The Solar Corona

B. C. LowHigh Altitude Observatory

National Center for Atmospheric Research

The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Researchunder sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

The White-Light Corona

Mark IV CoronameterMauna Loa Solar Observatory

The Magnetic Sun

The Magnetic Corona

Activity Maximum 1980

Activity Minimum 1994

A CME out to 32 R_Sun

A Shower of MeV Protons

The 2-3 Million-Degree Corona

Solar EUV Output

Orbit Height of the SMM Satellite

Coronal Drivers of Space Weather

• Variable heating of the Earth’s Upper Atmosphere

• Episodes of CME-Magnetospheric Interaction

• High-energy particles• Evolution of the corona-heliosphere

over the 11-year solar cycle

The Solar Corona as a Hydromagnetic Atmosphere

• Maintained at million-degree temperatures – cooling time ~ 1 day – dissipative heating• A nearly perfect conductor of heat: – solar-wind expansion• A nearly perfect conductor of electricity: – low-beta plasma atmosphere dominated by a ~10G global magnetic field reversing in cycles of 11 years

2/5T ~

2/3T ~

Time-Dependent Ideal MHD

..... 0)(pρdt

d

..... )Bv(t

B

0)v(ρt

ρ

..... r̂r

GMρpB)B(

4π

1

dt

vdρ

γ

2Sun

Magnetic Helicity

• The magnetic vector potential:

• Magnetic helicity:

• Helicity transport:

0

V

dV A.BA.B H ; h

B A. vv. . hht

;AB

Magnetic Helicity & Linkage Numbers

N H

The Hydromagnetic Induction Equation

“The magnetic field is frozen into the embedding plasma with perfect electrical conductivity. The perfect conductor is a singular limit of the weakly resistive conductor; being nearly perfect is not the same as just being perfect. ”

BBvB 2

t

1Lv

4

R 002M

c

The Surprisingly Dissipative Corona

• Quiescent heating & flares – heating by a turbulent dissipation of spontaneous current sheets (Parker 1994)

1Lv

R 00M

Petschek Reconnection

A Good Question

• If magnetic reconnection under conditions of high electrical conductivity makes a plasma readily dissipative, what are we to say about its canonical properties of being an excellent electrical conductor? Can magnetic reconnection short away all the electric currents in a magnetized plasma under conditions of ?

1Lv

R 00M

Limits on Magnetic Reconnection under

• Longevity of astronomical-scale magnetic flux, e.g., potential fields as minimum-energy ground states: “very hard to get rid of magnetic flux”.

• Conservation of (relative) magnetic helicity within “sufficiently large” magnetic structures (Taylor 1974, Berger 1984): “very hard to get rid of magnetic twist”.

1Lv

R 00M

Petschek Reconnection

Coalescence of Two Ropes of Twisted Fields

N H

The Ideal and Dissipative Nature of High-Temperature Plasmas

• Magnetic reconnection under does not destroy but transfer magnetic flux and helicity among subsystems of flux.

• Despite its dissipative nature, there is a limit to how much magnetic energy magnetic reconnection can liberate. The approximate conservation of magnetic helicity stores magnetic energy against flaring – origin of long-lived coronal structures.

1Lv

R 00M

Emergence of a Twisted Magnetic Field(The Magnetic End-Product of a Confined Flare)

Manchester et al. 2004

Magnetic Flux Ropes in the Solar Atmosphere

Potential State withZero Helicity

Minimum-Energy Statewith a conserved Net Helicity

Sigmoidal Plasma Structures and Magnetic Flux Ropes

The sigmoid separatrix flux surface (Parker 1994,Titov & Demoulin 1999, Low

& Berger 2003)

Fan & Gibson (2003)

Preferred Sigmoidal X-ray Plasma Structures in the two Hemispheres

• Left- and right-handed twisted flux ropes are preferred in the northern and southern hemispheres respectively (Canfield, Petstov, Rust, …..).

• Helicity Rule holds for all solar cycles.

North

South

A Role of CMEs in Coronal Evolution

• Large-scale expulsion of coronal mass clear out into interplanetary space:

• Is there a collective effect of the CMEs on the solar corona over an 11-year solar cycle? Is energy release the only consequence of the CMEs for the corona?

g1510

SolarWindCMEs dt

dM

dt

dM

05.0

Magnetic-flux Emergence and the Complementary Roles of Flares and CMEs

• Magnetic reconnection as flares serves to shed excess energy and simplify field topologies but cannot destroy the large-scale magnetic flux threading across the solar photosphere.

• Under its approximate conservation law, the magnetic-helicity emerging into the corona can be removed either by the mutual cancellation of opposite helicities or by an outward transport into interplanetary space, in order to avoid an unbounded accumulation in the corona – the global helicity rule identifies the latter mechanism with the CMEs.

Creation & Removal of Magnetic Flux Across a Geometric Surface

CMEs and Coronal Magnetic-Field Reversals

• CMEs are episodes of hydromagnetic expulsions of the magnetic flux and helicity of the old cycle out into the interplanetary solar wind, to make room for the new-cycle flux of the opposite polarity (Low & Zhang 2004).

• SMM & LASCO observations suggest a direct association between the progress of a field reversal at a solar pole and the rates of CMEs taking off near that (Gopalswamy et al. 2003).

Gopalswamy et al. 2003

The Solar-Heliospheric Outflow of Magnetic Flux and Helicity

• There is a global transport of magnetic flux system from the solar interior out into the solar wind, obeying the Helicity Rule. Complementary roles for flares & prominence and CME eruptions.

• Sub-photospheric origin of atmospheric magnetic helicity–are we seeing clear through into the interior dynamo?

• The hydromagnetic interplay between dissipative (flares) and ideal (CMEs) processes is the basic drama of solar activity that is the origin of space weather (Zhang & Low 2005, Ann. Rev. Astron Astrophys.).

References

• Hundhausen, A. J. 1997, in Cosmic Winds and the Heliosphere, ed. J. R.Jokipii, C. P. Sonnett, \& M. S. Giampapa, U. of Arizona Press, p. 259

• Low, B. C. 2001, JGR 106, 25141 & references therein

• Zhang, M., \& B. C. Low 2005, ARAA vol. 43, in press, download: /toshi/ftp/pub/zhm/ZhangLow.pdf & references therein.