Skip to main content
SpringerLink
Log in
Book cover

Formation, Evolution, and Dynamics of Young Solar Systems pp 63–90Cite as

Wind-Driven Global Evolution of Protoplanetary Disks

  • Chapter
  • First Online:

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 445))

Abstract

It has been realized in the recent years that magnetized disk winds likely play a decisive role in the global evolution of protoplanetary disks (PPDs). Motivated by recent local simulations , we first describe a global magnetized disk wind model, from which wind-driven accretion rate and wind mass loss rate can be reliably estimated. Both rates are shown to strongly depend on the amount of magnetic flux threading the disk. Wind kinematics is also affected by thermodynamics in the wind zone (particularly far UV heating/ionization), and the mass loss process can be better termed as “magneto-photoevaporation.” We then construct a framework of PPD global evolution that incorporates wind-driven and viscously driven accretion as well as wind mass loss. For typical PPD accretion rates, the required field strength would lead to wind mass loss rate at least comparable to disk accretion rate, and mass loss is most significant in the outer disk (beyond ∼ 10 AU). Finally, we discuss the transport of magnetic flux in PPDs, which largely governs the long-term evolution of PPDs.

This is a preview of subscription content, log in via an institution.

Notes

  1. 1.

    While the FUV luminosity from young stars is only a very small fraction ( ∼ 10−3) of the stellar luminosity, it is primarily absorbed in the disk surface and the energy deposited plays a dominant role in heating and ionizing the surface layer (e.g., Bergin et al. 2007).

  2. 2.

    In reality, X-rays may be able to heat deeper layers. The situation is discussed in Bai (2016) and it was concluded that this effect does not strongly affect our model results.

  3. 3.

    The value quoted from Perez-Becker and Chiang (2011) corresponds to a vertical column, whereas in our calculation it corresponds to the radial column towards the star. The two numbers differ by a factor of a few ( ∼ 3) depending on the level of disk flaring, though here we have ignored the difference.

References

  • Alexander, R., Pascucci, I., Andrews, S., Armitage, P., Cieza, L.: The dispersal of protoplanetary disks. Protostars and Planets VI, pp. 475–496. University of Arizona Press, Tucson (2014), 1311.1819

    Google Scholar 

  • Andrews, S.M., Wilner, D.J., Hughes, A.M., Qi, C., Dullemond, C.P.: Protoplanetary disk structures in Ophiuchus. Astrophys. J. 700, 502–1523 (2009), 0906.0730

    Google Scholar 

  • Andrews, S.M., Wilner, D.J., Hughes, A.M., Qi, C., Dullemond, C.P.: Protoplanetary disk structures in Ophiuchus. II. Extension to fainter sources. Astrophys. J. 723, 1241–1254 (2010), 1007.5070

    Google Scholar 

  • Ansdell, M., Williams, J.P., van der Marel, N., Carpenter, J.M., Guidi, G., Hogerheijde, M., Mathews, G.S., Manara, C.F., Miotello, A., Natta, A., Oliveira, I., Tazzari, M., Testi, L., van Dishoeck, E.F., van Terwisga, S.E.: ALMA survey of Lupus protoplanetary disks I: dust and gas masses (2016) ArXiv e-prints 1604.05719

    Google Scholar 

  • Armitage, P.J.: Dynamics of protoplanetary disks. Annu. Rev. Astron. Astrophys. 49, 195–236 (2011), 1011.1496

    Google Scholar 

  • Armitage, P.J., Simon, J.B., Martin, R.G.: Two timescale dispersal of magnetized protoplanetary disks. Astrophys. J. Lett. 778, L14 (2013), 1310.6745

    Google Scholar 

  • Bai, X.N.: Wind-driven accretion in protoplanetary disks. II. Radial dependence and global picture. Astrophys. J. 772, 96 (2013), 1305.7232

    Google Scholar 

  • Bai, X.N.: Hall-effect-controlled gas dynamics in protoplanetary disks. I. Wind solutions at the inner disk. Astrophys. J. 791, 137 (2014), 1402.7102

    Google Scholar 

  • Bai, X.N.: Hall effect controlled gas dynamics in protoplanetary disks. II. Full 3D simulations toward the outer disk. Astrophys. J. 798, 84 (2015), 1409.2511

    Google Scholar 

  • Bai, X.N.: Towards a global evolutionary model of protoplanetary disks. Astrophys. J. 821, 80 (2016), 1603.00484

    Google Scholar 

  • Bai, X.N., Stone, J.M.: The effect of the radial pressure gradient in protoplanetary disks on planetesimal formation. Astrophys. J. Lett. 722, L220–L223 (2010), 1005.4981

    Google Scholar 

  • Bai, X.N., Stone, J.M.: Local study of accretion disks with a strong vertical magnetic field: magnetorotational instability and disk outflow. Astrophys. J. 767, 30 (2013a), 1210.6661

    Google Scholar 

  • Bai, X.N., Stone, J.M.: Wind-driven accretion in protoplanetary disks. I. Suppression of the magnetorotational instability and launching of the magnetocentrifugal wind. Astrophys. J. 769, 76 (2013b), 1301.0318

    Google Scholar 

  • Bai, X.N., Stone, J.M.: Hall effect-mediated magnetic flux transport in protoplanetary disks. Astrophys. J. 836, 46 (2017). doi:10.3847/1538-4357/836/1/46, 1612.03912

    Google Scholar 

  • Bai, X.N., Ye, J., Goodman, J., Yuan, F.: Magneto-thermal disk wind from protoplanetary disks. Astrophys. J. 818, 152 (2016), 1511.06769

    Google Scholar 

  • Balbus, S.A., Hawley, J.F.: A powerful local shear instability in weakly magnetized disks. I - linear analysis. II - nonlinear evolution. Astrophys. J. 376, 214–233 (1991)

    Google Scholar 

  • Baruteau, C., Crida, A., Paardekooper, S.J., Masset, F., Guilet, J., Bitsch, B., Nelson, R., Kley, W., Papaloizou, J.: Planet-disk interactions and early evolution of planetary systems. Protostars and Planets VI, pp. 667–689. University of Arizona Press, Tucson (2014), 1312.4293

    Google Scholar 

  • Bergin, E.A., Aikawa, Y., Blake, G.A., van Dishoeck, E.F.: The chemical evolution of protoplanetary disks. Protostars and Planets V, pp. 751–766.University of Arizona Press, Tucson (2007) astro-ph/0603358

    Google Scholar 

  • Blandford, R.D., Payne, D.G.: Hydromagnetic flows from accretion discs and the production of radio jets. Mon. Not. R. Astron. Soc. 199, 883–903 (1982)

    Article  ADS  MATH  Google Scholar 

  • Carrera, D., Johansen, A., Davies, M.B.: How to form planetesimals from mm-sized chondrules and chondrule aggregates. Astron. Astrophys. 579, A43 (2015), 1501.05314

    Google Scholar 

  • Casse, F., Ferreira, J.: Magnetized accretion-ejection structures. V. Effects of entropy generation inside the disc. Astron. Astrophys. 361, 1178–1190 (2000), astro-ph/0008244

    Google Scholar 

  • Casse, F., Keppens, R.: Magnetized accretion-ejection structures: 2.5-dimensional magnetohydrodynamic simulations of continuous ideal jet launching from resistive accretion disks. Astrophys. J. 581, 988–1001 (2002), arXiv:astro-ph/0208459

    Google Scholar 

  • Chiang, E.I., Goldreich, P.: Spectral energy distributions of T Tauri stars with passive circumstellar disks. Astrophys. J. 490, 368–376 (1997), arXiv:astro-ph/9706042

    Google Scholar 

  • Desch, S.J., Turner, N.J.: High-temperature Ionization in protoplanetary disks. Astrophys. J. 811, 156 (2015), 1508.07878

    Google Scholar 

  • Fedele, D., van den Ancker, M.E., Henning, T., Jayawardhana, R., Oliveira, J.M.: Timescale of mass accretion in pre-main-sequence stars. Astron. Astrophys. 510, A72 (2010), 0911.3320

    Google Scholar 

  • Ferreira, J., Pelletier, G.: Magnetized accretion-ejection structures. III. Stellar and extragalactic jets as weakly dissipative disk outflows. Astron. Astrophys. 295, 807 (1995)

    Google Scholar 

  • Fromang, S., Latter, H., Lesur, G., Ogilvie, G.I.: Local outflows from turbulent accretion disks. Astron. Astrophys. 552, A71 (2013), 1210.6664

    Google Scholar 

  • Gorti, U., Hollenbach, D., Dullemond, C.P.: The impact of dust evolution and photoevaporation on disk dispersal. Astrophys. J. 804, 29 (2015), 1502.07369

    Google Scholar 

  • Gressel, O., Turner, N.J., Nelson, R.P., McNally, C.P.: Global Simulations of protoplanetary disks with Ohmic resistivity and ambipolar diffusion. Astrophys. J. 801, 84 (2015), 1501.05431

    Google Scholar 

  • Guilet, J., Ogilvie, G.I.: Transport of magnetic flux and the vertical structure of accretion discs - I. Uniform diffusion coefficients. Mon. Not. R. Astron. Soc. 424, 2097–2117 (2012), 1205.6468

    Google Scholar 

  • Guilet, J., Ogilvie, G.I.: Global evolution of the magnetic field in a thin disc and its consequences for protoplanetary systems. Mon. Not. R. Astron. Soc. 441, 852–868 (2014), 1403.3732

    Google Scholar 

  • Haisch, K.E. Jr., Lada, E.A., Lada, C.J.: Disk frequencies and lifetimes in Young clusters. Astrophys. J. Lett. 553, L153–L156 (2001), astro-ph/0104347

    Google Scholar 

  • Hartigan, P., Edwards, S., Ghandour, L.: Disk accretion and mass loss from Young stars. Astrophys. J. 452, 736 (1995)

    Article  ADS  Google Scholar 

  • Hawley, J.F., Gammie, C.F., Balbus, S.A.: Local three-dimensional magnetohydrodynamic simulations of accretion disks. Astrophys. J. 440, 742–763 (1995)

    Article  ADS  Google Scholar 

  • Hayashi, C.: Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Prog. Theor. Phys. Suppl. 70, 35–53 (1981)

    Article  ADS  Google Scholar 

  • Henning, T., Semenov, D.: Chemistry in protoplanetary disks. Chem. Rev. 113, 9016–9042 (2013), 1310.3151

    Google Scholar 

  • Johansen, A., Youdin, A., Mac Low, M.: Particle clumping and planetesimal formation depend strongly on metallicity. Astrophys. J. Lett. 704, L75–L79 (2009), 0909.0259

    Google Scholar 

  • Kato, S.X., Kudoh, T., Shibata, K.: 2.5-Dimensional nonsteady magnetohydrodynamic simulations of magnetically driven jets from geometrically thin disks. Astrophys. J. 565, 1035–1049 (2002)

    Google Scholar 

  • Kenyon, S.J., Hartmann, L.: Spectral energy distributions of T Tauri stars - disk flaring and limits on accretion. Astrophys. J. 323, 714–733 (1987)

    Article  ADS  Google Scholar 

  • Klahr, H., Hubbard, A.: Convective Overstability in radially stratified accretion disks under thermal relaxation. Astrophys. J. 788, 21 (2014), 1403.6721

    Google Scholar 

  • Konigl, A.: Self-similar models of magnetized accretion disks. Astrophys. J. 342, 208–223 (1989)

    Article  ADS  Google Scholar 

  • Krasnopolsky, R., Li, Z.Y., Blandford, R.: Magnetocentrifugal launching of jets from accretion disks. I. Cold axisymmetric flows. Astrophys. J. 526, 631–642 (1999), arXiv:astro-ph/9902200

    Google Scholar 

  • Kunz, M.W.: On the linear stability of weakly ionized, magnetized planar shear flows. Mon. Not. R. Astron. Soc. 385, 1494–1510 (2008), 0801.0974

    Google Scholar 

  • Lesur, G., Kunz, M.W., Fromang, S.: Thanatology in protoplanetary discs. The combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones. Astron. Astrophys. 566, A56 (2014), 1402.4133

    Google Scholar 

  • Li, Z.Y.: Magnetohydrodynamic disk-wind connection: self-similar solutions. Astrophys. J. 444, 848–860 (1995)

    Article  ADS  Google Scholar 

  • Lovelace, R.V.E., Berk, H.L., Contopoulos, J.: Magnetically driven jets and winds. Astrophys. J. 379, 696–705 (1991)

    Article  ADS  Google Scholar 

  • Lubow, S.H., Papaloizou, J.C.B., Pringle, J.E.: Magnetic field dragging in accretion discs. Mon. Not. R. Astron. Soc. 267, 235–240 (1994)

    Article  ADS  Google Scholar 

  • Lynden-Bell, D.: On why discs generate magnetic towers and collimate jets. Mon. Not. R. Astron. Soc. 341, 1360–1372 (2003), astro-ph/0208388

    Google Scholar 

  • Lyra, W.: Convective overstability in accretion disks: three-dimensional linear analysis and nonlinear saturation. Astrophys. J. 789, 77 (2014), 1405.3437

    Google Scholar 

  • Marcus, P.S., Pei, S., Jiang, C.-H., Barranco, J.A., Hassanzadeh, P., Lecoanet, D.: Zombie vortex instability. I. A purely hydrodynamic instability to resurrect the dead zones of protoplanetary disks. Astrophys. J. 808(1), 16, A87 (2015). http://adsabs.harvard.edu/abs/2015ApJ...808...87M

  • Natta, A., Testi, L., Alcalá, J.M., Rigliaco, E., Covino, E., Stelzer, B., D’Elia, V.: X-shooter spectroscopy of young stellar objects. V. Slow winds in T Tauri stars. Astron. Astrophys. 569, A5 (2014), 1406.5630

    Google Scholar 

  • Nelson, R.P., Gressel, O., Umurhan, O.M.: Linear and non-linear evolution of the vertical shear instability in accretion discs. Mon. Not. R. Astron. Soc. 435, 2610–2632 (2013), 1209.2753

    Google Scholar 

  • Okuzumi, S., Hirose, S.: Modeling magnetorotational turbulence in protoplanetary disks with dead zones. Astrophys. J. 742, 65 (2011), 1108.4892

    Google Scholar 

  • Okuzumi, S., Takeuchi, T., Muto, T.: Radial transport of large-scale magnetic fields in accretion disks. I. Steady solutions and an upper limit on the vertical field strength. Astrophys. J. 785, 127 (2014), 1310.7446

    Google Scholar 

  • Ostriker, E.C.: Self-similar Magnetocentrifugal disk winds with cylindrical asymptotics. Astrophys. J. 486, 291–306 (1997), astro-ph/9705226

    Google Scholar 

  • Ouyed, R., Pudritz, R.E., Stone, J.M.: Episodic jets from black holes and protostars. Nature 385, 409–414 (1997)

    Article  ADS  Google Scholar 

  • Panoglou, D., Cabrit, S., Pineau Des Forêts, G., Garcia, P.J.V., Ferreira, J., Casse, F.: Molecule survival in magnetized protostellar disk winds. I. Chemical model and first results. Astron. Astrophys. 538, A2 (2012), 1112.3248

    Google Scholar 

  • Pascucci, I., Sterzik, M.: Evidence for disk photoevaporation driven by the central star. Astrophys. J. 702, 724–732 (2009), 0908.2367

    Google Scholar 

  • Pelletier, G., Pudritz, R.E.: Hydromagnetic disk winds in young stellar objects and active galactic nuclei. Astrophys. J. 394, 117–138 (1992)

    Article  ADS  Google Scholar 

  • Perez-Becker, D., Chiang, E.: Surface layer accretion in conventional and transitional disks driven by far-ultraviolet ionization. Astrophys. J. 735, 8 (2011), 1104.2320

    Google Scholar 

  • Porth, O., Fendt, C.: Acceleration and collimation of relativistic magnetohydrodynamic disk winds. Astrophys. J. 709, 1100–1118 (2010), 0911.3001

    Google Scholar 

  • Pudritz, R.E., Norman, C.A.: Centrifugally driven winds from contracting molecular disks. Astrophys. J. 274, 677–697 (1983)

    Article  ADS  Google Scholar 

  • Pudritz, R.E., Rogers, C.S., Ouyed, R.: Controlling the collimation and rotation of hydromagnetic disc winds. Mon. Not. R. Astron. Soc. 365, 1131–1148 (2006), astro-ph/0508295

    Google Scholar 

  • Raettig, N., Lyra, W., Klahr, H.: A parameter study for baroclinic vortex amplification. Astrophys. J. 765, 115 (2013), 1212.4464

    Google Scholar 

  • Ramsey, J.P., Clarke, D.A.: Simulating protostellar jets simultaneously at launching and observational scales. Astrophys. J. Lett. 728, L11 (2011), 1012.3723

    Google Scholar 

  • Rosenfeld, K.A., Andrews, S.M., Hughes, A.M., Wilner, D.J., Qi, C.: A spatially resolved vertical temperature gradient in the HD 163296 disk. Astrophys. J. 774, 16 (2013), 1306.6475

    Google Scholar 

  • Shakura, N.I., Sunyaev, R.A.: Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973)

    ADS  Google Scholar 

  • Simon, J.B., Bai, X.N., Armitage, P.J., Stone, J.M., Beckwith, K.: Turbulence in the outer regions of protoplanetary disks. II. Strong accretion driven by a vertical magnetic field. Astrophys. J. 775, 73 (2013a), 1306.3222

    Google Scholar 

  • Simon, J.B., Bai, X.N., Stone, J.M., Armitage, P.J., Beckwith, K.: Turbulence in the outer regions of protoplanetary disks. I. Weak accretion with no vertical magnetic flux. Astrophys. J. 764, 66 (2013b), 1210.4164

    Google Scholar 

  • Simon, J.B., Lesur, G., Kunz, M.W., Armitage, P.J.: Magnetically driven accretion in protoplanetary discs. Mon. Not. R. Astron. Soc. 454, 1117–1131 (2015), 1508.00904

    Google Scholar 

  • Spruit, H.C.: Magnetohydrodynamic jets and winds from accretion disks. In: Wijers, R.A.M.J., Davies, M.B., Tout, C.A. (eds.) NATO ASIC Proceedings 477: Evolutionary Processes in Binary Stars, pp. 249–286 (1996)

    Google Scholar 

  • Stoll, M.H.R., Kley, W.: Vertical shear instability in accretion disc models with radiation transport. Astron. Astrophys. 572, A77 (2014), 1409.8429

    Google Scholar 

  • Suzuki, T.K., Inutsuka, S.i.: Disk winds driven by magnetorotational instability and dispersal of protoplanetary disks. Astrophys. J. Lett. 691, L49–L54 (2009)

    Google Scholar 

  • Suzuki, T.K., Inutsuka, S.i.: Magnetohydrodynamic simulations of global accretion disks with vertical magnetic fields. Astrophys. J. 784, 121 (2014), 1309.6916

    Google Scholar 

  • Takeuchi, T., Okuzumi, S.: Radial transport of large-scale magnetic fields in accretion disks. II. Relaxation to steady states. Astrophys. J. 797, 132 (2014), 1310.7380

    Google Scholar 

  • Testi, L., Birnstiel, T., Ricci, L., Andrews, S., Blum, J., Carpenter, J., Dominik, C., Isella, A., Natta, A., Williams, J.P., Wilner, D.J.: Dust evolution in protoplanetary disks. Protostars and Planets VI, pp. 339–361.University of Arizona Press, Tucson (2014), 1402.1354

    Google Scholar 

  • Tsukamoto, Y., Iwasaki, K., Okuzumi, S., Machida, M.N., Inutsuka, S.: Bimodality of circumstellar disk evolution induced by the hall current. Astrophys. J. Lett. 810, L26 (2015), 1506.07242

    Google Scholar 

  • Turner, N.J., Fromang, S., Gammie, C., Klahr, H., Lesur, G., Wardle, M., Bai, X.N.: Transport and accretion in planet-forming disks. Protostars and Planets VI, pp. 411–432. University of Arizona Press, Tucson (2014) 1401.7306

    Google Scholar 

  • Tzeferacos, P., Ferrari, A., Mignone, A., Zanni, C., Bodo, G., Massaglia, S.: On the magnetization of jet-launching discs. Mon. Not. R. Astron. Soc. 400, 820–834 (2009)

    Article  ADS  Google Scholar 

  • Tzeferacos, P., Ferrari, A., Mignone, A., Zanni, C., Bodo, G., Massaglia, S.: Effects of entropy generation in jet-launching discs. Mon. Not. R. Astron. Soc. 428, 3151–3163 (2013)

    Article  ADS  Google Scholar 

  • Vlahakis, N., Tsinganos, K., Sauty, C., Trussoni, E.: A disc-wind model with correct crossing of all magnetohydrodynamic critical surfaces. Mon. Not. R. Astron. Soc. 318, 417–428 (2000), astro-ph/0005582

    Google Scholar 

  • Walsh, C., Millar, T.J., Nomura, H.: Chemical processes in protoplanetary disks. Astrophys. J. 722, 1607–1623 (2010), 1008.4305

    Google Scholar 

  • Walsh, C., Nomura, H., Millar, T.J., Aikawa, Y.: Chemical processes in protoplanetary disks. II. On the importance of photochemistry and X-ray ionization. Astrophys. J. 747, 114 (2012), 1201.2613

    Google Scholar 

  • Wardle, M., Koenigl, A.: The structure of protostellar accretion disks and the origin of bipolar flows. Astrophys. J. 410, 218–238 (1993)

    Article  ADS  Google Scholar 

  • Weidenschilling, S.J.: The distribution of mass in the planetary system and solar nebula. Astrophys. Space Sci. 51, 153–158 (1977)

    Article  ADS  Google Scholar 

  • Williams, J.P., Best, W.M.J.: A parametric modeling approach to measuring the gas masses of circumstellar disks. Astrophys. J. 788, 59 (2014), 1312.0151

    Google Scholar 

  • Wurster, J., Price, D.J., Bate, M.R.: Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe? Mon. Not. R. Astron. Soc. 457, 1037–1061 (2016), 1512.01597

    Google Scholar 

  • Xu, R., Bai, X.N., Oberg, K.: Runaway freeze-out of volatiles in weakly turbulent protoplanetary disks (2016). ArXiv:160900796 1609.00796

    Google Scholar 

  • Youdin, A.N., Shu, F.H.: Planetesimal formation by gravitational instability. Astrophys. J. 580, 494–505 (2002), arXiv:astro-ph/0207536

    Google Scholar 

  • Yu, M., Willacy, K., Dodson-Robinson, S.E., Turner, N.J., Evans II, N.J.: Probing planet forming zones with rare CO isotopologues. Astrophys. J. 822, 53 (2016), 1603.08930

    Google Scholar 

  • Zanni, C., Ferrari, A., Rosner, R., Bodo, G., Massaglia, S.: MHD simulations of jet acceleration from Keplerian accretion disks. The effects of disk resistivity. Astron. Astrophys. 469, 811–828 (2007), arXiv:astro-ph/0703064

    Google Scholar 

Download references

Acknowledgements

I thank my collaborators, Jiani Ye, Jeremy Goodman, Feng Yuan, and Jim Stone for their contribution to part of the works presented here, and an anonymous referee for helpful comments. Finally, I acknowledge support from Institute for Theory and Computation at Harvard-Smithsonian Center for Astrophysics.

Author information

Authors and Affiliations

  1. Institute for Advanced Study, Tsinghua University, Beijing, 100084, China

    Xue-Ning Bai

  2. Tsinghua Center for Astrophysics, Tsinghua University, Beijing, 100084, China

    Xue-Ning Bai

  3. Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA, 02138, USA

    Xue-Ning Bai

Authors
  1. Xue-Ning Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xue-Ning Bai .

Editor information

Editors and Affiliations

  1. The Niels Bohr Institute, Niels Bohr International Academy, Copenhagen, Denmark

    Martin Pessah

  2. The Niels Bohr Institute, Niels Bohr International Academy, Copenhagen, Denmark

    Oliver Gressel

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Bai, XN. (2017). Wind-Driven Global Evolution of Protoplanetary Disks. In: Pessah, M., Gressel, O. (eds) Formation, Evolution, and Dynamics of Young Solar Systems. Astrophysics and Space Science Library, vol 445. Springer, Cham. https://doi.org/10.1007/978-3-319-60609-5_3

Download citation

Publish with us

Policies and ethics

Search

Navigation