Probing Magnetic Fields in the Solar Convection Zone with Meridional Flow Zhi-Chao Liang 22 Dec. 2015, MPS, Göttingen Liang, Z.-C. & Chou, D.-Y., 2015, Probing Magnetic Fields at the Base of the Solar Convection Zone with Meridional Flows Liang, Z.-C. & Chou, D.-Y., 2015, Effects of Solar Surface Magnetic Fields on the Time-Distance Analysis of Solar Subsurface Meridional Flows
Outline Introduction meridional flow, time-distance helioseismology Data analysis Dopplergrams -> cross-covariance function -> travel-time Systematic effects contamination from surface magnetic regions center-to-limb variation Results: Solar cycle variation of meridional flow at base of convection zone (BCZ) -> magnetic field at BCZ
Probing Magnetic Fields in the Solar Convection Zone with Meridional Flow How to probe magnetic field at BCZ (Base of Convection Zone)? Solar magnetic field changes with the solar cycle Search for solar-cycle variations of physical quantities at BCZ Many attempts have been made: Sound speed perturbation Zonal flow/rotation profile Meridional flow At the BCZ, energy density of meridional flow (½ ρv 2 ): ½ ρv 2 < B 2 /8π << gas pressure
Measurement Method Time-Distance Helioseismology (Duvall et al. 1993) Δ solar surface mid-point x 1 x 2 τ - τ + ray path The greater separation distance Δ The deeper the lower turning layer anomaly/flow Most contribution comes from the bottom of ray path δτ = τ + -τ - flow <τ> = (τ + +τ - )/2 thermal anomaly
Meridional flow observation in the past Surface observations (tracers, Doppler shifts, ) Pole-ward motion Peak velocity about 10 ~ 20 m/s Smaller magnitude at solar maximum Subsurface measurements (time-distance, ring diagram, ) Extends to entire convection zone Smaller magnitude at solar maximum in upper convection zone Additional component superimposed on meridional flow at solar maximum in upper convection zone (0.9 R sun )? Lower convection zone? North pole South pole??
Giles et al. (1997); Giles (1999) Typical measurement of travel-time difference: sine-shape latitudinal dependence MDI data Period: 1996 Δ = 1~6 deg r > 0.96 R sun south δτ < 0 southward equator δτ > 0 northward north
Chou & Dai (2001) Chou & Ladenkov (2005) Beck, Gizon, & Duvall (2002) Solar minimum Solar maximum MDI data Δ= 17 deg r = 0.9 R sun Mean value subtracted Positive: pole-ward flow TON data Δ = 16~22 deg r = 0.86~0.9 R sun Both data show an additional component centered at active latitude superimposed on the meridional flow during the solar maximum
MDI medium-l Data Dopplergrams ψ (x, t) Acoustic-power map Σ t ψ 2 (x, t) Magnetogram for comparison 15-year data (1996 ~ 2010) One image per minute Doppler images of 192x192 pixels Pixel scale = 0.6 deg/pix
MDI medium-l Data m -averaged power spectrum p 1 Gaussian-weighted binning of full-resolution MDI Dopplergrams to reduce the spatial aliasing at high-l (Kosovichev et al. 1997) Sensitive to p modes up to l = 300 No signal of f modes Δ = 7 ~ 75 deg r = 0.96 ~ 0.54 R sun
Cross-Covariance Function computation Prepare the data cube Subtract 1-hr running mean (remove main component of solar rotation) Frequencies below 1.5 mhz are filtered out. Hann window is applied to smooth 1.5~2 mhz (remove granulation and supergranulation noise) Remap to heliographic longitude-latitude coordinate (cylindrical projection) Track Doppler images for each latitude (remove differential rotation) Unit size: 120deg x 120deg x 24hr Cross-covariance function (CCF) computation Geometry: arc-to-arc in north-south direction Subtended angle: 30 deg (12-sector geometry) Compute CCF between a pair of opposite points (take care of the distance distortion) Average CCFs over the arc Step size is 0.6 deg in longitude, latitude, and travel distance. CCF averaging Longitude < 45 deg Monthly x x c x Δ = x-x x c is the central point between x and x
Example of Cross-Covariance Function C (Δ, τ) 15-year longitude-average C (Δ=18 deg, τ)
Travel-time measurement Fit a Gabor wavelet to the CCF (Duvall et al. 1997) Fit a cosine function to the demodulated CCF One-parameter fit Gizon & Birch (2002,2004)
Initial result of δτ measurement δτ τ (N S) -τ (S N) North pole δτ > 0 Take anti-symmetric component to remove the leakage from solar rotation due to misalignment of MDI instrument => P angle uncertainty (Giles 1999; Beck et al 2002) Averaging range Δ = 7 ~ 11 deg Depth = 0.93 ~ 0.96 R sun Longitude = +/- 45 deg Period = 1996~2010 South pole δτ < 0
Initial result of δτ measurement 5 travel distance ranges Gaussian smoothing with FWHM=1yr in time and FWHM=7.2deg in latitude MDI instrument starts to flip 180deg every 3 months after mid-2003: => discarded Additional component centered at active latitude (Chou & Dai 2001; Beck, Gizon, & Duvall 2002) Question: contamination from surface magnetic fields?
Many complication could be introduced by the surface magnetic field Local flow around active regions Damping mechanism (inhomogeneous absorption) Wilson depression Shower-glass effect Direct effect of the magnetic fields
Excluding surface magnetic fields in longitudinal average Masking area Sunspot center is of the order of thousand gauss Background fluctuation is of the order of 10~20 gauss Excluding the pairs which have at least one point inside the magnetic regions with field strength greater than thresholds Not applying any filter involving the space, e.g. phase-speed filter, directional filter
With vs. without B-field B-field included B-field (50 gauss) excluded
Difference between including and excluding the B-field north δτ Active latitude δτ south This phenomenon reported a decade ago was interpreted as a divergent flow It mimics an effective downward flow It is a local and near-surface effect It is unrelated to large-scale meridional flow
Threshold of 50 G vs. 600 G threshold: 50 gauss threshold: 600 gauss
Strong vs. weak magnetic fields Period: 2000-2001 Weak magnetic regions may also contaminate the measurement Threshold of 50 gauss is good enough
Another systematic effect: Center-to-limb variation (Duvall & Hanasoge 2009; Zhao et al. 2012) NS EW NS-EW Zhao et al. 2012 Different observables have different amplitudes East-west measurement also shows a sine-shape curve Center-to-limb effect can be empirically removed by subtracting east-west measurement Cause is unclear east center Nonsense => Systematic effect west
δτ before center-to-limb correction (threshold: 50G) NS ( longitude < 45 deg) EW ( longitude < 15 deg) Subtracting δτ EW from δτ NS month by month? Or average δτ EW over 15 years to obtain the latitudinal dependence? Check the long-term variation of δτ EW
Latitude-averaged δτ vs. time NS ( longitude < 45 deg) EW ( longitude < 15 deg) Average over all available latitude δτ NS in panel A: smaller magnitude at solar maximum δτ EW is noisier than δτ NS due to narrower longitudinal average Fit with a linear function L(t)
Relative temporal change in latitude-averaged δτ Normalize L(t) by the value at middle time (2003.06) L NS and L EW are similar except for panel E Long-term trend: instrumental or calibration? Latitudinal dependence: <δτ EW > t Temporal dependence: L EW Center-to-limb correction: δτ NS - < δτ EW >L EW Except for panel E δτ NS - < δτ EW >L NS
Final results of δτ (center-to-limb effect removed)
Final results of δτ vs. latitude All panels Two minima are similar Maximum differs from minima Panel A Overall magnitude of maximum is smaller than that of minima inflow toward active latitude Panel D Different behaviors between solar maximum and minimum Behavior is opposite to previous panels Solar cycle variation at BCZ Panel E: δτ vanish
Final results of δτ vs. travel distance Average over 5~20deg latitude Gaussian smooth with FWHM=9deg in travel distance R sun > 0.92 δτ solar max < δτ solar min R sun =0.75~0.92 δτ solar max > δτ solar min R sun =0.65~0.75 (BCZ) δτ solar max < δτ solar min R sun < 0.65 Note that the actual depth range sampled by the wave packet associated with each travel distance is rather broad. both ~ 0
Is it possible that Δδτ at BCZ is caused by systematic effects? Without C-to-L correction (temporal trend is removed) Without removing surface magnetic region Difference between solar max and min still exists As long as the systematic effect is not time dependent, it would not affect the conclusion Surface effect: Decreases δτ in upper CZ Increases δτ in lower CZ Using more strict threshold will enhance Δδτ at BCZ
Order-of-magnitude estimate for the meridional flow at BCZ Assumptions: Ray approximation The contribution to δτ is solely from the region around the lower-turning point Only integral over a range around the lower-turning point At BCZ: Δδτ 0.05 sec Δv = 5 ~10 m/s Comparison: Giles (1999): v < 2~5 m/s Zhao et al. (2013): v = 5~10 m/s where v t is the meridional flow speed at the lower-turning point B 2 /8π > ½ ρv 2 -> ΔB > 2x10 3 G
Summary Effect of surface magnetic field on travel-time measurement Mimics down-flow inside active regions Local and unrelated to large-scale meridional flow Essential to remove it in studying subsurface meridional flow Need to be considered even when activity is low Threshold of 50 G is enough Meridional flow in convection zone varies with solar cycle Upper CZ: Inflow toward active latitude Overall magnitude at solar max < solar min Lower CZ: Opposite to upper CZ Evidence of magnetic fields at BCZ Future work Examine systematic effects to obtain a clean observation SDO/HMI vs. SOHO/MDI Inversion of travel time difference Thank you
Comparison between different methods of travel time measurement North-south travel time difference without center-to-limb correction Period: 1997 Δ = 18 deg Longitude < 45 Taking anti-symmetric component Gaussian smoothing in latitude with FWHM = 7.2 deg appendix
Coordinate for east-west measurement Original longitude-latitude coordinate 90deg-rotated coordinate Dotted lines: constant latitudes Red lines: great circles Blue box: area to be analyzed appendix
Gizon (2003) Solid: all available data Dashed: exclude active regions MDI data, two Carrington rotation in 1999 f-mode surface flow Inflow around active regions contaminate measurement of meridional flow This conclusion was challenged by Gonzalez Hernandez et al. (2008). appendix
Hathaway & Rightmire (2011) Surface meridional flow measured by tracing magnetic features appendix Mean value subtracted Inflow toward the active latitude
Duvall & Hanasoge (2009) North-south travel time difference Δ = 12.9 ~ 13.5 deg 4-sector, south 20-32 deg 12-sector, south 20-32 deg 12-sector, north 20-32 deg 4-sector, north 20-32 deg Gradient with longitude is subject to: Angle subtended by arc latitude appendix