distance to the centre of the milky way ˇ 27 000 ly. · 2017-01-26 · central black hole. the...

ImagesObservational Parameters

Outline of the model

Distance to the centre of the Milky way ≈ 27 000 ly.

Rosemberg Toala BLACK HOLES: WHAT DO WE OBSERVE?



Figure: Elliptical Galaxy M87. Photograph taken by the HST showingthe jet of ejected matter as it stretches nearly 5000 ly. Credit: NASA,ESA, and the Hubble Heritage Team (STScI/AURA)




Figure: Exposures of M87 at different wavelengths. Credit: NASA,National Radio Astronomy Observatory/National Science Foundation,John Biretta (STScI/JHU), and Associated Universities, Inc.




Three images of the radiogalaxy NGC 6251. Top:Outer radio lobes, using theCambridge one-mile tele-scope. Middle: Image of thejet powering the northwestlobe, using the Cambridge 5-km telescope (1977). Bot-tom: VLBI image of theparsec-scale compact sourcein the nucleus of the galaxyusing a three-telescope arrayin the USA.




Figure: Modern radio image of radio galaxy Cygnus A using the VeryLarge Array synthesis telescope in New Mexico, USA, in severalconfigurations. Images provided by NRAO, an NSF facility, managed byAUI.




Figure: Jets powered by the gravitational energy of a super massive blackhole in the core of the elliptical galaxy Hercules A. Combined imagingpower of the HST, and Very Large Array (VLA) radio telescope in NewMexico. Credit: NASA, ESA, S. Baum and C. O’Dea (RIT), R. Perleyand W. Cotton (NRAO/AUI/NSF), and the Hubble Heritage Team(STScI/AURA)




Figure: Local galaxy Arp 220, captured by the Hubble Space Telescope.The image shows the bright core of the galaxy, paired with an overlaidartist’s impression of jets emanating from it. Credit: NASA/JPL-Caltech.




Figure: Centaurus A. Located only 10 million light-years away, thispeculiar-looking galaxy contains the closest active galactic nucleus toEarth and has long been considered an example of an elliptical galaxydisrupted by a recent collision with a smaller companion spiral galaxy.Image VLA (radio) and Optical.




Figure: A close-up into Centaurus A centre.




Left: A VLA image of the supernova remnant W50; SS433 is thestrong radio source at the center. Right: High-resolution radioimage (NRAO/AUI/NSF) of the SS433 point source seen on theleft.




CLASSIFICATION

Historical:

Active Galactic Nuclei. E.g. Radio and Seyfert Galaxies,Quasars.

Intermediate mass Black Holes. As far as I know, none hasbeen detected.

X-ray binaries, Neutron stars, Pulsars and Magnetars.

By central mass:

Macroquasars, AGN. Massive and supermassive,105 − 108 − 1011 M�.

Miniquasars, IMBH, 102 − 104 M�.

Microquasars or stellar black holes, 4− 15 M�.

Unification: Black holes surrounded by an accretion disk.




DISTANCE

Very difficult to measure.

Parallax. Reliable only for short distances, a few parsecs.

D =1 UAsin p

≈ 1 UAp

Parsec := distance to an arc-second parallax using 1 UAas baseline≈ 3.26 light years.Different baselines: HubbleST, Hipparcos.Error ≈ milliarcseconds.




DISTANCE

Standard candles. Objects that belong to some class withknown brightness.Problems: Calibration. How standard are they?Hubble Law. D = vel

H0, vel = recessional velocity.

Problems: Depends on cosmological model, typically FLRW.Determine Hubble constant.




LUMINOSITY

Power = Energy/time emmited by a source.

Eddington: For a star, internal (outward) radiation pressure mustbalance Gravitational attraction (inward). This gives a limit for thetotal luminosity,

LEdd =4πGcM

kes= 3.2× 104 M

M�L�,

where G = gravitational constant, c = speed of light, M= mass,kes = opacity of ionised matter (electron scattering).




MASS

Newton mechanics: Use surrounding bodies, deduce orbits.

Actual measured orbits of dif-

ferent stars around our Galaxys

central black hole. The seven

stars listed at right were used

to determine the black hole

mass, which is approximately

4.1(±0.6) × 106 M�. Credit:

Ghez, A., et al., Astroph. J.,

689, 10441062, (2008).




MASS

Einstein’s General Relativity: Gravitational lensing, θ = 4GMDc2 ,

where D is distance from the affected radiation.

Also known as the “Einstein

Cross”. The photograph shows

four images of a very dis-

tant quasar which has been

multiple-imaged by a relatively

nearby galaxy acting as a grav-

itational lens. Credit: NASA,

ESA, and STScI.




SIZE

It is bounded by variations in luminosity.

Rmax = c ∆t

Angular radius.We have to know the distance.




TEMPERATURE

Every object emits thermal radiation.Energy depends on temperature of emitting body and wavelengthof radiation, also, on chemical composition, physical structure,angle of passage, polarization, emissivity and reflectivity ofinterface, etc.Black Body: Idealised object, absorbs all incident radiation,emissivity = 1, reflectivity = 0. Assume, E = E (λ,T ).They obey Planck’s law, integrating over all wavelengths givesStefan-Boltzmann law for total luminosity,

L = AσT 4,

A = area of interface, σ = Stefan-Boltzmann constant,T = Temperature.




TEMPERATURE

Wien’s displacement law:Peak of radiation de-pends on temperature.

λmax ∝1

T




SPECTRUM

Electromagnetic radiation is made outof waves/photons at different frequen-cies/wavelengths.Typical spectrum consists of:

Emission lines. Depends on thesource’s element composition.

Absorption lines. Missingradiation due to intervininggas/cloud.

It can also be shifted. Doppler effect,expansion of the Universe.




Each element has characteristic spectrum lines. E.g. Hydrogen.




ACCRETION

What is the process responsible for the enormous amount of energyreleased by all these objects?

It is important to know the mass, rotational velocity andelectric charge of central BH. This determines the backgroundspacetime.

Also, rate of fuel consumption and nature of surroundingenvironment. Geometry and density of ’disk’, as well aselectromagnetic properties are key to understanding theaccretion process and energy outcome.

Finally, angle of view relative to the spin axis is necessary tointerpret what we observe and what we do not.




ACCRETION

This illustration shows thepoint-of-view dependency ofthe unified AGN model.The broad-line (BLRG) andnarrow-line (NLRG) regionsare shown, as well as the”obscuring torus”. A num-ber of other AGN types arenamed as well. From Urryand Padovani, 1995.




SUMMARY OF VACUUM SOLUTIONS

Special Relativity, no gravity: Minkowski Spacetime.

The one-body problem: Schwarzschild → model for a BH.

Rotating one-body: Kerr.

Rotating and charged one-body: Kerr-Newman.




MINKOWSKI SPACETIME

Flat metric on R× R3,

ds2 = −dt2 + dx2 + dy2 + dz2.

In polar coordinates,

= −dt2 + dr2 + r2dθ2 + r2 sin2 θdφ2.

Causality.

Time-like, 〈v , v〉 < 0 . Test particles with mass move ontime-like geodesics.

Null, 〈v , v〉 = 0. Future and past null cones, t=r and t=-r.Photons follow null geodesics.

Spacelike, 〈v , v〉 > 0. E.g. Slices of constant time.‘Unphysical’ in the sense of cause-effect.




Global Structure

Conformal compactification: Preserves causality.Use spherical symmetry, focus on the 2D slices (t, r).Advanced and retarded null coordinates, u = t − r , v = t + r .Bring infinity to a bounded region, U = arctan u, V = arctan v .Back to time/space-like coords, t ′ = (U + V )/2, r ′ = (U − V )/2.

i+

i−

i0

r′=

0

J+

J−

Penrose-Carter diagram in the (t ′, r ′)-plane. Almost every point representsa sphere. Dashed lines correspond to{r = constant} and dotted to {t =constant}. Null curves are at 45◦.




SCHWARZSCHILD SPACETIME

Consider metric

ds2 = −(

1− 2M

r

)dt2 +

(1− 2M

r

)−1dr2 + r2dθ2 + r2 sin2 θdφ2

Where (t, r , θ, φ) are coordinates on R× (2M,∞)× S2.It is a solution of vacuum Einstein equations Ricµν = 0.It is geodesically incomplete. ‘Singularity’ at r = 2M is due tocoordinates.It can be extended using affine parameters along outgoing andingoing null geodesics.




II ′

IIB

IIW

r=

2Mr

=2M

I−

I+ I+

I−

r = 0

r = 0

i+i+

i− i−

i0i0

Figure: True singularity at r = 0, geodesically incomplete. Region I is thedomain of the original coordinates. Region I ′ is isometric I , “anotheruniverse”. IIB : Black Hole. IIW : White Hole.




THANKS!REFERENCES.

Meier, D. L. Black Hole Astrophysics: The Engine Paradigm.Springer. 2009.

Hubble site. www.hubblesite.org/

NASA. www.nasa.gov/


distance to the centre of the milky way ˇ 27 000 ly. · 2017-01-26 · central black hole. the...

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