Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...
Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...
Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...
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6.3.2 <strong>The</strong>rmal and chemical evolution<br />
In calcul<strong>at</strong>ing the evolution <strong>of</strong> the primordial clouds, we solve the com-<br />
prehensive chemical reaction network for all the species included in Johnson<br />
and Bromm (2006), and consider cooling due to H, H2, and HD. <strong>The</strong> tempera-<br />
ture <strong>of</strong> the CMB sets the lower limit to which the gas can cool radi<strong>at</strong>ively (e.g.<br />
Larson 1998). Assuming th<strong>at</strong> CRs with the above energy spectrum impinge<br />
upon the primordial gas cloud, we add the respective he<strong>at</strong>ing and ioniz<strong>at</strong>ion<br />
r<strong>at</strong>es. Once a low-energy CR enters the high-density region <strong>of</strong> the cloud, each<br />
time it ionizes an H <strong>at</strong>om, an electron with average energy < E >= 35 eV<br />
is released (Spitzer and Tomasko 1968). Including the ioniz<strong>at</strong>ion energy <strong>of</strong><br />
13.6 eV implies th<strong>at</strong> a CR proton loses approxim<strong>at</strong>ely 50 eV <strong>of</strong> kinetic energy<br />
upon each sc<strong>at</strong>tering. This places a limit on the number <strong>of</strong> sc<strong>at</strong>terings a CR<br />
can undergo in a cloud as well as a limit on the distance into the cloud th<strong>at</strong><br />
it can reach before it loses all its energy to ioniz<strong>at</strong>ion. This distance can be<br />
described <strong>by</strong> a penetr<strong>at</strong>ion depth<br />
where (Schlickeiser 2002)<br />
and<br />
−<br />
Dp(ɛ) ≈<br />
βcɛ<br />
− <br />
dɛ<br />
dt<br />
ion<br />
, (6.21)<br />
<br />
dɛ<br />
= 1.82 × 10<br />
dt ion<br />
−7 eV s −1 nH0f(ɛ), (6.22)<br />
f(ɛ) = (1 + 0.0185 lnβ)<br />
158<br />
2β 2<br />
β3 , (6.23)<br />
0 + 2β3