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Spectra of partially self-absorbed jets
Spectra of partially self-absorbed jets
Christian Kaiser
University of Southampton
Christian Kaiser
University of Southampton
OverviewOverview
• 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)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!
€
Fν ∝ν α , with α ≈ 0
The basicsThe 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:€
EdE ∝ E− pdE
€
Fν ∝ν 5 / 2
€
Fν ∝ν p−1( ) / 2
The basicsThe 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?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
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).
McC
ray
(196
9)M
cCra
y (1
969)
Radiative losses and gainsRadiative 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!
€
γ≤γthick, with ν = γ thick2 ν g
€
τ ν( ) ≈1
Two modelsTwo 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
€
r∝ x a
Model spectraModel spectra
Magnetic field
Perpendicular Parallel Isotropic
Ballistic flat linear N/A
Adiabatic flat for a=3/13 flat for a=3/19 flat for a=1/5€
B∝ r−1
€
B∝ r−2
€
B∝ r−4 / 3a
Model spectraModel 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 jetBallistic jetAdiabatic jetAdiabatic jet
Comparing with observationsComparing 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
Sti
rlin
g et
al.
(200
1)S
tirl
ing
et a
l. (2
001)
Comparing with observationsComparing 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
• 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
Future observational diagnosticsFuture 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 diagnosticsFuture observational diagnostics
• High-frequency cut-off probes close to black hole
• In Cygnus X-1 example, down to 5 RS in infrared
• High-frequency cut-off probes close to black hole
• In Cygnus X-1 example, down to 5 RS in infrared
SummarySummary
• 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?