R in Mitsuda et al Makishima et al Tanaka & Lewin 1995 Remillard & McClintock 2006 Second Foundation

12 Consider disk component of emission only Focus on 4-month monotonic decay of accretion disk Second Foundation (cont.)

13 L disk / L total > 75% (2-20 keV) No QPOs Weak power continuum (r < 0.075) Power-law/Comptonization minimal Remillard & McClintock 2006, ARAA, 44,49 Thermal Dominant State Second Foundation (cont.)

14 Smooth, monotonic decline of temperature as disk decays on a thermal time scale Second Foundation (cont.)

15 Inner disk radius R in quite constant Compare Tanaka & Lewin 1995 in XRBs Second Foundation (cont.)

16 Now, plot L disk /L lotal versus T in Second Foundation (cont.)

17 T in 4 Kubota et al Kubota & Makishima 2004 Kubota & Done 2004 Gierlinski & Done 2004 H

18 T in 4 T eff 4 Second Foundation f col = T in /T eff Davis et al. 2005, 2006 Conclusion: There exists a constant radius

19 Outline of Method for Estimating Spin  Fitting the X-ray continuum 

20 Measuring the Radius of a Star Measure the flux F received from the star Measure the flux F received from the star Measure the temperature T (from spectrum) Measure the temperature T (from spectrum) Then, assuming blackbody radiation: Then, assuming blackbody radiation: F and T give solid angle of star F and T give solid angle of star If we know distance D, we directly obtain R If we know distance D, we directly obtain R R

21 Measuring the Radius of the Disk Inner Edge We want to measure the radius of the ‘hole’ in the disk emission We want to measure the radius of the ‘hole’ in the disk emission Same principle as before Same principle as before From F and T get solid angle of hole From F and T get solid angle of hole Knowing D and i get R ISCO Knowing D and i get R ISCO From R ISCO and M get a * From R ISCO and M get a * Zhang et al. (1997) Gierlinski et al. 2001; Li et al. (2005); Zhang et al. (1997) Gierlinski et al. 2001; Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006);… Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006);… R ISCO

22 Estimates of Spin Obtained with this Method System a*a*a*a*Reference GRO J Shafee et al. (2006) 4U GRS McClintock et al. (2006) LMC X-3 <0.26 Davis et al. (2006)

23 Diving into the Method

24 How to Get Reliable Results? Need good estimates of M, D, i Need good estimates of M, D, i Should include all relativistic effects: Doppler beaming, grav. redshift, ray deflections  KERRBB (Li et al. 2006) Should include all relativistic effects: Doppler beaming, grav. redshift, ray deflections  KERRBB (Li et al. 2006) The system should be in the Thermal Dominant state The system should be in the Thermal Dominant state H/R < 0.1 L/L edd < 0.3 H/R < 0.1 L/L edd < 0.3 Deviations from blackbody (parameter f) should be estimated via a disk atmosphere model Deviations from blackbody (parameter f) should be estimated via a disk atmosphere model Shimura & Takahara (1995); Davis et al. (2005, 2006)

25 How to Get Reliable Results? (cont.) Need accurate theoretical profiles of disk flux F(R) and temperature T(R) Need accurate theoretical profiles of disk flux F(R) and temperature T(R)

26 R ISCO Zero-torque at ISCO H/R < 0.1 L/L edd < 0.3 S Flux vs. Radius Shafee, Narayan & McClintock (Poster #31) a * = 0 aa a * = 0.95

27 Bottom Line Errors due to hydro effects are modest. Shafee et al. (Poster #31)

28 Only a * and Mdot Determined from X-ray Spectrum M,D,i from ground-based observations M,D,i from ground-based observations f col from disk atmosphere model f col from disk atmosphere model Zero torque at ISCO for L/L edd < 0.3 Zero torque at ISCO for L/L edd < 0.3 Fit for a * and Mdot (Mdot  L/L edd ) only Fit for a * and Mdot (Mdot  L/L edd ) only T & flux  a * & Mdot T & flux  a * & Mdot

29 GRS KERBB: Fit for a * and mass accretion rate Mdot (L/L edd ) ASCA: keVRXTE: 3-25 keV 20 Thermal-Dominant Observations out of 640 a * = L/L edd = 0.18 a * = L/L edd = Energy (keV) Energy (keV) Flux McClintock, Shafee, Narayan et al. 2006

30 Observational Work in Progress HEASARC

31 Key Spin Targets M33 X-7: Gemini-N, Chandra, XMM M33 X-7: Gemini-N, Chandra, XMM GRS : VLBA, Gemini-S GRS : VLBA, Gemini-S LMC X-1: Magellan, SMARTS LMC X-1: Magellan, SMARTS A : Spitzer/ground-based A : Spitzer/ground-based XTE J : Magellan XTE J : Magellan Additional targets: Nova Mus 1991, XTE J , XTE J , GS , GRS … about a dozen in total

32 Pietsch et al M33 X-7 Preliminary Orosz et al P orb 3.45 days D = 845 +/- 25 kpc i = 74 +/- 2 deg M = 14 +/- 3 Msun O6 giant M 2 = 57 +/- 10 Msun R 2 = /- 1 Rsun T eff = 35,000 +/- 2500K Spin analysis underway Liu et al.

33 a * = McClintock, Shafee, Narayan et al Radio Jet v/c = 0.92 GRS Mirabel & Rodriguez 1994

34 GRS Distance (kpc) Gemini-S GNIRS proposal pending GRS McClintock, Shafee, Narayan et al. 2006

35 GRS Distance (kpc) VLBA observations underway

36 Nominal Spins of 4 BHs LMC X-3: a * = 0.2 GRO J : a * = 0.7 4U : a * = 0.8 GRS : a * = 0.99 McClintock, Shafee, Narayan, et al.

37 Discussion

38 Black Hole Spins Chiefly Natal Accretion torques inadequate to spin up BH in lifetime of system Accretion torques inadequate to spin up BH in lifetime of system King & Kolb 1999 GRS a prime example: GRS a prime example: Accretion of 4 M o onto a 10 M o hole  Accretion of 4 M o onto a 10 M o hole  a * ~ 0.77 << a * = 0.98 – 1 a * ~ 0.77 << a * = 0.98 – 1 Lee, Brown & Wijers 2002 Lee, Brown & Wijers 2002 Podsiadlowski, Rappaport & Han 2003 Podsiadlowski, Rappaport & Han 2003 McClintock, Shafee, Narayan, et al For discussion, see McClintock et al. 2006

39 Uses of Spin Data  Test Jet Models Blandford & Znajek (1977) Hawley & Balbus (2002) Validate core-collapse GRB models Validate core-collapse GRB models Collapsar: Enough J to form disk? Collapsar: Enough J to form disk? Woosley (1993) MacFadyen & Woosley (1999) Woosley & Heger (2006) Inform modelers of GW waveforms Inform modelers of GW waveforms Shafee et al. motivated first waveform work to include spin Shafee et al. motivated first waveform work to include spin Campanilli, Lousto & Zlochower (2006)  Test evolutionary model of binary black-hole formation Were GRS , GRO J ?, etc. GRB sources? Were GRS , GRO J ?, etc. GRB sources? Lee, Brown & Wijers (2002) Brown, Lee & Walter (2007) van den Heuvel et al. (2007)

40 3 Other Avenues to Spin Remillard & McClintock 2006, ARAA 44, 49 Fe line profile Fe line profile Fabian et al Fabian et al Reynolds & Nowak 2003 Reynolds & Nowak 2003 High-frequency X-ray QPOs ( Hz) High-frequency X-ray QPOs ( Hz) Abramowicz & Kluzniak 2001 Abramowicz & Kluzniak 2001 Torok et al Torok et al X-ray polarimetry X-ray polarimetry Lightman & Shapiro 1975 Lightman & Shapiro 1975 Connors, Piran & Stark 1980 Connors, Piran & Stark 1980

41 Conclusions  4 spins estimated: GRS : a* > 0.98 Straightforward methodology Straightforward methodology Fully relativistic disk model, KERRBB2: fit for a* and Mdot Fully relativistic disk model, KERRBB2: fit for a* and Mdot Thermal Dominant spectra only Thermal Dominant spectra only Accurate ground-based data on M, D & i essential Accurate ground-based data on M, D & i essential Advanced treatment of spectral hardening f col Advanced treatment of spectral hardening f col Future work Future work Amass a dozen spin estimate Amass a dozen spin estimate No torque assumption for L/Ledd < 0.3: hydro  GRMHD No torque assumption for L/Ledd < 0.3: hydro  GRMHD Test model for GRS Test model for GRS Examine possible effects of warm absorber Examine possible effects of warm absorber Attempt Fe K and HFQPO spin measurements Attempt Fe K and HFQPO spin measurements


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