Spectra of partially selfabsorbed jets

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Spectra of partially self-absorbed jets

• Christian Kaiser
• University of Southampton

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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

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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!

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The basics

• Magnetised plasma with electrons with an energy
  distribution of
• Peaked spectrum. Absorbed
• Optically thin

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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

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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

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Energy distributions with radiative losses

• Synchrotron emission leads to a high-energy
  cut-off
• Self-absorption mitigates the losses (somewhat).

McCray (1969)
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Radiative losses and gains

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

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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

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Model spectra
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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

Ballistic jet
Adiabatic jet
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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

Stirling et al. (2001)
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Comparing with observations

• Both models can be made to fit, but
• Adiabatic model way out of equipartition (106
  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

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Future observational diagnostics

• Jet extent at two frequencies (simultaneous)
• Factor 2 in observing frequency

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Future observational diagnostics

• High-frequency cut-off probes close to black hole
• In Cygnus X-1 example, down to 5 RS in infrared

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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?