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Cosmic Ray Anisotropy. Brian Kolterman LANL December 2006. The Hill. Trigger Rate. Dec. H.A. Time Binning. Sidereal: coordinates fixed with respect to background stars Universal: solar time, displays day-night effects as well as Compton-Getting effect - PowerPoint PPT Presentation
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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