Uncertainties in Low-Count STIS Spectra

We evaluate uncertainty calculations in the calstis pipeline for data in the low-count regime. Due to the low dark rate and read-noise free nature of MAMA detectors, observations of UV-dim sources can result in exposures with 0 or 1 counts in some pixels. In this regime, the “root-N” approximation widely used to calculate uncertainties breaks down, and one must compute Poisson confidence intervals for more accurate uncertainty calculations. The CalCOS pipeline was updated in 2020 to account for these low-count uncertainties. Here, we assess how STIS observations are currently affected by this phenomenon, describe a new Jupyter notebook exploring the issue, and introduce a new utility, stistools.poisson_err, to manually calculate Poisson confidence intervals for 1D STIS spectra. Additionally, we describe a related software bug in the stistools$.$inttag utility, which splits TIME-TAG data into sub-exposures. This newly fixed bug serves as a useful case-study for the proper use of Poisson confidence intervals.

💡 Research Summary

The paper addresses a critical statistical issue in the reduction of Hubble Space Telescope STIS (Space Telescope Imaging Spectrograph) data obtained with its MAMA (Multi‑Anode Microchannel Array) detectors. Because MAMA devices have virtually zero read noise and extremely low dark currents (≈0.001 count s⁻¹ pixel⁻¹ for NUV‑MAMA and ≈0.0002 count s⁻¹ pixel⁻¹ for FUV‑MAMA), observations of UV‑dim sources or long‑duration exposures often yield pixel‑wise counts of 0 or 1. In this low‑count regime the commonly used “root‑N” approximation (σ≈√N) fails, leading to under‑estimated uncertainties, especially when N≈0.

The authors first review the concept of confidence intervals for the true mean λ of a Poisson process given an observed count N. They explain that for small N the Poisson distribution is highly asymmetric and that separate upper (λ_u) and lower (λ_l) limits must be derived from the cumulative distribution. They discuss several analytic approximations (Gehrels 1986, Pearson, Sherpa‑Gehrels, Kraft‑Burrows‑Nousek) and conclude that the most robust implementation is the “frequentist‑confidence” interval provided by astropy.stats.poisson_conf_interval, which is based on the χ² relationship and yields λ_l=0 and λ_u≈1 for N=0, thereby avoiding a zero‑error result.

The current STIS pipeline (calstis) still employs the root‑N formula, σ = √(N‑B)·g + R, which reduces to σ≈√N for MAMA data because bias (B) and read noise (R) are zero. To quantify the impact, the authors analyze archival GJ 436 G140M observations (Program 12034). Near the strong Ly‑α emission line the counts are high enough that root‑N approximates the true error, but in the line wings and continuum regions the counts drop to near zero. Figure 4 demonstrates that the pipeline’s uncertainties collapse to zero, whereas the proper Poisson 84.13 % (1‑σ one‑sided) upper confidence limit remains ≈1 count, a substantial difference that could affect the detection of faint absorption features.

Rather than modifying the pipeline, the authors introduce a new Python utility, stistools.poisson_err, which wraps astropy’s Poisson confidence interval routine. The function accepts a 1‑D extracted spectrum (or any array of counts) and returns the asymmetric lower and upper errors for each pixel. A Jupyter notebook (Section 4.2) illustrates its use, allowing users to apply the correct uncertainties in post‑processing without altering the standard calstis workflow.

The paper also documents a software bug in stistools.inttag, the routine that splits TIME‑TAG data into sub‑exposures. The bug incorrectly accumulated counts across sub‑exposures, artificially lowering the observed N and thus exacerbating the under‑estimation of errors when the root‑N method was used. After fixing the bug, the sub‑exposures produce correct Poisson‑based uncertainties, reinforcing the importance of accurate bookkeeping in low‑count regimes.

In conclusion, the study emphasizes that low‑count STIS data require Poisson‑based error estimation rather than the traditional root‑N approximation. The provided stistools.poisson_err utility and the inttag bug fix give the community practical tools to obtain statistically sound uncertainties. The methodology is readily extensible to other instruments with similar detector characteristics (e.g., COS, JWST NIRISS), ensuring more reliable scientific interpretations when dealing with sparse photon counts.