Seismology of sunspot
atmosphere
Yuzef D.Zhugzhda
IZMIRAN
1
History of first observations
chromosphere:
umbral flashes in Ca II H+K (1969: Beckers & Tallant; Wittmann)
running PU waves in Hα
(1972: Giovanelli; Zirin & Stein)
photosphere:
umbra
(1972: Beckers & Schultz; Bhatnagar et al.)
penumbra (PU) (1976: Musman et al.)
CCTR (chromosphere-corona transition region):
umbra only (1982: Gurman et al.; 1984: Henze et al.)
(similar to chromosphere)
corona:
umbra only, debate (many observations related to flares),
UV and microwave oscillations above quiet umbra
(1999: Gelfreikh et al.; 2001: Shibasaki et al.)
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3-min oscillations
Chromosphere + transition region (TR):
dominant phenomena, sometimes flashes;
-large amplitudes; v: order of magnitude larger than in
photosphere, but kinetic energy (much) smaller;
-sometimes non-linear (sawtooth waveform);
-closely packed peaks
-oscillating element: ≤ 3´´–5´´ (that is smaller than for 5min. oscill. in the photosphere), followed by rapid quasicircular expansion (`chevrons´, also in phot.; Kobanov &
Makarchik, 2004);
-horizontal phase velocity: 60-70 km/s;
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The spectrum of chromospheric
oscillations in sunspot (Centeno et al
2006) consists of many “resonance”
peaks.
Hansteen et al, 2002
There is only one peak in the spectrum!
What is the matter?
Shibasaki (2001) observed also only
one peak in the spectrum of 3min
oscillations (observations at 17 GHz
emission).
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3-min oscillations were discovered when Deubner resolved
the spectrum of 5-min oscillations of quiet solar atmosphere.
That was time when it was realized that 5-min oscillations
were eigenoscillations of the Sun.
So, it is no surprise that eigenoscillations of sunspots were
considered as a model of 3 min oscillations (Uchida&Sakurai
1975, Chitre&Antia 1979, Cally&Bogdan 1993)
corona
Boundary conditions are not realistic. There is
no wave reflection from the boundaries and
”bottom” of sunspot.
Time-distance sismology of sunspots shows
that there is no trapped waves in sunspots.
photosphere
sunspot
Comvection
zone
3-min waves are running waves in
chromosphere.
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Thus, eigenoscillations of sunspots do not exist.
What is an explanation of multiple peaks in the
spectrum of 3-min oscillations in sunspots?
Zhugzhda&Locans 1981 found out a solution of the
problem. They considered propagation of waves
through sunspots and revealed that spectrum consisted
of many peaks. Sunspot atmosphere works as a
multichannel filter for waves.
Later on Zhugzhda, Locans and Staude 1983, 1984,
1985, Settele, Zhugzhda and Staude 1999, 2001
explored wave propagation in distinct empirical models
of sunspot atmosphere.
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Fast waves
Slow waves
This approximation was used for the first time by
Syrovatsky&Zhugzhda (1967). It works in rather strong
field when slow waves are longitudinal ones and fast waves
are evanescent. Of course it is valid as well for k=0. This
approximation is valid for chromosphere and temperature
minimum.
This is the transmission
function for slow waves
which are running through
sunspot atmosphere from
photosphere to corona
Slow waves are not acoustic waves!
The interpretation was based on the concept of chromospheric resonance. In
fact, resonance layer with partly transparent boundaries works as a FabryPerot filter at resonance frequencies. The appearance of peaks in the
spectrum were interpreted as a result of the occurrence of chromospheric
resonance frequencies. That’s why sometimes this theory is considered as a
theory of chromospheric resonance or resonance theory.
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Two scenario of wave of wave propagation in fourlayer isothermal model of sunspot atmosphere
Red arrows
show incident
and reflected
waves
Temperature
profile is
shown by
solid blue
curve
c
o
r
o
n
a
Frequencies
above cut-off
frequency of
temperature
minimum
chromosphere
Temperature
minimum
Frequencies
below cut-off
frequency of
temperature
minimum
For frequencies below cut-off frequency sunspot atmosphere works as a Fabry-Pero filter
for slow waves. But no more then one passband is possible. Passband appears for
frequency for which reflection coefficients of waves from temperature minimum and
from chromosphere-corona transition region are approximately the same. Thus
passband due to chromospheric resonance appears only for limited range of
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temperature plautoo thickness.
The effect of nonlinearity on linear filter theory of sunspot atmosphere
Waves of 3-min period form shocks in upper chromosphere and transition region.
Question arises whether linear theory can be applied to the treatment of
atmospheric filter for slow waves.
Passbands appear due to interference which occurs in the temperature minimum
and photosphere where waves amplitudes are small and linear theory works.
The effect of nonlinearity on filter properties arises due to nonlinear dissipation
which leads to decreasing of amplitudes of waves reflected from upper
atmosphere.
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Transmission functions in four-layer isothermal model of sunspot atmosphere
Transmission function equals to ratio of transmitted flux to incident flux
Fabry-Perot
filter at
frequency of
chromospheric
resonance
Cut-off
frequency of
temperature
minimum
To take into account nonlinear absorption transmission functions were
obtained for distinct coefficients of reduction of reflected waves.
Curve 1 is for the case without wave absorption. Curves 2,3,4,5 show the effect
of decreasing of amplitude of waves reflected from corona which appears due
to overtaking of shock waves in the upper chromosphere and transition region.
Curve 5 corresponds to complete absorption of waves in upper atmosphere.
Nonlinear absorption leads to increase of transmission for all passbands.
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Antireflection effect and high frequency passbands of transmission function
To explore high-frequency passbands wave functions were obtained.
Chromospheric resonance.
Half of wavelength.
First antireflection
passband.
Second antireflection
passband.
Three quarters of
wavelength.
Five quarters of
wavelength.
Antireflection effect is well-known in optics and acoustics. Quarter wavelength
layers are used for blooming of optics.
Wave functions show that this effect is responsible for high-frequency
passbands of transmission function.
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Empirical models of sunspot chromosphere by Lites, Maltby and Staude
Nonlinear antireflection
is taken into account
only for main peaks in
the spectrum
Curves 1 show transmission
functions for white incident
noise
Lites
Staude
Maltby
Curves 2 show
transmission function for
red incident noise
Lites
Maltby
Staude
Red lines show the spectrum of incident noise in arbitrary units
Chromospheric resonance
Cut-off frequency
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Basics of sunspot atmosphere seismology
•The frequency of chromospheric resonance defines thickness of
temperature plautoo in chromosphere
• Cut-off frequency of temperature minimum is defined by the second
passband in spectrum
•High frequency passbands define the thickness of chromosphere plus
temperature minimum.
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(Centeno et al 2006)
Spacing between blooming
peaks defines thickness of
chromosphere
antireflection
Cut-off peak in the spectrum
defines sound speed in
temperature minimum
Chromospheric resonance ?
Cut-off frequency
Peak due to chromospheric
resonance defines the size of
temperature plato in
chromosphere.
antireflection
But chromospheric
resonance peak is
strong enough when
its frequency is close
to cut-off frequency
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Exploration of nonuniformity of sunspot chromosphere is possible
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The formation level of chromosperic line He I 10830 with respect to the
formation level of photosperic line Si 10827
The time delay of chromospheric oscillations with respect to photospheric ones
defined by Centeno et al (2006) makes possible to find out the formation level of
chromosperic line He I 10830 with respect to the formation level of photosperic
line Si 10827.
Lite
s
T= 6770 K
Maltby
T= 6660 K
Staude
T= 7390 K
Sound speed is a function not only of temperature but ratio of specific heats.
It was crucial to use modified models of Lites, Maltby and Staude which
include detailed dependence of g on depth. But the inclusion of nonadiabatic
effects is still needed.
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Conclusion
• “Resonance” peaks in the spectrum of cromospheric oscillations in sunspots
appear not only due to chromospheric Fabry-Perot filter but also due to cut-off
effect of temperature minimum and antireflection effect of temperature plateau
and temperature minimum.
• Nonlinear dissipation of shocks increases antireflection effect of the sunspot
chromosphere.
• No one of three empirical models of sunspot atmosphere reproduces perfectly
the spectrum of oscillations.
• The observation of 3 min oscillations provides good check of sunspot models.
• Relative positions of formation levels of lines can be defined from observations.
• It is not clear whether Fabry-Perot chromospheric filter works effectively in all
sunspots.
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