Spectra of partially self-absorbed jets Christian Kaiser University of Southampton Christian Kaiser University of Southampton

Overview Blandford-Königl (BK) model Energy losses and gains of electrons Model spectra with losses and gains Comparison with the VLBA jet of Cygnus X-1 Future observational diagnostics Blandford-Königl (BK) model Energy losses and gains of electrons Model spectra with losses and gains Comparison with the VLBA jet of Cygnus X-1 Future observational diagnostics

Blandford & Königl (1979) THE model for flat radio spectra with extreme surface brightness temperature. Flat spectra: 718 citations since publication (2.3 per month!) ONLY applicable for jets at large angle to line of sight! THE model for flat radio spectra with extreme surface brightness temperature. Flat spectra: 718 citations since publication (2.3 per month!) ONLY applicable for jets at large angle to line of sight!

The basics Magnetised plasma with electrons with an energy distribution of: Peaked spectrum. Absorbed: Optically thin: Magnetised plasma with electrons with an energy distribution of: Peaked spectrum. Absorbed: Optically thin:

The basics Need to adjust jet properties to get the peaks ‘right’. Important ingredients: –Structure of magnetic field –Energy evolution of electrons In BK model: –B-field perpendicular to jet –No energy losses of electrons Need to adjust jet properties to get the peaks ‘right’. Important ingredients: –Structure of magnetic field –Energy evolution of electrons In BK model: –B-field perpendicular to jet –No energy losses of electrons

No energy losses? “We assume that relativistic electrons can be accelerated continuously within the jet,…” “There must […] be ongoing particle acceleration to compensate for the cooling associated with adiabatic decompression…” Hmmm… “We assume that relativistic electrons can be accelerated continuously within the jet,…” “There must […] be ongoing particle acceleration to compensate for the cooling associated with adiabatic decompression…” Hmmm…

Energy distributions with radiative losses Synchrotron emission leads to a high- energy cut-off Self-absorption mitigates the losses (somewhat). Synchrotron emission leads to a high- energy cut-off Self-absorption mitigates the losses (somewhat). McCray (1969)

Radiative losses and gains Radiative losses halted for electrons with Lorentz factors where the optical depth This does not affect adiabatic losses! Radiative losses halted for electrons with Lorentz factors where the optical depth This does not affect adiabatic losses!

Two models Ballistic jet: –Free expansion, conical shape –Only radiative losses –Limiting case Adiabatic jet: –Confined by external medium so that –Both adiabatic and radiative losses Ballistic jet: –Free expansion, conical shape –Only radiative losses –Limiting case Adiabatic jet: –Confined by external medium so that –Both adiabatic and radiative losses

Model spectra Magnetic field PerpendicularParallelIsotropic BallisticflatlinearN/A Adiabaticflat for a=3/13flat for a=3/19flat for a=1/5

Model spectra Of course, still get optically thin/thick regions at extremes Energy losses can steepen optically thin spectrum …or lead to peaks at high frequencies Of course, still get optically thin/thick regions at extremes Energy losses can steepen optically thin spectrum …or lead to peaks at high frequencies Ballistic jet Adiabatic jet

Comparing with observations VLBA jet of Cygnus X-1 Can measure flux and extent at one frequency NO information on second frequency NO information on high frequency cut-off VLBA jet of Cygnus X-1 Can measure flux and extent at one frequency NO information on second frequency NO information on high frequency cut-off Stirling et al. (2001)

Comparing with observations Both models can be made to fit, but… Adiabatic model way out of equipartition (10 6 times more energy in magnetic field) VERY thin jets (opening angle ~5”) Problem: long extent of observed jet needs –High optical density far out –Strong magnetic field Both models can be made to fit, but… Adiabatic model way out of equipartition (10 6 times more energy in magnetic field) VERY thin jets (opening angle ~5”) Problem: long extent of observed jet needs –High optical density far out –Strong magnetic field

Future observational diagnostics Jet extent at two frequencies (simultaneous) Factor 2 in observing frequency Jet extent at two frequencies (simultaneous) Factor 2 in observing frequency

Future observational diagnostics High-frequency cut-off probes close to black hole In Cygnus X-1 example, down to 5 R S in infrared High-frequency cut-off probes close to black hole In Cygnus X-1 example, down to 5 R S in infrared

Summary Even with radiative and adiabatic losses self-absorbed jets produce flat spectra No need for mysterious re-acceleration Finding the high frequency cut-off will probe very close to black hole BUT: Narrow jets may tell us of the need for more physics? Even with radiative and adiabatic losses self-absorbed jets produce flat spectra No need for mysterious re-acceleration Finding the high frequency cut-off will probe very close to black hole BUT: Narrow jets may tell us of the need for more physics?