Transcript “ Spectropolarimetric investigation of the propagation of magnetoacoustic waves and shock formation in sunspot atmospheres” Centeno, R., Collados, M., Trujillo-Bueno, J. Edgar Carlin Ramírez Instituto.

“ Spectropolarimetric investigation of the propagation of
magnetoacoustic waves and shock formation in sunspot
atmospheres”
Centeno, R., Collados, M., Trujillo-Bueno, J.
2005
Edgar Carlin Ramírez
Instituto de Astrofísica de Canarias
Master de Astrofísica. Universidad de La Laguna.
17 de Noviembre de 2008
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Main Sections
 Introduction.
 Data reduction and inversion.
 Analysis.
 Theory
 Results of the model.
 Conclusions.
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Introduction.
Physic Scenary.
 Sunspots Structure. Density, Temperature, B field, atmospheric layers, surrounding diffuse
light, oscillations…
 Spectral range: powerful diagnostic window.
*SiI line (10827.09 A) Photospheric info.
*HeI 10830 triplet. Chrromospheric info.  10830.5 & 10830.34 A (red,blended)
*Water vapor line: calibration
10829.09 A (blue, weak)
 Observations. (VTT with TIP)
* 2 different sunspots.
* 4 Stokes Parameters simultaneously
* T sampling=0.5 s  integration to improve S/N in 1 image.
* Temporal series (1 hour).
* Correlation tracker device.
Edgar Carlin Ramírez
I
U
Q
V
Magnetoacoustic waves and shocks in sunspots
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Data reduction & Inversion (I).
Reduction.
 Flat-fields, dark currents.
 Polarimetric calibration images.
 Crosstalk:
between I, Q, U…  force continuum pol. to zero.
between Q, U, V…  statistical techniques.
Inversion.
 Full Stokes Inversion in both lines for every timestep during observation.
 Similar results in comparison with doppler shifts method.
Easier, but doesn’t supply another
important physical magnitudes.
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Data reduction & Inversion (II).
Reduction results.
 Temporal evolution of Stokes V.
HeI Stokes V
Chromospheric velocities.
(sawtooth shape)
Photospheric velocities.
(Seemingly at rest)
SiI Stokes V
Inversion results.
 Temporal
evolution
of LOS
velocity.of(for
1 pointforofpoints
the slitofinside
the
umbra)
Velocity maps
: temporal
evolution
Velocity
the slit
inside
umbra.
Photospheric
velocity signal:
Chromosphere
Photosphere
~400 m/s peak to peak
5 min period (3.3 mHz)
Chromospheric velocity signal:
~10-15 Km/s peak to peak
3 min band (5-8 mHz)
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Analysis (for 1 sunspot ). Fourier techniques.
Power Spectra.
 Promediated over the entire umbra.
5 min signal
3 min band
Secondary
peaks
Phase Spectra.
 Phase difference between Chromo and
Photosphere (“+” signs).
Noisy with Δφav=0: Non-correlated
signals No propagation.
No so noisy but Δφav ≈ 0:
No propagation, standing waves.
Increasing tendecy: Propagation.
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Theory.
Models of propagation. (see Ferraro & Plumpton 1958)
Small perturbation with frequency w +
Plane-parallel isothermal atmosphere +
Vertical B
+…
2 solutions:
a) Alfvén wave : uz//B//K ┬ A
b) Sound wave : uz//B//K // A
↔
↕
I) …+ adiabaticity + stratification:
 A(z) damped  No propagation
 Propagation
II) …+ radiative
losses + stratification:
iKz*Z
A(z)= e
Newton’s Cooling Law & Field free aproximation
 Kr
A(z)> damped
 No
propagation
Ki : mainly
propagating
 Kr
Propagation
< Ki : mainly damped

W`ac=W`ac(τR,w)
Wac =cut-off frequency= γ*g*/2c
g= gravity
2= γ*g*Ho
cX=mean
absorption
If coefficient
K= Δz*w/c with c =cte  Δφ α w
γσ=cp/cv=
5/3(monoatomic plasma)
R= Stefan-Boltzmann constant
nondispersive
Δφ=K*Δz
 Scale height
Ho= Pressure
If K= f(w)  Δφ ≠ cte*w
dispersive
II
I
Δφ=Phase difference between 2 fixed heights 
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Results of the model (I).
Fitting.
 The model fit the phase spectra (for both data sets).
3 free parameters adjusted in
the fit:
 Fit the amplification spectra (for both DS).
Crhomo power spectra / Photo power spectra
↓ S/N  not reliable
 Reasonable agreement with observations.
 The power above 4 mHz reaches the chromosphere.
 Lower frequencies don´t propagate up to chromosphere.
 Height difference between layers of formation of HeI and SiI is the same for both sunspots.
 Lower temperature in the biggest sunspot (number 1).
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Results of the model (II).
Filtering.
Filtering the velocity maps in the 4-5 mHz band…
Forward Delay = 38 s
Amp. factor =20
(Applied to PS for matching)
Chromospheric signal (CS)
Photospheric signal (PS)
Theoretical delay obtained with our simple model:
From phase spectra … vg= dw/dk  delay= Δz/vg
 Good agreement with observations.
 Time delay between PS and CS very dependent on the frequency.
Nonlinear interactions have been disregarded… Is this still valid?
Clear correlation between PS and CS in 6 mHz range.
And so, there isn´t nonlinear frequency terms introducing distortion.
Edgar Carlin Ramírez
Nonlinear interactions between
5 min modes can´t be the origin
of the 3 min signal.
Linear aprox. Is valid in
our 4-8 mHz
Magnetoacoustic waves and shocks in sunspots
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Conclusions
 A simple model with stratified isothermal atmosphere and radiative losses is a good first
approximation to the propagation of waves in photosphere in the 4-8 mHz band.
 Time delay between PS and CS very dependent on the frequency (from few tens of seconds to
several minutes).
 Height difference between layers of formation of HeI and SiI is the same for both sunspots.
 The power above 4 mHz reaches the chromosphere. As they go upward their amplitude increases
due to the rapid decrease in density  develop chromospheric shock waves
 Nonlinear interactions between 5 min modes can´t be the origin of the 3 min signal.
Edgar Carlin Ramírez
Magnetoacoustic waves and shocks in sunspots
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Edgar Carlin Ramírez
10/10
Magnetoacoustic waves and shocks in sunspots
SiI inversion: LILIA code.
Takes into account Zeeman effect. Assumes LTE .
Output: velocities, B, … with the stratification in atmosphere.
log (τ500)=2 is selected.
 HeI inversion: similar code. Without stratification.