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Ionization Rate

Figure 4.3: Ionization fractions $X/n_{\rm H}$ are plotted against the number density $n_{\rm H}$. The ionization rate of an H$_2$ molecule by cosmic rays outside the cloud is taken $\zeta_0 = 1 \times 10^{-17} {\rm s^{-1}}$. 20% of C and O and 2% of metallic elements are assumed to remain in the gas phase and the rest in grains.
\begin{figure}\centering\leavevmode
\epsfxsize =.45\columnwidth \epsfbox{eps/nnu2002.ps}\end{figure}

In the dense clouds, the ionization fraction is low. Since the uv/optical radiations from stars can not reach the cloud center, potential ionization comes from the cosmic ray particles. In this case the rate of ionization per volume is given as $\zeta n_n$, where $\zeta\sim 10^{-17}{\rm s^{-1}}$. In Figure 4.3, the ionization fraction for various density is shown (Nakano, Nishi, & Umebayashi 2002). This clearly shows that the fraction of ions decrease approximately in proportion to $n_{\rm H}^{-1/2}$ for $n_{\rm H}\mbox{\raisebox{0.3ex}{$<$}\hspace{-1.1em}
\raisebox{-0.7ex}{$\sim$}} 10^8{\rm cm^{-3}}$. This is understood as follows: Equilibrium balance between one kind of ion $m^+$ and its neutral $m^0$

\begin{displaymath}
m^0 \leftrightarrow m^+ + e^{-},
\end{displaymath} (4.35)

is considered. The recombination (reaction from the right to left) rate per unit volume is expressed $\alpha n_e n_{m^+}$, while the ionization rate (left to right) per unit volume is $\zeta n_{m^0}$, where $\alpha $ means the recombination rate coefficient. Nakano (1984) obtained in the range of $10^2{\rm cm^{-3}}\mbox{\raisebox{0.3ex}{$<$}\hspace{-1.1em}
\raisebox{-0.7ex}{...
...isebox{0.3ex}{$<$}\hspace{-1.1em}
\raisebox{-0.7ex}{$\sim$}} 10^8{\rm cm^{-3}}$
\begin{displaymath}
\rho_i = C \rho_n^{1/2},
\end{displaymath} (4.36)

where the numerical factor $C=4.46\times 10^{-16}{\rm g^{1/2} cm^{-3/2}}$.


next up previous contents
Next: Ambipolar Diffusion Up: Ambipolar Diffusion Previous: Ambipolar Diffusion   Contents
Kohji Tomisaka 2007-07-08