Propagation of cosmic rays in the Solar system

Charged cosmic ray nuclei entering the Solar system haveto overcome the magnetic field that is carried by the solarwind. The solar wind is an outflow of material from the Sunthat was predicted by L. Biermann. The magnetic field structure was explained in 1958 by Parker. The magnetic fieldfrozen in the ionized material and is expanding away fromthe Sun. In the vicinity of the Earth the solar wind velocityis between 300 and 600 km/s which corresponds to an average kinetic energy of 500 MeV/particle. The magnetic fieldstrength is about 3x10-5 G which is about 40 times lower thanthe kinetic energy of the solar wind particles. The Parker spiral has two components: radial and azimutal

The modulation of the galactic cosmic rays particles in thesolar system was first observed as an anti-correlation of theneutron monitors data with the sunspot numbers on the Sun.The sunspot number, which measures the number of activeregions on the Sun, has roughly an 11 year cycle, ½ of themagnetic cycle on the Sun. There is 1 – 2 yrs delay after thesunspot number changes.

Swarthmore/Newark neutronmonitor data.

There is a standard spherically symmetric model of solarmodulation (Gleeson & Axford) that accounts for -- cosmic ray diffusion through the magnetic field carried by the solar wind -- the convection by the ouward motion of the solar wind -- the adiabatic deceleration of the galactic cosmic rays in this flow

The diffusion coefficient used is k = C0R where R is the particle rigidity. The solar wind speed is 400 km/s. The solarmodulation parameter r1rh (v/k) dr. The data is best fit with

MeV. For r1 = one AU and rh (radius of the helio-sphere of 50 AU. Current data suggests the heliosphericradius is significanly bigger (a factor of 2?). In this force fieldapproximation the solar modulation is expressed in terms ofthis single parameter. A particle of energy EIS in interstellar

space would reach Earth with E = EIS - |Z|

The flux of particles of this energy and type is related to the Interstellar flux IS as

Comparison of the proton flux measuredabove 20 GeV with theLEAP experiment withsolar modulation using200, 400, 600, 800and 1,000 MeV.

The values used today are between 400 MeV at solar minimumto 1400 MeV for solar maximum. The decrease of the particleflux is three times higher than the decrease of the energy ofthe individual particles.

Galactic cosmic ray modulation in differentparts of the Solar system. (H. Moraal)

The solid lines show the numerical solutions, whilethe dashed lines showthe force field solutionsat different distances fromthe Sun.

The end of the heliospherehere is at 90 AU. The solu-tions for different distancesare shown divided by 101/2.

There are significant indications that positively andnegatively charged particles modulate in different waysand in different solar polarities. One indication is thedifferent shape of the neutron monitors counts as a function of the solar polarity.

Direction of the solar magnetic fieldduring different solar polarities, Cosmicray particles generally gyrate aroundthe magnetic field lines in the Solarsystem.

Regions of outward andInward polarities areseparated by the currentsheet which is shown here in 3D. The combina-tion of solar rotation andradial flow of the solarwind creates this compli-cated shape of the current sheet.

All graphs on black are by J.W. Bieber

In the presence of magnetic field charged particles move inSpiral trajectory around the magnetic field lines. The Larmor(or gyro radius) is rg = m v sin /(qB) where is the thepitch angle to the field line.

The efficient particle transport is perpendicular to the magnetic field lines. The negatively charged particles(electrons and antiprotons) drift in the opposite way.

When the solar polarity reverses the drift directionalso reverses.

Positive solar polarity Negative solar polarity

The motion is more complicated because the current sheet isnot a plane.

Long term behaviour of the neutron monitor data during different solar polarity periods. Note also the time delay thatvaries between a fraction of an year to two years.

Intensity of protons and antiprotonsIn different solar polarities asCalculated by Bieber et al.

The BESS detector

Detection of protons and antiprotons in the BESS1999 and 2000 flights.Antiprotons are bend by themagnets in the opposite way which results in negative rigidity.

Comparison of the BESS andother measurements to calculations of the fluxes forpositive Solar polarity.

Comparison of the measurements in different Solar polarity to predictions of different solar modulation models.The interstellar fluxes (LIS) do not depend of the Solarpolarity but the modulation does.

In spherically symmetricmodels the modulation does not depend on the solar polarity but fitting the detectedfluxes requires different parameter.

Ratio of the positron to the electron fluxes measured by thePAMELA experiment. The lines are the solar modulatedfluxes calculated by Bieber et al. The paper is not publishedYet so I cannot give you more details about it.

Geomagnetic field effects: The charged particles that we detect have to also penetrate the Earth magnetic field.The geomagnetic field is an offset dipole field where the magnetic pole in the Northern hemisphere is at latitude 81 deg and longitude 84.7oW. This is actually the South magnetic pole;The North magnetic pole is close to the South rotational pole.

The rigidity cutoff was calculated analytically by Stoermer as

where is the particle zenith angle and B is the particle azimutal angle measured clockwise from the direction of the North magnetic pole. It includes the East-West effect: more positively charged particles come from the West at thezenith angle than from the East. It is the opposite for negativelycharged particles such as electrons and antiprotons.

The geomagnetic cutoff has to be taken into account when accurate calculations are made of different particles that reach experiments on the surface of the Earth. The figure shows the zenith angle dependence of protons of different energy that can reach the atmosphere and interact in it. The calculationwas made for the location of Kamiokande where the big Japanese neutrino experiment SuperK is located. Since we deal with neutrinos that reach the experiment from all direction wehad to deal with the whole magnetic field of the Earth.