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Estimating the Spin of Stellar-Mass Black Holes. Jeffrey McClintock Harvard-Smithsonian CfA STScI Black Hole Symposium April 25, 2007. Chronological List of Team Members. This effort to measure spin requires a 50-50 mix of theory & observation. Int roduction. The Essentials. - PowerPoint PPT Presentation
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Estimating the Spin of Estimating the Spin of Stellar-Mass Black HolesStellar-Mass Black Holes
Jeffrey McClintockJeffrey McClintock
Harvard-Smithsonian CfAHarvard-Smithsonian CfA
STScI Black Hole SymposiumSTScI Black Hole SymposiumApril 25, 2007April 25, 2007
Chronological List of Team MembersChronological List of Team MembersNameName YearYear
Jeffrey McClintockJeffrey McClintock
Ramesh NarayanRamesh Narayan
Li-Xin LiLi-Xin Li
Rebecca ShafeeRebecca Shafee
Ronald RemillardRonald Remillard
Shane DavisShane Davis
Jerome OroszJerome Orosz
Danny SteeghsDanny Steeghs
Charles BailynCharles Bailyn
Michael MunoMichael Muno
Thomas MegeathThomas Megeath
2004.32004.3
2004.32004.3
2004.32004.3
2005.12005.1
2005.22005.2
2005.32005.3
2005.92005.9
2005.92005.9
2006.22006.2
2006.22006.2
2006.22006.2
NameName YearYear
Wolfgang PietschWolfgang Pietsch
Mark ReidMark Reid
Vik DhillonVik Dhillon
Stuart LittlefairStuart Littlefair
Vivek DhawanVivek Dhawan
Joel HartmanJoel Hartman
Manuel TorresManuel Torres
Jack SteinerJack Steiner
Lucas MacriLucas Macri
Jifeng LiuJifeng Liu
2006.22006.2
2006.72006.7
2006.92006.9
2007.12007.1
2007.12007.1
2007.12007.1
2007.22007.2
2007.22007.2
2007.22007.2
2007.22007.2
This effort to measure spin requires a 50-50 mix of theory & observation.
IntIntroductionroduction
The EssentialsThe Essentials Objects: Objects: Stellar-mass BHs in X-ray binariesStellar-mass BHs in X-ray binaries
Method: Method: Spin via fitting the X-ray continuumSpin via fitting the X-ray continuum
Absolute Requirements:Absolute Requirements: Accurate values of BH mass, i & DAccurate values of BH mass, i & D “ “Thermal-Dominant” X-ray dataThermal-Dominant” X-ray data State-of-the-art relativistic modelsState-of-the-art relativistic models
Li, Zimmerman, Narayan & McClintock 2005Li, Zimmerman, Narayan & McClintock 2005
Shaffee, McClintock, Narayan, Davis, Li & Remillard 2006Shaffee, McClintock, Narayan, Davis, Li & Remillard 2006 McClintock, Shafee, Narayan, Remillard, Davis & Li 2006McClintock, Shafee, Narayan, Remillard, Davis & Li 2006
Number of BH Number of BH binaries binaries
known = 21known = 21
Courtesy J. Orosz
Ii
M ~ 10 Msun
Number of BH Number of BH binaries binaries
known = 21known = 21
Courtesy J. Orosz
Ii
M ~ 10 Msun
Black Holes are Extremely Black Holes are Extremely SimpleSimple
MassMass:: MM SpinSpin:: J = J = aa**GMGM22/c (0 < /c (0 < aa** < 1) < 1)
(Electric Charge: Q)(Electric Charge: Q)
21 BH masses M have been measured
Obvious next frontier: Measure BH spin a* (much harder)
ffT ~ 2 keV42%
T ~ 1 keV6%
a* = 1
a* = 0
RISCO = 15 km
RISCO = 90 km
RISCO: Extreme-Kerr vs. Schwarzschild
Two FoundationsTwo Foundations1.1. ISCOISCO2. Thermal Dominant State2. Thermal Dominant State
A disk terminates at RISCO and gas falls
freely onto the BH inside this radius.
Thus, disk emission has a “hole” of radius RISCO at center.
If we measure the size of the hole, we will obtain a*
90 km
15 km
RISCO a*
First FoundationInnermost Stable Circular Orbit (ISCO)
• 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: Tin & Rin
Mitsuda et al. 1984 Makishima et al. 1986 Tanaka & Lewin 1995 Remillard & McClintock 2006
Second Foundation
• Consider disk component of emission only
• Focus on 4-month monotonic decay of accretion disk
Second Foundation (cont.)
• Ldisk / Ltotal > 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.)
• Smooth, monotonic decline of temperature as disk decays on a thermal time scale
Second Foundation (cont.)
Second Foundation (cont.)Second Foundation (cont.)
• Inner disk radius Rin quite constant Compare Tanaka & Lewin 1995 in XRBs
Second Foundation (cont.)
Second Foundation (cont.)Second Foundation (cont.)
• Now, plot Ldisk/Llotal versus Tin
Second Foundation (cont.)
Second Foundation (cont.)Second Foundation (cont.)
Tin4
Kubota et al. 2001Kubota & Makishima 2004Kubota & Done 2004Gierlinski & Done 2004
H1743-322
Tin4
Teff4
Second Foundation
fcol = Tin/Teff
Davis et al. 2005, 2006
Conclusion: There exists a constant radius
Outline of Method for Outline of Method for Estimating SpinEstimating Spin
Fitting the X-ray continuum Fitting the X-ray continuum
Measuring the Radius of a StarMeasuring the Radius of a Star
Measure the flux Measure the flux FF received from the starreceived from the star Measure the temperature Measure the temperature T T (from spectrum)(from spectrum) Then, assuming Then, assuming blackbodyblackbody radiation: radiation:
FF and and TT give give solid anglesolid angle of star of star If we know distanceIf we know distance DD,, we directly obtainwe directly obtain RR
2 2 4
2
4
4 4
R F=
D T
L D F R Tπ π σ
σ
= =
⎛ ⎞⎜ ⎟⎝ ⎠
R
Measuring the Radius of the Disk Measuring the Radius of the Disk Inner EdgeInner Edge
We want to measure the radius of the We want to measure the radius of the ‘hole’‘hole’ in the disk emission in the disk emission
Same principle as beforeSame principle as before From From FF and and TT get get
solid angle of holesolid angle of hole Knowing Knowing DD and and ii
get get RRISCOISCO
From From RRISCOISCO and and MM get get aa** Zhang et al. (1997)Zhang et al. (1997) Gierlinski et al. 2001; Li et al. (2005); 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);…
RISCO
Estimates of Spin Obtained with Estimates of Spin Obtained with this Methodthis Method
SystemSystem aa** ReferenceReference
GRO J1655-40GRO J1655-40 0.65-0.750.65-0.75 Shafee et al. (2006)Shafee et al. (2006)
4U1543-474U1543-47 0.7-0.80.7-0.8 Shafee et al. (2006)Shafee et al. (2006)
GRS 1915+105GRS 1915+105 0.98-1.00.98-1.0 McClintock et al. (2006)McClintock et al. (2006)
LMC X-3LMC X-3 <0.26<0.26 Davis et al. (2006)Davis et al. (2006)
Diving into the MethodDiving into the Method
How to Get Reliable Results?How to Get Reliable Results? Need good estimates of Need good estimates of M, D, iM, D, i
Should include all Should include all relativistic effectsrelativistic effects: Doppler beaming, : Doppler beaming,
grav. redshift, ray deflections grav. redshift, ray deflections KERRBBKERRBB (Li et al. 2006) (Li et al. 2006)
The system should be in the The system should be in the Thermal DominantThermal Dominant state state
H/R < 0.1 H/R < 0.1 L/LL/Ledd edd < 0.3< 0.3
Deviations from blackbodyDeviations from blackbody (parameter (parameter ff) should be ) should be
estimated via a disk atmosphere model estimated via a disk atmosphere model Shimura & Takahara (1995); Davis et al. (2005, 2006)
How to Get Reliable Results?How to Get Reliable Results?(cont.)(cont.)
Need accurate theoretical profiles of Need accurate theoretical profiles of
disk flux F(R) and temperature T(R)disk flux F(R) and temperature T(R)
RISCO
RISCO
Zero-torque at ISCOH/R < 0.1L/Ledd < 0.3
S
Flux vs. RadiusShafee, Narayan & McClintock (Poster #31)
a* = 0
aaa* = 0.95
Bottom LineErrors due to hydro effects are modest.
Shafee et al.(Poster #31)
Only Only aa** and and MdotMdot Determined Determined
from X-ray Spectrumfrom X-ray Spectrum M,D,iM,D,i from ground-based observations from ground-based observations
ffcolcol from disk atmosphere model from disk atmosphere model
Zero torqueZero torque at ISCO for L/L at ISCO for L/Leddedd < 0.3 < 0.3
Fit for Fit for aa** and and MdotMdot (Mdot (Mdot L/L L/Leddedd) only) only
T & flux T & flux a a* * & Mdot& Mdot
GRS 1915+105GRS 1915+105
KERBB: Fit for a* and mass accretion rate Mdot (L/Ledd)
ASCA: 1.2-10 keV RXTE: 3-25 keV
20 Thermal-Dominant Observations out of 640
a* = 0.988L/Ledd = 0.18
a* = 0.994L/Ledd = 0.21
2 5 Energy (keV)
5 10 20 Energy (keV)
Flux
Flux
McClintock, Shafee, Narayan et al. 2006
Observational Work Observational Work in Progressin Progress
HEASARC
Key Spin TargetsKey Spin Targets M33 X-7: Gemini-N, Chandra, XMMM33 X-7: Gemini-N, Chandra, XMM
GRS 1915+105: VLBA, Gemini-SGRS 1915+105: VLBA, Gemini-S
LMC X-1: Magellan, SMARTSLMC X-1: Magellan, SMARTS
A0620-00: Spitzer/ground-basedA0620-00: Spitzer/ground-based
XTE J1550-564: MagellanXTE J1550-564: Magellan
Additional targets:Additional targets: Nova Mus 1991, XTE J1859+226, Nova Mus 1991, XTE J1859+226,
XTE J1650-500, GS 2000+25, GRS 1009-45… XTE J1650-500, GS 2000+25, GRS 1009-45… about a dozen in totalabout a dozen in total
Pietsch et al. 2006
M33 X-7
PreliminaryOrosz et al. 2007
Porb 3.45 days
D = 845 +/- 25 kpc i = 74 +/- 2 degM = 14 +/- 3 Msun
O6 giantM2 = 57 +/- 10 MsunR2 = 18.5 +/- 1 RsunTeff = 35,000 +/- 2500K
Spin analysis underwayLiu et al.
a* = 0.98-1.0McClintock, Shafee, Narayan et al. 2006
Radio JetRadio Jetv/c = 0.92v/c = 0.92
GRS 1915+105
Mirabel & Rodriguez 1994
GRS 1915+105
6 8 10 12 14 Distance (kpc)
Gemini-S GNIRS proposal pending
GRS 1915+105
McClintock, Shafee, Narayan et al. 2006
GRS 1915+105
Distance (kpc) VLBA observations underway
Nominal SpinsNominal Spinsof 4 BHsof 4 BHs
LMC X-3: a* = 0.2GRO J1655-40: a* = 0.7
4U 1543-47: a* = 0.8
GRS 1915+105: a* = 0.99
McClintock, Shafee, Narayan, et al.
DiscussionDiscussion
Black Hole Spins Chiefly NatalBlack Hole Spins Chiefly Natal
Accretion torques inadequate to spin up BH in Accretion torques inadequate to spin up BH in lifetime of systemlifetime of system
King & Kolb 1999King & Kolb 1999
GRS 1915+105 a prime example:GRS 1915+105 a prime example:
Accretion of 4 MAccretion of 4 Moo onto a 10 M onto a 10 Mo o hole hole
aa* * ~ 0.77 << a~ 0.77 << a* * = 0.98 – 1= 0.98 – 1 Lee, Brown & Wijers 2002Lee, Brown & Wijers 2002 Podsiadlowski, Rappaport & Han 2003Podsiadlowski, Rappaport & Han 2003
McClintock, Shafee, Narayan, et al. 2006McClintock, Shafee, Narayan, et al. 2006
For discussion, see McClintock et al. 2006
Uses of Spin DataUses of Spin Data Test Jet ModelsTest Jet Models
Blandford & Znajek (1977)Blandford & Znajek (1977)Hawley & Balbus (2002)Hawley & Balbus (2002)
Validate core-collapse GRB modelsValidate core-collapse GRB models Collapsar: Enough J to form disk?Collapsar: Enough J to form disk?
Woosley (1993)Woosley (1993)MacFadyen & Woosley (1999)MacFadyen & Woosley (1999)
Woosley & Heger (2006)Woosley & Heger (2006)
Inform modelers of GW waveformsInform modelers of GW waveforms Shafee et al. motivated first waveform work to include spinShafee et al. motivated first waveform work to include spin
Campanilli, Lousto & Zlochower (2006)Campanilli, Lousto & Zlochower (2006)
Test evolutionary model of binary black-hole formationTest evolutionary model of binary black-hole formation Were GRS 1915+105, GRO J1655-40?, etc. GRB sources?Were GRS 1915+105, GRO J1655-40?, etc. GRB sources?
Lee, Brown & Wijers (2002)Lee, Brown & Wijers (2002)Brown, Lee & Walter (2007)Brown, Lee & Walter (2007)
van den Heuvel et al. (2007)van den Heuvel et al. (2007)
3 Other Avenues to Spin3 Other Avenues to SpinRemillard & McClintock 2006, ARAA 44, 49Remillard & McClintock 2006, ARAA 44, 49
Fe line profileFe line profile Fabian et al. 1989Fabian et al. 1989 Reynolds & Nowak 2003Reynolds & Nowak 2003
High-frequency X-ray QPOs (100-450 Hz)High-frequency X-ray QPOs (100-450 Hz) Abramowicz & Kluzniak 2001Abramowicz & Kluzniak 2001 Torok et al. 2005Torok et al. 2005
X-ray polarimetryX-ray polarimetry Lightman & Shapiro 1975Lightman & Shapiro 1975 Connors, Piran & Stark 1980Connors, Piran & Stark 1980
ConclusionsConclusions 4 spins estimated: 4 spins estimated: GRS 1915+105: a* > 0.98GRS 1915+105: a* > 0.98
Straightforward methodologyStraightforward methodology Fully relativistic disk model, KERRBB2: fit for Fully relativistic disk model, KERRBB2: fit for a* and Mdota* and Mdot Thermal Dominant Thermal Dominant spectra onlyspectra only Accurate ground-based data on Accurate ground-based data on M, D & i essentialM, D & i essential Advanced treatment of spectral hardening Advanced treatment of spectral hardening ffcolcol
Future workFuture work Amass a Amass a dozendozen spin estimate spin estimate No torque assumption for L/Ledd < 0.3:No torque assumption for L/Ledd < 0.3: hydro hydro GRMHD GRMHD Test model Test model for GRS 1915+105for GRS 1915+105 Examine possible effects of Examine possible effects of warm absorberwarm absorber AttemptAttempt Fe K and HFQPO Fe K and HFQPO spin measurementsspin measurements