NSM rates over time for different delay time distributions, normalized to the z = 0 rate. The dotted line shows the P. Madau & M. Dickinson (2014) star formation rate, while the dashed line shows a constant star formation rate. The colored lines show the P. Madau & M. Dickinson (2014) star formation rate convolved with different delay time distributions. More extended delay time distributions result in lower integrated numbers of NSMs, because the z = 0 rate is closer to the rate in the past. The legend shows C_SFH for different delay time distributions and star formation histories, where C_SFH is the enhancement in the number of NSMs relative to z = 0 due to the shape of the star formation history.