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Gamma ray and antiparticles ($e^+$ and $\overline{p}$) as tools to study the propagation of cosmic rays in the Galaxy

P. Lipari

in 35th International Cosmic Ray Conference

Contribution: pdf


The spectra of cosmic rays observed at the Earth are determined by
the properties of their sources and by the properties of their propagation
in the Galaxy. Disentangling the source and propagation effects
is a problem of central importance for cosmic ray astrophysics.
To address this problem, the study of the fluxes of antiparticles
($e^+$ and $\overline{p}$) and of the diffuse Galactic flux of
$\gamma$ can be a very powerful tool,
because it is expected that the dominant mechanism of production
is identical for all three components,
namely the creation of the particles as secondary products in the interactions of primary cosmic rays. In this case, the shape and relative size
of the source spectra for the three particles is reasonably well known.
Folding the inclusive hadronic cross section with the (power law) energy distribution
of the primary particles one obtains secondary source spectra that
for $E \gtrsim 20$~GeV, in good approximation,
are also of power law form, with the same spectral index of the primary particles.
The predicted ratios at production are $e^+/\overline{p} \simeq 2$
and $\gamma/e^+ \simeq 5$.
The observed spectra of $e^+$, $\overline{p}$ and $\gamma$
are power laws with spectral indices
$\alpha_{e^+} \simeq \alpha_{\overline{p}} \simeq \alpha_\gamma \simeq 2.7$--2.8,
with an observed ratio $e^+/\overline{p} \simeq 2$, equal to the ratio
at production. These results suggests that the propagation effects for charged particles
have only a weak energy dependence, and are approximately
equal for $e^+$ and $\overline{p}$. This implies that the total energy losses
for $e^\pm$ during propagation in the Galaxy is negligible, and
therefore that the cosmic ray Galactic residence time is sufficiently short.
An intriguing possibility is that a marked softening of the
energy spectrum of the flux of $(e^+ + e^-)$ observed by the
Cherenkov telescopes at $E \approx 0.9$~TeV is the manifestation of the critical energy
where the energy losses of $e^\mp$ becomes important. This assumption determines the Galactic residence time as of order $T_{\rm age} (1~{\rm TeV}) \approx 1$~Myr.
A comparison of the fluxes of antiparticles and the diffuse Galactic $\gamma$ flux allows then to estimate the effective cosmic ray confinement volume as
$V_{\rm CR} \simeq 300$~kpc$^3$. These tentative conclusions
are in potential conflict with common interpretations
of the fluxes of secondary nuclei (such as lithium, beryllium and boron)
and require significant production of secondary nuclei inside or near the accelerators.
Models where the cosmic ray confinement time is significantly longer
than 1~Myr require a new hard source of positrons in the Galaxy, that must
be fine tuned in spectral shape and absolute normalisation.
The implications of this puzzle are of profound importance for
high energy astrophysics and the modelling of the cosmic ray accelerators.