Cosmic Ray Physics in Space, June 2017

Propagation of Galactic Cosmic Rays in the Heliosphere:

A global View

Marius Potgieter

Centre for Space Research, North-West University,

Potchefstroom, South Africa

Outline of presentation

• The heliosphere

• Modulation boundaries

• New heliopause spectra (HPS)

• Observations of GCRs

• Transport and modulation theory

Diffusion theory

• Numerical models

Complexity

• Modeling results and implications

The schematic heliosphere

Owens and Forsyth. Living Rev. 2013

Scherer, K., & Ferreira, S. E. S. 2005 Ferreira, S. E. S., & Scherer, K. 2004, ApJ

Major heliospheric structures (e.g. HD simulated)

Meridional plane

TS was observed

by V1 at 94 AU,

by V2 at 84 AU…

V1 crossed the HP

at 121.5 AU

V1 now at ~138 AU

from the Sun

V2 still inside the

inner heliosheath

at ~114 AU

http://voyager.jpl.

nasa.gov/

Fact sheet:

Heliosphere is

highly

asymmetric

V1

V2

HP

TS

HP

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Co

sm

ic R

ays

Perc

en

tag

e (

10

0%

in

Ma

rch

19

87

)

85

90

95

100

85

90

95

100

Year

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Tilt

An

gle

s (

De

gre

es

)

0

20

40

60

80

0

20

40

60

80

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Su

ns

po

t N

um

be

rs

0

50

100

150

200

250

0

50

100

150

200

250

Modulation of Galactic Cosmic Rays Observed at the Earth with two solar activity proxies

Cosmic rays

at sea-level

Hermanus

Monthly

averaged

sunspot

numbers

HCS tilt

angles

Wilcox

Solar

Observatory

Global modulation of cosmic ray protons: mid-2006 to end of 2009

PAMELA proton observations

at the Earth PAMELA-SA bilateral cooperation:

Mirko Boezio & colleagues

Proton spectra published

Adriani et al. ApJ 2013

Potgieter et al. Solar Phys 2014

PhD’s: Valeria Di Felice, Nico De Simone,

Valerio Formato, Riccardo Munini, Etienne

Vos, Jan-Louis Raath

Radial profile of galactic and Jovian electrons at 12 MeV

Conclusions:

Extraordinary type of

modulation in heliosheath

(HS) …

The HS indeed acts as a

strong modulation ‘barrier’

for these low energy

electrons …

Radial distance (AU)

0 10 20 30 40 50 60 70 80 90 100 110 120

Diffe

ren

tia

l in

ten

sity (p

art

. m

-2 s

-1 s

r-1 M

eV

-1)

10-3

10-2

10-1

100

101

102 Scenario 3

Scenario 2

Voyager 1

Scenario 1

Jovian

With the HP position and LIS

known, we can attempt to

predict intensity of 12 MeV

galactic electrons at the

Earth …

Potgieter & Nndanganeni, Astrophys. Space Sci. 2013

PhD Rendani Nndanganeni 2015

V1: 4-16 MeV; Webber (private comm.)

TS

HP

GCR protons K.E. > 70 MeV

GCR electrons 7 to ~100 MeV

ACR protons 7 to 60 MeV

TSPs 0.5 to 30 MeV

Stone et al. 2013

What happened in August 2012?

The Heliopause Spectra: Voyager 1, PAMELA and AMS2

Observations and GALPROP computations

Bisschoff & Potgieter, 2015 Vos & Potgieter, 2015

Potgieter & Vos, 2017

GALPROP; Plain Diffusion, and with re-acceleration

The conceptual and simulated HCS (wavy current sheet)

Kota, 2010

1

3 ln

Df f Q( r, p,

ff t

t p)

f K VV v

Time-dependent, pitch-angle-averaged distribution function

Diffusion

Convection with solar wind

Particle Drifts

Adiabatic energy changes

Any local source

Parker (Planet. Space Science, 13, 9, 1965)

Second order Fermi acceleration

2

2

pp

1 f... ... p D

p pp

Transport equation for the transport, modulation and

acceleration of cosmic rays in the heliosphere

,pc mvc

Pq Ze

0 02 .A A

P E E E E EZ Z

Solar wind radial profile: Observations and Simplifications

Solar wind latitudinal profile: Observations and Simplifications

Theory and dimensional complexity (1D to 2D to 3D)

3

2• • •

• • • •

1( ) ( ) ( ) 0

3

1( ) ( ) 0

3 ln

ff f p f

t p p

f ff f

t p

V V

V V

K

K

Eugene Parker published his solar wind, heliosphere and transport theory in

several papers between 1958 and 1965.

His transport equation (TPE) is:

f is the distribution function with I = p2f, with p momentum

Assumption of small anisotropies

V is the solar wind velocity

K is the diffusion tensor

Theory and dimensional complexity (1D to 2D to 3D)

Analytical solution of Parker’s basic TPE (1960’s and 1970’s)

• Convection-diffusion approach

• Force-Field approach

Steady-state numerical models

1D approach (early 1970’s) One DC (diffusion coefficient)

2D approach (late 1970’s) Two DC’s

3D approach (early 1980’s) Particle drifts and two DC’s

3D approach (early 1990’s) Particle drifts and three DC’s

Time-dependent models

1D approach (early 1980’s)

2D approach (early 1990’s)

3D approach NOT DOABLE IN INFINITE-DIFFERENCES METHODS

Need approach of Stochastic Differential Equations

Simplified solutions of the TPE

expHP

e

r

Earth LIS

r

Vdrf f

Convection-diffusion approach

[ ]

Boundary

Earth

r

boundary Earth

r

V VM dr r r

=

Modulation parameter

1• • ( • ) ( • ) 0

3 ln

f ff f

t p

V V K

•

0

f f

fVf

r

S V

K

Simplified solutions of the TPE

Force-Field approach

S V - • 0

1 lnexp , with

3 ln

B

E

r

Earth Boundary

r

fC f f CVf

r

CVdr ff f C

p

K

This resembles an energy loss without considering the adiabatic process

Approximated Force-Field approach

0

0

( 2 )( ) ( )

( )( 2 )LIS

T T Ej T j T

T T E

1 2 2Valid if is separable ( ) ( ) with when 1r P P :

Complexity & Dimension issues

2 2

2 2

2

1 10

3 ln

, ( ) ( , )

B

Anywhere

Boundary

r

r

f f fV r r V

r r r r r p

r V r r P

Vdr

Input and

Ouput : Adiabatic energy loss now taken care of...

: V LIS,

Approximation :

1 D spherically symmetric, steady-state, numerical approach

Force Field gives an indication of the modulation level (depth), nothing

more, nothing about the physics responsible, always ‘forced’

approximated solutions in 1 D, so that your heliosphere looks like this:

Comparison of 1 D modeling approaches

Caballero et al. (2004)

Protons

Solid lines: 1D numerical

Dotted lines: Convection –

Diffusion model

Dashed lines: FF model

Kinetic energy (MeV)

TPE in heliocentric spherical coordinates

Diffusion tensor based on a simple HMF geometry

21

Gradient, curvature and current sheet drifts:

Basic concepts

Gradient, curvature and current sheet drifts:

Basic Drift Theory (and the trouble with it)

sin ,sinA rr

AKv

r

1

i,

s nA rK

A

rrK

rv

,A

A

rv K

A complex HMF geometry

Modified Parker type HMF

Fisk (1996) type HMF

Smith & Bieber 1991

Observed HMF magnitude at the Earth

Drift direction

of electrons in

A > 0 cycle

Drift direction

of electrons in

A < 0 cycle

Charge-sign dependent modulation

Particle drifts in the heliospheric polar regions; SDE approach

Jan-Louis Raath’s MSc thesis, Nov. 2014

Proton trajectories in the heliosphere along the HCS

Impact of SDE models

Decreasing diffusion causes

increasing drift effects

Decreasing HCS tilt angle

Effects of the wavy HCS on proton modulation

Raath, Potgieter, Strauss, ASS, 2015

Rigidity (GV)

10-1 100 101

La

titu

din

al g

rad

ien

t (%

/de

gre

e)

0.0

0.1

0.2

0.3

0.4

0.5

Ulysses 1995

A > 0

Tilt 100

Tilt 750

A > 0

Major features of observed modulated cosmic rays near Earth: Required as validation for ALL numerical models

Langner, Potgieter & Webber, JGR, 2003; ASR, 2004

Observed and computed spectra crossings at Earth, for A > 0 and A < 0 solar minima polarity cycles…

Computed latitudinal gradients compared to Ulysses-KET observations, for A > 0, solar minimum to maximum…

Kinetic energy (GeV)10-2 10-1 100 101

Diffe

ren

tia

l in

ten

sity

(pro

ton

s M

eV

-1m

-2s-1

sr-1

)

10-2

10-1

100

1011997

1987LIS

A < 0

A > 0

A > 0

A < 0

Highest every recorded cosmic ray protons in 2009

Kinetic energy (GeV)

0.1 1

Diffe

rential in

tensity

( part

.m-2

. s-1

. sr-1

. MeV

-1)

0.1

1

1977: Evenson et al. (1983)

1977: von Rosenvinge et al. (1979)

1998: Sanuki et al. (2000)

1965: Fan et al. (1966)

1965: Ormes and Webber (1968)

1965: Balasubrahmanyan et al. (1965)

1996: McDonald et al. (1998)

1987: McDonald et al. (1998)

December 2009 PAMELA

Previous solar minima spectra

Blue open symbols: A > 0 cycles

Red filled symbols: A < 0 cycles

Red data points: A < 0 cycles Blue data points: A > 0 cycles

Strauss R.D., Potgieter M.S. Is the highest cosmic rays yet to come? Solar Physics, 289, 8, 3197-3205, 2014

Proton modulation during the unusual 2009 minimum period

Potgieter, Vos, Boezio et al. 2014

Vos & Potgieter, 2015

Proton Radial and Latitudinal Modeling and Observations

Consequences for Diffusion & Drift Theory

At Earth

Protons

Electrons

PAMELA Electron Observations and Modeling

O. Adriani, et al. Time dependence of the e- flux

measured by PAMELA during the July 2006- December

2009 solar minimum, ApJ. 810, 142, 2015.

M.S. Potgieter, E.E. Vos, R. Munini, M. Boezio, V. Di

Felice. Modulation of galactic electrons in the

heliosphere during the unusual solar minimum of 2006

to 2009: A modelling approach. ApJ 810, 141 2015.

Consequences for electron diffusion theory

Protons Electrons

Protons

Electrons

New evidence of charge-sign-

dependent (drift) modulation for 2006-

2009 from PAMELA…!

But, much smaller than anticipated

from modelling of previous solar

minimum activity periods….!

The 2009 minimum was different…

PAMELA Observations and Charge-sign Dependence

V. Di Felice, R. Munini, E.E. Vos, M.S.

Potgieter. New evidence for charge-sign

dependent modulation during the solar

minimum of 2006 to 2009. ApJ. 834, 89, 2017.

Potgieter & Vos, A&A, 2016

Modeling of drift effects during a very quiet solar minimum

Prediction for next A > 0 solar minimum cycle

PAMELA Electrons and Positrons for 2009

See PhDs of Riccardo Munini (2016) and Etienne Vos (2016)

Numerical modeling with particle drifts

2009

Drift & HCS effects in electron, proton and positron modulation

Observed electron to positron ratios over time

Difference between computed spectra for protons,

electrons and positrons

At the Earth for solar minimum Electrons & Positrons

Kinetic Energy (GeV)

10-3 10-2 10-1 100 101Diffe

rere

ntia

l In

ten

sity (

pa

rt/m

2/s

/sr/

Me

V)

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

Electrons at Earth

Electron LIS

Postron LIS

Positrons at Earth

Proton LIS

Protons at Earth

Concluding Remarks

• Electron, proton, helium and carbon HPS (very LIS) are established…

• Finally, we can study and determine the total modulation of GCRs…

• Comprehensive modeling gives significantly useful insights…

• In particular concerning drift effects

• Combined with observations we have made good progress

• Towards a general diffusion and drift theory… but

• We need to address the complications introduced by the heliosheath.

• Need more good observational data…

42

Solar wind velocity profiles in the heliosphere

Thank you !

Computed modulation of galactic electrons and positrons

at solar minimum for two polarity cycles

Electrons Positrons

Langner & Potgieter, Solar wind termination shock and heliosheath effects on charge-sign dependent modulation for protons and

anti-protons, JGR, 109, 2004; Potgieter & Langner, Heliospheric modulation of cosmic ray positrons and electrons: Effects of the

heliosheath and solar wind termination shock, ApJ, 602, 2004.

Positron fraction at the Earth

Effects of solar modulation with particle drifts

Strauss & Potgieter, Adv. Space Res., 2014