Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...

and
where
ΓCR(D) = 5 × 10 −29 erg cm −3 s −1
×
Eheat nH0 6 eV 1 cm3
ɛmin
106 eV
ζCR(D) = 5 × 10 −18 s −1
I(ɛ) =
UCR
2 × 10−15 erg cm−3 −1 UCR
2 × 10 −15 erg cm −3
I(ɛ) (6.27)
ɛmin
×
106 −1 I(ɛ), (6.28)
eV
ɛmax
ɛmin f(ɛ)
x ɛ
e ɛmin
−D/Dpdɛ x+1 ɛmax ɛ
dɛ
ɛmin
ɛmin
. (6.29)
The factor Eheat is equal to 6 eV for the minihalo case because, though
CRs lose about 50 eV of energy after each ionization, only about 6 eV of that
energy goes toward heating in a neutral medium (see Spitzer and Scott 1969;
Shull and van Steenberg 1985). The value of Eheat increases for media with
larger ionization fractions due to an increase in Coulomb interactions between
the newly freed electrons and the medium, and for the ionization fractions
typical of the virialization shock case, one has Eheat 26 eV.
The minimum kinetic energy, ɛmin, with which the CRs impinge upon
the gas clouds can be roughly estimated by assuming that during Fermi ac-
celeration a particle will acquire the velocity of the shock wave itself after
crossing it a single time (see Bell 1978b). This gives a minimum energy
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