“ “ Spectropolarimetric investigation of the propagation of Spectropolarimetric investigation of the propagation of magnetoacoustic waves and shock formation in sunspot magnetoacoustic waves and shock formation in sunspot

atmospheres”atmospheres”

Edgar Carlin Ramírez

Centeno, R., Collados, M., Trujillo-Bueno, J. 2005

Instituto de Astrofísica de CanariasMaster de Astrofísica. Universidad de La Laguna.

17 de Noviembre de 2008

Main Sections

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

Introduction.

Data reduction and inversion.

Analysis.

Theory

Results of the model.

Conclusions.

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Introduction. Introduction.

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

Physic Scenary.

Sunspots Structure. Density, Temperature, B field, atmospheric layers, surrounding diffuse light, oscillations…

I

Q

U

V

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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.

Data reduction & Inversion (I).

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

Flat-fields, dark currents.

Polarimetric calibration images.

Crosstalk: between I, Q, U… force continuum pol. to zero. between Q, U, V… statistical techniques.

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Reduction.

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.

Velocity maps : temporal evolution of Velocity for points of

the slit inside umbra. Chromosphere Photosphere

Inversion results. Temporal evolution of LOS velocity. (for 1 point of the slit

inside the umbra)

Data reduction & Inversion (II).

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

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Temporal evolution of Stokes V. Reduction results.

Chromospheric velocities. (sawtooth shape)

Photospheric velocities.

(Seemingly at rest)

HeI Stokes V

SiI Stokes V

Photospheric velocity signal:

~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)

Analysis (for 1 sunspot ). Fourier techniques.

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

Promediated over the entire umbra.

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Power Spectra.

Phase Spectra.

5 min

signal

3 min band Secondary

peaks

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.

A(z) damped No propagation

Propagation

A(z) damped No propagation

Propagation

X=mean absorption coefficientσR= Stefan-Boltzmann constantHo= Pressure Scale height

II) …+ radiative losses + stratification:

Newton’s Cooling Law & Field free aproximation

Kr > Ki : mainly propagatingKr < Ki : mainly damped

Theory.

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

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Models of propagation. (see Ferraro & Plumpton 1958)Small perturbation with frequency w + Plane-parallel isothermal atmosphere + Vertical B +…

I) …+ adiabaticity + stratification:

2 solutions:a) Alfvén wave : uz//B//K ┬ A ↔↔b) Sound wave : uz//B//K // A ↕↕

A(z)= eiKz*Z

Wac =cut-off frequency= γ*g*/2cg= gravityc2= γ*g*Hoγ =cp/cv= 5/3(monoatomic plasma)

Δφ=Phase difference between 2 fixed heights

I

II W`ac=W`ac(τR,w)

Δφ=K*Δz

If K= Δz*w/c with c =cte Δφ α w nondispersive

If K= f(w) Δφ ≠ cte*w dispersive

Fit the amplification spectra (for both DS).

Crhomo power spectra / Photo power spectra

Results of the model (I).

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

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Fitting. The model fit the phase spectra (for both data sets). 3 free parameters adjusted in the fit:

↓ 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).

Results of the model (II).

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

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Filtering.

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?

Chromospheric signal (CS)Photospheric signal (PS)

Filtering the velocity maps in the 4-5 mHz band…

Forward Delay = 38 sAmp. factor =20(Applied to PS for matching)

Nonlinear interactions

between 5 min modes

can´t be the origin of

the 3 min signal. Clear correlation between PS and CS in 6 mHz range. And so, there isn´t nonlinear frequency terms introducing distortion.

Linear aprox. Is

valid in our 4-

8 mHz

Conclusions

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

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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.

Chicken

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chicken/chickenchicken/chicken

Chicken, chicken chicken chicken chicken.

chicken chicken chicken chicken chicken chicken

chicken chicken chicken chicken chicken chicken (chicken) .

chicken: chicken chicken.

Chicken:

chicken chicken+chicken = chicken chicken chicken

Chicken, chicken chicken chicken!!

Extra

Magnetoacoustic waves and shocks in sunspotsMagnetoacoustic waves and shocks in sunspotsEdgar Carlin Ramírez

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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.