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

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-' ~ 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 a TI/*. ( u ) 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. Gaunt factors Approximate analytic formulas for g,/ in the various regimes in which large-angle scatterings and small-angle scatterings are dominant, in which I \ 103 "Small angle. u P , ''Small angle, tail region 1 1 " U P I tail region I" 102 "Large angle, 10 tail region'' / I v 1 ~ Rybicki & k I ' "Large angle region" Lightman c - 10 ' 1 "Smdll angle, "Small angie. classicdl reqion" U P region" 10 ? \/3 4 k ~ -T Ln[ ~ (; ~ I 10 10 10 3 10 10 1 10 100 k l ~~ / 2 K 1 , fonnurcCe focthe gaunt factor g&, T) Figure 5.2 Approximate d y t i c for thermal bremrstmhlung. Here glr is denoted by G and the energv Writ Ry = 13.6 eK (Taken from Novikm, I. D. ~JUI K. S 1973 in Black Hdes, Les ll~ome, . Houches, Eds. C. Dewin and B. Dewin, Gordon and Breach, New Yo&)

161 Thermal Bremsstmhlung EnriSsion 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 &. The values of grr graphs o f 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 Gaunt factors (5.15a) 6.0 I 1 1 0 3 1 5.0 4.0 3.0 Rybicki & Lightman 2.0 1.0 . _ I 0 10 ’ 10 10 3 10 7 100 10’ 103 1 0 2 U Figure 5.3 Numerical values of the gaunt factor gdv, and the temperaturn variable is y f T). Here the requemy - wnable is u= 4.8 X IO”v/ T - 1.58 X and Latter, R . Asttwphys. J. SuppL, 6 , 10sZ’/ T. (Taken from Karzas, W. 1961, 167.)

Bremsstrahlung Intensity Ghisellini Fig. 2.1 The bremsstrahlung intensity from a source of radius R = 10 15 cm, density n e = n p = 10 10 cm − 3 and varying temperature. The Gaunt factor is set to unity for simplicity. At smaller temperatures the thin part of I ν is larger ( ∝ T − 1 / 2 ), even if the frequency integrated I is smaller ( ∝ T 1 / 2 ) A. Marconi Relativistic Astrophysics 2016/2017 4

From Bremsstrahlung to Black Body Ghisellini Fig. 2.2 The bremsstrahlung intensity from a source of radius R = 10 15 cm, temperature T = 10 7 K. The Gaunt factor is set to unity for simplicity. The density n e = n p varies from 10 10 cm − 3 ( bottom curve ) to 10 18 cm − 3 ( top curve ), increasing by a factor 10 for each curve. Note the self-absorbed part ( ∝ ν 2 ), the flat and the exponential parts. As the density increases, the optical depth also increases, and the spectrum approaches the black-body one A. Marconi Relativistic Astrophysics 2016/2017 5

Line vs Continuum emission Courvoisier 10 − 22 Total (solar) Continuum Total Emissivity (erg cm 3 s − 1 ) Lines 10 − 23 10 − 24 10 6 10 7 10 8 Temperature (K) A. Marconi Relativistic Astrophysics 2016/2017 6

Line vs Continuum emission Courvoisier 140 Total Emissitivity/Continuum emissitivity 120 100 80 60 40 20 0 10 5 10 6 10 7 10 8 Temperature (K) A. Marconi Relativistic Astrophysics 2016/2017 7

Free-bound radiation: “Edges” Courvoisier – 1 7 10 H He – 1 8 10 EFFECTIVE CROSS SECTION σ e ( cm 2 ) He + – 1 9 10 – 2 0 10 C N – 2 1 10 O Ne Mg – 2 2 10 C Si S S Si A – 2 3 10 Mg Si – 2 4 10 AI 3 2 10 1 10 10 º WAVELENGTH (Angstroms) Fig. 1.10 The effective cross-section of the interstellar medium (cross-section per hydrogen atom or 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)

Emission from hot gas 10 2 10 1 10 0 10 − 1 10 − 2 4 πν J ν 10 − 3 10 − 4 10 − 5 10 − 6 10 − 7 10 − 4 10 − 3 10 − 2 10 − 1 10 0 10 1 10 2 ν [keV] Emissivity of a plasma with T=10 6 (green), 10 8 K (red) computed with CLOUDY (www.nublado.org) for a gas with Z=2Z ⊙ , density n H =10 cm -3 and column density N H = 10 21 cm -2

Clusters of galaxies: Coma Coma Cluster (XMM-Newton) A. Marconi Relativistic Astrophysics 2016/2017 10

Clusters of galaxies: Coma Coma cluster (XMM-Newton) A. Marconi Relativistic Astrophysics 2016/2017 11

Clusters of galaxies: Coma A. Marconi Relativistic Astrophysics 2016/2017 12

Clusters of galaxies: Coma A. Marconi Relativistic Astrophysics 2016/2017 13

Clusters of galaxies: Coma A. Marconi Relativistic Astrophysics 2016/2017 14

Cluster A 1413 f - - compo- - 10 15 Polytropic KBB model Isothermal KBB model Total Mass (< R) (M O ) Isothermal β model • 10 14 100 1000 Radius R (kpc)

Cooling Flows: A 2052 40 a b 1 20 ∑ (ct/s/arcmin 2 ) n e (10 − 3 cm − 3 ) 10 8 6 0.1 4 2 c d 20 3.5 Pressure (10 − 11 dyn/cm 2 ) 3 Temperature (keV) 2.5 10 8 2 6 4 1.5 2 10 100 10 100 Radius (arcsec) Radius (arcsec) A. Marconi Relativistic Astrophysics 2016/2017 16

Cooling Flows Longair ( a ) ( b ) 10 12 10 11 10 8 Cooling Time Temperature 10 10 (yr) (K) 10 9 10 8 0.1 1 0.1 1 Radius (Mpc) Radius (Mpc) 0.1 ( c ) ( d ) Integrat e d Mass Deposition 1000 Electron Density Rate (M yr –1 ) 0.01 (cm –3 ) 10 –3 100 10 –4 0.1 1 0.1 1 Radius (Mpc) Radius (Mpc) 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 10 10 years within a radius of 200 kpc (Fabian, 1994). A. Marconi Relativistic Astrophysics 2016/2017 17

Cooling Flows Longair 0.08 0.06 Counts/s/A ˚ 0.04 0.02 10 12 14 16 18 ˚ Wavelength (A) 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 fm ow 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). A. Marconi Relativistic Astrophysics 2016/2017 18

Cooling Flows ( 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). A. Marconi Relativistic Astrophysics 2016/2017 19

Sound Waves …

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