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

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1 Radiation proesses and mehanisms in astrophysis R Subrahmanyan Notes on ATA letures at UWA, Perth May 009

2 Synhrotron radiation - 1 Synhrotron radiation emerges from eletrons moving with relativisti speeds in a magnetized plasma. The magneti field auses the eletrons to gyrate the trajetories are spiral. The aeleration of the eletrons beause the veloity vetor hanges keeping the speed the same results in EM radiation from the eletrons. If the speeds are non-relativisti, the radiation is elliptially polarized depending on the loation of the observer and at the gyration frequeny. If the eletrons are moving with relativisti speeds, the emission is onfined to a one along the instantaneous veloity vetor. This radiation one from a single eletron sweeps aross the sky and any stationary observer will reeive pulses of EM radiation as the one sweeps past. The net radiation from an ensemble of eletrons results in what is termed as synhrotron radiation. The reeived emission from a region of spae ontaining a uniform magneti field will be partially linearly polarized.

3 Synhrotron radiation - Single eletron moving with speed v in a uniform magneti field. B Magneti field B Magneti field energy density U B = B /(μ o ) Eletron speed = v/ Eletron Lorentz fator Pith angle a 1/ 1 v a v x B fore = ev x B v v v x B fore = ev x B = rate of hange in momentum d ( m ) dt This results in a helial trajetory of the harged partile with a pith angle a, where a is the angle the partile veloity makes with the B field sin / Gyration diretion depends on the sign of the harge: eletrons and positrons gyrate in opposite diretions.

4 Synhrotron radiation - Gyration is owing to the v x B fore: m eb r eb B r m Gyro-frequeny Cylotron frequeny Partile energy does not hange, partile speed does not hange. Aeleration due to magneti field is perpendiular to the diretion of motion. B field does no work on the partile. Gyration is aompanied by uniform drift along the B field. Gyro-frequeny is independent of the pith angle the angle the harge makes with the B field. Radiation field due to an aelerated harged partile: E 1 4 Gyration in the plane of the sky produes irularly polarized radiation. Gyration perpendiular to the sky plane produes linear polarization. In between the polarization is elliptial. The radiation will slow the speed of the harged partile. q sin r The observed field will have a sinusoidal variation over time, at the gyration frequeny. o

5 Synhrotron radiation - 4 What if the partile speed, as it gyrates in a B field, is relativisti? Consider a partile gyrating with relativisti speeds in a plane perpendiular to the sky The B field is on the sky plane The `disturbanes in the field due to aelerations travel at fixed speed. The radiation part of the E field is proportional to the Apparent a. of the harged partile Whih is the aeleration at the retarded time (t o r/) E Towards the telesope When the partile moves towards the telesope, the aeleration on the sky plane appears quiker and the radiation is more intense When the partile moves away, the aeleration appears smaller and radiation intensity is diminished Radiation appears to be pulsed! time

6 Synhrotron radiation - 5 Equivalent viewpoint: when a relativisti harged partile is aelerated perpendiular to its veloity, the radiation is emitted in a one, with half angle 1/g rad. The pulses are observed when the radiation one sweeps aross the telesope. Width of the pulse = time taken for the pulse to sweep past the observer loated at angle a to B-field t t t em obs obs ( / ) /( sin) t em 1/( B (1 ) t em /( ) sin) gyration _ B period /( sin) Defines a ritial frequeny 1/ t obs ( eb / m) sin or exatly: eb sin 1.6 m B nt m 10GeV GHz

7 Synhrotron radiation - 6 Spetrum of the reeived radiation (owing to B-field aeleration of a single eletron) The observed E field is a sequene of pulses spaed π/ω B and eah of the pulses has a width t obs 1/ (onvolution of a sequene of impulses with the field shape of a single pulse) This gives a spetrum that is a sequenes of impulses at harmonis of ω B with an envelope that peaks at a frequeny lose to (produt of a sequene of impulses and the FT of the single pulse profile) eb sin 4 m At freq << n S(n) ~ n (1/) At freq >> n S(n) ~ n (1/) exp(- n/n ) Radiation peaks at 0.9 x n The gyrating relativisti partile emits most of its power at frequenies around (g x gyration frequeny) and not at its gyration frequeny This is the envelope of the impulses, whih onstitute the spetrum.

8 Synhrotron radiation - 7 Total radiated power from a single partile P q 6 o For a relativisti eletron moving with Lorentz fator g P B q 4 6 o Zero Using relations: T 8 q 4 om The radiated power from a single eletron: And for isotropi pith angle distribution: U B B This synhrotron radiation may be viewed as a sattering of harged partiles off a magneti field energy density, just as inverse-compton sattering is off radiation field energy density. sin / 0 P U T B sin P 4 T B U

9 Synhrotron radiation - 8 Radiated power ~ g => more energeti partiles loose more energy Radiated power ~ 1/( m o ) beause s T ~ 1/( m o ) => massive partiles (protons) radiate poorly Radiated power ~ B => radiation losses are inreased in regions with greater B fields 4 P TU B Power radiated - de/dt = P Radiation loss timesale t 1/ 1 / = E / (-de/dt) 0.8(0.1nT / B) (10GeV / E) Gyr In extreme ases (pulsar polar aps) radiation timessale < gyration time. In most diffuse astrophysial plasmas in whih B is small, the emission is `stationary.

10 Synhrotron radiation - 9 Single eletron with energy g radiates total power In a narrow band of frequenies around Approximately, the radiation from a single eletron is P U T B eb sin 4 m If eletrons with a wide range of energies are gyrating in the B field and radiating, a wide range of frequenies are produed. P(, ) sin sin ( ) TU B If a power-law: N( ) d K p d desribes the partile energy distribution. The total emission spetrum is: P tot ( ) P(, ) N( ) d KB ( p1)/ ( p1)/ A partile energy distribution index p => radiation spetral index s=-(p-1)/ A power-law eletron energy distribution results in a power law radiation spetrum

11 Synhrotron radiation - 10 If B field is uniform, radiation is anisotropi even if eletrons are uniformly distributed in pith angle The radiation will be isotropi if the B field is tangled. Synhrotron emission : Eletron + B field -> Eletron in lower energy state + B field + radio photon Synhrotron absorption : Eletron + B field + radio photon -> Eletron in higher energy state + B field Synhrotron stimulated emission : Eletron + radio photon + B field -> Eletron in lower energy state + radio photons + B field All three proesses will our in a synhrotron plasma. Eletrons with energy gm absorb and radiate at frequeny eb sin 4 m A relativisti eletron with pith angle will radiate and absorb photons moving at angles lose to with respet to the B field

12 Example in astrophysis a radio galaxy Linear size ~ 100 kp Synhrotron power ~ 10 5 W/Hz at 1.4 GHz Radiation spetral index s = -0.8, p=.6 Assume that the synhrotron spetrum is limited to 1 MHz to 100 GHz. Soure luminosity L ~ 1.5 x 10 5 J/s Assuming equipartition onditions: Total eletron energy U 51 e =.4 x 10 J Magneti field B = 0.4 nt Partile energy density u e = 1.5 x 10-1 J/m Magneti field energy density u B = 6.6 x J/m Partile pressure p= u p / = 5 x Ps Eletrons radiating at 1.4 GHz in this B field will have Eletron energy gm = 5 GeV Lorentz fators g = Gyration period ~ 1 min Gyration radius ~.4 x m ~ 0. A.U. Radiative lifetimes t 1/ = 0.1 Gyr

SPECTRUM OF THE COMA CLUSTER RADIO HALO SYNCHROTRON RADIATION

SPECTRUM OF THE COMA CLUSTER RADIO HALO SYNCHROTRON RADIATION OUTLINE OF THE LESSON REMINDER SPECIAL RELATIVITY: BEAMING, RELATIVISTIC LARMOR FORMULA CYCLOTRON EMISSION SYNCHROTRON POWER AND SPECTRUM EMITTED