Separation of gain fluctuations and continuum signals in total power spectrometers with application to COMAP

TL;DR

This paper presents a time-domain, three-parameter model to simultaneously fit and separate $1/f$ gain fluctuations and continuum signals in total-power spectrometers, with application to the COMAP Pathfinder. By modeling the gain as $G_{\nu,t} = \bar{G}_\nu(1+\delta G_t)$ and the continuum as $T_{\nu,t} = \bar{T}_\nu + \delta T_t(1+\alpha_t\bar{\nu}) + \delta T_{\nu,t}^{\text{noise}}$, the authors derive a per-time-sample linear system for $(\delta G_t, \delta T_t, \delta T_t\alpha_t)$, leveraging stable system-temperature spikes as spectral calibrators to break degeneracies. A $1/f$ prior on $\delta G_t$ further stabilizes the solution, improving separation of gain from continuum, as demonstrated in simulations and Jupiter scans. The method yields substantial improvements for Galactic continuum mapping (reducing noise by factors of several on beam and larger scales) and offers competitive gains for CO LIM, while highlighting sensitivities to mean system temperature accuracy. Overall, the approach provides a robust pathway to cleaner total-power measurements in the presence of correlated gain noise and spectral continuum signals, with practical impact for both Galactic and extragalactic science in COMAP.

Abstract

We describe a time-domain technique for separating $1/f$ gain fluctuations and continuum signal for a total power spectrometer, such as the CO Mapping Array Project (COMAP) Pathfinder instrument. The $1/f$ gain fluctuations of such a system are expected to be common-mode across frequency channels. If the instrument's system temperature is not constant across channels, a continuum signal will exhibit a frequency dependence different from that of common-mode gain fluctuations. Our technique leverages this difference to fit a three-parameter frequency model to each time sample in the time-domain data, separating gain and continuum. We show that this technique can be applied to the COMAP Pathfinder instrument, which exhibits a series of temporally stable resonant noise spikes that effectively act as calibrators, breaking the gain degeneracy with continuum signals. Using both simulations and observations of Jupiter, we explore the effect of a $1/f$ prior for the gain model. We show that the model is capable of cleanly separating Jupiter, a bright continuum source, from the gain fluctuations in the scan. The technique has two applications to COMAP. For the COMAP observations performing line intensity mapping (LIM), the technique better suppresses atmospheric fluctuations and foregrounds than the COMAP LIM pipeline. For the Galactic COMAP observations, which map Galactic continuum signals, the technique can suppress $1/f$ gain fluctuations while retaining all continuum signals. This is demonstrated by the latest COMAP observations of $λ$-Orionis, where our method produces far cleaner maps than a destriper alone, typically reducing the noise power by a factor of 7 on beam scales and up to 15 on larger scales.

Figures (11)

• Figure 1: Temporal power spectrum of a single frequency channel (black) and a 1024-channel band-average (red) of a single COMAP scan. The averaging of channels suppresses the spectrally uncorrelated white noise, but not the highly correlated $1/f$ gain noise.
• Figure 2: The measured mean system temperature of three detectors for a randomly selected scan. The temperatures deviate somewhat from a flat profile, most notably the sharp spikes, which typically reach brightness temperatures of 100--200K.
• Figure 3: An example of the three frequency templates that are fitted for in our algorithm: (i) The continuum brightness ($1/T\nu$), which is the template for fitting $\delta T_t$. (ii) The continuum slope template ($\bar{\nu} /\bar{T}_\nu$), which is the template for fitting $\alpha_t\delta T_t$. (iii) The frequency-constant template, which is the fit for the 1/f gain $\delta G_t$. The flat continuum template ($1/\bar{T}_\nu$) and the gain template (constant) are highly degenerate.
• Figure 4: Ground truths and results from the simulations with a correct prior. Top: Ground truth (black) of the top-hat continuum signal, together with a single fit (teal) and the average of 100 simulations (orange), showing that the average appears to approach the ground truth, indicating an unbiased solution. Bottom: The same simulation results for the gain, where the single ground truth (black) is shown together with a single solution (teal). The average of 100 simulations (orange) appears to average towards zero, indicating that there was no leakage of continuum into the gain solution.
• Figure 5: Binned maps of the joint gain-continuum solution to a scan of Jupiter, both with a prior on $\delta G_t$ (top row) and without (bottom row). All maps are in units of $K$. The first three columns show the binned maps of the three parameters (the gain $\delta G_t$, the continuum brightness temperature $\delta T_t$, and the continuum slope $\delta T_t \alpha_t$), while the last column shows the frequency-averaged absolute residual after subtracting the joint model from the data. The central $\delta T_t$ pixel has an amplitude of $\approx 2.0K$ in both results.