1.14.7. Summary of main results and discussion
The results obtained allowed the estimate of the expected distribution of gamma ray emissivity in the Heliosphere or in some stellar-sphere, to estimate the expected fluxes of gamma rays and their time variations for observations of gamma rays from the solar wind or from the nearest stellar winds. According to Eq. 1.14.20 gamma ray emissivity in the interplanetary space will be bigger than in the interstellar space only in the inner part of the Heliosphere at r < 3 AU and with decreasing of r gamma ray emissivity will increase as about « r ~2 . In the main part of the Heliosphere gamma ray emissivity will be many times smaller than in the interstellar space. This means that the Heliosphere, as well as many stellar-spheres, can be considered as holes in the galactic background gamma ray emissivity distribution.
According to Eq. 1.14.26 and Table 1.14.1 the biggest expected gamma ray
flux from the solar wind («1 = 5 cm ) in the direction 2° from the Sun and near the minimum of solar activity will be about the same as from interstellar matter
(no ~ 0.1 cm ) with a size ~ 10 cm (at about two orders more than the size of the Heliosphere). This expected gamma ray flux decreases by time several times during maximum of solar activity and decreases by about two orders with increasing angle p up to the opposite direction from the Sun (see Table 1.14.2).
Let us compare this variable gamma ray flux with the background gamma ray flux from galactic CR interactions with interstellar matter. In the direction perpendicular to the disc plane background gamma ray flux is formatted on the distance about 200
pc = 6 x 10 cm, therefore this background gamma ray flux will be about 6 x10
times more than the largest expected from solar wind gamma ray flux in the direction 2° from the Sun. From this, it follows that it is now not possible to measure gamma rays from the solar wind generated by galactic CR modulated by the solar activity cycle. But in the future, with the increasing of accuracy of gamma ray telescopes and by using the big variability of this very weak gamma ray source, it will be possible to investigate this phenomenon and obtain some additional information about the solar wind's matter distribution and galactic CR modulation in the Heliosphere.
If measurements of gamma rays from the solar wind generated by galactic CR are made outside the Heliosphere, the following effect can be observed: in directions not far from the Sun this gamma ray flux will be about two orders larger than from interstellar matter of the same size as the Heliosphere, but in measurements at large angles from the Sun gamma ray flux much smaller than expected from interstellar matter of the same size as the Heliosphere will be observed. According to Eq. 1.14.29 the ratio of total gamma ray flux from the solar wind or from stellar wind O Sw to the gamma ray flux from the same volume of interstellar medium O M will be
which will be changed in time according to Table 1.14.2 with the solar or stellar cycle and depends on Ey. Table 1.14.2 shows that J(b, A) for the Heliosphere increases from 0.73 to 1.29 with decreasing a(ey , t) from 0.8 to 0, and with increasing b from 0.13 to 0.45, so that for the rough estimates we can put J(b,A)=1. In this case Eq. 1.14.31 for the solar wind (r1 = 1AU, ro = 100AU,
«1 = 5cm , no ~0.1cm ) gives ~ 7.5x 10 . It means that the Heliosphere can be considered as a deep variable hole in the background gamma ray emissivity distribution.
The value of ratio (Eq. 1.14.31), stellar wind density n^t at the distance 1 AU from the star and dimension of the hole rogt are determined mainly by the value of mass loosing rate by star Mst (for the Sun MSun 10—14 MSun/year) and speed of wind «1st on the distance 1 AU from the star:
n1St = n1w1M St/(1StM Sun ) roSt = ro (1StM St IU1M Sun )2, (1.14.32) from which it follows that
Here we assume that conditions around the star (CR and magnetic field pressure) are the same as near the Sun. Eq. 1.14.32 shows that the dimension of holes in gamma ray emissivity increases with increasing of stellar wind speed and the rate of mass loosing in degree 'A The depths of the gamma ray hole according to Eq. 1.14.33 increases with stellar wind velocity in square. For example, for a star with
A^St ~ 10—8MS^/year and w^t = 108cm/sec,we obtain n^t = 2x 106cm —3, roSt = 15 x105AU, and O Stw/oSw ~ V^. Let us note that in this case observation along a line near the star (see Table 1.14.1) will give a gamma ray flux
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