Solar cycle. Auringonpilkkusykli Heinrich Schwabe: 11 year solar cycle. ~11 years

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1 Sun

2 Solar cycle Auringonpilkkusykli 1844 Heinrich Schwabe: 11 year solar cycle ~11 years

3 Auringonpilkkusykli Solar cycle Butterfly diagram: Edward Maunder 1904 New cycle Spots appear at mid-latitudes Migration towards the equator

4 Solar cycle and Earth 1852 Edward Sabine: clear connection between the sunspot number and geomagnetic activity at Earth 80 Sunspot number AA indeksi

5 Where we are: 09/2014

6 Solar wind 6

7 Why solar wind? There must be a mechanism to transfer solar activity to the Earth: Lindeman 1919: Quasi-neutral gas emissions from the Sun Chapman 1929: Solar flares emit plasma clouds Chapman and Ferraro 1931: Sun emits particle bursts which cause magnetic storms Ludwig Biermann 1951: Cometary tails require a fast corpuscular flow in addition to radiation pressure Solar wind-induced tail (ions) continuous solar wind Hale-Bopp Radiation pressure tail (neutral/dust)

8 Theory of solar wind formation Let s first investigate coronal plasma in the gravitational field of the Sun Tool: MHD Continuity equation and equation of momentum: r +Ñ rv = 0 t v r + rv Ñ v =-Ñ p + J B + rg t Assume steady plasma flow and spherical symmetry (physical properties functions of r only), neglect magnetic forces Þ 1 d 2 rvr = 0 2 r dr dv dp GM rv =- -r dr dr r 2 S

9 Chapman s attempt to solution (1957) Chapmann assumed that the corona is in equilibrium dp GM Þ - - r = dr r e 0 2 Pressure balance between pressure gradient and gravitation in a static atmosphere p p= 2nkT Þ r = m 2 kt ìgmemæ1 1 öü Solution for pressure: p( r) = p0 exp í ç - ý î 2kT èr Røþ Where: p( Re) = p0 at the base of corona r R p p 0 > < e

10 Assume heat outflow through a sphere (radius r) const. where the heat conduction coefficient is With the boundary conditions: T = T 0, when r = R 8, and T 0 when r Letting T 0 = 10 6 K, the temperature at 1 AU is 10 5 K, which is quite OK. the pressure becomes which at r approaches to a constant that is many orders of magnitudes higher than the pressure thought to exist in the interstellar medium

11 Parker s solution (1958): Isothermally expanding solar wind Apparently Chapman s static solution cannot represent an equilibrium state between corona and the interstellar space. (however, it correctly suggested that interplanetary space is filled with solar plasma) Parker reconsidered the problem with non-zero flow speed 1 d 2 rvr = 0 2 r dr dv dp GM rv =- -r dr dr r e 2 2 r vr = const. 2 Þ 4p r nv = const. i.e. mass flow through a sphere with surface area 4pr 2 Although the solar wind certainly cools when expanding, assume that the expansion is isothermal (T = const.)

12 Þ where is the isothermal sound speed (g = 1) this equation has a critical point: with critical radius: r c = GM 2v e 2 c v= v c v < v c : subsonic solar wind v > v c : supersonic solar wind Integration gives a family of curves:

13 Five regimes of solutions not consistent with observations unphysical unphysical stellar breeze (subsonic: v < v c ) Solution IV through the critical point ( C = 3) is the solar wind: subsonic near the Sun supersonic beyond the critical point Parker predicted the existence of a continuous supersonic expansion of corona

14 The wind velocity of an isothermal Parker wind, for different values of the temperature T0.

15 Observations of solar wind first observations: Soviet Lunik-2 and Lunik-3 probes in 1960 Mariner 2 while flying towards Venus confirmed the continuous solar wind and observed in it fast and slow streams repeating at 27-day interval Skylab : coronal holes sources of fast solar wind streams Ulysses: latitudinal variations of the solar wind (October 1990s ->) - perihelion 1.3 AU - aphelion 5.3 AU Helios 1 & 2: - Launched: Helios 1 December 1974 Helios 2 January perihelion within the orbit of Mercury, 0.3 AU

16 currently monitoring the upstream solar wind: SOHO, Wind, ACE, SDO, Stereo Satellites at L1 monitoring the solar wind: - Wind (launched Nov 1994) - ACE (launched Aug 1997) - SOHO (launched Dec 1995) Lagrangian points: five positions where the gravitational pull of the two large masses precisely cancels the centripetal acceleration required to rotate with them

17 Energy considerations Is there enough free energy in the coronal base for accelerating the solar wind? assume: e, p +, let n = n(r), T = T(r), n e» n p» n thermal energy of the gas in volume V The free energy is the enthalpy: should be enough to win gravitational potential energy density Assuming T = K E» 0.5 F Not enough for expansion! There must be (a) mechanism(s) to pump extra energy (Q) to the gas Observations: E + Q» F Magnetic field neglected in above treatment

18 Toward more realistic models Unrealistic assumptions of the Parker model include: - constant temperature - predicts that the solar wind speed grows to infinity Energy equation: Takes into account cooling of the expanding Sun k = k 0 T 5/2 ; k 0» Wm 1 K 1 ; T is given in Kelvin F is the observed energy flux far from the Sun Combination of Parker s expanding wind and Chapman s heat transfer

19 Solar wind properties consists primarily of protons and electrons, 5% of alpha particles + several types of heavier ions At 1 AU: Average is a quite meaningless concept here!

20 1. Fast wind in high speed streams High speed kms -1 Low density 3 cm -3 Low particle flux 2 x 10 8 cm -2 s -1 Helium content 3.6%, stationary Source Signatures The two basic types of solar wind coronal holes stationary for long times, all streams are alike, Alfvénic fluctuations 2. Low speed wind of "interstream" type Low speed kms -1 High density 10 cm -3 High particle flux 3.7 x 10 8 cm -2 s -1 Helium content below 2%, highly variable Source Signatures helmet streamers near current sheet, generally very variable, sector boundaries imbedded,

21 Interplanetary magnetic field (IMF) solar wind carries the Sun s magnetic field throughout the solar system magnetic field is frozen into the solar wind recall: magnetic Reynolds number in the near Earth solar wind average magnitude at 1 AU: ~ 6 nt

22 solar wind blows out radially field frozen- into the solar wind sources of the IMF attached to the rotating Sun

23 The interplanetary magnetic field (IMF) Let s derive the form of the spiral close to the Sun: radial flow, B is nearly radial assume, that flow remains radial B is frozen-in to the rotating surface and to the outflowing plasma Flow speed perp.to B : V = V sin Y For large r : Archimedes spiral known in this context as the Parker spiral V sin Y = W( r - R 8 )cos Y Þ tan Y = W( r - R V 8 )

24 Calculation of B: Assume that B is radial and constant on the surface. 1. Radial component on the equatorial plane Write B and V in spherical coordinates (r,q,f): Now Þ B µ r - r 2 2. Azimuthal component in the equatorial plane Induction equation: Ñ ( V B) = 0 Þ Thus at large distances B µ r - and B 1 f B f spiral field

25 3. Off-equatorial (q p /2) B is more complicated i.e., the winding opens up toward high latitudes B Thus, far from the Sun: B The spiral angle is» 44º at Earth (1 AU)» 57º at Mars (1.5 AU)» 88º at Neptune (30 AU) f f r r -1-2 in the ecliptic (tight spiral) in the polar directions

26 Above analysis assumes that the IMF is too weak to affect the coronal outflow i.e. magnetic energy density 2 B 2m is much less than the kinetic energy density 0 ru 2 2 Þ v> V A (Alfven speed) where A At 1 AU: v ~10 V A Close to the base of corona: u << V A The distance where solar wind becomes super-alfvenic (magnetic equals kinetic energy density) is denoted by Alfven radius r A

27 Angular momentum loss solar magnetic field plays an important role in the angular momentum loss magnetic field enforces co-rotation with the Sun out to the Alfvén radius Write the force balance as Use Ampère s law and multiply by r 3 to get The mass flux r 2 r m V r and the magnetic flux r 2 B r are constants and integration gives where the constant of integration L contains the mechanical angular momentum and angular momentum carried with the magnetic field

28 use Br Vr = B V -rw f f to replace B f : Þ where is the the radial Alfvén Mach number

29 When r=r A, V r = V A and M A =1 Observations: r A» 12 R 8 r=r A Co-rotating Thus the angular momentum of the Sun decreases due to the solar wind: Magnetic braking Angular momentum transferred form the Sun by the magnetic field to the charged particles

30 Sources of the solar wind: Coronal holes plasma escapes on open flux tubes Corona seen during solar eclipses helmet streamer plasma confined by magnetic field near solar minimum - clear polar holes near solar maximum - holes all over the Sun

31 solar minimum: large polar coronal hole

32 Coronal holes may remain stable over many solar rotations

33 How does the real solar wind look like? Formation of the heliospheric current sheet (Pneuman and Knopp)

34 The real current sheet is curved Ballerina skirt (Alfvén) The Earth can be toward sector or in away sector

35 OMNI data, May 2007 red: towards sector green: away sector

36 The ballerina dancing through the solar cycle Maximum The magnetic topology of the large-scale heliosphere Minimum Hoeksema, 1995 Minimum

37 Coordinate Systems X Geocentric Solar Ecliptic (GSE) X = Earth-Sun Line Z = Ecliptic North Pole Y Geocentric Solar Magnetic (GSM) W E X = Earth-Sun Line Z = Projection of dipole axis on GSE YZ plane Radial Tangential Normal (RTN) R R = Sun to Spacecraft unit vector T = (Wx R) / (W x R) where Omega is Sun's spin axis N completes the right-handed triad T (spacecraft centred coordinate system) W E

38 Magnetic field magnitude (nt) Temperature (K) Density (cm -3 ) Speed (km/s)

39 Transient solar wind component coronal mass ejections B mag T Np Vp Gosling et al., 1987

40 Disturbed solar wind

41

42 Ulysses observations

43

44 Minimum and maximum epochs are very different!

45 The heliosphere

46 The heliosphere Estimate of the heliospheric boundary in the upstream interstellar wind Pressure balance: In solar wind (S) dynamic pressure dominates everywhere V constant up to termination shock The interstellar side (G) less well-known pressure 0.1 ppa or less Heliopause Termination shock at» 140 AU at about 2/3 of the distance to heliopause

47 Bastille Day: Interplanetary observations Magnetic field magnitude (nt) ~60 nt North-south component (nt) Intense southward IMF for several hours! Speed (km/s) Speed > 1000 km/s Dynamic pressure (npa) shock 28 hours travel time Magnetic cloud 47

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