Investigating the Center-to-Limb Effects in Helioseismic Data Using 3D Radiative Hydrodynamic Simulations

TL;DR

The paper addresses center-to-limb systematic biases in helioseismic observations by using 3D radiative hydrodynamic simulations that include solar rotation to generate synthetic observables for nine viewing angles and analyzing their $ l$ and ring-diagram spectra. It synthesizes the Fe I 6173 Å line to obtain continuum intensity $I_c$ and Doppler velocity $V_D$, enabling direct comparison of $f$- and $p$-modes and pseudo-modes across longitudes. Key findings show that oscillation power generally decreases toward the limb for both observables, with East–West asymmetries tied to rotation that intensify with frequency; $f$- and $p$-mode amplitudes and widths shift with longitude, and the two observables exhibit distinct pseudo-mode behavior and background changes. These results provide a physics-based framework to correct full-disk helioseismic data and demonstrate the value of realistic 3D simulations for disentangling geometric from physical biases in solar observations, with implications for improving analyses of SDO/HMI and Solar Orbiter data.

Abstract

Full-disk observations from missions such as the SDO and SOHO have enabled comprehensive studies of solar oscillations and dynamics. Interpreting helioseismic and photospheric data is complicated by systematic center-to-limb variations. To explore the physical origin of these variations, we perform local 3D radiative hydrodynamic simulations that include effects of solar rotation to generate 24-hour synthetic time series of continuum intensity and Doppler velocity for nine viewing angles spanning from -75 to 75 degrees. The simulations reveal a systematic decrease in oscillation power toward the limbs and a pronounced East-West asymmetry that increases with frequency, primarily due to rotation-induced flows. With increasing angular distance from the disk center, the amplitudes and widths of the surface gravity (f) and resonant pressure (p) modes decrease. In contrast, the amplitudes of the corresponding pseudo-modes with frequencies above the acoustic cut-off frequency increase in the intensity power spectra but are suppressed in the velocity spectra. The local helioseismology ring-diagram analysis of the simulation data further demonstrates anisotropic broadening of the modes and distinct differences in background noise and pseudo-mode structure between the intensity and velocity data. These results indicate that the center-to-limb effects arise from both geometric projection and physical factors such as line-formation height and potential effects of the radial differential rotation. The findings provide a framework for correcting helioseismic observations and demonstrate that realistic 3D radiative hydrodynamic simulations are a powerful tool for disentangling geometric and physical biases in solar data.

Figures (14)

• Figure 1: Panel a) Variations with longitude of the Doppler velocity (${\rm V_D}$; blue curve) and the continuum intensity (${\rm I_c}$; red curve). Panel b: Comparison of the time variations of ${\rm V_D}$ at $\pm 60^{\mathrm{o}}$ longitudes (red solid and blue dashed curves) and the disk center (black curve) shows 5-minute variations, contribution of the solar rotation, and dynamics of the atmosphere for areas closer to the solar limb. Panel c): The logarithm of the oscillation power spectrum (the $\ell$-$\nu$ diagram) from synthetic Doppler velocity at the disc center overplotted with the $f$- and $p$-modes (white curves) fitted to the observed power spectra from SDO/HMI by Reiter2020. The vertical bars in panel a) correspond to $1\sigma$ variations for the time difference of ${\rm V_D}$.
• Figure 2: Center to limb variations in the power spectra of the continuum intensity (panel a) and the Doppler velocity (panel b), and the oscillation power changes for five resonance modes for the continuum intensity spectrum (panel c) and six modes from the Doppler velocity spectrum (panel d).
• Figure 3: Variations of the acoustic power as a function of the frequency at different distances from the disc center for the continuum intensity (panel a) and the Doppler velocity (panel b). The resulting power from a series of 17 power maps covering eight frequency ranges from 0.5 to 8.5 mHz. Each power map is computed for 1 mHz frequency ranges.
• Figure 4: The power spectra distribution as a function of the angular degree and frequency (the $\ell-\nu$ diagrams) obtained for the continuum intensity (panel a) and Doppler velocity fluctuations (panel b) at different distances from the disk center. The presented diagrams are the result of averaging 17 diagrams from an 8-hour time series with a 1-hour time shift. The $\ell - \nu$ diagrams are obtained after applying the running time differencing to the 2D time series of the continuum intensity and the Doppler velocity, and subtracting the mean values.
• Figure 5: Comparison of the oscillation power for the continuum intensity (panel a) and Doppler velocity (panel b) at $\pm 60^{\mathrm{o}}$ longitudes toward the East (blue curves) and West (red curves) limbs at selected frequencies. The plots are extracted from the $\ell-\nu$ diagrams shown in Figure \ref{['fig:l-nu_diff']}. The dashed black curves correspond to the disk center ($0^{\mathrm{o}}$) and are given as a reference.