1. Search for Cosmic Ray Anisotropy with the Alpha Magnetic Spectrometer on the International Space Station
G. LA VACCA University of Milano-Bicocca INFN Milano-Bicocca
on behalf of the AMS-02 collaboration
5-Sep-2016

2. Motivation for CR anisotropy search with AMS
Sez. Milano-Bicocca
Motivation for CR anisotropy search with AMS
AMS-02 observes structures in the spectra of e+, e-, p, He that cannot be fully explained within the current physical knowledge. These features may be connected to new phenomena which could induce some degree of anisotropy in their fluxes:
Local environment (galactic magnetic field, effects due to the solar activity at low rigidity)
Local sources (pulsars for e+ and e-, local SNRs or Wolf-Rayet stars for p and He)
AMS02 Proton Flux PRL 114, (2014)
AMS02 Positron Fraction PRL 113, (2014)

3. Sez. Milano-Bicocca
AMS-02: the detector
AMS: A TeV precision, multipurpose particle physics spectrometer in space.
TRD: to identify e+ and e-
TOF: measure Z, E
Tracker: measure Z, P, incoming direction
ECAL: measure lepton energy
Proton background is reduced to the per mil level with a cut based selection on the TRD and ECAL estimators
Selected particles for this analisys in [16:350]GeV, from 05/2011 to 11/2015:
positrons
electrons
protons

4. Sez. Milano-Bicocca
AMS-02: operation
Since May 2011, AMS-02 is operating 24/7 on board of ISS:
400Km altitude
orbit inclination 51.6° relative to the Earth Equator
South Geographic Pole
AMS-02 exposure in Galactic cordinates
BEING IN SPACE:
A long term, (nearly) full-sky observation and a three-dimensional measurement of the tiny CR anisotropy signals;
Primary CR detected before interacting with the atmosphere;
In Low Earth Orbits, the presence of the magnetosphere: CR directions after trajectory reconstruction in magnetosphere, rigidity cut-off;
Not uniform exposure.

5. Methodology for anisotropy search
Sez. Milano-Bicocca
Methodology for anisotropy search
RELATIVE ANISOTROPIES: other CR species as reference for detector exposure:
other cosmic ray species (e.g. p used for leptons, also at magnetosphere border)
same cosmic ray species (at different energy)
A likelihood fit procedure has been set up to compare the species under study to the reference sky map. It takes into account the differences in the exposure for different rigidities. A spherical harmonics expansion of the relative anisotropy is obtained:
φ 𝑏,ℓ = 𝑙=0 ∞ 𝑚=−𝑙 +𝑙 𝑎 𝑙𝑚 𝑌 𝑙𝑚 (𝑏,ℓ)
For the three dipole components (𝑙=1):
North-South
Forward-Backward
East-West
𝜌 𝑁𝑆 = 3 4𝜋 𝑎 10
𝜌 𝐹𝐵 = 3 4𝜋 𝑎 11
𝜌 𝐸𝑊 = 3 4𝜋 𝑎 1−1
𝛿= 𝜌 𝑁𝑆 𝜌 𝐹𝐵 𝜌 𝐸𝑊 2
Dipole amplitude:

6. Positrons vs. electrons
Sez. Milano-Bicocca
Positrons vs. electrons
Dipole components in galactic coordinates
No significant deviation from isotropy is found

7. Positrons vs. electrons
Sez. Milano-Bicocca
Positrons vs. electrons
Dipole upper limit in galactic coordinates
Upper limit ẟ scaled to the statistics
No significant deviation from isotropy is found
𝛿 𝑒 + 𝑒 − (>16GeV) < 2% at 95% C.L.
Significance map

8. Back-tracing in magnetosphere
Sez. Milano-Bicocca
Back-tracing in magnetosphere
The back-tracing allows to reconstruct the trajectories of the cosmic rays detected by AMS02 at ISS altitude in a deterministic way up to the border of the magnetosphere.

9. Back-tracing in magnetosphere
Sez. Milano-Bicocca
Back-tracing in magnetosphere
Model description
Internal Field: IGRF-12 model is a standard mathematic description of the Earth main magnetic field and its annual rate of change (secular variation)
External Field: Tsyganenko 2005 model: includes all external currents contributions to external magnetic field. It describes the Earth magnetosphere during both quiet and active solar periods.
Magnetosphere border
in the day-side, variable from 15 to 10 Earth Radii, according to the solar wind pressure
in the night-side, fixed to 25 Earth Radii
Back-tracing
Protons in [16:350]GV
Focusing towards the equator
At ISS altitude
At magnetosphere border

10. Back-tracing in magnetosphere
Sez. Milano-Bicocca
Back-tracing in magnetosphere
The reference sky map
The magnetosphere introduces a displacement with respect the asymptotic direction. This displacement decreases with rigidity.
M. Ackermann et al. 2012
The sky observed outside the magnetosphere depends on the considered rigidity and on the particle charge.
Sky maps from opposite charge particles cannot be compared at magnetosphere border: e+ vs. p and e- vs. p* (*negative charge BT p)

11. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Positrons vs. protons
Dipole components in galactic coordinates
No significant deviation from isotropy is found

12. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Positrons vs. protons
Dipole upper limit in galactic coordinates
Upper limit ẟ scaled to the statistics
No significant deviation from isotropy is found
𝛿 𝑒 + 𝑝 (>16GeV) < 2% at 95% C.L.
Significance map

13. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Electrons vs. protons*
Dipole components in galactic coordinates
No significant deviation from isotropy is found
*Protons back-traced with negative charge

14. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Electrons vs. protons*
Dipole upper limit in galactic coordinates
Upper limit ẟ scaled to the statistics
No significant deviation from isotropy is found
𝛿 𝑒 − 𝑝 (>16GeV) < 0.6% at 95% C.L.
Significance map
*Protons back-traced with negative charge

15. Protons vs. protons Original idea: look for directional
Sez. Milano-Bicocca
Protons vs. protons
Original idea: look for directional
dependence of energetic protons.
Use low energy protons as reference map, well above geomagnetic cut-off, low solar modulation effects.
Reference sample
High energy proton map
Proton sample above 80GV

16. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Protons vs. protons
Dipole components in galactic coordinates
No significant deviation from isotropy is found

17. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Protons vs. protons
Dipole upper limit in galactic coordinates
Upper limit ẟ scaled to the statistics
No significant deviation from isotropy is found
𝛿 𝑝 𝐻 𝑝 𝐿 (>80GV) < 0.3% at 95% C.L.
Significance map

18. GSE – Geocentric Solar Ecliptic coordinate system
Sez. Milano-Bicocca
Seasonal variation
Seasonal variation of the relative anisotropies is studied by dividing the period of analysis (May 2011 – Nov 2015) in seasons (4 seasons per year)
Check for possible time dependence of the signal;
Detect possible signal dependence as function of position in the heliosphere or correlation with solar activity and solar events.
GSE – Geocentric Solar Ecliptic coordinate system

19. No significant deviation from isotropy is found
Sez. Milano-Bicocca
Seasonal variation
No significant deviation from isotropy is found
Results for electrons and protons
Electrons vs. protons
[16:350]GV
Upper limit ẟ scaled to the statistics
Nov-11
May-12
Feb-13
Aug-13
May-14
Feb-15
Aug-15
Protons vs. protons
>80GV
Nov-11
May-12
Feb-13
Aug-13
May-14
Feb-15
Aug-15

20. Sez. Milano-Bicocca
Conclusions
Positron and electron angular distributions are compatible with isotropy, at all energies and both at ISS location and at magnetosphere border.
Upper limits are set on the dipole anisotropy strenght:
𝛿 𝑒 + 𝑒 − >16GV <2% at 95% C.L.
𝛿 𝑒 + 𝑝 >16GV <2% at 95% C.L.
𝛿 𝑒 − 𝑝 >16GV <0.6% at 95% C.L.
Proton sky at high rigidity is compatible with the proton distribution at low rigidity. The upper limit on dipole anisotropy is
𝛿 𝑝 𝐻 𝑝 𝐿 >80GV <0.3% at 95% C.L.
No significant seasonal variation observed in all observables.

21. Conclusions Projection of 95% upper limits on ẟ to 2024
Sez. Milano-Bicocca
Conclusions
Projection of 95% upper limits on ẟ to 2024
Current limit in e+/e-with 4.5 years of data
16 < E < 350 GeV