Cosmic RayCosmic Ray Anisotropy

Brian KoltermanBrian Kolterman

LANL December 2006LANL December 2006

The Hill

H.A.

Dec.

TriggerRate

Time Binning

• Sidereal: coordinates fixed with respect to background stars

• Universal: solar time, displays day-night effects as well as Compton-Getting effect

• Anti-Sidereal: non-physical, added for test of “sidebands”

Forward Backward Asymmetry

FBn =Rn(F )−Rn(B)Rn(F ) + Rn(B)

FB

An (θ) =γn cosn(θ −φn)Rn(θ) =γn cosn(θ −φn) +1

Rn(F ) =γn cosn(θ −φn +α) +1Rn(B) =γn cosn(θ −φn −α)+1

θ = Right Ascention

A(θ) = An(θ)n=1

3

∑

Forward Backward Asymmetry

FBn =−γnsinnα sinn(θ '−φn)

1+γn cosnα cosn(θ '−φn)≈−γnsinnα sinn(θ '−φn)

for γn = 1

θ ' = Hour Angle = Local Sidereal Time(degrees) - θ

Fit FBn to Cn cosnθ '+ Dnsinnθ '

Define An =−γnsinnα

then Cn =−Ansinnφn and Dn =An cosnφn

Cn2 + Dn

2 =An2 =γn

2 sin2 nα

tan−1(−Cn

Dn

) =φn

Determining the Fourier components of the Sky Anisotropy

Sidereal Sky Map (Six Years)

Sidereal Sky Profiles (Six Years)

Sidereal Sky Profiles (Six Years)

Sidereal Sky (1st & 2nd 3 Years)

Sid. Profiles (1st & 2nd 3 Years)

Central Valley Position

Central Valley Depth

Central Valley Depth

Fit Parameters

Energy Dependence

E =EΦ(E)

θ ,E∑ A(θ,E)

Φ(E)θ ,E∑ A(θ,E)

Φ E( ) ∝ E−2.7

A θ,E( ) = Effective Area

For θ = 0° −25° E =2.3 TeV

For θ = 25° −50° E =4.0 TeV

Energy Dependence

2.3 TeV 4.0 TeV

Energy Dependence

Systematic Checks

• Valley Position in UT & Anti-ST

• UT Compton-Getting effect

• Anti-Sidereal Analysis

• Seasonal Effects

• Stability of Fitting Procedure

• Monte Carlo

• Coronal Mass Ejections

Valley Position in UT & Anti-ST

UT Compton-Getting Effect (1935)

EARTHSUN12 UT

0 UT

CR Excess6 UT

CR Deficit18 UT

Δα(θ )

α= [(2 + γ )(v0 / c)]cosθ

Δα (θ )

α= fractional asymmetry ≈ 10−3 −10−4

v0 = velocity of detector relative to isotropic frame

γ = CR spectral index = 2.7

θ = CR angle relative to v0

v0 ≈30 km/s

Universal Time Sky Map

Universal Time Profiles

Anti-Sidereal Sky Map

Seasonal Sky Maps

Winter-Spring = Nov. - Apr.

Spring-Summer = Apr. - Jul.

Summer-Fall = Jul. - Nov.

Stability of Fitting Procedure

Yr 1 Yr 6

Monte Carlo Checks

• No Anisotropy

• Reproduction of Observed Sky (w/scaling)

• Square Hole Input (ST & UT)

• Galactic Ridge

• Sidereal Sky With Inner Galaxy Removed

• UT Modulation (Seasonal Effects)

Monte Carlo Checks

Monte Carlo Checks

Monte Carlo Checks

Monte Carlo Checks

Input Output

Sidereal Sky Map

Coronal Mass EjectionsApr. 12 2001

Before After