Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Slow magneto-acoustic waves in coronal loops
E. Verwichte1, V.M. Nakariakov2, D. Berghmans1, J.-F. Hochedez1
1 Solar
Physics Department
Royal Observatory of Belgium
2 Space
and Astrophysics Group
University of Warwick
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Coronal seismology
comparison between
a high-cadence observation of propagating dissipative
slow magneto-acoustic waves in large coronal loops
with
a one-dimensional, analytical model of propagating, weakly nonlinear
slow magneto-acoustic waves in dissipative, stratified coronal loops
of variable cross-section.
and measure
properties of the solar corona: e.g. geometry, fine-structuring, dissipation
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Observations
JOP80 high-cadence program
May 13 1998, AR8218
Use TRACE and EIT
Instrument
Band pass
Temperature
Sound speed
Cadence
Pixel size
Start time
End time
EIT
195 Å
1.6 MK
192 km/s
15 s
2.59
17h31m50s
18h29m07s
TRACE
171 Å
1.0 MK
152 km/s
25 s
0.5
17h03m28s
18h07m17s
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Evidence of upwards propagating disturbances in large loops
2 3 4 56 7
1
17:10:12
17:12:00
17:13:48
17:15:36
17:17:24
75
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Characteristics of disturbances
The slow waves are measured along loop paths.
The same paths are chosen in the two band passes.
Characteristics of slow waves along the 7 paths
Path
VP (km/s)
α (°)
1
2
3
4
5
6
7
average
101 ± 11
111 ± 7
94 ± 7
60 ± 7
107 ± 17
97 ± 12
108 ± 9
101
53
67
58
60
56
57
55
58
85 ± 26
74 ± 5
86 ± 5
53 ± 6
87 ± 12
83 ± 4
72 ± 10
84
P (s)
44
60
55
61
54
56
64
56
12,38
4-8
4-8, 35
10
15
17
21
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Characteristics of disturbances indicate slow magneto-acoustic waves
Projected propagation speed VP = 65-150 km/s , always below
sound speed of band pass
projection angle α is found.
Higher VP in EIT 195 compared to TRACE 171 is explained by the
difference in sound speed at each band pass.
projection angle α is consistent, also with limb observation
Propagation speed does not change over 100 Mm
straight loop
Periods P = 5-20 min
Intensity amplitude = 8-12 % of background
Intensity amplitude decays with distance
weakly nonlinear
dissipation
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Intensity along path: distance vs. time
Royal Observatory
of Belgium
Projected distance (Mm)
Time
The projection angle
α is found from
observations:
α= 54° ± 5°°
Intensity along wave front
(integrated between the two
dashed lines)
Path 6
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Fine-structuring of coronal loops
¥Same path in TRACE and EIT sequence, co-aligned within 1-2 EIT pixels
(< 3600 km)
Observe propagating waves in both temperatures, but at different speeds
but Vprop / CS = constant
travel through same volume of space
Only possible if loop has fine-structuring (< 3600 km) with sharp Tgradients (possible due to inhibited perpendicular thermal conduction).
Valuable to have simultaneous observations at diff. T (but not too different
so that same structure can be observed) at high resolution and cadence
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Loop intensity and relative intensity of variations
along loop path following the wave front (TRACE)
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Analytical model
Loop is a 1D longitudinal structure along z-coordinate.
Loop is stratified : gravity along z : g = g¥ dh/dz (1+h/R¥)-2
Loop cross-section A(z) varies with distance.
Loop is isothermal and in hydrostatic equilibrium : CS = const.
dissipative MHD:
with compressive viscosity and parallel thermal conduction
weakly nonlinear: ε = V / CS << 1
weakly dissipative: of order ε
weakly stratified limit: λ / H << 1
coordinate stretching Z = ε2 z, ξ = z - CS t
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Evolutionary equation of slow magneto-acoustic waves
1 dA
γ + 1 ∂V η ρ0 (0) ∂ 2V
∂V
1
V −
=0
V+
−
V+
2
2CS ∂ξ 2 ρ0 (Z) ∂ξ
A(Z) dZ
∂Z 2H(Z)
stratification cross-section nonlinearity
(γ −1)
1
4
η=
η0 +
κ
ρ0 (0)CS 3
CP
2
dissipation
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Expected relative intensity and dissipation
From theory and typical coronal values:
Only viscosity: η= 0.08 Mm
With thermal conduction: η up to two orders of magnitude larger.
We assume from observations:
Straight loop
constant α
Linear waves
Harmonic wave: V ∝ cos(kξ
ξ)
A increases 4 x over 100 Mm
Relative intensity along wave front
ηk2 Z ρ0 ( Z')
−
2 0 ρ0 ( 0)
2V(0) 1
1
δi
(Z) =
e
I0
CS ρ0 (Z) A(Z)
ρ0 (0) A(0)
−1
dZ'
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Straight loop h(Z) = sin(π/4) Z, ρ0 = 8 1013 kg/m3, T = 1 MK, k = 2 π / (C 300s).
0
S
η= 0.3 Mm, η = 1.0 Mm and η = 3.0 Mm
loop cross-section = constant
Straight loop h(Z) = sin(π/4) Z, ρ0 = 8 10-13
kg/m3, T0 = 1 MK, k = 2 π / (CS 300s),
η = 0.3 Mm, A(Z) = A(0) (1 + (2n/2-1) Z / ∆Z)
with n=0,1,2,3
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Comparing observation with model
Estimate the rate of dissipation
in the corona.
If we assume a wave period
of 5 minutes, we obtain
η= 1.5 ± 0.8 Mm
η= 24 ± 12 Mm (20 min period)
observation
model
In agreement with
theoretical expectations
Slow magneto-acoustic waves in coronal loops
E. Verwichte, V.M. Nakariakov, D. Berghmans, J.-F. Hochedez
Royal Observatory
of Belgium
Future observations :
Solar Orbiter and High Resolution Imager
Significant signal
SNR 2d 2
L
< ∆t <
Asun Aeff P0a
Vprop
For same resolution and cadence:
25 x shorter exposure time.
For full resolution:
4 x longer exposure time
Following dynamics,
no motion blurring
HRI: 5 x closer to sun and
10 x higher resolution
For using full resolution and no motion blurring:
L = 2 √Asun and V = 200 km/s (slow) & 2000 km/s
(fast): ∆t < 0.5-0.05 s
need to improve Aeff by a factor of 100-1000 (e.g.
BOLD project).