1. (with Nikolaos D. Kylafis)
The energy distribution of electrons in radio jets
Alexandros Tsouros
University of Crete
(with Nikolaos D. Kylafis)
Bologna, 19 September 2017

2. Introduction
In order to understand the context, I feel that an introduction on stellar-mass X-ray transients is appropriate.
X-ray transients exhibit, during an outburst, a characteristic “q”-shaped curve, sometimes called a hysteresis curve (next slide).
I will use GX as the prototype.

3. GX 339-4

4. Similar behavior for BH, NS, WD!4

5. The physics of the curve
The timescale of a typical black hole XRT outburst is ~ 1 year
Unlike AGN, if you miss one today, you’ll catch one next year
In simulations and theoretical studies, the main parameter used is the accretion rate.
The appearance of the accretion flow wrt the accretion rate is as follows:

6. GX Revisited

9. GX – The full picture!
(Last time, I promise)

10. The energy distribution
Having said all that, one asks the question : what is the energy distribution of the electrons in the jet?
Ever since 1979, we have been assuming a power law distribution. (Blandford & Koenigl 1979; but see also Jones & Hardee 1979).
However, now we know that the jet originates in the hot inner flow (ADAF-like).
Thus, at least at the bottom of the jet, and possibly higher up, the electrons obey a thermal distribution.
Question: what radio spectrum does a thermal jet produce?
Answer: the same as for a power-law distribution of electrons!!!

11. Typical jet spectra (Giannios,2005)

12. Thermal and power-law distributions

13. Emissivity of the various distributions for 10^11 Hz

14. The model (Ballistic jet)
We assume a parabolic jet and a bulk velocity of .
Emission timescale is , and so can be ignored.
We consider geometries of the sort
We assume either a perpendicular or a parallel magnetic field.
From electron number conservation and magnetic flux conservation we have
Solve the RT equation!

15. The model (Adiabatic jet)
We again assume a constant flow velocity:
Here, cooling due to adiabatic expansion cannot be ignored. The temperature, kT, in units of the electron rest energy, is given by
The radius, density, and magnetic field evolve as in the ballistic case.

16. Results (Parabolic, Ballistic Jet)
For a power law: 0<α<0.2
(see Giannios,2005)
For Maxwellian distribution: 0<α<0.5
As the source MAXI J (Russel T.D. et al. 2014) goes through the outburst, it interchanges between α=0.2 and α=0.5

17. Results (Adiabatic jet)
With adiabatic cooling included, we find an interesting functional relationship:

18. Summary & conclusions
Work on jets with a thermal distribution of electrons (Falcke & Markoff 2000, for Sgr A*; Pe’er & Casella 2009).
Largely, however, our community has ignored the possibility of a thermal distribution of electrons in jets.
This must change! Now we know more than in 1979!
The thermal distribution is no longer merely a mathematical inquiry, but rather a necessity of nature.
THANK YOU