The Noise Floor of an Azimuthal-Average Template Fit: Minimum Detectable Amplitude for a Fixed Low-Multipole Profile on the Planck Sky

A fixed low-multipole profile fitted to azimuthal averages about a chosen axis returns one number, an amplitude, and that number is only as informative as the scatter of the same fit on skies with no profile present. This paper derives that scatter, calibrates it against the rotated-axis null measured on Planck PR3 data (standard deviation 6.13 microK for the SMICA map), and tabulates the smallest amplitude the statistic can certify. For a Planck-like mask fraction and noise level the estimator's standard deviation is 6.13 microK, so a one-sided 95 per cent detection requires 10.08 microK, a 99 per cent detection 14.26 microK, and a three-sigma detection 18.39 microK. The registered amplitude cap of 21.69 microK therefore sits at 3.54 standard deviations: the test could have seen a profile at the cap with room to spare, while the measured amplitude of 5.79 microK amounts to 0.94 standard deviations and is properly read as no detection. Masking and noise degrade the floor in a simple, tabulated way. The study is simulated and computed, not measured.