Contours of the parameters α and β/H_* that lead to a signal above LISA’s power law sensitivity with a S/N threshold of 10 (see Fig. 1). The top panels take a fixed value of the wall velocity v_w = {0.4, 0.6, 0.8, 1} (indicated in different colors) and scan over temperatures to construct the contours, while the lower panels fix the temperature in GeV T_* = {10, 10², 10³, 10⁴, 10⁵, 10⁶} and scan over wall velocities to construct the contours. Left and right panels correspond to ε_turb = 0.1 and 1, respectively. The results shown correspond to the sound-wave template based on the fit from the Higgsless simulations (cf., Sect. 2.1), as this choice does not affect the magnetic field parameters in Fig. 3. Colored contours correspond to regions of the parameter space where H_*τ_nl ≲ 1, while their continuation by dashed contours corresponds to regions where H_*τ_nl ≳ 1.