Testing astrophysical black holes Cosimo Bambi...Cosimo Bambi (Fudan University) 3 Cosimo Bambi “Testing black hole candidates with electromagnetic radiation” arXiv: 1509.03884

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

“Testing black hole candidates with electromagnetic radiation”

arXiv: 1509.03884 [gr-qc]

Invited review paper submitted to Rev. Mod. Phys.


Introduction

● Introduction





● Conclusions


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


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



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


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?)


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)


From Remillard & McClintock 2006


From Remillard & McClintock 2006


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


Important remarks

● Introduction





● Conclusions


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


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)


Black holes:Kerr solution

● Kerr metric

● Johannsen-Psaltis metric


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


Important remarks






Important remarks






Important remarks






Important remarks






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










Continuum-fitting method

● Introduction





● Conclusions


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


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


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


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


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


Continuum-fitting method results to date


Step 1: computation of the image


Step 2: calculation of the disk's spectrum


Constraints from the continuum-fitting method[Kong, Li & Bambi (2014)]








Constraints from the continuum-fitting method[Bambi (2014)]

● Cardoso-Pani-Rico parametrization


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


Iron K-alpha line

● Introduction





● Conclusions


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


Iron K-alpha line analysis

● It is another popular technique used by astronomers to try to estimate the spin parameter of BH candidates


Constraints from the iron K-alpha line Example with N = 103

From Jiang, Bambi & Steiner (2015)


Constraints from the iron K-alpha line Example with N = 105

From Jiang, Bambi & Steiner (2015)


Constraining power of the iron K-alpha line in the CPR framework

From Jiang, Bambi& Steiner (2015b)


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


Exotic objects


Iron K-alpha line(Interior solutions or Boson stars)

Regular solution Singular solution

From Bambi & Malafarina (2013)


Iron K-alpha line(Traversable wormholes)

Constraint: a < 0.02

Metric


Impact of the emissivity profile

I ~ rq for r < rbreak

I ~ r-3 for r > rbreak


The special case of SgrA*

● Introduction





● Conclusions


SgrA*

● No measurements at present, but very promising source for the future

● Light curves/centroid tracks (GRAVITY)

● Shadow (EHT)

● Pulsars

● Spectrum


SgrA*



→ frequency at the ISCO radius

● Shadow (EHT)

● Pulsars

● Spectrum


SgrA*




● Shadow (EHT)

→ measurement of the photon capture sphere

● Pulsars

● Spectrum


SgrA*




● Shadow (EHT)


● Pulsars

→ clean measurement of the spin

● Spectrum


SgrA*




● Shadow (EHT)


● Pulsars

→ clean measurement of the spin

● Spectrum

→ sensitive even to the geometry outside the equatorial plane


Shadow + pulsar


Shadow + pulsar + hot spot


Accretion structure

From Lin et al. (2015)


Accretion structure

From Lin et al. (2015)


Conclusions

● Introduction





● Conclusions


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...


Thank you!

Documents

Testing astrophysical black holes Cosimo Bambi...Cosimo Bambi (Fudan University) 3 Cosimo Bambi “Testing black hole candidates with electromagnetic radiation” arXiv: 1509.03884