Lecture 5 - University of Waterloo

Testing the No-Hair Theorem
with Observations of Black Holes
in the Electromagnetic Spectrum
Tim Johannsen
CITA National Fellow
University of Waterloo/Perimeter Institute

Testing the No-Hair Theorem Observationally
Kerr black hole?
Something else?
‣ Expand spacetime in multipole moments (mass M, spin a, …)
‣ Parameterize quadrupole moment:
‣ Use observations to measure (at least) 3 moments
‣ Check whether:
q ( a
2 )
i.e.: 0
2
q a
Ryan 1995, 1997a,b
Barack & Cutler 2004, 2007
Collins & Hughes 2004
Glampedakis & Babak 2006
Brink 2008, 2009
Gair et al. 2008
Li & Lovelace 2008
Will 2008
Vigeland & Hughes 2010
Johannsen & Psaltis 2010a, 2011b
Vigeland et al. 2011

A New Metric for Rapidly Spinning Black Holes
2 2Mr
4aMr
sin
ds 1
)
a
sin
where
2
1
h(
r,
)
dt
1
h(
r,
dtd
1
h(
r,
)
2 2
2
h(
r,
)sin
r
2
dr
d
h(
r,
)
2 2
2
4
2 2 2 2a
Mr sin a ( 2Mr)
sin
a
2
d
r
2
2Mr
a
2
r a
2 2 cos
2
h(
r,
)
3
rM
2
3
Johannsen & Psaltis 2011, PRD, 83, 124015

Quadrupole Effects:
1. Location of the ISCO 2. Lightbending
Johannsen & Psaltis 2011b, PRD, 83, 124015
Johannsen 2012, Adv. Astron., 2012, 1

1. Imaging the Shadow of Sgr A*
Inclination Angle: 68 o +5 o
Spin: 0.0
Spin Position Angle: -52 o
-20 o
+0.64
+17 o
-15 o
Broderick, Fish, Doeleman, Loeb 2011, ApJ, 735, 110
• Assume Kerr black hole in ADAF/RIAF model
Broderick et al. 2009, ApJ, 697, 1164
• Current VLBI data (JCMT – CARMA – SMT)
Doeleman et al. 2008, Nature, 455, 78; Fish et al. 2011, ApJ, 727, 36

Broderick, Johannsen, Loeb, Psaltis 2012
Testing the No-Hair Theorem with Sgr A*
= 0.4 = -0.8
Shape of shadow depends uniquely on mass, spin, disk inclination
...as well as on quadrupole moment
e.g., Falcke et al. 2000, ApJ, 528, L13
Johannsen & Psaltis 2010b, ApJ, 718, 446

Bright Emission Ring!
e.g., Beckwith & Done 2005, MNRAS, 359, 1217
The Photon Ring
clearly distinguishable
independent of
flow properties
‣ ideal for imaging!
Johannsen & Psaltis 2010b, ApJ, 718, 446

Moscibrodzka et al. 2009,
ApJ, 706, 497
Shcherbakov & Penna 2011,
ASP Conf. Ser., 439, 372
Dexter et al. 2009, ApJ, 703, L142
Photon Rings
A ubiquitous signal,
independent of the details
of the accretion flow

Broderick, Johannsen, Loeb, Psaltis 2012
Johannsen & Psaltis 2010a, ApJ, 716, 187

Broderick, Johannsen, Loeb, Psaltis 2012
Johannsen & Psaltis 2010a, ApJ, 716, 187

Broderick, Johannsen, Loeb, Psaltis 2012
Johannsen & Psaltis 2010a, ApJ, 716, 187

Independent Measurement: M, a, ε (mod i)
Johannsen & Psaltis 2010b, ApJ, 716, 187
Diameter:
Displacement:
Asymmetry:
measures mass
measures spin
measures quadrupole moment

Combined Mass Measurement of Sgr A*
Johannsen, Psaltis, Gillessen, Marrone, Ozel, Doeleman, & Fish 2012, ApJ, 758, 30
Planned VLBI array: JCMT, CARMA, SMT, ALMA, SPT, SMA

Millimetron
RadioAstron Newsletter Dec. 8, 2011
VLBI from Space

Masses of other SMBHs with VLBI
5-telescope
array
Millimetron
mission
Johannsen et al., ApJ, 758, 30

Galactic BHs and AGN
from Gou et al. 2011, ApJ, 742, 85

Iron K- and L- Lines
in 1H0707-495
Fabian et al. 2009, Nature, 459, 540

2. Relativistically Broadened Iron Lines
Johannsen & Psaltis, arXiv:1202.6069
Psaltis & Johannsen, 2012, ApJ, 745, 1

Required Precision for Future Instruments
Inclination 30 o
Inclination 60 o
Johannsen & Psaltis, arXiv:1202.6069

Observational Tests of the No-Hair Theorem
1. VLBI-Imaging of Sgr A*
Event Horizon Telescope
2. Fluorescent Iron Lines
e.g., ASTRO-H, ATHENA
ASTRO-H
3. Variability
Need Timing Mission to detect higher
order harmonics and resolve model
degeneracies.
e.g., LOFT