Citation: | Kim, H., Connor, H. K., Jung, J., Walsh, B. M., Sibeck, D., Kuntz, K. D., Porter, F. S., Paw U, C. K., Nutter, R. A., Qudsi, R., Nakamura, R., and Collier, M. (2024). Estimating the subsolar magnetopause position from soft X-ray images using a low-pass image filter. Earth Planet. Phys., 8(1), 173–183. DOI: 10.26464/epp2023069 |
The Lunar Environment heliospheric X-ray Imager (LEXI) and Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) missions will image the Earth’s dayside magnetopause and cusps in soft X-rays after their respective launches in the near future, to specify global magnetic reconnection modes for varying solar wind conditions. To support the success of these scientific missions, it is critical to develop techniques that extract the magnetopause locations from the observed soft X-ray images. In this research, we introduce a new geometric equation that calculates the subsolar magnetopause position (
The Earth’s dayside magnetospheric system, namely the magnetosheath and cusps, emits soft X-rays as high-charge-state solar wind ions, such as O7+ exchange electrons, with the Earth’s exospheric neutrals (e.g., Lisse et al., 1996; Cravens 1997; Walsh et al. 2016; Sibeck et al., 2018). The Roentgen SATellite mission (ROSAT; Trümper, 1982) discovered X-rays from the Earth’s magnetosphere generated through this solar wind charge exchange process (Cravens et al. 2001). The X-ray Multi-Mirror Mission (XMM-Newton; Jansen et al. 2001) observed strong emission of soft X-rays (0.05–2.0 keV) when it looked through the dayside magnetosphere (Carter et al., 2010, 2011), supporting the hypothesis that the magnetosheath is a strong soft X-ray emitter, as speculated by the modeling study of Robertson and Craven (2003). These observations provided substantial motivation to design future space missions that visualize the interaction between the solar wind and magnetosphere in soft X-rays. In this context, the Lunar Environment heliospheric X-ray Imager (LEXI; Walsh et al., 2020) and the Solar wind Magnetosphere Ionosphere Link Explorer (SMILE; Branduardi-Raymont et al., 2018) are scheduled to launch in 2024 and 2025, respectively.
The LEXI imager is one of 10 instruments to be deployed on the lunar surface by the Firefly Aerospace lunar lander under the National Aeronautics and Space Administration (NASA) Commercial Lunar Payload Services project. The LEXI imager will provide
Recently, various techniques have been developed to extract the magnetopause position from soft X-ray images (Collier and Connor 2018; Jorgensen et al., 2019a, b; Sun TR et al., 2020). Some of these utilize a limb-brightening effect, a phenomenon in which an object appears to become brighter toward its edges (e.g., Oiler and Rogers, 2020). A line-of-sight (LOS) tangent to the magnetopause has a longer path in the magnetosheath than do other LOSs. Because the Earth’s magnetosheath emits soft X-rays, more soft X-rays are accumulated along this LOS. As a result, the magnetopause can be recognized as a curved line of peak emissions in the soft X-ray images. Collier and Connor (2018) and Sun TR et al. (2020) used these LOSs of peak emissions (i.e., tangent vectors to the magnetopause) to trace the magnetopause.
Collier and Connor (2018) introduced a technique that reconstructs the global three-dimensional (3D) magnetopause from two-dimensional (2D) soft X-ray images under steady solar wind conditions. First, they derived an equation to calculate the magnetopause position as a function of the spacecraft positions and the angles of soft X-ray emission peaks. They then simulated soft X-ray images expected from a virtual spacecraft by using a global magnetohydrodynamic (MHD) model. Finally, they extracted the magnetopause positions from the 2D images by using their analytical magnetopause equation. The results showed good agreement with the magnetopause positions obtained from the MHD model.
Sun TR et al. (2020) introduced another magnetopause tracing technique that uses the limb-brightening effect. First, they defined a function for the magnetopause shape similar to the one by Shue et al. (1997) and created a chart of various magnetopause positions. Second, they simulated the soft X-ray image expected from a virtual satellite by using a global MHD model and obtained the magnetopause curve by connecting the peak emission pixels in the image. Third, they investigated which magnetopause in their chart created a similar magnetopause curve in the soft X-ray image. Finally, they concluded that the real magnetopause position was the same as the magnetopause shape on their chart that gave the best-match curve to the curve in the satellite image. Their tracing results showed good agreement with the MHD magnetopause locations.
Collier and Connor (2018) and Sun TR et al. (2020) used ideal soft X-ray images so that the peak emission angles could be easily identified. However, a real soft X-ray image is not smooth because of various X-ray sources in the sky, the instrumental background, and Poisson noise (Sibeck et al. 2018; Jung et al. 2022). It is not always easy to obtain accurate peak emission angles from real soft X-ray images with moderate signal-to-noise ratios, which creates an additional challenge for magnetopause tracing. In this work, we introduce a novel method that estimates subsolar magnetopause positions from synthetic soft X-ray images by using a new geometric equation and image filtering. We apply this technique to synthetic soft X-ray images from LEXI, but our technique is equally applicable to images from SMILE or other future soft X-ray imaging missions positioned outside the magnetosphere.
Section 2 describes how we simulate synthetic soft X-ray images from a global MHD model and trace the subsolar magnetopause locations from the images. Section 3 validates our tracing method for various LEXI locations, look directions, and solar wind conditions by using the magnetopause positions obtained from the MHD model as ground truth. Finally, Section 4 summarizes our results and presents concluding remarks.
To simulate near-Earth soft X-rays, we use the Open Geospace Global Circulation Model (OpenGGCM), a global magnetosphere–ionosphere model that solves resistive MHD equations with current-driven resistivities in nonuniform Cartesian grids. Its simulation box covers from ~
We also use the simple exospheric neutral density model from Cravens et al. (2001) to obtain the neutral hydrogen density (
nn=25(10RER)3, | (1) |
where
The soft X-ray emissivity along the LOS (
Rx=ς4π∫npnnvreldl, | (2) |
vrel=√v2p+v2th=√v2p+3kBTm, | (3) |
where Rx is in
Equation (2) simplifies to
Rx=ς4πQ, | (4) |
where
Q=∫npnnvreldl, | (5) |
where
ROSATcounts[deg−2s−1]=Q×3.86×10−20counts[cm4deg−2]. | (6) |
The conversion ratio from the ROSAT to the LEXI count rate is estimated to be 0.03149. By multiplying this ratio to Equation (6), the LEXI count rate is expressed as a function of Q:
LEXIcounts[deg−2s−1]=Q×1.22×10−21counts[cm4deg−2]. | (7) |
We derive an equation that estimates the geocentric distance to the subsolar magnetopause (
{R}_{\rm{s}}\approx {{D}}={\boldsymbol{S}}\,{\rm{sin}}\,{{\lambda } }, | (8) |
{\boldsymbol{\lambda }}={\rm{cos}}^{-1}\left[\frac{\left({\left|{\boldsymbol{S}}\right|}^{2}+{\left|{\boldsymbol{S}}-{\boldsymbol{L}}\right|}^{2}-{\left|{\boldsymbol{L}}\right|}^{2}\right)}{2\left|{\boldsymbol{S}}\right|\left|{\boldsymbol{S}}-{\boldsymbol{L}}\right|}\right]\pm {\alpha}. | (9) |
The law of cosines is used for Equation (9). Figure 1 illustrates the
We validate Equation (8) by tracing
Although Equation (8) provides accurate
We create synthetic soft X-ray images by considering a constant galactic background, the LEXI instrument response, and Poisson noise. Figure 3 schematically shows the imaging process, going from an ideal soft X-ray image to a synthetic soft X-ray image. Figure 3a shows an ideal image for the near-Earth solar wind charge exchange emission, the same as in Figure 2b. We add a uniform galactic background of 0.27 counts/pix/s to all the pixels in Figure 3a and then divide the total counts (i.e., near-Earth X-ray + galactic background) by 1.6 to take into account the LEXI optics and filter performance. By including this uniform background, we can obtain total X-ray count rates closer to reality and thus create Poisson noise at a reasonable level. Figure 3b shows the total soft X-ray count rates that arrive at the LEXI detector after passing its optics. Focused optical imaging systems, such as telescopes and microscopes, always blur images of actual objects, and a point spread function (PSF) describes this blurred pattern. We convolve the total soft X-ray counts in Figure 3b with the LEXI PSF. This convolution slightly reduces the number of counts, as shown in Figure 3c. Assuming that the uncertainty in the number of counts is given by the Poisson distribution (Sibeck et al., 2018), we add random Poisson noise to Figure 3c and obtain the realistic LEXI soft X-ray image in Figure 3d. As described in the following section, we conduct the
Note that we simplify the calculation of synthetic images. The actual sky background is not uniform, and the instrument background is not considered. However, the sky background is relatively well known from the ROSAT all-sky survey (Snowden et al., 1997), and the instrument background will be obtained through the upcoming LEXI calibration. We can subtract these backgrounds from the actual X-ray images. The processed LEXI images after removal of this background are expected to be similar to our synthetic images, like the one in Figure 3d. Our technique can be applied to these processed images. Details for realistic image calculation can be found in Sibeck et al. (2018) and the references therein.
It is challenging to determine an accurate soft X-ray peak angle (
To obtain an accurate
Figure 5 shows the filtering process used on a LEXI soft X-ray image. Figure 5a is the synthetic soft X-ray image, and Figure 5b is that image in the frequency domain after the 2-D fast Fourier transform. The main information in the image is distributed in the center, where low-frequency features reside. Next, we create a Gaussian low-pass filter
G(x,y)=\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{d(x,y)}^{2}}{{2{f}_{\mathrm{c}}}^{2}}\right) , | (10) |
where
We now estimate how well our magnetopause tracing technique performs with the filtered LEXI images. Figure 6 shows an example of
We now estimate
Overall,
The magnetopause motion provides important information on the mode of the dayside reconnection. The LEXI imager can reveal whether the reconnection happens globally or locally, fast or slow, and steadily or intermittently by observing the magnetopause motion from soft X-ray images. We test whether our tracing method can trace the magnetopause motion when the IMF rotates from northward to southward. To consider time-varying X-ray emission patterns, we calculate near-Earth X-ray counts every minute with 1-min exposure, accumulate the X-ray counts for the past 5 min, and finally obtain an ideal near-Earth soft X-ray image every 5 min with 5-min exposure. We then create 1000 synthetic images from the ideal soft X-ray image by introducing 1000 random trials with Poisson noise distributions, smooth the 1000 synthetic images by applying the image filtering as described in Figure 5, and obtain
Figure 8 shows the test results. The top panel shows the IMF Bz at a 5-min resolution under a constant solar wind density of
In this article, we introduced and validated a new technique that traces a subsolar magnetopause position from a synthetic LEXI soft X-ray image. We derived an equation for the subsolar magnetopause position as a function of the satellite location, the look direction, and the angle of maximum soft X-ray emission under two assumptions: (1) that the look direction of the maximum soft X-ray emission lies tangent to the magnetopause, and (2) that the magnetopause near a subsolar point is nearly spherical. We created synthetic soft X-ray images with a uniform galactic background, a PSF, and random Poisson noise. To overcome the background noise in the synthetic soft X-ray image, we filtered the image in the frequency domain by using a Gaussian low-pass filter with a cutoff frequency of 0.05. We then estimated the subsolar magnetopause position and its accuracy for various solar wind densities and different LEXI locations. Our tracing method estimated the subsolar magnetopause position with an accuracy of <
This work was supported by NASA (Grant Nos. 80NSSC19K0844, 80NSSC20K1670, 80MSFC20C0019, and 80GSFC21M0002). HC gratefully acknowledges support from NASA Goddard Space Flight Center internal funding programs (HIF, Internal Scientist Funding Model, and Internal Research and Development).
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Andrey Samsonov, Graziella Branduardi-Raymont, Steven Sembay, Andrew Read, David Sibeck, Lutz Rastaetter. 2024: Simulation of the SMILE Soft X-ray Imager response to a southward interplanetary magnetic field turning. Earth and Planetary Physics, 8(1): 39-46. DOI: 10.26464/epp2023058 | |
S. Parsons, D. J. Hall, O. Hetherington, T. W. Buggey, T. Arnold, M. W. J. Hubbard, A. Holland. 2024: SMILE soft X-ray Imager flight model CCD370 pre-flight device characterisation. Earth and Planetary Physics, 8(1): 25-38. DOI: 10.26464/epp2023057 | |
S. Sembay, A. L. Alme, D. Agnolon, T. Arnold, A. Beardmore, A. Belén Balado Margeli, C. Bicknell, C. Bouldin, G. Branduardi-Raymont, T. Crawford, J. P. Breuer, T. Buggey, G. Butcher, R. Canchal, J. A. Carter, A. Cheney, Y. Collado-Vega, H. Connor, T. Crawford, N. Eaton, C. Feldman, C. Forsyth, T. Frantzen, G. Galgóczi, J. Garcia, G. Y. Genov, C. Gordillo, H-P. Gröbelbauer, M. Guedel, Y. Guo, M. Hailey, D. Hall, R. Hampson, J. Hasiba, O. Hetherington, A. Holland, S-Y. Hsieh, M. W. J. Hubbard, H. Jeszenszky, M. Jones, T. Kennedy, K. Koch-Mehrin, S. Kögl, S. Krucker, K. D. Kuntz, C. Lakin1, G. Laky, O. Lylund, A. Martindale, J. Miguel Mas Hesse, R. Nakamura, K. Oksavik, N. Østgaard, H. Ottacher, R. Ottensamer, C. Pagani, S. Parsons, P. Patel, J. Pearson, G. Peikert, F. S. Porter, T. Pouliantis, B. H. Qureshi, W. Raab, G. Randall, A. M. Read, N. M. M. Roque, M. E. Rostad, C. Runciman, S. Sachdev, A. Samsonov, M. Soman, D. Sibeck, S. Smit, J. Søndergaard, R. Speight, S. Stavland, M. Steller, TianRan Sun, J. Thornhill, W. Thomas, K. Ullaland, B. Walsh, D. Walton, C. Wang, S. Yang. 2024: The Soft X-ray Imager (SXI) on the SMILE Mission. Earth and Planetary Physics, 8(1): 5-14. DOI: 10.26464/epp2023067 | |
TianRan Sun, Hyunju Connor, Andrey Samsonov. 2024: Preface to the Special Issue on Modeling and Data Analysis Methods for the SMILE mission. Earth and Planetary Physics, 8(1): 1-4. DOI: 10.26464/epp2023089 |
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4. | Cucho-Padin, G., Connor, H., Jung, J. et al. A feasibility study of 4-D tomography of soft X-ray magnetosheath emissivities using multi-spacecraft measurements. Frontiers in Astronomy and Space Sciences, 2024. DOI:10.3389/fspas.2024.1379321 |
5. | Sun, T., Connor, H., Samsonov, A. Preface to the Special Issue on Modeling and Data Analysis Methods for the SMILE mission. Earth and Planetary Physics, 2024, 8(1): 1-4. DOI:10.26464/epp2023089 |