MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Multi-instrumental and -wavelength observations on
coronal waves and oscillations
D. Yuan
Email: Ding.Yuan@warwick.ac.uk
Centre for Fusion, Space and Astrophysics
Department of Physics, University of Warwick
Gibbet Hill Road, Coventry CV4 7AL, UK
Thanks to V.M. Nakariakov, V. Verwichte, M.J. Aschwanden, C. Foullon and
N. Chorley.
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
1
2
3
MHD waves and coronal seismology
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
Novel Coronal seismology
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
MHD waves in magnetised plasma
Ideal MHD in homogeneous
plasma
ρ(x, t) = ρ0
B(x, t) = B0
Dispersion Relation:
Alfvén wave: ω 2 = VA2 kq2
Magnetoacoustic waves:
ω 4 − (Cs2 + VA2 )k 2 ω 2 +
Cs2 VA2 kq2 k 2 = 0
Group speed:
Fast magnetoacoustic wave
(expanding red ring)
Slow magnetoacoustic wave
(propagating blobs)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
MHD waves in cylindrical geometry
Ideal MHD in magnetic cylinder
(
B0 , ρ0 , p0 ,
B0 (r ), ρ(r ), p0 (r ) =
Be , ρe , pe ,
r < a;
r > a.
Dispersion Relation (Edwin & Roberts 1983):
′
2
ρe (ω 2 −kz2 VAe
)m0
2
where mα
=
′
In (m0 a)
K (me a)
2
+ρ0 (kz2 VA0
−ω 2 )me n
=0
In (m0 a)
Kn (me a)
2
2
(kz2 Csα
−ω 2 )(kz2 VAα
−ω 2 )
2 +V 2 )(k 2 C 2 −ω 2 ) , α
(Csα
z Tα
Aα
= 0, e
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
MHD waves in cylindrical geometry
Figure.The phase speed ω/kz
as function of kz a for
magneto-acoustic waves in a
cylindrical fluxtube for
coronal conditions
VAe > VA > CT > Cs ,
n = 0, 1, 2, 3 correspond to
sausage, kink and flute
modes (solid, dotted, dashed,
dash-dotted curves) see
Nakariakov & Verwichte
2005
Fast modes
Slow modes
↓
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
Fundamental standing and propagating sausage modes
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
Fundamental standing and propagating kink modes
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
MHD waves in magnetised plasma
MHD modes in cylindrical geometry
Coronal seismology
First kink oscillation observed with TRACE
Figure: Loop position as function of time, fitting with
a(t) = a0 sin(2πt/P + φ) exp(−t/τ ) (Nakariakov et
al.1999, Nakariakov & Ofman 2001)
2
Ck2 = ( 2L
P ) =
D. Yuan
2 +ρ V 2
ρ0 VA0
e Ae
ρ0 +ρe
=
2B02
µρ0 (1+ρe /ρ0 )
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Part II: Coronal seismology with two adjacent
oscillating loops
D. Yuan 1 , V.M. Nakariakov
D. Yuan
1
and M.J. Aschwanden
2
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Solar Dynamics Observatory(SDO) and Atmospheric
Imaging Assembly (AIA)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Solar Dynamics Observatory(SDO) and Atmospheric
Imaging Assembly (AIA)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Solar Dynamics Observatory(SDO) and Atmospheric
Imaging Assembly (AIA)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Transverse oscillation triggered by a M2.9 GOES flare
AIA 195 A, 2010-10-16 19:22:36 UT
Oscillating Loop
NS (arcsec from Sun center)
-200
Flare center
-400
-600
-800
0
200
400
600
EW (arcsec from Sun center)
800
Figure: The location of the M2.9 flare and oscillating loops (Aschwanden &
Schrijver ApJ 2011)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Observation with AIA EUV 171Å
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Observation with AIA EUV 171Å
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Smaller FOV with AIA EUV 171Å and 131 Å
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
DEM Forward Modelling
The image Rflux is defined as
,x,y )
Rλ (T )dT , where Rλ (T ) is the filter
Fλ (x, y ) = dEM(T
dT
response function, dEM/dT is the differential emission
measure (DEM).
The DEM is simplified as single Gausian,
[log(T )−log(Tp (x,y ))]2
dEM(T ,x,y )
= EMp (x, y ) exp(−
)
dT
2σ2 (x,y )
T
The best fit is obtained by minimising the goodness-of-fit
P obs
model (x,y ,λ )
k )−F
k
χ2 (x, y ) = (n−n1 free ) k F (x,y ,λ
σ2 (x,y ,λ )
F
k
See Aschwanden & Boerner 2011 Solar Phys.
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
DEM Forward Modelling of coronal loops
A linear cross-section background is removed
2
0)
F obs (x) = Fλloop exp(− (x−x
) + c0 + c1 (x − x0 )
2σ2
w
The loop width is defined as FWHM w (s) = 2.35σw (s),
where s is the length along the loop
The loop electron q
density is estimated by assuming unit filling
loop
loop
factor, ne (s) = EMw (s)(s)
See Aschwanden & Boerner 2011 Solar Phys.
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
101016_19.20-Loop #171A/ 0 - iter: 1
Temperature log(Te)
DEM modelling of loop # 0
171A
1680
Density log(ne)
1660
1640
1620
1600
3100 3120 3140 3160 3180 3200 3220 3240
Figure: First iteration: Te = [0.5, 10] MK,
σT = [0.1, 1]; second iteration,
Te1 = [Te0 ± 3∆Te0 ], σT 1 = [σT 0 ± 3∆σT 0 ]
log(Te)= 5.95_
5.95+ 0.10
log(σT)= 0.07_
0.07+ 0.07
7.5
7.0
6.5
6.0
5.5
9.0
8.9
8.8
8.7
8.6
8.5
8.4
8.3
12
10
0
5
10
15
20
25
20
25
log(ne)= 8.56_
8.56+ 0.10
0
5
10
15
w= 3.24_
3.24+ 0.19 nw= 25 pix
8
6
4
2
0
5
Goodness-of-fit χ
1560
Loop width w(Mm)
1580
8.0
0
5
10
15
20
25
20
25
χ= 0.83_
0.83+ 0.53
4
3
2
1
0
0
D. Yuan
5
10
15
Loop length s[Mm]
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Temperature log(Te)
DEM modelling of loop # 1
171A
101016_19.20-Loop #171A/ 1 - iter: 1
1680
Density log(ne)
1640
1620
1600
log(Te)= 6.11_
6.11+ 0.03
log(σT)= 0.08_
0.08+ 0.10
7.5
7.0
6.5
6.0
5.5
9.0
1660
0
5
10
15
20
25
20
25
log(ne)= 8.66_
8.66+ 0.08
8.9
8.8
8.7
8.6
8.5
3120
3140
3160
3180
3200
3220
3240
Figure: First iteration: Te = [0.5, 10] MK,
σT = [0.1, 1]; second iteration,
Te1 = [Te0 ± 3∆Te0 ], σT 1 = [σT 0 ± 3∆σT 0 ]
12
10
0
5
10
15
w= 2.65_
2.65+ 0.22 nw= 25 pix
8
6
4
2
0
5
Goodness-of-fit χ
1560
Loop width w(Mm)
1580
3100
8.0
0
5
10
15
20
25
20
25
χ= 0.45_
0.45+ 0.46
4
3
2
1
0
0
D. Yuan
5
10
15
Loop length s[Mm]
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Summary of the measured parameters
First iteration:
Second iteration:
loop #0
loop #0
log(Te ) = 5.91 ± 0.16
log(Te ) = 5.95 ± 0.10
σT = 0.12 ± 0.06
σT = 0.07 ± 0.07
log(ne ) = 8.62 ± 0.15
log(ne ) = 8.56 ± 0.10
w = 3.24 ± 0.54
w = 3.24 ± 0.19
2
χ2 = 0.83 ± 0.53
χ = 1.00 ± 0.64
loop #1
loop #1
log(Te ) = 6.11 ± 0.07
log(Te ) = 6.11 ± 0.03
σT = 0.13 ± 0.07
σT = 0.08 ± 0.10
log(ne ) = 8.67 ± 0.12
log(ne ) = 8.66 ± 0.08
w = 2.65 ± 0.64
w = 2.65 ± 0.22
2
χ2 = 0.45 ± 0.46
χ = 0.86 ± 0.70
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Coronal seismology: loop #0
B0
L
P
ni
ne /ni
P
Bkink
Bapex
Bavg
q
L
8πµmp ni (1 + ne /ni ) = 5.3 ± 0.9 G
P
= 143 ± 20 Mm, (3D stereoscopic reconstruction)
= 373 ± 30 s = 6.2 ± 0.5 min
=
= 108.55±0.08cm−3
≃ (VAi /VAe )2 = 0.08 ± 0.01, assuming VAe = Vexc = Lexc /Texc
r
2L 1 + ne /ni
2L
=
=
Ck
VAi
2
Comparison with Aschwanden & Schrijver 2011 ApJ
= 4.0 ± 0.7 G (seismological value)
= 6 G (dipole potential field model)
Z
−1
−1
=
B(s) ds
= 11 G (Alfvén transit time averaging)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Coronal seismology: loop #1
B0
B1
L0
L1
P1
P0
=
L0 P1 ni 0 0.5
( ) = 0.50 ± 0.12
L1 P0 ni 1
= 0.89 (assuming coplanarity)
= 0.90 (forwarding modelling)
0.5
σ(B0 /B1 ) = 2σ 2 (L) + 2σ 2 (P) + (0.5σ(ni 0 ))2 + (0.5σ(ni 1 ))2
B1
= 0.24
B0
=
= 10.6 ± 3.1 G
(B0 /B1 )
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Conclusion
The coronal loops are found isothermal with very thin
temperature profile.
A novel coronal seismology method is developed based on
relative measurement.
B2
2
B2
Equilibrium condition p0 + 2µ0 = pe + B2µe = p1 + 2µ1 does not
apply, thus the standard model has to be improved (twisted
flux tube model?)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Solar Dynamics Observatory
Multi-wavelength observation with SDO
Differential emission measure
Estimation of magnetic fields
Conclusion
Work in progress
The phase speed in the twisted flux tube model only depends
on Bz , no influence from Bθ (Ruderman, private
2Bz2
2
communcation): Ck2 = ( 2L
P ) = µρ0 (1+ρe /ρ0 )
The equilibrium condition changes to
B 2 +B 2
B 2 +B
p0 + z02µ θ0 = p1 + z12µ θ1
We obtain a measure of relative twist, a new entry to coronal
seismology.
A new model of twisted flux tube has to be developed. This
also supports the constant cross-setions along the loop
(Klimchuk 1992 PASJ).
Is the stability condition retained ?
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Leakage of long period oscillations from the
chromosphere to the corona
D. Yuan , V.M. Nakariakov, N. Chorley and C. Foullon
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Long period oscillations at various solar atmospheric levels
Long period oscillations (tens to hundreds min) were detected
as modulations to the sunspots radio emissions (Gelfreikh et
al. 2006, Chorley et al. 2010)
Long period oscillations (10 - 30 min) are measured in the
corona by EIT (Berghmans & Clette 1999), TRACE
(McIntosh et al 2008), STEREO/EUVI (Marsh et al 2009),
Hinode (Wang et al 2009)
Theoretical study disapprove their connectivity, only the
periods below the cut-off period (200-300 s at chromosphere)
are non-evanescent as acoustic wave (Bel & Leroy 1977).
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Long period oscillations in the outer heliosphere
the 30 min oscillation were detected at 1.9 R⊙ in a polar
coronal hole with the polarised white light brightness (Ofman
et al. 2000)
The low-energy charged particle flux were found to be
modulated by the interplanetary magnetic field, which may be
of solar origin (similar period of the solar interior p- and
g -modes, see Thomson et al. 1995)
A high correlation was found between the ultra-low frequency
(ULF) of the Earth’s magnetosphere and the solar wind
density variations. There was unexplained ULF at 0.1, 0.2 0.6
mHz that were speculate to be related with solar g -mode
(Kepko & Spence 2003).
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Courtesy of NASA
0
10
20
30
40
50
60
70
80
60
50
90
100
60
Sunspot oscillations 10 - 102 min
❤ Polar plume and interplume oscillation ∼ 30 50
min
40
40
❄
❤ Charge particle flux
30 mod
30
✻
20
10
✛
20
Corona oscillation: (10 - 30 min)
Solar gravity modes: (16 min - 28 h)
D. Yuan
10
Multi-instrumental and -wavelength observations on coronal wave
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Courtesy of NASA
0
10
20
30
40
50
60
70
60
80
90
100
60
Charge particle flux modulation by interplanetary magnetic field
50 at
50
❄
40
40
✻
30
20
30
20
High correlation of ULF and SW density variation at sub-mHz regio
10
10
0
0
10
20
30
0
and -wavelength
on 100
coronal wave
40D. Yuan 50 Multi-instrumental
60
70
80 observations
90
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
NOAA AR8253
Figure: NOAA AR8253 observed by TRACE 171 Å (left), the region of interest
(middle), NoRH 17 GHz radio intensity map (right) at 1998-07-01 00:01 UT
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Dataset
radio
195Å
171Å
00:00
04:00
08:00
12:00
16:00
Start Time (30−Jun−98 00:00:00)
20:00
00:00
04:00
08:00
12:00
16:00
Start Time (01−Jul−98 00:00:00)
20:00
00:00
04:00
08:00
12:00
16:00
Start Time (02−Jul−98 00:00:00)
20:00
00:00
04:00
08:00
12:00
16:00
Start Time (03−Jul−98 00:00:00)
20:00
00:00
04:00
08:00
12:00
16:00
Start Time (04−Jul−98 00:00:00)
20:00
Figure: Daily Observation over AR8253 by TRACE and NoRH
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Orbital Effect
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Non-linear Mapping
Assume CCD temperature T = T0 + δT cos( 2πt
P + φ), where
P ≃ 96 min,1/P ≃ 0.17 mHz
Average Intensity I = F (T (t)) is a non-linear mapping of
T (t), and expand it in Taylor series:
dF
d 2F
δT +
(δT )2 + . . .
dT
2!dT 2
2πt
2πt
+ φ) + a2 cos2 (
+ φ) + . . .
= a0 + a1 cos(
P
P
2πt
2πt
2πt
= b0 + b1 cos(
) + b2 cos(
) + b3 cos(
) + ...
P
P/2
P/3
F (T ) = F (T0 ) +
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Power Spectrum
Figure: Power spectra of a macro-pixel of 3 × 3 and 20 × 20 in 171 Å
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Power Spectra
Figure: Power spectra of the macro pixel (171Å) after filtering out orbital
artifact (left panel, ŷ (t) = y (t) − (a0 + a1 sin ωt + a2 cos ωt), Ferraz-Mello
1981 AJ) and NoRH sunspot emission (right panel)
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Significance tests
Horne & Baliunas Test (see Horne & Baliunas ApJ 1986)
The data noise are purely Gaussian
The probability of PN (ω) = PX (ω)/σ 2 is of height > z is
Pr [PN (ω) > z] = e −z
The false alarm probability is FAP = 1 − (1 − e −z )Ni
Fisher’s Randomization test (Linnell Nemec & Nemec AJ
1985)
Independent of noise distribution
Shuffle the time series yδk ↔ yδj
if |tδk − tδj | = Tn = 2π/ω0 , there is probality that we detect a
higher peak at ω0
Repeat M times, if a higher peak is detected for K times,
p = K /M
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Detected peaks
Table: Summary of the detected peaks and significance tests.
TRACE 171Å
f (mHz)
P (min)
p-value
TRACE 195Å
f (mHz)
P (min)
p-value
NoRH 17 GHz
f (mHz)
P (min)
p-value
Average frequency (mHz)
0.222 ± 0.008
75 ± 2.7
< 0.01
[0.202 ± 0.008]
[83 ± 3.3]
< 0.01
0.220 ± 0.020
75 ± 6.9
< 0.01
0.221 ± 0.020
0.302 ± 0.008
55 ± 1.4
< 0.01
[0.320 ± 0.008]
[52 ± 1.3]
0.20
0.314 ± 0.019
53 ± 3.2
< 0.01
0.312 ± 0.020
0.579 ± 0.008
29 ± 0.4
< 0.01
0.559 ± 0.009
30 ± 0.5
< 0.01
0.582 ± 0.019
29 ± 0.93
< 0.01
0.573 ± 0.020
All listed frequencies and corresponding periods have FAP < 0.01 according to
the Horne & Baliunas test, except for the values indicated between square
brackets (found in the 195 Å time series and of potential relevance given their
closeness to significant values found in other bandpasses). The p-value
indicates the false alarm probability from the Fisher randomisation test.
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave
MHD waves and coronal seismology
Novel Coronal seismology
Leakage of long period oscillations
Long period oscillations at solar interior, atmosphere and beyond
Multi-instrument observation with TRACE and Nobeyama
Orbital effect
Results
Conclusion
Conclusion
The orbital frequency and its harmonics have strong impact on the
intensity of EUV images, due to the non-linearity of orbital
environment, detection efficiency, and complexity of telescope
system. It has to be accounted when studying the long period
intensity oscillation. it applies to other missions in the sun
synchronous orbits, Hinode, Yohkoh, Corona-photon etc.
0.221 mHz, 0.312 mHz and 0.573 mHz oscillations are both
detected in TRACE EUV light curves and NoRH radio 17 GHz
emission.
Their detectability in the corona can be the leakage along the
magnetic field line from the chromosphere or the remnants of
evanescent waves with large penetration depth.
There values are well wanted solar interior g -mode, 0.221 mHz and
and 0.573 mHz are close to l = 2, n = −3 or l = 3, n = −5, and
l = 3, n = −3 and l = 1, respectively.
D. Yuan
Multi-instrumental and -wavelength observations on coronal wave