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 Collaborators: Ingo Buesching, Stefan Ferreira, Students: Driaan Bisshoff, DuToit Strauss, Etienne Vos RICAP May 2009
Cosmic Rays from the Galaxy Charged Particle Populations inside heliosphere
Heliospace 500 AU Voyager 1: Dec 2004 250 AU Bow Shocks Voyager 2: Aug 2007 The heliosphere
Hydrodynamic part Hydrodynamic part A 5 fluid model based on the Kausch (1998) model : A 5 fluid model based on the Kausch (1998) model : > mass density ρ , velocity u, u, pressure pressure P P and and Q Q sources sources > mass density ρ , velocity � i ( u ) Q , � + � � = related to the interaction between the various species. related to the interaction between the various species. i i i , i � t � > describe the balance of mass, momentum and > describe the balance of mass, momentum and � i ( u ) ( u u P I ) Q energy of the protons in solar wind and LISM, neutral � + � � + = energy of the protons in solar wind and LISM, neutral i i i i i i m t � hydrogen, pickup ions, and additional is GCR’ hydrogen, pickup ions, and additional is GCR ’s and s and P ACR’ ACR ’s s � � � � 2 i u i + + � � i t 2 1 � � � � � Realistic heliospheric geometry and and Realistic heliospheric geometry i solar wind flow profile solar wind flow profile u P � � � � 2 i i i i i u u Q , � + = � � i i e i , 2 1 � � � � i Magnetic part Magnetic part > Magnetized flow is calculated by solving Faraday’ ’s law assuming ideal MHD s law assuming ideal MHD > Magnetized flow is calculated by solving Faraday B � Magnetic field Magnetic field ( u B ) 0 + �� � = t � Cosmic ray transport part Cosmic ray transport part Cosmic ray transport and acceleration calculated by Parker (1965) TPE : Cosmic ray transport and acceleration calculated by Parker (1965) TPE : f 1 f � � ( V v ) f ( K f ) ( V ) = � + � � �� + �� �� + �� sw D s sw t 3 ln R � � > including all major modulation mechanisms : > including all major modulation mechanisms : diffusion, drifts, convection and energy changes diffusion, drifts, convection and energy changes
Hydrodynamic modeling of major heliospheric structures HP 245 AU HP 140 AU TS 93AU TS 155 AU Scherer, K., & Ferreira, S. E. S. 2005, ASTRA, 1, 17 TS 205 AU Ferreira, S. E. S., & Scherer, K. 2004, ApJ, 616, 1215
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 A < 0 A < 0 A > 0 A < 0 A > 0 100 95 90 (100% in May 1965) 85 22-year cycle 77.5 80 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Time (Years)
Modulation-Acceleration Model Transport equation for the modulation and acceleration of cosmic rays in the heliosphere f f 1 � � K f V f v f V Q( r, p, t ) [ ] ( ) = � � � � � � � � � � + � � + D ln t p 3 � � Time-dependent, pitch-angle-averaged distribution function Diffusion Convection with solar wind Particle Drifts Adiabatic energy changes Any local source 1 f � � � � 2 ... ... p D = + Second order Fermi acceleration � � pp 2 p p p � � � � Parker (Planet. Space Science, 13, 9,1965)
Heliospheric CR Modulation Processes As for electrons
Heliosphere & Cosmic Ray Modulation Mechanisms The wavy current sheet (HCS)
The wavy heliospheric current sheet (HCS) Hoeksema's "Tilt Angles" (Averaged over one solar rotation) Extreme solar 80 activity L - values 70 Maximum solar 60 activity 50 40 Moderate solar activity 30 20 Minimum solar 10 activity 0 1975 1985 1995 2005 Time (Years) Tilt angle of the HCS: proxy for solar activity
Drifts during a complete solar activity cycle 0 100 80 20 60 40 40 Tilt angle (degr.) 60 20 0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Time (Years)
Computed Galactic Spectra (LIS?) 10 4 10 3 e - 10 2 10 1 ) p -1 e + .s 10 0 -1 He .sr 10 -1 -2 .m 10 -2 -1 C 10 -3 10 -4 B (part.MeV 10 -5 p- 10 -6 10 -7 10 -3 10 -2 10 -1 10 0 10 1 Kinetic energy (GeV/nuc) Moskalenko and Strong, 2002. Langner, 2002, 2005;
10 -2 10 -2 B/C Tilt = 10 degrees Tilt = 10 degrees ) 1 AU 1 AU -1 Boron Boron observations 10 -3 10 -3 .sr -1 .s and model -2 10 -4 10 -4 .m -1 results 10 -5 10 -5 LIS LIS 2 A > 0 A > 0 Differential intensity A < 0 A < 0 10 -6 10 -6 ((MeV/nuc) 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 10 -1 10 -1 Tilt = 10 degrees Tilt = 10 degrees ) 1 AU 1 AU -1 Carbon Carbon 10 -2 10 -2 .sr -1 .s -2 10 -3 10 -3 .m -1 10 -4 10 -4 LIS LIS 2 A > 0 A > 0 Differential intensity A < 0 A < 0 10 -5 10 -5 ((MeV/nuc) 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 Tilt = 10 degrees Tilt = 10 degrees 1 AU 1 AU 10 -1 10 -1 B/C LIS A > 0; 1 AU A < 0; 1 AU LIS 2 A > 0; 60 AU A > 0; 1 AU Potgieter & Langner, A < 0; 60 AU A < 0; 1 AU Annales Geophys. 2004 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 Kinetic energy (GeV/nuc) Kinetic energy (GeV/nuc)
Major features of cosmic rays near Earth 0.5 1997 A > 0 LIS Ulysses 1995 ) 10 1 0.4 1987 -1 sr -1 s 0.3 A < 0 -2 10 0 Tilt 10 0 m -1 0.2 A > 0 (%/degree) 10 -1 Tilt 75 0 0.1 Latitudinal gradient Differential 0.0 (protons MeV 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 Kinetic energy (GeV) Rigidity (GV) Observed spectra crossings at Earth, Observed small latitudinal gradients, especially at low energies; compared to from A > 0 and A < 0 solar minima polarity Ulysses-KET observations; for A > 0, solar cycles… minimum to maximum… Langner, Potgieter & Webber, JGR, 2003; ASR, 2004
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 Ratio of Protons to Anti-protons At Earth vs. LIS At Earth vs. LIS Solar minimum modulation Solar minimum modulation Two concecutive magnetic field Two concecutive magnetic field polarities 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).
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