Modeling heavy neutral atoms
traversing the heliosphere
Hans-Reinhard Müller1,2 & Jill Cohen1
1
Department of Physics and Astronomy
Dartmouth College, Hanover NH, USA
2
CSPAR, University of Alabama, Huntsville, USA
NESSC
Acknowledgements to colleagues:
UNH
Maciej Bzowski3, Vladimir Florinski2,
Eberhard Möbius4, Gary Zank2, NASA5
15 Nov 2011
3
Space Research Centre, Polish Academy of Sciences,
Warsaw, PL
4
SSC, University of New Hampshire, Durham, USA
5
NNX10AC44G, NNX10AE46G, NNX11AB48G,
NNG05EC85C
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
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.
indirect path
e= 3.3,
yISM = +4 AU
sun
direct path
e=26.6
yISM = -34 AU
|
Example: ISM from right in –x direction
Point of interest: (x= -50AU, y= -30AU)
Path 1: direct
Path 2: indirect
Operational definition: Direct path
is shorter than indirect path.
e: orbital eccentricity
Unknowns to solve for:
Impact parameter yISM and
(vx, vy) at point of interest; can
be calculated with analytical
formula
Trajectories of primary ISM helium: Direct and indirect paths
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
Direct and indirect paths
Point of
interest:
X = -1.0
Y = +1.7
indirect
phase space density
f, normalized so that
peak f in ISM is one.
Only f > 0.001 are
shown.
4
2
direct
2
4
primary He PSD at (-0.5,+0.87)
4
2
2
4
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.
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
PSD at (-1,-1): indirect He
Calculation method
Multiple uses conserved quantities:
(1) 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.
(2) 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.
(3) 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.
(4) Charge exchange losses. Charge exchange with ions derived from
background MHD requires trajectory calculation; resolution matches the MHD
grid.
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
primary He PSD at (-0.5,+0.87)
PSD if no losses accounted for
x=-0.5AU, y=+0.87 AU
ISM He at -26 km/s, 7000 K
PSD if no losses accounted for
primary He PSD at (-0.5,+0.87)
PSD if no losses accounted for
x=-0.5AU, y=+0.87 AU
ISM He at -26 km/s, 7000 K
PSD with ch. ex. losses
primary He PSD at (-0.5,+0.87)
PSD if no losses accounted for
x=-0.5AU, y=+0.87 AU
ISM He at -26 km/s, 7000 K
PSD with photoioniz. losses
primary He PSD at (-0.5,+0.87)
PSD if no losses accounted for
x=-0.5AU, y=+0.87 AU
ISM He at -26 km/s, 7000 K
PSD with all losses
Charge exchange loss
Photoionization loss
PSD
along upwind symmetry axis:
Helium PSD at (200, 0)
(x=200, y=0)
(x=200, y=0)
20
20
f
15
1
f
1
15
10
10
0.1
0.1
vy
vy
5
0
0.01
5
0.01
0
-5
-5
-10
0.001
0.001
-10
-15
-15
-20
-40
-30
-20
vx
vx - vy
-10
-20
-10
0
10
20
vz
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.
heliopause
Termination shock
Locations of PSD shown next
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
primary He PSD at a point with r=2AU distance
PHYSICS OF PSD RING ON SYMMETRY AXIS
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
vx - vy
vz - vy
DIRECT PSD
INDIRECT PSD
WITH LOSSES INCLUDED
primary He PSD at a point with r=2AU distance
Helium PSD at (-200, 0)
(x=-200, y=0)
15
(x=-2
20
f
1
10
15
5
10
0
vy
vy
0.1
0.01
-5
-10
5
0
-5
0.001
-15
-10
-20
-15
-40
vx - vy
-30
-20
vx
-10
-20
vy - vz
-10
0
vz
vy 10
- vz
Far downstream, the preferred perpendicular velocity is smaller, creating a 3D PSD as a
cross between a torus and a Maxwellian.
20
with losses
NUMBER DENSITY in interstellar units
INTEGRATED PSD
DIRECT-only
no loss
with losses
NUMBER DENSITY in interstellar units
INTEGRATED PSD
DIRECT-only
no loss
INTEGRATED DIRECT
and INDIRECT PSD
with losses
NUMBER DENSITY in interstellar units
no loss
no loss
with losses
INTEGRATED PSD
DIRECT – only
INTEGRATED DIRECT
and INDIRECT PSD
VX VELOCITY in km/s
with losses
INTEGRATED PSD
DIRECT – only
no loss
TEMPERATURE in K
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.
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.
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.
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.