Bias on τ due for the null-test-based systematics templates. The blue line shows the distribution of τ for the reference CMB+noise simulations, the red line shows the resulting distribution when including also the null systematic maps built from the instrument-based simulations. The vertical magenta line shows the value of τ estimated for the single CMB realization to which the null maps from actual data, as opposed to the null maps from the instrumental simulations, were added. The dotted line shows the input value to the simulation, τ = 0.065. Top: D₁₂₋₃₄ null combination. Bottom: D₂₄₋₁₃ null combination.