Ionization rates, radiation pressure, and ENA survival probabilities

1
Ionization rates, radiation pressure, and ENA
survival probabilities

• M. Bzowski
• Space Research Centre PAS
• Warsaw, Poland

2
ENA Transmission Function

• Interpretation of detected ENA needs
  determination of the creation site, energy
  change, and attenuation of flux.
• Energy change and trajectory deflection affected
  by solar gravity and solar radiation pressure
• Attenuation ionization processes, dependent on
  heliospheric conditions and on the trajectory

3
ENA transmission function
Transmission function w is calculated from
Energy change needs solving of equation of
motion backwards in time, from detection site to
creation site
Effective force is modified by solar radiation
pressure, which is a function of the
line-integrated solar flux Itot, and of radial
velocity of atoms vr. Itot is a function of
heliolatitude ? and it fluctuates in time.
Since ionization rate is also a function of
trajectory, also calculation of w requires
solving of equation of motion.
Hence solving of equation of motion must be done
numerically.
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Radiation pressure factor ?
Solar Ly-alpha profile is variable during solar
cycle line-integrated flux is the sole parameter
to determine the profile.
Tobiska et al., SOLAR 2000
Lowest-energy H ENA atoms above IBEX detection
threshold (50 km/s) most sensitive to
vr-dependent radiation pressure.
Model based on Lemaire et al., 2002
Since IBEX observes atoms at vr 0, potentially
all H atoms affected.
5
Radiation pressure factor ? function form
Profiles of ? are fitted to full-disk
observations by Lemaire et al. The function form
and its numerical parameters are the following

• Source
• Tarnopolski, S., Thesis, Space Research Centre
  PAS 2008
• Tarnopolski, S., Bzowski, M. 2007, Neutral
  interstellar hydrogen in the inner heliosphere
  under influence of wavelength-dependent solar
  radiation pressure, submitted to AA,
  astro-ph/0701133 v1
• Bzowski, M. 2008, Survival probability and
  energy modification of hydrogen Energetic Neutral
  Atoms on their way from the termination shock to
  Earth orbit, Astron. Astrophys., in press DOI
  10.1051/0004-6361200809393 (astro-ph/0801.2190
  v3)

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Net Ly-? flux Itot
and most probably a function of heliolatitude
Is a strongly variable function of time
Itot in polar plot (solid line at 1 AU and
beyond)
Auchere, 2005
Itot as a function of heliolatitude ?,
approximated by
Tobiska et al., SOLAR 2000
Currently modeled as sine cosine series
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Energy modifications
Energy change between source region and IBEX are
mild, except for the lowermost channels
Relatively weak modulation in energy as a
function of heliolatitude due to Itot(?)
Solid trajectories close to ecliptic
Broken trajectories from poles
solar max.
solar min.
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Survival probability (transmission function)
Expected number of Poisson counts during nominal
mission from 100 to 1300 (Prested et al.
2008) hence desired accuracy of transmission
function from 10 in ecliptic to 2 at poles.
Local ionization rate a sum of charge exchange,
EUV, and electron impact.
All three ionization rates variable in time and
functions of heliolatitude.
Charge exchange additionally a function of
relative speed between ENA and solar wind.
From head-on collision at TS, geometry changes to
side-collision just prior detection, i,e. vrel
changes from vENA vSW to (vENA2 vSW2)1/2.
Survival probability is a function of location in
Earth orbit (month) due to the inclination of
ecliptic to solar equator and latitudinal
anisotropy of the ionization rate.
Additionally, it is a function of the ENA energy
at 1 AU, and of the heliolatitude of the look
direction.
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Heliospheric conditions
Solar wind speed assumed to be purely radial,
invariable with solar distance, two-modal slow
in an equatorial band, fast beyond.
Equatorial speed will be modeled using OMNI.
Currently a sine cosine series.
Polar speed assumed to be constant in time, equal
to the values measured by Ulysses.
Solar wind proton density assumed to feature a
similar latitude profile as speed (inverted)
falls off with distance as 1/r2. Equatorial
values from OMNI time dependence approximated
by sine cosine series.
Additionally, some north-south asymmetry, both in
speed and density, added in agreement with
Ulysses (McComas et al. 2000).
Boundaries of the slow-wind band assumed to
evolve in time, as measured from Ly-? groove
observations and correlated with coronal holes
boundaries. A model of evolution of boundaries,
based on SOLAR 2000, adopted temporarily.
Electrons treated separately density adopted as
SW proton density 4 alpha content
temperature profiles as Ulysses measured in the
slow and fast wind regimes. Hence latitudinal
profile of electron-impact rate correlates with
charge exchange.
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Heliospheric conditions contd
Charge exchange rate proportional to speed and
density,depends on energy
Photoionization rate treated similarly as Itot.
Probably, also features latitudinal anisotropy,
though details poorly known. Currently, adopted
as spherically symmetric, from SOLAR 2000.
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Survival probability dependence on ?
Transmission function depends on radiation
pressure directly because it affects exposure
time to ionization. For time-invariable Itot and
low energy H ENA, survival probability of ENA
detected at a given energy is higher than those
registered at the same energy for low Itot. This
is because the exposure time for solar max
conditions is lower, because ENA are heavily
braked only a few months prior detection.
Itot max/Itot min survival probability ratio
Poisson limit
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Survival probability (various effects)
Various effects affect the transmission function,
but most of them exceed the Poisson limit of 10
only at small energies. Farthest-reaching are
photoionization and fluctuations due to
fluctuations of solar wind and EUV radiation.
photoionization
Role of fluctuations of heliospheric parameters
electron-impact
Poisson limit
Cx cross-section uncertainty
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Survival probability seasonal effects
Depending on the IBEX position wrt solar equator
(7.25?), the arrival direction of ENA, and the
heliolatitude range of slow-wind region (?25?),
the transmission function will vary for identical
ENA velocities at the source region in a yearly-
and solar-cycle sequence.
Exact variations in the slow/fast wind boundaries
(shape, ramp steepness, variations with
longitude) unknown. Key parameter length of the
line of sight in the slow wind region.
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Survival probability yearly modulation in polar
values
Yearly modulation of the transmission function
occurs due to changing in position of IBEX with
respect to the boundaries of the slow-wind
region. Estimated Poisson limit for 1 month of
observations 10. Hence should be observable
only close to solar minimum and only in
lowest-energy channels (lt 0.107 keV).
0.01 keV
0.015 keV
solar min
0.029 keV
0.107 keV
0.209 keV
5.9 keV
North- and south-pole modulations anticorrelate.
solar min
solar max
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Survival probability latitudinal modulation
Latitudinal modulation of survival probability
(as a function of heliolatitude of line of sight)
maximum of the effect expected for solar
minimum conditions. Profiles change with the
position of IBEX around the Sun.
This effect strongly depends on the (poorly
known) latitudinal profile of the solar wind.
Amplitude is a strong function of the range of
the slow-wind band.
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Survival probability latitudinal modulation
Latitudinal modulation of survival probability
(as a function of heliolatitude of line of sight)
maximum of the effect expected for solar
minimum conditions. Profiles change with the
position of IBEX around the Sun.
This effect strongly depends on the (poorly
known) latitudinal profile of the solar wind.
Amplitude is a strong function of the range of
the slow-wind band.
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Survival probability latitudinal modulation
Latitudinal modulation of survival probability
(as a function of heliolatitude of line of sight)
maximum of the effect expected for solar
minimum conditions. Profiles change with the
position of IBEX around the Sun.
This effect strongly depends on the (poorly
known) latitudinal profile of the solar wind.
Amplitude is a strong function of the range of
the slow-wind band.
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Survival probability latitudinal modulation
Latitudinal modulation of survival probability
(as a function of heliolatitude of line of sight)
maximum of the effect expected for solar
minimum conditions. Profiles change with the
position of IBEX around the Sun.
This effect strongly depends on the (poorly
known) latitudinal profile of the solar wind.
Amplitude is a strong function of the range of
the slow-wind band.
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Survival probability latitudinal modulation
For higher-activity phases, when the range of the
slow wind is larger, the anisotropy is reduced.
0.107 keV
minimum
0.209 keV
mid-phase
maximum
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Transmission functionconclusions

• Effects exceeding the 10 Poisson limit include
• Daily-to-monthly fluctuations in the heliospheric
  conditions (for E lt 1 keV)
• Solar-cycle variations in Itot (for E lt 0.02
  keV)
• Photoionization (for E lt 0.5 keV)
• Electron-impact ionization (for E lt 0.07 keV)
• Yearly modulation of polar LOS (for E lt 0.2 keV)
• Charge exchange with solar-wind alphas (for E gt
  6 keV)
• Latitudinal modulation of survival probability
  expected during solar minimum for E lt 0.8 keV