МИКРОВОЛНОВОЕ И СУБ-ТГЦ ИЗЛУЧЕНИЕ ВСПЫШЕЧНОЙ ПЕТЛИ

В.Ф. Мельников, ГАО РАН, Санкт-Петербург, РоссияJ.E.R. Costa, INPE, S.J. Campos, Brazil

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

7-я Ежегодная Конференция "Физика плазмы в солнечной системе"

(6 - 10 февраля 2012 г., ИКИ РАН)

2011 2

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.

2011 3

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

Costa, Simões, Giménez de Castro

4

Normal extention of microwave spectrum With sub-THz component

SST

OVSA

Types of Radio Spectra in microwave – sub-THz range

Costa, Simões, Giménez de Castro

5

August 25, 2001

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

August 25, 2001

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

April 12, 2001

GOES X2.0 GOES X5.3

Types of Radio Spectra in microwave – sub-THz range

2011 6

So far: About 15 major flares (GOES M3.2 - > X28) have been detected at frequencies 200, 400 GHz

• 7 to 8 normal events reportedKaufmann 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 reportedKaufmann et al. 2002, 2004; Lüthi et al. 2004b; Silva et al. 2007; Cristiani et al. 2008

Trottet et al, 2011

2011 7

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.

2011 8

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:

a) the importance of Razin suppression on the formation of observed gyrosynchrotron spectra in microwave bursts; and

b) the spatial distribution of gyrosynchrotron emission generated by anisotropic fluxes of accelerated electrons in inhomogeneous flaring loops

2011 9

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):

f

E

cf

ds

Bdc

s

fc

t

f

0

2

2

1ln

),,,(1 223

0

tsESfc

Kinetics of Nonthermal Electrons in Kinetics of Nonthermal Electrons in Magnetic Magnetic LoopsLoops

2011 10

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 ~ 104 sfu.

We assume that the magnetic field is distributed exponentially along the loop: B(s)=Bmin exp(-s2/sB

2) 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.

Different acceleration models give three basic predictions on

the position of the acceleration site and pitch angle distribution

homogeneous at the looptop near a footpoint

isotropic longitudinal perpendicular

2011 12

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:

2011 13

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

2011 14

Magnetic field distribution is assumed to be B(s)=Bmin exp(-s2/sB

2) 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 small plasma density in the lower parts of the magnetic loop)

34 GHz 400 GHz

tm

ts

2011 15

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.

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

FP1 LT FP2 FP1 LT FP2

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

2011 16

Razin-effectLienard-Wiechert potentials: In vacuo:

e is the electron charge, and R is the radius-vector of the electron moving with velocity v taken at the retarded time t’ = t-nR/c.

H(t) = rot A(t)

E(t) = -(1/c) ∂A/ ∂t - ∆φ

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

2011 17

In a plasma, a refraction index

n =1 - fp2/ f 2 < 1

the denominator can never be very close to 0, even if v is close to c. So a relativistic electron has an emission efficiency comparable with a

nonrelativistic one, i.e. much lower than in vacuo. This causes a strong suppression of radiation in the plasma, especially at lower frequencies,

f < fR=20n0/B

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

In plasma:

2011 18

Left hand spectra are from the middle part of the loop

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

Gyrosynchrotron frequency spectrum in different parts of a flaring loop

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

17 GHz

400 GHz

2011 19

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)

t1

t2

2011 20

Bmin=400 G, Bmin=100 G, n0max=1013 cm-3 n0max=1012 cm-3

2011 21

Conclusions

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 >= 200 GHz. 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.

2011 22

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

2011 23

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

2011 24

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 mOn 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 mLaboratory studies; technical balloon flightMission concepts

2011 25

Thank you for your attention!

2011 26

Абстракт

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.

2011 27

Initial and boundary conditions

.0)0,,,( sEf Initial condition, t

,0),,0,( min tsEf .0),,0,( max tsEf Boundary condition, s

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

(no electrons at moment t = 0)

Boundary condition, E : , Emax = 10 MeV Emin = 30 keV

1

230

20

212

fcf

sc

t

f

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

0),,,(

0),,,(

min

max

tsEEf

tsEEf

2011 28

Injection function:

)/()( 01 EEES

constS )(2

]/)(exp[)( 20

213 ssssS

]/)(exp[)( 20

214 ttttS

In the case of isotropic injection:

]/)(exp[)( 20

212 S

),()()()(),,,( 4321 tSsSSEStsES

2011 29

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

Plasma density distribution is the same, as for the previous caseTemperature distribution is homogeneous, T = 107 K

17 GHz

400 GHz

Sub-THz gyrosynchrotron spectral peak has been disappeared!

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

2011 30

Note, however, that the influence of the free-free absorption on the gyrosynchrotron sub-THz spectral peak can be strongly decreased if we:

1) make the temperature distribution more homogeneous along the loop

2) decrease the plasma density and, in parallel, 3) decrease the magnetic field strength in the loop

The last two conditions make the Razin frequency almost unchanged:

fR=20n0/B ~ const

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.