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)
Plan of the talk Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 2
Cosimo Bambi Testing black hole candidates with electromagnetic radiation arxiv: 1509.03884 [gr-qc] Invited review paper submitted to Rev. Mod. Phys. 3
Introduction Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 4
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 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 Weak fields Today: Cosmological tests (dark matter/dark energy) Black holes Large scales Strong fields 6
7
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 8
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?) 9
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) 10
From Remillard & McClintock 2006 11
From Remillard & McClintock 2006 12
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) Cosimo (Fudan FromBambi Ghez etuniversity) al., ApJ 620 (2005) 744 13
Important remarks Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 14
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 15
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) 16
Black holes: Kerr solution Kerr metric Johannsen-Psaltis metric 17
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 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 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 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 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 22
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 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 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 25
Continuum-fitting method Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 26
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 27
Continuum-fitting method 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 Gou et al., ApJ 742 (2011) 85 28
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 29
Novikov-Thorne Model Geometrically thin and optically thick accretion disk Relativistic generalization of the Shakura-Sunyaev model Assumptions: Selection criterion: 0.08 LEDD < L < 0.30 LEDD 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 30
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 31
Continuum-fitting method results to date 32
Step 1: computation of the image 33
Step 2: calculation of the disk's spectrum 34
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] 35
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] 36
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] 37
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] 38
Constraints from the continuum-fitting method [Bambi (2014)] Cardoso-Pani-Rico parametrization 39
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 40
Iron K-alpha line Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 41
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 42
Iron K-alpha line analysis It is another popular technique used by astronomers to try to estimate the spin parameter of BH candidates 43
Constraints from the iron K-alpha line Example with N = 103 From Jiang, Bambi & Steiner (2015) 44
Constraints from the iron K-alpha line Example with N = 105 From Jiang, Bambi & Steiner (2015) 45
Constraining power of the iron K-alpha line in the CPR framework From Jiang, Bambi & Steiner (2015b) 46
Constraining power of the iron K-alpha line in the CPR framework 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 From Jiang, Bambi & Steiner (2015b) 47
Exotic objects 48
Iron K-alpha line (Interior solutions or Boson stars) Regular solution Singular solution From Bambi & Malafarina (2013) 49
Iron K-alpha line (Traversable wormholes) Metric Constraint: a < 0.02 50
Impact of the emissivity profile I ~ rq for r < rbreak I ~ r-3 for r > rbreak 51
The special case of SgrA* Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 52
SgrA* No measurements at present, but very promising source for the future Light curves/centroid tracks (GRAVITY) Shadow (EHT) Pulsars Spectrum 53
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 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) measurement of the photon capture sphere Pulsars Spectrum 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 clean measurement of the spin Spectrum 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 sensitive even to the geometry outside the equatorial plane 57
Shadow + pulsar 58
Shadow + pulsar + hot spot 59
Accretion structure From Lin et al. (2015) 60
Accretion structure From Lin et al. (2015) 61
Conclusions Introduction Important remarks Continuum-fitting method Iron K-alpha line The special case of SgrA* Conclusions 62
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... 63
Thank you! 64