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Partially Ionized Plasmas in Astrophysics

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Partially Ionized Plasmas in Astrophysics Space Sci Rev (2018) 214:58 https://doi.org/10.1007/s11214-018-0485-6 Partially Ionized Plasmas in Astrophysics José Luis Ballester1 · Igor Alexeev2 · Manuel Collados3 · Turlough Downes4 · Robert F. Pfaff5 · Holly Gilbert6 · Maxim Khodachenko7 · Elena Khomenko3 · Ildar F. Shaikhislamov8 · Roberto Soler1 · Enrique Vázquez-Semadeni9 · Teimuraz Zaqarashvili7,10 Received: 29 June 2017 / Accepted: 2 February 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract Partially ionized plasmas are found across the Universe in many different as- trophysical environments. They constitute an essential ingredient of the solar atmosphere, molecular clouds, planetary ionospheres and protoplanetary disks, among other environ- ments, and display a richness of physical effects which are not present in fully ionized plasmas. This review provides an overview of the physics of partially ionized plasmas, in- cluding recent advances in different astrophysical areas in which partial ionization plays a B J.L. Ballester [email protected] I. Alexeev [email protected] M. Collados [email protected] T. Downes [email protected] R.F. Pfaff [email protected] H. Gilbert [email protected] M. Khodachenko [email protected] E. Khomenko [email protected] I.F. Shaikhislamov [email protected] R. Soler [email protected] E. Vázquez-Semadeni [email protected] T. Zaqarashvili [email protected] 58 Page 2 of 149 J.L. Ballester et al. fundamental role. We outline outstanding observational and theoretical questions and dis- cuss possible directions for future progress. Keywords Plasmas · Magnetohydrodynamics · Sun · Molecular clouds · Ionospheres · Exoplanets 1 Introduction Plasma pervades the Universe at all scales, and the term plasma universe was coined by Hannes Alfvén to point out the important role played by plasmas across the universe (Alfven 1986). In general, the study of plasmas beyond Earth’s atmosphere is called Plasma Astro- physics, and includes many different astrophysical environments such as the Sun, the he- liosphere, magnetospheres of the Earth and the planets, the interstellar medium, molecular clouds, accretion disks, exoplanet atmospheres, stars and astrospheres, cometary tails, ex- oplanetary ionospheres, etc. In these environments, the ionization level varies from almost no ionization in cold regions to fully ionized in hot regions which, consequently, leads to a wide range of parameters being relevant to astrophysical plasmas. Furthermore, in some cases the plasma is influenced by, or coupled to, embedded dust, giving rise to dusty plas- mas. While the use of non-ideal Magnetohydrodynamics (MHD for short) is relatively in- frequent in solar physics, in recent years the study of partially ionized plasmas has become a hot topic because solar structures such as spicules, prominences, as well as layers of the solar atmosphere (photosphere and chromosphere), are made of partially ionized plasmas (PIP for short). On the other hand, considerable developments have taken place in the study of partially ionized plasmas applied to the physics of the interstellar medium, molecular clouds, the formation of protostellar discs, planetary magnetospheres/ionospheres, exoplan- ets atmospheres, etc. For instance, molecular clouds are mainly made up of neutral material which does not interact with magnetic fields. However, neutrals are not the only constituent of molecular clouds since there are also several types of charged species which do inter- act with magnetic fields. Furthermore, the charged fraction also interacts with the neutral material through collisions. These multiple interactions produce many different physical 1 Departament de Física & Institut d’Aplicacions Computacionals de Codi Comunitari (IAC3), Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain 2 Skobeltsyn Institute of Nuclear Physics (MSU SINP), Lomonosov Moscow State University, Leninskie Gory, 119992, Moscow, Russia 3 Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, 38205 Tenerife, Spain 4 Centre for Astrophysics & Relativity, School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland 5 NASA/Goddard Space Flight Center, Mail Code 674.0, Greenbelt, MD 20771, USA 6 Solar Physics Laboratory, Heliophysics Science Division, Goddard Space Flight Center, Mail Code 671, Greenbelt, MD 20771, USA 7 Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria 8 Institute of Laser Physics SB RAS, Novosibirsk, Russia 9 Instituto de Radioastronomia y Astrofísica (IRyA), UNAM, Campus Morelia, Apdp Postal 3-72 (Xangari), Morelia, Michoacán 58089, México 10 Abastumani Astrophysical Observatory, Ilia State University, Tbilisi, Georgia Partially Ionized Plasmas in Astrophysics Page 3 of 149 58 effects which may have a strong influence on star formation and molecular cloud turbu- lence. A further example can be found in the formation of dense cores in molecular clouds induced by MHD waves. Because of the low ionization fraction, neutrals and charged par- ticles are weakly coupled and ambipolar diffusion plays an important role in the formation process. Even in the primeval universe, during the recombination era, when the plasma, from which all the matter of the universe was formed, evolved from fully ionized to neutral, it went through a phase of partial ionization. Partially ionized plasmas introduce physical effects which are not considered in fully ionized plasmas, for instance, Cowling’s resistivity, isotropic thermal conduction by neutrals, heating due to ion/neutral friction, heat transfer due to collisions, charge exchange, ionization energy, etc., which are crucial to fully under- stand the behaviour of astrophysical plasmas in different environments. Therefore, in this comprehensive review we focus on the description of PIP in different astrophysical areas in which this type of plasmas play a key role. The scheme of the review is as follows: In the second, third and fourth sections, general equations for a multifluid magnetized plasma are introduced as well as MHD waves and numerical techniques suitable for numerical simula- tions including PIP; next, the remaining sections are devoted to describe the physics of PIP in astrophysical environments such as the solar atmosphere, planetary ionospheres, molecu- lar clouds and exoplanets atmospheres and magnetospheres. 2 Formulation of the Multifluid Plasma Description 2.1 Conservation Equations for Individual Micro-States It is assumed that a PIP is composed of multiple kind of particles such as electrons, ions that can have different ionization states I ≥ 1 and excited to states E ≥ 0, neutral particles with I = 0andE ≥ 0, as well as dust grains, positively or negatively charged with E = 0. The con- cept of a fluid can be applied separately to each of these components in all the environments of interest. Therefore the behavior of such a plasma can be described by a set of equations of mass, momentum and energy conservation for each of the components. Separate sets of equations can be written for particles in a given micro-state {aIE} corresponding to a given chemical element or dust grain a. Electrons can be treated as a separate fluid, in which case the notation of a micro-state {aIE} reduces to just e. The conservation equations are derived as usual from the moments of Boltzmann equation and have the following form: ∂ρ aIE + ∇(ρ u ) = S (1) ∂t aIE aIE aIE ∂(ρ u ) aIE aIE + ∇(ρ u ⊗ u + pˆ ) = ρ r (E + u × B) + ρ g + R (2) ∂t aIE aIE aIE aIE aIE aI aIE aIE aIE ∂ 1 1 e + ρ u2 + ∇ u e + ρ u2 + pˆ u + q ∂t aIE 2 aIE aIE aIE aIE 2 aIE aIE aIE aIE aIE U = + aIE + + MaIE SaIE ρaIEuaIEg ρaIEraIuaIEE (3) ma In these equations, the term SaIE includes mass variation due to ionization/recombination and excitation/de-excitation processes; RaIE in the momentum equation includes varia- tion of momentum due to elastic collisions, inelastic collisions (ionization/recombination, excitation/de-excitation and momentum transfer); and MaIE provides collisional energy 58 Page 4 of 149 J.L. Ballester et al. gains/losses due again to elastic collisions, ionization/recombination, excitation/de-excita- tion and thermal exchange. Their properties are discussed later in this section. The pressure ˆ = ˜ ⊗ ˜ ˜ tensor, paIE ρaIE caIE caIE , is defined through random velocities, caIE, taken with respect ˜ = − to the mean velocity of each individual component, caIE v uaIE (note that this makes the system of reference for velocities different for all components). The heat flow vector is given = 1 ˜2 ˜ by qaIE 2 ρaIE caIEcaIE .ThevariableeaIE is the internal energy that makes up of thermal energy by random motion and potential energy of ionization/excitation states 1 3 e = ρ c˜2 + n U = p + n U , (4) aIE 2 aIE aIE aIE aIE 2 aIE aIE aIE = 1 2 where pαIE is the scalar pressure, pαIE 3 ραIE cαIE ,and = raI qaI/maI (5) is charge over mass ratio. The rest of the notation is standard. The above equations are written in conservation form. The momentum conservation equation can be also rewritten as Du ρ aIE = ρ r (E + u × B) + ρ g − ∇pˆ + R − u S , (6) aIE Dt aIE aI aIE aIE aIE aIE aIE aIE − leading to appearance of the uaIESaIE term on the right hand side. Similarly, the energy conservation equation can be written for the internal energy alone leading to ∂e aIE + ∇(u e + q ) + pˆ ∇u = Q , (7) ∂t aIE aIE aIE aIE aIE aIE where the collisional internal energy gain/loss term is explained below. Generally speaking, conservation equations as above can be written as well for photons as another type of fluid particles. However, since photons move at the speed of light and are mass-less, the conser- vation equations for them acquire the particular form of the radiative transfer equations (see, e.g., Mihalas 1986). The source terms on the right-hand side of these equations result from collisions of par- ticles in micro-state {aIE} with particles in other micro-states (generally including photons, or the radiation field), and are the mass collision term, SaIE, the momentum collision term, RaIE, and the internal energy collision term, QaIE.
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