Testing Astrophysical Black Holes Cosimo Bambi Fudan University http://www.physics.fudan.edu.cn/tps/people/bambi/ Black Holes and Friends 2 11-13 April 2016, Fudan University (Shanghai, China)
Plan of the talk Introduction ● Continuum-fitting method ● X-ray reflection spectroscopy ● Transfer function ● Conclusions ● Cosimo Bambi (Fudan University) 2
Introduction Introduction ● Continuum-fitting method ● X-ray reflection spectroscopy ● Transfer function ● Conclusions ● Cosimo Bambi (Fudan University) 3
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) 4
Tests of general relativity 1915 → General relativity (Einstein) ● 1919 → Deflection of light by the Sun (Eddington) ● 1960s-present → Solar System experiments Weak fields ● 1970s-present → Binary pulsars ● Today: Large scales Cosmological tests (dark matter/dark energy) ● Black holes ● Strong fields Cosimo Bambi (Fudan University) 5
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/M 2 ) ● Kerr bound: |a * | < 1 ● Cosimo Bambi (Fudan University) 6
Black hole candidates (Observations) Stellar-mass BH candidates in X-ray ● binary systems (5 – 20 Solar masses) Supermassive BH candidates in galactic ● nuclei (10 5 – 10 10 Solar masses) Intermediate-mass BH candidates in ● ULXS (10 2 – 10 4 Solar masses?) Cosimo Bambi (Fudan University) 7
Stellar-mass BH candidates Dark objects in X-ray binary systems ● Mass function: ● In general, a good estimate of M C 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) 8
From Remillard & McClintock 2006 Cosimo Bambi (Fudan University) 9
From Remillard & McClintock 2006 Cosimo Bambi (Fudan University) 10
Supermassive BH candidate in the Galaxy We study the orbital motion of individual stars ● Point-like central object with a mass of 4x10 6 Solar masses ● Radius < 45 AU (600 R Sch ) ● From Ghez et al. 2005 Cosimo Bambi (Fudan University) 11
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) 12
Testing the Kerr solution around black hole candidates No satisfactory formalism at present ● Strong gravity, no expansion in M/r ● Proposals: Johannsen-Psaltis (2011), Johannsen (2013), Cardoso-Pani- ● Rico (2014), Konoplya-Rezzolla-Zhidenko (2016), etc. Cosimo Bambi (Fudan University) 13
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) 14
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) 15
Continuum-fitting method Introduction ● Continuum-fitting method ● X-ray reflection spectroscopy ● Transfer function ● Conclusions ● Cosimo Bambi (Fudan University) 16
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) From Gou et al. 2011 Cosimo Bambi (Fudan University) 17
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 From Gou et al. 2011 Cosimo Bambi (Fudan University) 18
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 – E ISCO Cosimo Bambi (Fudan University) 19
Novikov-Thorne Model Geometrically thin and optically thick accretion disk ● Relativistic generalization of the Shakura-Sunyaev model ● Selection criterion: Assumptions: 0.08 L EDD < L < 0.30 L EDD 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 – E ISCO Cosimo Bambi (Fudan University) 20
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) 21
Continuum-fitting method results to date Cosimo Bambi (Fudan University) 22
Step 1: computation of the image Cosimo Bambi (Fudan University) 23
Step 2: calculation of the disk's spectrum Cosimo Bambi (Fudan University) 24
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] Cosimo Bambi (Fudan University) 25
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] Cosimo Bambi (Fudan University) 26
Constraints from the continuum-fitting method [Kong, Li & Bambi (2014)] Cosimo Bambi (Fudan University) 27
Constraints from the continuum-fitting method [Bambi (2014)] Cardoso-Pani-Rico parametrization ● Cosimo Bambi (Fudan University) 28
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) 29
X-ray reflection spectroscopy Introduction ● Continuum-fitting method ● X-ray reflection spectroscopy ● Transfer function ● Conclusions ● Cosimo Bambi (Fudan University) 30
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) From Gou et al. 2011 Cosimo Bambi (Fudan University) 31
Disk reflection Cosimo Bambi (Fudan University) 32
Reflected spectrum Cosimo Bambi (Fudan University) 33 From Garcia et al. 2013
Model parameters Photon index of the power-law component ● Ionization parameter ● Iron abundance ● Inclination angle of the disk ● Emissivity profile... ● Spacetime metric (spin + possible deformation parameters) ● [Assumption: inner edge of the disk at the ISCO radius] Cosimo Bambi (Fudan University) 34
Iron line Cosimo Bambi (Fudan University) 35
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 – E ISCO Cosimo Bambi (Fudan University) 36
Novikov-Thorne Model Geometrically thin and optically thick accretion disk ● Relativistic generalization of the Shakura-Sunyaev model ● Selection criterion: Assumptions: 0.08 L EDD < L < 0.30 L EDD 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 – E ISCO Cosimo Bambi (Fudan University) 37
Current spin measurements Cosimo Bambi (Fudan University) 38 From Bambi, Jiang & Steiner 2016
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