Observations of Magnetospheric Solar Wind Charge Exchange

Solar wind charge exchange (SWCX) emission was discovered when comets proved to be strong emitters in the ROSAT soft X-ray energy bands (Lisse et al. 1996). The emission is produced when highly charged ions in the solar wind (e.g., O⁷⁺) capture an electron from nearby neutrals (Cravens 1997). The newly created ions are in an excited state and emit soft X-ray photons (< 2 keV) as they de-excite into the ground state. Besides comets, SWCX emission is produced in planetary exospheres, Earth's magnetosheath, and the heliosphere. The last two components (named m-SWCX and h-SWCX from now on) are a challenge for X-ray astrophysicists, since they contribute a variable foreground with similar spectral characteristics to some astrophysical thermal plasmas (e.g., Local Hot Bubble (LHB), Galactic halo) for CCD-like spectral resolution (Cox 1998; Kuntz 2019).

The most conspicuous signature of SWCX ever observed was the excess emission, named "Long-Term Enhancements—LTEs," in the ROSAT All-Sky Survey (RASS) light curves and uncleaned maps of the keV band (e.g., Snowden et al. 1994, 2009). Cravens et al. (2001) first modeled the LTEs and demonstrated the correlation of their signal variation with solar wind flux variations using both m-SWCX and h-SWCX contributions.

Heliospheric SWCX is produced by charge exchange with interstellar neutrals, hydrogen and helium, flowing through the heliosphere into interplanetary space. The two species have different density distributions owing to the Sun's effects (Figure 1). Hydrogen is strongly ionized through proton charge exchange and subject to radiation pressure, which excludes the atoms from an area of 1–2 au around the Sun (e.g., Quémerais et al. 1999, 2006; see also the left panel of Figure 1). For helium, the ionization is much lower (mostly produced by EUV photons) and the radiation pressure is too weak to counterbalance solar gravitation, which forms an enhanced neutral density region (the He-focusing cone) in the downstream direction of the Sun (e.g., Dalaudier et al. 1984; see also the right panel of Figure 1). Both density distributions are roughly axisymmetric around the interstellar flow velocity vector and closely reflect the changes of the 11 yr solar activity cycle. Thus, the main h-SWCX signatures are solar cycle scale variations (Qu et al. 2022) and spatial effects due to variations in neutral column densities (Koutroumpa et al. 2009; Galeazzi et al. 2014). Short-scale temporal variations due to the solar wind intrinsic variability tend to be smoothed out owing to the large emissive volume of the heliosphere.

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Magnetospheric SWCX is produced from collisions with neutrals in Earth's outer hydrogen layer of the atmosphere, spreading from ∼10R_E in the subsolar region and up to the Moon's orbit on the nightside (Baliukin et al. 2019). Earth's magnetopause generally prevents the solar wind from interacting with the denser neutral layers, so the emission is mostly limited to the subsolar and flank portions of the magnetosheath and the polar cusps where ions can penetrate more deeply through open magnetic field lines (e.g., Robertson et al. 2006). However, during explosive events, such as coronal mass ejections, that induce geomagnetic storms, the magnetopause boundaries are pushed back, exposing the denser layers of the geocorona to enhanced solar wind fluxes (e.g., Sun et al. 2019). Therefore, the m-SWCX signal is mostly recognizable through its short-timescale variations due to extreme solar wind conditions and is the predominant source of LTE variability.

The two components are generally indistinguishable from each other (and from diffuse galactic sources) without proper modeling, since they are observed simultaneously in any direction, except in the strictly antisolar direction on the nightside of Earth, where m-SWCX should be negligible. The only studies that managed to isolate the m-SWCX signal are Dark Moon observations with ROSAT (Schmitt et al. 1991) and Chandra (Wargelin et al. 2004), since more distant signals (heliospheric and galactic) are blocked by the Moon's body.

Many studies attempted to characterize the SWCX contamination in X-ray observations by targeting the highly variable m-SWCX. Several cases of enhanced m-SWCX (and h-SWCX) emission were observed with Chandra, XMM-Newton, and Suzaku. The general approach consists in investigating the correlation between temporal or spectral changes in the measured signal and solar wind variability (e.g., Snowden et al. 2004; Kuntz & Snowden 2008; Carter et al. 2010, 2011; Ezoe et al. 2011; Henley & Shelton 2012; Ishikawa et al. 2013; Ishi et al. 2019). Some papers also include modeling of the m-SWCX variable component (Wargelin et al. 2014; Whittaker et al. 2016) and occasionally the h-SWCX more stable component as well (Slavin et al. 2013). Most of these cases were fortuitous observations of m-SWCX variations, and the multitude of different cases and ample discussions highlight the complexity of the problem and its parameters (observing geometry, solar wind conditions, etc.). One study was specifically designed to investigate the m-SWCX emission of the dayside magnetosheath, while viewing a dark area of galactic emission, and compare it to an m-SWCX emission model (Snowden et al. 2009). The long (∼100 ks) observation was performed during the 2008 solar minimum, and although the signal was faint, the correlation with the model was significant to better than 99.9%.

In this work, we detail our efforts to separate spectral contributions due to m-SWCX from those of h-SWCX and the astrophysical background in the X-ray spectral regime. Our approach begins with a novel observation strategy designed to compare observations of the same field of view with look directions both away from and through the emissive portions of Earth's magnetosheath, thus minimizing the m-SWCX contributions in one set of spectra and maximizing the same in another. A similar observation approach is not as effective for h-SWCX emission since the emission is present in nonnegligible amounts in every direction. Instead, we rely on a previously validated method to calculate the spectral contribution due to h-SWCX in each observation based on the observed time history of the solar wind, the line of sight for each observation, and a physical emission model (Ringuette et al. 2021). Consequently, we independently determine the amplitudes and shapes of the spectral components of the astrophysical background, h-SWCX, and m-SWCX.

Section 2 describes our observation strategy, data preparation methods, and the resulting list of observations. Section 3 presents our spectral modeling procedure, both for the set of spectra taken away from the most emissive portions of Earth's magnetosheath, called tail spectra, and spectra taken of the same celestial positions but through the flanks of Earth's magnetosheath, called flank spectra. The results of our spectral analyses are detailed in Section 4, including detection of higher-temperature components in the Galactic halo in two of our chosen fields of view. We report significant excess in O vii emission for four flank spectra, likely due to m-SWCX contributions, and we extend our analysis in Section 5 to compare the observed excesses with those predicted by a physical model and discuss the results there. Section 6 compares the spectral analysis results obtained here with those obtained in recent works. We present our conclusions in Section 7.

2.1. Observing Strategy

Our goal in this work is to separate the contributions of m-SWCX emission from those of h-SWCX and the astrophysical background. This is particularly challenging owing to the similar spectral shapes of the three types of contributions, specifically the indistinguishable spectral shapes of the two types of SWCX emission and the warm–hot component of the Galactic halo in the astrophysical background of the same observations. We approach this challenge by first designing a novel two-pronged observation strategy. One set of observations is designed with lines of sight through the tail of Earth's magnetosheath to minimize m-SWCX spectral contributions, with a second set of the same fields of view with lines of sight through the flanks of Earth's magnetosheath.

Such an observation strategy demands a large amount of observation time, which is generally difficult to obtain. Additionally, the SWCX emission we aim to detect is diffuse and faint, requiring a large grasp. The spectral range of the emission also requires the observation instrument to have at least moderate energy resolution in the lower-energy X-rays. These requirements were well met by the HaloSat CubeSat mission (Kaaret et al. 2019; LaRocca et al. 2020a; Zajczyk et al. 2020).

The HaloSat CubeSat mission was the first astrophysics CubeSat mission funded by NASA. The instrument collected moderate-resolution spectra in the soft X-rays from low Earth orbit during the recent solar minimum for approximately 2 yr (late 2018 to early 2021). The nonimaging instrument mapped diffuse emission from the O vii line across the entire celestial sphere (Kaaret et al. 2020). The instrument design requirements for HaloSat were specifically chosen for the study of the Galactic halo, which also fit well with SWCX as its secondary science goal, specifically the instrument's 14° diameter nonimaging field of view for each of three nearly identical silicon drift detectors, the 0.4–7 keV energy range, and the 85 eV energy resolution at 676.8 eV. As part of the mission planning, 12 fields of view chosen to minimize bright sources in the 0.4–7 keV energy range and extensive observations of each were planned. Observations of each field of view were planned with lines of sight down the tail of Earth's magnetosheath, where the expected m-SWCX contribution is negligible, as well as observations of the same fields of view but with lines of sight through the flanks of Earth's magnetosheath (see Figure 2). The observation limitations of the instrument prevented lines of sight through the brighter portions of Earth's magnetosheath on the dayside of the orbit, and the modeling limitations of our h-SWCX model required the chosen fields of view to be near the ecliptic plane. The 12 chosen fields of view are within 15° of the ecliptic plane (see Table 1 and the LHB_nH_ecl3.fits file in Ringuette 2023).

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Table 1. Low-background Observations

Target Name	Galactic Coordinates (l, b)	Start Time (UTC) a	End Time (UTC) a	Sun Angle	Exposure Time (ks)
MSWCX1	1264, −446	11/21/2018 13:35	11/22/2018 03:50	1404 ± 01	26.2
		10/21/2019 08:40	10/22/2019 08:03	16753 ± 009	22.3
		01/09/2019 09:24	01/09/2019 23:39	930 ± 01	30.0
MSWCX2	1527, −544	11/22/2018 20:26	11/23/2018 10:41	1474 ± 01	25.2
		10/19/2019 07:32	10/20/2019 06:55	171 83 ± 009	19.1
MSWCX3	1639, −466	11/24/2018 18:42	11/25/2018 08:57	1557 ± 01	25.5
		08/25/2019 00:49	08/26/2019 00:13	1121 ± 02	58.2
		10/21/2019 09:03	10/22/2019 08:26	1665 ± 01	54.4
		11/03/2019 15:48	11/04/2019 15:11	17185 ± 002	47.8
		08/14/2019 19:00	08/15/2019 18:20	1012 ± 02	33.2
MSWCX4	1562, −289	10/29/2019 13:27	10/30/2019 12:47	1644 ± 01	37.9
		10/31/2019 14:33	11/01/2019 13:57	1662 ± 01	43.1
		08/19/2019 21:54	08/21/2019 21:53	967 ± 03	105.9
MSWCX5	2188, 286	02/25/2019 06:20	02/25/2019 20:36	15348 ± 009	22.6
		01/22/2020 09:41	01/23/2020 09:01	1671 ± 01	45.6
		02/13/2020 20:44	02/14/2020 19:57	1638 ± 01	18.2
		11/04/2019 16:46	11/05/2019 16:07	908 ± 02	30.6
MSWCX6	1996, 424	01/17/2019 02:43	01/17/2019 16:59	1606 ± 01	23.4
		02/24/2019 15:19	02/25/2019 05:33	1542 ± 01	27.1
		03/15/2019 05:29	03/15/2019 19:45	1380 ± 01	31.4
		02/02/2020 14:49	02/03/2020 14:12	169599 ± 0003	48.6
MSWCX7	2113, 504	02/25/2019 22:07	02/26/2019 12:21	16399 ± 008	31.4
		03/19/2019 17:20	03/20/2019 07:33	1443 ± 01	22.9
		02/10/2020 19:24	02/11/2020 18:48	17053 ± 004	48.5
		03/09/2020 08:19	03/10/2020 07:42	1542 ± 02	52.0
		03/11/2020 09:19	03/12/2020 08:42	1516 ± 02	51.1
		05/10/2020 12:41	05/12/2020 12:17	926 ± 03	71.9
MSWCX8	2416, 454	02/24/2019 14:56	02/25/2019 05:12	17211 ± 001	15.2
		03/24/2019 20:34	03/25/2019 10:50	1506 ± 01	23.7
		03/25/2020 16:01	03/26/2020 15:24	1491 ± 02	47.9
		05/21/2019 16:51	05/22/2019 14:31	950 ± 02	17.4
MSWCX9	2166, 614	02/23/2019 23:55	02/24/2019 14:11	166586 ± 0007	34.4
		03/11/2019 09:05	03/11/2019 23:20	16017 ± 008	32.8
		03/22/2019 06:58	03/22/2019 21:13	15037 ± 009	34.3
		03/19/2020 13:12	03/20/2020 12:35	1520 ± 02	42.3
		05/26/2019 19:54	05/27/2019 17:41	888 ± 02	24.5
		05/18/2020 16:09	05/22/2020 16:35	94± 1	212.7
MSWCX10	2641, 653	02/16/2019 22:23	02/17/2019 12:40	1527 ± 01	23.2
		03/28/2019 16:56	03/29/2019 07:12	16621 ± 009	23.4
		04/16/2020 01:56	04/17/2020 00:54	1479 ± 02	17.2
		12/24/2018 23:57	12/25/2018 14:13	987 ± 01	35.0
		05/31/2019 22:55	06/01/2019 22:18	1037 ± 02	37.8
		12/20/2019 17:12	12/21/2019 16:35	936 ± 02	47.7
		12/22/2019 18:14	12/23/2019 17:37	957 ± 02	46.7
		12/24/2019 19:16	12/25/2019 10:41	976 ± 01	37.1
MSWCX11	920, −487	09/11/2019 10:39	09/13/2019 10:39	1663 ± 01	58.4
MSWCX12	734, −664	08/03/2019 12:29	08/04/2019 11:52	1389 ± 02	19.6
		08/21/2019 23:04	08/22/2019 22:28	1569 ± 02	59.1
		10/04/2019 02:00	10/04/2019 22:18	1583 ± 01	41.4
		06/26/2019 14:20	06/27/2019 13:43	1038 ± 02	52.4
		06/19/2020 05:34	06/22/2020 05:33	986 ± 04	152.7

Note.

^a Dates and times given with month, day, and year (MM/DD/YYYY) followed by the time in UTC in hours and minutes.

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2.2. Data Preparation

Spectral modeling was performed separately for observations with average Sun angles greater than 110°, called "tail" observations, and for observations with lines of sight closer to the Sun, called "flank" observations, due to the presence of the flanks of Earth's magnetosheath along the line of sight and the possible m-SWCX contributions from them. All tail observations of the same field of view were combined into a composite spectrum of that field of view to increase the statistics in the analysis. In contrast, all flank observations were analyzed separately to increase the likelihood of detecting the highly temporally varying m-SWCX emission.

The spectral components in the tail spectra fall into three categories: the slowly varying h-SWCX emission, the invariant astrophysical background (for the timescale of the instrument observation), and the remaining particle background. In addition to these components, the flank spectra possibly contain emission from m-SWCX. Our approach to modeling these components is described in the following subsections.

3.1. Modeling Heliospheric SWCX

Ringuette et al. (2021) tested two methods to calculate the amplitude of the h-SWCX emission in a given observation using a physical model of the expected spectral shape, empirical relations derived from solar wind data, H and He neutral distributions, the solar wind data temporally and spatially relevant for the observation timing and direction, and the location and look direction of the instrument for that observation. The first method assumed a uniformly slow solar wind with constant charge exchange cross sections, while the second method included the variation of solar wind speed and fluxes with heliolatitude. Neither model proved successful for predicting the amount of h-SWCX in the observations taken near the southern ecliptic pole, but the two models' performances were indistinguishably consistent with the observations near the solar ecliptic plane. Since the two methods performed equally well in the ecliptic plane, we take the liberty of choosing the second, more physical model and limit our choice of fields of view to those near the ecliptic plane.

The chosen spectral model for the h-SWCX emission present in our observations calculates the spectral shape and amplitudes of the emission. We use the same method to predict the spectral shape of the h-SWCX emission in both the tail and flank spectra with one approximating assumption. In the earlier work, the observations taken were along the tail of the He-focusing cone, justifying the assumption in that work of 100% neutral He emission and negligible amounts of neutral H emission along those lines of sight, with contributions from more distant solar wind charge exchange interactions taken as negligible. That same assumption of 100% He emission is not justified in this work since the look directions of the observations are typically much farther than 30° from the center of the He-focusing cone, with a minimum angle of 283 (see the right panel of Figure 1). The differing contributions of ions resulting from the changing balance between the neutral He and neutral H percentages shift the position of the averaged emission line (compare the second and third columns in Table 2). However, the maximum difference in SWCX emission line energies was determined in that work to be 6 eV by comparing the line energies resulting from assuming 100% neutral He emission and 100% neutral H emission, well below HaloSat's energy resolution (Zajczyk et al. 2020). Therefore, we assume the emission due to the neutral population along the lines of sight to be 50% neutral He and 50% neutral H and simply take the ion line energies calculated in that work as reasonable approximations (see Table 2 below).

Table 2. SWCX Spectral Shape

Ion(s)	Energy (100% H) (keV)	Energy a (100% He) (keV)	Line Ratio (100% H)	Line Ratio (100% He)*	Line Ratio (H = He)
S ix, N vi, C vi, N vii	0.4445	0.4434	(Q)/(O vii a) = 0.966	(Q)/(O vii a) = 0.925	(Q)/(O vii a) = 0.946
O vii a	0.5646	0.5633	1.0	1.0	1.0
O vii b	0.6792	0.6792	(Q)/(O vii a) = 0.126	(Q)/(O vii a) = 0.126	(Q)/(O vii a) = 0.126
O viii a	0.6531	0.6531	1.0	1.0	1.0
O viii b	0.8081	0.8031	(Q)/(O viii a) = 0.320	(Q)/(O viii a) = 0.549	(Q)/(O viii a) = 0.434
Ne ix a	0.9091	0.9087	1.0	1.0	1.0
Ne ix b	1.1004	1.1004	(Q)/(Ne ix a) = 0.100	(Q)/(Ne ix a) = 0.100	(Q)/(Ne ix a) = 0.100

Notes. Primary ion lines are indicated with an "a" and secondary lines with a "b." During spectral fitting, the low-energy line is either held fixed relative to O VII a with the given ratio or fitted simultaneously with the other primary lines.

^a Columns repeated from Ringuette et al. (2021). The energies reported in the third column and the line ratios in the last column are used in this work as reasonable approximations.

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Our assumption of the equal balance of emission from the H and He neutral populations along the lines of sight also affects the line ratios reported in Table 2 of that work, specifically the line ratios for the low-energy emission line and the secondary O viii emission line. As described in the previous work, the low-energy line is the combination of several ion lines at the low end of HaloSat's energy range typically observed as a blended peak (see row 1 of Table 2 and the small peak below 0.5 keV in the SWCX spectral component in Figures 3 and 4). The primary lines are the emission lines of a given ion with the largest intensity (e.g., the O vii a emission line in the second row of Table 2), and the line ratios are the intensity ratios between this primary line and the less intense secondary line of each ion (e.g., 0.126 for O vii b / O vii a in Table 2).

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Since we have assumed an equal balance of emission from neutral H and neutral He along the line of sight, we have assumed that the line ratios are the mean of the ratios expected for a pure H interaction and for a pure He interaction (see the last three columns of Table 2). The difference between these line ratios and those used for this work is 0.1 for the secondary O vii emission and 0.02 for the low-energy line. Given the typical line intensity of a few line units (LU = photons cm⁻² s⁻¹ sr⁻¹) for the low-energy line observed in the previous work, the resulting line ratio difference of about 0.02 for the low-energy emission line results in a difference of emission on the order of the detection uncertainty in the line. For the secondary O viii emission line, which has a slightly lower typical line intensity of about 1 LU, the line ratio difference results in a difference in line intensity smaller than the observation error reported in that work. Therefore, our choice of line ratio convention does not significantly affect our conclusions.

Table 2 presents the line energies and line ratios used in this work to represent the shape of the h-SWCX contribution in each spectrum (see the third and last columns). Given the presumably negligible contribution of m-SWCX in the tail composite spectra, we fix the calculated amplitudes and line energies of the modeled SWCX emission lines during the spectral fitting process. For the flank spectra, we instead fit for the amplitudes of the primary emission lines, including the low-energy line, hold the line energy positions and line ratios constant as in the tail spectral analysis process, and compare the observed line intensities to those predicted by the h-SWCX model.

3.2. Modeling the Astrophysical and Non-X-Ray Components

4.1. Galactic Halo

We report the final parameters for the Galactic halo component in each of the 12 composite tail spectra analyzed in Table 3, including the calculated Galactic column densities for each field of view. The target name, Galactic coordinates, and exposure time for each field of view are given in the first three columns, followed by the calculated absorption in the fourth column. The fitted temperature and emission measure of the Galactic halo component in each field are given in the fifth and sixth columns with the fitted 90% confidence intervals, followed by the number of degrees of freedom (dof) and the reduced χ² for each spectral fit in the seventh and penultimate columns. The last column gives the number of flank spectra obtained for each field of view.

Table 3. Galactic Halo Results

Target Name	Galactic Coordinates (l, b)	Tail Exp. Time (ks)	nH (1020 cm−2)	Warm–Hot Temperature (keV)	Warm–Hot Emission Measure a	dof	X2 v	Number of Flank Obs.
MSWCX1	1264, −446	48.6	3.63	0.212 ± 0.013	14.3 ± 2.4	179	1.091	1
MSWCX2	1527, −544	44.3	2.65	${0.210}_{-0.015}^{+0.016}$	${12.6}_{-2.3}^{+2.2}$	158	0.903	0
MSWCX3 b	1639, −466	185.9	6.94	${0.194}_{-0.024}^{+0.026}$	${6.8}_{-1.3}^{+1.5}$	441	1.014	1
				${0.73}_{-0.10}^{+0.12}$	${1.65}_{-0.55}^{+0.33}$
MSWCX4	1562, −289	81.0	13.33	${0.238}_{-0.019}^{+0.024}$	${9.9}_{-2.2}^{+1.9}$	271	1.110	1
MSWCX5	2188, 286	86.4	3.04	${0.223}_{-0.018}^{+0.020}$	7.1 ± 1.6	295	1.024	1
MSWCX6 b	1996, 424	130.6	1.94	${0.181}_{-0.019}^{+0.0083}$	9.2 ± 1.2	421	1.103	0
				${0.85}_{-0.16}^{+0.20}$	${0.96}_{-0.51}^{+0.31}$
MSWCX7	2113, 504	206.0	2.09	${0.201}_{-0.009}^{+0.010}$	9.5 ± 1.1	498	1.062	1
MSWCX8	2416, 454	86.8	2.19	0.202 ± 0.016	8.4 ± 1.6	282	1.095	1
MSWCX9	2166, 614	143.9	1.10	0.197 ± 0.010	${10.1}_{-1.3}^{+1.2}$	414	1.125	2
MSWCX10	2641, 653	63.9	1.76	0.204 ± 0.015	${10.2}_{-1.9}^{+2.0}$	270	0.941	5
MSWCX11	920, −487	58.4	4.90	${0.193}_{-0.024}^{+0.023}$	${8.5}_{-2.4}^{+2.6}$	231	0.987	0
MSWCX12	734, −664	120.1	1.30	0.208 ± 0.011	10.4 ± 1.3	351	1.190	2

Notes.

^a Emission measure in units of ×10⁻³ cm⁻⁶ pc. All errors are 90% confidence intervals. ^b These two spectra were best fit with a double thermal component for the Galactic halo emission. The temperature and emission measure for the second thermal component for MSWCX3 (MSWCX6) are given below the warm–hot parameters for each of the two targets in the table and were detected at a significance of 4.97σ (3.09σ) with F-test probabilities of 2.65 × 10⁻⁵ (1.69 × 10⁻²) comparing double to single thermal components.

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As indicated in the table, spectral testing of the MSWCX3 and MSWCX6 fields of view concluded that a significant higher-temperature component is present in both fields of view. The temperature and emission measure of the higher-temperature components in these two fields of view are given in the table footnote, along with the significance of each component and the related null probabilities. The final spectral fits for these two composite tail spectra are presented in Figures 3 and 4.

Ringuette et al. (2021) considered alternate contributions, such as emission from T Tauri or M-dwarf stars, for the high-temperature components reported in that work. Here we must reject the hypothesis of any possible contribution from these types of stars in both the MSWCX3 and MSWCX6 fields of view since they are both more than 30° from the Galactic plane, where T Tauri stars and M-dwarf stars are populous. We also find that the fitted temperatures of the second thermal component are consistent with the value reported in Das et al. (2019b): ${1.09}_{-0.64}^{+1.9}$ keV (90% CI) based on the Ne X absorption line, but not with the temperatures reported in Das et al. (2019a) for emission. Following the same argument in the Ringuette et al. (2021) work, we also conclude that the small-amplitude, high-temperature emission could possibly be from diffuse gas of ≈ 10⁷ K in the Galactic halo along the line of sight.

4.2. SWCX

The fitted parameters in Table 3 were held fixed during the spectral analysis of the flank spectra obtained for the same field of view, while the best-fit line intensities for the primary and low-energy lines were obtained. The final line intensities for the most significant line, O vii, are given in Table 4 and compared to those predicted by the h-SWCX model. The first three columns give the target name, observation start date in UTC, and cleaned exposure time for each flank observation obtained. The fourth column presents the best-fit line intensity for the O vii line, followed by the predicted h-SWCX O vii line intensity and the difference between them, each with 1σ errors. The final two columns show the number of dof and the reduced χ² for each spectral fit.

Table 4. SWCX Results

Target Name	Start Date(MM/DD/YYYY hh:mm)(UTC)	Exposure Time (ks)	m-SWCX + h-SWCX Observed O vii (LU)	Predicted h-SWCX O vii (LU)	Difference (Obs-Exp) (LU)	dof	X2 v
MSWCX1	1/09/2019 09:24	30.0	${0.39}_{-0.24}^{+0.59}$	1.135 ± 0.048	$-{0.74}_{-0.24}^{+0.59}$	130	1.014
MSWCX3 a	8/14/2019 19:00	33.2	${2.05}_{-0.41}^{+0.44}$	0.707 ± 0.036	${1.35}_{-0.41}^{+0.44}$ a	115	1.042
MSWCX4 a	8/19/2019 21:54	105.9	1.78 ± 0.25	0.727 ± 0.032	${1.06}_{-0.26}^{+0.25}$ a	263	1.028
MSWCX5	11/04/2019 16:46	30.6	${2.47}_{-0.57}^{+0.58}$	1.658 ± 0.050	${0.82}_{-0.57}^{+0.58}$	106	0.894
MSWCX7	5/10/2020 12:41	71.9	1.53 ± 0.39	0.902 ± 0.040	0.62 ± 0.39	218	0.981
MSWCX8 a	5/21/2019 16:51	17.4	${4.09}_{-0.72}^{+0.84}$	1.470 ± 0.075	${2.62}_{-0.72}^{+0.84}$ a	70	0.919
MSWCX9	5/26/2019 19:54	24.5	${2.72}_{-0.68}^{+0.67}$	1.477 ± 0.069	1.24 ± 0.68	103	1.004
MSWCX9	5/18/2020 16:09	212.7	${1.59}_{-0.22}^{+0.23}$	0.937 ± 0.044	0.65 ± 0.23	448	1.149
MSWCX10	12/24/2018 23:57	35.0	${2.84}_{-0.60}^{+0.58}$	1.050 ± 0.047	${1.79}_{-0.60}^{+0.59}$	109	0.824
MSWCX10 a	5/31/2019 22:55	37.8	${3.20}_{-0.50}^{+0.49}$	1.444 ± 0.077	${1.75}_{-0.51}^{+0.50}$ a	172	1.350
MSWCX10	12/20/2019 17:12	47.7	${2.11}_{-0.49}^{+0.50}$	1.087 ± 0.069	${1.03}_{-0.49}^{+0.50}$	199	1.016
MSWCX10	12/22/2019 18:14	46.7	1.48 ± 0.49	1.125 ± 0.061	0.35 ± 0.49	170	1.035
MSWCX10	12/24/2019 19:16	37.1	${1.52}_{-0.54}^{+0.53}$	0.984 ± 0.058	0.53 ± 0.54	126	1.326
MSWCX12	6/26/2019 14:20	52.4	${0.67}_{-0.41}^{+0.43}$	1.497 ± 0.058	$-{0.82}_{-0.41}^{+0.44}$	183	1.257
MSWCX12	6/19/2020 05:34	152.7	${0.64}_{-0.26}^{+0.25}$	1.107 ± 0.044	−0.47 ± 0.26	371	1.077

Note. All reported errors are 1σ errors. The errors on the observed line intensities were calculated from the fitted 90% confidence intervals from XSPEC.

^a The significance of the observed value above the expected value is greater than 3σ for these observations (3.31σ, 4.12σ, 3.62σ, and 3.45σ, respectively).

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Figure 5 provides a more visual comparison of the fitted and predicted O vii line intensities. The fitted O vii line intensities are plotted against the predicted line intensities, with error bars representing the 1σ errors given in Table 4. The solid line indicates the null hypothesis of the best-fit line intensities being equal to those predicted for a given observation. Values plotted above this line indicate observed emissions greater than the predicted emissions, and values plotted below this line show an observation with lower observed emission than predicted by the model. Out of the 15 flank observations obtained, 4 are noted to have fitted O vii line intensities more than 3σ above the predicted value for that observation (see footnote of Table 4). The observation with an O vii line intensity excess greater than 4σ is indicated in Figure 5 with a red square, and the remaining three observations with excesses above 3σ but below 4σ are indicated with yellow diamonds. These four observations are further analyzed in the next section.

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The m-SWCX component in each of the four observations highlighted in Figure 5 was calculated following the method described in Section 6.2.1 of Ringuette et al. (2021). The O vii emission due to the m-SWCX contribution was calculated by integrating the product of the ion flux, the neutral density, and the charge exchange cross section along the line of sight according to (as done in Section 6.2.1 of Ringuette et al. 2021)

$$\begin{eqnarray}\begin{array}{rcl}I & = & \displaystyle \frac{1}{4\pi }{\displaystyle \int }_{{\rm{obs}}}^{\infty }{F}_{O+7}(s){N}_{{\rm{H}}}(s){\sigma }_{{\rm{H}},O+7}{Y}_{{\rm{O}}\,{\rm{VII}},H}{ds}\\ & = & \displaystyle \frac{1}{4\pi }\displaystyle \frac{{N}_{O+7}}{{N}_{P}}{\displaystyle \int }_{{\rm{obs}}}^{\infty }{N}_{P}(s){V}_{P}(s){N}_{H}(s){\sigma }_{H,O+7}{Y}_{O\,{\rm{VII}},H}{ds}.\end{array}\end{eqnarray} \tag{ 1 }$$

The proton density and velocity are again highly variable along this path, so they were extracted from BATS-R-US simulation runs (Tóth et al. 2005). The input values to the simulation runs were chosen to reflect the solar wind conditions during the observing times included in the cleaned observations. The four simulation run outputs are accessible on the CCMC website (see the Acknowledgment section for more details).

The calculated O vii line intensities for the asterisked MSWCX3, MSWCX4, MSWCX8, and MSWCX10 observations in Table 4 are 0.107, 0.044, 0.053, and 0.055 LU, respectively. Notably, these values are all an order of magnitude lower than the observed O vii excesses. We find that 1.02–2.57 LU are not accounted for in the four highlighted observations. Since the observations were conducted in the same manner as those analyzed in the 2021 paper, the same calculations in that paper concerning atmospheric contamination apply to these observations. In short, no significant atmospheric contamination is found to significantly contribute at the O vii energy.

We are therefore left to conclude one or more of the following: (1) the solar wind parameters used in the calculations do not properly represent the solar conditions along the observational lines of sight through the emissive portions of Earth's magnetosphere, (2) the BATS-R-US model output produced does not accurately simulate the proton density and velocity in the regions sampled, and (3) there are other possible contributions to the O vii line energy band that we do not yet understand.

Our previous work on modeling the h-SWCX emission in the ecliptic plane showed that currently available observational solar wind data are a reasonable approximation of the long-term averaged solar wind behavior along lines of sight away from the emissive portions of Earth's magnetosphere, as is relevant for h-SWCX emission calculations. However, the highly variable behavior of the solar wind, both temporally and spatially, can result in dramatic differences between the solar wind conditions at the instrument and near Earth as demonstrated in the difficulty of forecasting space weather based on data observed at L1. Consider the oft-occurring situation of an oblique shock front propagating through the L1 location. The enhancement in the solar wind in the passing front is registered by the solar wind instruments near that location, but the shock front never reaches Earth owing to the direction of its overall velocity vector, so the forecasted solar wind enhancement and subsequent geomagnetic storm effects are not observed at Earth. It is these and similar known differences between the solar wind data and the observed effects near Earth that are likely a cause of a portion of the O vii emission not being accounted for.

Concerning the accuracy of the BATS-R-US model close to Earth, we acknowledge our probable lack of understanding on the best ways to use the model. We propose that there are improvements to be made in this area and look to collaborate with geospace researchers on this matter in a future work. To our knowledge, this work and our previous work are the first validation efforts of the BATS-R-US model for the proton density and velocity near Earth. As such, it is common that the match between observational and simulated data is qualitatively reasonable but quantitatively poor. We also note that the modeled predictions do not give any uncertainty in the predicted values and that the calculation of uncertainties in modeled data is a topic of current research. We applaud the significant efforts of the BATS-R-US modeling team and their contribution to the field and invite them to use this work to investigate our own errors in our modeling efforts and what other causes there may be of the differences between these data and the model results. Perhaps this and similar works could propel the long-standing collaboration between astrophysics and heliophysics into a new territory: model validation studies of heliophysics models using astrophysics SWCX data.

As a secondary result, this work reports two fields of view with nonnegligible absorbed higher-temperature components, specifically MSWCX3 and MSWCX6 with hot temperatures of ${0.73}_{-0.10}^{+0.12}$ and ${0.85}_{-0.16}^{+0.20}$ keV and corresponding emission measures with significances of 4.97σ and 3.09σ, respectively. Ringuette et al. (2021) also reported nonnegligible absorbed high-temperature emission with a slightly higher temperature of ∼1 keV for both fields of view analyzed using the same spectral analysis methods. Additionally, Bluem et al. (2022a) reported several fields of view with significant absorbed higher-temperature components. The "hot" temperatures reported there are typically lower but do not exclude the corresponding values reported here. The values reported here for the lower-temperature components range from ∼0.18 to ∼0.24 keV, with the largest two values occurring for the fields of view within 30° of the Galactic equator. Excluding those fields as done in the Bluem et al. (2022a) work results in a temperature range of ∼0.18–0.21 keV, which is not consistent with the stacked fit temperature reported in the Bluem et al. (2022a) work but is included in the range of individual fitted temperatures reported there.

Figures 6 and 7 compare the results per field in more detail using the results reported here and in the VizieR catalog associated with the mentioned paper (Bluem et al. 2022b). The figures present the fitted temperatures (top panels) and emission measures (bottom panels) for both the warm (Figure 6) and hot (Figure 7) components of the absorbed emission. One main difference in the two analyses is that this work reports a hot temperature and emission measure only if the fitted hot emission measure was at least 3σ above zero; otherwise, a single-temperature model was assumed. In contrast, the Bluem et al. (2022a) analysis includes the hot temperature component in the spectral model for all fields regardless of the component's significance. In addition, the Bluem works exclude fields of view within 30° of the Galactic plane (e.g., MSWCX4 and MSWCX5, aka VizieR ID numbers 71 and 72; see Table 5). Despite the differing analysis methods, the temperatures and emission measures are generally consistent for the two fields where this analysis detected a significant hot emission measure and retained that component in the spectral model. Otherwise, the temperatures of the warm component reported in Bluem et al. (2022b) are typically lower than those reported here. The two fields analyzed solely in this paper have a warm emission measure in the same range as the other emission measures and a slightly higher but not inconsistent warm temperature than the other temperatures reported here.

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The residuals due to the gain shift and edge effect reported in Bluem et al. (2022a) are not observed here (see Figures 3 and 4), namely a spike in the residuals near 0.6 keV and an edge effect near 1.8 keV, possibly due to the lower statistics from the lower exposure times (see Appendices A and B of Bluem et al. 2022a). Unfortunately, the new analysis methods were not available in time to apply to this work. While it would be interesting to reanalyze these fields with the gain shift and edge correction incorporated, it is beyond the scope of this work.

The warm component temperatures reported in this work are typically higher than those reported in Bluem et al. (2022a) and the associated VizieR catalog (Bluem et al. 2022b) owing to the differing analysis methods. One such difference is the more complete representation of SWCX emission lines in this work. Excluding the collection of low-energy SWCX emission lines in that work may have motivated the addition of the lower-energy background power law. Those photon indices were linked across detectors just as the astrophysical parameters were, possibly signaling a link to a nonlocal cause (e.g., low-energy SWCX emission along the line of sight). Similarly excluding the higher-energy SWCX emission lines could have improperly but slightly enhanced the emission measure of the higher-temperature component, several of which are barely above 3σ (see Table 5 for a sample). As a result, more of the detected hot components in the related VizieR catalog likely have a true significance lower than 3σ.

At the time of writing, the VizieR catalog also contains spectral results for hot components with emission measures within 3σ of zero, which would have been deemed negligible and replaced with a single temperature component in the approach presented here (see MSWCX10 in Table 5). Including these insignificant higher-temperature components as a standard feature in a spectral fit decreases the fitted temperature of the warm component and assumes that the higher-temperature component is universal yet clumpy as found for the warm temperature emission (Kaaret et al. 2020), as would be expected if the emission were associated with the Galactic halo. In the case of the higher-temperature component, this "clumpiness" includes the possibility of gaps in the cloud of material producing the emission (e.g., an emission measure consistent with zero), conceptually similar to a partly or mostly cloudy sky in terrestrial weather. However, excluding those components as done in this work assumes that such higher-temperature emission is not universal, which would be correct if the emission is not associated with the Galactic halo. The work done here primarily focuses on finding a reasonable model for the astrophysical emission as one step toward separating emission generated by m-SWCX from the other sources, not debating what the source of one of the components is. We choose the second assumption and only report higher-temperature components for which a significant emission measure is determined. However, we include the spreadsheets containing the information for our spectral fits for all fields with both the warm and hot components on the associated GitHub repository for the interested reader (Ringuette 2023).

Further observations and work remain to be done on this topic, particularly observations with higher spectral resolution to distinguish the source of the emission by finely resolving the emission lines. In the meantime, it would be interesting for the Bluem et al. (2022a) work to be repeated with a more complete SWCX representation such as the one used here. To investigate a possible scenario where the emission is not associated with the Galactic halo, one could remove all higher-temperature components with a significance less than 3σ in the reanalyzed work and change those to instead be modeled with a single-temperature model. One could reperform the stacked analysis done there separately for both the spectra with a significant higher-temperature component and spectra without such a component to better understand the different scenarios.

In addition, it is curious that there is a signature at 3 keV in the stacked CGM spectrum compared to the lack of such a signature in both the Crab and CasA spectra (compare Figures 11, 13, and 14b in that work) and the ECL stacked spectrum (Figure 8 of Ringuette et al. 2021), even though those spectra have good statistics and were created with similar count rate cuts on the same high energy band (0.25, 0.25, and 0.50 counts s⁻¹ on the 3–7 keV energy band; see also the related note in Bluem et al. 2023). Once the spectral modeling is refined as suggested here, one could further investigate the signature at 3 keV, namely to investigate a possible faint signature of higher-energy emission in the stacked CGM spectrum at higher Galactic latitudes. One possible path for this investigation would be to raise the count rate cut value until the edge disappears and compare spectral fit results for a variety of physically motivated spectral models (e.g., lingering higher-energy emission from a previously active Galactic jet). Detection of a temperature component higher than those discussed in this work and Bluem et al. (2022a) could simply be indicative of a wider range of Galactic halo temperatures than currently modeled as posited in that paper.

We primarily report significant detections of m-SWCX in four observations. Our observational strategy separated the m-SWCX emission from the similarly shaped emission of h-SWCX and the warm–hot Galactic halo contributions. These observations were planned as part of the secondary science goal of HaloSat—to study SWCX. We successfully obtained clean observations of dark portions of the sky with lines of sight away from the emissive portions of Earth's magnetosheath (tail observations) and clean observations of the same fields of view with lines of sight through more emissive portions of Earth's magnetosheath (flank observations). By using the tail observations and our previously validated model of h-SWCX emission, we were able to determine the excess O vii emission in four flank observations (1.06–2.62 LU) as compared to the astrophysical background and the expected contribution from the h-SWCX along the line of sight.

The excess O vii emission observed is not explained by atmospheric contamination or by the simulation results obtained for the m-SWCX contribution to the O vii emission line. We therefore conclude that the excess emission is a result of the spatial and temporal variability of the solar wind, causing poor predictions and simulations of m-SWCX contributions near Earth. It is also possible that we have not used the model in the manner most relevant to the situation. Additionally, it is also quite possible that there are other sources of O vii emission along the line of sight that we do not yet understand. We recommend a collaboration between astrophysicists and space weather modelers as the two fields mature further to improve modeling efforts through similar model validation studies.

Second, we report a nonnegligible (4.97σ and 3.09σ) absorbed ∼1 keV high-temperature component in 2 out of the 12 fields of view analyzed near the ecliptic plane. Both fields of view are far from the ecliptic plane, precluding T Tauri and M-dwarf stars as possible emission sources for this component. The high-temperature emission could be from diffuse gas with a temperature near 10⁷ K in the Galactic halo along the line of sight.

Improved results for m-SWCX detection can be obtained with additional X-ray observations of the same fields of view with lines of sight through the emissive portions of Earth's magnetosheath near solar maximum, when the desired emission enhancement typically occurs more often owing to the enhanced solar activity. Additionally, the detection of high-temperature components can be further investigated with additional X-ray observations of the same fields of view and an updated analysis procedure as described in Section 6.

The processing files used in this analysis are available online through HEASARC's archive and on the related GitHub repository, which includes the scripts used in this analysis (Ringuette 2023). As of the date of this writing, all data from the HaloSat mission are available through the same HEASARC archive. The HaloSat CubeSat reentered the atmosphere in 2021 January.

All spectral analyses were performed using XSPEC v12.11.1 (Arnaud 1996), which minimizes the differences between the data and the total model by changing the free parameters until the best fit is found. The spectral analysis was performed with the original calibration files, specifically the ARF and RMFs posted on the related GitHub repository (Ringuette 2023). All Python codes used in this analysis were written in Python 2.7.15 and are available at the same GitHub repository. The authors acknowledge the use of SWICS data provided by the ACE Science Center (http://www.srl.caltech.edu/ACE/ASC/) and especially wish to extend their thanks to Jim Raines for endless discussions on the data. The authors also acknowledge the use of OMNI data provided by NASA/GSFC's Space Physics Data Facility's OMNIWeb service and magnetospheric simulation results from the Community Coordinated Modeling Center at Goddard Space Flight Center. The CCMC is a multiagency partnership between NASA, AFMC, AFOSR, AFRL, AFWA, NOAA, NSF, and ONR. The SWMF/BATS-RUS model was developed by Tamas Gombosi et al. at the Center for Space Environment Modeling, University of Michigan. The model runs used in this work are named KD_Kuntz_071921_1, KD_Kuntz_071921_2, KD_Kuntz_071921_3, and KD_Kuntz_071921_4 and are available by request through the CCMC website. The full metadata record for these runs can be obtained at https://ccmc.gsfc.nasa.gov/ungrouped/GM_IM/GM_main.php. The HaloSat mission was supported by NASA grant NNX15AU57G. A portion of R.R.'s work was supported by ADNET Systems Inc., and D.K.'s modeling work was supported by CNES and performed with the High Performance Computer and Visualisation platform (HPCaVe) hosted by UPMC-Sorbonne Université.