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7- я Ежегодная Конференция "Физика плазмы в солнечной системе" (6 - 10 февраля 2012 г., ИКИ РАН). МИКРОВОЛНОВОЕ И СУБ-ТГЦ ИЗЛУЧЕНИЕ ВСПЫШЕЧНОЙ ПЕТЛИ. В . Ф . Мельников , ГАО РАН , Санкт - Петербург , Россия J.E.R. Costa , INPE, S.J. Campos, Brazil

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7-я Ежегодная Конференция

"Физика плазмы в солнечной системе"

(6 - 10 февраля 2012 г., ИКИ РАН)


В.Ф. Мельников, ГАО РАН, Санкт-Петербург, Россия

J.E.R. Costa, INPE, S.J. Campos, Brazil

P.J.A. Simoes, CRAAM, Sao Paulo, Brazil

observations of flares in the 200 400 ghz domain
Observations of flares in the 200-400 GHz domain
  • 200-400 GHz measurements of flares have been obtained since year 2000:

- routinely with SST at 212 and 405 GHz

- short observing campaigns with KOSMA and BEMRAK at 230, 345 and 210 GHz resp.

  • Multi-beam observations at 210 GHz: estimate position and size of the radio emitting region.

About 15 major flares (GOES M3.2 - > X28) have been detected.


Time profiles and intensities of sub-THz bursts

Sub-THz events occur in strong X-class solar flares

Their intensity in microwaves and sub-THz range reaches

Ff = (1-10) 104 sfu

They are long: several munutes

The time profiles at sub-THz and microwaves are similar and some seconds delayed against hard X-ray time profiles

Kaufmann P. et al. Ap.J. (2004), v603 L121-L124


Types of Radio Spectra in microwave – sub-THz range

Normal extention of microwave spectrum

With sub-THz component



Costa, Simões, Giménez de Castro


Microwave Spectrum+ Sub-THz- April 12, 2001 – 10:17UT (Adapted from Luthi etal, 2004 – A&A 415, 1123).

Microwave Spectrum+ Sub-THz- August 25, 2001 – 16:31UT (Adapted from Raulin etal, 2004 – S.Phys. 223, 181).

Types of Radio Spectra in microwave – sub-THz range

August 25, 2001

August 25, 2001

April 12, 2001



Costa, Simões, Giménez de Castro

So far: About 15 major flares (GOES M3.2 - > X28) have been detected at frequencies 200, 400 GHz
  • 7 to 8 normal events reported

Kaufmann et al 2001, 2002; Trottet et al. 2002;

Lüthi et al. 2004a; Raulin et al. 2003, 2004;

Cristiani et al. 2007a, 2010;

Giménez de Castro et al. 2009

  • 5 THz events reported

Kaufmann et al. 2002, 2004; Lüthi et al. 2004b;

Silva et al. 2007; Cristiani et al. 2008

Trottet et al, 2011

sub thz spectral component enigma emission mechanisms proposed
Sub-THz spectral component enigma:emission mechanisms proposed
  • - synchrotron radiation from positrons emitted in pion or radioactive decay after nuclear interactions (Trottet et al., 2004)
  • inverse Compton radiation (Kaufmann et al., 1986)
  • - gyrosynchrotron emission from a compact source (Kaufmann and Raulin 2006, Silva et al. 2007)
  • - free-free emission from an optically thick source (Silva et al. 2007, Fleishman and Kontar, 2010)
  • - Cherenkov emission from chromospheric layers (Fleishman and Kontar, 2010)
  • - synchrotron emission in stochastic medium (Fleishman and Kontar, 2010)
  • However, none of them can explain the full set of known properties of sub-THz emission and its relations to other emissions like microwave, hard X-ray etc.
gs interpretation of the sub thz spectral component
GS-interpretation of the sub-THz spectral component

Silva etal (2007) have shown that strong and well separated microwave and sub-teraherz spectral peaks can be explained by the gyrosynchrotron emission of energetic electrons being injected, respectively, into two interacting magnetic loops, one large with relatively weak magnetic field (microwave source), another small with strong magnetic field (sub-THz source).

However, the source of sub-THz component has to be extremely small (L<108 cm). It should also have very large magnetic field, B>2000 G, and very high number density of non-thermal electrons, n_e(E>50keV)>1012cm-3, in order to be optically thick up to about 300-400GHz, as well as to provide a sufficient instantaneous total number of electrons, N_t(E>50~keV)>5x1035, for fitting to very high observed flux density, F_f ~104sfu.

  • In this paper we propose an idea that can solve the above mentioned difficulties taking into account some recent findings concerning:
  • the importance of Razin suppression on the formation of observed gyrosynchrotron spectra in microwave bursts; and
  • the spatial distribution of gyrosynchrotron emission generated by anisotropic fluxes of accelerated electrons in inhomogeneous flaring loops

Kinetics of Nonthermal Electrons in Magnetic Loops

In a magnetic loop, a part of injected electrons are trapped due to magnetic mirroring and the other part directly precipitates into the loss-cone. The trapped electrons are scattered due to Coulomb collisions and loose their energy and precipitate into the loss-cone.

A real distribution strongly depends on the injection position in the loop and on the pitch-angle dependence of the injection function

S(E,,s,t), and also on time

(Melnikov et al. 2006; Gorbikov and Melnikov 2007, Reznikova etal, 2009).

Non-stationary Fokker-Plank equation (Lu and Petrosian 1988):

parameters for our model simulations
Parameters for our model simulations

For our simulations we take parameters in the sub-THz source derived from observations of the flare 2 November 2003 (Silva et al 2007) that presents a good example of the two simultaneously observed spectral peaks,

microwave at f ~ 15 GHz, and

sub-THz at f > 200 GHz,

both with high intensity Ff ~ 104sfu.

We assume that the magnetic field is distributed exponentially along the loop: B(s)=Bmin exp(-s2/sB2) with the mirror ratio Bmax/Bmin=2.

Plasma density distribution is chosen as: n0=n0min exp(s2/s12),

where s12= b_s2/ln(104), n0min=5 1010 cm-3,

b_s=3 109 cm is the distance from the center to the end of a loop.


near a footpoint


at the looptop




Different acceleration models give three basic predictions on the position of the acceleration site and pitch angle distribution

suitable model
Suitable model:

In this model a compact source of electrons is located at the loop top with the “beam-like” injection directed toward the left foot.

Left FP

Pitch-angle distribution of injection function:


Electron distribution over length of the model loop for electron energy E=405 keV and for two values of pitch-angles

In the case of beamed injection of accelerated electrons from the loop top region, we can get a strong peak of the electron number density near the footpoints where the magnetic field is also strong.

The upper plot shows the distribution for electrons rotating almost perpendicular to the magnetic field lines, with pitch-angle 89.36o.

The lower plot is for electrons propagating along field lines with small pitch-angle 12.17o


400 GHz

34 GHz



Gyrosynchrotron brightness and frequency spectrum in different parts of a flaring loop (Case of small plasma density in the lower parts of the magnetic loop)

Magnetic field distribution is assumed to be

B(s)=Bmin exp(-s2/sB2) with the mirror ratio Bmax/Bmin=2

The peak of non-thermal electrons near the footpoints can easily produce strong radio emission at frequencies up to THz range.

However, even in this case, the spectral maximum is located at frequencies much less than 400 GHz under all reasonable parameters of non-thermal electrons and magnetic field!


Gyrosynchrotron brightness and frequency spectrum in different parts of a flaring loop (Case of high plasma density in the lower parts of the magnetic loop – strong Razin effect)

Low plasma density

High plasma density



n0min=5 x 1010 cm-3 , n0max=1013 cm-3

Due to the strong chromosphere heating during the flare energy release, the plasma density in the lower parts of the loop can be strongly enhanced.

razin effect

Lienard-Wiechert potentials:

In vacuo:

e is the electron charge, and Ris the radius-vector of the electron moving with velocityvtaken at the retarded time t’= t-nR/c.

H(t) = rotA(t)

E(t) = -(1/c) ∂A/ ∂t - ∆φ

The potentials are closely connected with vectors of magnetic and electric fields:


In plasma:

In a plasma, a refraction index

n =1 - fp2/ f 2 < 1

the denominator can never be very close to 0, even ifv is close to c. So a relativistic electron has an emission efficiency comparable with a nonrelativisticone, i.e. much lower than in vacuo.

This causes a strong suppression of radiation in theplasma, especially at lower frequencies,

f < fR=20n0/B

(Razin, 1960; Ramaty 1969; Klein 1987, Fleishman & Melnikov, 2003).

gyrosynchrotron frequency spectrum in different parts of a flaring loop
Gyrosynchrotron frequency spectrum in different parts of a flaring loop

Left hand spectra are from the middle part of the loop

Right hand spectra are generated from the lower parts of the loop

17 GHz

400 GHz

The frequency spectra of GS emission coefficients from lower parts of the loop have the maximum near 400 GHz due to the Razin effect .


Total gyrosynchrotron frequency spectrum of the flaring loop


Frequency spectra obtained by integration over the whole flaring loop for two moments of time t1 and t2 on the rise phase of the burst.

Two spectral components in the microwave and sub-THz regions are clearly seen.


The microwave component shows an increase of the peak frequency with time (due to the self-absorption effect)

The peak frequency for sub-THz component remains constant (due to the Razin effect)

  • The difficulties of gyrosynchrotron interpretation associated with
  • the unrealistically small size,
  • large non-thermal electrons number density ne, and
  • large magnetic field
  • can be overcome if the lower frequency turnover of the sub-THz
  • spectral peak is caused by Razin suppression.
  • In this case, the only requirement is a relatively high value of the Razin frequency: fR = 20 n0/B >= 200GHz. Such the value normally can be realized in the lower parts of flaring loops.
  • The large flux density of some sub-THz bursts, Ff ~ 104 sfu, associated with X-class solar flares, is reached not due to the large non-thermal electrons number density, but due to the large area occupied by arcades (a large number of corresponding flaring loops) usually present in such flares.
which observed properties of the sub thz emission can be explained by our model
Which observed properties of the sub-THz emission can be explained by our model?

-- separate spectral peak at sub-THz;

-- variability of the low frequency spectral index of sub-THz emission (alpha=1-6);

-- presence and absence of the separate spectral peak at sub-THz; (depends on specific conditions in a flaring loop);

-- fast temporal changes of the sub-THz intensity;

-- time delays between microwave / sub-THz and hard X-ray time profiles

what properties of the sub thz emission we predict to be observed
What properties of the sub-THz emission we predict to be observed?

-- brightness spatial distribution with strong peaks near footpoints of flare loops;

-- the size of sub-THz sources can be large enough (no need to be too small, like 0.5'', as for the simple GS mechanism);

-- magnetic field strength can be not too strong (>2000G) and number density of nonthermal electrons should not to be too high (N(>50keV) ~ 1012cm-3 )!

Future observations in sub-THz to THz range are needed to check the validity of these predictions

needs of observations at higher frequencies
Needs of observations at higher frequencies

ALMA? Space borne FIR experiments

Solar T: P. Kaufmann (PI)

Golay cells for photometry at 45 m and 100 m

On NASA balloon with GRIPS (SSL Berkeley)

Schedule: technical flight in 2012-2013;

long duration flight in Antarctica in 2013-2014

DESIR: K.-L. Klein (PI)

Arrays of microbolometers for photometry and source

location at 35 m and 100 m

Laboratory studies; technical balloon flight

Mission concepts



Предложен гиросинхротронный механизм одновременной генерации двух спектральных пиков (микроволнового и суб-терагерцового) радиоизлучения солнечных вспышек в рамках модели одиночной тонкой вспышечной петли.

Ключевым в модели является образование повышенной концентрации релятивистских электронов в нижней части петли, где соотношение плотности плазмы n0 к магнитному полю B достаточно велико, чтобы частота Разина fR=20 n0/B достигала значений fR ~ 200 ГГц.

Установлено, что в этом случае суб-терагерцовая и микроволновая спектральные компоненты излучения генерируются в различных частях вспышечной петли - вблизи оснований и в ее вершине, соответственно.

Низкочастотная часть суб-терагерцового спектрального пика синхротронного излучения формируется за счет эффекта Разина и ее источник является оптически тонким. Последнее позволяет получить суб-терагерцовый пик излучения как суммарное излучение от протяженной аркады вспышечных петель с общим размером до десятков угловых секунд.

initial and boundary conditions

Initial condition, t

(no electrons at moment t = 0)

Boundary condition,s

(precipitated electrons do not come back into the magnetic loop)

Boundary condition,µ : There exists the exact solution for |µ|1:

Boundary condition,E: , Emax = 10 MeV

Emin = 30 keV

Initial and boundary conditions

. (35)

injection function
































In the case of isotropic injection:

Injection function:

. (35)

influence of the free free absorption on the sub thz emission spectrum
Influence of the free-free absorption on the sub-THz emission spectrum

17 GHz

Sub-THz gyrosynchrotron spectral peak has been disappeared!

Instead, we obtain a significant free-free emission spectral increase!

400 GHz

Plasma density distribution is the same, as for the previous case

Temperature distribution is homogeneous, T = 107 K


As we can see, free-free emission itself can be very important for producing sub-THz spectral component.

This can happen in the case of strong chromospheric evaporation in the lower part of flaring loops.

  • Note, however, that the influence of the free-free absorption on the gyrosynchrotron sub-THz spectral peak can be strongly decreased if we:
  • make the temperature distribution more homogeneous along the loop
  • decrease the plasma density and, in parallel,
  • decrease the magnetic field strength in the loop
  • The last two conditions make the Razin frequency
  • almost unchanged:
  • fR=20n0/B ~ const