D D D S D X Synchrotron Self-bsorption 10 21 log ν (p 1)/2 ν 5/2 t low ν: synchrotron emitting electrons can absorb synchrotron log ν photons: synchrotron after Shu, ig. 18.6 self-absorption. or a power law electron distribution p, total spectral shape is: or low frequencies: P ν B 1/2 ν 5/2 or large frequencies: P ν ν (p 1)/2 (independent of p!) t very high frequencies, additional break due to electron energy losses. The transition frequency can be used to measure the strength of the B-ield. See text-books on radio astronomy. Synchrotron adiation 19 D S D X Jet Spectrum 10 25 (87; Perlman et al., 2002) Spectral shape of jet emission is a power law synchrotron radiation Typical power law index: α 0.65 between radio and optical.
D D D S D X Jet Polarization 10 26 polarization in two-sided jet sources ( 1): up to 40% B-field orientation: close to core: B jet axis away from core ( 10% jet length): B jet axis B-field can change orientation again in knots (B-field configuration in 4296; Killeen, Bicknell & kers, 1986, ig. 25b) Jet motion in 3120 (arscher et al., 2002) 3120: Sy 1, BH 3 10 7 from reverberation mapping O T: ØÑÓÚ» ½¾¼Öܺ Ú Jet Physics 5 D S D X Superluminal otion, 10 29 3120: pparent speed of jet: 5c 87: pparent speed of jet: 6c polarization in one-sided jet sources ( 2): similar to 1, i.e., 40% and higher B-field orientation in 2: parallel to jet axis throughout the jet Superluminal motion: The apparent velocities measured in many G jets are v > c. irst discovered in 1971 in 3273. (-field configuration in G 6251, note: B-field is perpendicular to -field!; Perley, Bridle & Willis, 1984, ig. 17) Biretta/STSc
D D D D S D X Superluminal otion, 10 30 S D X Superluminal otion, 10 32 t 0 t 1 8 6 β0.500 β0.900 β0.990 φ onsider blob moving towards us with speed v and angle φ with respect to line of sight, emitting light signals at t 0 and t 1 t 0 + t e ight travel time: Observer sees signals separated by Observed distance traveled in plane of sky: t o t e t e v c cos φ ( 1 v c cos φ ) t e (10.36) l v t e sinφ (10.37) v app /c 4 2 0 0 45 90 135 180 φ [deg] Jet otion 3 Jet otion 5 D D D D S D X Superluminal otion, 10 31 S D X relativistic invariant, 10 33 φ t 0 t 1 pparent velocity deduced from observations: v app l t o or v/c large and φ small: v app > c v t e sinφ ( 1 v c cosφ) t e v sinφ (10.38) cosφ) ( 1 v c So, if φ is known, we can determine real speed. n order to determine φ, we have to make use of an useful relativistic invariant: in all frames of reference. nu ν 3 const. (10.39) Proof: The number of photons with momentum in interval p, p + d 3 is given by ( ) d3 p d 2n (10.40) where n: photon number, d 3 p: phase volume, h 3 : volume of phase space cell. nergy flowing through volume element d 3 x d(cdt): ( ) d3 p d hν d 2nhν d(cdt) h 3 h 3 (10.41)
D D D D S D X relativistic invariant, 10 34 S D X elativistic berration 10 36 Since p hν/c: Therefore or d 3 p p 2 dp dω ( ) 2 hν h dν c c dω ( ) d3 p d 2nhνcd dt h 3 ( ) 3 h ν 2 dν dω (10.42) c 2hν3 n d dt dωdν (10.43) c2 d d dt dωdν 2hν3 c n 2 (10.44) Therefore ν 2h 3 c n 2 (10.45) and since n is just a number, /ν 3 is orentz-invariant. 2 π+φ φ 1 ow take a source emitting blobs symmetrically in two directions. rom q. (10.49) the ratio of fluxes from the blobs is ( ) 1 1 + β cos φ 3+α (10.50) 2 1 β cos φ adiation from a blob moving towards observer is strongly boosted. Jet can be expressed as a series of blobs. But the number of blobs observed scales as (γ(1 v cos φ)) 1, such that for jets: 1 2 ( ) 1 + β cos φ 2+α (10.51) 1 β cos φ One sidedness of jets is a relativistic effect. rom measuring 1 / 2, we can in principle determine φ. Jet otion 7 Jet otion 9 D D D D S D X elativistic berration 10 35 S D X elativistic berration 10 37 elativistic invariance: ν /ν 3 const. where ν is the intensity. Therefore, observed intensity of a moving blob: Because of the relativistic Doppler effect: (ν obs ) ν 3 obs ν obs (ν em) ν 3 em ν em γ(1 β cos φ) (10.46) (10.47) (β v/c) and thus (ν obs ) ν 3 (ν em ) (ν em ) obs νem 3 (γ(1 β cos φ)) 3 (10.48) Specifically, for a blob with a power law spectrum: ν α em (ν obs ) (γ(1 β cos φ)) (γ(1 β cos φ)) α ν α obs ν α obs 3 (γ(1 β cos φ)) 3 (γ(1 β cos φ)) 3+α (10.49) (where is the normalization constant of the power law). 1 / 2 10 6 10 4 10 2 10 0 β0.500 β0.900 β0.990 0 45 90 φ [deg]
D D D D S D X Jet Statistics, 10 38 S D X Jet Statistics, 10 40 Kellermann et al. (2004): argest survey of jets performed so far. Wavelength 2 cm (15 GHz) ll G with flat spectra (α < 0.5 for S ν ν α ) and fluxes above 1.5 Jy at 15 GHz Survey started in 1994, ended in 2001, typically 7 observations per source 208 features in 110 G (Seyfert, B ac, Quasars). movies and images at ØØÔ»»ÛÛÛºÒÖ Óº Ù»¾Ñ ÙÖÚ Ý (recommended!) 40 30 20 10 0 24 26 28 (Kellermann et al., 2004, ig. 6) elation between β and luminosity: larger scatter at higher This does not mean that lower sources have lower speeds, since observational effects also play a role: sample is flux limited faintest sources are close, and probably represent the most normal sources probability that high orentz factor jets point in our direction grows with sampled volume, so perhaps the distribution is a selection effect. Jet Propagation and ormation 1 Jet Propagation and ormation 3 Distribution of observed velocities: apparent velocity range: β 15 Quasars: tail up to β 34 others: mainly β 6 n many sources, bent trajectories are observed, which do not follow jet axis do blobs follow pre-existing channel? nonballistic motion? difference between bulk motion and pattern motion?
Jet propagation is very hydrodynamics: generally solved numerically umerical simulation of a ach6 jet (Top: density, bottom: pressure ind et al., 1989). Turbulent structure due to Kelvin-Helmholtz instability (hydrodynamical instability in shear flows) -field structure of G 1265 (O dea & Owen, 1986) G 1265: radio galaxy in Perseus cluster, moving with 2000 km s 1 through intergalactic medium. (O/U; O dea & Owen, 1986) (O/U/Owen et al.) 375 in bell 400 at λ 20 cm: twin radio jets from double core.
D D D D S D X Jets and G, 10 46 S D X Jets and G, 10 48 adio lobe physics: Total energy content of lobe for a power law distribution of electrons, n() n 0 p : U e 2 1 n() d n 0 2 p ( ) 2 p 2 2 p 1 ntegrating over the synchrotron spectrum (q. (10.26)) gives the total synchrotron luminosity produced by this electron population: Using the characteristic frequency 4σ TU B n 0 3m 2 ec 4 ( 3 p 2 3 p ) 1 3 p (10.52) (10.53) ω c γ 2 ω eb ( ) 2 (10.18) m e c m e c 2 1 and 2 can be expressed in terms of the frequency band over which the power law is observed, ν 1, ν 2. fter some messy calculation one obtains: where is some constant. U e (10.54) B 3/2 Jet Propagation and ormation 9 adio lobes: Typical luminosity is a few times 10 44 erg s 1 Typical B-fields are 10 4 G ssuming equipartition: typical energy content of a radio lobe: 10 60 erg corresponding to 10 7 supernovae lobe lifetime t / 10 8 yr jets and lobes are rather long lived phenomena quipartition holds only approximately true for jets and lobes (see, e.g., Heinz & Begelman 1997). Jet Propagation and ormation 11 D D D D S D X Jets and G, 10 47 S D X Jet ormation 10 49 The total kinetic energy in particles is U particles au e ab 3/2 (10.55) where a > 1 (since there are other particles than electrons in the lobe). Therefore the total energy of the radio lobe is U tot U particles + U B a B2 + (10.56) B3/2 8π The minimum of U tot is reached for ( ) 6πa 2/7 B min (10.57) while the equipartition B-field, for which U particles U B is ( ) 8πa 2/7 B eq (10.58) Dynamics of jet formation are better studied in Galactic black holes with jets ( microquasars ) because of shorter timescales. ind clear X-ray radio correlation (similar also seen in some G such as 3120) universal disk-jet-connection Since the total energy for equipartition is 1.01U min, one often assumes synchrotron sources are in equipartition. irst noticed by Burbidge (1959). (GS 1915+105; irabel et al., 1998)
D D S D X Jet ormation 10 50 X-ray binaries: S radio S 0.7 X adio and X-ray fluxes are correlated: evidence for interaction between disk and jet! Temperature profile and B-field configuration of a HD-jet (Gallo, ender & Pooley, 2003) Jet Propagation and ormation 13 (Kigure & Shibata, 2005, ig. 6) D D D D S D X Jet ormation 10 52 S D X Jet ormation 10 54 volution of a newly launched jet (Kigure & Shibata, 2005) To study jet confinement and propagation: use magnetohydrodynamical simulations (ckinney, 2006, ig. 1) log ρ (left) and log ρ and B for a jet launched via a disk. Outer radius is 10 4 G/c 2.