Maria Cristina Rabello-Soares

A Comparison of Solar p-Mode Parameters from the Michelson Doppler Imager and the Global Oscillation Network Group: Splitting Coefficients and Rotation Inversions

Using contemporaneous helioseismic data from the Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) onboard SOHO, we compare frequency-splitting data and resulting inversions about the Suns internal rotation. Helioseismology has been very successful in making detailed and subtle inferences about the solar interior. But there are some significant differences between inversion results obtained from the MDI and GONG projects. It is important for making robust inferences about the solar interior that these differences are located and their causes eliminated. By applying the different analysis pipelines developed by the projects not only to their own data but also to the data from the other project, we conclude that the most significant differences arise not from the observations themselves but from the different frequency estimation analyses used by the projects. We find that the GONG pipeline results in substantially fewer fitted modes in certain regions. The most serious systematic differences in the results, with regard to rotation, appear to be an anomaly in the MDI odd-order splitting coefficients around a frequency of 3.5 mHz and an underestimation of the low-degree rotational splittings in the GONG algorithm.

On the Determination of Michelson Doppler Imager High-Degree Mode Frequencies

The characteristics of the solar acoustic spectrum are such that mode lifetimes get shorter and spatial leaks get closer in frequency as the degree of a mode increases for a given order. A direct consequence of this property is that individual p-modes are resolved only at low and intermediate degrees and that at high degrees individual modes blend into ridges. Once modes have blended into ridges, the power distribution of the ridge defines the ridge central frequency, and it will mask the true underlying mode frequency. An accurate model of the amplitude of the peaks that contribute to the ridge power distribution is needed to recover the underlying mode frequency from fitting the ridge. We present the results of fitting high-degree power ridges (up to l = 900) computed from several 2-3 month long time series of full-disk observations taken with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory between 1996 and 1999. We also present a detailed discussion of the modeling of the ridge power distribution, and the contribution of the various observational and instrumental effects on the spatial leakage, in the context of the MDI instrument. We have constructed a physically motivated model (rather than some ad hoc correction scheme) that we believe results in a methodology that can produce an unbiased determination of high-degree modes once the instrumental characteristics are well understood. Finally, we present preliminary estimates of changes in high-degree mode parameters with epoch and thus solar activity level and discuss their significance. These estimates are preliminary because they rely on a simple—if not simplistic—ridge-to-mode correction scheme to account for errors in the plate scale used for the spherical harmonic decomposition. Such a correction scheme produced residual systematics that, as we show, are not always constant with time. These cannot be properly corrected without reprocessing the data back to the level of the spherical harmonic decomposition.

Taiwan Oscillation Network

The Taiwan Oscillation Network (TON) is a ground-based network to measure solar intensity oscillations to study the internal structure of the Sun. K-line full-disk images of 1000 pixels diameter are taken at a rate of one image per minute. Such data would provide information onp-modes withl as high as 1000. The TON will consist of six identical telescope systems at proper longitudes around the world. Three telescope systems have been installed at Teide Observatory (Tenerife), Huairou Solar Observing Station (near Beijing), and Big Bear Solar Observatory (California). The telescopes at these three sites have been taking data simultaneously since October of 1994. Anl – v diagram derived from 512 images is included to show the quality of the data.

On the choice of parameters in solar-structure inversion

ABSTRA C T The observed solar p-mode frequencies provide a powerful diagnostic of the internal structure of the Sun and permit us to test in considerable detail the physics used in the theory of stellar structure. Among the most commonly used techniques for inverting such helioseismic data are two implementations of the optimally localized averages (OLA) method, namely the subtractive optimally localized averages (SOLA) and multiplicative optimally localized averages (MOLA). Both are controlled by a number of parameters, the proper choice of which is very important for a reliable inference of the solar internal structure. Here we make a detailed analysis of the influence of each parameter on the solution and indicate how to arrive at an optimal set of parameters for a given data set.

Inferences on the solar envelope with high-degree modes

We investigate the structure of the Sun by helioseismic inversion of a set of p-mode frequencies which includes new precise observations of modes with high degree ( l< 1000) obtained from the MDI instrument on the SOHO satellite (Rhodes et al. 1998). Such data have the potential to improve the resolution of the solar structure in the near-surface region, to provide detailed tests of the equation of state and constrain the envelope helium abundance. In order to suppress the uncertainties in the treatment of the surface layers in helioseismic inversion procedures, we introduce here the use of a new surface term, developed on the basis of higher-order asymptotic theory of acoustic modes and suitable for the handling of high-degree mode frequencies.

Comparison of Two Fitting Methods for Ring Diagram Analysis of Very High l Solar Oscillations

A new method of fitting tridimensional power spectra of solar oscillations is described and compared with a previous one whose use has been more common. The new method fits the parameters of the Lorentzian profiles in a bidimensional k - ω diagram constructed from an azimuthal average of the tridimensional one. The horizontal velocities are then determined keeping these parameters fixed, greatly reducing the computation time. Both methods are compared for two radial orders (n = 3, 4) of a tridimensional power spectrum obtained for a region of about 15° square around solar disk center. The images used in this work correspond to a 3 day set of 1080 × 1080 pixel intensity images obtained at the Observatorio del Teide on 1994 November 8-10 with the Taiwanese Oscillation Network (TON) instrument. The results of the fitted velocities agree within the estimated errors for the two methods. The reduction of the computing time obtained with the new method makes it convenient for the ring diagram analysis.

HMI ring diagram analysis I. The processing pipeline

The combination of high resolution, spatial coverage, and continuity of photospheric Doppler and other data from HMI has allowed us to embark on a program of systematic exploration of solar subsurface flows and thermal structure variations using the technique of ring-diagram analysis on an unprecedented scale. Two ring-diagrams pipelines exist: a synoptic program aimed at mapping the evolution of the circulation and local subsurface flows on a global scale from the surface to depths of down to 0.9Rsun, and a targeted program designed to provide a comprehensive view of the thermal structure anomalies associated with loci of magnetic activity over the course of their life cycles. In this paper we describe the analysis techniques implemented in the processing pipelines.

Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings

We present a detailed analysis of solar acoustic mode frequencies and their rotational splittings for modes with degree up to 900. They were obtained by applying spherical harmonic decomposition to full-disk solar images observed by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory spacecraft. Global helioseismology analysis of high-degree modes is complicated by the fact that the individual modes cannot be isolated, which has limited so far the use of high-degree data for structure inversion of the near-surface layers (r>0.97R⊙). In this work, we took great care to recover the actual mode characteristics using a physically motivated model which included a complete leakage matrix. We included in our analysis the following instrumental characteristics: the correct instantaneous image scale, the radial and non-radial image distortions, the effective position angle of the solar rotation axis, and a correction to the Carrington elements. We also present variations of the mode frequencies caused by the solar activity cycle. We have analyzed seven observational periods from 1999 to 2005 and correlated their frequency shift with four different solar indices. The frequency shift scaled by the relative mode inertia is a function of frequency alone and follows a simple power law, where the exponent obtained for the p modes is twice the value obtained for the f modes. The different solar indices present the same result.

Solar-cycle Variation of Sound Speed near the Solar Surface

We present evidence that the sound-speed variation with solar activity has a two-layer configuration, similar to the one observed below an active region, which consists of a negative layer near the solar surface and a positive one in the layer immediately below the first one. Frequency differences between the activity minimum and maximum of solar cycle 23, obtained applying global helioseismology to the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, is used to determine the sound-speed variation from below the base of the convection zone to a few Mm below the solar surface. We find that the sound speed at solar maximum is smaller than at solar minimum at the limit of our determination (5.5 Mm). The min-to-max difference decreases in absolute values until ~7 Mm. At larger depths, the sound speed at solar maximum is larger than at solar minimum and the difference increases with depth until ~10 Mm. At this depth, the relative difference (δc 2/c 2) is less than half of the value observed at the lowest depth determination. At deeper layers, it slowly decreases with depth until there is no difference between maximum and minimum activity.

HMI ring diagram analysis II. Data products

The combination of high resolution, spatial coverage, and continuity of photospheric Doppler and other data from HMI has allowed us to embark on a program of systematic exploration of solar subsurface flows and thermal structure variations using the technique of ring-diagram analysis on an unprecedented scale. There are two ring-diagrams pipelines, as described in [1]. In this paper we discuss the synoptic pipeline execution and describe the data being processed and produced.