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