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We present our calculation of electromagnetic effects, induced by thespectator charge on Feynman-$x_F$ distributions of charged pions in peripheral$Pb+Pb$ collisions at CERN SPS energies, including realistic initialspace-time-momentum conditions for pion emission. The calculation is performedin the framework of our simplified implementation of the fire-streak model,adopted to the production of both $\pi^-$ and $\pi^+$ mesons. Isospin effectsare included to take into account the asymmetry in production of $\pi^+$ and$\pi^-$ at high rapidity. A comparison to a simpler model from the literatureis made. We obtain a good description of the NA49 data on the $x_F$- and$p_T$-dependence of the ratio of cross sections $\pi^+/\pi^-$. The experimentaldata favors short times ($0.5<\tau<2$~fm/$c$) for fast pion creation in thelocal fire-streak rest frame. The possibility of the expansion of thespectators is considered in our calculation, and its influence on theelectromagnetic effect observed for the $\pi^+/\pi^-$ ratio is discussed. Inaddition we discuss the relation between anisotropic flow and theelectromagnetic distortion of $\pi^+/\pi^-$ ratios, and study the influence oftransverse expansion of fire streaks as well as their vorticity on thisdistortion. In this latter study we find that inclusion of rotation of firestreaks in our model gives a satisfactory description of the rapiditydependence of pion directed flow. We conclude that {our implementation of the}fire-streak model, which properly describes the centrality dependence of$\pi^-$ rapidity spectra at CERN SPS energies, also provides a quantitativedescription of the electromagnetic effect on the $\pi^+/\pi^-$ ratio as afunction of $x_F$.

Spectator induced electromagnetic effects in heavy-ion collisions and space-time-momentum conditions for pion emission