OBSERVATION OF MICROWAVE OSCILLATIONS

WITH SPATIAL RESOLUTION

V.E. Reznikova1, V.F. Melnikov1, K. Shibasaki2, V.M. Nakariakov3

1Radiophysical Research Institute, Nizhny Novgorod, Russia2Nobeyama Radio Observatory, NAOJ, Japan

3University of Warwick, UK

NRO, 17 - March, 2005

Quasi-periodical pulsations with short periods 1-20 s

Observations without spatial resolution: Kane et al. 1983, Kiplinger et al. 1983,

Nakajima 1983, Urpo et al. 1992.

Only a few observations with spatial resolution: Asai A. et al. 2001, Melnikov et al. 2002, Grechnev V.V. et al.

2003.

Nobeyama Radioheliograph

Frequency: 17 GHz, 34 GHz

Spatial resolution: 10" (17GHz) 5" (34GHz)

Temporal resolution: 0.1 sec

The flare of 12-Jan-2000

Time profile of total fluxes and spectrum (NoRP)

Microwave time profiles (NoRH)(a,c) NoRH time profiles of the

averaged correlation amplitude: (t)

(b, d) Modulation depth :

0 – slowly varying component of

the emission, obtained by 10-s smoothing the observed signal (t)

0

0)(

t

0

0)(

t

Fourier spectra

Radio pulsation analysis (NoRH) - 2

P1 = 14 - 17 sP2 = 8 - 11 s

Analysis of HXR emission pulsation (WBS/Yohkoh)

Fourier spectra

Spatial structure of microwave

and XR-sources

L = 2.5109 cm (~ 34") d = 6108 cm (~ 8")

L = 2.5109 cm (~ 34") d = 6108 cm (~ 8")

Pulsations in different parts of the loop

Two main spectral components: P1 = 14 - 17 s (more pronounced at the apex ) P2 = 8 - 11 s (relatively stronger at the loop legs)

∆F/F = [F(t)- F0]/F0

Phase shift between oscillations in different parts of the loop

srad 3.15.0

srad 2.25.1

srad 7.05.0 LT

NFP

SFP

Results of analysis:• Pulsations in microwaves and HXR without spatial resolution

are synchronous• Observations with spatial resolution show pulsations to exist

everywhere in the source• they are synchronous at two frequencies 17 and 34 GHz• two dominant spectral components with periods P1 = 14-17 s

and P2 = 8-11 s are clearly seen everywhere in the source• pulsations at the legs are almost synchronous with the quasi-

period P2 = 8-11 s • at the loop apex the synchronism with the legs’ pulsations is

not so obvious, but definitely exists on the larger time scale, P1 = 14-17 s

• phase shift between oscillations from 3 different sources is very small for the P1 component, less than 0.5rad or 1.3s. However it is well pronounced for the P2 spectral component.

Spectrum slope in different parts of the loop

= ln (F34/F17) / ln (34/17)

Near footpoints < 0, near apex > 0

What is the origin of the depression of radiation at 17 GHz

in the upper part of the loop?

• Cyclotron absorption?

• Gyrosinchrotron self-absorption? • Razin suppression?

What is the reason for low frequency depression in the

upper part of the loop?

• Cyclotron absorption? - MDI/SOHO:

at the photosphere level В ≤ 100G around SFP

В ≤ 400G around NFP => fb ~ 1 GHz↓↓

fpeak ~ 20 GHz => spectral peak was at least at

s = fpeak / fb ~ 20

No!

What is the reason for low frequency depression in the

upper part of the loop?

• Gyrosinchrotron absorption?If τ > 1 at 17 GHz =>

- the modulation depth of the emission is expected to be much less pronounced at 17 GHz;

- time profiles of the emission intensity would be smoother than at 34 GHz;

If the modulation of the flux is due to temporal magnetic field

variations :

• f < fpeak ( thick ) :

• f > fpeak ( thin ) :

- the oscillations of the flux at low frequencies (optically thick case) and high frequencies (optically thin case) would be in anti-phase;

Iν В 0.90 -0.22 В4 Iν В 0.90 -0.22 В4

Iν В –0.5-0.085 В-0.9 Iν В –0.5-0.085 В-0.9

Dulk & Marsh, 1982

The observations show just opposite:

- modulation depth at 17 GHz is even higher than at 34 GHz;

- oscillations are in phase at both frequencies;

- observable Тв is less than it is expected from theory;

↓↓

Gyrosinchrotron absorption - No!

Computed Тв(f) dependence for the optically thick source:

=5.3; =75;

Using Dulk, 1985

17GHz 34GHz

B= 100 G

B=400 GB=750 G

Razin suppression (Razin 1960)

• in the medium, where nν < 1 (f p > fB)

• peak frequency depends on the Razin frequency:

• in solar flaring loops: Melnikov, Gary and Nita, 2005 (in press)

sin20

sin3

2 2

B

N

f

ff e

B

pR

Microwave diagnostic of physical parameters inside the loop

ModelModel simulation of gyrosynchrotron spectrumsimulation of gyrosynchrotron spectrum:

N ~ 1~ 1001111 с сmm-3-3

Loop apex: BB 70 G

Loop legs: BB 100 G

N ~ 1~ 1001111 с сmm-3-3

Loop apex: BB 70 G

Loop legs: BB 100 G

LT

FP

Electron’s life time in the loop: Enl

9

0

106.2

(for Ee > 160 keV)

Decay time scales:

no = 1011 сm-3; L = 2.5109 сm; =3÷5

Ee = 1 MeV => l ~ 26 s;

dec ~ 4÷5 s

5.2

l

dec

High value of N0 => short decay time scales (2÷5 s) for burst

sub peaks

SXR - diagnostic at the time of burst maximum (GOES)

SXR- diagnostic at the later stage of the burst (Yohkoh/SXT)

Column emission measure per pixel:

Observable shift of the brightness peaks between 17 and 34 GHz

17 GHz

34 GHz

Cross-section spatial profiles of the intensity for a model flaring loop

34 GHz

17 GHz

cms

sssB9

1

311

106.9

,))/((120

plasma

high energy electrons

Most probable mechanisms for the quasi-periodic microwave

pulsations:Aschwanden, 1987

(for a review)

• oscillation of В in the loop;• variation of angle between В and line of sight;• variation of mirror ratio in the loop, modulating the

loss cone condition;• quasi periodical regime of acceleration / injection

itself;

P~10 s => important role of МHD- oscillations in coronal loop during the flare

Amplitude of magnetic field perturbations

Assuming the pulsations are produced by• variations of the value В in flaring loop: I/I 15 % , if = 5 => relative perturbation of B

B/B 34%

• variations of the viewing angle between the B and the line-of-sight:

if 80, =5 1215

Iν В -0.22+0.90Iν В -0.22+0.90

Iν (sin ) -0.43+.65 Iν (sin ) -0.43+.65

Dulk & Marsh, 1982

Possible MHD-modes of magnetic tube oscillations in coronal conditions:

“sausage”

Zaitsev & Stepanov, 1975Edwin & Roberts, 1983

Mihailovsky, 1981

“kink” “ballooning“

m – azimuthal mode number

Dispersive curves of MHD modesUsing the loop parameters derived from microwave & X-ray diagnostics:

CA0 = 600 km/s

CAe= 3,300 km/s

Cs0 = 340 km/s

Cse = 200 km/s

• sausage (m=0) - solid;• kink (m=1) - dotted;• ballooning(m=2) - dashed

(m=3) - dashed-dotted

}

}

}}}}

l = 1

l = 2

l = 3

l = 4

l = 5

l = 6

Interpretation of the pulsations with Р1 in terms of the Global Sausage Mode:

P1=16s & λ=2L

k = 2π/λ ω=2 π/P

↓↓

Vph = ω/k = 3130 km/s

corresponding normalised longitudinal wave number ka ≈ 0.54 => a ≈ 4.3 Mm

Interpretation of the pulsations with Р1 = 14÷17s in terms of the

Global Sausage Mode:

Nakariakov, Melnikov & Reznikova – 2003 ( A&A 412, L7)

AeGSM C

LP

2

AeGSM C

LP

2 ~ ~ 114 s4 slower limit:

0

62.2

AGSM C

aP

0

62.2

AGSM C

aP ~ ~ 1717 s supper limit:

(from existence condition)

Interpretation of the pulsations with Р2 in terms of the kink mode (2d and 3d

harmoniks)

P2 = 9 s

λ = L

λ = L/2

Conclusions

• Interpretation of quasi-periodic 16s radio pulsations in terms of the Global Sausage Mode (with the nodes at the footpoints) explains all the observational findings for P1 component

• The second periodicity P2= 9s can be associated with several modes:

- Kink mode (2d or 3d longitudinal harmonic)

- Ballooning mode (2d longitudinal harmonic)

Thank you for the attention!

What about f-f absorption?

• N = 1011 cm -3

• B = 50 G• d = 6×108 cm• T = 3×106 K• Θ = 80°

Pressure balance equation

I = /(1 e)I = /(1 e)

Transfer equation solution:

1) τ = L << 1 - optically thin source

I (t) ≈ (t) L; (t) ∞ n (t) =>

I = I(t); = (t); =(t)

I (t) ∞ n (t)

2) τ = L >> 1 - optically thick source

I (t) ≈ (t) / (t); (t) ∞ n (t), ∞ n (t) =>

I (t) ∞ γ n (t) / n (t) = γ I (t) ∞ γ

Influence of high plasma density: Razin effect

at 17 GHz

Maximum gyrofrequency in the source:If B=400 GfB = 2.8 x 10e6 x 400 = 1.120 GHz

Maximum plasma frequency in the source:If N=10 11cm-3

fp = 9 x 10e3 x 3.3 x 10e5 = 29.7 10e8 = 2.9 GHz

• Va = B/(4πnmp)1/2

• Vs = (3kT/mp) 1/2