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This article has an erratum: [https://doi.org/10.1051/0004-6361/202450732e]


Fig. 7.

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Phase of the kernel of the integral over θ and its critical points. (a) Dependence on the colatitude, θ, of the phase of the type of oscillating exponential that is encountered after we superpose the contributions of the constituent rotating rings of the source distribution that have the same colatitude but differing radii (see Sect. 2.2). The curves ae correspond to successively increasing values of the azimuthal coordinate of the observation point, φP. Note that for curves b and d (shown in red), this phase vanishes at one of its turning points. (b) Dependence of the separation between the locations of the maximum and minimum of a phase, θmax − θmin, with nearby turning points on the distance of the observer from the source, , and on the departure, θP − θPS, of the colatitude of the observer, θP, from the critical colatitude, θPS, at which the maximum and minimum of such a phase coalesce. This figure shows that θmax − θmin decreases as with increasing distance when .

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