Injection of cosmic rays from the wind-supernovae takes place in the stellar wind, which has a typical temperature due to cooling of around 20000 K. Therefore many elements with low first ionization potential will be doubly ionized, and so should be preferred in injection. Therefore we expect that those elements will be enhanced in the cosmic ray abundances.
This is in contrast to another well developed model of injecting cosmic
rays from spallation of energetic dust particles
(Ellison et al.
1997; Meyer et al.1997; Ramaty et al.1997).
What are the differences observationally between these two models?
), which is considered to be supported
by the energy dependence of the B/C ratio as a function of energy. Therefore,
the model uses an injection spectrum of
E-2.1...2.2. The Kraichnan
spectrum is valid for a medium, which is made stiff in one dimension by
a strong magnetic field. In the context of the standard leaky box model this
allows a straightforward interpretation of the B/C-ratio, but it is only marginally
consistent with the cosmic ray electron spectrum, which suggests an injection
spectrum near E-2.3;
-decay as a result of pp-collisions corresponding to the average spectrum of CRs
of about E-2.7, and so is inconsistent with the EGRET data. This could be remedied
by argueing that the EGRET gamma spectrum is due to inverse Compton exclusively;
such an argument has some strength because the EGRET emission extends to
fairly high latitudes in the Galaxy. The gamma spectrum based on the
model here will be discussed separately (Rhode et al. in preparation);
The abundances of cosmic rays is predicted to correspond to the
abundances in the main acceleration sites, in the stellar winds for all elements
from helium. Therefore the prediction has been that all these primary
elements should have the spectrum
E-2.67+0.00-0.04 below the knee, and
correspondingly
E-3.07+0.00-0.14 above the knee. The knee
itself is at a given rigidity and so is predicted to show a gradual change from
the lower abundances to enriched abundances
(Stanev et al.1993; Glasmacher et al.1999a, 1999b).
We furthermore predict that a major component of the cosmic ray
abundances should be traceable to the abundances in the stellar winds, folded
appropiately with the number of stars along the main sequence. This
will be elaborated on in a separate paper (CRVIII).
Nuclear reactions produce various chemical elements and their isotopes, which then get transported through the star, escpecially in stars at high rotation. This transport is due to the Voigt-Eddington circulations induced by rotation. The mixing then brings the various isotopes and chemical elements to the base of the wind zone, and then they get transported out with the wind. Therefore, any decay of these nuclei has some time to have happened before the star explodes as a supernova, and the shock races through the wind, accelerating particles to become cosmic rays. The observed isotope ratios (e.g. Connell & Simpson 1997) can be tested against such a prediction.
It has been argued for decades that the Galaxy should emit gamma rays
from the decay of
particles resulting from collisions of cosmic ray
protons, and interstellar medium protons, with a probably small contribution from nuclear
collisions of higher element nuclei such as helium (much of the early
work was done by Stecker 1971). The data originally collected
appeared to confirm this hypothesis very nicely. One could even fit in
detail the bumps and wiggles of the column density of the interstellar medium
with the gamma ray emission, confirming rather well and quantitatively the
expectations of the model. There has been a worry for a long time, that
in such a fit, the radial variation of the cosmic rays deduced appeared to
be small, while we believe to know from other galaxies, that at least the
electron component has a clear radial drop off, and so one might think the
proton component ought to show such a gradient as well.
Recently the gamma ray spectrum of the Galaxy has been measured much
better with the EGRET satellite (Hunter et al.1997). It turned out, that once again, the spatial variation of the gamma ray emission can be fit rather well,
while the spectrum can not be fitted; the authors in that paper used the approach
that the local cosmic ray intensity is correlated with the local gas density,
while as the cosmic ray spectrum they used the spectrum measured at Earth (demodulated
from Solar wind effects). The observed gamma ray spectrum is much too
flat to match the expectation based on the average oberseved cosmic ray spectrum
- as deduced from either direct measurements or from radio data, once again connecting
electrons and protons in this argument; below a few GeV this may be compensated
for by invoking various models for inverse Compton emission and Bremsstrahlung,
but at energies beyond 10 GeV the discrepancy becomes quite pronounced.
This has caused quite a stir, but sofar no obvious solution appears to be convincing
(Mori 1997; Pohl et al.1997).
The gamma ray emission can be fitted very well with a proton spectrum
which is quite a bit flatter than the observed proton spectrum
(Gaisser et al.1998; Protheroe & Stanev 1997), perhaps suggesting that we see the sources of cosmic rays. The picture suggested here would lead to the following.
As one goes up the main sequence from about 15 
,
the mass in the
shell produced by the stellar wind increases slowly, to become quite
substantial for very high mass stars at the end of their lifetimes, just before
the stars explode. Therefore, one might expect that the leakage of
cosmic ray particles may not be diffusive for lower stellar masses.
However, there are many more lower mass stars, and so the -producing
collisions are dominated by the interaction in the shells of the lower mass
stars, where the leakage is probably convective, and not diffusive.
Then the interaction is with the primary spectrum, and so the gamma ray spectrum
is predicted to match a proton (and helium) energy spectrum of
E-7/3. This is consistent with the gamma-ray spectral fit, which
shows a minimum 
-fit in a spectral range between 2.3 and 2.4 (Rhode et al., in preparation).
In the wind shells around stars of the mass range above 15 solar masses
gamma rays are produced from pp-interactions; in the same channel we
produce positrons. Therefore we predict the positrons to to arise from two
contributions: for the mass range 15 to 25 solar masses positrons are
produced with a spectrum identical to the source spectrum, and for the
mass range above about 25 solar masses positrons are produced with a spectrum
which is E-5/9 steeper. The sum of these two contributions needs to be
balanced against the three contributions for electrons: a) electrons
arise directly from those supernovae that explode into the interstellar
medium, with a predicted spectrum of
.
As noted earlier
(Biermann & Strom 1993) the electrons from supernovae that explode into the
interstellar medium, suffer from adiabatic losses, and so their contribution
does not fully reflect the abundance of the progenitor stars. b)
Electrons are both accelerated and also produced in pp-collisions as secondaries
with a spectrum of
E-2.67+0.00-0.04 in the convective interaction
mode in the wind shells around stars of zero age mass 15 to 25 solar masses. c)
The stars with higher mass have a diffusive interaction for energetic
particles in their wind shell and so make primary electrons again with
E-2.67+0.00-0.04, and secondary electrons and positrons with
E-26/9, where we omit the uncertainties. This will be discussed separately
(Paper CR VI).
Anti-protons have the again pp-collisions as sources, but of course get produced only at some higher energy. Both zero age mass ranges, 15-25 solar masses, and above 25 solar masses, again contribute just as for positrons, and with the corresponding spectra. This will be discussed separately (Sina et al., in preparation).
Radioactive nuclei that arise as a consequence of spallation decay. Since the production is predicted here to be happening in the thick wind shells around very massive progenitor stars, the decay has all subsequent time available from diffusive leakage from the Galaxy. For this diffusive leakage we adopted the description based on a Kolmogorov spectrum for the turbulence. The recent data have been discussed by Connell & Simpson (1997), Simpson & Connell (1998), Connell (1998), and Connell et al. (1998). In the model presented here the interaction is all the same, independent of isotope, and since we measure at rather low particle energy, almost certainly in the energy range, where the transport in the interaction shell is convective (and, presumably, also the interstellar transport), and therefore the ratios are not expected to depend on energy except through time-dilation at relativistic speeds. However, the initial ratio of the isotopes is fixed as they leave the source region, and the ratio changes as the particles are transported through the Galaxy, and therefore the grammage seen by the particles should all be identical, and their isotope ratio should just reflect the different times available. With the data as available, no differentiation to a standard leaky box model is possible. We will develop this approach separately.
One of the strongest tests for this model is the calculation of the expected gamma ray emission at high TeV and PeV photon energies, to be compared with CASA-MIA data and future MILAGRO data. While we have done some preliminary tests of this (to be published) that encourage us, we have not finished this test. For this test the bend, the knee, in the cosmic ray spectrum has to be taken into account, since in this model it is there already in the source.
Copyright ESO 2001