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Adaptation of the LOWL Pipeline for PICARD Medium-l Program

Adaptation of the LOWL Pipeline for PICARD Medium-l Program. David Salabert Sebastian Jim é nez-Reyes, Pere Pall é Instituto de Astrof í sica de Canarias. Peak-fitting pipelines.

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Adaptation of the LOWL Pipeline for PICARD Medium-l Program

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  1. Adaptation of the LOWL Pipeline for PICARD Medium-l Program David Salabert Sebastian Jiménez-Reyes, Pere Pallé Instituto de Astrofísica de Canarias

  2. Peak-fitting pipelines • Two “production” peak-fitting pipelines: p-mode parameters provided on a routine basis by the GONG (Tucson) and MDI (Stanford) projects. > GONG pipeline: 108-day time series > MDI pipeline: 72-day time series > Modes up l = 200 • + several other peak-fitting pipelines developed (e.g., Korzennik, …) • All those pipelines have their own specifications: > m-components fitted individually or simultaneously / m-averaged tech. > adapted for short or long time series > include or not the leakage matrix > use Lorenztian or asymmetric profiles to describe the mode > …

  3. LOWL/ECHO instruments > LOWL/ECHO: velocity imaging instrument > Spatial resolution (25’’): large range of p-mode degrees observed, optimized for intermediate and low degrees (LOW-L degrees) > LOWL: February 24, 1994 (Mauna Loa, Hawaii) > Network ECHO: Experiment for Coordinated Helioseismic Observations Observatorio del Teide, Tenerife (December 1999) + LOWL (Hawaii) replaced in September 2000 > Shutdown in 2006

  4. LOWL pipeline • Developed by S. Jiménez-Reyes • Written in fortran 90 • Fits the (2l+1) components simultaneously by minimizing a set of a-coefficients (the number of fitted a-coefficients being customizable) • Includes the leakage matrix information: both l-leaks and m-leaks • Possibility to use asymmetric profile

  5. LOWL pipeline • Velocity image determination using the blue and red intensity images • Calibration of the velocity images and analysis of the non-linearities of the instrumental signal • Computation of the time-series for each oscillation mode (n,l,m) by applying a spherical harmonic decomposition to the velocity maps • Spectral analysis of the time-series, • allowing to study the main features • of the acoustic modes

  6. LOWL pipeline • To extract a single (l, m) mode from resolved observations, a spatial filter has to be applied to the velocity images spherical harmonics • BUT, the spherical harmonics are not orthogonalover the observed area (half of the Sun) imperfect isolation of the individual modes (l,m)  leads to the existence of other modes in the Fourier spectrum for a givenl,m

  7. LOWL pipeline:Leakage matrix • Fourier transform for a given (l,m) mode (yl,m) is not given by the Fourier transform of a single mode (xl,m), but rather as a sum over several modes as: • with • contribution from eachone of the modes (l’,m’) to a given mode (l,m) •  LEAKAGE MATRIX • - 2 types of leakage: • m-leakage: correlation between different m-components with equal l • l-leakage: correlation between different degrees l • Leakage: main source of systematic errors

  8. LOWL pipeline:Fitting procedure • - fit all the multiplets m(2l+1) of a given degree lsimultaneously • fits computationally expensive and complicated  • p-mode profile approximated by a Lorentzian profile: • Frequencies n,l,m for each m-component (2l+1) represented by: • wheren,l , the unperturbed central • frequency of the multiplet • Pl(m), Clebsch-Gordon polynomials (Pl(l)=l) • ai(n,l)’s, shift in frequency induced • mainly by the internal rotation. • 9 ai(n,l)’s are fitted

  9. LOWL Pipeline: Fitting procedure Power spectrum of each m-component of a given degree l fitted simultaneously

  10. LOWL Pipeline: Fitting procedure Note the presence of the sidebands at 11.57 Hz : fitted mode multiplets : fitted leaked modes (l  3)

  11. LOWL Pipeline: Fitting procedure Note the presence of the sidebands at 11.57 Hz : fitted mode multiplets : fitted leaked modes (l  3)

  12. Currently adapting this pipeline… > To apply to rebinned 256x256 (“macro-pixel like”) MDI intensity images and to evaluate the mode measurement with the PICARD Medium-l program. > Be ready to provide to the PICARD community p-mode parameters when data become available. > Provide mode frequencies, a-coefficients, amplitudes, lifetimes, … from the PICARD time series on a routine basis.

  13. Low-Frequency Solar p Modes:Observations Obtained from m-Averaged Spectra David Salabert John Leibacher, Thierry Appourchaux, Frank Hill

  14. m-averaged spectrum: average the (2l+1) m-componentsof an oscillation multiplet (n, l) > Rotational and structural effects: degeneracy lift of mode frequency into (2l+1) m-multiplets. > The shifts (a-coefficients) are determined as we are searching for the low-frequency modes. >Several way to find the best estimates of the a-coefficients: - minimum likelihood, - narrowest peak in the m-averaged spectrum, - smallest entropy. > Considerably improves SNR even when the m-components have too low SNR to be measured in the individual-m spectra.

  15. l = 12, n = 4 mode at ~ 1187 μHz m-averaged spectrum technique m-ν diagram m-averaged spectrum Figure-of-merit (a1)

  16. l = 10,n = 5 mode at ~ 1288 μHz l = 12,n = 4 mode at ~ 1187 μHz l = 4,n = 4 mode at ~ 913.5 μHz l = 33,n = 1 mode at ~ 931 μHz

  17. a1 a2 a3 a4 a5 a6 Frequency (ν) ν/ sqrt[l(l+1)] 3960 days of GONG data Six first a-coefficients estimated using the m-averaged spectrum technique of the low-frequency p modes (1 ≤ l ≤ 35)

  18. Mode asymmetries Mode linewidths (FWHMs) Mode amplitudes background level 3960 days of GONG dataFitted mode parameters

  19. 2088-day: comparison with other measurement (Korzennik 2005)

  20. MDI 72-day & GONG 108-day time series Example of a m-averaged spectrum with 72 days of MDI observations MDI 72-day time series GONG 108-day time series

  21. MDI 72-day time series

  22. GONG 108-day time series

  23. Conclusions > New method to measure and fit the low-frequency modes in spatially-resolved data > Lower frequencywhere classic peak-fitting methods fail because low SNR > Better precision of the fitted modes > Rotation/Structure: deeper and better resolution throughout the Sun > Method being extended towards modes with higher degrees and frequencies Development for a parallel “routine” peak-fitting pipeline for the 108-day GONG data

  24. Overall summary • Two separate and distinct peak-fitting pipelines: > pipeline_1: developed for the LOWL data which fits the (2l+1) m-components simultaneously (includes l-leaks and m-leaks) > pipeline_2: m-averaged spectrum technique developed for GONG and MDI data and adapted to measure and fit modes with low SNR where the classic peak-fitting methods fail. • Both pipelines can be applied to the PICARD medium-l data to provide mode parameters.

  25. (Garcia, R.A, et al. 2007) Low-frequency p modes: WHY…? • Lower reflection points in outer part of the Sun less sensitive to turbulence and magnetic fields in the outer layers, where the physics is poorly understood • Longer lifetime frequency and splitting determination more accurate • Modes l ≤ 35: sensitive to structure of solar core and radiative interior • Open questions: • Deep radiative interior and solar core • > rotation (…faster…???) • > structure (density, temperature, chemical composition …) • Turbulence models: Mode damping and excitation mechanisms and physical properties of outer layers • ….

  26. l = 1, m = -1 mode amplitude low-frequency range mode linewidth: α (1/lifetime) Low-frequency p modes: BUT… (Acoustic) p-mode power spectrum (GONG) • Difficult to measure low-frequency modes, because: • Decreasing signal-to-noise ratio (SNR) as frequency decreases > classic methods of peak fitting the individual-m spectra fail • Very long lifetimes, as much as several years • >long-duration, high-quality data available today (GONG, MDI, BiSON, GOLF)

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