Heliosphere - Lectures 5 September 27, 2005 Space Weather Course Solar Wind, Interplanetary Magnetic Field, Solar Cycle Chapter 12-Gombosi (The Solar Wind) Chapter 6 - Kallenrode (The Solar Wind) Chapter 12- Parker (The Solar Wind)

Before we start:

Overview of what we will see in Lecture Lecture 5 (Sep. 27, 2005) -Solar wind formation and acceleration (how the Sun generates it’s solar wind. Why Does the Sun has a wind?) - Interplanetary magnetic field (How the Magnetic Field from the Sun is carried into space? How does it look?)

@P.Frisch Lecture 6 (Oct. 4, 2005) -Corotating interaction regions (what are they? How do they form?) -Heliosphere during the solar cycle (the Sun changes every 11 years-so how the Heliosphere Reacts to that?) -CMEs in the interplanetary space (magnetic clouds), (How CMEs propagate in the heliosphere) -interplanetary shocks (CMEs pile up material forming shocks-how those shocks propagate in space) -shock physics (what happens at a shock?)

@P.Frisch Lecture 7 (after John Guillary) -energetic particles in the heliosphere (galactic, anomalous cosmic rays and solar energetic particles) (who are they? Where do they come from? Which ones are the most hazardous to Earth?) -Solar wind interaction with the nearby interstellar medium. (the solar system interacts with the interstellar medium-how this interacts happens? How it affects the Heliosphere, Earth and Space Weather?

The Heliosphere A global view of the Heliosphere

Magnetic Structure of the Sun Helmet Streamers Open and closed Field Lines Magnetic Structure of the Sun Streamer Belt Helmet streamer Coronal Holes Fast Wind Slow Wind

The Solar Wind At the beginning of the twentieth century, a particle of flow from the Sun Towards Earth was suggested by Birkeland (1908) to explain the Relationship between aurorae and sunspots (“The Norwegian aurora Polaris expedition : On the cause of magnetic storms and the Origin of terrestrial magnetism”) (Description is in chapter 04 Gombosi) (Also chapter 6 from Kallenrode) Chapman (1919) (“an outline of a theory of magnetic storms”) and Chapman and Ferraro (1931) (“A new theory of magnetic storms”) suggested the emission of clouds of ionized particles during flares only. Except for these plasma clouds, interplanetary space was assumed to be Empty.

Cont. of historic background Evidence to the contrary came from observations of comet tails: the tail of a comet neither follows the path of the comet nor is directed Exactly radially from the Sun; but deviates several degrees from The radial direction. Hoffmeister (1943) suggested that solar particles and the solar light pressure shape the comet tails. Characteristics of the Solar Wind: It is a continuous flow of charged particles. It is supersonic With a speed of ~ 400 km/s (x 40 the sound speed) (a parcel of plasma travels from Sun-Earth in ~ 4 days). The Solar wind carry the solar magnetic field out in the Heliosphere; the magnetic field strength amounting to ~ nanoteslas at Earth. Two distinct plasma flows are observed: Fast and Slow Wind

Solar Wind: Bi-Modal Structure Property (1 AU)Slow WindFast Wind Flow Speed400 km/s 750 km/s Density 7 cm -3 3 cm -3 Variance "large", >50%Variance "small", <50% Temperature T(proton, 1AU) ~ 200,000 K T(proton, 1 AU) ~ 50,000 K Solar Wind Bi Modal Structure

Slow Solar Wind: Speeds between km/s Average density is ~ 8 ions/cm 3 (1AU) Solar Minimum -slow wind originates from regions close to The current sheet at the heliomagnetic equator. 2% of the ions are He (highly variable) Solar Maxima - slow wind originates above the active regions in the Streamer belt and 4% of the ions are He Compared to the fast wind, the slow wind is highly variable and turbulent The proton temperature is 3x10 4 K (low!) The electron temperature is similar to fast… Fast Solar Wind: originates in coronal holes (the dark parts of the Corona dominated by open field lines) The streams are often stable over a long time period. Has flow speeds between km/s; average density is low ~ 3 ions/cm 3 (1AU) 4% of the ions are He The proton temperature is about 2x10 5 K The electron temperature is about 1x10 5 K Fast and Slow Wind

More on the slow and fast winds.. For the fast and slow winds: (to the magnetic field) Also the momentum flux on average is similar. Same is true for the total energy flux (despite the fact that Kinetic energy, potential energy, thermal energy, electron and proton heat flux, wave energy, are different. Charge states of heavy ions indicate a T ~ 10 6 K in the corona The photosphere is only 5800K - So one of the basic questions in understanding the corona and solar wind is: how can the corona be heated up to a Million Kelvin?

Origin of Solar Wind First theory of an extended corona was by Chapman (1957) Static atmosphere with energy transfer by conduction alone. The mathematical theory was put forward by Eugene Parker (Astrophysical Journal 1958) - very controversial Solar wind was first sporadically detected by Lunik 2 and 3 (soviet space probes) but the first continuous observations was made with Mariner 2 Spacecraft (Neugebauer, M. & Snyder, C.W., JGR 1966) (further reading M. Velli ApJ 1994) Mariner 2 data

The equations that describe a magnetized conducting fluid (ideal MHD) are: continuity momentum magnetic field energy Whole gas as a single conducting fluid + Maxwell equations (here dE/dt=0) (  m  0; conduction  ) MHD equations (Description is in chapter 04 Gombosi)

More on solar wind (further reading M. Velli ApJ 1994; Priest, E. chapter 12) If you neglect the effect of heat conduction and magnetic fields: If we assume stationary solar atmosphere (u=0) Chapman’s assumed isothermal corona; so p=n p kT+n e kT~

Problems with Static corona Then, we get That gives, Where the index B indicate the Base of the corona As r , p  cte For T B ~ 10 6 K p  ~ 3 x10 -4 p B >> any reasonable interstellar Pressure!!! So a Hot Static Corona cannot exist

Parker (1958) Astrophys, J 128, 664 -> Corona cannot be in static equilibrium but instead it is continuously expanding outwards (In the absence of a strong pressure at infinity (“lid”) to hold the corona-it must stream outward as the “solar wind”) Parker Solution: (neglecting electromagnetic effects) The momentum equation: Outflow plasma Pressure gradient gravity

More on parker solution Substituting we get: Where is the local sound speed. Assuming a S =cte (isothermal solar corona) and integrating in both sides: Depending on the constant C this equation have 5 different solutions: There is a critical point A where du/dr is undefined: When u=a s, so that both coefficient of du/dr and the right hand side vanish.

The solar wind solution V: it starts as a subsonic flow in the lower corona, accelerates with increasing radius. At the critical point r C it becomes supersonic. (C=-3). At large distances where v>>v c, the velocity And the density fall of as so that the pressure vanish at infinity. For T=10 6 K the predicted flow speed at 1AU is 100km/s. Classes I and II: have double valued solutions which are unphysical Class III: posseses supersonic speeds at the Sun what are not observed So we have left solutions IV and V …. A

lachzor page 239 T. Gombosi Solar Breeze (Type IV): subsonic Parker’s solution for different coronal temperatures For example, for T=10 6 K, and coronal density of 2x10 8 cm -3, r c =6R s. The solar wind accelerates to up to 40R S, and afterwards propagates to a nearly constant speed of 500km/s The speed increases only weakly with height and the critical Velocity is not acquired at the critical radius. The flow Then continues to propagate radially outward But then slows down and can be regarded as a solar breeze.

More on parker solution The parker solar wind is a simplified model because the coronal Temperature does not remain constant as it expands. Although the hydrodynamic description of the solar wind is a reasonable and valuable Approach: a fundamental problem that was neglected is the heating of the corona. Some heating mechanism is needed (especially near the critical point) Limitations and Assumptions: Isotropy: It is established that T( r) ~ r - ,, where  is the polytropic index And still allow for solar wind type solutions. (at earth the typical Plasma temperature is a factor of 10 lower). Electron and proton temperatures are not theh same as it assumed in the model (modify slightly the numbers) Consideration of only one particle species (protons). (another set of equations needs to be considered->leading to a reduction Of the flow speed) No Magnetic or Electric Field considered. In a MHD model The critical point is lowed in the corona (~ 2 Rs) but the general form Of the solution is the same.

Brief notes on Coronal Heating Heating by Waves and Turbulence: Altough non-thermal broadening Of some spectral lines indicated the existence of waves or turbulence In the lower corona, it is not completely understood which kind of Waves these are, how they propagate outward and whether the observations Are indicative of wave fields or of turbulence. March, E. (1994) Theoretical models for The solar wind, Adv. Space Phys. 14, (4) (103). Impulsive Energy Release: Even for coronal heating by MHD waves, The field is only used as carrier for the waves while its energy is neglected. The conversion of field energy into thermal energy could provide a heating mechanism. Reconnection happens when field of opposite polarity Encounter. The photosphere is in continuous motion with bubbles rising and falling And plasma flowing in and out. Thus on a small scale magnetic field configurations suitable for reconnection will form frequently, converting magnetic field into thermal energy.,

Interplanetary Magnetic Field The magnetic induction equation can be written The sun rotates with a period of 27 days. In the rotating frame a vector A: So the flow speed in the corotating system is The time derivative of B in the rotating system is: And the induction equation in the rotating frame is:

Expanding the right hand side you get The left hand side is the total time derivative of B in the system rotating with the Sun: DB/Dt So In the Steady State and There is a scalar potential :

Taking the product of With u and B This means that that in the rotating frame The magnetic field and plasma vectors are always Parallel in the rotating frame And some math…Look at page 243 of Gombosi’s book

The Geometry of the Magnetic Field First: no polar components and Since u’ and B are parallel to each other the ratio between B  and B r needs to be the same: Where we assumed that u SW is the assymptotic velocity of the solar wind and that At large distances r>>R S the plasma velocity is practically radial (in the non corotating frame) So:

From Maxwell Equations: in spherical coordinate system is And so that leads to Substi. In the expression of B we get:

At large distance from the Sun r>>R S We can see that and (fall more slowly!) As we go outward in the solar system the magnetic field becomes more and more azimuthal

Coronal Structure and Magnetic Field An assumption that we made was: corona was spherically symmetric! But close to the Sun it’s a poor approximation: regions of open and close field lines To have a realistic solar magnetic field you need to solve: And assuming that at all times the solution only depends on r and  Pneuman and Kopp (1971) solve iteratively starting with a dipole

The solution obtained: MHD model Zeus-3D (Asif ud-Duola, Stan Owcki) Initial State: solid lines-Dipole Final State: dashed lines The lines are drawn outward by the plasma And become open Coronal plasma in static equilibrium: balance between Pressure gradient and gravity Field lines from opposite polarities: Heliospheric Current Sheet

Heliospheric Current Sheet Non alignement of the magnetic axis and the rotation axis produces the ballerina skirt

Solar Cycle and the Heliosphere During solar minima: the magnetic field is approximately a dipole. The orientation of the dipole is almost aligned with the rotation axis. During declining phase of the solar activity: the solar dipole is most noticeably tilted relative to the rotation axis During solar maxima: the Sun’s magnetic field is not dipolelike.

How wide is the current sheet? 7º  B

Global View of the Magnetic Field Meridional Plane ISW Opher et al.