modeling heavy neutral atoms traversing the heliosphere

Modeling heavy neutral atomstraversing the heliosphere

Hans-Reinhard Müller1,2 & Jill Cohen1

1 Department of Physics and Astronomy Dartmouth College, Hanover NH, USA2 CSPAR, University of Alabama, Huntsville, USA

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, PL4 SSC, University of New Hampshire, Durham, USA5 NNX10AC44G, NNX10AE46G, NNX11AB48G, NNG05EC85C

MotivationSecondary 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.

Path 1: directPath 2: indirect

Operational definition: Direct path is shorter than indirect path.

e: orbital eccentricity

direct pathe=26.6yISM = -34 AU

sun

indirect pathe= 3.3,yISM = +4 AU

|

Example: ISM from right in –x directionPoint of interest: (x= -50AU, y= -30AU)

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

Method: Keplerian trajectories

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 eThe latter two are sometimes combined into an eccentricity vector A(cf. Laplace-Runge-Lenz vector).

Direct and indirect pathsPoint of interest:X = -1.0Y = +1.7

primary He PSD at (-0.5,+0.87)

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.

4

2

24

4

2 2 4

phase space density f, normalized so that peak f in ISM is one.Only f > 0.001 are shown.

indirect

direct

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

indirect

direct

vy-vz slice

vy-vz slice

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

Calculation methodMultiple 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


PSD if no losses accounted for

x=-0.5AU, y=+0.87 AUISM He at -26 km/s, 7000 K





PSD with ch. ex. losses




PSD with photoioniz. losses




PSD with all losses

PSD

Charge exchange loss Photoionization loss

along upwind symmetry axis:Helium PSD at (200, 0)

vx - vy vy - vz

vx

vy

-40 -30 -20 -10-20

-15

-10

-5

0

5

10

15

20

f1

0.1

0.01

0.001

(x=200, y=0)

vz

vy

-20 -10 0 10 20

-15

-10

-5

0

5

10

15

20f

1

0.1

0.01

0.001

(x=200, y=0)

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.

Locations of PSD shown next

Termination shock

heliopause

primary He PSD at a point with r=2AU distance

vx -

vy

vz -

vy

DIR

EC

T P

SD

IND

IRE

CT

PS

D

PHYSICS OF PSD RING ON SYMMETRY AXIS

primary He PSD at a point with r=2AU distance

vx -

vy

vz -

vy

DIR

EC

T P

SD

IND

IRE

CT

PS

D

WITH LOSSES INCLUDED

Helium PSD at (-200, 0)

vx - vy vy - vz

Far downstream, the preferred perpendicular velocity is smaller, creating a 3D PSD as a cross between a torus and a Maxwellian.

vy - vzvx

vy

-40 -30 -20 -10

-20

-15

-10

-5

0

5

10

15f

1

0.1

0.01

0.001

(x=-200, y=0)

vzv

y-20 -10 0 10 20

-15

-10

-5

0

5

10

15

20f

1

0.1

0.01

0.001

(x=-200, y=0)

INT

EG

RA

TE

D P

SD

D

IRE

CT

-on

ly

NU

MB

ER

DE

NS

ITY

in in

terstellar un

its

no

loss

with

losses

INT

EG

RA

TE

D D

IRE

CT

an

d I

ND

IRE

CT

PS

D

NU

MB

ER

DE

NS

ITY

in in

terstellar un

its

no

loss

with

losses

INTEGRATED PSD DIRECT – only

VX VELOCITY in km/s

no

loss

with

losses

INTEGRATED DIRECT and INDIRECT PSD

INT

EG

RA

TE

D P

SD

D

IRE

CT

– o

nly

TEMPERATURE in K

no

loss

with

losses

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.

Time dependent heliosphere

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.

Secondary neutrals; further steps

FiltrationAside 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.

modeling heavy neutral atoms traversing the heliosphere

Documents

case of helium

helium flow

neutral distributions

helium oxygen ion

velocity space

interstellar velocity

velocity dependent

x directionpoint