Testing astrophysical black holes Cosimo Bambi Fudan University http://www.physics.fudan.edu.cn/tps/people/bambi/ 29 October 2015 Interdisciplinary Center for Theoretical Studies (USTC, Hefei)
Testing astrophysical black holes
Cosimo BambiFudan University
http://www.physics.fudan.edu.cn/tps/people/bambi/
29 October 2015Interdisciplinary Center for Theoretical Studies (USTC, Hefei)
Cosimo Bambi (Fudan University) 2
Plan of the talk
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 3
Cosimo Bambi
“Testing black hole candidates with electromagnetic radiation”
arXiv: 1509.03884 [gr-qc]
Invited review paper submitted to Rev. Mod. Phys.
Cosimo Bambi (Fudan University) 4
Introduction
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 5
Tests of general relativity
● 1915 → General relativity (Einstein)
● 1919 → Deflection of light by the Sun (Eddington)
● 1960s-present → Solar System experiments
● 1970s-present → Binary pulsars
Today:
● Cosmological tests (dark matter/dark energy)
● Black holes
Cosimo Bambi (Fudan University) 6
Tests of general relativity
● 1915 → General relativity (Einstein)
● 1919 → Deflection of light by the Sun (Eddington)
● 1960s-present → Solar System experiments
● 1970s-present → Binary pulsars
Today:
● Cosmological tests (dark matter/dark energy)
● Black holes
Weak fields
Strong fields
Large scales
Cosimo Bambi (Fudan University) 7
Cosimo Bambi (Fudan University) 8
Black holes in GR (Theory)
● Final product of the gravitational collapse → Black hole
● 4D General Relativity → Kerr black hole
● Only 2 parameters: the mass M and the spin J (a* = J/M2)
● Kerr bound: |a*| < 1
Cosimo Bambi (Fudan University) 9
Black hole candidates (Observations)
● Stellar-mass BH candidates in X-ray binary systems (5 – 20 Solar masses)
● Supermassive BH candidates in galactic nuclei (105 – 1010 Solar masses)
● Intermediate-mass BH candidates in ULXS (102 – 104 Solar masses?)
Cosimo Bambi (Fudan University) 10
Stellar-mass BH candidates
● Dark objects in X-ray binary systems
● Mass function:
● In general, a good estimate of MC
and i is necessary
● Maximum mass for relativistic stars about 3 Solar masses (see Rhoades & Ruffini 1974 and Kalogera & Baym 1996)
Cosimo Bambi (Fudan University) 11
From Remillard & McClintock 2006
Cosimo Bambi (Fudan University) 12
From Remillard & McClintock 2006
Cosimo Bambi (Fudan University) 13
Supermassive BH candidate in the Galaxy
● We study the orbital motion of individual stars
● Point-like central object with a mass of 4x106 Solar masses
● Radius < 45 AU (600 RSch
)
From Ghez et al., ApJ 620 (2005) 744
Cosimo Bambi (Fudan University) 14
Important remarks
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 15
Solar System experiments:Schwarzschild solution in the weak field limit
● Parametrized Post-Newtonian formalism (PPN formalism)
● Weak field limit (M/r << 1)
● Solar System experiments
Cosimo Bambi (Fudan University) 16
Testing the Kerr solution around black hole candidates
● No satisfactory formalism at present
● Strong gravity, no expansion in M/r
● Proposals: Johannsen-Psaltis (2011), Cardoso-Pani-Rico (2014), Rezzolla-Zhidenko (2014)
Cosimo Bambi (Fudan University) 17
Black holes:Kerr solution
● Kerr metric
● Johannsen-Psaltis metric
Cosimo Bambi (Fudan University) 18
Important remarks
● The study of the properties of the electromagnetic radiation emitted by the gas in the accretion disk can test the Kerr metric, not the Einstein equations
● The Kerr metric is the unique uncharged BH solution of GR, but it is a solution of many other theories of gravity
● If we want to test the Einstein equations, we need to study the perturbations around the Kerr background (see Barausse & Sotiriou 2008)
● It is not enough to observe relativistic features absent in Newtonian gravity (common misunderstanding in the literature). In order to test the Kerr BH hypothesis it is necessary to check that observational data exclude deviations from the Kerr solution. Non-Kerr BHs typically look like Kerr BHs with different spin
Cosimo Bambi (Fudan University) 19
Important remarks
● The study of the properties of the electromagnetic radiation emitted by the gas in the accretion disk can test the Kerr metric, not the Einstein equations
● The Kerr metric is the unique uncharged BH solution of GR, but it is a solution of many other theories of gravity
● If we want to test the Einstein equations, we need to study the perturbations around the Kerr background (see Barausse & Sotiriou 2008)
● It is not enough to observe relativistic features absent in Newtonian gravity (common misunderstanding in the literature). In order to test the Kerr BH hypothesis it is necessary to check that observational data exclude deviations from the Kerr solution. Non-Kerr BHs typically look like Kerr BHs with different spin
Cosimo Bambi (Fudan University) 20
Important remarks
● The study of the properties of the electromagnetic radiation emitted by the gas in the accretion disk can test the Kerr metric, not the Einstein equations
● The Kerr metric is the unique uncharged BH solution of GR, but it is a solution of many other theories of gravity
● If we want to test the Einstein equations, we need to study the perturbations around the Kerr background (see Barausse & Sotiriou 2008)
● It is not enough to observe relativistic features absent in Newtonian gravity (common misunderstanding in the literature). In order to test the Kerr BH hypothesis it is necessary to check that observational data exclude deviations from the Kerr solution. Non-Kerr BHs typically look like Kerr BHs with different spin
Cosimo Bambi (Fudan University) 21
Important remarks
● The study of the properties of the electromagnetic radiation emitted by the gas in the accretion disk can test the Kerr metric, not the Einstein equations
● The Kerr metric is the unique uncharged BH solution of GR, but it is a solution of many other theories of gravity
● If we want to test the Einstein equations, we need to study the perturbations around the Kerr background (see Barausse & Sotiriou 2008)
● It is not enough to observe relativistic features absent in Newtonian gravity (common misunderstanding in the literature). In order to test the Kerr BH hypothesis it is necessary to check that observational data exclude deviations from the Kerr solution. Non-Kerr BHs typically look like Kerr BHs with different spin
Cosimo Bambi (Fudan University) 22
Important remarks
● The study of the properties of the electromagnetic radiation emitted by the gas in the accretion disk can test the Kerr metric, not the Einstein equations
● The Kerr metric is the unique uncharged BH solution of GR, but it is a solution of many other theories of gravity
● If we want to test the Einstein equations, we need to study the perturbations around the Kerr background (see Barausse & Sotiriou 2008)
● It is not enough to observe relativistic features absent in Newtonian gravity (common misunderstanding in the literature). In order to test the Kerr BH hypothesis it is necessary to check that observational data exclude deviations from the Kerr solution. Non-Kerr BHs typically look like Kerr BHs with different spin
Cosimo Bambi (Fudan University) 23
Correlated important remarks
● Technically, a black hole is a region causally disconnected to future null infinity and the event horizon is its boundary
● Observationally, we can test the existence of an apparent horizon. To test the existence of an event horizon we should know the future, which is impossible. A long-living apparent horizon behaves like an event horizon
Cosimo Bambi (Fudan University) 24
Correlated important remarks
● Technically, a black hole is a region causally disconnected to future null infinity and the event horizon is its boundary
● Observationally, we can test the existence of an apparent horizon. To test the existence of an event horizon we should know the future, which is impossible. A long-living apparent horizon behaves like an event horizon
Cosimo Bambi (Fudan University) 25
Correlated important remarks
● Technically, a black hole is a region causally disconnected to future null infinity and the event horizon is its boundary
● Observationally, we can test the existence of an apparent horizon. To test the existence of an event horizon we should know the future, which is impossible. A long-living apparent horizon behaves like an event horizon
Cosimo Bambi (Fudan University) 26
Continuum-fitting method
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 27
Today
● Continuum-fitting method → only stellar-mass black hole candidates (Zhang, Cui & Chen, 1997)
● Iron line → stellar-mass and super-massive black hole candidates (Fabian et al., 1989)
Gou et al., ApJ 742 (2011) 85
Cosimo Bambi (Fudan University) 28
Continuum-fitting method
Gou et al., ApJ 742 (2011) 85
● The soft X-ray component of the spectrum of stellar-mass BH candidates is the thermal spectrum of a geometrically thin and optically thick accretion disk
Cosimo Bambi (Fudan University) 29
Novikov-Thorne Model
● Geometrically thin and optically thick accretion disk
● Relativistic generalization of the Shakura-Sunyaev model
Assumptions:
● Disk on the equatorial plane
● Gas's particles move on nearly geodesic circular orbits
● No magnetic fields
● No heat advection; energy radiated from the disk surface
● Inner edge of the disk at the ISCO, where stresses vanish
→ Efficiency = 1 – EISCO
Cosimo Bambi (Fudan University) 30
Novikov-Thorne Model
● Geometrically thin and optically thick accretion disk
● Relativistic generalization of the Shakura-Sunyaev model
Assumptions:
● Disk on the equatorial plane
● Gas's particles move on nearly geodesic circular orbits
● No magnetic fields
● No heat advection; energy radiated from the disk surface
● Inner edge of the disk at the ISCO, where stresses vanish
→ Efficiency = 1 – EISCO
Selection criterion:0.08 L
EDD < L < 0.30 L
EDD
Cosimo Bambi (Fudan University) 31
Continuum-fitting method in Kerr background
● 5 parameters (BH mass, BH spin, BH distance, viewing angle, mass accretion rate)
● BH mass, BH distance, viewing angle → BH spin, mass accretion rate
Cosimo Bambi (Fudan University) 32
Continuum-fitting method results to date
Cosimo Bambi (Fudan University) 33
Step 1: computation of the image
Cosimo Bambi (Fudan University) 34
Step 2: calculation of the disk's spectrum
Cosimo Bambi (Fudan University) 35
Constraints from the continuum-fitting method[Kong, Li & Bambi (2014)]
Cosimo Bambi (Fudan University) 36
Constraints from the continuum-fitting method[Kong, Li & Bambi (2014)]
Cosimo Bambi (Fudan University) 37
Constraints from the continuum-fitting method[Kong, Li & Bambi (2014)]
Cosimo Bambi (Fudan University) 38
Constraints from the continuum-fitting method[Kong, Li & Bambi (2014)]
Cosimo Bambi (Fudan University) 39
Constraints from the continuum-fitting method[Bambi (2014)]
● Cardoso-Pani-Rico parametrization
Cosimo Bambi (Fudan University) 40
Constraints from the continuum-fitting method[Bambi (2014)]
● Cardoso-Pani-Rico parametrization
Conclusion:The continuum-fitting method is currently the most robust
technique, but the shape of the spectrum is simple.We can only measure one parameter of the background geometry
Cosimo Bambi (Fudan University) 41
Iron K-alpha line
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 42
Iron K-alpha line
● The illumination of the cold disk by the primary component produces spectral lines by fluorescence. The strongest line is the iron K-alpha line at 6.4 keV
From Gou et al., ApJ 742 (2011) 85
Cosimo Bambi (Fudan University) 43
Iron K-alpha line analysis
● It is another popular technique used by astronomers to try to estimate the spin parameter of BH candidates
Cosimo Bambi (Fudan University) 44
Constraints from the iron K-alpha line Example with N = 103
From Jiang, Bambi & Steiner (2015)
Cosimo Bambi (Fudan University) 45
Constraints from the iron K-alpha line Example with N = 105
From Jiang, Bambi & Steiner (2015)
Cosimo Bambi (Fudan University) 46
Constraining power of the iron K-alpha line in the CPR framework
From Jiang, Bambi& Steiner (2015b)
Cosimo Bambi (Fudan University) 47
Constraining power of the iron K-alpha line in the CPR framework
From Jiang, Bambi& Steiner (2015b)
Conclusion:The iron line technique is potentially more powerful than the
continuum-fitting method, but we need:1) a high photon number count,2) the correct theoretical model
Cosimo Bambi (Fudan University) 48
Exotic objects
Cosimo Bambi (Fudan University) 49
Iron K-alpha line(Interior solutions or Boson stars)
Regular solution Singular solution
From Bambi & Malafarina (2013)
Cosimo Bambi (Fudan University) 50
Iron K-alpha line(Traversable wormholes)
Constraint: a < 0.02
Metric
Cosimo Bambi (Fudan University) 51
Impact of the emissivity profile
I ~ rq for r < rbreak
I ~ r-3 for r > rbreak
Cosimo Bambi (Fudan University) 52
The special case of SgrA*
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 53
SgrA*
● No measurements at present, but very promising source for the future
● Light curves/centroid tracks (GRAVITY)
● Shadow (EHT)
● Pulsars
● Spectrum
Cosimo Bambi (Fudan University) 54
SgrA*
● No measurements at present, but very promising source for the future
● Light curves/centroid tracks (GRAVITY)
→ frequency at the ISCO radius
● Shadow (EHT)
● Pulsars
● Spectrum
Cosimo Bambi (Fudan University) 55
SgrA*
● No measurements at present, but very promising source for the future
● Light curves/centroid tracks (GRAVITY)
→ frequency at the ISCO radius
● Shadow (EHT)
→ measurement of the photon capture sphere
● Pulsars
● Spectrum
Cosimo Bambi (Fudan University) 56
SgrA*
● No measurements at present, but very promising source for the future
● Light curves/centroid tracks (GRAVITY)
→ frequency at the ISCO radius
● Shadow (EHT)
→ measurement of the photon capture sphere
● Pulsars
→ clean measurement of the spin
● Spectrum
Cosimo Bambi (Fudan University) 57
SgrA*
● No measurements at present, but very promising source for the future
● Light curves/centroid tracks (GRAVITY)
→ frequency at the ISCO radius
● Shadow (EHT)
→ measurement of the photon capture sphere
● Pulsars
→ clean measurement of the spin
● Spectrum
→ sensitive even to the geometry outside the equatorial plane
Cosimo Bambi (Fudan University) 58
Shadow + pulsar
Cosimo Bambi (Fudan University) 59
Shadow + pulsar + hot spot
Cosimo Bambi (Fudan University) 60
Accretion structure
From Lin et al. (2015)
Cosimo Bambi (Fudan University) 61
Accretion structure
From Lin et al. (2015)
Cosimo Bambi (Fudan University) 62
Conclusions
● Introduction
● Important remarks
● Continuum-fitting method
● Iron K-alpha line
● The special case of SgrA*
● Conclusions
Cosimo Bambi (Fudan University) 63
Conclusion
● Continuum-fitting method → We can obtain some “allowed regions”, we cannot do better
● Iron line → **Probably** we can obtain some “allowed regions”, we can do better in the future (if the model is correct)
We are now trying to fit the iron line of Cygnus X-1 (Jiang, Guainazzi, Steiner)
● SgrA* → Promising source for the future (no observations yet)
● Other methods (QPOs, polarization, jet power, etc.) → Not yet mature (or available), maybe in the future...
Cosimo Bambi (Fudan University) 64
Thank you!