5 Energetic neutral atoms from the pick-up ions

Figure 8: PUI-ENA H spectra ($\alpha =-2$) from outside and from inside of the termination shock. Three directions of the ENA flux are shown: from the LISM apex, from the direction at right angle to it in the ecliptic plane, and from the anti-apex direction. The post-shock spectrum is shown by the thicker lines.

Figure 9: PUI-ENA H spectra ($\alpha =-3$) from outside and from inside of the termination shock. Three directions of the ENA flux are shown: from the LISM apex, from the direction at right angle to it in the ecliptic plane, and from the anti-apex direction. The post-shock spectrum is shown by the thicker lines.

Figure 10: PUI ENA H flux as a function of direction for 16 keV H ($\alpha =-2$ case). The post-shock and pre-shock contributions are shown by the dashed lines. The angle $\theta$ is counted from the apex direction.

The post-shock PUI distribution cannot as yet be observed in situ. One possibility is an indirect observation using as messengers the energetic neutral atoms (ENA), into which the PUI are converted by capturing electrons from the atoms of the background at the occasion of charge-exchange collisions (the first discussion of the heliospheric ENA was given by Hsieh et al. 1992). Below we calculate the flux of ENA corresponding to the PUI distributions derived above.

The flux of ENAs observed at the point $\vec{x}_0$ from the direction $\vec{n}$: $j_{\rm ENA}(\vec{x}_0,\vec{n},E)$, can be obtained integrating along the line-of-sight $\vec{x}_s=\vec{x}_0+s\vec{n}$ the flux of pick-up ions relative to the neutral component multiplied by the density of the background neutral atoms and by the charge-exchange cross section. The neutral components move at low speed in the fixed frame, so that we can use as a good approximation the PUI flux in the fixed frame: $j_{\rm PUI}$ and neglect the difference between the velocity relative to the observer and that relative to the neutral background:

$$j_{\rm ENA}(\vec{x}_0,\vec{n},E)= \int_0^\infty {\rm d}s \ j_{\rm... ...{\rm cx,H}(E)+n_{\rm He}(\vec{x}_s)\sigma_{\rm cx,He}(E)]{\rm ext}(\vec{x}_s,E)$$ (26)

where ext $(\vec{x}_s,E)$ is the extinction factor describing the losses of the second generation by charge-exchange and stripping.

Figure 11: PUI ENA H flux as a function of direction for 16 keV H ($\alpha =-3$ case). The post-shock and pre-shock contributions are shown by the dashed lines. The angle $\theta$ is counted from the apex direction.

Figure 12: ENA flux: the data points show the flux (units (cm2 s sr keV)-1) of $\rm mass=1$particles in low energy channels ($\sim$58-88 keV) observed during quiet times (low ion flux) by CELIAS/HSTOF instrument. The results are the revised ones, taking the cross-calibration with ACE and IMP8 into account (Hilchenbach et al. 2000). Superimposed curve represents the calculated flux in the field of view of the instrument, of 63 keV hydrogen ENAs from PUI transcharging for the case $\alpha =-3$ (the flux for $\alpha =-2$ case is too high by an order of magnitude).

The PUI ENA hydrogen flux corresponding to the model pick-up proton distributions is presented in Figs. 8-12. The calculations were done for the case of observations from the inner solar system (e.g. Earth's orbit) with the line-of-sight directed radially away from the Sun. Figures 8 and 9 show the PUI ENA spectrum for the cases $\alpha =-2$ and $\alpha =-3$, respectively. Note that the pre-shock ENA flux is negligible compared to the post-shock contribution in the normal turbulence ($\alpha =-3$) case. This is obviously due in part to the effect of plasma motion (if the pre-shock PUI velocity distribution in the plasma frame would be cut off at the solar wind energy there would be no sunward ENA flux at all). In the $\alpha =-2$case the result is opposite due to strong pre-acceleration: this case is, however, unrealistic.

Figures 10, 11 illustrate the directional dependence of the ENA flux for the sample energy value of 16 keV (the flux for 63 keV for the case $\alpha =-3$ is shown in Fig. 12). In the normal turbulence case ($\alpha =-3$) there is a pronounced peak in the flux from the anti-apex direction, provided the energy is not too low (see also Fig. 9). The peak is due to the concentration of the PUI in the heliotail (Figs. 4 and 5) due to convection by the plasma flow and to the asymmetric shape of the heliopause. The position of the minimum of the flux is away from the apex. The (unrealistic) $\alpha =-2$ case, where the flux is dominated by the contribution from the pre-shock region, behaves differently, with the maximum flux coming from the apex direction.

5.1 Comparison with observations

The first detection of what may be the ENA of heliospheric origin is due to CELIAS/HSTOF (Hilchenbach et al. 1998). The acronym denotes the High-energy Suprathermal Time-of-Flight sensor (HSTOF) of the Charge, Element and Isotope Analysis System (CELIAS). It is operating on board of the SOHO spacecraft, situated near the Lagrangian point L1 between Earth and the Sun. The instrument has the line-of-sight directed $37^\circ$ west off the Sun, with the field-of-view $\pm 2^\circ$ wide in longitude and $\pm$$17^\circ$ in latitude. During the course of one year it scans over all directions in the ecliptic plane.

The observations of ENA are possible only during the periods of relatively low ion flux intensity, the "quiet times''. For these periods, the $\rm mass=1$   events in the low energy channels (58-88 keV) were interpreted as neutral hydrogen atoms. The results are shown in Fig. 12. These include the changes due to in-flight new calibration of the instrument (Hilchenbach et al. 2000) which raised the previous estimations of the flux by a factor of 10. Note that there are many data points for the two first years of observations (1996 and 1997) which were characterized by low solar activity. The quiet time $\rm mass=1$ flux in the 55-80 keV range peaked during the periods near $\rm DOY=200$, close to the time ( $\rm DOY=194$) when the instrument's line-of-sight was directed towards anti-apex of the LISM. In 1998 the contact with SOHO was lost for a period of time including DOY 200. The high solar activity during 1999 reduced the quiet time periods, and in 2000 the situation was even worse due to a big solar flare ("Bastille Day flare'' of June 14th). The observations are compared with the calculated ENA hydrogen flux from the pick-up proton distribution for the $\alpha =-3$ case, at 63 keV (which approximates the average energy of the observed particles in the 58-88 keV range). With no adjustments in the model parameters, the calculated flux intensity is close to the observed flux. Note a small shift of the observed flux peaks from the anti-apex position. This is not necessarily inconsistent with the PUI ENA model, because the direction towards the heliotail may be different from the anti-apex due to the interstellar magnetic field (Fahr et al. 1988; Ratkiewicz et al. 1998; Czechowski & Grzedzielski 1998).

Figures 13 and 14 present the results for the ENA energy spectrum. To derive the spectrum from the SOHO data one must subtract the flux of protons which penetrate into the instrument from the measured total mass=1 flux. The uncertainty in the quiet time proton flux (assumed to follow a power law of E^-2.5) and in the probability of proton transmission would introduce a systematic error in the ENA flux. Only for the three lowest energy data points this error is expected to be small (<10%, Hilchenbach et al. 2000). The calculated spectrum is clearly steeper than the data.