Cosmic Ray Cosmic Ray Anisotropy Brian Kolterman Brian Kolterman LANL December 2006 LANL December 2006
Jan 09, 2016
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