Simulating the Solar Shadow Allen I. MincerNYULANL 6/2/05

The General ProblemIntegrate the equations:

Numerical approach:

Tried AIM version using kinematic equations and steps with midpoint acceleration, better than 4th order Runge Kutta, OK for Moon but not precise or fast enough for Sun.

Old Comparison

Stoermer Rule, as Modified by Henrici

Aim Modified Version:

Some More Calculation Details

New Method UsedOld method sent particles from Earth to Moon to find nominal shadow direction, then started at Moon and generated events to Milagro.But D(Earth-Sun) ~ 400 D(Earth-Moon) and A(Sun) ~ 105 A(Moon).Would need to generate ~105 times the events to get the same shadow statistics.Instead, using Liouvilles theorem, isotropic C.R.s + B fields give isotropic C.R.s at Earth, unless absorbed.Generate backwards going C.R.s from Milagro to Sun. Shadow if sun is hit.

Preliminary Run10 day run late March.Pick sun position every 100 seconds.For each position, pick energy on E-2.7 spectrum starting at 0.5 TeV.For each position generate 10K events centered on the vertices of a 100 x 100 grid 5 degrees around straight line to sun : 0.1 degree steps in , cos.Run 4 cases: B Earth only Sun dipole parallel to Earths dipole B Earth + Sun dipole parallel to Earths dipole B Earth + Sun dipole perp. to Earths dipole

B Earth

Solar dipole parallel Earths, No B Earth

Solar Dipole parallel Earths

Rotating Solar Dipole perp Earths

Comparisons

Conclusion/conjecture:As B field increases, major change is fewer shadowed particles, since localized B large enough to cause ~degree type shifts will prevent particles from being shadowed.

Build in realistic fields.Improve effective area,Detector resolution.Compare with Solar data shadow under different solar conditions.

To Do: