Modeling heavy neutral atoms traversing the heliosphere

1. Hans-Reinhard Müller1,2 & Jill Cohen1 1 Department of Physics and Astronomy Dartmouth College, Hanover NH, USA 2 CSPAR, University of Alabama, Huntsville, USA Modeling heavy neutral atomstraversing the heliosphere NESSC UNH 15 Nov 2011 Acknowledgements to colleagues: Maciej Bzowski3, Vladimir Florinski2, Eberhard Möbius4, Gary Zank2, NASA5 3 Space Research Centre, Polish Academy of Sciences, Warsaw, PL 4 SSC, University of New Hampshire, Durham, USA 5NNX10AC44G, NNX10AE46G, NNX11AB48G, NNG05EC85C

2. Motivation Secondary neutral oxygen revealed in IBEX-Lo spring measurements Presence of secondary helium component is hinted at when analyzing the helium flow focusing cone Secondary particles are produced in neutralizing charge exchange collisions of a helium (oxygen) ion somewhere in the heliosphere. Ion source is ISM or solar wind plasma. Assuming that the global heliospheric plasma distribution is known, one still needs to know the neutral distributions to calculate the production rates of secondary neutrals. -> Task: Develop efficient calculator for secondary neutral PSD -> Solution:Analytic reverse trajectory calculator As precursor, develop, use, and explore same method to calculate the primary neutral PSD

3. The Sun’s attractive central potential ensures that every point in the heliosphere can be reached in two ways by a “cold” interstellar helium neutral with interstellar velocity -26.3 km/s. Path 1: direct Path 2: indirect Operational definition: Direct path is shorter than indirect path. e: orbital eccentricity Trajectories of primary ISM helium: Direct and indirect paths indirect path e= 3.3, yISM = +4 AU sun direct path e=26.6 yISM = -34 AU Unknowns to solve for:Impact parameter yISM and(vx, vy) at point of interest; can be calculated with analytical formula | Example: ISM from right in –x direction Point of interest: (x= -50AU, y= -30AU)

4. The movement (=trajectory) of heavy neutral particles in the heliosphere is describable as Kepler orbit, as the force acting on it is a central force (solar gravity, minus outward radiation pressure). • The trajectory is confined to a plane. • In the case of helium and heavier species, radiation pressure negligible and the central potential is time independent. (For H and D, the radiation pressure becomes important, which is time- and velocity dependent.) • => there are conserved quantities constant along the entire trajectory, namely: • Total energy=kinetic+potential • Angular momentum • Direction of perihelion • Eccentricity e • The latter two are sometimes combined into an eccentricity vector A(cf. Laplace-Runge-Lenz vector). Method: Keplerian trajectories

5. Direct and indirect paths Point of interest: X = -1.0 Y = +1.7

6. primary He PSD at (-0.5,+0.87) indirect phase space density f, normalized so that peak f in ISM is one. Only f > 0.001 are shown. direct Slice (@vz=0) through the 3D helium velocity distribution function at x=-0.5AU, y=+0.87 AU, with ISM He at -26.3 km/s, 7000 K.

7. indirect vy-vz slice direct vy-vz slice vx-vy slice through the 3D helium velocity distribution function at x=-0.5AU, y=+0.87 AU

8. PSD at (-1,-1): indirect He

9. Calculation method • Multiple uses conserved quantities: • Determining peak of PSD. Position of peak in velocity space can be calculated instantly. Typically, there are two solutions: “direct” and “indirect” path. A warm ISM Maxwellian => 2 peaks in PSD at r. Close to downwind symmetry axis, 2 PSD effectively merge. • Backtracking. Calculate entire primary PSD: Investigate all velocities v in vicinity of peaks. Single-step calculation to give f0, the phase space density at (r, v) without losses included. • Photoionization losses. A one-step calculation gives loss of helium due to photoionization; the answer depends essentially only on the position angle with respect to perihelion. • Charge exchange losses. Charge exchange with ions derived from background MHD requires trajectory calculation; resolution matches the MHD grid.

10. Loss processes for primary helium … on their path from the interstellar medium to the innermost heliosphere. The dominant loss process is photoionization.; He + ν→ He+ 1AU rate: β1 ~ 10-7 s-1→ elsewhere, rate: βph= β1 (1AU / r)2 Next are charge exchange losses, in order of dominance (Bzowski 2010, 2011): He + He++→ He++ + He double charge exchange – large cross section; dominant in the supersonic solar wind where there are ample α particles. He + He+→ He+ + He simple helium charge exchange; dominant in the interstellar medium region where there is ample He+ He + p → He+ + H helium-proton charge exchange with ubiquitous plasma protons everywhere

11. primary He PSD at (-0.5,+0.87) PSD if no losses accounted for PSD if no losses accounted for x=-0.5AU, y=+0.87 AUISM He at -26 km/s, 7000 K

12. primary He PSD at (-0.5,+0.87) PSD if no losses accounted for PSD with ch. ex. losses x=-0.5AU, y=+0.87 AUISM He at -26 km/s, 7000 K

13. primary He PSD at (-0.5,+0.87) PSD if no losses accounted for PSD with photoioniz. losses x=-0.5AU, y=+0.87 AUISM He at -26 km/s, 7000 K

14. primary He PSD at (-0.5,+0.87) PSD if no losses accounted for PSD with all losses x=-0.5AU, y=+0.87 AUISM He at -26 km/s, 7000 K

15. Charge exchange loss Photoionization loss PSD

16. along upwind symmetry axis:Helium PSD at (200, 0) vx - vy vy - vz Slices through the helium PSD at a point upwind of the heliopause. The slices are parallel to two different velocity coordinate planes, through maximum of PSD. At this location, the He PSD is a 3D Maxwellian centered on vx = -27 km/s.

17. Locations of PSD shown next heliopause Termination shock

18. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

19. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

20. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

21. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

22. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

23. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

24. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy

25. PHYSICS OF PSD RING ON SYMMETRY AXIS

26. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

27. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

28. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

29. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

30. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

31. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

32. primary He PSD at a point with r=2AU distance vx - vy DIRECT PSD INDIRECT PSD vz - vy • WITH LOSSES INCLUDED

34. Helium PSD at (-200, 0) vx - vy vy - vz vy - vz Far downstream, the preferred perpendicular velocity is smaller, creating a 3D PSD as a cross between a torus and a Maxwellian.

35. no loss INTEGRATED PSD DIRECT-only • NUMBER DENSITY in interstellar units with losses

36. no loss INTEGRATED PSD DIRECT-only • NUMBER DENSITY in interstellar units with losses

37. no loss INTEGRATED DIRECT and INDIRECT PSD • NUMBER DENSITY in interstellar units with losses

38. no loss with losses INTEGRATED PSD DIRECT – only INTEGRATED DIRECT and INDIRECT PSD • VX VELOCITY in km/s

39. no loss INTEGRATED PSD DIRECT – only with losses • TEMPERATURE in K

40. Time dependent heliosphere • The PSD function of primary neutrals can be established at any arbitrary point (x,y,z) in the heliosphere in this way; moments can be calculated easily. • This holds for particles for which radiation pressure is time-independent, or zero outright. • The good news is that the trajectories (shape etc) are not changed by a time-dependent MHD background nor by a time-dependent photoionization rate – only the PSD are time-dependent then, and the loss computations need a higher level of house-keeping.

41. Secondary neutrals; further steps Similar to loss of primary helium, secondary helium is produced by charge exchange of neutral partners with He++ or He+ ions. Estimates pinpoint bow-shock decelerated interstellar He+as dominant source for secondary helium in the heliosphere. Production terms of secondary neutral He due to charge exchange can be calculated at each point; for this, primary PSD needs to be known throughout the heliosphere. With production terms, the PSD of secondary neutral He can be calculated for each arbitrary point in the heliosphere, with Keplerian methods paralleling those from above. Both primary and secondary PSD can for example be converted to fluxes at IBEX, and compared with measurement to constrain ISM parameters.

42. Filtration • Aside on the definition of filtration: • Preferred definition for purpose of measurements, boundary conditions for other theoretical studies, etc: • filtration = nHe@1AU / nHe∞ • (nHe∞ = number density of neutral helium in pristine LISM) • However, consider: • nHe@1AU consists of several distinct particle populations: • primary ISM neutrals • secondary ISM neutrals • a small contribution of secondary SW neutrals • Primary: He from pristine LISM, going through heliosphere to 1 AU while suffering losses due to photoionization, charge exchange, e- impact. • Secondary: He+ from pristine LISM, undergoing neutralizing charge exchange and then going to 1 AU while suffering losses. • SW: Solar Wind He++ undergoing neutralizing charge exchange (in the heliosheath?) to be directed back to 1 AU, while suffering losses.

43. Conclusions • Kepler orbit equations are a very efficient way to calculate primary interstellar heavy neutrals throughout the heliosphere. Can be used for transport calculations to/from pristine ISM; source terms for secondary neutrals. • In contrast to high-energy H, heavy atoms (helium upwards) are not proceeding on straight lines in the inner heliosphere in energy ranges that IBEX measures. • Helium PSD (and similarly, O) can be characterized throughout the heliosphere. In the innermost heliosphere, even direct-path PSD becomes quite unlike a Gaussian. • The PSD near the downwind symmetry axis (including in the focusing cone) are special.