M.Phys.&M.Math.Phys.

High-EnergyAstrophysics

GarretCo0er

garret.co0er@physics.ox.ac.uk

High-EnergyAstrophysicsMT2016Lecture6

High-Energy Astrophysics: Synopsis

1)  Supernovablastwaves;shocks.

2)  AcceleraKonofparKclestoultra-relaKvisKcenergies.

3)  Synchrotronemission;totalpowerandspectrum

4)  Synchrotronself-absorpKon,populaKonageing,radiogalaxies.

5)  AccreKondiscs:structuresandluminosiKes.

6)  AccreKondiscs:spectra,evidenceforblackholes.

7)  RelaKvisKcjets;relaKvisKcprojecKoneffects;DopplerboosKng.

8)  CosmicevoluKonofAGN;high-energybackgroundradiaKonandcosmic

accreKonhistoryofblackholes.

9)  Bremsstrahlung;inverse-Comptonsca0ering;clustersofgalaxies;Sunyaev-

Zel’dovicheffect.

10) Cosmicraysandvery-high-energygammarays;Cherenkovtelescopes.

Today’s lecture: Accretion Discs II; Black Holes • Recap of concepts & disc luminosity. • Spectrum of thin disc. • Evidence for accretion onto black holes in AGN

Recap of accretion concepts and results so far

• The Eddington Luminosity sets the balance between radiation pressureoutwards and gravitational force inwards in a system where matter isaccreting onto a compact object.

• L =

4⇡GMc

where is the opacity of the accreting material.

• for the case of AGN it is often convenient to set LEdd

=

4⇡GMcm

p

�

T

butgenerally must be calculated precisely depending on the composition andionisation state of the material involved.

• If the material accreting onto an object radiates away some of its GPE onthe way in, L = ✏

˙

Mc

2, we get a characteristic limiting accretion rate,˙

M

Edd

=

4⇡GMm

p

✏c�

T

.

• Qualitatively, a cloud of collisional material with some angular momentummust eventually form a disc.

• It is generally hypothesised that tidal interactions between galaxies canforce gas with high angular momentum in the outer regions into a state oflow angular momentum where is falls towards the nucleus and forms a disc.The details are nowadays the topic of intensive study by numericalsimulation.

• In a potential that is Keplerian (or close to it) near the nucleus, a thin discsupported by its own gas pressure must be cold compared to the virialtemperature, i.e. it must have a highly supersonic rotation speed.

Luminosity of a thin accretion disc

We can estimate the luminosity f the disc if we propose that the gravitationalenergy of the particles must be radiated away as heat as they move into tighterquasi-Keplerian orbits. The average total energy of a particle in a circularKeplerian orbit of radius r is

E = �1

2

GMm

r

,

so for an annulus between r and r +dr, the energy which must be dissipatedwill be

L(r) =

d

dt

dE

dr

=

1

2

G

˙

MM

r

2

dr

where ˙

M is the accretion rate and M is the mass of the central object.

Note that here we are assuming the disc radiates away the GPE efficiently. Tojustify this completely we need to consider the viscous dissipation of heatexplicitly. Longair 3rd ed. 455-458 gives a walk through, for the full treatment,which gives a different pre factor of 3/8 in the thin disc case, see e.g. theShakura-Sunyaev analysis (posted on the course website).

Temperature structure of a physically thin, optically thick disc

If the disc is optically thick, each annulus between r and r +dr will radiate as ablackbody with the luminosity derived above. Hence via Stefan’s Law(remembering the disc has two surfaces), the annulus at at r will radiate with2�T

4 ⇥ 2⇡rdr. Thus

�T

4

=

3G

˙

MM

8⇡r

3

and so

T (r) =

✓3G

˙

MM

8⇡r

3

�

◆1/4

Spectrum of the thin disc

We are now in a position to describe the form of the overall spectrum of the disc,i.e. the sum of all the black-body contributions at different radii.

I

⌫

/Z

r

outer

r

inner

2⇡rB

⌫

{T (r)}dr

where from lecture 1 we have

B

⌫

/ ⌫

3

⇣e

h⌫/kT � 1

⌘�1

From before we have T / r

�3/4 so dr / (1/T )

1/3

d(1/T ) and we can integratedT instead of dr. Including B

⌫

explicitly we therefore have

I

⌫

/Z

r

outer

r

inner

✓1

T

◆4/3

⌫

3

⇣e

h⌫/kT � 1

⌘�1

✓1

T

◆1/3

d

✓1

T

◆

We can proceed by changing variable x = (h⌫/kT )—recall from thesecond-year thermo problem set where you used the same substitution to derivethe functional form u(T ) / T

4. This yields

I

⌫

/⌫

3

⌫

8/3

Zx

outer

x

inner

x

4/3

(

e

x � 1

)

�1

x

1/3

dx

The integral dx is just a numerical constant so we now have the shape of thespectrum over most of its range:

I

⌫

/ ⌫

1/3

.

Note, though, that the low- and high-frequency ends will have a different form:

• From the outer edge of the disc we will see the Rayleigh-Jeans tail ofT

outer

, I⌫

/ ⌫

2.

• From the inner edge, an exponential cut-off I⌫

/�e

�h⌫/kT

inner

�.

Theoretical spectrum of thin accretion disc.

1994ApJS...95....1E

Evidence for black holes in AGN There are several canonical pieces of evidence that supermassive black holes really are there at the heart of AGN. Among these are: • Variability (in combination with Eddington luminosity). • Stellar velocity dispersions. • Rotation speeds inferred from emission lines. • X-ray line profiles.

444 L. Miller et al.: The X-ray spectral variability of MCG–6-30-15

Fig. 3. The fit of model B to the principal component spectra: (left) Suzaku 0.5�45 keV, (right) XMM-Newton 0.4�10 keV; (top) eigenvector one,(bottom) o�set component. The model is shown in units of Ef(E), points with error bars show the “unfolded” component spectrum values.

Table 5. Fit parameters and statistics for the joint fit of Model B toeigenvector one and the o�set components, for each dataset, table en-tries as in Table 4.

Model Bparameter Suzaku XMM-Newton

� 2.23 2.21log �REFLIONX 2.04 1.94Galactic NH 0.051 0.045Chandra�����& XMM-Newton���zoneszone 1 log � 2.36 2.14

NH 0.45 0.41zone 2 log � 0.22 �0.42

NH 0.07 0.04zone 3 log � (3.85) (3.85)

NH 2.60 2.90additional o�set component absorption zoneszone 4 log � 1.95 2.04

NH 34.0 28.1zone 5 log � 1.35 1.89

NH 3.59 9.81

�2/d.o.f. 261/332 257/309

5. Results – model fits to data

5.1. Fitting methodology and initial constraints

Fitting to the PCA components should only be considered asyielding an indication of the model components that may be

required, for two reasons. First, although the o�set componentand eigenvector one alone provide a good description of thevariable X-ray spectrum at energies above 2 keV (Tables 2, 3),more complex source behaviour is implied at softer energies.Second, there is no unique interpretation of the o�set compo-nent: this component essentially describes the appearance of thesource around its lowest possible flux state, and the o�set com-ponent spectrum we deduce may either be pure reflection orpure absorption, for a source with a variable absorption cover-ing fraction, or some combination of the two, as indicated bythe PCA. Hence we need to test the model against the actualdata. This is done in this section. Model B is summarised byFig. 4 which shows the model fitted to the mean Suzaku spec-trum as described below and showing the three emission compo-nents of the model (“direct” power-law, with ionised absorption;“partially-covered” power-law, with higher opacity absorptionfrom zone 5; and low-ionisation reflection with absorptionfrom zone 4). We also show the component of cosmic X-raybackground emission included in the fit to������data.

The full dataset that we investigate here comprises obser-vations taken at a number of epochs with a variety of instru-ments. In fitting to the data we require the model to fit simultane-ously any data that were obtained simultaneously (e.g.���and��data for XMM-Newton or���and���data for Suzaku ). Wedo allow variations in model parameter values between datasetstaken at di�erent epochs, although the model components arenot changed.

Next time

Relativistic jets