Samsonov A. A., Sibeck D. G., Imber J., 2007, J. Geophys. Res.: Space Phys., 112, A12220

Samsonov A. A., Bogdanova Y. V., Branduardi-Raymont G., Sibeck D. G., Toth G., 2020, Geophys. Res. Lett., 47, e2019GL086474

Sanz-Forcada J., Ribas I., Micela G., Pollock A. M. T., Garcia-Alvarez D., Solano E., Eiroa C., 2010, A&A, 511, L8

Savani N. P. et al., 2017, Space Weather, 15, 441

Schaefer B. E., King J. R., Deliyannis C. P., 2000, ApJ, 529, 1026

Schneider D. A., Kent D. V., Mello G. A., 1992, Earth Planet. Sci. Lett., 111, 395

Schoepfer S. D., Algeo T. J., van de Schootbrugge B., Whiteside J. H., 2022, Earth Sci. Rev., 232, 104099

Schulte P. et al., 2010, Science, 327, 1214

Schwarz E., Symons D. T. A., 1969, Phys. Earth Planet. Inter., 2, 11

Schwenn R., Dal Lago A., Huttunen E., Gonzalez W. D., 2005, Ann. Geophys., 23, 1033

Scolini C., Verbeke C., Poedts S., Chané E., Pomoell J., Zuccarello F. P., 2018, Space Weather, 16, 754

See V., Jardine M., Vidotto A. A., Petit P., Marsden S. C., Jeffers S. V., do Nascimento J. D., 2014, A&A, 570, A99

See V. et al., 2017, MNRAS, 466, 1542

Shaw G. H., 2008, Geochemistry, 68, 235

Shaw J. A., 2019, in Creath K., Lakshminarayanan V., Shaw J. A., eds, Proc. SPIE Conf. Ser. Vol. 11099, Light in Nature VII. SPIE, Bellingham, p. 28

Shcherbakova V. V., Biggin A. J., Veselovskiy R. V., Shatsillo A. V., Hawkins L. M. A., Shcherbakov V. P., Zhidkov G. V., 2017, Geophys. J. Int., 209, 1265

Sheeley N. R., Jr, Howard R. A., Koomen M. J., Michels D. J., Schwenn R., Mühlhäuser K. H., Rosenbauer H., 1985, J. Geophys. Res.: Space Phys., 90, 163

Shen F., Feng X. S., Wu S. T., Xiang C. Q., Song W. B., 2011, J. Geophys. Res.: Space Phys., 116, A04102

Shibayama T. et al., 2013, ApJS, 209, 5

Sibeck D. G., Lopez R. E., Roelof E. C., 1991, J. Geophys. Res.: Space Phys., 96, 5489

Sihver L., Mortazavi S. M. J., 2021, J Biomed. Phys. Eng., 1, 663

Skumanich A., 1972, ApJ, 171, 565

Skumanich A., 2019, ApJ, 878, 35

Slavin J. A., Holzer R. E., 1979, J. Geophys. Res., 84, 2076

Slavin J. A. et al., 2009, Science, 324, 606

Smirnov A. V., Kulakov E. V., Foucher M. S., Bristol K. E., 2017, Sci. Adv., 3, e1602306

Sterenborg M. G., Cohen O., Drake J. J., Gombosi T. I., 2011, J. Geophys. Res.: Space Phys., 116, A01217

Strugarek A., Brun A. S., Matt S. P., Réville V., 2014, ApJ, 795, 86

Strugarek A., Brun A. S., Matt S. P., Réville V., 2015, ApJ, 815, 111

Svensmark H., 2012, MNRAS, 423, 1234

Tarduno J. A., Cottrell R. D., Watkeys M. K., Bauch D., 2007, Nature, 446, 657

Tarduno J. A. et al., 2010, Science, 327, 1238

Tarduno J. A., Blackman E. G., Mamajek E. E., 2014, Phys. Earth Planet. Inter., 233, 68

Tarduno J. A. et al., 2020, Proc. Natl. Acad. Sci., 117, 2309

Thallner D., Biggin A. J., McCausland P. J. A., Fu R. R., 2021, J. Geophys. Res.: Solid Earth, 126, e2021JB022292

Thomas B. C. et al., 2005, ApJ, 634, 509

Thomassot E., O'Neil J., Francis D., Cartigny P., Wing B. A., 2015, Proc. Natl. Acad. Sci., 112, 707

Tian F., Kasting J. F., Liu H.-L., Roble R. G., 2008a, J. Geophys. Res.: Planets, 113, 1

Tian F., Solomon S. C., Qian L., Lei J., Roble R. G., 2008b, J. Geophys. Res.: Planets, 113, 1

Torok T. et al., 2018, 856, 75

Toth G., 1996, Astrophys. Lett. Commun., 34, 245

Tu L., Johnstone C. P., Gudel M., Lammer H., 2015, AA, 577, L3

Valet J. P., Fournier A., 2016, Rev. Geophys., 54, 410

Valet J. P., Fournier A., Courtillot V., Herrero-Bervera E., 2012, Nature, 490, 89

Valet J.-P. et al., 2014, Earth Planet. Sci. Lett., 397, 67

van der Boon A. et al., 2022, Earth Sci. Rev., 231, 104073

van Zijl J. S. V., Graham K. W. T., Hales A. L., 1962, Geophys. J. R. Astron. Soc., 7, 169

Varela J., Pantellini F., Moncuquet M., 2015, Planet. Space Sci., 119, 264

Varela J., Pantellini F., Moncuquet M., 2016a, Planet. Space Sci., 120, 78

Varela J., Pantellini F., Moncuquet M., 2016b, Planet. Space Sci., 122, 46

Varela J., Pantellini F., Moncuquet M., 2016c, Planet. Space Sci., 125, 80

Varela J., Pantellini F., Moncuquet M., 2016d, Planet. Space Sci., 129, 74

Varela J., Reville V., Brun. A. S., Pantellini F., Zarka P., 2016e, A&A, 595, A69

Varela J., Reville V., Brun A. S., Zarka P., Pantellini F., 2018, A&A, 616, A182

Varela J., Brun A. S., Zarka P., Strugarek A., Pantellini F., Reville V., 2022a, Space Weather, 20, e2022SW003164

Varela J., Reville V., Brun A. S., Zarka P., Pantellini F., 2022b, A&A, 659, A10

Verosub K. L., Banerjee S. K., 1977, Rev. Geophys., 15, 145

Vidotto A. A. et al., 2014, MNRAS, 441, 2361

Wang J. Y., Wang C., Huang Z. H., Sun T. R., 2014, J. Geophys. Res.: Space Phys., 119, 1887

Wang M., Lu J., Liu Z., Pei S., 2012, Chin. Sci. Bull., 57, 1438

Wang Y. L., Raeder J., Russell C. T., Phan T. D., Manapat M., 2003, J. Geophys. Res.: Space Phys., 108, SMP 8

Wang Y. L., Raeder J., Russell C. T., 2004, Ann. Geophys., 22, 1001

Wang Y. M., Ye P. Z., Wang S., Xue X. H., 2003, Geophys. Res. Lett., 30, 1

Weber E. J., Davis L. J., 1967, ApJ, 148, 217

Wei Y. et al., 2014, Earth Planet. Sci. Lett., 394, 94

Whitmire D. P., Jackson A. A. IV, 1984, Nature, 308, 713

Wood B. E., Muller H. R., Zank G. P., Linsky J. L., Redfield S., 2005, ApJ, 628, L143

Worm H.-U., 1997, Earth Planet. Sci. Lett., 147, 55

Wu C., Lepping R. P., 2015, Sol. Phys., 290, 1243

Wu C.-C., Lepping R. P., 2002, J. Geophys. Res.: Space Phys., 107, SSH 3

Wu C.-C., Lepping R. P., Gopalswamy N., 2006, Sol. Phys., 239, 449

Wu C.-C. et al., 2016, J. Geophys. Res.: Space Phys., 121, 1839

Xu X. et al., 2015, Sci. Rep., 5, 8080

Yoshihara A., Hamano Y., 2000, Phys. Earth Planet. Inter., 117, 295

Zenchenko T. A., Breus T. K., 2021, Atmosphere, 12, 1

Zendejas J., Segura A., Raga A., 2010, Icarus, 210, 539

Zhang H. et al., 2022, ApJ, 937, 1

## APPENDIX A: EXTENDED IONOSPHERE MODEL

The ionosphere model is upgraded to evaluate the effect of the ionosphere expansion on the bow shock and magnetopause standoff distance. The ionospheric domain is now divided in two sections. At $R = 2.3 - 2.5R_E$, it is defined the coupling region between the upper atmosphere and the ionosphere. From $R = 2.5R_E$ to the ionosphere upper limit (an input of the model) is defined the upper ionosphere region.

Special conditions are imposed in the coupling region between the upper atmosphere and the ionosphere. The plasma density is stratified with respect to the Alfvén velocity and the module of the Alfvén velocity is fixed ($v_A = 2 \times 10^4 \text{ km s}^{-1}$) and does not evolve
Samsonov A. A., Sibeck D. G., Imber J., 2007, J. Geophys. Res.: Space Phys., 112, A12220

Samsonov A. A., Bogdanova Y. V., Branduardi-Raymont G., Sibeck D. G., Toth G., 2020, Geophys. Res. Lett., 47, e2019GL086474

Sanz-Forcada J., Ribas I., Micela G., Pollock A. M. T., Garcia-Alvarez D., Solano E., Eiroa C., 2010, A&A, 511, L8

Savani N. P. et al., 2017, Space Weather, 15, 441

Schaefer B. E., King J. R., Deliyannis C. P., 2000, ApJ, 529, 1026

Schneider D. A., Kent D. V., Mello G. A., 1992, Earth Planet. Sci. Lett., 111, 395

Schoepfer S. D., Algeo T. J., van de Schootbrugge B., Whiteside J. H., 2022, Earth Sci. Rev., 232, 104099

Schulte P. et al., 2010, Science, 327, 1214

Schwarz E., Symons D. T. A., 1969, Phys. Earth Planet. Inter., 2, 11

Schwenn R., Dal Lago A., Huttunen E., Gonzalez W. D., 2005, Ann. Geophys., 23, 1033

Scolini C., Verbeke C., Poedts S., Chané E., Pomoell J., Zuccarello F. P., 2018, Space Weather, 16, 754

See V., Jardine M., Vidotto A. A., Petit P., Marsden S. C., Jeffers S. V., do Nascimento J. D., 2014, A&A, 570, A99

See V. et al., 2017, MNRAS, 466, 1542

Shaw G. H., 2008, Geochemistry, 68, 235

Shaw J. A., 2019, in Creath K., Lakshminarayanan V., Shaw J. A., eds, Proc. SPIE Conf. Ser. Vol. 11099, Light in Nature VII. SPIE, Bellingham, p. 28

Shcherbakova V. V., Biggin A. J., Veselovskiy R. V., Shatsillo A. V., Hawkins L. M. A., Shcherbakov V. P., Zhidkov G. V., 2017, Geophys. J. Int., 209, 1265

Sheeley N. R., Jr, Howard R. A., Koomen M. J., Michels D. J., Schwenn R., Mühlhäuser K. H., Rosenbauer H., 1985, J. Geophys. Res.: Space Phys., 90, 163

Shen F., Feng X. S., Wu S. T., Xiang C. Q., Song W. B., 2011, J. Geophys. Res.: Space Phys., 116, A04102

Shibayama T. et al., 2013, ApJS, 209, 5

Sibeck D. G., Lopez R. E., Roelof E. C., 1991, J. Geophys. Res.: Space Phys., 96, 5489

Sihver L., Mortazavi S. M. J., 2021, J Biomed. Phys. Eng., 1, 663

Skumanich A., 1972, ApJ, 171, 565

Skumanich A., 2019, ApJ, 878, 35

Slavin J. A., Holzer R. E., 1979, J. Geophys. Res., 84, 2076

Slavin J. A. et al., 2009, Science, 324, 606

Smirnov A. V., Kulakov E. V., Foucher M. S., Bristol K. E., 2017, Sci. Adv., 3, e1602306

Sterenborg M. G., Cohen O., Drake J. J., Gombosi T. I., 2011, J. Geophys. Res.: Space Phys., 116, A01217

Strugarek A., Brun A. S., Matt S. P., Réville V., 2014, ApJ, 795, 86

Strugarek A., Brun A. S., Matt S. P., Réville V., 2015, ApJ, 815, 111

Svensmark H., 2012, MNRAS, 423, 1234

Tarduno J. A., Cottrell R. D., Watkeys M. K., Bauch D., 2007, Nature, 446, 657

Tarduno J. A. et al., 2010, Science, 327, 1238

Tarduno J. A., Blackman E. G., Mamajek E. E., 2014, Phys. Earth Planet. Inter., 233, 68

Tarduno J. A. et al., 2020, Proc. Natl. Acad. Sci., 117, 2309

Thallner D., Biggin A. J., McCausland P. J. A., Fu R. R., 2021, J. Geophys. Res.: Solid Earth, 126, e2021JB022292

Thomas B. C. et al., 2005, ApJ, 634, 509

Thomassot E., O'Neil J., Francis D., Cartigny P., Wing B. A., 2015, Proc. Natl. Acad. Sci., 112, 707

Tian F., Kasting J. F., Liu H.-L., Roble R. G., 2008a, J. Geophys. Res.: Planets, 113, 1

Tian F., Solomon S. C., Qian L., Lei J., Roble R. G., 2008b, J. Geophys. Res.: Planets, 113, 1

Torok T. et al., 2018, 856, 75

Toth G., 1996, Astrophys. Lett. Commun., 34, 245

Tu L., Johnstone C. P., Gudel M., Lammer H., 2015, AA, 577, L3

Valet J. P., Fournier A., 2016, Rev. Geophys., 54, 410

Valet J. P., Fournier A., Courtillot V., Herrero-Bervera E., 2012, Nature, 490, 89

Valet J.-P. et al., 2014, Earth Planet. Sci. Lett., 397, 67

van der Boon A. et al., 2022, Earth Sci. Rev., 231, 104073

van Zijl J. S. V., Graham K. W. T., Hales A. L., 1962, Geophys. J. R. Astron. Soc., 7, 169

Varela J., Pantellini F., Moncuquet M., 2015, Planet. Space Sci., 119, 264

Varela J., Pantellini F., Moncuquet M., 2016a, Planet. Space Sci., 120, 78

Varela J., Pantellini F., Moncuquet M., 2016b, Planet. Space Sci., 122, 46

Varela J., Pantellini F., Moncuquet M., 2016c, Planet. Space Sci., 125, 80

Varela J., Pantellini F., Moncuquet M., 2016d, Planet. Space Sci., 129, 74

Varela J., Reville V., Brun. A. S., Pantellini F., Zarka P., 2016e, A&A, 595, A69

Varela J., Reville V., Brun A. S., Zarka P., Pantellini F., 2018, A&A, 616, A182

Varela J., Brun A. S., Zarka P., Strugarek A., Pantellini F., Reville V., 2022a, Space Weather, 20, e2022SW003164

Varela J., Reville V., Brun A. S., Zarka P., Pantellini F., 2022b, A&A, 659, A10

Verosub K. L., Banerjee S. K., 1977, Rev. Geophys., 15, 145

Vidotto A. A. et al., 2014, MNRAS, 441, 2361

Wang J. Y., Wang C., Huang Z. H., Sun T. R., 2014, J. Geophys. Res.: Space Phys., 119, 1887

Wang M., Lu J., Liu Z., Pei S., 2012, Chin. Sci. Bull., 57, 1438

Wang Y. L., Raeder J., Russell C. T., Phan T. D., Manapat M., 2003, J. Geophys. Res.: Space Phys., 108, SMP 8

Wang Y. L., Raeder J., Russell C. T., 2004, Ann. Geophys., 22, 1001

Wang Y. M., Ye P. Z., Wang S., Xue X. H., 2003, Geophys. Res. Lett., 30, 1

Weber E. J., Davis L. J., 1967, ApJ, 148, 217

Wei Y. et al., 2014, Earth Planet. Sci. Lett., 394, 94

Whitmire D. P., Jackson A. A. IV, 1984, Nature, 308, 713

Wood B. E., Muller H. R., Zank G. P., Linsky J. L., Redfield S., 2005, ApJ, 628, L143

Worm H.-U., 1997, Earth Planet. Sci. Lett., 147, 55

Wu C., Lepping R. P., 2015, Sol. Phys., 290, 1243

Wu C.-C., Lepping R. P., 2002, J. Geophys. Res.: Space Phys., 107, SSH 3

Wu C.-C., Lepping R. P., Gopalswamy N., 2006, Sol. Phys., 239, 449

Wu C.-C. et al., 2016, J. Geophys. Res.: Space Phys., 121, 1839

Xu X. et al., 2015, Sci. Rep., 5, 8080

Yoshihara A., Hamano Y., 2000, Phys. Earth Planet. Inter., 117, 295

Zenchenko T. A., Breus T. K., 2021, Atmosphere, 12, 1

Zendejas J., Segura A., Raga A., 2010, Icarus, 210, 539

Zhang H. et al., 2022, ApJ, 937, 1

## APPENDIX A: EXTENDED IONOSPHERE MODEL

The ionosphere model is upgraded to evaluate the effect of the ionosphere expansion on the bow shock and magnetopause standoff distance. The ionospheric domain is now divided in two sections. At $R = 2.3 - 2.5R_E$, it is defined the coupling region between the upper atmosphere and the ionosphere. From $R = 2.5R_E$ to the ionosphere upper limit (an input of the model) is defined the upper ionosphere region.

Special conditions are imposed in the coupling region between the upper atmosphere and the ionosphere. The plasma density is stratified with respect to the Alfvén velocity and the module of the Alfvén velocity is fixed ($v_A = 2 \times 10^4 \text{ km s}^{-1}$) and does not evolve
during the simulation, defined as

$$ \rho = \frac{|B|^2}{\mu_0 v_A^2}. \qquad (A1) $$

The hydro-static equilibrium between the upper atmosphere and the ionosphere is set by fixing the plasma pressure with respect to the sound speed of the SW ($c_{sw}$) and the upper atmosphere ($c_p$):

$$ p = \frac{n}{\gamma} \left( \frac{(c_p - c_{sw})(r^3 - R_s^3)}{R_{inn}^3 - R_s^3} + c_{sw} \right)^2, \qquad (A2) $$

with $c_p = \sqrt{\gamma K_B T_p / m_p}$ with $T_p$ the plasma temperature at the upper atmosphere and $T_{sw}$ the SW temperature.

The plasma density and magnetic field are free to evolve in the upper ionosphere region, thus the upper ionosphere can be compressed by the effect of the SW as well as the Earth magnetic field lines. Only the slope of the pressure is constrained following equation (A2).

The field-aligned currents ($J_{FAC}$) are calculated in the upper ionosphere and the coupling region between the upper atmosphere and the ionosphere based on (Büchner et al. 2003) model:

$$ J_{FAC} = J - J_{\perp}, \qquad (A3) $$

where

$$ J = \frac{1}{\mu_0} \nabla \times B, \qquad (A4) $$

$$ J_{\perp} = J - \frac{J_r B_r + J_{\theta} B_{\theta} + J_{\phi} B_{\phi}}{|B|^2} B, \qquad (A5) $$

with **J** the plasma current, **J**<sub>⊥</sub> the perpendicular component of the plasma current along the magnetic field line, $\mu_0$ the vacuum magnetic permeability, and **B** the magnetic field.

Next, the electric field is calculated using the Pedersen conductance ($\sigma$) empirical formula,

$$ \sigma = \frac{40 E_0 \sqrt{F_E}}{16 + E_0^2}, \qquad (A6) $$

with $E_0 = K_B T_E$ the mean energy of the electrons, $F_E = n_E \sqrt{E_0 / (2\pi m_E)}$ the energy flux, and $K_B$ the Boltzmann constant ($T_E$ and $m_E$ are the electron temperature and mass, respectively). Thus, the electric field ($E$) linked to the FAC is:

$$ E = \sigma J_{FAC}. \qquad (A7) $$

When the electric field is calculated, the velocity of the plasma in the coupling region between the upper atmosphere and the ionosphere is:

$$ v = \frac{E \times B}{|B|^2}. \qquad (A8) $$

This paper has been typeset from a TeX/LA TeX file prepared by the author.
during the simulation, defined as

$$ \rho = \frac{|B|^2}{\mu_0 v_A^2}. \qquad (A1) $$

The hydro-static equilibrium between the upper atmosphere and the ionosphere is set by fixing the plasma pressure with respect to the sound speed of the SW ($c_{sw}$) and the upper atmosphere ($c_p$):

$$ p = \frac{n}{\gamma} \left( \frac{(c_p - c_{sw})(r^3 - R_s^3)}{R_{inn}^3 - R_s^3} + c_{sw} \right)^2, \qquad (A2) $$

with $c_p = \sqrt{\gamma K_B T_p / m_p}$ with $T_p$ the plasma temperature at the upper atmosphere and $T_{sw}$ the SW temperature.

The plasma density and magnetic field are free to evolve in the upper ionosphere region, thus the upper ionosphere can be compressed by the effect of the SW as well as the Earth magnetic field lines. Only the slope of the pressure is constrained following equation (A2).

The field-aligned currents ($J_{FAC}$) are calculated in the upper ionosphere and the coupling region between the upper atmosphere and the ionosphere based on (Büchner et al. 2003) model:

$$ J_{FAC} = J - J_{\perp}, \qquad (A3) $$

where

$$ J = \frac{1}{\mu_0} \nabla \times B, \qquad (A4) $$

$$ J_{\perp} = J - \frac{J_r B_r + J_{\theta} B_{\theta} + J_{\phi} B_{\phi}}{|B|^2} B, \qquad (A5) $$

with **J** the plasma current, **J**$_{⊥}$ the perpendicular component of the plasma current along the magnetic field line, $\mu_0$ the vacuum magnetic permeability, and **B** the magnetic field.

Next, the electric field is calculated using the Pedersen conductance ($\sigma$) empirical formula,

$$ \sigma = \frac{40 E_0 \sqrt{F_E}}{16 + E_0^2}, \qquad (A6) $$

with $E_0 = K_B T_E$ the mean energy of the electrons, $F_E = n_E \sqrt{E_0 / (2\pi m_E)}$ the energy flux, and $K_B$ the Boltzmann constant ($T_E$ and $m_E$ are the electron temperature and mass, respectively). Thus, the electric field ($E$) linked to the FAC is:

$$ E = \sigma J_{FAC}. \qquad (A7) $$

When the electric field is calculated, the velocity of the plasma in the coupling region between the upper atmosphere and the ionosphere is:

$$ v = \frac{E \times B}{|B|^2}. \qquad (A8) $$

This paper has been typeset from a TeX/LA TeX file prepared by the author.