Probing Accretion and Spacetime with Black Hole Binaries

1
Probing Accretion and Spacetime with Black Hole
Binaries
Shane DavisIAS
Omer BlaesIvan HubenyNeal TurnerJulian
KrolikJim StoneShigenobu Hirose
Chris DoneMathew MiddletonMarek
GierlinskiRebbeca ShafeeRamesh NarayanJeff
McClintockRon RemillairdLi-Xin Li
2
Issues Addressed in This Talk

• How does the release of gravitational binding
  energy lead to thermal radiation?
• Are thin disk (?-disk) models sufficient to
  explain black hole X-ray binary (BHB)
  observations?

3
The thin disk model

• H/R ltlt 1
• Constant accretion rate time-steady
• Gravitational binding energy released locally
• as radiation

The ?-disk model

• determines surface
  density ?
• Vertical dissipation
• distribution

4
The Multicolor Disk Model (MCD)

• Assumes simple temperature distribution
• Spectrum assumed to be color-corrected blackbody

?F?
?
?F?
?
5
Disk Dominated Spectra
LMC X-3
Gierlinski Done 2004

• L prop. to T4 suggests fcol and emitting area
  are constant

6
Comparison with Previous Spectral Models

• Previous ?-disk models provide mixed results
• Shimura Takahara (1995) full atmosphere
  calculation, free-free emission and Compton
  scattering stars
• Merloni, Fabian Ross (2000) relativistic
  effects, constant density, f-f emission and
  Compton scattering blue curve
• Small scatter in L-T relation as L varies by over
  an order of magnitude

Gierlinski Done 2004
7
Our Models, Briefly

• Use conservation laws with Kerr metric to
  calculate one-zone model
• Full disk model is determined by 4 parameters
  M, a/M, L/LEdd, ?
• Calculate self-consistent vertical structure and
  radiative transfer in a series of concentric
  annuli
• Each annulus is determined by 3 parameters
• ( assumptions) Teff, Q, (gQ z), ?
• Calculate photon geodesics in a relativistic
  spacetime (ray tracing) -- determined by a/M and
  i

8
Model Parameters
L/LEdd
Inclination
Spin
Mass
9
Luminosity vs. Temperature

• We generate artificial spectra and fit MCD model
• Then, we follow the procedure of Gierlinski
  Done (2004) to calculate Ldisk/Ledd and Tmax
• Model a0, i70o, M10 solar masses, and ?0.01

10
Spin Estimates

• With independent estimates for the inclination,
  mass, and distance, thermal component only has
  two free parameters -- luminosity and spin (same
  number as diskbb)
• Fits with our models suggest moderate
• (a/M lt 0.9) values for several sources

Shafee et al. 2005
11
Broadband Fits to LMC X-3
Our Model
MCD

• MCD model is too narrow -- need relativistic
  broadening ??2 100
• Best fit find spinning black hole with a/M0.27

12
What Have We Learned?

• Our detailed accretion disk models can reproduce
  the spectra of disk dominated BHBs (statistically
  significant improvement over MCD for broad-band
  spectra of LMC X-3)
• Models qualitatively reproduce the observed
  evolution with luminosity spectral modeling may
  constrain the nature of angular momentum
  transport (i.e. measure ?) and black hole spin

What Have I Skipped?

• Dissipation, magnetic stresses, inhomogeneities,
  etc. can affect the spectra -- more progress is
  needed to make these methods more robust

13
Luminosity vs. Temperature

• Slight hardening is consistent with some
  observations
• Allows one to constrain surface density and
  accretion stress
• Models become effectively optically thin at high
  accretion rates

?0.1
?0.01
?0.001
14
Summary of Fit Results
a0 ?0.01
a0.65 ?0.1
a0.1 ?0.01
15
II. Adding Real Physics Dissipation, Magnetic
Stresses Inhomogeneities
16
Local MRI Simulations(with radiaton)

• Shakura Sunyaev (1973)
• Turner (2004) Mass more centrally concentrated
  towards midplane in simulations.
• Magnetic fields produced near midplane are
  buoyant
• and dissipate near surface

Turner (2004)
17
Dissipation Profile

• Modified dissipation profile changes structure
  significantly
• Where -dF/dm is small (large), density is larger
  (smaller)
• Note that T and ? near ? are similar

Turner Profile
SS73 Profile
18
Dissipation Profile

• but modified dissipation profile has limited
  affect on the spectrum.
• This particular annulus is very effectively
  optically thick and ? is close to surface

Turner Profile
SS73 Profile
19
Dissipation Profile

• Consider same dissipation profile, but in an
  annulus that is not effectively optically thick.
• Spectrum with modified dissipation profile is
  effectively optically thick, but has a much
  greater surface temperature

Turner Profile
SS73 Profile
20
Dissipation Profile

• For this annulus, the spectra from the modified
  dissipation profile is considerably harder
• This will exacerbate the discrepancy between
  observations and models unless disks stay
  optically thick

Turner Profile
SS73 Profile
21
Black Hole Accretion Disk Spectral Formation
22
Spectral Formation

• Depth of formation ? optical depth where (?es
  ?abs)1/21
• ? gt ? absorbed
• ? lt ? escape
• Therefore Thomson scattering produces modified
  blackbody
• Compton scattering gives softer Wien spectrum
  which Shimura Takahara claim is consistent with
  fcol1.7 for BHBs

?? 0
?es 1
(?es ?abs)1/2 1
?abs 1
23
How can we improve on these models?

• Include metals with bound-free opacity solve
  non-LTE populations
• More accurate radiative transfer and better
  treatment of Compton Scattering
• Can consider the effects of more complicated
  physics e.g. dissipation, magnetic stresses,
  and inhomogeneities

24
Magnetic Stresses

• B2/8? dF/dm taken from simulations of Hirose et
  al.
• Gas pressure dominated -- dF/dm has little effect
  on the structure
• Extra magnetic pressure support lengthens scale
  height hr
• ??/(?es hr)

No B field
B field
Simulation
25
Magnetic Stresses

• Lower ? and higher T combine to give somewhat
  harder spectrum
• In this case lower ? alters statistical
  equilibrium -- lower recombination rate relative
  to photoionization rate give more highly ionized
  matter with lower bound-free opacity

No B field
B field
26
Inhomogeneities

• Radiation pressure dominated accretion disks
  expected to be homogeneous due to photon bubble
  instability and/or compressible MRI
• May make disk thinner and (therefore) denser
  (Begelman 2001, Turner et al. 2005)
• May also affect the radiative transfer

Neal Turner
27
Inhomogeneities

• 2-D Monte Carlo calculations photon bubbles help
  thermalize the spectrum, making it softer
• Photon emission and absorption dominated by
  denser regions.

28
Non-aligned Jet

• XTE J1550-564 is a microquasar
• Hannikainen et al. (2001) observe superluminal
  ejections with v gt 2 c
• Ballistic model
• Orosz et al. (2002) found i72o
• Non-aligned jets not uncommon -- usually assumed
  that BH spin differs from binary orbit and inner
  disk aligns with BH -- Bardeen-Petterson effect
• Best fit inclination, spin i43o, a0.44

29
Spectral States of BHBs

• Spectral states specified by relative
  contributions of thermal (disk) and non-thermal
  emission (corona)
• High/Soft state is dominated by thermal disk-like
  component

Done Gierlinski 2004
30
Spectral Dependence on Surface Density

• Spectra largely independent of ? for large
  surface density
• (? gt 103 g/cm2)
• As disk becomes marginally effectively thin,
  spectra become sensitive to ? and harden rapidly
  with decreasing ?

31
Binaries Provide Independent Constraints on
Models

• Orosz and collaborators derive reasonably precise
  estimates from modeling the light curve of
  secondary
• e.g. XTE J1550-564

32
Luminosity vs. Temperature

• Measured binary properties limit parameter space
  of fits
• Simultaneous fits to multiple observations of
  same source constrain spin/torque
• Spectra are too soft to allow for extreme
  spin/large torques

33
Stellar Atmospheres Disk Annuli vs. Stellar
Envelopes

• The spectra of stars are determined by Teff, g,
  and the composition
• Annuli are determined by, Teff, Q (where gQ z),
  ?, the composition, and the vertical dissipation
  profile F(m)
• Teff, Q, and ? can be derived from radial disk
  structure equations
• Standard assumption is

34
Luminosity vs. Temperature
Gierlinski Done 2004
35
Effect of bound-free opacity

• Bound-free opacity decreases depth of formation
  ??
• Absorption opacity approximately grey
• Spectrum still approximated by diluted blackbody

36
The Multicolor Disk Model (MCD)

• Consider simplest temperature distribution
• Assume blackbody and integrate over R replacing R
  with T (TmaxfcolTeff)

37
Effective Temperature Teff
38
Gravity Parameter Q
39
Comparison Between Interpolation and Exact Models

• Interpolation best at high L/Ledd
• Exact Blue curve
• Interpolation Red Curve