An improved multi-ridge fitting method for ring-diagram helioseismic analysis

Abstract

Context. There is a wide discrepancy in current estimates of the strength of convection flows in the solar interior obtained using different helioseismic methods applied to observations from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The cause for these disparities is not known. Aims. As one step in the effort to resolve this discrepancy, we aim to characterize the multi-ridge fitting code for ring-diagram helioseismic analysis that is used to obtain flow estimates from local power spectra of solar oscillations. Methods. We updated the multi-ridge fitting code developed by Greer et al. (2014, Sol. Phys., 289, 2823 to solve several problems we identified through our inspection of the code. In particular, we changed the 1) merit function to account for the smoothing of the power spectra, 2) model for the power spectrum, and 3) noise estimates. We used Monte Carlo simulations to generate synthetic data and to characterize the noise and bias of the updated code by fitting these synthetic data.Results. The bias in the output fit parameters, apart from the parameter describing the amplitude of the p-mode resonances in the power spectrum, is below what can be measured from the Monte-Carlo simulations. The amplitude parameters are underestimated; this is a consequence of choosing to fit the logarithm of the averaged power. We defer fixing this problem as it is well understood and not significant for measuring flows in the solar interior. The scatter in the fit parameters from the Monte-Carlo simulations is well-modeled by the formal error estimates from the code. Conclusions. We document and demonstrate a reliable multi-ridge fitting method for ring-diagram analysis. The differences between the updated fitting results and the original results are less than one order of magnitude and therefore we suspect that the changes will not eliminate the aforementioned orders-of-magnitude discrepancy in the amplitude of convective flows in the solar interior. Key words. Sun: helioseismology -Methods: data analysis Schou et al. 2012) onboard the Solar Dynamics Observatory (SDO; Pesnell et al. 2012) are automatically computed by the SDO/HMI ring-diagram pipeline (Bogart et al. 2011a,b) on a daily basis since the SDO launch in 2010.The HMI ring pipeline codes separately fit each single ridge (single radial order n) in the power in slices at constant horizontal wavenumber or slices in temporal frequency. Greer et al. (2014) developed an alternative approach based on simultaneously fitting multiple ridges (multiple radial orders) at each horizontal wavenumber. Greer et al. (2015) introduced another in-Article number, page 1 of 18

Rotation suppresses giant-scale solar convection

“…Our results put on a firm theoretical footing the earlier suggestions of Miesch et al ( 4 ) and Featherstone and Hindman ( 5 ). We also corroborate and provide context to the observations of Hanasoge et al ( 1 , 3 ), as well as more recent observations ( 11 ). Our estimates leave the flow amplitude only somewhat smaller than previous mixing-length models, which ignore rotational effects.…”

“…The discrepancies are still surprising even if they are measured at different depths. The disagreement between these results remains unresolved ( 11 ).…”

Helioseismological determination of the subsurface spatial spectrum of solar convection: Demonstration using numerical simulations

“…On the other hand, we cannot resolve the inconsistency of these results with those obtained by Greer et al (2015) using ringdiagram analysis at this stage. A deeper analysis of that method is required to resolve this issue, see also Nagashima et al (2020). We are confident that by a careful and detailed evaluation of all aspects of both methods this discrepancy can be understood and resolved.…”

Helioseismological determination of the subsurface spatial spectrum of solar convection: Demonstration using numerical simulations

“…On the other hand, we cannot resolve the inconsistency of these results with those obtained by Greer et al (2015) using ring-diagram analysis at this stage. A deeper analysis of that method is required to resolve this issue, see also Nagashima et al (2020). We are confident that by a careful and detailed evaluation of all aspects of both methods this discrepancy can be understood and resolved.…”