Heliospheric Modulation of Leptons: Theoretical Perspective Modeling - - PowerPoint PPT Presentation

Heliospheric Modulation of Leptons: Theoretical Perspective

Modeling of Galactic Cosmic Rays with Opposite Charge in the Heliosphere

Marius Potgieter

Unit for Space Physics North-West University Potchefstroom, South Africa RICAP May 2009 Collaborators: Ingo Buesching, Stefan Ferreira,

Students: Driaan Bisshoff, DuToit Strauss, Etienne Vos

Cosmic Rays from the Galaxy

Charged Particle Populations inside heliosphere

Bow Shocks

500 AU

250 AU

Heliospace

The heliosphere

Voyager 1: Dec 2004 Voyager 2: Aug 2007

Cosmic ray transport part Cosmic ray transport part Hydrodynamic part Hydrodynamic part

, 2 2 ,

( ) , ( ) ( ) 2 1 , 2 1

i i i i i i i i i i m i i i i i i i i i i e i i

Q t P Q t P t P Q

• +

=

• +

+ =

• +

+

• +

=

• u

u u u I u u u u i i i

> describe the balance of mass, momentum and > describe the balance of mass, momentum and energy of the protons in solar wind and LISM, neutral energy of the protons in solar wind and LISM, neutral hydrogen, pickup ions, and additional is GCR hydrogen, pickup ions, and additional is GCR’ ’s and s and ACR ACR’ ’s s > mass density > mass density ρ ρ, velocity , velocity u, u, pressure pressure P P and and Q Q sources sources related to the interaction between the various species. related to the interaction between the various species.

A 5 fluid model based on the A 5 fluid model based on the Kausch (1998)

Kausch (1998) model :

model :

1 ( ) ( ) ( ) 3 ln

s

f f f f t R

• =

+ +

• +
• D

v

sw sw

V K V

> including all major modulation mechanisms : > including all major modulation mechanisms : diffusion, drifts, convection and energy changes diffusion, drifts, convection and energy changes Realistic heliospheric geometry Realistic heliospheric geometry and and solar wind flow profile solar wind flow profile

Magnetic part Magnetic part ( ) t

• +
• =
• B

u B

> Magnetized flow is calculated by solving Faraday > Magnetized flow is calculated by solving Faraday’ ’s law assuming ideal MHD s law assuming ideal MHD Magnetic field Magnetic field

Cosmic ray transport and acceleration calculated by Cosmic ray transport and acceleration calculated by Parker (1965)

Parker (1965) TPE :

TPE :

TS 93AU HP 140 AU TS 155 AU HP 245 AU TS 205 AU

Scherer, K., & Ferreira, S. E. S. 2005, ASTRA, 1, 17 Ferreira, S. E. S., & Scherer, K. 2004, ApJ, 616, 1215

Hydrodynamic modeling of major heliospheric structures

Cosmic rays are excellent indicators of solar cycle variations

Modulation of galactic cosmic rays at Neutron Monitor energies

Hermanus NM (4.6 GV) South Africa

Time (Years)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

(100% in May 1965)

80 85 90 95 100

77.5

A > 0 A < 0 A < 0 A > 0 22-year cycle A < 0

[ ]

( )

• =
• +
• +
• 1

3

ln

D

f f Q( r, p, f f t t p ) f

• K

V V 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)

Transport equation for the modulation and acceleration of cosmic rays in the heliosphere

Modulation-Acceleration Model

Second order Fermi acceleration

• =

+

• 2

2

pp

1 f ... ... p D p p p

Heliospheric CR Modulation Processes

As for electrons

The wavy current sheet (HCS)

Heliosphere & Cosmic Ray Modulation Mechanisms

Tilt angle of the HCS: proxy for solar activity

L - values

Hoeksema's "Tilt Angles" (Averaged over one solar rotation)

Time (Years)

1975 1985 1995 2005 10 20 30 40 50 60 70 80 Maximum solar activity Minimum solar activity

The wavy heliospheric current sheet (HCS)

Moderate solar activity Extreme solar activity

Drifts during a complete solar activity cycle

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 20 40 60 80 100

Time (Years) Tilt angle (degr.)

20 40 60

Kinetic energy (GeV/nuc)

10-3 10-2 10-1 100 101

(part.MeV

• 1

.m

• 2

.sr

• 1

.s

• 1

)

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104

p He e+ C e- p- B

Moskalenko and Strong, 2002. Langner, 2002, 2005;

Computed Galactic Spectra (LIS?)

10-2 10-1 100 101 Differential intensity ((MeV/nuc)

• 1

.m

• 2

.s

• 1

.sr

• 1

) 10-6 10-5 10-4 10-3 10-2

LIS A > 0 A < 0 Tilt = 10 degrees 1 AU Boron

10-2 10-1 100 101 Differential intensity ((MeV/nuc)

• 1

.m

• 2

.s

• 1

.sr

• 1

) 10-5 10-4 10-3 10-2 10-1

LIS A > 0 A < 0 Tilt = 10 degrees 1 AU Carbon

Kinetic energy (GeV/nuc) 10-2 10-1 100 101 B/C 10-1

LIS A > 0; 1 AU A < 0; 1 AU A > 0; 60 AU A < 0; 60 AU Tilt = 10 degrees 1 AU

10-2 10-1 100 101 10-6 10-5 10-4 10-3 10-2

LIS 2 A > 0 A < 0 Tilt = 10 degrees 1 AU Boron

10-2 10-1 100 101 10-5 10-4 10-3 10-2 10-1

LIS 2 A > 0 A < 0 Tilt = 10 degrees 1 AU Carbon

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

LIS 2 A > 0; 1 AU A < 0; 1 AU Tilt = 10 degrees 1 AU

B/C

• bservations

and model results

Potgieter & Langner, Annales Geophys. 2004

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

(protons MeV

• 1

m

• 2

s

• 1

sr

• 1

)

10-2 10-1 100 101

1997 1987

LIS

A < 0 A > 0

Rigidity (GV) 10-1 100 101 Latitudinal gradient (%/degree)

0.0 0.1 0.2 0.3 0.4 0.5 Ulysses 1995 Tilt 100 Tilt 750 A > 0

Major features of cosmic rays near Earth

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

Observed spectra crossings at Earth, from A > 0 and A < 0 solar minima polarity cycles… Observed small latitudinal gradients, especially at low energies; compared to Ulysses-KET observations; for A > 0, solar minimum to maximum…

Modulation of galactic protons and anti-protons at solar minimum

Modulation of galactic electrons and positrons at solar minimum

Ratio of Electrons to Positrons

At Earth Solar minimum modulation Two concecutive magnetic field polarities

Ratio of Electrons to Positrons

At Earth Solar maximum modulation Two concecutive magnetic field polarities

Ratio of Electrons to Positrons

At Earth vs. LIS

Solar minimum modulation

Two concecutive magnetic field polarities

Ratio of Protons to Anti-protons

At Earth vs. LIS Solar minimum modulation

Two concecutive magnetic field polarities

The Wonders of Heliospace

Profile of the Latitudinal Solar Wind

Charged-sign Dependent Modulation over two Solar Maxima

Electron measurements form ISEE/ICE (Clem et al., 1996; Evenson, 1998) and KET (Heber et al, this conference). He measurements from IMP (McDonald, 1998; McDonald et al., 2001).