Database for Imaging and Transport with Energetic Neutral Atoms (ENAs)

Transcription

1 Database for Imaging and Transport with Energetic Neutral Atoms (ENAs) Nicholas Lewkow Harvard-Smithsonian Center for Astrophysics University of Connecticut April 26, 213 Collaborators Vasili Kharchenko [1,2] Peng Zhang [3] Marko Gacesa [4] Brad Snios [2] Michael Winder [2] Daniel Violette [2] Joshua Squires [2] [1] Harvard-Smithsonian CfA [2] University of Connecticut [3] Duke University [4] Max Planck Institute

2 Introduction Energetic neutral atoms (ENAs) are significantly more energetic than local thermal environment Planetary atmosphere E.1 ev Local interstellar cloud E.1 ev Local interstellar bubble E 1 ev ENAs result from charge exchange (CX) collisions between hot ions and neutral gases Produced in any environment with hot plasma and cold gas Solar wind (SW) ions Magnetospheric ions Earth ENAs Mars ENAs (Brandt et al., 25) (Brinkfeldt, et al., 25) Titan ENAs (Brandt et al., 25)

3 Introduction IBEX full sky map (McComas et al., 29) ENAs offer a way to image space plasmas No interaction with magnetic fields Plasma velocity during creation is maintained through ENAs ENAs may be a large source of energy deposition in astrophysical environments Precipitation of ENAs in planetary atmospheres induce atomic escape fluxes Parameters needed for accurate modeling Energy transfer/relaxation rates Collision induced emissions and reactions Production rates of secondary hot atoms (SHAs) Transport/thermalization rates Energy balance in astrophysical systems Accurate quantum mechanical (QM) cross sections needed to study interaction between ENAs and astrophysical environments

4 Atomic Collisions: Database Database for atomic/molecular collisions in astrophysical environments Energy relaxation governed by collisional dynamics Require energy-angular dependent cross sections Collision energy.1 ev-1 kev Inelastic channels not considered in current energy interval Current QM elastic atom-atom cross sections H+H e Number of Partial Waves e H+H CM Collision Energy [ev] Number of partial waves needed for convergence of scattering amplitude f(θ) Asymptotic wavefunction Scattering Amplitude DCS ψ(r ) e ikz +f(θ) eikr f(θ) = 1 (2l+1)e iδ dσ l sin δ l P l (cos θ) r k dω = f(θ) 2 l=

5 Atomic Collisions: Differential Cross Sections Differential Cross Section [a 2 ] e.5 kev (x1) 1.5 kev (x1) 5. kev Differential Cross Section [a 2 ] kev (x1) 1.5 kev (x1) 5. kev Lab Scattering Angle [deg] Expt: Nitz et al. (1987) QM cross sections compared with available laboratory data Semi-classical Eikonal method also compared with QM results δ(ρ) = 1 ( ) U ρ2 + z 2 v 2 dz [ ] f(θ) = ik e 2iδ(ρ) 1 J (kθρ)ρ dρ Lab Scattering Angle [deg] Expt: + Gao et al. (1989) o Newman et al. (1986) Differential Cross Section [a 2 ] kev.5 kev (x1) 1. ev 1.5 kev (x1) Lab Scattering Angle [deg] Expt: + Smith et al. (1996) o Schafer et al. (1987)

6 Atomic Collisions: Total Cross Sections Total elastic cross section σ EL(E) Cross sections available for several small energy intervals No cross sections available over entire interval mev - kev σ EL(E) = f(θ, E) 2 dω Total diffusion cross section σ DF (E) Useful for energy-momentum transfer without solving Boltzmann equation σ DF (E) = f(θ, E) 2 (1 cos θ) dω Total Cross Section [a 2 ] He+ 3 He 4 He+ 3 He He+ 4 He H+H CM Collision Energy [ev] Diffusion Cross Section [a 2 ] e H+H CM Collision Energy [ev]

7 Atomic Collisions: Probability Densities Probability Density Normalized Cumulative Probability ρ(e, θ) = 2π sin θ f(e, θ) 2 σ(e) π ρ(e, θ) dθ = 1 P (E, θ) = θ ρ(e, θ ) dθ Scattering Angle (deg) e Collision Energy (ev) P (E,θ) deg collisions.5 deg 5. kev 1.5 kev.5 kev.12 deg Lab Scattering Angle [deg] P (E,θ) Extremely forward peaked! Several collisions to thermalize Very little momentum transferred per collision

8 Atomic Collisions: Thermalization Average Energy Loss Per Collision [ev] e H+H Collision Energy [ev] < δe >= E 2mpmt (m p + m t) 2 Number of Collisions ( ) σdf (E) σ EL(E) H+H e Final Energy [ev] N (E i, E f ) = Ei E f de < δe >

9 Atom-Molecule Collisions Model Martian Atmosphere Many atmospheres have significant molecular constituents Accurate QM atom-molecule cross sections extremely difficult to calculate Complex potential surfaces Lots of scattering channels Empirical scaling methods may be used for unknown atom-atom, atom-molecule collisions Krasnopolsky, 22.

10 Atom-Molecule Collisions: Reduced Coordinates Lewkow et al., 212. Reduced energy coordinates ρ = θ sin θ f(e, θ) 2 τ = Eθ Reduced velocity coordinates ρ = θ sin θ f(e, θ) 2 τ = Eθ µ Universal amplitude fit f(e, θ) 2 = exp [ A (log τ) 2 + B log τ + C ] θ sin θ A =.13 B = 1. C = 2.7

11 Atom-Molecule Collisions: Universal Amplitude Scaled atom-molecule cross sections O+CO 2 collision 1.5 kev lab frame θ sin θ f(e,θ) 2 [deg a 2 ] Quantum He+X O+CO 2 H+O 2 Universal Amplitude Differential Cross Section [a 2 ] Expt (Smith et al., 1996) Universal Amplitude E θ / µ [ev deg/u] CM Scattering Angle [deg] Atom-molecule cross sections require a scaling of ρ to match atom-atom cross sections and the universal amplitude curve ρ(e, θ) ρ(e, θ) λ where λ = 1.4

12 ENA Production Simple models used No magnetic SW streamlines used No SW ion energy loss J sw(r) = N swu sw R 2 R 2 exp Solar wind flux density ( i R σ cx i n i(r ) dr ) N sw Ion density at R u sw SW velocity at R σ cx CX cross section n neutral density 1 Interstellar Medium ENA production rate q(r) = J sw(r) i 12 σi cx n i(r) Martian Atmosphere Distance from Sun [AU] Helium Hydrogen ENA Production [cm -3 s -1 ] Target gas: H and He Homogeneous distribution Altitude [km] Hydrogen Helium ENA Production [cm -3 s -1 ] Target gas: H, He, O, and CO 2 Non-homogeneous distribution

13 Transport: Martian Atmosphere Monte Carlo transport 1 ENA Created SHA Created ENA Escape Thermalize ENA Created Percentage of Ensemble Solar Zenith Angle [deg] 2 Escape Thermalize Thermalization height Altitude [km] Altitude [km] Normalized Frequency x Average Energy Loss per Collision [ev] 1 6 particle ensemble collisions to thermalize 2 SHAs created per ENA

14 Transport: Interstellar Medium Local bubble T = 1 6 K (86 ev) Low density, 95% ionized Local clouds T = 6 K (.5 ev) High density, 25% ionized ENAs may have large displacements during thermalization Helium ENAs thermalize faster than hydrogen ENAs More energy transferred per collision Vergley et al., (21) Frisch et al., (211) 12 ENA Energy [ev] Log 1 Percent Ensemble Number of Collisions x H He Distance from Star [LY] Displacement [LY] Energy [ev]

15 Conclusions ENAs offer a way to image remote space plasmas Accurate modeling of interactions between ENAs and astrophysical environments requires angular-energy dependent cross sections Database of QM atomic collisions H+H e Collision energies.1 ev - 1 kev Empirical model for unknown atom-molecule collision developed Newly computed database used in transport of ENAs in interstellar medium and Martian atmosphere Forward peaked QM cross sections require several collisions and large displacements before thermalization