K. E. Korreck1,2, T. H. Zurbuchen1, S. T. Lepri1, & J. Raines1

1. University of Michigan - AOSS Department2. Now at Harvard-Smithsonian Center for Astrophysics

Heavy Ion Heating In Coronal Mass Ejection

Shocks

Heating in collisionless shocksHeating in collisionless shocks

Collisionless shock heating based on Collisionless shock heating based on three factors:three factors:VVshockshock: shock speed: shock speed

θθBnBn: magnetic field angle to shock normal: magnetic field angle to shock normalββ: ratio of thermal and magnetic pressure: ratio of thermal and magnetic pressure

Quasi-Parallel (0<Quasi-Parallel (0<θθ<45<45) vs Quasi-) vs Quasi-Perpendicular (45<Perpendicular (45<θθ<90<90) Shocks heat ) Shocks heat differently differently

Mass proportional heatingMass proportional heating

3/16 comes from the strong shock 3/16 comes from the strong shock approximation of the RH conditionsapproximation of the RH conditions

All ions speeds would be the same if All ions speeds would be the same if the heating was mass proportionalthe heating was mass proportional

2

16

3mvkT =

Composition of the Solar WindComposition of the Solar Wind

The composition of The composition of the solar wind the solar wind allows us to study allows us to study many different ionsmany different ions

Protons dominateProtons dominate He is the next He is the next

abundant elementabundant element O 6+ is the next O 6+ is the next

most abundantmost abundant

ElementElement AbundanceAbundance

HH 9292

HeHe 7.87.8

CC 0.020.02

OO 0.060.06

Other Other HeaviesHeavies

0.120.12

Shock heating is strongly M/Q Shock heating is strongly M/Q dependentdependent

Lee & Wu 2000

Ratio of Tdw/Tup shows a strong dependence on the mass to charge ratio of an ion

CME driven shocksCME driven shocks

Berdichevsky et al., Berdichevsky et al., 1997: 1997: HeHe2+2+/H/H++

observations on observations on UlyssesUlysses

Most shocks Most shocks produce shock produce shock heating greater than heating greater than mass-proportionalmass-proportional

CME shock study CME shock study

Plasma data courtesy of SWICS, SWEPAM, MAG.Plasma data courtesy of SWICS, SWEPAM, MAG.

Shock properties characterized by C. Smith, UNH.Shock properties characterized by C. Smith, UNH.

Total Number of Total Number of ShocksShocks

2121

Quasi- Quasi- PerpendicularPerpendicular

1717

Quasi-ParallelQuasi-Parallel 44

Mach NumberMach Number 1.1-5.91.1-5.9

BetaBeta 0.01-1.40.01-1.4

Shock Shock analysisanalysis

Data were taken Data were taken with the ACE with the ACE satellite satellite magnetic anglemagnetic angle magnetic field magnetic field

strengthstrength temperaturetemperature thermal velocitiesthermal velocities

Heavy elements are Heavy elements are analyzed at time-analyzed at time-resolution of 1 hour. resolution of 1 hour.

12 minute interval 12 minute interval that includes shock that includes shock is skipped.is skipped.

M/Q = 1,..,5.6M/Q = 1,..,5.6

Selection criteria Selection criteria

Selection of shocks: During 1 hour Selection of shocks: During 1 hour intervalintervalΔΔB/B<20%B/B<20%ΔΔT/T<20%T/T<20%

Thermal speed are obtained from Thermal speed are obtained from distribution functions. distribution functions.

Moments calculates by Gaussian Moments calculates by Gaussian fits.fits.

Heavy ionsHeavy ions

Non-Maxwellian Non-Maxwellian velocity distribution velocity distribution functions appear in functions appear in 75% of the cases.75% of the cases.

The suprathermal The suprathermal tail appears after tail appears after the shockthe shock

Perpendicular shocks: effect of Perpendicular shocks: effect of initial conditionsinitial conditions

Ions do not Ions do not start in start in thermal thermal equilibrium.equilibrium.

More More “thermalized”“thermalized”ions get ions get moremoreenergy.energy.

(Tup/T

down) io

n/(Tup/T

down) p

+

Mass

Momentum

Energy

3 species, electrons, 3 species, electrons, protons and heavy protons and heavy ionsions

Ion jump conditions Ion jump conditions [n[niiuuii]=0]=0 [u[u22

ii T Ti,lli,ll]=0]=0 [0.5m[0.5miiuuii

2 2 + 3/2 kT+ 3/2 kTi,lli,ll ]=0]=0

More energy More energy transferred than transferred than theory predicts theory predicts

Parallel shocks Parallel shocks (Buergi, 1985)(Buergi, 1985)

Scaling with plasma betaScaling with plasma beta

Fe plotFe plot

Heating mechanism at the CME Heating mechanism at the CME shock frontshock front

From bow shock From bow shock studies by Fuselier and studies by Fuselier and Schmidt (1997)Schmidt (1997)

Protons assumed to be Protons assumed to be dominatedominate

Heavy ions are treated Heavy ions are treated as a test particleas a test particle

Protons create a Protons create a potential as they slow potential as they slow down over the shockdown over the shock

This potential causes This potential causes the heavies to speed the heavies to speed up to conserve energyup to conserve energy

eeΦΦ

shockshock

( )α

α 211,2,

cpi vv +−=

Heating mechanism at the CME Heating mechanism at the CME shock front (continued)shock front (continued)

Relating to Relating to ββ

Using the data for Using the data for Fe 10+ in black and Fe 10+ in black and purple is the purple is the predicted value predicted value using the above using the above equationequation

βαα

pi

A

i

i

mv

ckTM

v

v21,

22

21,

22, )1(2 +−=

Dependence of heating on shock Dependence of heating on shock properties ?properties ?Shock Alfvenic Shock Alfvenic

Mach Number: No Mach Number: No observed observed dependencedependence

Important Important DependencesDependencesShock angleShock angleUpstream (proton) Upstream (proton)

plasma plasma ββ

Summary for heavy ion heatingSummary for heavy ion heating

CME Shock heating has a strong M/Q CME Shock heating has a strong M/Q dependence.dependence.

Perpendicular shocks impart a larger fraction Perpendicular shocks impart a larger fraction of energy to heavies.of energy to heavies.

The heating rate does not depend on Mach The heating rate does not depend on Mach number, but upstream proton number, but upstream proton ββ

We need models to interpret these data. We need models to interpret these data. Obviously, heavies are sensitive to kinetic Obviously, heavies are sensitive to kinetic effects.effects.

ββ trends can be applied to other trends can be applied to other astrophysical shocks to predict magnetic astrophysical shocks to predict magnetic fieldfield