Top: model differences for the sound-speed profile similar to those of Fig. 5, in the sense (reference model) – (modified model), but with a smaller fifth-force coupling 𝒴 = 10⁻³. The plot zooms into the solar region where our estimates of systematics from opacity and diffusion may become negligible compared to that of the fifth force, in order to clearly illustrate the peak of the fifth-force effect in the radiative zone. The error bar shows approximately the error of helioseismic inversions at that point, ∼10⁻⁴, to highlight the precision down to which helioseismic reconstructions of the solar sound speed can constrain the coupling 𝒴. The insignificance of the opacity and diffusion uncertainties compared to the fifth force for this solar region is discussed in Sect. 4. Bottom: an illustration of the mechanism behind the ‘clean’ peak of the fifth-force effect on the speed of sound profile around r ≃ 0.25 R_⊙, where the systematics from uncertainties related to opacity and diffusion become negligible compared to the effect of the fifth force (see also Fig. 5). The reference model at standard gravity is the GS98 model (see Table 2 and text). The plots assume for illustration the ideal-gas approximation for the sound-speed profile, where , and neglect the small variation of the adiabatic index Γ₁ (see also Fig. 5). Right panel: fractional difference of the sound-speed profile and its components under an increase of the opacity by 5%, but the picture is similar for uncertainties in diffusion. Left panel: how the picture changes for the fifth-force effect. For a detailed discussion we refer to the text around Eq. (27).