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Tomographic Reconstruction of the Solar K-Corona Using Neural Fields

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Abstract

We explore the application of neural fields for tomographic reconstructions of the solar corona using data from the Large Angle and Spectrometric Coronagraph (LASCO)-C2 instrument. We first demonstrate their ability to recover the electron-density volume in a synthetic static case, utilizing a simulated 3D model of the corona. Our results show that neural fields provide an efficient and accurate representation of the electron-density data. By comparing the synthesized polarized brightness from the modeled electron densities and the observations, we validate the performance of the method in recovering the electron-density structure accurately. Furthermore, we extend our analysis to the dynamic case, considering time-dependent reconstructions. To this end, we incorporate the temporal dimension into the neural field. The results demonstrate that neural fields can effectively capture the temporal variability of the coronal electron density. We apply the developed tomographic strategy to real observations from the LASCO-C2 instrument. Using a sequence of LASCO-C2 images, we reconstruct the electron-density distribution of the solar corona for a specific period. The reconstructed electron densities are able to reproduce the observed features of the polarized brightness with fidelity, although some streamers are not properly fitted. The results indicate that neural fields provide a powerful tool for tomographic reconstructions, yielding electron-density maps with minimal artifacts and improved agreement with observations. Neural fields offer several advantages, including efficient interpolation, easy to implement implicit and explicit regularization, and the ability to capture temporal variability. The proposed approach has the potential to enhance our understanding of the complex dynamics and structures of the solar corona, enabling more accurate and detailed analyses of coronal features.

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Data Availability

Data, together with training and evaluation scripts, are available at https://github.com/aasensio/nf_corona.

Notes

  1. See https://www.predsci.com/portal/home.php.

  2. https://lasco-www.nrl.navy.mil/content/retrieve/polarize/.

References

  • Asensio Ramos, A., Díaz Baso, C.J., Kochukhov, O.: 2022, Approximate Bayesian neural Doppler imaging. Astron. Astrophys. 658, A162. DOI. ADS.

    Article  ADS  Google Scholar 

  • Billings, D.E.: 1966, A guide to the solar corona. ADS.

  • Bintsi, K.-M., Jarolim, R., Tremblay, B., Santos, M., Jungbluth, A., Mason, J.P., Sundaresan, S., Vourlidas, A., Downs, C., Caplan, R.M., Muñoz Jaramillo, A.: 2022, SuNeRF: Validation of a 3D Global Reconstruction of the Solar Corona Using Simulated EUV Images. ArXiv e-prints. arXiv. DOI. ADS.

  • Butala, M.D., Hewett, R.J., Frazin, R.A., Kamalabadi, F.: 2010, Dynamic three-dimensional tomography of the solar corona. Solar Phys. 262, 495. DOI. ADS.

    Article  ADS  Google Scholar 

  • Casini, R., Judge, P.G.: 1999, Spectral lines for polarization measurements of the coronal magnetic field. II. Consistent treatment of the Stokes vector forMagnetic-dipole transitions. Astrophys. J. 522, 524. DOI. ADS.

    Article  ADS  Google Scholar 

  • Collette, A.: 2013, Python and HDF5 O’Reilly.

    Google Scholar 

  • Cranmer, S.R., Kohl, J.L., Noci, G., Antonucci, E., Tondello, G., Huber, M.C.E., Strachan, L., Panasyuk, A.V., Gardner, L.D., Romoli, M., Fineschi, S., Dobrzycka, D., Raymond, J.C., Nicolosi, P., Siegmund, O.H.W., Spadaro, D., Benna, C., Ciaravella, A., Giordano, S., Habbal, S.R., Karovska, M., Li, X., Martin, R., Michels, J.G., Modigliani, A., Naletto, G., O’Neal, R.H., Pernechele, C., Poletto, G., Smith, P.L., Suleiman, R.M.: 1999, An empirical model of a polar coronal hole at solar minimum. Astrophys. J. 511, 481. DOI. ADS.

    Article  ADS  Google Scholar 

  • Crifo-Magnant, F., Picat, J.P.: 1980, A density model for the North polar coronal hole at the 1973 eclipse. Astron. Astrophys. 88, 97. ADS.

    ADS  Google Scholar 

  • Frazin, R.A., Janzen, P.: 2002, Tomography of the solar corona. II. Robust, regularized, positive estimation of the three-dimensional electron density distribution from LASCO-C2 polarized white-light images. Astrophys. J. 570, 408. DOI. ADS.

    Article  ADS  Google Scholar 

  • Frazin, R.A., Kamalabadi, F.: 2005, Rotational tomography for 3d reconstruction of the white-light and euv corona in the post-soho era. Solar Phys. 228, 219. DOI. ADS.

    Article  ADS  Google Scholar 

  • Frazin, R.A., Vásquez, A.M., Kamalabadi, F.: 2009, Quantitative, three-dimensional analysis of the global corona with multi-spacecraft differential emission measure tomography. Astrophys. J. 701, 547. DOI. ADS.

    Article  ADS  Google Scholar 

  • Frazin, R.A., Vásquez, A.M., Kamalabadi, F., Park, H.: 2007, Three-dimensional tomographic analysis of a high-cadence LASCO-C2 polarized brightness sequence. Astrophys. J. 671, L201. DOI.

    Article  ADS  Google Scholar 

  • Frazin, R.A., Lamy, P., Llebaria, A., Vásquez, A.M.: 2010, Three-dimensional electron density from tomographic analysis of LASCO-C2 images of the K-corona total brightness. Solar Phys. 265, 19. DOI. ADS.

    Article  ADS  Google Scholar 

  • Harris, C.R., Millman, K.J., van der Walt, S.J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N.J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M.H., Brett, M., Haldane, A., Fernández del Río, J., Wiebe, M., Peterson, P., Gérard-Marchant, P., Sheppard, K., Reddy, T., Weckesser, W., Abbasi, H., Gohlke, C., Oliphant, T.E.: 2020, Array programming with NumPy. Nature 585, 357. DOI.

    Article  ADS  Google Scholar 

  • Huang, X., Ye, Z., Liu, H., Shi, B., Wang, Z., Yang, K., Li, Y., Weng, B., Wang, M., Chu, H., et al.: 2021, Meta-Auto-Decoder for Solving Parametric Partial Differential Equations. ArXiv preprint. arXiv.

  • Hunter, J.D.: 2007, Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90.

    Article  Google Scholar 

  • Jarolim, R., Bintsi, M., Santos, M., Tremblay, B., Jungbluth, A., Mason, J.P., Munoz-Jaramillo, A., Sundaresan, S., Vourlidas, A.: 2022, 3D reconstructions of the solar atmosphere using neural radiance fields. In: AGU Fall Meeting Abs. 2022, SH45D. ADS.

    Google Scholar 

  • Kaiser, M.L., Kucera, T.A., Davila, J.M., St.Cyr, O.C., Guhathakurta, M., Christian, E.: 2008, The STEREO mission: an introduction. Space Sci. Rev. 136, 5. DOI. ADS.

    Article  ADS  Google Scholar 

  • Kingma, D.P., Ba, J.: 2014, Adam: a Method for Stochastic Optimization. ArXiv e-prints. arXiv.

  • Kramar, M., Inhester, B., Lin, H., Davila, J.: 2013, Vector tomography for the coronal magnetic field. II. Hanle effect measurements. Astrophys. J. 775, 25. DOI. ADS.

    Article  ADS  Google Scholar 

  • Lionello, R., Linker, J.A., Mikić, Z.: 2008, Multispectral emission of the sun during the first whole sun month: magnetohydrodynamic simulations. Astrophys. J. 690, 902. DOI.

    Article  ADS  Google Scholar 

  • Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: 2020, Nerf: representing scenes as neural radiance fields for view synthesis. In: European Conference on Computer Vision, Springer, Berlin, 405.

    Google Scholar 

  • Minnaert, M.: 1930, On the continuous spectrum of the corona and its polarisation. With 3 figures. (Received July 30, 1930. Z. Astrophys. 30, 209. ADS.

    ADS  MATH  Google Scholar 

  • Morgan, H.: 2015, Astrophys. J. Suppl. 219, 23. DOI.

    Article  ADS  Google Scholar 

  • Morgan, H.: 2019, An atlas of coronal electron density at 5R ⊙. II. a spherical harmonic method for density reconstruction. Astrophys. J. Suppl. 242, 3. DOI. ADS.

    Article  ADS  Google Scholar 

  • Munro, R.H., Jackson, B.V.: 1977, Physical properties of a polar coronal hole from 2 to 5 R sun. Astrophys. J. 213, 874. DOI. ADS.

    Article  ADS  Google Scholar 

  • Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: 2019, PyTorch: an imperative style, high-performance deep learning library. In: Wallach, H., Larochelle, H., Beygelzimer, A., d’é-Buc, F., Fox, E., Garnett, R. (eds.) Advances in Neural Information Processing Systems 32, Curran Associates, Red Hook, 8024. http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf.

    Google Scholar 

  • Quémerais, E., Lamy, P.: 2002, Two-dimensional electron density in the solar corona from inversion of white light images – application to SOHO/LASCO-C2 observations. Astron. Astrophys. 393, 295. DOI. ADS.

    Article  ADS  Google Scholar 

  • Rahaman, N., Baratin, A., Arpit, D., Draxler, F., Lin, M., Hamprecht, F., Bengio, Y., Courville, A.: 2019, On the spectral bias of neural networks. In: Chaudhuri, K., Salakhutdinov, R. (eds.) Proc. Machine Learning Res., PMLR 97, 5301. https://proceedings.mlr.press/v97/rahaman19a.html.

    Google Scholar 

  • Riley, P., Lionello, R., Linker, J.A., Cliver, E., Balogh, A., Beer, J., Charbonneau, P., Crooker, N., DeRosa, M., Lockwood, M., Owens, M., McCracken, K., Usoskin, I., Koutchmy, S.: 2015, Inferring the structure of the solar corona and inner heliosphere during the Maunder minimum using global thermodynamic magnetohydrodynamic simulations. Astrophys. J. 802, 105. DOI. ADS.

    Article  ADS  Google Scholar 

  • Sitzmann, V., Martel, J., Bergman, A., Lindell, D., Wetzstein, G.: 2020, Implicit neural representations with periodic activation functions. Adv. Neural Inf. Process. Syst. 33, 7462.

    Google Scholar 

  • Tancik, M., Srinivasan, P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J., Ng, R.: 2020, Fourier features let networks learn high frequency functions in low dimensional domains. Adv. Neural Inf. Process. Syst. 33, 7537.

    Google Scholar 

  • The SunPy Community Barnes, W.T., Bobra, M.G., Christe, S.D., Freij, N., Hayes, L.A., Ireland, J., Mumford, S., Perez-Suarez, D., Ryan, D.F., Shih, A.Y., Chanda, P., Glogowski, K., Hewett, R., Hughitt, V.K., Hill, A., Hiware, K., Inglis, A., Kirk, M.S.F., Konge, S., Mason, J.P., Maloney, S.A., Murray, S.A., Panda, A., Park, J., Pereira, T.M.D., Reardon, K., Savage, S., Sipőcz, B.M., Stansby, D., Jain, Y., Taylor, G., Yadav, T., Rajul, D.T.K.: 2020, The SunPy project: open source development and status of the version 1.0 core package. Astrophys. J. 890. DOI.

  • Tomczyk, S., Card, G.L., Darnell, T., Elmore, D.F., Lull, R., Nelson, P.G., Streander, K.V., Burkepile, J., Casini, R., Judge, P.G.: 2008, An instrument to measure coronal emission line polarization. Solar Phys. 247, 411. DOI. ADS.

    Article  ADS  Google Scholar 

  • van de Hulst, H.C.: 1950, The electron density of the solar corona. Bull. Astron. Inst. Neth. 11, 135. ADS.

    ADS  Google Scholar 

  • Vibert, D., Peillon, C., Lamy, P., Frazin, R.A., Wojak, J.: 2016, Time-dependent tomographic reconstruction of the solar corona. Astron. Comput. 17, 144. DOI. https://www.sciencedirect.com/science/article/pii/S2213133716301019.

    Article  ADS  Google Scholar 

  • Wang, S., Wang, H., Perdikaris, P.: 2021, On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks. Comput. Methods Appl. Mech. Eng. 384, 113938. DOI. https://www.sciencedirect.com/science/article/pii/S0045782521002759.

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgments

I thank R. Frazin for useful discussions during the initial phases of this work. I acknowledge the community effort devoted to the development of the following open-source packages that were used in this work: numpy (numpy.org, Harris et al., 2020), matplotlib (matplotlib.org, Hunter, 2007), PyTorch (pytorch.org, Paszke et al., 2019), SunPy (sunpy.org, The SunPy Community Barnes et al., 2020), and h5py (Collette, 2013).

Funding

This work was supported by the State Research Agency (AEI) of the Spanish Ministry of Science, Innovation and Universities (MCIU) and the European Regional Development Fund (FEDER) under a grant with reference PGC2018-102108-B-I00.

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  1. Instituto de Astrofisica de Canarias, 38205, C/ Via Lactea, s/n, La Laguna, Tenerife, Spain

    Andrés Asensio Ramos

  2. Departamento de Astrofisica, Universidad de La Laguna, 38205, La Laguna, Tenerife, Spain

    Andrés Asensio Ramos

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Asensio Ramos, A. Tomographic Reconstruction of the Solar K-Corona Using Neural Fields. Sol Phys 298, 135 (2023). https://doi.org/10.1007/s11207-023-02226-2

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