Bremsstrahlung 160 Bremsstmhlung =(2hv/m)'/', and using dw=2rdv, we - - PowerPoint PPT Presentation

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Bremsstrahlung 160 Bremsstmhlung =(2hv/m)'/', and using dw=2rdv, we - - PowerPoint PPT Presentation

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Bremsstrahlung 160 Bremsstmhlung =(2hv/m)'/', and using dw=2rdv, we obtain where umin T - gJp d W 2*re6( 2 s )'I2 - -=- 1/2zZn n,e-hv/kT- (5*14a) dVdtdv 3mc3 3km e r Evaluating eq. (5.14) in CGS units, we have for the emission (erg s-' ~

slide-1
SLIDE 1

Bremsstrahlung

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SLIDE 2

Gaunt factors

160

Bremsstmhlung

where umin

=(2hv/m)'/', and using dw=2rdv, we obtain

  • =-

d W

2*re6(

  • 2 s )'I2

T -

1/2zZn n,e-hv/kT-

gJp

(5*14a)

e r

dVdtdv

3mc3 3km Evaluating eq. (5.14) in CGS units, we have for the emission (erg s-' ~ r n - ~ Hz- 9 Here GAT,

v) is a velocity averaged Gaunt factor. The factor T-'/' in Eq.

(5.14) comes from the fact that d W / d V d l d w a u - ' [cf. Eq. (5.11) and

( u )

a TI/*.

The factor ePh"IkT comes from the lower-limit cutoff in the velocity integration due to photon discreteness and the Maxwellian shape for the velocity distribution. Approximate analytic formulas for g,/ in the various regimes in which large-angle scatterings and small-angle scatterings are dominant, in which

103 102 10

~

1

/ I v

k I '

10 '

10 ?

10

\

"Small angle. u P , tail region 1 1 " "Large angle, tail region'' "Large angle region"

c -

1 "Smdll angle, classicdl reqion"

I

''Small angle,

U P I

tail region I" "Small angie.

U P region"

~

\/3

4 k (;

~ -T Ln[ ~

I

10 10 3 10 10

1

10 100 k l

~~

/ 2 K 1

,

Figure 5.2 Approximate d y t i c fonnurcCe focthe gaunt factor g&, T) for thermal bremrstmhlung. Here glr is denoted by G

and

the energv Writ Ry = 13.6 eK (Taken

from Novikm, I. D. ~JUI

ll~ome,

  • K. S

. 1973 in Black Hdes, Les Houches, Eds. C. Dewin and

  • B. Dewin, Gordon and

Breach, New Yo&)

Rybicki & Lightman

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SLIDE 3

Gaunt factors

Thermal Bremsstmhlung EnriSsion

161

the uncertainty principle (U. P.) is important in the minimum impact parameter, and so on are indicated in Fig. 5.2. Figure 5

. 3 gives numerical

graphs o f &. The values of grr for u--hv/kT>>l are not important, since the spectrum cuts off for these values. Thus g/r is of order unity for u-1 and is in the range 1 to 5 for 10--4<u<

  • 1. We see that good order of

magutude estimates can be made by setting g

f , to unity.

We also see that bremsstrahlung has a rather “flat spectrum” in a log-log plot up to its cutoff at about hv-kT. (This is true only for optically thin

  • sources. We have not yet considered absorption of photons by free elec-

trons.) To obtain the formulas for nonthermal bremstrahlung, one needs to know the actual distributions of velocities, and the formula for emission from a single-speed electron must be averaged over that distribution. To do this one also must have the appropriate Gaunt factors. Let us now give formulas for the total power per unit volume emitted by thermal bremsstrahlung. This is obtained from the spectral results by integrating Eq. (5.14) over frequency. The result may be stated as (5.15a)

6.0

1 1 0 3 1

I

. _

I

5.0 4.0

3.0

2.0 1.0

10

10 3 10 7 10 ’ 100

10’

1 0 2

103

Figure 5.3 Numerical values of the gaunt factor gdv,

T). Here the requemy 10sZ’/ T. (Taken from Karzas, W. and Latter, R

.

1961,

  • Asttwphys. J. SuppL, 6

,

167.)

U

wnable is u= 4.8 X IO”v/ T

and the temperaturn variable is y f

  • 1.58 X

Rybicki & Lightman

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SLIDE 4
  • A. Marconi

Relativistic Astrophysics 2016/2017

Bremsstrahlung Intensity

4

  • Fig. 2.1 The bremsstrahlung

intensity from a source of radius R = 1015 cm, density ne = np = 1010 cm−3 and varying temperature. The Gaunt factor is set to unity for

  • simplicity. At smaller

temperatures the thin part of Iν is larger (∝T −1/2), even if the frequency integrated I is smaller (∝T 1/2)

Ghisellini

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SLIDE 5
  • A. Marconi

Relativistic Astrophysics 2016/2017

From Bremsstrahlung to Black Body

5

  • Fig. 2.2 The bremsstrahlung

intensity from a source of radius R = 1015 cm, temperature T = 107 K. The Gaunt factor is set to unity for

  • simplicity. The density

ne = np varies from 1010 cm−3 (bottom curve) to 1018 cm−3 (top curve), increasing by a factor 10 for each curve. Note the self-absorbed part (∝ν2), the flat and the exponential parts. As the density increases, the

  • ptical depth also increases,

and the spectrum approaches the black-body one

Ghisellini

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SLIDE 6
  • A. Marconi

Relativistic Astrophysics 2016/2017

Line vs Continuum emission

6

Total (solar) Continuum Lines Temperature (K) Total Emissivity (erg cm3 s−1) 106 10−24 10−23 10−22 108 107

Courvoisier

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SLIDE 7
  • A. Marconi

Relativistic Astrophysics 2016/2017

Line vs Continuum emission

7

Temperature (K) Total Emissitivity/Continuum emissitivity 140 120 100 80 60 40 20 105 106 107 108

Courvoisier

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SLIDE 8

Free-bound radiation: “Edges”

10

3

10

– 2 4

10

– 2 3

10

– 2 2

10

– 2 1

10

– 2

10

– 1 9

10

– 1 8

10

– 1 7

10

2

10 1 WAVELENGTH (Angstroms) EFFECTIVE CROSS SECTION σe (cm2) AI Si Si Si S S A O N C C He+ He H Mg Mg Ne

º
  • Fig. 1.10 The effective cross-section of the interstellar medium (cross-section per hydrogen atom
  • r proton of the interstellar medium). Solid line – gaseous component with normal composition

and temperature; dot-dash – hydrogen in its molecular form; long dash – HII region about a B star; long dash-dash-dash – HII region about an O star; short dash – dust (Cruddace et al. 1974, Fig. 2,

  • p. 500, reproduced by permission of the AAS)

Courvoisier

slide-9
SLIDE 9

10−4 10−3 10−2 10−1 100 101 102 ν [keV] 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 4πνJν

Emission from hot gas

Emissivity of a plasma with T=106 (green), 108 K (red) computed with CLOUDY (www.nublado.org) for a gas with Z=2Z⊙, density nH=10 cm-3 and column density NH = 1021 cm-2

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SLIDE 10
  • A. Marconi

Relativistic Astrophysics 2016/2017

Clusters of galaxies: Coma

10

Coma Cluster (XMM-Newton)

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SLIDE 11
  • A. Marconi

Relativistic Astrophysics 2016/2017

Clusters of galaxies: Coma

11

Coma cluster (XMM-Newton)

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SLIDE 12
  • A. Marconi

Relativistic Astrophysics 2016/2017

Clusters of galaxies: Coma

12

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SLIDE 13
  • A. Marconi

Relativistic Astrophysics 2016/2017

Clusters of galaxies: Coma

13

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SLIDE 14
  • A. Marconi

Relativistic Astrophysics 2016/2017

Clusters of galaxies: Coma

14

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SLIDE 15

Cluster A 1413

f

  • compo-
  • 1014

1015

Polytropic KBB model Isothermal KBB model Isothermal β model

100 1000 Total Mass (< R) (MO)

  • Radius R (kpc)
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SLIDE 16
  • A. Marconi

Relativistic Astrophysics 2016/2017

Cooling Flows: A 2052

16

10 100 10 100 Radius (arcsec) Radius (arcsec) Temperature (keV) ∑ (ct/s/arcmin2) ne (10−3 cm−3) Pressure (10−11 dyn/cm2) 1 0.1 3.5 3 2.5 2 1.5 40 20 10 8 6 4 2 20 10 8 6 4 2

a b c d

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SLIDE 17
  • A. Marconi

Relativistic Astrophysics 2016/2017

Cooling Flows

17

0.1 0.1 1000 100 0.01 10–3 10–4 Temperature (K) Cooling Time (yr) Electron Density (cm–3) Integrated Mass Deposition Rate (M yr–1) 1 0.1 Radius (Mpc) Radius (Mpc) 0.1 1 Radius (Mpc) 0.1 1 Radius (Mpc) 1 108 1012 1011 1010 109 108

(a) (b) (d) (c)

The properties of the intracluster gas in the cluster Abell 478 obtained by deprojecting images taken by the ROSAT X-ray Observatory (White etal., 1994). The cooling time of the gas is less than 1010 years within a radius of 200 kpc (Fabian, 1994).

Longair

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SLIDE 18
  • A. Marconi

Relativistic Astrophysics 2016/2017

Cooling Flows

18

0.08 0.06 0.04 0.02 10 12 14 Wavelength (A) ˚ ˚ Counts/s/A 16 18

Comparison of the observed high resolution X-ray spectrum of the cluster of galaxies S´ ersic 159–03 observed by the ESA XMM-Newton satellite with the predicted spectrum of a standard cooling fmow model without heating. The strong lower excitation lines from ions such as Fe  are absent, indicating the lack of cool gas in the cluster (de Plaa etal., 2005).

Longair

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SLIDE 19
  • A. Marconi

Relativistic Astrophysics 2016/2017

Cooling Flows

19

(a) (b)

The central regions of the Perseus Cluster of galaxies observed by the Chandra X-ray Observatory. (a) The central regions of the cluster showing the cavities evacuated by the radio lobes which are shown by the white contour lines (Fabian etal., 2000). (b) An unsharp-mask image of the central regions of the cluster showing the various features caused by the expanding radio lobes. Many of the features are interpreted as sound waves caused by the weak shock wave associated with the expansion of the radio lobes (Fabian etal., 2006).

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SLIDE 20

Sound Waves …

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SLIDE 21

Hydra Cluster

Optical (stars) Radio (synchrotron) X (bremss.) Composite image