We combine unresolved-Sun velocity and intensity observations at multiple wavelengths from the Helioseismic and Magnetic Imager and Atmospheric Imaging Array onboard the Solar Dynamics Observatory to investigate the possibility of multi-spectral mode-frequency estimation at low spherical harmonic degree. We test a simple multi-spectral algorithm using a common line width and frequency for each mode and a separate amplitude, background and asymmetry parameter, and compare the results with those from fits to the individual spectra. The preliminary results suggest that this approach may provide a more stable fit than using the observables separately

A-M Broomhall

Fossum A

Howe R

K Jain

Nigam R

Press W H

R Howe

W J Chaplin

Y Elsworth

Journal of Physics : Conference Series

English

Howe, R. (Rachel)

Broomhall, Anne-Marie

Chaplin, William James

Elsworth, Yvonne

Jain, K.

Warwick Research Archives Portal Repository

http://wrap.warwick.ac.uk            Original citation: Howe, R., Broomhall, A. -M., Chaplin, W. J., Elsworth, Y. and Jain, K.. (2013) Low-degree multi-spectralp-mode fitting. Journal of Physics: Conference Series, Volume 440 . Article number 012011. ISSN 1742-6596  Permanent WRAP url: http://wrap.warwick.ac.uk/59072                                Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions.  This article is made available under the Creative Commons Attribution 3.0 (CC BY 3.0) license and may be reused according to the conditions of the license.  For more details see: http://creativecommons.org/licenses/by/3.0/    A note on versions: The version presented in WRAP is the published version, or, version of record, and may be cited as it appears here.  For more information, please contact the WRAP Team at: publications@warwick.ac.uk  This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 137.205.202.72This content was downloaded on 23/01/2014 at 15:54Please note that terms and conditions apply.Low-degree multi-spectral p-mode fittingView the table of contents for this issue, or go to the journal homepage for more2013 J. Phys.: Conf. Ser. 440 012011(http://iopscience.iop.org/1742-6596/440/1/012011)Home Search Collections Journals About Contact us My IOPscienceLow-degree multi-spectral p-mode fittingR Howe1, A-M Broomhall1,2,3, W J Chaplin1, Y Elsworth1and K Jain41School of Physics and Astronomy, University of Birmingham, UK2Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick,Coventry, CV4 7AL3Institute of Advanced Study, University of Warwick, Coventry, CV4 7AL4National Solar Observatory, 950 N Cherry Ave., Tucson, AZ 85719, USAE-mail: rhowe@nso.eduAbstract. We combine unresolved-Sun velocity and intensity observations at multiplewavelengths from the Helioseismic and Magnetic Imager and Atmospheric Imaging Arrayonboard the Solar Dynamics Observatory to investigate the possibility of multi-spectral mode-frequency estimation at low spherical harmonic degree. We test a simple multi-spectralalgorithm using a common line width and frequency for each mode and a separate amplitude,background and asymmetry parameter, and compare the results with those from fits to theindividual spectra. The preliminary results suggest that this approach may provide a morestable fit than using the observables separately.1. IntroductionThe 1700 and 1600 A˚ bands of the Atmospheric Imaging Assembly (AIA) onboard the SolarDynamics Observatory (SDO) are formed higher in the solar atmosphere than the lines typicallyused for Doppler velocity measurements – around 360 km for the 1700 A˚ and 480 km for the1600 A˚ band [1], extending from the upper photosphere into the chromosphere. They neverthlessshow a clear p-mode spectrum for integrated-Sun measurements [2]. Although the velocity andintensity spectra formed at different heights differ in many details and reflect different modephysics, the underlying mode frequency and lifetime should be independent of the height offormation or the details of the observation, allowing us to use several spectra together to obtainan improved estimate of the underlying mode parameters. In this article, we attempt to improveour estimates of the parameters of low-degree p-modes, using data from AIA and from theHelioseismic and Magnetic Imager (HMI) also onboard SDO.2. DataThe data used cover 691 days starting with 13 May 2010, giving a frequency resolution of 17nHz. Time series were formed from the AIA 1600 A˚ and 1700 A˚ bands and the HMI DopplerVelocity [V], Continuum Intensity [Ic], and Line Core Intensity [Lc, formed by subtracting theLine Depth observable from Ic], using the DATAMEAN keyword supplied with each HMI andAIA image in the JSOC database1. The heights of formation of the HMI observables are around1 http:/jsoc.stanford.edu/Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/012011Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd 125 km for HMI Ic, 100 km for HMI V, and 270 km for HMI Lc [3; 4]. All time series wereinterpolated to a uniform 45-second cadence; long-term and daily trends were also removed.3. AnalysisIn this preliminary work we took a simple approach to multi-spectral fitting, in which all fivespectra were fitted simultaneously for each ℓ = 0, 2 and ℓ = 1, 3 pair of modes. Each mode hadonly one frequency, linewidth and rotational splitting parameter, but the amplitude, asymmetryand background parameters were independent for each spectrum. The peak profile was that of[5]:P (x) = A(1 + Sx)2 + S2(1 + x2)+B, (1)where A is the amplitude, S is the asymmetry parameter, B is the background parameter andx = 2(ν − ν0)/γ, γ being the FWHM and ν0 the central frequency. For the sake of a morestable fit we fixed the rotational splitting at 0.41 µHz and also fixed the amplitude ratios of therotationally split components, but the relative amplitudes of ℓ = 1, 3 and ℓ = 0, 2 mode pairswere not constrained.We use an AMOEBA-based [6] maximum likelihood estimation fitting algorithm, with a firstpass on a lightly (15-bin) smoothed power spectrum to improve the first guesses for the finalfit. We fit each ℓ = 0, 2 and ℓ = 1, 3 pair separately in a 50-µHz frequency window. Foreach mode pair, the observables were scaled so that all of the smoothed spectra had the samemaximum value and roughly the same weight in the fit. Formal uncertainties on the estimatedparameters were approximated using the inverse of a numerically computed Hessian matrix,neglecting off-diagonal terms to save computing time.In Figure 1 we show some sample multi-spectral fits with the first-guess and final modelssuperimposed on the spectrum. This figure also serves to illustrate the differing signal-to-noiseratios of the various observables, with HMI Ic having the lowest signal-to-noise and HMI V thehighest. After fitting, we rejected results where the fit did not converge properly (non-finiteerror), as well as those with unreasonably small line widths or negative amplitude parameters.This weeding does not remove all of the obviously “out of line” fits, particularly when signal-to-noise is poor, and some further criteria will be needed in future work. To test the efficacyof the simultaneous fitting, we fitted the five spectra both together and individually using thesame model and first-guess parameters.4. Results and discussionIn Figure 2 we show the linewidth and frequency parameters from the multi-spectral and single-spectral fits, with frequency being represented by the difference between the input first-guessand final estimated frequency so as to show the scatter. By definition all of the frequency andwidth estimates fall on top of one another for the multi-spectral case, so HMI V dominates theleft-hand panels because it was plotted last and has the largest number of successful fits. Thereare a couple of cases where the multi-spectral fit failed for HMI V but succeeded for HMI Lc,which show as green points. Clearly the scatter in the frequency and width estimates is largerin the single-fit case for the noiser observables, with many of the width estimates falling so faroff the curve as to indicate that the fit has effectively failed in these cases.Figures 3, 4 and 5 show the amplitude, background and asymmetry for each observable.For every observable except HMI V (which has much the highest signal-to-noise ratio), thesimultaneous fit results in a larger number of successful parameter determinations than theindividual fits, where success is defined as having all of the parameters for a given mode andobservable pass the simple checks outlined above. The amplitude and background results alsoseem to follow a smoother curve for the multi-spectral fits, particularly for the weak ℓ = 3Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/0120112Figure 1. Sample segments of spectra for the various observables. The light-blue curve showsthe first-guess model and the red curve the final fit.Figure 2. Fitted frequency relative to first-guess frequency (top) and fitted line width (bottom)for the multi-spectral fit (left) and for the individual spectral fits (right). Black represents AIA1600 A, blue AIA 1700 A, light blue HMI Ic, green HMI Lc, and red HMI V; the different degreesare shown as circles (ℓ = 0), squares (ℓ = 1), diamonds (ℓ = 2) and triangles (ℓ = 3).Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/0120113Figure 3. Comparison of fitting results from multi-spectra (left) and single (right) fits showingamplitude for each observable. The different degrees are shown as circles (ℓ = 0), squares (ℓ = 1),diamonds (ℓ = 2) and triangles (ℓ = 3).Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/0120114Figure 4. Comparison of fitting results from multi-spectral (left) and single-spectrum (right)fits showing background parameter for each observable. Circles indicate ℓ = 0, 2 pairs andsquares ℓ = 1, 3.Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/0120115Figure 5. Comparison of fitting results from multi-spectral (left) and single (right) fits, showingasymmetry parameter for each observable. The different degrees are shown as circles (ℓ = 0),squares (ℓ = 1), diamonds (ℓ = 2) and triangles (ℓ = 3).Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/0120116modes in the intensity observables. This may be because the information from the HMI Vhelps to fix the frequency of these modes and ensure that the correct peak is being fitted evenwhen it is buried in the noise. The asymmetry estimates are noisier, but the predominantlynegative asymmetry for HMI V, and positive asymmetry for HMI Ic, are clearly seen, whereasthe observables formed higher in the atmosphere – the AIA bands and HMI Lc – show atendency towards positve asymmetry at low frequencies and negative at high frequencies. Asthe asymmetry depends on the interaction of the modes with the solar background noise, suchas granulation, this may perhaps be understood as a lesser influence of granulation higher in theatmosphere. At the highest frequencies, close to the acoustic cut-off, where the modes are broadand not resolved, the fitting is less robust and the trend is less clear, but there are hints that theHMI Ic asymmetry decreases again, while those for the other observables may be increasing.The results from this preliminary exercise are promising, but there is plenty of room toimprove the method. A more sophisticated fitting algorithm might well give better results evenfor the single-spectrum case. To take full advantage of the multiple observables we need to usethe phase and coherence information as well as the power spectra. We hope to do this in futurework.AcknowledgmentsHMI data courtesy of SDO (NASA) and the HMI consortium. The National Solar Observatoryis operated by the Association of Universities for Research in Astronomy (AURA), Inc. under acooperative agreement with the National Science Foundation. This work was partly supportedby NASA grant NNH12AT11I to NSO. RH acknowledges computing support from NSO.References[1] Fossum A and Carlsson M 2005 Astrophys. J. 625 556–562[2] Howe R, Hill F, Komm R, Broomhall A, Chaplin W J and Elsworth Y 2011 Journal ofPhysics Conference Series 271 012058–+[3] Norton A A, Graham J P, Ulrich R K, Schou J, Tomczyk S, Liu Y, Lites B W, Lo´pez AristeA, Bush R I, Socas-Navarro H and Scherrer P H 2006 Solar Phys. 239 69–91 (PreprintarXiv:astro-ph/0608124)[4] Fleck B, Couvidat S and Straus T 2011 Solar Phys. 271 27–40 (Preprint 1104.5166)[5] Nigam R and Kosovichev A G 1998 Astrophys. J. Lett. 505 L51–54[6] Press W H, Flannery B P and Teukolsky S A 1989 Numerical recipes. The art of scientificcomputing (FORTRAN Version) (Cambridge University Press)Eclipse on the Coral Sea: Cycle 24 Ascending (GONG 2012, LWS/SDO-5, and SOHO 27) IOP PublishingJournal of Physics: Conference Series 440 (2013) 012011 doi:10.1088/1742-6596/440/1/0120117

and Kosovichev A G

Solar Phys.

Low-degree multi-spectral p-mode fitting

Howe, Rachel

Chaplin, William

Jain, K

University of Birmingham Research Portal

Low-degree multi-spectral p -mode fitting

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Low-degree multi-spectral<i>p</i>-mode fitting

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Low-degree multi-spectral p-mode fitting

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