Introduction
Observation
Data noise
Methods
Conclusion
The measurement of the apparent phase speed of
propagating disturbances
D. Yuan and V. M. Nakariakov
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
See paper Yuan & Nakariakov 2012 A&A (submitted)
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
1
Introduction
2
Observation
3
Data noise
AIA image flux noise
Uncertainties in the enhance time-distance plot
4
Methods
Cross-fitting technique
2D coupled fitting
Best similarity match
5
Conclusion
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Introduction
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
AIA observation
(b)
(a) 27-Oct-11 04:30:01
Time (min)
100
Y (arcsec)
(c)
25
50
0
-50
20
15
10
5
-100
-250 -200 -150 -100 -50
X (arcsec)
0
0 5 10 15 0 5 10 15
Distance (Mm)
p q
p q p q p q
N {°
21
C psm , tk h q{N with N 50.
D psm , tk q rC psm , tk q B psm , tk qs{B psm , tk q, where B psm , tk q Figure:
a) AIA 171 Å image on AR 11330. A cut was taken C sm , tk as indicated with black bar. b)
Running difference R1 (R2 ): R sm , tk
C sm , tk
C sm , tk l with l
9. c) D1 (D2 ):
h
D. Yuan and V. M. Nakariakov
N {2
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
AIA image flux noise
Uncertainties in the enhance time-distance plot
AIA image flux noise
2
p q σphoton
pF q
2
σnoise
F
2
σdark
2
σreadout
2
σsubtract
2
σdigit
p q
2
σcompress
2
σspikes
F
F
1.152
p1 0.252 q 17.7
?
2.3 0.06F p DNq
a
σphoton pF q F {Gλ
σcompress 0.25σphoton
σreadout 1.15 DN
σdigit 0.5 DN
σdark 0.5 DN
a
σsubtract 2 0.52 0.7 DN
σspike pF q 0.006 0.15F 0.0009F
4
0.52 p0.0009F q2
ref.: Yuan & Nakariakov 2012, Aschwanden et al 2001, Boerner et al 2011
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
AIA image flux noise
Uncertainties in the enhance time-distance plot
Data noise σnoise(F) (DN)
AIA image flux noise
12
10
Figure:
8
σtotal
σphoton
σcompress
σdespike
σothers
6
4
2
0
10
100
1000
Flux value (DN)
pq
The data noise σnoise F (+) as a function of pixel flux F in AIA 171 Å images
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
AIA image flux noise
Uncertainties in the enhance time-distance plot
Uncertainties in enhance time-distance plot
Running difference
a plot:
σ pR psm , tk qq σ 2 pC psm , tk qq
σ 2 pC psm , tk 9 qq
Background-removed time-distance plot:
σ pD psm , tk qq σ pC psm , tk qq{B psm , tk q
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
CFT method
For X psm , tk q, either R1 (R2 ) or D1 (D2 )
At each pixel, X psm , q is fitted with As cospωs t
At each image (time), X p, tk q is fitted with
At cospkt x φt q δt
Vp
φs q
δs
ω{k is obtained combining the average of the above fits.
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
Distance (Mm)
CFT method and its application
15
15
10
10
5
5
k (Mm-1)
0
1.5
0
5
10
15
20
25
0
1.5
0.00 0.02 0.04 0.06
vp=ω/k
1.0
1.0
0.5
0.5
0.0
0
5
10
15
20
Time (min)
25
0.0
0.00 0.02 0.04 0.06
ω (rad/s)
CFT application to R1 : ω 0.0347 0.00002 rad{s, k 0.738 0.002 Mm1 ,
181.2 0.1 s, Vp 47.0 0.1 km{s
Figure:
P
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
DCF method and its application
Distance (Mm)
15
10
5
0
0
Figure:
5
10
DCF application to R1 : P
D. Yuan and V. M. Nakariakov
15
20
Time (min)
25
240.7 0.7 s,Vp 48.8 0.2 km{s.
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
BSM methods
A parametric model
? image is generated with
MVp ,P,φ psm , tk q 2RMS pX psm , tk qq cospωtk
ksm
The similarity is quantified as
Lp pM, R q m°
N k °N
φq.
1{2
|M psm , tk q X psm , tk q| .
For each combination of Vp P r20, 120s km{s, P P r150, 200s s
and φ P r0, 2π s, Lp pM, R q is calcualted.
s
t
2
m 1 k 1
Locating Lmin
in the parametric space, and selecting a set of
p
1% above minimum, We are able to get the mean values and
their uncertainies.
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
BSM method and its application
Distance (Mm)
15
10
5
0
0
Figure:
5
10
BSM application to R1 , P
D. Yuan and V. M. Nakariakov
15
20
Time (min)
25
180.0 1.8 s,Vp 47.0 2.6 km{s.
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
BSM method and its application to regularised image
Distance (Mm)
15
10
5
0
0
Figure:
5
10
BSM application to R1σ , P
D. Yuan and V. M. Nakariakov
15
20
Time (min)
25
180.0 1.0 s,Vp 48.0 1.3 km{s.
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
Comparison of the measurements
Table:
A comparison of the measured results of CFT, DCF and BSM methods
R1
R2
R1σ
R2σ
D1
D2
D1σ
D2σ
P (s)
Vp (km/s)
P (s)
Vp km/s
P (s)
Vp km/s
P (s)
Vp (km/s)
P (s)
Vp (km/s)
P (s)
Vp km/s
P (s)
Vp km/s
P (s)
Vp (km/s)
0.1
0.1
0.2
0.3
CFT
181.2
47.0
179.7
48.1
...
...
...
...
180.0
45.8
180.0
48.6
...
...
...
...
0.1
0.2
0.2
0.4
D. Yuan and V. M. Nakariakov
0.7
0.2
0.9
0.3
DCF
240.7
48.8
177.2
65.8
...
...
...
...
198.9
44.5
250.5
51.4
...
...
...
...
0.7
0.2
2.2
0.5
1.8
2.6
2.0
4.5
1.0
1.3
1.0
2.6
1.0
1.4
1.0
2.8
1.31.0
2.30.9
BSM
180.0
47.0
178.0
49.0
180.0
48.0
180.0
50.0
180.0
47.0
178.0
49.0
180.0
48.0
180.0
50.0
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
Comparison of the measurement
Vp (km/s)
60
55
R1
R2
45
40
200
Period (s)
D1
D2
50
190
R1
R2
CFT
DCF
BSM
BSM(σ)
CFT
DCF
BSM
BSM(σ)
D1
D2
CFT
DCF
BSM
BSM(σ)
CFT
DCF
BSM
BSM(σ)
180
170
160
Figure:
A Comparison of the measurement CFT, DCF, BSM and its application to regularised images BSM(σ).
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Cross-fitting technique
2D coupled fitting
Best similarity match
55
50
50
Vp (km/s)
55
45
40
45
40
35
200
35
200
190
190
Period (s)
Period (s)
Vp (km/s)
Comparison of the measurement
180
170
160
0
50
100 150 200
Lag Time (s)
0
10
20
30
40
Detrending Time (min)
Figure:
180
170
160
0
50
100 150 200
Lag Time (s)
0
10
20
30
40
Detrending Time (min)
The meaurement of R1 and D1 as functions of lag time and detrending time respectively (left panels),
and those of R2 and D2 (right panels). The measurements of CFT, BSM and BSM (σ) are plotted with , and
respectively.
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis
Introduction
Observation
Data noise
Methods
Conclusion
Conclusion
CFT, DCF and BSM are valid and robust methods to
meaurement the phase speed of propagating disturbances.
CFT, DCF and BSM are in general more robust in measuring
background removed samples than running differences.
Samples with longer valid detection lengh are more suitable
for the above methods. They sustain more variability of lag
time and detrending time.
D. Yuan and V. M. Nakariakov
The measurement of the apparent phase speed of propagating dis