Parameters of the Gaussian-plus-continuum fit to the simulated positive-half velocity waves. σ_fit stands for the Gaussian standard deviation, A_fit for its amplitude, and C_fit for the continuum. The filled circle sizes are proportional to dark matter halo masses. Tiny error bars on the standard deviation and amplitude resulting from fitting the envelopes highlight the adequacy of the model choice. Halos shown in Figs. 3–5 are identified with red name tags and additional small filled red circles. The dashed grey lines stand for the surfaces that encompass 95% of the halos of a given mass bin. The mass bin increases from dark to light grey. Histograms of the amplitude and standard deviation values for the full sample of halos (solid black line) and per bin of mass (dashed grey lines) are given in the top and right panels, respectively, together with medians. The more massive the halos are the larger the amplitude is, and to a lesser extent the standard deviation is, on average. The scatter in the standard deviation values increases with the decrease in mass, probably because the environment plays a more important role for the halos of the smallest mass bin, while massive halos are more active in shaping their environment.