In this section, we present results obtained from our model computations. The first subsection shows that the three populations of H atoms have clearly distinct spectral features. Those features are averaged out for multiple scattered components of the intensity. In the second subsection, we present intensities, line shifts and line widths at 1 AU. The last part outlines the differences between the 3p model and the results of Quémerais (2000) obtained for the hot model.
Before detailing the results of the 3p model, it is interesting to try and separate the different terms due to the three hydrogen populations. For this, we will consider only the first order of scattering. For higher orders of scattering the spectral features tend to be averaged over the different populations.
We have computed the line profiles in the case of the
self-absorbed approximation (SA). The three moments, intensity,
apparent velocity and apparent temperature can be computed for
each of the populations and for the sum of the three components.
For each of these computations, the observer is at 1 AU from the
sun and is looking radially away from the sun.
Figures 4 and 5 show actual line profiles for both upwind and downwind directions. The HSWA population (dotted line) is much hotter than the other two populations. Although it is optically thin, it is slightly absorbed by the other two populations. The PIA component (dash-dot line) is faster than the HIA component (dashed line).
Tables 3 and 4 show the intensity, apparent velocity and apparent
temperature for the self-absorbed line profiles as a function of
the angle from upwind. Those values are also computed for each of
the three populations. Although the HSWA component intensity
is fairly small in the upwind direction (less than 5% of total),
it represents a larger fraction in the downwind direction mainly
because it is much more isotropic than the other two components.
The slower component (HIA) is the one which is the more
depleted in the downwind cavity because ionization processes are
more effective for slower atoms in the solar rest frame.
angle | Total | HSWA | PIA | HIA |
(![]() |
(R) | (%) | (%) | (%) |
0 | 862 | 4.3 | 43.2 | 52.5 |
20 | 839 | 4.4 | 43.2 | 52.4 |
40 | 770 | 4.7 | 43.4 | 51.9 |
60 | 670 | 5.2 | 44.0 | 50.8 |
80 | 561 | 5.9 | 44.6 | 49.5 |
100 | 459 | 6.9 | 44.9 | 48.3 |
120 | 367 | 8.1 | 45.3 | 46.7 |
140 | 281 | 10.0 | 46.8 | 43.2 |
160 | 210 | 12.9 | 50.8 | 36.3 |
180 | 179 | 14.9 | 54.3 | 30.8 |
Apparent velocity in km s-1 | |||||
angle | Total | HSWA | HIA | PIA | |
0![]() |
-28.18 | -24.90 | -24.63 | -31.36 | |
30![]() |
-25.09 | -23.27 | -22.19 | -27.65 | |
60![]() |
-16.59 | -18.08 | -15.38 | -17.47 | |
90![]() |
-4.75 | -10.64 | -5.66 | -3.14 | |
120![]() |
7.24 | -2.98 | 4.64 | 11.53 | |
150![]() |
15.49 | 2.59 | 12.70 | 22.53 | |
180![]() |
17.64 | 4.84 | 15.84 | 27.03 | |
Apparent temperature in K | |||||
angle | Total | HSWA | HIA | PIA | |
0![]() |
17 590 | 18 1415 | 13 508 | 4928 | |
30![]() |
17 927 | 18 0469 | 14 187 | 5307 | |
60![]() |
19 817 | 18 3057 | 15 928 | 6154 | |
90![]() |
24 104 | 19 0651 | 18 085 | 6978 | |
120![]() |
30 475 | 20 0469 | 19 020 | 6981 | |
150![]() |
40 026 | 20 8312 | 17 718 | 6483 | |
180![]() |
48 744 | 21 1575 | 16 282 | 5902 |
Table 4 shows that the HSWA component is apparently much
hotter than the other two components. When computing the line
profile, we see that this component does not affect the center of
the backscattered line but only contributes to the wings. In that
sense, we will only consider the two cooler components when
computing apparent temperatures in the rest of this work because
they are the ones which correspond to line center photons. When
computing apparent temperatures, we must give a temperature for
the line center. Including the HSWA component term leads to
overestimates of the line width because the actual profile is far
from the Gaussian shape.
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0 | 1033 | -27.3 | 11 608 | 1.08 | 0.75 | 0.83 | 0.87 | 0.89 | 0.88 |
10 | 1035 | -27.0 | 11 436 | 1.07 | 0.74 | 0.83 | 0.88 | 0.90 | 0.89 |
20 | 1022 | -26.0 | 11 478 | 1.06 | 0.74 | 0.82 | 0.88 | 0.90 | 0.89 |
30 | 986 | -24.2 | 11 491 | 1.06 | 0.74 | 0.82 | 0.87 | 0.91 | 0.89 |
40 | 953 | -21.9 | 11 471 | 1.05 | 0.73 | 0.81 | 0.88 | 0.92 | 0.90 |
50 | 896 | -19.0 | 11 687 | 1.05 | 0.72 | 0.81 | 0.87 | 0.92 | 0.90 |
60 | 837 | -15.6 | 11 929 | 1.04 | 0.72 | 0.80 | 0.87 | 0.93 | 0.91 |
70 | 785 | -11.8 | 12 301 | 1.02 | 0.70 | 0.78 | 0.86 | 0.94 | 0.92 |
80 | 723 | -7.8 | 12 715 | 1.01 | 0.70 | 0.78 | 0.86 | 0.96 | 0.93 |
90 | 666 | -3.6 | 13 219 | 1.00 | 0.68 | 0.76 | 0.86 | 0.98 | 0.94 |
100 | 616 | 0.6 | 13 833 | 0.98 | 0.67 | 0.75 | 0.85 | 0.99 | 0.95 |
110 | 562 | 4.7 | 14 269 | 0.97 | 0.66 | 0.73 | 0.85 | 1.01 | 0.97 |
120 | 514 | 8.5 | 14 624 | 0.95 | 0.64 | 0.71 | 0.86 | 1.03 | 0.98 |
130 | 461 | 12.0 | 15 053 | 0.93 | 0.62 | 0.70 | 0.85 | 1.03 | 0.99 |
140 | 411 | 14.9 | 15 533 | 0.92 | 0.61 | 0.68 | 0.85 | 1.03 | 0.98 |
150 | 365 | 17.3 | 16 135 | 0.90 | 0.59 | 0.66 | 0.83 | 1.01 | 0.96 |
160 | 329 | 19.0 | 16 670 | 0.87 | 0.57 | 0.64 | 0.81 | 0.99 | 0.95 |
170 | 302 | 19.7 | 16 735 | 0.85 | 0.55 | 0.62 | 0.82 | 1.00 | 0.95 |
180 | 290 | 20.0 | 16 568 | 0.84 | 0.55 | 0.62 | 0.83 | 1.01 | 0.97 |
An example of a 3p full radiative transfer line profile is shown in Fig. 6. This has been computed for an observer at 1 AU crosswind from the sun and looking radially away from the sun. The primary term (sum of the three populations) is shown by the the dashed line. The total line is shown by the thick line and the secondary term, due to photons that have been scattered more than once between the sun and the observer, is shown by the dotted line. From Table 5, we see that the dotted line (secondary term) represents a bit more than 30% of the total intensity.
Table 5 gives the numerical values of the 3p total intensity, apparent velocity and apparent temperature as a function of the angle from the upwind direction. These values where obtained for a observer at 1 AU from the sun looking radially away from the sun. Note that, as stated above, the apparent temperature is computed using only the PIA and HIA populations which represent the temperature of the core of the line. Intensities and apparent velocities are computed using all three populations. The next three columns of Table 5 give the intensity ratio of the three approximations mentioned above with the total intensity. We have also compared the apparent temperatures obtained from the approximation with the apparent temperature obtained for the complete calculation. In general, the temperature obtained from the primary term is in good agreement with the apparent temperature found for the complete calculation, except in the upwind direction where the apparent temperature is underestimated. The self-absorbed case also gives a correct approximation. As usual is such computations, the optically thin case tends to underestimate the apparent temperature by roughly 15%, i.e. here by 1500 K. On the other hand, the optically thin case gives the best approximation for the total intensity. Note however that the upwind to downwind ratio is significantly changed by multiple scattering effects. This result was also observed in the case of the hot model by (Keller et al. 1981; Hall 1992; Quémerais & Bertaux 1993; Quémerais 2000). Multiple scattering effects tend to fill the downwind cavity when compared to the optically thin case. This decreases the contrast between the upwind and downwind directions.
The results of Table 5 are shown in Figs. 7-9. Figure 8
shows that the apparent velocity is not very sensitive to the way
the background profile is computed. However, the optically thin
case gives an approximation of the apparent velocity which is
always within 1 km s-1 of the actual value. The other two
approximations are within 3 km s-1. In Fig. 9, we have displayed
the apparent temperature of the line profiles as a function of the
upwind direction. This apparent temperature corresponds to the sum
of the two cooler populations, the PIA and HIA
populations. We see in this figure that the full 3p calculation,
the primary and self-absorbed calculations give very similar
values in the downwind hemisphere. Yet the full 3p calculation
is larger in the upwind direction, because it adds a component
which is slower (less Doppler shifted) than the two primary
components. In the upwind direction, the difference is roughly
1500 K. When comparing those data with optically thin or
self-absorbed model computations, as done by Costa et al. (1999),
one must roughly remove 1500 K to the observed value in the upwind
direction to account for multiple scattering effects.
Our interest here is to find ways to discriminate between interface models and hot models as seen from one AU. The reader is referred to Quémarais (2000) for the computation of the Hot model UV background results.
First, it must be pointed out that the main difference between the two types of models can be seen on the spectral profile of the backscattered line (Figs. 4-6). Indeed, the three-population type line profiles are much more dissymmetric than hot model line profiles. This is due to the existence of the faster unperturbed lism component and slower HIA component which are averaged in a unique population in the case of the hot model.
Furthermore, the existence of the hot component (HSWA) in the 3p model is a very obvious tool in this study. It has no counterpart in the Hot model. This result will used to reanalyze the hydrogen cell measurements of the SWAN instrument which are very sensitive to doppler shift.
If we consider the intensity measurements, we note that the two types of models are very similar in the upwind hemisphere. The upwind to crosswind intensity ratio will not give any useful information. The upwind to downwind intensity ratio could be used here, unfortunately this requires to have a very good knowledge of the effective radiation pressure at the time of observation. Indeed, we know that changes of the radiation pressure have effects on the upwind to downwind intensity ratio which are of the same order of magnitude as the one we are seeing between the two types of hydrogen distributions. This becomes even more difficult if we consider solar cycle variation of the radiation pressure as shown by Bzowski et al. (2001). At the present time, the uncertainty on the actual radiation pressure from the sun does not allow us to discriminate between the two types of hydrogen models by simply studying the upwind over downwind intensity ratio. Let us note also that the apparent velocity is sensitive to the value of the radiation pressure.
Finally, we can compare the apparent temperature deduced from
these models (Fig. 9). We see that the line width is larger in
the downwind direction in the case of the existence of the
heliospheric interface. However, the change is rather small (10%)
and once again the uncertainty on the various interstellar and
solar parameters will prevent an easy diagnostic from observations
obtained at one AU from the sun. We can also note that the
apparent temperature of the 3p model as a function of the angle
with the upwind direction is almost constant within 50
of the
upwind direction (see Fig. 9). This is not true for the hot
model. In that second case, we find an increase of 600 K at
50
from the upwind value. A similar effect was described by
Costa et al. (1999) from the study of hydrogen cell data. Further
data analysis will be required to clarify this point.
Copyright ESO 2002