# WawHelioGlow: a model of the heliospheric backscatter glow. II. The
helioglow buildup and the potential significance of the anisotropy in the
solar EUV output

M. A. Kubiak Space Research Centre PAS (CBK PAN),
Bartycka 18A, 00-716 Warsaw, Poland  M. Bzowski Space Research Centre PAS (CBK
PAN),
Bartycka 18A, 00-716 Warsaw, Poland  I. Kowalska-Leszczynska Space Research
Centre PAS (CBK PAN),
Bartycka 18A, 00-716 Warsaw, Poland  M. Strumik Space Research Centre PAS (CBK
PAN),
Bartycka 18A, 00-716 Warsaw, Poland

###### Abstract

The helioglow is a fluorescence of interstellar atoms inside the heliosphere,
where they are excited by the solar EUV. Because the mean free path between
collisions for the interstellar gas is comparable to the size of the
heliosphere, the distribution function of this gas inside the heliosphere
strongly varies in space and with time and is non-Maxwellian. Coupling between
realistically modeled solar factors and the distribution function of
interstellar neutral gas is accounted for in a helioglow model that we have
developed. WawHelioGlow is presented in the accompanying Paper I. Here, we
present the evolution of the gas density, solar illumination, helioglow source
function, and other relevant parameters building up the helioglow signal for
selected lines of sight observed at 1 au. We compare these elements for
various phases of the solar cycle and we present the sensitivity of the
results to heliolatitudinal anisotropy of the solar EUV output. We assume a
realistic latitudinal anisotropy of the solar wind flux using results from
analysis of interplanetary scintillations. We compare the simulated helioglow
with with selected maps observed by the SOHO/SWAN instrument. We demonstrate
that WawHelioGlow is able to reproduce fundamental features of the sky
distribution of the helioglow. For some phases of the solar cycle, the model
with an anisotropy of the solar EUV output better reproduces the observations,
while for other phases no EUV anisotropy is needed. In all simulated cases,
the solar wind anisotropy following insight from interplanetary scintillation
measurements is present.

##  1 Introduction

The heliospheric backscatter glow is the fluorescence of interstellar neutral
(ISN) gas inside the heliosphere, resonantly excited by the solar EUV
radiation. Discovery of a diffuse EUV background (Bertaux & Blamont, 1971;
Thomas & Krassa, 1971) was, in fact, crucial to the discovery of the
heliosphere (Blum & Fahr, 1970). Initially, investigations of the helioglow of
ISN H and He were mostly focused to determine the flow vector and the
temperature of ISN gas. Discovering that the temperatures and flow vectors of
ISN H and He seem to differ from each other led to the conclusion that there
must be a region of strong interaction between the plasma and neutral gas
which results in a processing of ISN H but not of ISN He (Lallement & Bertaux,
1990; Lallement et al., 1993; Lallement, 1996). Very soon it was realized that
the Lyman-$\alpha$ helioglow bears imprints of the heliolatitudinal structure
of the solar wind, which can be retrieved by appropriate analysis of the
helioglow distribution in the sky (Witt et al., 1979, 1981; Lallement et al.,
1985, 1986, 1995, 2010; Bzowski et al., 2003; Summanen et al., 1997;
Katushkina et al., 2013, 2019; Koutroumpa et al., 2019; Pryor et al., 1996,
1998). However, in all these papers, with the notable exceptions of the
studies by Pryor et al., it was assumed that the solar wind varies with
heliolatitude, but the solar EUV output does not.

An alternative method to study the solar wind structure is analysis of
interplanetary scintillations (IPS). The method of interplanetary
scintillation solar wind tomography relies on observationally discovered
correlation between the level of the solar wind electron density fluctuations
and the solar wind speed (Hewish et al., 1964; Coles & Maagoe, 1972; Coles &
Rickett, 1976; Kojima, 1979; Asai et al., 1998). The density fluctuations are
observed as scintillations in the time series of compact radio sources
distributed in the sky nearby the Sun. This method is independent of both the
ISN gas distribution inside the heliosphere and the assumptions on the
latitudinal behavior of the solar EUV output; so far it has only been able to
provide the solar wind speed at various heliolatitudes, but not the density.

Based on solar wind profiles obtained from tomographic analysis of IPS
observations (Jackson et al., 1998; Tokumaru et al., 2010), it was possible to
study the evolution of the solar wind velocity structure over the two past
solar cycles (Sokół et al., 2013, 2020). However, detailed conclusions from
these studies are sometimes at odds with those obtained from the helioglow
analysis (Katushkina et al., 2013, 2019).

Here, we present results of application of the WawHelioGlow code, extensively
presented in Kubiak et al. 2021 (Paper I 111M. A. Kubiak et al., WawHelioGlow:
a model of the heliospheric backscatter glow. I. Model definition) to the
calculation of the helioglow of H and He, observed at 1 au from the Sun. We
discuss the behavior of the factors making up the helioglow along selected
lines of sight. We point out important differences depending on the geometry
and solar cycle phase of the observations on one hand, and on the species (H
or He) on the other hand. We pay special attention to the expected signatures
of a heliolatitudinal anisotropy of the solar EUV output and we qualitatively
demonstrate that including this effects may improve the agreement of the
simulated distribution of the helioglow in the sky with measurements. In
addition to the Lyman-$\alpha$ glow, we briefly present the similarities and
differences in the formation of the helioglow of helium. In this latter case,
the hypothetical EUV anisotropy is expected to be the principal source of
heliolatitude structure of the glow because photoionization is the main source
of ionization losses. However, this effect is expected to be well visible only
relatively close to the Sun, which may be a challenge for numerical codes. We
demonstrate that WawHelioGlow is able to address these challenges without
difficulty.

The paper should be read with Paper I at hand since we frequently refer to its
formulae and figures.

##  2 Calculations

The WawHelioGlow code is based on the (n)WTPM model of interstellar neutral
(ISN) gas inside the heliosphere (Tarnopolski & Bzowski, 2009; Sokół et al.,
2015). The code for H is employed with the radiation pressure taken from
Kowalska-Leszczynska et al. (2020), which uses the composite solar
Lyman-$\alpha$ flux (Machol et al., 2019). The ionization model is adapted
from Sokół et al. (2020). Additionally, electron impact ionization is included
following Bzowski et al. (2013b) based on the OMNI2 solar wind data (King &
Papitashvili, 2005). The EUV-related factors, i.e., the illumination of ISN
gas by the Sun, the photoionization rate, and the radiation pressure assume
that the solar flux is anisotropic in heliolatitude (see Figure 1 and Equation
29 in Paper 1).

Figure 1: Heliolatitudinal profiles of the total ionization rates of H and He
(green and purple, respectively) for the epochs of simulations: 1996.43 and
2001.43 (solid and broken lines, respectively), and the anisotropy of the
solar illumination of the gas (blue; see the function $I_{\lambda\phi}(\phi)$,
Equation 29 in Paper I). All presented profiles are normalized to the 0°
heliolatitude. The total ionization rates for this latitude for H were
$8.235\times 10^{-7}\,\text{s}^{-1}$ for 1996 and $5.516\times
10^{-7}\,\text{s}^{-1}$ for 2001. For He, they are, respectively, $1.292\times
10^{-7}\,\text{s}^{-1}$ and $1.718\times 10^{-7}\,\text{s}^{-1}$.

The calculations for hydrogen are performed assuming that the population of
ISN atoms responsible for the helioglow comprises two sub-populations: the
primary and the secondary, with the parameters identical to those listed in
Table 1 in Kowalska-Leszczynska et al. (2018). The simulations were performed
for these two populations separately. Because of the adoption of the single-
scattering, optically thin approximation, the results of calculations for
individual populations can be arithmetically co-added to yield a full
helioglow signal. The results from the two-population model are compared with
a one-population approach with carefully selected parameters to best match the
two-population case. For helium, the one population model was used.

If the solar factors, i.e., ionization, radiation pressure, and illumination
featured spherical symmetry, the ISN gas distribution would show an axial
symmetry around the upwind–downwind line. Since this latter line is inclined
at an angle of $\sim 5\arcdeg$ to the ecliptic plane, and we consider
observations performed at 1 au from the Sun in the ecliptic plane, the
expected distribution of the helioglow in the sky would show certain
characteristic asymmetries. In our model, however, we do not assume a
spherical symmetry of the solar factors, as illustrated in Figure 1.

In this paper, we used a model of the ionization factors based on available
observations of the solar factors (solar wind and the EUV radiation). The
total ionization rate is a sum of the rates of photoionization, charge
exchange of ISN atoms with solar wind protons and, for He, additionally with
solar wind alpha particles, and of electron impact. The charge exchange rate
is based on the model of evolution of the solar wind speed and density based
on IPS observations. This reaction is the dominant one for H and almost
negligible for He. Photoionization is the second important factor for H and
the dominant one for He. The latitudinal profile of the photoionization rates
for H and He are adopted from Sokół et al. (2020) as the in-ecliptic rates for
a given time. Beyond the ecliptic the rates are modulated by the function
given in Equation 29 in Paper I with the parameter $a$ equal either to 0.85,
which results in the profile shown with the blue line in Figure 1, or to 1,
which yields a spherically symmetric rate. Electron impact rate is the least
intense for both H and He (Ruciński et al., 1996), and its relative
contribution to the total rate rapidly drops with the solar distance, becoming
negligible outside a few au (Ruciński & Fahr, 1991). Its rate is proportional
to the total electron density in the solar wind, equal to a sum of the proton
and doubled alpha densities. Consequently, its latitudinal profile follows
that of the solar wind density. Here, we neglect the difference in the
electron-impact rates for the slow and fast wind conditions (see, e.g.,
Bzowski et al., 2013b).

The latitudinal profiles of the total ionization rate may be complex in shape
and vary with time. Example profiles for the solar minimum and maximum for the
two discussed species are presented in Figure 1. As a result of the ionization
rate anisotropies, the helioglow distribution in the sky features additional
asymmetries.

We consider the ionization model as a realistic one. In its construction, we
deliberately did not use any insight from analysis of helioglow observations.
With this, we are able to verify to what extent the helioglow is sensitive to
anisotropies of the EUV. We also investigate to what extent a helioglow model
is capable of reproducing helioglow observations, if this model is based on
first principles and only on available observations of relevant quantities
that are not based on helioglow-related information. This comparison is
briefly presented in Section 4. Before that, however, we demonstrate the
behavior of the factors building up the signal (Sections 3.2–3.3) along
carefully selected lines of sight (Section 3.1).

##  3 Buildup of the signal from hydrogen

###  3.1 Selection of lines of sight and the simulation grid

Calculation of the intensity of the helioglow involves two spatial parameters:
the observer location in space $\boldsymbol{{r}}_{\text{obs}}$ and the
direction into which the observer is looking $\boldsymbol{{\hat{l}}}$
(Equation 3 in Paper I). The observer locations were chosen to facilitate
referring the simulation results on one hand to the available maps of the
helioglow obtained by the SWAN experiment, and on the other hand to the
geometry of the planned experiment GLOWS. SWAN takes full-sky maps of the
helioglow approximately once a day, with two exclusion zones: one centered at
the Sun, and another one around the spacecraft, usually, in the anti-solar
direction (Bertaux et al., 1997). GLOWS scans a small circle with a radius of
75°, centered in the ecliptic plane at a longitude shifted by 4° relative to
that of the Sun. The simulation grid (Figure 2) features concentric rings
around the center of the planned GLOWS scanning circle. They cover the entire
sky except a region within 36° off the Sun. The absolute ecliptic coordinates
of the grid points vary with the location of the observer.

Figure 2: The simulation grid for a map of the helioglow for an observer
located at 1 au at longitude 255.85° (close to the upwind direction). The
direction towards the Sun is thus towards longitude 75.85°. The directions of
lines of sight are located at concentric rings (small purple rectangles)
centered at 4° off the Sun’s direction. The empty space is the exclusion zone
around the Sun. The large green dots represent the selected lines of sight
(see text), located at both sides of the Sun in the ecliptic plane and in the
polar plane.

Out of this grid, we select several characteristic lines of sight, marked as
large green dots in Figure 2. They include the antisolar line as well as lines
at $\pm 36\arcdeg,\pm 72\arcdeg$, and $\pm 90\arcdeg$ in the ecliptic plane
and in the plane perpendicular to the ecliptic, going through the northernmost
and southernmost points in the abovementioned rings. This makes a total of six
lines of sight selected in each of the two perpendicular planes for each
observer locations.

In the following, we analyze elements building up the source function of the
helioglow by placing the observer in the ecliptic plane approximately at the
upwind, downwind, and crosswind location for observations performed on the
days of the year for which SWAN maps are available. These days were chosen
during the minimum (the epoch 1996) and the maximum of the solar activity (the
epoch 2001).

Figure 3: Color-coded magnitudes of the source function of the hydrogen glow
for the primary population in three selected planes centered at the observer.
The reference system is Cartesian, with the Sun at the origin. The upper left
panel shows the ecliptic plane seen from the north ecliptic pole. The observer
(marked with the black circle marked up “obs”) is at the upwind direction at 1
au from the Sun, at the corner of the white $\pm 10\arcdeg$ exclusion zone. In
the upper right panel, a polar plane is seen from the crosswind direction in
the ecliptic plane. The polar plane includes the inflow direction and the
north-south axis, but in the projection presented in the upper right panel he
is now to the right from the Sun. The lower panel presents a plane
perpendicular to the upwind-downwind direction, seen from the downwind
direction. The observer is located within this plane, which implies that the
plane is offset by 1 au upwind from the Sun. All three panels are in a
Cartesian reference frame, with the axes scaled in au. The black lines
represent selected lines of sight. The color scale is in arbitrary units.

To facilitate understanding the spatial distribution of these lines of sight
and the helioglow source function, we present the distribution of the source
function in three selected heliocentric planes (see Figure 3), color coded and
with superimposed selected lines of sight. The source function features well-
defined maxima in space (red and dark-red regions), where formation of the
helioglow is the most intense. Isocontours of the source function reflect on
one hand the geometry of the gas flow, and on the other hand, the imprints of
the ionization losses in the ISN gas.

Figure 3 clearly shows the symmetries and asymmetries of the system. In the
ecliptic plane (upper left panel) there is a symmetry in the source function
distribution relative to the solar direction. Since the observer is at the
upwind line, the upwind line is for him antisolar. Consequently, the symmetry
of the ISN H density relative to the upwind direction and the symmetry of the
ionization losses and the solar illumination coincide.

The upper-right panel in Figure 3 shows a plane including the two ecliptic
poles. A north-south asymmetry relative to the ecliptic plane is clearly
visible: the region of the highest magnitude of the source function is larger
in the northern hemisphere than in the southern. This is because of the $\sim
5\arcdeg$ inclination of the flow direction of ISN gas to the ecliptic plane
and to the solar equator, and because we use a 3D model of the ionization
losses, which results in a different densities in the north and south ecliptic
hemispheres for the selected time moment. As a result, a more abundant gas
yields a larger source function for the helioglow, because the solar
illumination is assumed to be north-south symmetric relative to the solar
equator.

A similar effect is visible in the lower panel of Figure 3, which shows a
plane perpendicular to the direction towards the Sun. This panel demonstrates
that the density distribution is organized relative to the solar equator plane
and not the ecliptic plane.

###  3.2 Individual elements of the source function along selected lines of
sight

In this section, we analyze individual elements building up the source
function $J_{\text{glow}}$ (Equation 2 in Paper I) and their relations
depending on the observer location and the direction of the line of sight.

Figure 4: Variation of the elements of the source function of the helioglow
along the line of sight for the conditions of solar minimum: the density of
ISN H ($n_{\text{H}}(l)$; upper left panel; cm-3), the illumination
$s_{\text{H}}$ (arbitrary units), the mean radial velocity of the gas relative
to the Sun ($\langle v_{r}(l)\rangle$; lower left panel; km s-1), the source
function ($J_{\text{glow}}(l)$, Equation 2; upper right panel; arbitrary
units), the latitude of the line of sight at $l$ (middle right panel; degree),
and the partial helioglow intensity ($I_{\text{glow}}(l)$, Equation 35; lower
right panel; arbitrary units). The equation numbers refer to Paper I. The
units are identical for the given quantities shown in all figures. Note that
with our definitions, $s_{\text{H}}$ is equal by number to the radiation
pressure compensation factor $\mu(l)$ (Equation 33), calculated for $\langle
v_{r}(l)\rangle$. The observer is located at the upwind position at 1 au in
the ecliptic plane, the epoch (1996.43) corresponds to the minimum of the
solar activity between solar cycles 22 and 23, the ISN H parameters correspond
to the primary population. The horizontal axis measures the distance from the
observer in au along the line of sight. The observer is scanning the polar
plane to the north and to the south of the ecliptic plane (cf. Figure 2 and
the upper right panel in Figure 3). The northern and southern lines of sight
are given in solid and broken lines, respectively. The 180° line of sight is
antisolar. Figure 5: Scattering phase function $\psi(l)$ along the line of
sight for H and He (left and right panels, respectively; Equations 8 and 9 in
Paper I) for the upwind vantage point. For the other vantage points discussed
in the paper, $\psi(l)$ are practically identical.

Figure 4 presents the elements forming the signal along the selected lines of
sight: the gas density, the solar illumination that excites this gas (which is
proportional to the local radiation pressure factor $\mu$; see Section 2.6.1
in Paper I), the mean radial velocity of the gas relative to the Sun (Equation
12 in Paper I), the latitude along the line of sight, and the source function
of the helioglow (Equation 2 in Paper I). The figure is completed by the
partial helioglow intensity $I_{\text{glow}}(l)$ (Equation 35 in Paper I,
first row, $\int\limits_{0}^{L}J_{\text{glow}}dl$, cumulative intensity from
the observer to a given distance). The phase function $\psi_{\text{H}}$ for H
(Equation 8 in Paper I) is presented in the left panel of Figure 5. Note that
for the lines of sight discussed in this paper, $\psi(l)$ depends almost
solely on the elongation of the line of sight from the Sun (i.e., on the
angular separation of the aiming point of the line of sight from the Sun’s
center) and, consequently, $\psi(l)$ is almost identical for the equivalent
line of sight elongations for all vantage points discussed. The same is true
for the helium lines of sight, discussed in Section 5.

The phase function modifies the source function relatively little, since its
(minimum, maximum) values are equal to (0.90, 1.17), as shown in Figure 2 in
Paper I. The magnitude of the illumination of the gas drops with the square of
solar distance, but additionally is modulated by the radial speed of the gas
(cf. the middle and lower left panels in Figure 4). In the case presented in
this figure, the observer is upwind from the Sun and is looking downwind.
Consequently, the speed of the gas varies from extreme negative close to the
observer (the gas approaching the Sun) to extreme positive (the gas receding
from the Sun far from the observer). For the secondary population, the
qualitative behavior is similar, but the amplitude is lower by 5–10 km s-1
because the inflow speed of the secondary population is lower than that of the
primary. The modulation of the illumination in this observation geometry is
from $\sim 0.5$ to $\sim 1.1$, i.e., the variation is approximately by a
factor of 2. This illustrates the need to take the actual form of the solar
Lyman-$\alpha$ line into account.

The factor that features the largest amplitude along the line of sight is the
density (upper left panel in Figure 4), which in the geometry used in this
figure varies by more than two orders of magnitude. This causes the source
function to significantly vary, featuring a maximum within $\sim 1$ au from
the observer (depending on the offset of the line of sight from the Sun),
going down by an order of magnitude at $\sim 10$ au. As illustrated in the
lower right panel, approximately half of the magnitude of the helioglow in
this viewing geometry is formed within 3—5 au from the observer, and there is
a clear modulation of the source function as the line of sight is the nearest
to the Sun, which in this viewing geometry is between $\sim 0.75$ au from the
observer for the offset of 36° and $\sim 0.4$ au for an offset of 72°.

Figure 6: Variation of selected elements of the helioglow source function for
the location of the observer at 1 au upwind in the ecliptic plane, for solar
maximum conditions, the primary population. The left column presents the case
with the polar anisotropy of the illumination, the right column that with
spherical symmetry of these factors assumed. The lines of sight are within the
polar plane (see Figure 2 and the upper right panel in Figure 3). The offsets
of the lines of sight from the scanning circle center are listed in the upper
left panel, positive to the north (solid lines), negative to the south of the
Sun (broken lines). The quantities presented include, from top to bottom: the
source function $J_{\text{glow}}$, the density $n_{\text{H}}$, the
illumination $s_{\text{H}}$, and the partial helioglow intensity
$I_{\text{glow}}$, shown as a function of the distance along the line of sight
$l$.

###  3.3 Effect of the latitudinal anisotropy in the solar EUV output

The anisotropy of the solar EUV output potentially affects the helioglow in
several ways. The first and direct effects is the illumination: whatever the
gas distribution in space is, it is illuminated differently at the poles and
differently at the solar equator. However, the solar EUV radiation is also
responsible for photoionization of ISN gas and for radiation pressure. Both
these factors affect the distribution of the gas in space. It can be expected
that the latitudinal anisotropies of the solar output at different
wavelengths, if not identical, are at least directly proportional. However,
their effects on the helioglow need to be carefully studied. Reducing the EUV
flux above the solar poles relative to that at the equator will result in
reducing the illumination, but also reducing the radiation pressure and the
ionization losses, which in turn is expected to increase the gas density in
these regions and to compensate for the reduced illumination, at least partly.
The effect requires a careful modeling, which we performed in this study.

To investigate the effect of a latitudinal anisotropy of the solar EUV output,
we simulated the helioglow either including or excluding this effect.
Including the EUV anisotropy modifies the solar illumination of the ISN gas
and the latitudinal anisotropy of the ionization rate. According to the
adopted model of the H ionization rate, photoionization in the ecliptic plane
contributes from $\sim 15\%$ to $\sim 30\%$ to the total ionization rate in
1996 and 2001, respectively (Figure B1 in Sokół et al., 2020). In the absence
of the anisotropy of the EUV flux, these ratios at the solar poles are equal
to $\sim 30\%$, respectively (i.e., no change between the times of high and
low solar activity). The latitudinal modulation of the photoionization rate is
identical as in Equation 29 and Figure 1 in Paper 1 changes these relations,
appropriately reducing the contributions from photoionization at the poles and
modifying the density of ISN H in the polar regions.

Another effect is a change in the illuminating flux. Since the total EUV flux
affects the solar spectral flux non-linearly, the reduction in the spectral
flux at the poles is by 25% in 1995 and 20% in 2001.

The effects of the EUV anisotropy on the production of the helioglow are
illustrated in Figure 6. Clearly, the location along the line of sight of the
maximum of the source function $J_{\text{glow}}$ varies very little, but the
magnitude of the maximum does change for all line of sight elongations (the
top row in Figure 6). The effect on the density along the line of sight (the
second row in the figure) in the region of the maximum of $J_{\text{glow}}$ is
visible for the lowest-elongation lines, but almost absent in the other ones,
in particular for the elongations close to these of the future GLOWS
experiment. Most of the effect is due to the change in the illumination
itself. This is shown in the third row of Figure 6. As a result, a difference
between the total intensities is expected to be similar to that of the
anisotropy ratio $a$. More discussion of the anisotropy effect is offered in
Section 4.

###  3.4 Effects of the vantage point location on the observed helioglow

The formation of the helioglow signal along the line of sight strongly depends
on the observer location relative to the inflow direction of ISN gas, i.e., on
the vantage point. This is illustrated in Figures 7–9, which provide a
comparison of the source function, gas density, solar illumination, and the
helioglow intensity buildup as a function of distance along the line of sight
for the vantage point at the upwind, crosswind, and downwind points at 1 au in
the ecliptic plane. Here, we only point out to the most salient aspects.

Figure 7: Selected elements building up the helioglow: the source function
(top row), the gas density (second row), the illumination $s_{\text{H}}$
proportional to the $\mu$ factor (third row), and the partial helioglow
intensity as a function of distance along the line of sight (bottom row), for
the solar minimum and maximum conditions (left and right columns,
respectively). The observer is at 1 au in the ecliptic plane upwind, the lines
of sight are within the ecliptic plane. The elongation of the lines of sight
from the Sun are presented in the upper-left panel. The vertical bar marks the
location of the maximum emissivity region for the line of sight $-90\arcdeg$.
Figure 8: Equivalent to Figure 7 for the crosswind vantage point.  Figure 9:
Equivalent to Figure 7 for the downwind vantage point.

First, it is important to realize how the points belonging to the lines of
sight for an observer at the upwind, downwind, and crosswind locations are
distributed in space. One can think of the lines of sight discussed in the
aforementioned figures as a bunch of lines extending from the observer
location. Going from the upwind to the crosswind and downwind locations
rotates this bunch along the ecliptic with the pivot point at the Sun’s
center. Within the ecliptic plane, the right-hand and left-hand elongations
offer a mirror symmetry for each other for a vantage point either upwind or
downwind. One should note that the exact symmetry is present in terms of
geometry only, while for spatial distribution of the gas and its illumination,
the symmetry is only approximate. The left-hand elongations for the upwind
vantage point have their equivalents as the right-hand elongations downwind.
The same is true for the two crosswind vantage points at the ecliptic; in the
paper we show only one of them. An example of the ecliptic bunch of lines of
sight is shown for the upwind observer in Figure 3 (upper left panel).

What is different between the different vantage points in the context of the
helioglow signal creation is the density and radial velocity distributions of
the ISN gas along the lines of sight, which result in different illuminations
and, consequently, differences in the source function. For the upwind vantage
point (Figure 7), the observer is immersed in the relatively dense gas as
compared to the downwind vantage point. As we go along the line of sight, the
densities increase for all lines of sight with high elongations, as those
planned for the GLOWS experiment onboard IMAP. However, for lines of sight
with low elongations, the densities initially drop as the distance to the Sun
rapidly decreases and start to recover approximately at 1 au from the
observer. This behavior is qualitatively similar for the solar minimum and the
solar maximum conditions.

Because of the variation in radial speed, the illumination along these lines
of sight is also similar. Generally, for the upwind location, the lines of
sight probe the downwind hemisphere, where the densities are lower than upwind
(if the same distance from the Sun is considered), and because of the solar
forcing the spread in the directions of individual atoms is larger. This
results in different radial velocities of the gas for the upwind and downwind
locations.

In result, for the upwind observer location and high elongations, the source
function values are relatively high already at the vantage point. The function
drops significantly below the vantage-point level at distances beyond
${\sim}4$ au for the solar minimum and ${\sim}7$ au for the solar maximum.
This means that the formation of the signal starts immediately from the
vantage point. However, for the low elongations, the source function shows a
qualitatively different behavior, with a maximum at the observer, a drop to a
minimum value at 1–2 au, and a buildup to a second local maximum at several au
from the observer. This second maximum corresponds to the maximum emissivity
region of the ISN gas. The distance to this region strongly varies with the
elongation, especially for low elongations. Since far away from the Sun (i.e.,
outside of the hydrogen cavity) the gas densities are approximately the same,
one can expect that the variability of the helioglow signal is generated
somewhere closer. In this context, the behavior of the source function in the
proximity of the observer is important, even if most of the helioglow is
generated farther. On the other hand, measurements from the upwind vantage
point can be considered as “contaminated” by the local contribution, if more
distant regions are of main interest.

For the crosswind location (Figure 8), there is a large asymmetry in the
signal creation between the two sides of the Sun. At the observer site, the
density of the gas is comparable to that at the upwind location during solar
minimum conditions but very low for the maximum conditions. A portion of the
signal is formed directly close to the observer, as was the case for the
upwind location. The distance to the maximum of the source function vary
little for the lines of sight running upwind from the Sun, but vary profoundly
for those running downwind from the Sun, both as a function of elongation and
of the phase of the solar cycle.

For the downwind location (Figure 9), the viewing geometry makes a mirror
symmetry with respect to the upwind one, but the density distributions along
the line of sight are very different: they are very low at the observer, and
increase in a significant way only starting from $\sim 1$ au down the lines of
sight (measuring the significance by the magnitude of the source function).
This is true for both the minimum and the maximum of the solar activity, even
though details differ between the two phases. As a result, the entire signal
reaching the detector is formed far away from the observer (beyond $\sim 1$ au
along the line of sight). Thus, the signal observed from the downwind vantage
point (Figure 9) is created in the crosswind locations in the heliosphere and
farther upwind; the locations in the downwind hemisphere do not contribute
almost at all.

We have discussed so far only lines of sight presented in Figures 7–9, which
are located in the ecliptic plane. Out-of-ecliptic effects are discussed
separately further in the paper in Section 3.6. In this context it is
important to note that for all vantage points, the lines of sight at a given
elongation and not in the ecliptic plane traverse very similar latitudes out
of the ecliptic and have identical distances to the Sun and the phase
scattering function. In other words, lines of sight at identical angles along
a Sun-centered scanning radius traverse identical ecliptic latitudes and
similar heliolatitudes regardless of the vantage point. This is important for
the choice of the scanning circle radius planned for the IMAP/GLOWS
experiment.

###  3.5 The helioglow variation for various phases of the solar activity

Figures 7–9 also illustrate the differences in the formation of the helioglow
signal between the epochs of low and high solar activity.

The illumination during the solar maximum is larger by a factor of 1.8-1.9 for
all observer locations. This is true basically throughout the lines of sight,
with some variations within $\sim 1$ au from the observer. The difference in
the illumination seems to be the decisive factor in the magnitude of the
helioglow, which is larger for the solar maximum for all lines of sight
investigated. This is because while the density features large variations
between the lines of sight, solar cycle phases, and vantage points, they are
to large extent restricted to a region within a few au from the Sun (a little
farther downwind) and a large portion of the helioglow signal originates from
relatively remote distances outside the hydrogen cavity. It is instructive to
compare the contributions to the signal from the farthest portions of the
lines of sight, where they penetrate regions where solar-cycle-related
variations of the density practically cease (see Figures 4 (upper row) and 5
in Sokół et al., 2019).

Another aspect of the variation of the helioglow with the solar activity is
variation of its heliolatitude distribution. This is illustrated in Figures 14
and 15 – see the middle and bottom panels in the left column. On one hand, the
helioglow clearly reacts to the presence or absence of a latitudinal
anisotropy in the illumination, but on the other hand to the different
heliolatitudinal structures of the solar wind during the high and the low
solar activity. The evolution of this structure adopted in the modeling is
presented in Figure 6 in Sokół et al. (2020).

###  3.6 Polar vs ecliptic lines of sight

Figure 10: Comparison of selected elements making up the helioglow signal for
polar and ecliptic lines of sight (cf. Figure 3, upper panels). The solar
minimum conditions, the upwind vantage point. The left column presents polar
(north and south) lines of sight (cf. Figure 3, the upper right panel), the
right column the ecliptic lines of sight. The solar elongations are listed in
the upper left panel. From top to bottom: the source function, the density of
ISN H, the illumination of ISN H, and the partial intensity, shown along the
lines of sight.

In this section, we point out that lines of sight with carefully selected
elongations from the Sun are well suited to investigate the heliolatitudinal
effects of the solar radiation and solar wind. We limit the discussion to the
upwind viewing geometry; the conclusions for the other geometries are similar.

The latitudes of the points within the lines of sight aimed towards low
ecliptic latitudes clearly remain low. Thus, the entire information obtained
from these lines of sight is obtained from low heliolatitudes. By contrast,
the latitude of the points belonging to the lines of sight directed to the
north or to the south of the Sun have varying heliolatitudes. This is
illustrated in Figure 7 in Sokół et al. (2013). To maximize a differentiation
between the signal from ecliptic and polar lines of sight at identical
elongations from the Sun, the elongation angle must be carefully selected.
Elongation 90°, i.e., directing the line of sight towards celestial poles does
not always provide an optimum viewing geometry. For the upwind locations,
these lines of sight never cross the solar polar line; the gas contributing to
the signal has not undergone the maximum of ionization losses at the polar
latitudes. This holds true for almost all vantage points except a region
straddling the downwind direction.

Therefore, it seems advantageous for maximizing the effect of polar ionization
on the helioglow to aim at an angle less than 90° from the Sun. A reasonable
selection seem to be an elongation of $\sim 70\arcdeg-75\arcdeg$. In this
case, the line of sight intersects the solar polar axis close to the region of
maximum emissivity. The latitude of the polar lines of sight is presented in
the middle right panel in Figure 4. The effects are illustrated in Figure 10,
which compares the elements comprising the source function along polar and
ecliptic lines of sight for the upwind vantage point. This is true for both
the north and the south polar lines of sight.

It is instructive to compare the signal creation along the lines of sight at
the same elongations from the Sun but either maintained in the polar, or in
the ecliptic plane (compare the left and right columns in Figure 10). On one
hand, this viewing geometry is very well suited for investigations of the
anisotropy of the solar EUV output – notice the difference in the illumination
between the polar and ecliptic lines of sight, which exists even though the
radial velocities of the gas are very similar for both geometries/planes. But
also the densities differ, which is mostly related to different ionization
losses of ISN H, that exist because of the anisotropic charge exchange rate.
Therefore, the lines of sight at elongations of $\sim 75\arcdeg$ can be used
to investigate the latitudinal structure of the solar wind. Hence, it seems
that observations taken along a scanning circle of $\sim 75\arcdeg$ are able
to provide sufficient information to establish the latitudinal structure of
the solar wind and to study the solar EUV anisotropy. Such observations are
planned for the GLOWS experiment onboard the IMAP spacecraft

###  3.7 Two-population vs one-population model

The charge exchange interaction between ISN H atoms and the slowed down and
heated interstellar protons in the outer heliosheath results in the creation
of a secondary population of ISN H and a strong filtration of the primary
population (Baranov & Malama, 1993). In this section, we check if the
helioglow intensity distribution obtained from the WawHelioGlow model is
sensitive to the details of these two populations. We verify a hypothesis that
the helioglow intensity observed from 1 au can be simulated using a one-
population approach, with the inflow parameters carefully derived from those
of the two heliospheric populations of ISN gas. We start, however, with
comparing the helioglow signal formation from the primary and the secondary
populations (Figure 11).

Figure 11: Comparison of selected elements building up the contributions to
the helioglow signal from the primary (left column) and the secondary
components of ISN H (right column). From the top, the panels show the source
function, the gas density, the radial velocity, and the partial helioglow
intensity at $l$ from the observer. The simulation was performed for the
observer at the downwind location during the maximum of the solar activity,
the lines of sight are in the ecliptic plane, their elongations from the Sun
are indicated in the upper left panel

For the primary and secondary populations, the adopted parameters were similar
to those obtained by Bzowski et al. (2008, 2009) concerning the densities and
the temperatures. The directions were adjusted to better represent the state
of the art. The primary population was simulated using the velocity vector
determined by Bzowski et al. (2015) for ISN He, and the secondary had a
velocity vector identical to that found by Kubiak et al. (2016) for the
secondary population of ISN He. While obtained for ISN He, not H, a study by
Izmodenov & Alexashov (2015) suggests that the angle between the inflow
directions of the two populations of ISN H is similar in magnitude to that for
He and that these directions should be in the same plane. The magnitudes of
the parameters are the following: primary:
$\lambda=255.745\arcdeg,\phi=5.169\arcdeg,v=25.784$ km s-1, $T=7443$ K,
$n=0.031$ cm-3; secondary: $\lambda=251.57\arcdeg,\phi=11.95\arcdeg,v=18.744$
km s-1, $T=16300$ K, $n=0.054189$ cm-3. The longitudes $\lambda$ and latitudes
$\phi$ of the inflow directions are in the J2000 ecliptic coordinates.

The profiles of the densities of the two populations along the corresponding
lines of sight are different. The density of the primary at the observer
location downwind is almost nil, so almost entire gas population is due to the
secondary population. The density gradient of the primary population along the
line of sight is much steeper than that of the secondary. However, the
behavior of the source functions along $l$ are similar to each other, with the
maxima for the two populations located within $\sim 1$ au from each other.
Since the density of the secondary population at the termination shock is
larger than that of the primary, also the absolute density of the secondary
near the region of the maxima of the source function are larger and the
magnitude of the source function of the secondary is larger. However, these
differences are not large and the contributions from the two populations to
the signal can be regarded as comparable.

The illuminations of the two populations for this observer location are also
comparable because the radial velocity profiles along the selected lines of
sight are similar between the two populations. This is specific for the
downwind location of the observer because generally, due to the speed
difference at the termination shock, the radial speeds differ. The source
function becomes significantly larger than 0 at $\sim 1$ au from the observer
and at these distances, the radial velocities quickly become similar for a
given elongation (except the lowest). As a result, the profiles of
$J_{\text{glow}}(l)$ are similar between the two populations, even though the
absolute magnitude is larger for the denser secondary population. This
analysis suggests that restricting most of the discussion to the primary
population is justified.

Now, we compare the sky distribution of the Lyman-$\alpha$ helioglow
calculated assuming a mixture of the primary and secondary population (Baranov
& Malama, 1993) with a one-population approach with the parameters carefully
selected to best reproduce the superposition of the primary and the secondary
flows. The calculations are carried out identically as for the case of the
primary and secondary populations.

For the one-population case, the parameters were obtained as weighted averages
of the primary and secondary populations:
$\lambda=252.5\arcdeg,\phi=8.9\arcdeg,v=21.26$ km s-1, $T=12\,860$ K,
$n=0.085$ cm-3.

Figure 12: A sky map of the intensity of the helioglow for the two-population
(purple) and one-population cases (green, upper panel) and the ratio of the
differences to the intensity for the two-population case
($1-$1Maxwell/(primary), lower panel). The observer is at the downwind
location at 1 au. The units in the upper panel are arbitrary.  Figure 13:
Selected elements making up the helioglow signal for the sum of the primary
and the secondary populations of ISN H along the lines of sight, compared with
their equivalent quantities for the one-population approximation. The observer
is at the 1 au downwind position in the ecliptic plane. Two lines of sight are
presented: at 36° and 90° off the Sun in the polar plane. We show the density
(upper left), the illumination (middle left), the mean radial velocity of the
gas (lower left), the source function (upper right), the source functions
ratio ($1-$1Maxwell/(primary), middle right), and the partial intensity
increase with $l$ (lower right). The green and black lines mark the one-
population approximation for the elongation angles 36° and 90°, respectively.
The purple and blue lines mark the sum of the primary and secondary population
for the elongation angles 36° and 90°, respectively. The dashed and dotted
lines mark the primary and the secondary populations in the illumination and
radial velocity panels.

A sky map of the helioglow for a sum of the primary and the secondary
populations and for the one-population approximation is presented in Figure
12. A comparison of the elements making up the helioglow for the sum of the
primary and the secondary populations and for the one-population model for
selected lines of sight is shown in Figure 13. We investigate the differences
between the helioglow intensities simulated for the entire sky for these two
cases for a vantage point at the downwind location. It is expected that the
differences are maximum for this vantage point, since most of the gas
contributing to the helioglow signal is already after the closest approach of
the atoms to the Sun. Modifications of atom trajectories and the ionization
losses are most intense closest to the Sun and the gas density dependence on
the input parameters is the strongest.

The differences in the helioglow distributions between the two cases are very
small: from 1% in the upwind region to 2–3% in the downwind region of the map.
We verified that for different vantage points and phases of the solar cycle,
the differences are similar. The behavior of the factors contributing to the
helioglow along selected lines of sight is presented in Figure 13. The
densities agree very well, the source function as well. Larger differences are
in the illumination; they result from differences in radial velocities between
the populations in question. However, the illumination for the primary and the
secondary population average to an effective illumination very similar to that
for the one-population case. The differences are smaller than the uncertainty
in the model prediction due to the uncertainties in the models of radiation
pressure and ionization losses.

From this insight it seems, then, that analysis of photometric observations of
the helioglow, performed from 1 au and aimed at retrieving the ionization
structure can be performed using the one-population approach.

##  4 Comparison of modeling results for the WawHelioGlow code with SOHO/SWAN
observations

In this section, we present a comparison of full-sky maps obtained from the
WawHelioGlow code with selected maps obtained from SOHO/SWAN. We show
differences in the helioglow distribution for almost identical locations in
the orbit for solar activity minimum and maximum conditions, and demonstrate
the effects of including or excluding the latitudinal anisotropy in the solar
EUV output discussed in Paper I and in the previous sections.

Figure 14 presents a comparison of SOHO/SWAN observations and modeling results
for June 5, 1996, when the satellite was approximately in the upwind location.
This date corresponds to solar minimum conditions. The SWAN/SOHO maps were
obtained from the SOHO/SWAN database, where the maps are available in the FITS
format (SOHO-SWAN, 2020; Bertaux et al., 1995).

Figure 14: Comparison of modeling results from the WawHelioGlow model with
SOHO/SWAN observations during minimum of solar activity. The map presented in
panel (a)(upper left) shows raw SOHO/SWAN measurements in the ecliptic
coordinates, obtained on June 5, 1996, when the satellite was approximately in
the upwind location. The white irregular regions indicate the locations of the
solar and antisolar masks. The black solid line marks the Galactic equator.
The map is normalized (see text). Panel (b)(middle left) shows results of
helioglow modeling performed using the WawHelioGlow code with no EUV
anisotropy included. Panel (c)(lower left) presents corresponding simulation
results with the polar EUV anisotropy included. The white circular regions in
panels (b) and (c) are the solar exclusion zone. The Sun location is shown by
the black circle, and the dashed lines mark the ecliptic and meridional cuts
shown in the right column of plots. In the right column, a comparison of cuts
through the maps is shown for (d)(upper) ecliptic, (e)(middle) meridional-
downwind and (f)(lower) meridional-upwind cases. In the right-column plots,
the red circles represent the SOHO/SWAN measurements (i.e., the sum of the
glow and the point-source background, normalized), while the green and blue
lines show modeling results for the EUV anisotropy included (blue) or excluded
(green).

In the raw SOHO/SWAN signal (see Figure 14(a), upper left), the Lyman-$\alpha$
glow is the slowly varying component, on which signal from point sources is
superposed. The point sources are clustered along the galactic equator, as
discussed, e.g, by Strumik et al. (2020). Below the map containing the raw
SOHO/SWAN data, results of the helioglow simulation are shown with the
anisotropy of the solar EUV output included or excluded (lower left and middle
left respectively). In all plots, we use the photon flux density normalized to
an average value, taken over the ecliptic plane in the observed or the
corresponding simulated map. For the SOHO/SWAN observations, the glow
averaging process requires subtracting the point-source background, which was
performed using a method proposed by Strumik et al. (2020). In this method, a
phenomenological heliospheric-glow approximator is computed using an approach
based on machine learning techniques.

In Figure 14(b) (middle left), helioglow simulations without anisotropy in the
solar EUV output are presented (i.e., $a=1$ in Equation 29 in Paper I).
Corresponding simulation results with $a=0.85$ are shown in Figure 14(c)
(lower left). Visual cross-inspection of the three maps shown in Figure
14(a)–(c) confirms general validity of the WawHelioGlow model presented in
this paper for description of the SOHO/SWAN observations. A comparison of the
mid- and high-latitude regions in the maps reveals that for this particular
case, the model without the EUV anisotropy (Figure 14(b)) better reproduces
the observed modulation of the H glow in the sky as compared with the model
with $a=0.85$, shown in Figure 14(c). This conclusion is supported by analysis
of ecliptic and meridional cuts through the maps. Figure 14(d) (upper right)
presents the ecliptic cut through the maps. The model curves (green and blue
lines) show a good fit for the lower envelope of the SOHO/SWAN observations
(red circles). These observations are contaminated by the point-source
background, which is visible in the cuts as narrow spikes; the model of the
helioglow is not expected to fit to these spikes. In the meridional cuts
presented in Figure 14(e) and (f) (middle right and lower right,
respectively), the higher the latitude, the larger the difference between the
models, as expected. Clearly, the model without the EUV anisotropy (green
line) better reproduces the observations as compared with the model with the
anisotropy (blue line). In the meridional cuts, the range of latitudes between
$-40\arcdeg$ and 0° is strongly affected by the presence of unresolved point-
sources in the proximity of the galactic equator. Therefore, in this region an
apparent discrepancy between the observations and modeling results naturally
occurs.

Figure 15 shows a comparison of the SOHO/SWAN observations and modeling
results for June 5, 2001, which corresponds to solar maximum conditions.

Figure 15: Similar to Figure 14 but for the solar maximum conditions (2001).
The raw SOHO/SWAN measurements presented in panel (a) were obtained on June 5,
2001. The model computations were performed for this date, accordingly.

Figures 14 and 15, illustrate the influence of the solar cycle effects on the
H glow. The low-emission region in the proximity of the Sun is significantly
larger during the solar maximum as compared to the solar minimum conditions.
The modulation of the signal changes from an eye-like structure during the
solar minimum to a more circular pattern during the solar maximum. Again, the
difference between the models with and without darkening is most pronounced in
mid- and high-latitude regions.

This finding is confirmed by analysis of the ecliptic and meridional cuts
shown in Figure 15(d)-(f) (right row). An important difference with respect to
Figure 14(d)-(f) is the type of model that fits the SOHO/SWAN observations.
For the solar maximum, generally the model with an EUV anisotropy (blue line)
better reproduces the observations (red circles). This is in agreement with
modeling by Cook et al. (1980, 1981). One should note that in the modeled
solar-minimum WawHelioGlow model (see Figure 14(b) and (c)) an equatorial
attenuation of the signal for the range of longitudes between 180° and 360° is
visible. Such an effect is not observed for the solar-maximum maps shown in
Figure 15(b) and (c). Similarly to the solar-minimum case, for the meridional
cuts in the range of latitudes between -40° and 0°, the strong discrepancy
between the Lyman-$\alpha$ glow model and the SOHO/SWAN observations can be
attributed to the unresolved point sources in the proximity of the galactic
equator.

The insight presented in this section must be regarded as preliminary and
incomplete. Without much more extensive analysis, it cannot be determined if
the anticorrelation of the solar EUV anisotropy with the phase of the solar
cycle is real. Certainly, however, the EUV anisotropy is a frequently
neglected effect that needs to be better investigated based on available and
future observations, and consequently needs to be implemented in models of the
helioglow.

##  5 Buildup of the signal from helium

In this section, we present an analysis of the elements of the source function
for the helium glow and we point out important differences between the buildup
of the helioglow signal for H and He due to very different spatial
distributions of the densities and velocities of ISN H and He close to the Sun
(cf Figures 4—6 in Sokół et al., 2019) and the very different spectral
profiles of the solar Lyman-$\alpha$ and He I 58.4 nm lines (cf Figure 3 in
Paper I).

Modeling of the helium glow was carried out to verify the code operation in
the absence of radiation pressure and for lines of sight approaching much
closer to the Sun than for H, which results in a much more rapid variation
with the distance $l$ from the observer. We show that the WawHelioGlow code is
capable of taking these effects into account without problem.

###  5.1 Modeling details

For the illumination, we used the Gaussian profile (Equation 20 in Paper I)
with the background level $s_{\text{bkg}}=0.01$. For ionization, we adopted
the photoionization, electron-impact, and charge exchange rates from Bzowski
et al. (2013a) and the latitudinal anisotropy of photoionization as identical
to those for ISN H. While Sokół et al. (2020) recently updated the ionization
rate estimates, especially that of the photoionization rate, details of
ionization losses do not significantly modify the discussion of the elements
of the helium helioglow source function we present.

The inflow parameters (the velocity vector and the temperature) were adopted
as identical to those for the primary population of ISN H (note that the
currently best estimate for these parameters is available from direct-sampling
observations of ISN He from IBEX; Bzowski et al., 2015; Swaczyna et al.,
2018). We neglected the secondary population of ISN He because it contributes
very little to the signal, featuring a density of only $\sim 5\%$ of the
density of the primary population (Kubiak et al., 2016, 2019).

Based on our analysis, for observations at 1 au, it is sufficient to cut off
the integration according to Equations 35 and 36 in Paper I at $\sim 20$ au
from the observer. Since the size of the helium cavity is much smaller than
that of hydrogen (cf Figure 11 in Sokół et al., 2019), in the analysis we used
lines of sight much closer to the Sun than those for ISN H, with the
elongations equal to 8°, 35°, and 56°. Generally, the distribution of ISN He
is very uniform inside the heliosphere, except for two regions: a region
inside a few tenths of au around the Sun, where it is depleted, and a cone at
the downwind side, where the density is gravitationally enhanced up to a
factor of 10. This is in stark contrast to ISN H, where in this region, the
density is strongly depleted due to ionization losses and repulsion of atoms
by the solar radiation pressure force.

###  5.2 Elements of the source function for the helium glow

The essential differences between the production of the hydrogen and helium
helioglow can be analyzed based on Figure 16, which must be contrasted with
Figure 4 for H.

Figure 16: Elements of the helium source function for an observer at 1 au
upwind for the solar minimum conditions. The lines of sight are in the polar
plane, with the solar elongations listed in the upper left panel (positive to
the north, negative to the south). The panels present the density
$n_{\text{He}}$ of ISN He at $l$ (upper left), the magnitude of the
illumination $s_{\text{He}}$ (Equation 20 in Paper I; center left), the mean
radial velocity of the gas at $l$ (lower left), the magnitude of the source
function $J_{\text{glow}}(l)$ (Equation 2 in Paper I; upper right), the
latitude of the line of sight $\phi_{\text{He}}$ (center right), and the
partial helioglow intensity $I_{\text{glow}}(l)$ (Equation 35 in Paper I;
lower right).  Figure 17: A comparison of the densities (left column) and
source function magnitudes (right column) along the lines of sight in the
ecliptic plane for the observer locations at 1 au in the ecliptic plane upwind
(top), crosswind (middle) and downwind (bottom). The elongations of the lines
of sight are indicated in the upper left panel. Negative elongation angles
mean looking to the left, positive angles to the right of the Sun. Figure 18:
For the viewing geometries identical to those presented in Figure 17, the
radial velocities (left column) and the illumination (right column) along the
lines of sight.

For large elongations from the Sun (35° and 56°), for observations carried out
from the upwind location situated in the ecliptic plane (Figure 16) the
distribution of ISN He is almost flat (see the upper left panel). Most of the
variation of the source function along the line of sight is, therefore, due to
the Doppler dimming effect, the drop of the illumination with the square of
solar distance, and the variation of the phase function (Figure 5, and
Equation 9 in Paper I). Doppler dimming is a well known effect: for the atoms
traveling with radial velocities resulting in Doppler shifts comparable to or
greater than the width of the illuminating spectral line, the excitation
function magnitude is low because only photons from far wings of the solar
line are able to excite these atoms. The radial velocity of ISN He, as shown
in the lower-left panel, varies from $\sim-50$ km s-1 near the observer up to
$\sim 20$ km s-1 for the downwind portion of the line of sight, which results
in a strong modulation of the illumination (the middle-left panel). Note that
for the lines of sight with low elongations, the increase in the magnitude of
the radial velocity is so large that due to the Doppler dimming only the
spectral background of the solar line is able to illuminate the gas.

The modulation of the excitation function along the line of sight for low
elongations is different from that for the high elongations ($\pm 35\arcdeg$
and $\pm 56\arcdeg$) because the low-elongation lines of sight intersect the
helium cone, and consequently the density within the line of sight in the
downwind region increases very significantly. This, together with the Doppler-
related increase in the illumination in a relatively narrow region behind the
Sun, results in a sharp spike in the source function. This behavior, however,
is only typical for line-of-sight elongations within a few degrees from the
Sun.

For all elongations for the upwind vantage point, the helioglow signal begins
to significantly increase only outside a few au from the observer, for the
locations in the lines of sight well in the downwind hemisphere. For other
locations, i.e., crosswind and downwind, the distribution of the density
within the lines of sight is very different, which results in significant
differences in the creation of the signal. This is illustrated in Figures 17
and 18. At the crosswind location (middle row in the figure), looking at the
two sides from the Sun results in the lines of sight going through the upwind
region (solid lines) and across the cone (broken lines). The source function
is non-negligible starting from the observer location. Then, having passed the
upwind/downwind line they drop off relatively quickly, but those going through
the cone feature a relatively narrow but strong enhancement, when the maximum
of density is traversed. Very different variation in the radial velocity
within these lines of sight result in very different illuminations. Anyway,
most of the signal is formed within 1–3 au from the observer.

At the downwind location, the lines of sight located in the ecliptic plane
show, not surprisingly, a strong left-right symmetry. Since the observed is
now located inside the helium cone, practically the entire signal is formed
within 1 au from the observer. The expected north/south asymmetry (not shown)
is mostly due to the $\sim 5\arcdeg$ inclination of the flow direction of ISN
gas to the ecliptic plane.

We conclude this section by pointing out that the WawHelioGlow code is able to
reproduce the effects expected in the formation of both the hydrogen and the
helium backscatter glows. Most interesting effects for He are expected for the
lines of sight with relatively low elongations from the Sun. Observing them
may be experimentally challenging because of the need to suppress the very
strong direct illumination from the Sun in the instrument optics. For H,
elongations of 70° are sufficient, as those planned for the GLOWS experiment
on board IMAP.

##  6 Summary and conclusions

We presented calculation results from the WawHelioGlow code, which was applied
to simulate the helioglow of ISN H and He. We analyzed the elements making up
the signal for carefully selected lines of sight and phases of the solar cycle
activity. We point out that the source function depends not only on the
obvious factors: the gas density and the magnitude of the solar illumination.
There are several other factors that vary non-trivially but within similar
amplitude ranges, and some of them have been frequently neglected. In the
first place, this is the non-flat shape of the solar Lyman-$\alpha$ profile,
which varies the illumination depending on the radial velocity of the atoms.
Another one is the variation of the illumination with heliolatitude. In the
paper, we showed how they modify the distribution of the helioglow in the sky
for various vantage points and line of sight directions. The sensitivity of
the helioglow intensity to all these factors varies, but from those discussed
in the papers, we have been unable to identify those that can be safely
neglected in all cases.

This implies that a helioglow model that may successfully be used to interpret
helioglow observations should be capable of taking all these effects into
account. We show that the WawHelioGlow model is able to do it and that, when
used in conjunction with state-of-the-art models of the solar illumination and
ionization factors, is able to reproduce full-sky maps of the helioglow, as
those obtained from SWAN, with a good fidelity.

We also demonstrated, based on a limited set of SWAN maps, that simulated maps
obtained from WawHelioGlow, in some cases agree better with observations when
a simple model of an anisotropy of the solar EUV output is adopted, in
addition to the solar wind anisotropy obtained from interplanetary
scintillation measurements. In other cases, in a different phase of the solar
cycle, the EUV anisotropy in the model seems to be unnecessary. This suggests
that the latitudinal anisotropy of the solar EUV output is varying during the
cycle of solar activity, which needs to be better investigated, and that
photometric observations of the helioglow performed from 1 au, as those
available from SWAN and planned for GLOWS can be used to that purpose. We plan
to investigate this effect in a future paper.

_Acknowledgments_.This study was supported by Polish National Science Center
grants 2019/35/B/ST9/01241, 2018/31/D/ST9/02852, and by Polish Ministry for
Education and Science under contract MEiN/2021/2/DIR.

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