Solar Wave-Field Simulation for Testing Prospects of Helioseismic Measurements of Deep Meridional Flows

Abstract

The meridional flow in the Sun is an axisymmetric flow that is generally poleward directed at the surface, and is presumed to be of fundamental importance in the generation and transport of magnetic fields. Its true shape and strength, however, is debated. We present a numerical simulation of helioseismic wave propagation in the whole solar interior in the presence of a prescribed, stationary, single-cell, deep meridional circulation serving as a test-bed for helioseismic measurement techniques. A deep-focusing time-distance helioseismology technique is applied to the artificial data showing that it can in fact be used to measure the effects of the meridional flow very deep in the solar convection zone. It is shown that the ray-approximation which is commonly used for interpretation of helioseismology measurements remains a reasonable approximation even for the very long distances between 12 • and 42 • corresponding to depths between 52 and 195 Mm considered here. From the measurement noise we extrapolate that on the order of a full solar cycle may be needed to probe the flow all the way to the base of the convection zone.

Detection of Equatorward Meridional Flow and Evidence of Double-Cell Meridional Circulation Inside the Sun

“…Note that no other filtering is applied in our analysis in order to avoid any complications in the Fourier domain when dealing with very large spatial scales. A deep-focusing time-distance measurement scheme (shown in Figure 1), which was described and validated by Hartlep et al (2013), is utilized. For each measurement, the solar oscillation signals are first averaged inside two 30…”

Verification of the helioseismic Fourier-Legendre analysis for meridional flow measurements

“…The generation of artificial helioseismic data is identical to the method described in Hartlep et al (2013), which makes use of a numerical code that solves the linearized propagation of helioseismic waves throughout the entire solar interior (Hartlep & Mansour 2005). This code has been used in previous studies to simulate the effects of various localized sound-speed perturbations, e.g.…”

“…As described in Hartlep et al (2013), the code has been extended to include the effects of mass flows onto the propagation of helioseismic waves. In short, the code models solar acoustic oscillations in a spherical domain by using the Euler equations that are linearized around a stationary background state.…”

“…In short, the code models solar acoustic oscillations in a spherical domain by using the Euler equations that are linearized around a stationary background state. As can be seen in Hartlep et al (2013), the equations are formulated in a non-rotating frame, and so rotation is accounted for by prescribing an appropriate flow. This approach saves computing the usual Coriolis and centrifugal forces that appear in the equations for a rotating frame.…”

“…For the background flow, we have imposed a stationary model of the solar meridional circulation according to Hartlep et al (2013). The flow model described there is based on the flow model in Rempel (2006).…”