The Interplanetary Medium and The Solar Wind

Transcription

1 The Interplanetary Medium and The Solar Wind The eruption of a looped solar filament that is rooted in a magnetically-active region near the apparent edge, or limb, of the Sun. The image, from the TRACE spacecraft, was made in the light of the (invisible) extreme ultraviolet spectrum, emitted from regions of the solar atmosphere where temperatures exceed more than two million degrees Fahrenheit. Coronal Mass Ejections I f sunspot magnetic fields are the gunpowder, flares the muskets and prominences the horse-drawn cannons in the venerable solar armory, coronal mass ejections or CMEs which came to be recognized but thirty years ago are truly the heavy artillery. Indeed, interplanetary CMEs are the primary 64 Giuseppe Consolini! INAF-Institute for Space Astrophysics and Planetology giuseppe.consolini@iaps.inaf.it

2 Introduction and some historical hints The first indirect evidence of solar wind dates back to about a hundred years ago, when it was observed that a perturbation of the Earth s magnetic field often follows the occurrence of large solar flares. The time delay between the occurrence of a solar flare and a jiggling of the Earth s magnetic field suggested that typical Sun-Earth transit time of solar wind should be of the order of 10 3 km/s. However, we have to wait until the early 40s to see the beginning of the physics of solar wind (Gotrian, 1939; Lyot, 1939; Edlen, 1942; Chapman, 1954). One of the first evidences of solar wind, i.e. of a corpuscular outcome radially flowing away from the Sun, was provided by the studies on the comet tail shape.

3 Introduction and some historical hints The Solar Wind is a flow of a tenuous ionized solar plasma and a remnant of the solar magnetic field, pervading the interplanetary space. The origin of solar wind is due to the huge difference in gas pressure between the solar corona and interstellar space. The importance of studying solar wind stands in two major points the role that solar wind plays in the field known an solar-terrestrial relations, i.e. the impact that it has on magnetospheric environments; the basic physical processes concerning its formation, expansion and complex nature (turbulent features).

4 A survey of solar wind properties Our knowledge of the solar wind properties is based on in-situ spacecraft observations covering a wide range of distances (from 0.3 AU on) and a wide interval of heliospheric latitude range. It consists largely of protons and electrons in nearly equal numbers (approx. 95%) and quasi-thermal equilibrium (?) with a small amount (5%) of alpha particles and other heavier ions. Solar Wind features at 1AU Proton density 6.6 cm Electron density 7.1 cm He 0.25 cm Mean flow speed 450 km/s Proton kinetic temperature 1.2 x 10 Electron kinetic temperature 1.4 x 10 Magnetic field 7 x 10 Embedded in the SW plasma there is a weak magnetic field that a 1AU is oriented in a direction parallel to the ecliptic plane with a 45 angle in respect to the Sun radial direction.

5 Introduction and some historical hints In the 50s Ludwig Biermann studying the phenomenon of the anti-solar acceleration of comet tails noticed that the standard explanation for the anti-solar orientation of comet tails (based on light radiation pressure) is inadequate to explain the observed outward acceleration of small inhomogeneities in comet tails.! This provided the evidence that solar wind is made of a corpuscular radiation Type I: gases origin affected by solar wind! Type II: dust tail Comet Hale-Bopp. Credit: Dimai & Ghirardo - Col. Druscie Obs., AAC

6 A survey of solar wind properties Apart from the principal ion species, it is possible to find several other secondary elements in the SW: 3 He ++ 4 He + O 7+ O 6+ C 3+ from Bame et al., Phys. Rev. Lett., 1968

7 A survey of solar wind properties SW plasma in comparison with other typical astrophysical and laboratory plasmas from Huba., NRL Plasma Formulary, 2007

8 A survey of solar wind properties Unnormalized energy per charge spectrum P1 and P2 = proton beams 1 and 2 = alpha beams Bulk velocity >> thermal velocity (peak width) c s = p 1 2 B = (T p + T e ) m p + m e 1 2 c s 60km/s Thus, SW is a supersonic flow from Asbridge et al., Solar Phys., 1974

9 A survey of solar wind properties Another feature of SW at 1AU is the super-alfvénic nature of proton flow, c A = s B 2 4 [CGS] 1AU c A 30km/s v bulk 450km/s They moves also faster than the fast magnetosonic wave velocity c fast c s + c A Proton/ions distribution functions shows also a very complex angular velocity distribution with different shapes parallel and perpendicular to the magnetic field. This feature is known as temperature anisotropy

10 A survey of solar wind properties 2D velocity distribution by Helios spacecraft IMF from Marsch et al., J. Geophys. Res., 1982 Temperature anisotropy can take both situations T >T T >T from Helios observations

11 A survey of solar wind properties Assuming that solar wind ions expands as an adiabatic gas, then we expect that pressure and density are related by a polytropic law,! p = n B T p = const n (1 ) T = const where γ > 1. Consequently, T and n behaves in the same way, i.e. are decreasing function with the distance. n R 2 T R 4/3 from Belcher et al., 1993

12 A survey of solar wind properties However, radial profile of solar wind temperature does not evolve adiabatically. A large discrepancy is observed. T R 1/2 The observed discrepancy suggests that to some extent a certain amount of heating occurs during the solar wind radial evolution. A plausible candidate for this heating process is the turbulence cascade mechanism (see e.g. Marino et al., ApJ, 2008) from Richardson et al., GRL, 1995

13 A survey of solar wind properties The other main constituent of solar wind are the electrons. Differently from ions, a treatment of solar wind electrons as a single fluid is not possible. Indeed, electron distributions show two different main components: a core, associated with a cold and dense population a halo, representing a hot and sparse population Both the two populations show a thermal velocity higher than bulk speed. from Feldman et al., J. Geophys. Res., 1975

14 A survey of solar wind properties 2D velocity electron distribution from Pilipp et al., J. Geophys. Res., 1987

15 A survey of solar wind properties Apart from the core and halo populations, sometime a third component is present: a narrow field-aligned high energy beam, called strahl. High energy strahls can propagate very far in the eliosphere without scattering, providing information on the deepest part of solar corona. The farthest propagation of strahl can be understood in terms of a very low collision frequency. ei =8 e 4 2 p 2m e Zne T 3/2 e ln T 3/2 e = D b o

16 A survey of solar wind properties One of the general features of both proton and electron distribution functions is its non-maxwellian character. This point suggests that many features of the SW have to be discussed assuming it to be a nonthermal plasma, i.e. in a nonequilibrium state. In 1992 A. Scudder suggested that a better distribution function for solar wind kinetic model is a truncated Lorentzian (Kappa) distribution f = 3/2 n 3/2 v 3 th ( + 1) ( 1/2) apple1+ v2 v 2 th + v 2 th = 2 3 BT m

17 A survey of solar wind properties Solar wind and interplanetary medium is permeated by magnetic field which can lead to hydromagnetic effects. Given a magnetic field this can exert a pressure! p mag = B2 4 that has to be compared with the gas (kinetic) pressure! p gas = n B (T p + T e ) At 1 AU we get p mag = 19 pp a p gas = 30 pp a

18 A survey of solar wind properties In spite of the average features described, the solar wind shows a very high variability in its features both in time and in space.

19 A survey of solar wind properties In spite of the average features described, the solar wind shows a very high variability in its features both in time and in space.

20 A survey of solar wind properties Between the various features of this high variability it is important to stress that one of the main properties of the solar wind is the presence of two different types of SW characterized by different speeds and physical properties. from Bruno and Carbone, 2005 Fast solar wind Slow solar wind

21 A survey of solar wind properties Fast and slow solar wind are characterized by very different physical properties of the constituting plasmas Fast wind: less dense and hotter 2.0x10 5 T [K] Slow wind: more dense and colder 0.5 Period # 1 Period # u [km/s] x Period #1 Period #2 T [K] n [cm -3 ] from Consolini, 2012 to be submitted from Bruno and Carbone, 2005

22 A survey of solar wind properties from Bruno and Carbone, 2005

23 A survey of solar wind properties This very high variability is due to the inherent magnetic field dynamics and structures. Furthermore the origin of fast and slow solar wind streams have to be connected with the different magnetic structures at the sun (open and closed field lines), as well as with the latitudinal magnetic field structure from McComas et al., 2003 Polar solar wind --> Fast Equatorial solar wind --> Slow

24 The interplanetary magnetic field The classic description of the interplanetary magnetic field in the outwardly moving solar wind is based on the concept of a frozen-on magnetic field. B(r) =B 0 B r 2 This simple concept however have to be combined with the solar rotation, which implies that the structure of the interplanetary magnetic field (IMF) is more complex than that of purely radial magnetic field. from Hundhausen, 1995

25 The interplanetary magnetic field The IMF structure is then that of a Archimedean spiral. B r (r) =B 0 B r 2 B ' (r) = B 0 R u R r At 1 AU we have r 400km/s u SW 400km/s ' 1AU 45 adapted from Pizzo, 1985

26 The interplanetary magnetic field The interaction between the solar magnetic field and the solar wind is described by the magnetic force j x B. u u = p + j B + F g Thus a more realistic model of the IMF and solar wind structure will require the finding of a magnetohydrodynamic system of equations. from Pneumann and Kopp, 1971 The presence of the magnetic field, indeed, affects the spherical symmetry of the solar wind expansion. The solution in the case of a isothermal corona in the case of a pure dipolar filed shows the formation of a current sheet and closed field lines overlying the dipole equator (Pneumann and Kopp, 1971).

27 The interplanetary magnetic field In contrast with its simplicity, the Pneumann and Kopp solution shows many characteristic ingredients of the real coronal magnetic field, which has clearly a more complex structure. Indeed a realistic description of the coronal magnetic field will require to include the complex magnetic structures emerging from the sun, so that a simple dipole model is only a very crude approximation. from Hundhausen, 1995

28 The interplanetary magnetic field Because the magnetic pattern is neither symmetric about the rotational axis, nor purely dipolar, the extension of this magnetic structure to the interplanetary medium produces a very complex structure of the IMF The rotation of the Sun implies that the magnetic pattern sweeps over the Earth, appearing in the so-called magnetic sectors, observed in the interplanetary space from Hundausen, 1977 Furthermore, there is a nonzero angle between the Earth s orbit and the rotational equator of the Sun, so that the Earth experiences a predominantly outward/ inward magnetic field every 6 months

29 The interplanetary magnetic field The presence of fast and slow solar wind streams, as well as of very fast solar ejecta (as CME) modify the pattern of the IMF generating regions of compression/rarefaction. adapted from Pizzo, 1985

30 Solar Wind Interaction with Planetary Magnetospheres Solar wind flowing into the heliosphere interacts with the planetary magnetic fields, which behaves as obstacles to the plasma flows, generating the planetary magnetospheres. from World Wide Web Site

31 Solar Wind Interaction with Planetary Magnetospheres The Earth s Ring Current adapted from De Michelis et al., 1999

32 f.it/cvs/tempeste.html Solar Wind Interaction with Planetary Magnetospheres The ground-based effects of the solar wind-magnetosphere interaction are the geomagnetic storms and substorms 15.5 x LOV (Lat: ; Long: ) x10 3 x10 4 X [nt] x10 4 x BFE (Lat: ; Long: ) NGK (Lat: ; Long: ) FUR (Lat: ; Long: ) BNG (Lat: 4.43 ; Long: ) 0: :00 0: :00 0: from Time [UT]

33 Solar Wind Interaction with Planetary Magnetospheres Geomagnetic storms and substorms are the consequences of the solar wind plasma entry into the magnetosphere region, which activates a complex system of ionospheric currents B [nt] Bz [nt] Bx [nt] By [nt] : : : : Dst [nt] v[km/s] N[cm -3 ] : : : : Time [UT] Time [UT] 0: : : : Time [UT] AE(t) t [day]

34 Solar Wind Interaction with Planetary Magnetospheres The main physical mechanism responsible for the energy, momentum and mass transfer from solar wind to magnetosphere is the magnetic reconnection Diffusion Region 2L 2l from INGV ~ B = r (~u ~ B)+ r 2 ~ B In the Sweet-Parker model the reconnection rate (i.e. the velocity of magnetic field energy conversion) is M i = 1 p Rmi R mi = Lc A adapted from MMS-SMART Web site

35 Solar Energetic Particles (SEP) The solar plasma eruptions (flares) can accelerate plasma to very high speed generating the solar cosmic rays, named SEP. Average Proton Flux [#/cm 2 s sr MeV] Global Fit Energy E [MeV] adapted from Laurenza et al., 2013

36 Solar Wind Turbulence: Introduction As already said in the previous Lecture, one of the most peculiar features of the solar wind magnetic field and plasma parameters is its very high temporal and spatial variability. This variability manifests in fluctuations whose order of magnitude is the same of the average quantities.! x x This notable fact suggests that a relevant information about the solar wind physics is contained in the fluctuating field. Since the early observations of Mariner 2 (Coleman, 1968) it was noted that turbulence might plays a fundamental role in the generation of the observed fluctuation field

37 Solar Wind Turbulence: Introduction The first evidence of turbulence in the solar wind was provided by Coleman (1968), which analyzing the spectral densities of solar wind related quantities evidenced how the energy is distributed over an extremely wide range of frequencies PSD P(f) f Range I : Range II : Range III : 1 $ f<10 4 Hz 3 2 < < 5 3, 10 4 apple f apple 10 1 Hz 2, f>10 1 Hz up to 1Hz from Russell, 1972

38 Solar Wind Turbulence: Introduction The intermediate range of scales whose typical scaling index is about 1.6 (Bavassano et al., 1982; Tu and Marsch, 1995) is very well in agreement with the typical spectral index predicted by Kolmogorov K41 theory of turbulence and/or by Kraichnan theory of Alfvénic MHD-turbulence. Another relevant feature of such a scaleinvariant PSD stands in its evolution with the radial distance (Bavassano et al., 1982; Denskat and Neubauer, 1983). PSD break moves to lower frequencies as the solar wind expands. This behavior provides the evidence for the presence of nonlinear interaction mechanisms from Bruno and Carbone, 2005

39 Solar Wind Turbulence: Introduction Another relevant property of the solar wind magnetic and plasma parameter fluctuations is the Alfvénic character of uncompressive fluctuations. v ± B 4 from Bavassano et al., 2000

40 Solar Wind Turbulence: Introduction Normalized cross-helicity v b c = v 2 + b 2 Normalized residual-energy R = hvi2 hbi 2 hvi 2 + hbi 2 from Bavassano et al., 1998 Anyway the solar wind fluctuation field is more complex, showing not only Alfvénic fluctuation but also magnetic structures and compressive fluctuations

41 Solar Wind Turbulence: Introduction from Bruno and Carbone, 2005 Another characteristic of the solar wind turbulent fluctuations is the occurrence of intermittency.

42 Solar Wind Turbulence: Introduction Intermittency manifest in several different quantities: anomalous scaling of structure functions (departure from self-similarity), non-gaussian and scaledependent probability distribution functions of observable increments. S q ( x) =h(y (x + x) Y (x)) q i x (q) S q ( x) ' S p ( x) p q Anomalous scaling of structure functions S q ( x) S p ( x) p q x µ(q,p) from Bruno and Carbone, 2005

43 Turbulence: general concepts The word turbulence derives from Latin word turba, initially used as a synonymous of disordered movements. In XX century, the notion was generalized to embrace far-from-equilibrium states in fluids and plasmas. Turbulence defines a state of a physical system with many interacting degree of freedom deviated far-from-equilibrium, showing spatial and temporal irregular features and accompained by dissipation (adapted from Falkovich, 2008) Study by Leonardo da Vinci ( ) related to the problem of reducing the rapids in the river Arno in Florence Turbulence still remains the last major unsolved problem in classical physics Feynman et al. (1977)

44 Turbulence: general concepts The key element of fluid turbulence is the idea of the Richardson cascade (inertial cascade), according which a perturbation at large scale propagates down to smaller scales via a cascading mechanism in which the energy, injected by the large scale perturbation, is distributed homogeneously to the smaller scale, where viscosity dissipates it (microscopic scales). Turbulence (fully developed turbulence) is observed when a large scale separation between injection scale and dissipation scales. This separation of scales is quantified by the well-known Reynolds number Re = ul 1

45 Turbulence: general concepts It is possible to grasp the main features of a turbulent flow by analyzing the Navier-Stokes equation (Landau & Lifshitz, 1959). u t +(u )u = 1 p + 2 u nonlinear term: coupling of scales viscosity term: dissipation (u )u u 2 L Re = nonlinear term viscosity term = u2 /L u/l = ul r 2 u u L 2 Re 1 laminar flow Re 1 turbulent flow

46 Turbulence: general concepts When R >> 1 we assist to a separation of scales, i.e. injection scale L >> dissipation scale λ (below this scale R < 1). This intermediated range of scales is named inertial range and is the range of scale in which the cascade works. The first quantitative description of the energy cascade is due to Kolmogorov (1941) via dimensional analysis. Let us assume stationarity, homogeneity, isotropy and the conservation of the energy flow in the inertial range along the spectrum, l ' u2 l l = l ' l u l l ' u3 l l ' u l ' 1/3 l 1/3

47 Turbulence: general concepts Let us now consider the spectral density at k 1/l! E(k)dk 1 2 u2 l from here assuming dk k 1/l, we get for the spectral density,! E(k) 2/3 l 5/3 / k 5/3 That is the very well-known 5/3 Kolmogorov spectrum (K41 theory). Along with the previous results, there exists an exact relationship directly derivable from the Navier-Stokes equation for the 3rd order-parallel structure function valid in the inertial range for fully developed turbulence: the Yaglom law h v (r + l) v (r) 3 i = 4 5 l

48 Turbulence: general concepts Let us now move to the case of turbulence in a magnetized plasma, which present some differences in respect to the fluid case (see Zimbardo, 2001). In this case the starting equations are the momentum equation and the induction +(u r)u = 1 r + B (B r)b + r2 r = r (u B)+c2 4 r2 B where ν is the viscosity and η is the plasma resistivity, moreover! r B =0 r u =0 The two equation display many similarities: are nonlinear, contain a dissipation term acting at smallest spatial scales

49 Turbulence: general concepts These similarities can be better appreciated by introducing the Elsasser variables, B z = u + p, = ±1! 4 By means of such a variables the previous equations can be written in a +(z r)z = 1 rp + + µ r 2 z + + µ r 2 z 2 2!! r z =0 µ = c2 4 In the following for brevity we will assume µ =

50 Turbulence: general concepts The symmetric form of MHD equations written using the Elsasser variables shows the equal importance of the velocity and magnetic fields in describing the evolution of the magnetofluid. In this framework the energy per unit mass is,! E = u2 2 + B2 8 = z+2 + z 2 4 Let us now compare the nonlinear term and the dissipative term! (z r)z z 2 L + µ 2 r 2 z µz L 2!! R m = r 4 BL c 2 In space plasmas (collisionless and not resistive) R m 1 so that nonlinear term is very important allowing a very extensive range for turbulence

51 Turbulence: general concepts To close consider the effects of nonlinear terms, let us assume a statistically homogeneous system and write:! B = hbi + b u = v where hui =0. Then! hz i = hbi p 4 = V A z = v + b p 4 Substituting and neglecting dissipative term (R, V A r z +( z r) z = 1 rp r z =0

52 Turbulence: general concepts Moving to the Fourier space (dropping the δ), equation reduces k V A z (k,t)+ X X [z (q,t) ip] z (p,t) k,p+q = P (k,t) p q Let us now move to evaluate the spectrum using the same heuristic approach of the fluid case. We start by evaluating the energy flow per mass unit, assuming only local interactions in the Fourier space! Thus,! k p q k ' E (k) T k where Tk σ is the energy effective transfer time (analogous to the eddy turnover time in fluid turbulence).

53 Turbulence: general concepts In contrast to fluid turbulence the nonlinear term represents the interaction among counter-propagating modes, so that this interaction is expected to last a finite time! A k 1 kv A The mode amplitude change for a single interaction is,! dz (k) kz (k)z (k) k A after N interactions z (k) p Ndz (k) Requiring a significant transfer of energy, i.e. z (k) z (k), we obtain for N N kz (k) A k 2 T A k = N A k V A k[z (k)] 2 k k[z (k)]2 [z (k)] 2 V A

54 Turbulence: general concepts When the flux is constant, we get a stationary state in which! z (k) z (k) z(k) Thus, from the previous equation we obtain! z ± (k) (V A ) 1/4 k 1/4 From this result we cal evaluate the spectral energy density obtaining, E(k)dk [z± (k)] 2 2 (V A ) 1/2 k 1/2! E(k) / k 3/2 Kraichnan spectrum

55 Turbulence: general concepts Evolution of Elsasser variable spectra with radial distance from Goldstein et al., 1995

56 References A.J. Hundhausen, The solar wind, in Introduction to the Space Physics, Kivelson M. G. and Russell C.T. eds., Cambridge University Press E.N. Parker, Solar wind, in Handbook of the Solar-Terrestrial Environment, Kamide Y. and Chian A. Editors, Springer R. Bruno & V. Carbone, The Solar Wind as a Turbulence Laboratory, Living Rev. Solar Phys., 2, 2005 G. Zimbardo, Solar wind magnetohydrodynamic turbulence, in Sun-Earth connections and Space Weather, M. Candidi et al. eds., SIF Conf. Proc. 75, 2001 V. Carbone & A. Poquet, An introduction to fluid and MHD turbulence for astrophysical flows: theory, observational and numerical data, and modeling, Lect. Notes Phys., 778, 71, 2009 C.T. Russell, Solar wind and interplanetary magnetic field: a tutorial, in Space Weather, Geophys. Monogr. Ser., vol. 125, edited by P. Song, H. J. Singer, and G. L. Siscoe, pp , AGU, Washington, D. C.,