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).

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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

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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

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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?