| Gas Temp | $n=0.001~\text{cm}^{-3}$ | $n=0.01~\text{cm}^{-3}$ | $n=0.1~\text{cm}^{-3}$ | $n=1~\text{cm}^{-3}$ |
|---|---|---|---|---|
| $10^1~\text{K}$ | $1.8\times10^{21}~\text{yr}$ | $1.8\times10^{20}~\text{yr}$ | $1.8\times10^{19}~\text{yr}$ | $1.8\times10^{18}~\text{yr}$ |
| $10^2~\text{K}$ | $5.8\times10^{18}~\text{yr}$ | $5.8\times10^{17}~\text{yr}$ | $5.8\times10^{16}~\text{yr}$ | $5.8\times10^{15}~\text{yr}$ |
| $10^3~\text{K}$ | $1.8\times10^{16}~\text{yr}$ | $1.8\times10^{15}~\text{yr}$ | $1.8\times10^{14}~\text{yr}$ | $1.8\times10^{13}~\text{yr}$ |
| $10^4~\text{K}$ | $5.8\times10^{13}~\text{yr}$ | $5.8\times10^{12}~\text{yr}$ | $5.8\times10^{11}~\text{yr}$ | $5.8\times10^{10}~\text{yr}$ |
| $10^5~\text{K}$ | $1.8\times10^{11}~\text{yr}$ | $1.8\times10^{10}~\text{yr}$ | $1.8\times10^{9}~\text{yr}$ | $1.8\times10^{8}~\text{yr}$ |
| $10^6~\text{K}$ | $6.8\times10^{8}~\text{yr}$ | $6.8\times10^{7}~\text{yr}$ | $6.8\times10^{6}~\text{yr}$ | $6.8\times10^{5}~\text{yr}$ |
| $10^7~\text{K}$ | $1.0\times10^{8}~\text{yr}$ | $1.0\times10^{7}~\text{yr}$ | $1.0\times10^{6}~\text{yr}$ | $1.0\times10^{5}~\text{yr}$ |
| $10^8~\text{K}$ | $1.0\times10^{8}~\text{yr}$ | $1.0\times10^{7}~\text{yr}$ | $1.0\times10^{6}~\text{yr}$ | $1.0\times10^{5}~\text{yr}$ |
$\tau_\text{sp}=a\Big|\frac{da}{dt}\Big|^{-1}\approx(0.17~\text{Gyr})\Big(\frac{a_{-1}}{\rho_{-27}}\Big)\Big[\Big(\frac{T_0}{T}\Big)^\omega+1\Big]$
These numbers assume a constant grain radius of 0.1 $\mu$m.