Uncertainties in Low-Count STIS Spectra

Abstract

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.

Figures (6)

• Figure 1: Poisson versus Gaussian Distribution for $\lambda = \mu = 1$ and 15. The Gaussian distributions are given $\sigma$ consistent with the root-N approximation of the Poisson distribution.
• Figure 2: Top: The upper and lower limits to the 1-$\sigma$ (1-sided 84.13%) confidence interval for the "frequentist-confidence" interval from astropy.poisson_conf_interval compared to the root-N approximation. The lower limit from the Poisson confidence interval (PCI) mostly overlaps the root-N approximation at this scale. Bottom: The residual between the Poisson confidence intervals and the root-N approximation. The upper-limit asymptotes to always be about +1 larger than the root-N approximation due to the discrete nature of the Poisson distribution.
• Figure 3: Top: The 1D extracted spectrum from STIS/G140M observations of M-dwarf GJ 436 just before a transit of its Neptune-sized exoplanet GJ 436b from Program 12034 (PI: Green, Dataset ID: obgh07020). Note the large Ly-$\alpha$ emission surrounded by regions of near-zero counts. The large background flux comes from geocoronal "airglow" of Ly-$\alpha$, while ISM absorption of the target flux results in absorption of the stellar line's core. Bottom: Uncertainties in the spectrum from the pipeline (solid gold), the manual root-N approximation (dashed light grey), and the manual root-N approximation plus the average dark count (dotted dark grey).
• Figure 4: Uncertainties for the data show in Figure \ref{['fig:gj436b']} longward of 1217 $\mathrm{\AA}$ where very few counts are detected. The pipeline-calculated uncertainties (grey) are significantly underestimated compared to the true $1\sigma$ Poisson upper 84.13% confidence interval (orange).
• Figure 5: Demonstration of the errors calculated from stistools.poisson_err using obgh07020. The errors from stistools.poisson_err (dashed) are shown to match manual Poisson confidence intervals calculated with astropy.stats.poisson_conf_interval (solid).