SPECTRUM OF THE COMA CLUSTER RADIO HALO SYNCHROTRON RADIATION

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Jonas Norton
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1 SPECTRUM OF THE COMA CLUSTER RADIO HALO SYNCHROTRON RADIATION

2 OUTLINE OF THE LESSON REMINDER SPECIAL RELATIVITY: BEAMING, RELATIVISTIC LARMOR FORMULA CYCLOTRON EMISSION SYNCHROTRON POWER AND SPECTRUM EMITTED BY A SINGLE ELECTRON SPECTRUM FROM A DISTRIBUTION OF ELECTRONS AND POLARIZATION EXTENDED RADIO EMISSION IN GALAXY CLUSTERS

3 LORENTZ TRANSFORMATIONS z S z S 1 t 1 t t z z 1 t 1 t t z z

4 LORENTZ TRANSFORMATION OF VELOCITIES S S u z z d ( d dt) dt u ( dt d dt d u 1 u ) 1 1/ u u u z d u dt 1 u u (1 u ) uz (1 u )

5 u u (1 u If photons u = If 1 RELATIVISTIC BEAMING S z ) u u tan 1 θ S z u (1 u ) sin (os ) θ u u usin tan u ( uos sin sin (1 os ) )

6 ORENTZ TRANSFORMATION OF ACCELERATIONS z S z S 1 u du du 3 3 a dt du a dt d dt dt ) ( u a ) ( 1 u d u du du a u a dt du a a dt du a a u a a 3 z z z a u a a 3

7 RELATIVISTIC LARMOR S FORMULA In a instantaneous rest frame K the partile has zero eloit a 3 a a a P de dt 4 ( a a ) ( 3 a a 3 q 3 q 3 ) Total emitted power (subtle: emitted and reeied might not be the same in etreme ases, angle transformation!) is Lorentz inariant so the power an be aluated in an frame

8 CYCLOTRON EMISSION Charged partile q in a magneti field B in the non-relatiisti limit Balane of entrifugal fore against Lorentz fore m r qb Charged partile emit a narrow line at the lotron frequen qb m.8b MHz B kev B in Gauss e for an eletron

9 CYCLOTRON EMISSION As in an other emission proess, also lotron absorption is possible lotron absorption lines In pratie, a lotron line is broadened b nonuniformit in the magneti field, b ollisional broadening, and (for energeti partiles) b relatiisti effets. If aeleration is not a perfet sinusoid, emission also at multiples of lotron frequen: harmonis

10 CYCLOTRON EMISSION Solar Astronom Planets (Jupiter in partiular) Magneti stars (white dwarfs and neutron stars)

11 SYNCHROTRON EMISSION Charged partile in a magneti field B in the relatiisti limit d q ( m) B dt d ( m ) q E 0 dt m sin eb The energ of the partile doesn t hange (besides emission of radiation oer a orbit). The Lorentz fore does not work. A fundamental frequen is the giration frequen ν B r L B a eb m L

12 a SYNCHROTRON POWER q sin ebsin 4 P 3 m e 3 m e q B B e U B re 8 m Energ densit magneti field Eletron lassial radius e 8 T r e 3 Thomson ross setion For an isotropi distribution of eloities ou aerage oer angles α (pith angle) sin d sin 3 d os(3) 9os

13 SYNCHROTRON POWER P 4 3 T U B You will find a similar epression for Inerse Compton emission. The analog is that the eletron sees a ariable eletro-magneti field (photons) with tpial frequen hν B E P m e 4 3 TU B B B s r Snhrotron lifetime is in man soures smaller than the age of the soure meaning ontinuous injetion or reaeleration

14 SYNCHROTRON SPECTRUM: A QUALITATIVE DISCUSSION There is a tpial frequen assoiated with the snhrotron proess and it is not the inerse of the reolution period (as for lotron) but it is related to the fration of time for eah orbit during whih the obserer reeies some radiation

15 SYNCHROTRON SPECTRUM: A QUALITATIVE DISCUSSION AB r L me ; rl eb l t e AB / m e eb t A t e AB / t e t e t e (1 ) t e Realling thegro angular frequen eb 1 1 ~ t e m e eb B t A me 3 1 B

16 SYNCHROTRON SPECTRUM: A QUALITATIVE DISCUSSION t A 3 sin B C B sin The pulse of the eletri field E(t) has this tpial width So ou an epet a broad spetrum etending to frequenies of the order ν before falling awa

18 SYNCHROTRON SPECTRUM 3 3 e Bsin P( ) F m C With detailed alulation this is the spetrum emitted b a single eletron. F is a funtion with a peak at 0.9 ω

19 FROM CYCLOTRON TO SYNCHROTRON The obserer sees a sinusoidal (in time) eletri field E(t). Inreasing the eloit, the pattern beomes asmmetri and the seond harmoni appears. Emission onentrated in the time Δt A Fourier transformation of E(t) ontains man harmonis, and the power is onentrated in harmonis with ν 1/Δt A.

20 SPECTRUM POWER LAW DISTRIBUTION Obsered spetra for snhrotron soures are power laws J( ) α is the spetral inde A number of proesses ields power law energ distribution for partiles, in partiular at high energies, i.e. shok aeleration N( E) de ke p de p is the partile inde The snhrotron spetrum is sharpl peaked, muh narrower than the width of the power law eletron energ spetrum, so we an simpl approimate that an eletron of energ E radiates its energ at the ritial frequen C L E m e L

21 SPECTRUM POWER LAW DISTRIBUTION de J ( ) d N( E) de dt Energ radiated in the range ν to ν+dν an be attributed to eletrons with energies in the range E to E+dE E L 1/ m e de me 1/ L 1/ d de dt 4 T 3 E m e B 8 J ( ) onst B ( p1)/ ( p1)/ ( p 1) / The emitted spetrum is determined b the slope of the eletron energ spetrum, rather than b the shape of the emission spetrum of a single eletron

22 SPECTRUM POWER LAW DISTRIBUTION

23 POLARIZATION p 1 p 7 / 3 An essential feature of snhrotron radiation is that it is polarized. The degree of polarization an be er high, i.e. for p=3 it is 75%. Howeer sometimes it is diffiult to ahiee this high leel of polarization due to disordered magneti fields.

24 RELATIVISTIC JETS M87 jet: morpholog is the same at radio, optial annd X-ra waelength. Power law spetrum, steepening due to losses, polarized. Onl one side jet is isible.

25 EXTENDED RADIO EMISSION IN CLUSTERS

26 EXTENDED RADIO EMISSION IN CLUSTERS Coma luster Radio halos fill the olume of the lusters, Mp etension. Gien the short snhrotron lifetime eletrons an t simpl diffuse. No deteted polarization

27 EXTENDED RADIO EMISSION IN CLUSTERS A3376 Radio relis linear strutures of Mp size, usuall at the outskirts of the diffuse etended emission. 0%-50% deteted polarization

28 SPECTRA OF RADIO HALOS COMA CLUSTER RADIO HALO SPECTRUM Power law spetra with α 1, in the best studied ase spetral maps show spetrum steepening in the outskirts (energ losses)

29 SPECTRA OF RADIO HALOS A356 RADIO SPECTRAL MAP

30 CONNECTION WITH CLUSTER MERGERS Radio emission related to mergers: shoks aelerate seed eletrons at relis, turbulene is responsible for radio halo emission

31 CONNECTION WITH CLUSTER MERGERS from Brown et al. 011 GMRT lusters literature RH SUMSS staking off-state Radio halo bimodalit of lusters: onl luminous massie mergers hae radio halos (strong support for primar models, i.e. reaelerated eletrons, not eletrons produes in p-p ollisions, i.e. seondar models).

32 Per domande/informazioni il mio sito web Posta elettronia:

Radiation processes and mechanisms in astrophysics 3. R Subrahmanyan Notes on ATA lectures at UWA, Perth 22 May 2009

Radiation processes and mechanisms in astrophysics 3. R Subrahmanyan Notes on ATA lectures at UWA, Perth 22 May 2009 Radiation proesses and mehanisms in astrophysis R Subrahmanyan Notes on ATA letures at UWA, Perth May 009 Synhrotron radiation - 1 Synhrotron radiation emerges from eletrons moving with relativisti speeds