1. “ Spectropolarimetric investigation of the propagation of magnetoacoustic waves and shock formation in sunspot atmospheres” “ Spectropolarimetric investigation of the propagation of magnetoacoustic waves and shock formation in sunspot atmospheres” Edgar Carlin Ramírez Centeno, R., Collados, M., Trujillo-Bueno, J. 2005 Instituto de Astrofísica de Canarias Master de Astrofísica. Universidad de La Laguna. 17 de Noviembre de 2008

2. Main Sections Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez Introduction. Data reduction and inversion. Analysis. Theory Results of the model. Conclusions.1/10

3. Introduction. Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez Physic Scenary. Sunspots Structure. Density, Temperature, B field, atmospheric layers, surrounding diffuse light, oscillations… I Q U V2/10 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.

4. Data reduction & Inversion (I). Magnetoacoustic waves and shocks in sunspots Edgar 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.3/10 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.

5. Velocity maps : temporal evolution of Velocity for points of the slit inside umbra. ChromospherePhotosphere 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 sunspots Edgar Carlin Ramírez4/10 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)

6. Analysis (for 1 sunspot ). Fourier techniques. Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez Promediated over the entire umbra.5/10 Power Spectra. Phase Spectra. 5 min signal 3 min band Secondary peaks Phase difference between Chromo and Photosphere (“+” signs). Noisy with Δφ av =0: Non-correlated signals  No propagation. No so noisy but Δφ av ≈ 0: No propagation, standing waves. Increasing tendecy: Propagation.

7.  A(z) damped  No propagation  Propagation  A(z) damped  No propagation  Propagation X=mean absorption coefficient σ R = Stefan-Boltzmann constant Ho= Pressure Scale height II) …+ radiative losses + stratification: Newton’s Cooling Law & Field free aproximation  Kr > Ki : mainly propagating Kr < Ki : mainly damped Theory. Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez7/10 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 : u z //B//K ┬ A ↔ ↕ b) Sound wave : u z //B//K // A ↕ A(z)= e iKz*Z Wac =cut-off frequency= γ*g*/2c g= gravity c 2 = γ*g*Ho γ =cp/cv= 5/3(monoatomic plasma) Δφ=Phase difference between 2 fixed heights  I II W`ac=W`ac(τ R,w) Δφ=K*Δz  If K= Δz*w/c with c =cte  Δφ α w nondispersive If K= f(w)  Δφ ≠ cte*w dispersive

8. Fit the amplification spectra (for both DS). Crhomo power spectra / Photo power spectra Results of the model (I). Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez8/10 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).

9. Results of the model (II). Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez9/10 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 s Amp. 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

10. Conclusions Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez10/10 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.

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12. Extra Magnetoacoustic waves and shocks in sunspots Edgar Carlin Ramírez10/10

13. SiI inversion: LILIA code. Takes into account Zeeman effect. Assumes LTE. Output: velocities, B, … with the stratification in atmosphere. log (τ 500 )=2 is selected. HeI inversion: similar code. Without stratification.