1. Synchrotron Radiation, continued Rybicki & Lightman Chapter 6 Also Course notes for “Essential Radio Astronomy” at NRAO, Condon & Ransom http://www.cv.nrao.edu/course/astr534/ERA.shtml

2. Synchrotron Theory: Summary of Results 1. Synchrotron = relativisitic electrons & B-field  Very spiky E(t) because of beaming For an electron having  ~ 10 4 the width of the pulse is B ~5x10 -6 G

3. The time between pulses is ~ E(t) t

4. 2. Spectrum of single energy electron: Critical frequency E= electron energy x= / c

5. Each electron of energy E contributes to the spectrum at x=1

6. p = spectral index of particle energies and s = spectral index of observed radiation Ergs/s 3. Spectral index related to energy index of electron energy distribution (Optically thin synchrotron)

7. 4.For optically thin synchrotron, the slope of the spectrum must always be greater than -1/3 because the low-frequency spectrum is a superposition of single spectra, and F(x) ~ -1/3 s > -1/3 Single electron spectrum

8. Summary: For optically thin emission For optically thick  Low-frequency cut-off Thick Thin

9. Synchrotron Radio Sources Map of sky at 408 MHz (20 cm). Sources in Milky Way are pulsars, Sne; Diffuse radio spectrum  Galactic B-field + cosmic rays

10. Milky Way magnetic field ~ 5 microGauss, along spiral arms measured via Zeeman splitting of OH masers pulsar dispersion measures polarization of starlight by dust aligned in B-field c.f. Earth’s Magnetic field: 500,000 microGauss Spectrum of Cosmic Rays in ISM of the Milky Way has p~2.4 Spectrum of synchrotron radiation s~0.7

11. Han 2010

13. Milky Way Interstellar Cosmic Ray Energy spectrum Casadel & Bindli 2004 ApJ 612, 262 energy spectrum has p~2.4 Synchrotron has s~0.7

14. M51 Polarization derived from Synchrotron (6 cm). Beck 2000 Coherent structure, B-field along arms

15. Milky Way B-field: Theory Vertical Field in Center B ~1mG Horizontal Field in Disc B ~ 3  G Supernova explosion. Scale Eddy turnover time Scale Rotation time VG2108years LG41020m 0107years l031018m V Cowley 2011

16. 6.Dynamo  amplification of primordial seed magnetic field E. Parker: Galactic Dynamo Differentital rotation & convection or SN explosions --> loops Loops align with existing B-field Net result is amplification Zirker, The Magnetic Universe

17. 7. Minimum Energy and Equipartition Synchrotron spectrum spectral index  electron energy index, but not B-field B-fields often estimated by assuming “ equipartition” Recall:Energy density of magnetic field What can we say about the minimum energy in relativistic particles and magnetic fields that is required to produce a synchroton source of a given luminosity?

18. What is U E ? Assume power-law electron energy distribution between energies E min and E max which produces synchrotron radiation between frequencies min and max Energy density of electrons Synchrotron radiation luminosity

19. Substitute and Energy per electron from synch.

20. Approximate each electron emits at energy E, and Soand So

21. Need total energy density in particles: electrons plus ions Let Don’t usually know what  is, but  ~ 40 for cosmic rays near Earth So total energy So there is a B for which U is minimum

22. Find minimum U by taking dU/dB and setting = 0

23. Result: Get minimum energy when “ Equipartition ” So given an optically thin synchrotron source of luminosity L, Assume equipartition, and then compute B numerical formulae on Condon & Ramson web site Physically plausible: B field cannot have U>>U(particles) and still have Coherent structures Large extragalactic jets have an enormous amount of particle energy as It is, so putting more energy into particles makes theory more difficult

24. Crab Nebula The Crab Nebula, is the remnant of a supernova in 1054 AD, observed as a "guest star" by ancient Chinese astronomers. The nebula is roughly 10 light-years across, and it is at a distance of about 6,000 light years from earth. It is presently expanding at about 1000 km per second. The supernova explosion left behind a rapidly spinning neutron star, or a pulsar is this wind which energizes the nebula, and causes it to emit the radio waves which formed this image. Radio emission of M1 = Crab Nebula, from NRAO web site

25. IR Optical RadioX-ray (Chandra)

26. Crab Nebula Spectral Energy Distribution from Radio to TeV gamma rays see Aharonian+ 2004 ApJ 614, 897 Synchrotron Self-Compton

27. Photon frequency (Hz) Electron Energy U, (eV) Electron lifetime (Yr) Radio (0.5 GHz) 5x10 8 3.0x10 8 109,000 Optical (6000A) 5x10 14 3.0x10 11 109 X-ray (4 keV)1x10 18 1.4x10 13 2.4 Gamma Ray1x10 22 1.4x10 15 0.024 = 9 days Synchrotron Lifetimes, for Crab Nebula Timescales << age of Crab  Pulsar is Replenishing energy

28. Guess what this is an image of?

29. Extragalactic radio sources : Very isotropic distribution on the sky 6cm radio sources North Galactic Pole Milky Way right ascension

30. Blowup of North Pole

31. VLA Core of jets: flat spectrum s=0 to.3 Extended lobes: steep spectrum s = 0.7-1.2

32. DRAGNS: Double-Lobed Radio-loud Active Galactic Nuclei www.jb.man.ac.uk/atlas/dragns.html

33. APOD April 13, 2011 Cen A, Full moon and CSIRO radio Observatory Radio lobes are ~ million light years across

34. FR I vs. FR II On large scales (>15 kpc) radio sources divide into Fanaroff-Riley Class I, II (Fanaroff & Riley 1974 MNRAS 167 31P) FRI: Low luminosity edge dark Ex.:Cen-A FRII: High luminosity hot spots on outer edge Ex. Cygnus A

35. Lobes are polarized  synchrotron emission with well-ordered B-fields Polarization is perpendicular to B

39. 8. Synchrotron spectra steepen with age Energy radiated by electrons So high energy electrons lose their energy faster than low energy electrons Spectrum steepens At high freqencies:

40. Typically: Cores have “flat spectra” s~0.5 Outer lobes have “steep spectra” s ~ 1.5-2

41. Real spectra can be complex: non-uniform B-fields, geometries (Kellerman & Owen 1988)