Towards Improved Heliosphere Sky Map Estimation with Theseus

Abstract

The Interstellar Boundary Explorer (IBEX) satellite has been in orbit since 2008 and detects energy-resolved energetic neutral atoms (ENAs) originating from the heliosphere. Different regions of the heliosphere generate ENAs at different rates. It is of scientific interest to take the data collected by IBEX and estimate spatial maps of heliospheric ENA rates (referred to as sky maps) at higher resolutions than before. These sky maps will subsequently be used to discern between competing theories of heliosphere properties that are not currently possible. The data IBEX collects present challenges to sky map estimation. The two primary challenges are noisy and irregularly spaced data collection and the IBEX instrumentation’s point spread function. In essence, the data collected by IBEX are both noisy and biased for the underlying sky map of inferential interest. In this article, we present a two-stage sky map estimation procedure called Theseus. In Stage 1, Theseus estimates a blurred sky map from the noisy and irregularly spaced data using an ensemble approach that leverages projection pursuit regression and generalized additive models. In Stage 2, Theseus deblurs the sky map by deconvolving the PSF with the blurred map using regularization. Unblurred sky map uncertainties are computed via bootstrapping. We compare Theseus to a method closely related to the one operationally used today by the IBEX Science Operation Center (ISOC) on both simulated and real data. Theseus outperforms ISOC in nearly every considered metric on simulated data, indicating that Theseus is an improvement over the current state of the art.

KEYWORDS:

• Deconvolution
• Ensemble models
• Generalized additive models
• Heliosphere
• Projection pursuit regression
• Regularization

Supplementary Materials

In the online supplementary materials of this article, we provide details on how the point spread function matrix K is constructed, additional GAM and PPR details, details on how ISOC maps are constructed, additional analyses supplementing Section 4, and a detailed table of the notation presented in the article. Additionally, the zip file contains R code and datasets to recreate Figures 2, 3, 4, 6, and 7. The R code and datasets can also be found at https://github.com/lanl/Theseus.

Acknowledgments

We thank the editor, associate editor, and two anonymous reviewers for their constructive and insightful feedback. We also thank C.C. Essix for her assistance and encouragement. Approved for public release: LA-UR-22-30879.

Disclosure Statement

The authors report there are no competing interests to declare.

Notes

1 For context, the outer boundary of the heliosphere, called the heliopause, is over 100 astronomical units from the Sun, where 1 astronomical unit is the mean distance between Earth and the Sun.

2 For the first few years of the IBEX mission, IBEX reorientation occurred approximately every 7 days, or once per orbit, not 4.5 days. In June 2011, the IBEX orbit was changed to a 9-day period orbit and since then, repoints are done twice per orbit.

3 Heliospheric ENA rates vary on the order of months and are treated as constant for each 6-month sky map.

4 Due to data quality issues, ESA 1—the lowest energy step—is not used.

5 180 sec × 6 ESA steps × 360 $1^{°}$ bins $=$ 388,800 sec $=$ 4.5 days, which is the duration of an arc.

6 For a $2^{°}$ sky map, $N_p=(180/2)*(360/2)=16,200$ pixels.

7 Recall the notational conventions of Section 3 and note here that the “hat” notation of $\widehat{\mathit{\theta }}$ is being used as a generic estimate of $\mathit{\theta }$, not as Theseus’s final estimate of $\mathit{\theta }$.

8 Further regularization was imposed on pixels proportional to their size. While all pixels are of the same size in degrees, they have different surface area sizes on a sphere as a function of latitude. Pixels near latitude 0 are the largest while pixels near latitudes –90 and 90 are the smallest. Smaller pixels were more severely regularized by using the penalty.factor argument in the glmnet() function. Without this extra regularization, the pixel estimate in $\dot{\mathit{\delta }}$ near latitudes –90 and 90 could wander appreciably from 0.

9 It is also of scientific interest, but outside the scope of this work, to estimate the ribbon center for non-simulated settings.

Additional information

Funding

Research presented in this manuscript was supported by the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory (LANL) under project number 20220107DR and by the NASA IBEX Mission as part of the NASA Explorer Program (80NSSC20K0719). Additionally, L.J.B. was supported by LANL’s LDRD Richard Feynman Postdoctoral Fellowship (20210761PRD1), while E.J.Z. acknowledges support from NASA grant 80NSSC17K0597 in the development of the ribbon models.