Map-making LFI

Noise Monte Carlo Simulation

Overview

Calculating and handling full pixel-to-pixel noise covariances in Planck maps if feasible only at low resolution. To support the analysis of high-resolution maps, a Monte Carlo set of noise maps were produced. These noise Monte Carlos were produced at two levels of the analysis: 1) LFI Monte Carlo (MC) as part of the LFI data processing, and 2) Full Focal Plane (FFP) Monte Carlo as part of the joint HFI/LFI data processing. This page describes the LFI noise MC. For the FFP MC, see HL-sims.

Inputs

The noise MC assumes a three-parameter noise model: white noise level ($\sigma$), slope, and knee frequency ($f_\mathrm{knee}$), so that the noise power spectrum is assumed to have the form

$ P(f) = \frac{2\sigma^2}{f_\mathrm{sample}}\left[1+\left(\frac{f}{f_\mathrm{knee}}\right)^\mathrm{slope}\right] $.

Here $f_\mathrm{sample}$ is the sampling frequency of the instrument. The first term corresponds to white noise and the second term to correlated ($1/f$) noise. The noise parameters were determined separately for each radiometer as described in TOI-Noise LFI, assuming they stayed constant over the mission.

The detector pointing was reconstructed from satellite pointing, focal-plane geometry, and

The noise was generated internally in the Madam map-making code using a Stochastic Differential Equation (SDE) method, to avoid time-consuming writing and reading noise timelines to/from disk. Noise for each pointing period was generated separately, using a double-precision random number seed constructed from the realization number, radiometer number, and the pointing period number; to allow regeneration of the same noise realization when needed. White noise and $1/f$ noise were generated separately.

The