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Fan Y (2021) Magnetic fields in the solar convection zone. Living Rev Sol Phys 18(1):5. https://doi.org/10.1007/s41116-021-00031-2

Fan Y, Fang F (2014) A simulation of convective dynamo in the solar convective envelope: maintenance of the solar-like differential rotation and emerging flux. Astrophys J 789(1):35. https://doi.org/10.1088/0004-637X/789/1/35. arXiv:1405.3926 [astro-ph.SR]

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Fan Y, Fisher GH, McClymont AN (1994) Dynamics of emerging active region flux loops. Astrophys J 436:907. https://doi.org/10.1086/174967

Fan Y, Zweibel EG, Lantz SR (1998) Two-dimensional simulations of buoyantly rising, interacting magnetic flux tubes. Astrophys J 493(1):480–493. https://doi.org/10.1086/305122

Fan Y, Abbett WP, Fisher GH (2003) The dynamic evolution of twisted magnetic flux tubes in a three-dimensional convecting flow. I. Uniformly buoyant horizontal tubes. Astrophys J 582(2):1206–1219. https://doi.org/10.1086/344798

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Gilman PA, Howard R (1985) Rotation rates of leader and follower sunspots. Astrophys J 295:233–240. https://doi.org/10.1086/163368

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Harvey KL (1993) Magnetic bipoles on the Sun. PhD thesis. Utrecht University

Hazra G, Nandy D, Kitchatinov L et al (2023) Mean field models of flux transport dynamo and meridional circulation in the Sun and stars. Space Sci Rev 219:39. https://doi.org/10.1007/s11214-023-00982-y arXiv:2302.09390 [astro-ph.SR]

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Hotta H, Rempel M, Yokoyama T (2016) Large-scale magnetic fields at high Reynolds numbers in magneto-hydrodynamic simulations. Science 351(6280):1427–1430. https://doi.org/10.1126/science.aad1893
D'Silva S, Choudhuri AR (1993) A theoretical model for tilts of bipolar magnetic regions. Astron Astrophys 272:621

Emonet T, Moreno-Insertis F (1998) The physics of twisted magnetic tubes rising in a stratified medium: two-dimensional results. Astrophys J 492(2):804–821. https://doi.org/10.1086/305074. arXiv:astro-ph/9711043 [astro-ph]

Fan Y (2001) Nonlinear growth of the three-dimensional undular instability of a horizontal magnetic layer and the formation of arching flux tubes. Astrophys J 546(1):509–527. https://doi.org/10.1086/318222

Fan Y (2008) The three-dimensional evolution of buoyant magnetic flux tubes in a model solar convective envelope. Astrophys J 676(1):680–697. https://doi.org/10.1086/527317

Fan Y (2021) Magnetic fields in the solar convection zone. Living Rev Sol Phys 18(1):5. https://doi.org/10.1007/s41116-021-00031-2

Fan Y, Fang F (2014) A simulation of convective dynamo in the solar convective envelope: maintenance of the solar-like differential rotation and emerging flux. Astrophys J 789(1):35. https://doi.org/10.1088/0004-637X/789/1/35. arXiv:1405.3926 [astro-ph.SR]

Fan Y, Gong D (2000) On the twist of emerging flux loops in the solar convection zone. Sol Phys 192:141–157. https://doi.org/10.1023/A:1005260207672

Fan Y, Fisher GH, Deluca EE (1993) The origin of morphological asymmetries in bipolar active regions. Astrophys J 405:390. https://doi.org/10.1086/172370

Fan Y, Fisher GH, McClymont AN (1994) Dynamics of emerging active region flux loops. Astrophys J 436:907. https://doi.org/10.1086/174967

Fan Y, Zweibel EG, Lantz SR (1998) Two-dimensional simulations of buoyantly rising, interacting magnetic flux tubes. Astrophys J 493(1):480–493. https://doi.org/10.1086/305122

Fan Y, Abbett WP, Fisher GH (2003) The dynamic evolution of twisted magnetic flux tubes in a three-dimensional convecting flow. I. Uniformly buoyant horizontal tubes. Astrophys J 582(2):1206–1219. https://doi.org/10.1086/344798

Favier B, Jouve L, Edmunds W et al (2012) How can large-scale twisted magnetic structures naturally emerge from buoyancy instabilities? Mon Not R Astron Soc 426(4):3349–3359. https://doi.org/10.1111/j.1365-2966.2012.21920.x. arXiv:1208.4787 [astro-ph.SR]

Ferriz-Mas A, Schüssler M (1995) Instabilities of magnetic flux tubes in a stellar convection zone II. Flux rings outside the equatorial plane. Geophys Astrophys Fluid Dyn 81(3):233–265. https://doi.org/10.1080/03091929508229066

Fuentes ML, Démoulin P, Mandrini CH et al (2003) Magnetic twist and writhe of active regions. On the origin of deformed flux tubes. Astron Astrophys 397:305–318. https://doi.org/10.1051/0004-6361:20021487. arXiv:1411.5626 [astro-ph.SR]

García RA, Mathur S, Salabert D et al (2010) CoRoT reveals a magnetic activity cycle in a Sun-like star. Science 329(5995):1032. https://doi.org/10.1126/science.1191064. arXiv:1008.4399 [astro-ph.SR]

García-Alvarez D, Lanza AF, Messina S et al (2011) Starspots on the fastest rotators in the β Pictoris moving group. Astron Astrophys 533:A30. https://doi.org/10.1051/0004-6361/201116646. arXiv:1107.5688 [astro-ph.SR]

Ghizaru M, Charbonneau P, Smolarkiewicz PK (2010) Magnetic cycles in global large-eddy simulations of solar convection. Astrophys J Lett 715(2):L133–L137. https://doi.org/10.1088/2041-8205/715/2/L133

Gilman PA, Howard R (1985) Rotation rates of leader and follower sunspots. Astrophys J 295:233–240. https://doi.org/10.1086/163368

Gizon L, Cameron RH, Pourabdian M et al (2020) Meridional flow in the Sun’s convection zone is a single cell in each hemisphere. Science 368(6498):1469–1472. https://doi.org/10.1126/science.aaz7119

Granzer T, Schüssler M, Caligari P et al (2000) Distribution of starspots on cool stars. II. Pre-main-sequence and ZAMS stars between 0.4 M☉ and 1.7 M☉. Astron Astrophys 355:1087–1097

Hale GE, Ellerman F, Nicholson SB et al (1919) The magnetic polarity of Sun-spots. Astrophys J 49:153. https://doi.org/10.1086/142452

Harvey KL (1993) Magnetic bipoles on the Sun. PhD thesis. Utrecht University

Hazra G, Nandy D, Kitchatinov L et al (2023) Mean field models of flux transport dynamo and meridional circulation in the Sun and stars. Space Sci Rev 219:39. https://doi.org/10.1007/s11214-023-00982-y arXiv:2302.09390 [astro-ph.SR]

Holzwarth V, Schüssler M (2003) Dynamics of magnetic flux tubes in close binary stars. II. Nonlinear evolution and surface distributions. Astron Astrophys 405:303–311. https://doi.org/10.1051/0004-6361:20030584. arXiv:astro-ph/0304498 [astro-ph]

Hotta H, Iijima H (2020) On rising magnetic flux tube and formation of sunspots in a deep domain. Mon Not R Astron Soc 494(2):2523–2537. https://doi.org/10.1093/mnras/staa844. arXiv:2003.10583 [astro-ph.SR]

Hotta H, Rempel M, Yokoyama T (2016) Large-scale magnetic fields at high Reynolds numbers in magneto-hydrodynamic simulations. Science 351(6280):1427–1430. https://doi.org/10.1126/science.aad1893
Howard RF (1996) Axial tilt angles of active regions. Sol Phys 169(2):293-301. https://doi.org/10.1007/BF00190606

Işık E (2015) A mechanism for the dependence of sunspot group tilt angles on cycle strength. Astrophys J Lett 813(1):L13. https://doi.org/10.1088/2041-8205/813/1/L13. arXiv:1510.04323 [astro-ph.SR]

Işık E, Schüssler M, Solanki SK (2007) Magnetic flux transport on active cool stars and starspot lifetimes. Astron Astrophys 464(3):1049-1057. https://doi.org/10.1051/0004-6361:20066623. arXiv:astro-ph/0612399 [astro-ph]

Işık E, Schmitt D, Schüssler M (2011) Magnetic flux generation and transport in cool stars. Astron Astrophys 528:A135. https://doi.org/10.1051/0004-6361/201014501. arXiv:1102.0569 [astro-ph.SR]

Işık E, Solanki SK, Krivova NA et al (2018) Forward modelling of brightness variations in Sun-like stars. I. Emergence and surface transport of magnetic flux. Astron Astrophys 620:A177. https://doi.org/10.1051/0004-6361/201833393. arXiv:1810.06728 [astro-ph.SR]

Işık E, Shapiro AI, Solanki SK et al (2020) Amplification of brightness variability by active-region nesting in solar-like stars. Astrophys J Lett 901(1):L12. https://doi.org/10.3847/2041-8213/abb409. arXiv:2009.00692 [astro-ph.SR]

Järvinen SP, Berdyugina SV, Tuominen I et al (2005) Magnetic activity in the young solar analog AB Dor. Active longitudes and cycles from long-term photometry. Astron Astrophys 432(2):657-664. https://doi.org/10.1051/0004-6361:20041998

Jeffers SV, Barnes JR, Collier Cameron A (2002) The latitude distribution of star-spots on He 699. Mon Not R Astron Soc 331(3):666-672. https://doi.org/10.1046/j.1365-8711.2002.05143.x

Jeffers SV, Cameron RH, Marsden SC et al (2022) The crucial role of surface magnetic fields for stellar dynamos: ε Eridani, 61 Cygni A, and the Sun. Astron Astrophys 661:A152. https://doi.org/10.1051/0004-6361/202142202. arXiv:2201.07530 [astro-ph.SR]

Jetsu L, Pohjolainen S, Pelt J et al (1997) Is the longitudinal distribution of solar flares nonuniform? Astron Astrophys 318:293-307

Jha BK, Karak BB, Mandal S et al (2020) Magnetic field dependence of bipolar magnetic region tilts on the Sun: indication of tilt quenching. Astrophys J Lett 889(1):L19. https://doi.org/10.3847/2041-8213/ab665c. arXiv:1912.13223 [astro-ph.SR]

Jiang J, Işık E, Cameron RH et al (2010) The effect of activity-related meridional flow modulation on the strength of the solar polar magnetic field. Astrophys J 717(1):597-602. https://doi.org/10.1088/0004-637X/717/1/597. arXiv:1005.5317 [astro-ph.SR]

Jiao Q, Jiang J, Wang ZF (2021) Sunspot tilt angles revisited: dependence on the solar cycle strength. Astron Astrophys 653:A27. https://doi.org/10.1051/0004-6361/202141215. arXiv:2106.11615 [astro-ph.SR]

Jouve L, Brun AS (2009) Three-dimensional nonlinear evolution of a magnetic flux tube in a spherical shell: influence of turbulent convection and associated mean flows. Astrophys J 701(2):1300-1322. https://doi.org/10.1088/0004-637X/701/2/1300. arXiv:0907.2131 [astro-ph.SR]

Jouve L, Proctor MRE, Lesur G (2010) Buoyancy-induced time delays in Babcock-Leighton flux-transport dynamo models. Astron Astrophys 519:A68. https://doi.org/10.1051/0004-6361/201014455. arXiv:1005.2283 [astro-ph.SR]

Jouve L, Brun AS, Aulanier G (2013) Global dynamics of subsurface solar active regions. Astrophys J 762(1):4. https://doi.org/10.1088/0004-637X/762/1/4. arXiv:1211.7251 [astro-ph.SR]

Jouve L, Brun AS, Aulanier G (2018) Interactions of twisted Ω-loops in a model solar convection zone. Astrophys J 857(2):83. https://doi.org/10.3847/1538-4357/aab5b6. arXiv:1803.04709 [astro-ph.SR]

Käpylä PJ, Mantere MJ, Brandenburg A (2012) Cyclic magnetic activity due to turbulent convection in spherical wedge geometry. Astrophys J Lett 755(1):L22. https://doi.org/10.1088/2041-8205/755/1/L22. arXiv:1205.4719 [astro-ph.SR]

Käpylä PJ, Brandenburg A, Kleeorin N et al (2016) Magnetic flux concentrations from turbulent stratified convection. Astron Astrophys 588:A150. https://doi.org/10.1051/0004-6361/201527731. arXiv:1511.03718 [astro-ph.SR]

Karak BB, Miesch M (2017) Solar cycle variability induced by tilt angle scatter in a Babcock-Leighton solar dynamo model. Astrophys J 847(1):69. https://doi.org/10.3847/1538-4357/aa8636. arXiv:1706.08933 [astro-ph.SR]

Komm R, Morita S, Howe R et al (2008) Emerging active regions studied with ring-diagram analysis. Astrophys J 672:1254-1265. https://doi.org/10.1086/523998

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Leighton RB (1969) A magneto-kinematic model of the solar cycle. Astrophys J 156:1. https://doi.org/10.1086/149943
Howard RF (1996) Axial tilt angles of active regions. Sol Phys 169(2):293-301. https://doi.org/10.1007/BF00190606

Işık E (2015) A mechanism for the dependence of sunspot group tilt angles on cycle strength. Astrophys J Lett 813(1):L13. https://doi.org/10.1088/2041-8205/813/1/L13. arXiv:1510.04323 [astro-ph.SR]

Işık E, Schüssler M, Solanki SK (2007) Magnetic flux transport on active cool stars and starspot lifetimes. Astron Astrophys 464(3):1049-1057. https://doi.org/10.1051/0004-6361:20066623. arXiv:astro-ph/0612399 [astro-ph]

Işık E, Schmitt D, Schüssler M (2011) Magnetic flux generation and transport in cool stars. Astron Astrophys 528:A135. https://doi.org/10.1051/0004-6361/201014501. arXiv:1102.0569 [astro-ph.SR]

Işık E, Solanki SK, Krivova NA et al (2018) Forward modelling of brightness variations in Sun-like stars. I. Emergence and surface transport of magnetic flux. Astron Astrophys 620:A177. https://doi.org/10.1051/0004-6361/201833393. arXiv:1810.06728 [astro-ph.SR]

Işık E, Shapiro AI, Solanki SK et al (2020) Amplification of brightness variability by active-region nesting in solar-like stars. Astrophys J Lett 901(1):L12. https://doi.org/10.3847/2041-8213/abb409. arXiv:2009.00692 [astro-ph.SR]

Järvinen SP, Berdyugina SV, Tuominen I et al (2005) Magnetic activity in the young solar analog AB Dor. Active longitudes and cycles from long-term photometry. Astron Astrophys 432(2):657-664. https://doi.org/10.1051/0004-6361:20041998

Jeffers SV, Barnes JR, Collier Cameron A (2002) The latitude distribution of star-spots on He 699. Mon Not R Astron Soc 331(3):666-672. https://doi.org/10.1046/j.1365-8711.2002.05143.x

Jeffers SV, Cameron RH, Marsden SC et al (2022) The crucial role of surface magnetic fields for stellar dynamos: ϵ Eridani, 61 Cygni A, and the Sun. Astron Astrophys 661:A152. https://doi.org/10.1051/0004-6361/202142202. arXiv:2201.07530 [astro-ph.SR]

Jetsu L, Pohjolainen S, Pelt J et al (1997) Is the longitudinal distribution of solar flares nonuniform? Astron Astrophys 318:293-307

Jha BK, Karak BB, Mandal S et al (2020) Magnetic field dependence of bipolar magnetic region tilts on the Sun: indication of tilt quenching. Astrophys J Lett 889(1):L19. https://doi.org/10.3847/2041-8213/ab665c. arXiv:1912.13223 [astro-ph.SR]

Jiang J, Işık E, Cameron RH et al (2010) The effect of activity-related meridional flow modulation on the strength of the solar polar magnetic field. Astrophys J 717(1):597-602. https://doi.org/10.1088/0004-637X/717/1/597. arXiv:1005.5317 [astro-ph.SR]

Jiao Q, Jiang J, Wang ZF (2021) Sunspot tilt angles revisited: dependence on the solar cycle strength. Astron Astrophys 653:A27. https://doi.org/10.1051/0004-6361/202141215. arXiv:2106.11615 [astro-ph.SR]

Jouve L, Brun AS (2009) Three-dimensional nonlinear evolution of a magnetic flux tube in a spherical shell: influence of turbulent convection and associated mean flows. Astrophys J 701(2):1300-1322. https://doi.org/10.1088/0004-637X/701/2/1300. arXiv:0907.2131 [astro-ph.SR]

Jouve L, Proctor MRE, Lesur G (2010) Buoyancy-induced time delays in Babcock-Leighton flux-transport dynamo models. Astron Astrophys 519:A68. https://doi.org/10.1051/0004-6361/201014455. arXiv:1005.2283 [astro-ph.SR]

Jouve L, Brun AS, Aulanier G (2013) Global dynamics of subsurface solar active regions. Astrophys J 762(1):4. https://doi.org/10.1088/0004-637X/762/1/4. arXiv:1211.7251 [astro-ph.SR]

Jouve L, Brun AS, Aulanier G (2018) Interactions of twisted Ω-loops in a model solar convection zone. Astrophys J 857(2):83. https://doi.org/10.3847/1538-4357/aab5b6. arXiv:1803.04709 [astro-ph.SR]

Käpylä PJ, Mantere MJ, Brandenburg A (2012) Cyclic magnetic activity due to turbulent convection in spherical wedge geometry. Astrophys J Lett 755(1):L22. https://doi.org/10.1088/2041-8205/755/1/L22. arXiv:1205.4719 [astro-ph.SR]

Käpylä PJ, Brandenburg A, Kleeorin N et al (2016) Magnetic flux concentrations from turbulent stratified convection. Astron Astrophys 588:A150. https://doi.org/10.1051/0004-6361/201527731. arXiv:1511.03718 [astro-ph.SR]

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Manek B, Brummell N (2021) On the origin of solar hemispherical helicity rules: simulations of the rise of magnetic flux concentrations in a background field. Astrophys J 909(1):72. https://doi.org/10.3847/1538-4357/abd859. arXiv:2101.03472 [astro-ph.SR]

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Parker EN (1975) The generation of magnetic fields in astrophysical bodies. X. Magnetic buoyancy and the solar dynamo. Astrophys J 198:205–209. https://doi.org/10.1086/153593
Leka KD, Barnes G, Birch AC et al (2013) Helioseismology of pre-emerging active regions. I. Overview, data, and target selection criteria. Astrophys J 762:130. https://doi.org/10.1088/0004-637X/762/2/130. arXiv:1303.1433 [astro-ph.SR]

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Linton MG, Dahlburg RB, Antiochos SK (2001) Reconnection of twisted flux tubes as a function of contact angle. Astrophys J 553(2):905–921. https://doi.org/10.1086/320974

Longcope DW, Klapper I (1997) Dynamics of a thin twisted flux tube. Astrophys J 488(1):443–453. https://doi.org/10.1086/304680

Longcope DW, Fisher GH, Pevtsov AA (1998) Flux-tube twist resulting from helical turbulence: the Σ-effect. Astrophys J 507(1):417–432. https://doi.org/10.1086/306312

López Fuentes MC, Demoulin P, Mandrini CH et al (2000) The counterkink rotation of a non-hale active region. Astrophys J 544(1):540–549. https://doi.org/10.1086/317180. arXiv:1412.1456 [astro-ph.SR]

Luo X, Gu S, Xiang Y et al (2022) Active longitudes and starspot evolution of the young rapidly rotating star USNO-B1.0 1388-0463685 discovered in the Yunnan-Hong Kong survey. Mon Not R Astron Soc 514(1):1511–1521. https://doi.org/10.1093/mnras/stac1406

Luoni ML, Démoulin P, Mandrini CH et al (2011) Twisted flux tube emergence evidenced in longitudinal magnetograms: magnetic tongues. Sol Phys 270(1):45. https://doi.org/10.1007/s11207-011-9731-8

Manek B, Brummell N (2021) On the origin of solar hemispherical helicity rules: simulations of the rise of magnetic flux concentrations in a background field. Astrophys J 909(1):72. https://doi.org/10.3847/1538-4357/abd859. arXiv:2101.03472 [astro-ph.SR]

Manek B, Brummell N, Lee D (2018) The rise of a magnetic flux tube in a background field: solar helicity selection rules. Astrophys J Lett 859(2):L27. https://doi.org/10.3847/2041-8213/aac723. arXiv:1805.08806 [astro-ph.SR]

Manek B, Pontin C, Brummell N (2022) The rise of buoyant magnetic structures through convection with a background magnetic field. Astrophys J 929(2):162. https://doi.org/10.3847/1538-4357/ac5828. arXiv:2204.13078 [astro-ph.SR]

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Matthews PC, Hughes DW, Proctor MRE (1995) Magnetic buoyancy, vorticity, and three-dimensional flux-tube formation. Astrophys J 448:938. https://doi.org/10.1086/176022

McClintock BH, Norton AA (2016) Tilt angle and footprint separation of small and large bipolar sunspot regions observed with HMI. Astrophys J 818:7. https://doi.org/10.3847/0004-637X/818/1/7

Miesch MS, Dikpati M (2014) A three-dimensional Babcock-Leighton solar dynamo model. Astrophys J Lett 785(1):L8. https://doi.org/10.1088/2041-8205/785/1/L8. arXiv:1401.6557 [astro-ph.SR]

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Moreno-Insertis F, Schüssler M, Ferriz-Mas A (1992) Storage of magnetic flux tubes in a convective overshoot region. Astron Astrophys 264(2):686–700

Moreno-Insertis F, Caligari P, Schüssler M (1994) Active region asymmetry as a result of the rise of magnetic flux tubes. Sol Phys 153(1–2):449–452. https://doi.org/10.1007/BF00712518

Nagy M, Lemerle A, Labonville F et al (2017) The effect of “rogue” active regions on the solar cycle. Sol Phys 292(11):167. https://doi.org/10.1007/s11207-017-1194-0. arXiv:1712.02185 [astro-ph.SR]

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Nelson NJ, Brown BP, Brun AS et al (2011) Buoyant magnetic loops in a global dynamo simulation of a young Sun. Astrophys J Lett 739(2):L38. https://doi.org/10.1088/2041-8205/739/2/L38. arXiv:1108.4697 [astro-ph.SR]

Nelson NJ, Brown BP, Brun AS et al (2013) Magnetic wreaths and cycles in convective dynamos. Astrophys J 762(2):73. https://doi.org/10.1088/0004-637X/762/2/73. arXiv:1211.3129 [astro-ph.SR]

Nelson NJ, Brown BP, Sacha Brun A et al (2014) Buoyant magnetic loops generated by global convective dynamo action. Sol Phys 289(2):441–458. https://doi.org/10.1007/s11207-012-0221-4. arXiv:1212.5612 [astro-ph.SR]

Parker EN (1955) The formation of sunspots from the solar toroidal field. Astrophys J 121:491. https://doi.org/10.1086/146010

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**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Authors and Affiliations

Maria A. Weber¹ · Hannah Schunker² · Laurène Jouve³ · Emre Işık⁴,⁵

M.A. Weber
mweber@deltastate.edu

E. Işık
isik@mps.mpg.de

H. Schunker
hannah.schunker@newcastle.edu.au
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Wright NJ, Drake JJ (2016) Solar-type dynamo behaviour in fully convective stars without a tachocline. Nature 535(7613):526–528. https://doi.org/10.1038/nature18638. arXiv:1607.07870 [astro-ph.SR]

Yeates AR, Muñoz-Jaramillo A (2013) Kinematic active region formation in a three-dimensional solar dynamo model. Mon Not R Astron Soc 436(4):3366–3379. https://doi.org/10.1093/mnras/stt1818. arXiv:1309.6342 [astro-ph.SR]

**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Authors and Affiliations

Maria A. Weber¹ · Hannah Schunker² · Laurène Jouve³ · Emre Işık⁴,⁵

M.A. Weber
mweber@deltastate.edu

E. Işık
isik@mps.mpg.de

H. Schunker
hannah.schunker@newcastle.edu.au
L. Jouve
ljouve@irap.omp.eu

1 Division of Mathematics and Sciences, Delta State University, 1003 W Sunflower Rd, Cleveland, 38733, MS, United States

2 School of Information and Physical Sciences, University of Newcastle, University Drive, Callaghan, 2308, NSW, Australia

3 IRAP/OMP/CNRS, Université Toulouse 3, 14 Avenue Edouard Belin, Toulouse, 31400, France

4 Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077, Göttingen, Germany

5 Department of Computer Science, Turkish-German University, Şahinkaya Cd. 94, Beykoz, 34800, Istanbul, Turkey

<figure><img src="image_7.png" /></figure>
L. Jouve
ljouve@irap.omp.eu

1 Division of Mathematics and Sciences, Delta State University, 1003 W Sunflower Rd, Cleveland, 38733, MS, United States

2 School of Information and Physical Sciences, University of Newcastle, University Drive, Callaghan, 2308, NSW, Australia

3 IRAP/OMP/CNRS, Université Toulouse 3, 14 Avenue Edouard Belin, Toulouse, 31400, France

4 Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077, Göttingen, Germany

5 Department of Computer Science, Turkish-German University, Şahinkaya Cd. 94, Beykoz, 34800, Istanbul, Turkey