La Heliosfera y el entorno espacial...

La Heliosfera y el entorno espacial terrestre

Sergio Dasso1,2 1 Instituto de Astronomía y Física del Espacio (IAFE), CONICET-UBA, Argentina

2 Departamento de Física, Facultad de Ciencias Exactas y Naturales, UBA, Argentina

Departamento de Física Juan José Giambiagi

Astropartículas y Física Solar – LAGO. Univ. San Francisco de Quito, 20-24 enero, 2014

Clase 1: •El Sol

•El ciclo solar •Radiación solar

•Marco teórico gral para Física Espacial •MHD

•Ondas de choque en el espacio •Reconección de líneas magnéticas


Interior del Sol

Zona Convectiva

Zona radiativa

Núcleo

1.5x106 K

ZONA RADIATIVA: Se extiende hasta 0.86R0 . La energía se transporta por radiación. Un fotón generado en el interior está sometido a constantes interacciones con el medio (tarda 107 años en llegar a la superficie).

NÚCLEO: Se extiende hasta 0.25R0 . La energía se produce por fusión de H que se transforma en He. Las reacciones nucleares transforman 7.1011 kg de H por segundo

ZONA CONVECTIVA: la materia realiza movimientos convectivos (como la ebullición). Se extiende hasta 1R0 y la energía se

transporta por convección


Atmósfera solar

Fotosfera: emisión térmica, 6000 K Cromosfera: dominado por líneas de emisión Corona: estructuras magnéticas


Ciclo de manchas solares • 1609: Galileo observa las manchas solares.

• Schwabe (1843) descubre el ciclo de 11 años.

• Mínimos de actividad (Maunder, 1645-1715)

• Hoy sabemos que las manchas trazan regiones de intensos campos magnéticos.

•El campo solar es bastante mas complicado que un dipolo, pero tambien es producido por corrientes eléctricas.


Gran variabilidad de radiación solar en EUV, X, radio

Variabilidad de la radiación electromagnética solar


Gran variabilidad de radiación solar en EUV, X, radio

Variabilidad de la radiación electromagnética solar

(pero mayor energía en visible e IR, poca variabilidad con actibidad solar)

Dynamics of charged particles in space The fundamental problem

Too many particles to follow detailed trajectory in the phase space !

Statistic (how many in the vicinity of a state): Kinetic Theory

[ ]))(())(()(

11 ttet

iiciimidtd

iidtd

irBvrEv

vr×+=

=

q

t

t

cc

πρ

π

40

4

=•∇=•∇

×∇−=

−×∇=

∂∂

∂∂

EB

EBJBE

))(()(),(

))((),(

1

1

ttet

tet

iiN

i i

iN

i iq

rrvrJ

rrr

−=

−=

∑∑

=

=

δ

δρ

More complex than gravity: One source of fields is not conserved, and it evolves self-consistently with the fields!


Typical plasma distribution function of H+ in the interplanetary space

Adapted, from

McComas et al., 2007, Rev of Geophys.


Full Kinetic Theory (KT): Evolution of f(v)

(weak or strong coupling)


Bulk (large and slow) scales can be modeled using MHD

(moments of f(v) and truncate KT) But in some point, the truncation needs

to be ‘repaired’ (a patch) [e.g., Book ‘Plasma Astrophysics’ by Somov, 2006]

Simplified KT +

to know the bulk behavior (scenario)

Conservación de la masa

Conservación de la cantidad de movimiento

0)( =•∇+∂∂ Uρρt

0)( =−γρpdtd

UgBBU 2)(41

∇++××∇+−∇= ρνρπ

ρ pdtd

Mass conservation

Linear momentum conservation

= 2

8BnkTπβ

MagnetoHydrodynamics (the groundwork) - From merging fluids and electromagnetism

- In general, valid for slow motions and smooth and large spatial scales

Energy (simplified): ideal gas, thermodynamics → polytropic (γ=Cp/Cv for adiabatic, γ=1 for isothermic)


Magnetic induction equation (from simplified Ohm´s law and Faraday) πσ

ηη4

...,)(2

2 ct

=+∇+××∇=∂∂ BBUB

0)( =•∇+∂∂ Uρρt

0)( =−γρpdtd

UgBBU 2)(41

∇++××∇+−∇= ρνρπ

ρ pdtd

Mass conservation



= 2

8BnkTπβ




Magnetic induction equation (from simplified Ohm´s law and Faraday) πσ

ηη4

...,)(2

2 ct

=+∇+××∇=∂∂ BBUB

BJ ×∇=π4c Ampere: J is decoupled, can be computed a posteriori, from B

0=•∇ B No magnetic monopoles

0)( =•∇+∂∂ Uρρt

0)( =−γρpdtd

UgBBU 2)(41

∇++××∇+−∇= ρνρπ

ρ pdtd

Mass conservation


= 2

8BnkTπβ



?

And electric field ‘hided’, can be computed from the Ohm law

More general cases can be used in MHD


Magnetic forces: Pressure and tension

)]2/()[(41)(

41 2B∇−∇•=××∇ BBBB

ππ

cRBB

dsdB

dsdB nss

ˆˆ)2/()ˆ( 22 +=

Magnetic pressure

Magnetic tension (restitutive force)

Cancellation of pressure force along B (thus, 2 forces are perpendicular to B)


Modos normales en MHD linealizada

Ondas de Alfvén

xrU

yrB

ˆ]/exp[)0,(

ˆ)0,(

220

0

DyUt

Bt

−=>

==

Frozen-in condition when η=0: B is transported by the fluid

Exercise: We ‘switch on’ the following (given) velocity profile (i.e., a kinematic problem) on an initial magnetic field (vertical and uniform) in an ideal medium. To find the evolution for the magnetic field B.

Hint: to solve the ideal induction equation.

x

y

t=0 t>0

B

0,0),( =∂=∂∂=∂ ztytyxyxt BBBuB

0,],exp[2),( 02

2

200 ==−−= zyx BBB

Dy

DtyUBtyB

B0


MagnetoHydrostatic (MHD equilibria) Hierachy (‘complexities’) for B configuration

Compl exness

•Current free (J=0) or Potential field (∇xB=0)

•Linear force free field, J=(αc/4π)B: ∇xB=αB (curvature force balanced by magnetic pressure)

•General fff, J//±B: ∇xB=α(r)B

•Equilibrium with one ignored coordinate (z): Grad-Shafranov formalism

•General equilibrium: BB ××∇+−∇= )(

410π

p

dAdB

dAdpA z

22

412 −−=∇ π

Elliptical equation: it requires information on A(x,y) for the ‘closed’ boundary of the domain to be properly solved

1<<β


MHD supports shock waves

In MHD, as in classical fluids, when an object travels faster than the velocity of the waves in the medium, it will drive a shock wave

•A substantial jump in |B|, |U|, and n occurs at a shock wave •Quantitative relationships can be derived for the jumps of

MHD quantities at the shock wave, e.g., the most simple {Bn}=0 •In the shock wave, due to that small scales are activated, dissipation will be efficient, even for very small values of η


MHD supports magnetic reconnection Changes in the magnetic topology of magnetic configuration of field lines


Opening ICMEs by Interchange Reconnection

• At CME liftoff – a. Partial disconnection (closed-closed) creates flux

rope coil – b. Interchange reconnection

(closed-open) opens coil • As ICME moves out into

heliosphere – Interchange reconnection at Sun

may continue to open field lines

Gosling, Birn, and Hesse [1995]

Crooker, Gosling, and Kahler [2002]

Main ideal MHD Invariants

∫∫ •=ΦS

dsB

gV

gBUdVE φρφπ

ρ −∇=

++= ∫ g,

8

22

21

( ) ||,,221 ωUω =×∇=+−= ∫ ωρνωσV

JdVdtdE

∫ •−=Φl

dcdtd lJ

σ

Main mechanisms for energy transference:

•Eu→EB (dynamo)

•EB→EU+diss(reconnection)

•spatial scales (turbulence)

moving slice of a magnetic flux tube

∫∫∫ •=V

c dVH BU

∫∫∫∫∫∫ •+− →∂∂+−= =•∇VV

jiji

c

dVUBdVdt

dH ωJU )()( 0for ρνηρνη


Main ideal MHD Invariants

∫∫ •=ΦS

dsB

gV

gBUdVE φρφπ

ρ −∇=

++= ∫ g,

8

22

21

( ) ||,,221 ωUω =×∇=+−= ∫ ωρνωσV

JdVdtdE

Main mechanisms for energy transference:

•Eu→EB (dynamo)

•EB→EU+diss(reconnection)

•spatial scales (turbulence)

moving slice of a magnetic flux tube

∫∫∫ •=V

c dVH BU

∫∫∫∫∫∫ •+− →∂∂+−= =•∇VV

jiji

c

dVUBdVdt

dH ωJU )()( 0for ρνηρνη

But turbulent dissipation

∫ •−=Φl

dcdtd lJ

σ

But turbulent dissipation


Fin clase 1

La Heliosfera y el entorno espacial...

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