Cosmic-Ray Isotopic Identification with the Geomagnetic Field for Space Experiments.

Transcription

1 ICRC 11 - Beijing August 11 Cosmic-Ray Isotopic Identification with the Geomagnetic Field for Space Experiments. W. GILLARD, F. BARAO, L. DEROME

2 L The cosmic-ray diffusion: A two zone diffusion model N t = Q(r, p )+ Source D xx N VN Spatial diffusion Galactic Wind : Convection + p p D pp p 1 p N p ṗn p 3 V N N τ f N τ 1/ Energetic diffusion Reacceleration Energy losses Lost by Fragmentation Lost by decay Secondary stable nuclei : -Dxx Ns +hδ(z) nυσs Ns = hδ(z) nυσps Np Solution : N s () = N p() nυσ ps + nυσ s D xx hl Secondary-to-Primary ratio Maurin et al., ApJ 555, 596 (1), A&A 394, 139 () Maurin et al., Apj 555, 585 (1) N s N p = D xx hl nυσ ps + nυσ s BUT L and Dxx are degenerated : The uncertainties on L do not permit to constrains the diffusion coeficient Dxx=βDR δ D/L

3 The cosmic-ray diffusion: A two zone diffusion model N t = Q(r, p )+ Source D xx N VN Spatial diffusion Galactic Wind : Convection + p p D pp p 1 p N p ṗn p 3 V N N τ f N τ 1/ Energetic diffusion Reacceleration Energy losses Lost by Fragmentation Lost by decay Secondary Unstable-to-primary ratio N β N p = nυσ pβ D xx h τ + nυσ β The diffusion of secondary unstable nuclei is independent of the hallo size (assuming Dτ << L ). The Unstable nuclei are important to constrain diffusion models

4 Identifying Cosmic-Ray Isotopes Classical method to identify isotopes rely on their mass estimation : To identify isotopes on an event by event bassis, mass measurement precision (σ) should be at most 3σ < ΔM, with ΔM the difference in isotop masses Table of required resolution to perform isotopic identification Isotopes D/H 3 He/ 4 He 1 Be/ 9 Be 6 Al/ 7 Al ΔM/M % 8 % 3 % 1 % From combined measurement of velocity & rigidity: Independent measurement of the particle momentum (or rigidity) and velocity allow to estimate the mass of the incoming particle and subsequently to identify isotopes. Mc = ZR γβ σm M = σp p γ σβ β For a reliable mass estimation, both, particle momentum and velocity, must be measured with a great precision.

5 Identifying Cosmic-Ray Isotopes From their energy losses in matter : de dx = K A Z z β 1 ln m ec γ β T max I CR Energy losses in the PAMELA tracker plan - With the courtesy of the PAMELA collaboration β δ(γβ)

6 Identifying Cosmic-Ray Isotopes From their energy losses in matter : de dx K A Z z p c + M c 4 p c CR Energy losses in the PAMELA tracker plan - With the courtesy of the PAMELA collaboration When Mc is comparable to pc, the energy losses measurement permit to estimate the particle masses and separate isotopes. When Mc << pc, the energy losses turn out to be independent of the masses. Energy losses largely spread arround the average energy losses Possible missidentification

7 The Geomagnetic Filter : Principle Use of the Earth Geomagnetic field as an isotopic filter : How does it work? R < Rc R > Rc Geomagnetic field shields Earth against charged particles. R c = M B r R = mc γβ Ze cos 4 B 1+ 1 cos 3 B sin θ B sin φ B, Rigidity cutoff translate to a velocity threshold : β c = RZe mc 1 RZe mc +1

8 The Geomagnetic Filter : Principle Use of the Earth Geomagnetic field as an isotopic filter : How does it work? m1 ; β1 βc m > m1 ; β1 β Geomagnetic field shields Earth against charged particles. R c = M B r R = mc γβ Ze cos 4 B 1+ 1 cos 3 B sin θ B sin φ B, Rigidity cutoff translate to a velocity threshold : β c = RZe 1 mc RZe mc +1 At equal velocity, heavier isotope penetrates deaper. The use of the Geomagnetic field as purpose to identify isotopes was first proposed by Balassubramayan et al. (1936) et Hubert (1974).

9 The Geomagnetic Filter : Example with 1 Be, 9 Be, 7 Be 1. 1 Rigidity [GV] 1 Depending on the value of β, their is three possible case :.8.6 I) β > βc( 7 Be) II) βc( 7 Be) > β > βc( 9 Be) III) βc( 9 Be) > β > βc( 1 Be) β c.4 β c ( 7 Be). β c ( 9 Be) β c ( 1 Be) Geomagnetic Latitude [ ] Velocity threshold, calculated for normal incident particle under the Stoermer approximation assuming a dipolar geomagnetic field.

10 The Geomagnetic Filter : Example with 1 Be, 9 Be, 7 Be 1. 1 Rigidity [GV] 1 Depending on the value of β, their is three possible case :.8.6 I) β > βc( 7 Be) II) βc( 7 Be) > β > βc( 9 Be) III) βc( 9 Be) > β > βc( 1 Be) β c.4 β c ( 7 Be). β c ( 9 Be) β c ( 1 Be) Geomagnetic Latitude [ ] Velocity threshold, calculated for normal incident particle under the Stoermer approximation assuming a dipolar geomagnetic field. All isotopes are above the geomagnetic cutoff : One can not distinguish isotopes Velocity distribution expected to be measured at different latitudes Velocity distribution (Arb. Unit) B = 5º B = 55º B = 65.7º ➓+➒+➐ β ➓+➒ +➐ ➓+➒+➐

11 The Geomagnetic Filter : Example with 1 Be, 9 Be, 7 Be 1. 1 Rigidity [GV] 1 Depending on the value of β, their is three possible case :.8.6 I) β > βc( 7 Be) II) βc( 7 Be) > β > βc( 9 Be) III) βc( 9 Be) > β > βc( 1 Be) β c.4 β c ( 7 Be). β c ( 9 Be) β c ( 1 Be) Geomagnetic Latitude [ ] Velocity threshold, calculated for normal incident particle under the Stoermer approximation assuming a dipolar geomagnetic field. 7 Be is bellow the geomagnetic cutoff : Incoming Isotopes is either a 9 Be or 1 Be Velocity distribution expected to be measured at different latitudes Velocity distribution (Arb. Unit) B = 5º B = 55º B = 65.7º ➓ ➒ ➓+ ➒ ➓ ➒ β

12 The Geomagnetic Filter : Example with 1 Be, 9 Be, 7 Be 1. 1 Rigidity [GV] 1 Depending on the value of β, their is three possible case :.8.6 I) β > βc( 7 Be) II) βc( 7 Be) > β > βc( 9 Be) III) βc( 9 Be) > β > βc( 1 Be) β c.4 β c ( 7 Be). β c ( 9 Be) β c ( 1 Be) Geomagnetic Latitude [ ] Velocity threshold, calculated for normal incident particle under the Stoermer approximation assuming a dipolar geomagnetic field. 7 Be and 9 Be are bellow the geomagnetic cutoff : Incoming Isotopes is a 1 Be Velocity distribution expected to be measured at different latitudes Velocity distribution (Arb. Unit) B = 5º B = 55º B = 65.7º β

13 The Geomagnetic Filter : Example with 1 Be, 9 Be, 7 Be β c Rigidity [GV] 1 Δβ β c ( 7 Be). β c ( 9 Be) β c ( 1 Be) Geomagnetic Latitude [ ] Velocity threshold, calculated for normal incident particle under the Stoermer approximation assuming a dipolar geomagnetic field. Only a small fraction of Isotope can be identified. Depending on the value of β, their is three possible case : I) β > βc( 7 Be) II) βc( 7 Be) > β > βc( 9 Be) III) βc( 9 Be) > β > βc( 1 Be) Velocity distribution (Arb. Unit) B = 5º B = 55º B = 65.7º Δβ β

14 The Geomagnetic Filter : Flux reconstruction The number of event in each bin of energy ΔN = ΔE ε D ε B ε f dt εd = Acc ε Detection efficiency εb Cutoff efficiency εf Geomagnetic filter efficiency I) β > βc( 7 Be) II) βc( 7 Be) > β > βc( 9 Be) III) βc( 9 Be) > β > βc( 1 Be) Estimation of the flux : I(E) ; II(E) ; III(E) The flux for each isotopes can be reconstructed using : Φ 1Be (E) = Φ III (E) Φ 9Be (E) = Φ II (E) - Φ III (E) Φ 7Be (E) = Φ I (E) - Φ II (E) Selection Efficiency Geomagnetic filter efficiency estimated for space experiment with 6º orbit inclination. Geomagnetic field was modeled with the IGRF model. I) β > βc(7be) II) βc(7be) > β > βc(9be) III) βc(9be) > β > βc(1be) Kinetic energy [GeV/nuc]

15 Conclusion We presented a method using the Geomagnetic field shielding property to filter isotopes from cosmic radiation. The method was presented under the dipolar and Stoermer approximations. Method based on a realistic Geomagnetic filed, accounting for the penumbra is under study. Method is well adapted to space born experiment which explore region of different geomagnetic cutoff 5% to 1% of the 1 Be could be identified up to an energy of 1 GeV/n. This method only rely on the velocity measurment of incoming nuclei Δβ c Geomagnetique Latitude [ ] 5 4 β c ( 1 H)-β c ( H) β c ( 3 He)-β c ( 4 He) β c ( 7 Be)-β c ( 9 Be) β c ( 9 Be)-β c ( 1 Be) PAMELA-ToF AMS-RICH 3 AMS-ToF β c ( 13 C)-β c ( 14 C) β c ( 6 Al)-β c ( 7 Al) β c ( 36 Cl)-β c ( 37 Cl) β c ( 54 Mn)-β c ( 55 Mn) 1 1 Rigidity [GV]

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17 Side Slides

18 The cosmic-ray diffusion: A two zone diffusion model N t = Q(r, p )+ Source D xx N VN Spatial diffusion Galactic Wind : Convection + p p D pp p 1 p N p ṗn p 3 V N N τ f N τ 1/ Energetic diffusion Reacceleration Energy losses Lost by Fragmentation The thin disk model : A simplified geometry - Thin gas disk (h) - Thin source disk (h) - Thick diffusion hallo (L>>h) Steady state assumption - N/ t = Plain diffusion - No convection : V = - No reacceleration : D pp = - Neglect energy losses Lost by decay

19 The cosmic-ray diffusion: A two zone diffusion model N t = Q(r, p )+ Source D xx N VN Spatial diffusion Galactic Wind : Convection + p p D pp p 1 p N p ṗn p 3 D xx hl D xx hl V N N τ f N τ 1/ Energetic diffusion Reacceleration Energy losses Lost by Fragmentation Primary stable nuclei : -Dxx Np +hδ(z) nυσp Np = hδ(z) Q Solution : Q() N p () = + nυσ p Secondary stable nuclei : -Dxx Ns +hδ(z) nυσs Ns = hδ(z) nυσps Np Solution : N s () = N p() nυσ ps + nυσ s Secondary-to-Primary ratio Lost by decay N s N p = D xx hl nυσ ps + nυσ s

20 The cosmic-ray diffusion: Secondary-to-primary ratio Secondary-to-primary flux ratio (e.g. B/C) constrains diffusion parameters L, Dxx, Vc, VA. Maurin et al., ApJ 555, 596 (1) A&A 394, 139 () L BUT L and Dxx are degenerated : Maurin et al., Apj 555, 585 (1) The uncertainties on L do not permit to constrains the diffusion parameters Dxx=βDR δ D /L

21 The cosmic-ray diffusion: Secondary unstable-to-primary ratio N t = Q(r, p )+ Source D xx N VN Spatial diffusion Galactic Wind : Convection + p p D pp p 1 p N p ṗn p 3 V N N τ f N τ 1/ Energetic diffusion Reacceleration Energy losses Lost by Fragmentation Secondary unstable nuclei : Lost by decay -Dxx Nβ +hδ(z) nυσ Nβ +Nβ/τ 1/ = hδ(z) nυσ Np Solution : N β () = N p() nυσ pβ D xx h τ + nυσ β Secondary Unstable-to-primary ratio N β N p = nυσ pβ D xx h τ + nυσ β The diffusion of secondary unstable nuclei is independent of the hallo size (assuming Dτ << L ).

22 Identifying Cosmic-Ray Isotopes From combined measurement of velocity & rigidity: Independent measurement of the particle momentum (or rigidity) and velocity allow to estimate the mass of the incoming particle and subsequently to identify isotopes. Mc = ZR γβ For a reliable mass estimation, both, particle momentum and velocity, must be measured with a great precision. σm M = σp p γ σβ β

23 Geomagnetic field Interne : modélisé par IGRF App. Dipolaire Stable dans le temps Externe : modélisé par Ts4 Déformé par la pression du vent solaire Dominant pour R > RT Très variable.

24 Geomagnetic field

25 Geomagnetic field

26 Geomagnetic field Rc Rc The penumbre structure is differents depending on the geomagnetic field models and it turn out to be more and more complicates at high geomagnetic latitude.