The Subsurface Structure of Sunspots as seen with 2- skip Time- Distance Helioseismology Tom Duvall MPS GöBngen Paul Cally, Damien Przybylski Monash Robert Cameron, Kaori Nagashima MPS GöBngen Z (Mm)
Talk outline 1 Historical observasons 2 Technique and inisal observasons of AR11899, Nov. 14-23, 213 with a relasvely large isolated sunspot that does not change much over 1 days. 3 Modeling of 2- skip travel Smes with ray theory and sunspot model. 4 Modeling of 2- skip travel Smes with linear wave simulason and sunspot model. 5 Conclusions and outline of follow- up work.
Galileo and others observed sunspots around 161. Below left is a sunspot drawing from Galileo s work. 4 Aug 215 2
Discovery of apparent bowl shape of sunspots by their appearance near the edge of the solar disk by Wilson in 1774.
Evershed s flow in sunspots, first seen by Evershed in 199 4 Aug 215 3
AMer Duvall et al. (1995) Some early 2- skip measurements of waves below sunspots.
CHAPTER 4. DATA ANALYSIS METHODS 51 4 3 ( ) 2 1.3.2.1-15 -1-5 5 1 15 τ (minutes) ψ. -.1 -.2 -.3 65 7 75 8 85 9 95 τ (minutes) Figure 4.7: This \time-distance diagram" shows some cross correlations typical of those used in this work. In the upper plot, the greyscale denotes the cross correlation amplitude as a function of the time lag and the distance. The lower plot displays the cross correlation for a particular distance ( = 24:1 ), near the maximum. The dashed line in the lower plot shows the function G() (equation 4.5), where the free paramaters have been determined by a non-linear least squares technique.
1-day average gradient y [Mm] 3 2 1-1 -2-3 1-day average intensity -2 2 x [Mm] 1.8.6.4.2 fractional intensity y [Mm] 3 2 1-1 -2-3 -2 2 x [Mm] Average intensity and intensity gradient for the 1 days of analysis of AR11899 on Nov. 14-23, 213. The bo@om two images are for the full tracked area and the top two are the subareas for which we measure travel Gmes. y [Mm] 15 1 5-5 -1-15 -1 1 x [Mm] 1.8.6.4.2 fractional intensity y [Mm] 15 1 5-5 -1-15 -1 1 x [Mm]
Covariances averaged over umbra, penumbra, quiet sun covariance 3 2 1-1 umbra penumbra quiet sun 3 mhz -2-3 2 4 6 8 1 time [minutes] covariance 4 2-2 umbra penumbra quiet sun 4 mhz -4 2 4 6 8 1 time [minutes]
y [Mm] y [Mm] 3 2 1-1 -2-3 -1-2 -3 phase time, 3.1 mhz -2 2 x [Mm] envelope time, 3.1 mhz 3 2 1-2 -2 2 x [Mm] times for 3.1 mhz -.4 -.6 -.8-1 -1.2-1.4-1 -2-3 -4 time [min.] time [min.] y [Mm] y [Mm] 3 2 1-1 -2-3 -1-2 -3 phase time, 4. mhz -2 2 x [Mm] envelope time, 4. mhz 3 2 1-2 -2 2 x [Mm] times for 4. mhz -.8-1 -1.2-1.4-1.6-1.8-2 -1-2 -3-4 -5 time [min.] time [min.] time [min.] -4-6 -8 phase time envelope time umbral boundary penumbral boundary time [min.] -4-6 -8 phase time envelope time umbral boundary penumbral boundary -4-2 2 4 y [Mm] -4-2 2 4 y [Mm]
1 23 44 66 87 19 131 152 174 195 217
IntegraCng the slowness (1/V) between the upper turning point (z II tp ) to the Wilson depressed level (z tp +Δz) gives an approximacon to the travel Cme difference.
Rays are launched from [- 6,] and land for the first skip at the grid points in the le= image. They are sca@ered and end up somewhere on the right side. From the inical [- 6,] and the final point, we infer midpoints, which are indicated in the right image.
Phase Cmes, midpoint inferred Group Cmes, midpoint inferred Phase Cmes, actual midpoints Group Cmes, actual midpoints Phase Cmes of Wilson depression Group Cmes of Wilson depression Azimuthally averaged ray travel Cmes for isothermal acouscc cutoff frequency ω I
Linear wave simulason with sunspot model. Simulated spot Average intensity for AR9787 2- skip covariances for spot, quiet sun and Gabor fits 1 covariance -1-2 spot data quiet sun data spot envelope quiet sun envelope spot phase time quiet sun phase time spot envelope time quiet sun, envelope time -3 45 5 55 6 65 7 75 8 time [minutes]
What have we learned so far? From observa6ons: 2- skip phase 6mes ~ 1 minute less than quiet sun reflec6ng from the umbra 2- skip envelope or group 6mes ~ 3 minutes less than quiet sun reflec6ng from the umbra Umbra and penumbra act differently Using Δ=12-24 deg, it is possible to resolve the umbra and penumbra Travel 6me differences of ~ 1 minute indicate an ouilow (not presented today) Amplitude of covariance func6on in penumbra smaller than quiet sun by 4% (not presented today) From ray calcula6ons: Group 6mes larger than phase 6mes also seen with magnitudes similar to observa6ons Ar6ficially suppressing the magne6c field does not change the travel 6mes very much Using two different formula6ons of the acous6c cutoff frequency does not make substan6ve difference Phase 6mes larger at 4 mhz than 3 mhz From simula6ons: Similar order phase and group 6mes seen in the umbra as for observa6ons
What do we do next? Observa6ons: Observe a variety of sunspots to look for differences with spot size, age Expand the frequency range Study the flow signals Ray calcula6ons: Simulate more closely what is done in the observa6ons Model the flows Simula6ons: Need bigger (horizontally and ver6cally) simula6ons to enable using larger Δ Measure sensi6vity to thermal Wilson depression and magne6c field by adjus6ng the sunspot model
Figure 1. Scatter plots of the actual (left panels) and mid-point-inferred (right panels) first-skip turning points for the grid of rays fired from ( 6, ) Mm with frequency 4 mhz (top) and 3 mhz (bottom). Points (actually) in the umbra are identified with green colouring, the penumbra with red, and the quiet Sun with blue. The green and red circles are the umbral and penumbral boundaries respectively. These figures use ω c = ω DG ; scattering with ω c = ω I is typically substantially increased.
Probing Sunspots with Two-Skip Helioseismology 3 Figure 2. Phase (blue) and group (gold) travel time differences, azimuthally averaged, as functions of radius r of the true (large dots) or mid-point-inferred (blue full or gold dashed) middle skip points. Left column: 3 mhz; right column: 4 mhz. Top row: full magnetic sunspot model using ω c = ω DG ; second row: full magnetic sunspot model using ω c = ω I ; third row: thermal spot with the same thermal and density structure, but with magnetic field artificially suppressed. All points were binned to 1 Mm 1 Mm squares and averaged both by bin and azimuthally. All data presented here has been pre-filtered to remove any rays with second skip distance outside the range ( 5 7, 7 5 ) times the first skip distance, or second skip direction more than 1 from the first skip direction. The full and dashed red curves represent respectively the equivalent phase and group speed thermal depths of the Wilson depression; see text for details. The grey vertical lines represent the umbral and penumbral boundaries.
4 Duvall, Cally & Przybylski to our rays to restrict first and second skip distance contrast to ( 5 7, 7 5 ) and direction change to 1. 3. The filtering leaves some radii in the penumbra bereft of points, illustrated by gaps in the points representing true central point travel times. Relaxing the filtering criterion of course fills these gaps, but at the expense of true and mid-point-inferred first skip points differing by wider margins. 4. The equivalent time phase speed Wilson depression match the measured times quite well, especially in the umbra, where results are more reliable. The group travel time perturbations are consistently smaller than predicted by the equivalent group speed depth. 5. There is little substantive difference between results obtained with ω DG and ω I. 6. There is little substantive difference between results with and without the magnetic field, indicating that the sunspot s thermal structure is primarily responsible for travel time shifts at these frequencies. The concept of the equivalent phase and group speed thermal depths of the Wilson depression is a simple though inexact device for converting between Wilson depression depth and travel time perturbations. Given that a ray passes through the surface layers of a sunspot very much faster than through the equivalent depths of quiet Sun (see figs. 3 and 4 of Cally 27), the two-way time difference between the magnetic and quiet cases is, to a first approximation, dominated by the quiet Sun travel time: δτ = 2 z tp z tp+ z dz/v, where V is either the vertical phase or group speed, z tp is the upper turning point in quiet Sun, and z < is the Wilson depression by which the atmosphere has been lowered in the spot. This correspondence is plotted in Figure 3. Figure 3. Equivalent depths (phase: full curves; group: dashed curves) for 3 mhz (blue) and 4 mhz (red). Despite ray travel times being quite insensitive to magnetic field at these frequencies, they are strongly sensitive to direction through inhomogeneities in the background thermal structure, especially at 4 mhz. Figure 4 shows phase travel time perturbations along the x and y axes through the spot centre in the magnetic case, with rays launched from ( 6, ). The curves hardly differ in the thermal case, indicating that the effect isn t directly magnetic. It is instead a consequence of the nature of the scattering on each axis. On the x-axis, by symmetry, the only scattering is in second skip distance. Increasing skip distance from the spot centre, the total timing of the now one-short/one-long (or vice versa) two-skip path relative to quiet Sun (symmetric) two-skip times reduces significantly out to about 2 Mm at 3 mhz and 1 Mm at 4 mhz, and then starts to increase as the scattering weakens. On the other hand, along the y-axis, the rays largely scatter laterally, thereby reducing the length (and timing) of the required equivalent quiet Sun path, and so the scattered rays travel time deficits rapidly diminish. The ray calculations presented here do not use the generalized ray theory of Schunker & Cally (26), and so do not allow for mode transmission (fast-to-slow; i.e, acoustic-to-magnetic) at the Alfvén-acoustic equipartition level. As the 4 mhz rays (for ω c = ω DG ) barely penetrate the a = c equipartition surface where mode conversion/transmission occurs, and 3 mhz rays do not reach it at all, this is unlikely to be of importance in the present context. (With ω c = ω I, some rays reach as high at a 2 /c 2 = 7 at 4 mhz.) The effect is much enhanced above 5 mhz, where significant processes involving the atmospheric fast wave are believed to be of importance for both atmospheric waves and interior seismology (Cally & Moradi 213; Moradi et al. 215; Rijs et al. 215). REFERENCES Cally, P. S. 27, Astronomische Nachrichten, 328, 286 Cally, P. S. & Moradi, H. 213, MNRAS, 435, 2589 Deubner, F. & Gough, D. 1984, ARA&A, 22, 593 4. DISCUSSION AND CONCLUSIONS Jurcák, J., Bello González, N., Schlichenmaier, R., & Rezaei, R. 215, submitted to A&A Khomenko, E. & Collados, M. 28, ApJ, 689, 1379
Probing Sunspots with Two-Skip Helioseismology 5 Figure 4. Phase travel time perturbations for rays from ( 6, ) with first skip turning point lying along the x-axis (full curves) and along the y-axis (dashed curves). The magnetic field inclination at z = is indicated on the top axis. Moradi, H. & Cally, P. S. 28, Journal of Physics Conference Series, 118, 1237 Moradi, H., Cally, P. S., Przybylski, D., & Shelyag, S. 215, MNRAS, 449, 374 Newington, M. E. & Cally, P. S. 21, MNRAS, 42, 386 Przybylski, D., Shelyag, S., & Cally, P. S. 215, ArXiv e-prints Rijs, C., Moradi, H., Przybylski, D., & Cally, P. S. 215, ApJ, 81, 27 Schmitz, F. & Fleck, B. 1998, A&A, 337, 487. 23, A&A, 399, 723 Schunker, H. & Cally, P. S. 26, MNRAS, 372, 551