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Table 5:

Two-dimensional shielding functions $\Theta [N(^{12}{{\rm CO}}),N({{\rm H}}_2)]$ for $b({{\rm CO}})=0.3$ km s-1, $T_{{\rm ex}}({{\rm CO}})=5$ K and $N(^{12}{{\rm CO}})/N(^{13}{{\rm CO}})=69$a.
$\log N({{\rm H}}_2)$ $\log{} ^{12}{{\rm CO}}$ (cm-2)
(cm-2) 0 13 14 15 16 17 18 19
12CO: unattenuated rate $k_{0,i}=2.592~\times~10^{-10}$ s-1
0 1.000 8.080(-1) 5.250(-1) 2.434(-1) 5.467(-2) 1.362(-2) 3.378(-3) 5.240(-4)
19 8.176(-1) 6.347(-1) 3.891(-1) 1.787(-1) 4.297(-2) 1.152(-2) 2.922(-3) 4.662(-4)
20 7.223(-1) 5.624(-1) 3.434(-1) 1.540(-1) 3.515(-2) 9.231(-3) 2.388(-3) 3.899(-4)
21 3.260(-1) 2.810(-1) 1.953(-1) 8.726(-2) 1.907(-2) 4.768(-3) 1.150(-3) 1.941(-4)
22 1.108(-2) 1.081(-2) 9.033(-3) 4.441(-3) 1.102(-3) 2.644(-4) 7.329(-5) 1.437(-5)
23 3.938(-7) 3.938(-7) 3.936(-7) 3.923(-7) 3.901(-7) 3.893(-7) 3.890(-7) 3.875(-7)
C17O: unattenuated rate $k_{0,i}=2.607~\times~10^{-10}$ s-1
0 1.000 9.823(-1) 8.911(-1) 6.149(-1) 3.924(-1) 2.169(-1) 4.167(-2) 2.150(-3)
19 8.459(-1) 8.298(-1) 7.490(-1) 5.009(-1) 3.196(-1) 1.850(-1) 3.509(-2) 1.984(-3)
20 7.337(-1) 7.195(-1) 6.481(-1) 4.306(-1) 2.741(-1) 1.556(-1) 2.645(-2) 1.411(-3)
21 3.335(-1) 3.290(-1) 3.039(-1) 2.293(-1) 1.685(-1) 9.464(-2) 1.460(-2) 6.823(-4)
22 1.193(-2) 1.191(-2) 1.172(-2) 1.095(-2) 9.395(-3) 5.644(-3) 1.183(-3) 2.835(-5)
23 3.959(-7) 3.959(-7) 3.959(-7) 3.959(-7) 3.958(-7) 3.954(-7) 3.924(-7) 3.873(-7)
C18O: unattenuated rate $k_{0,i}=2.392~\times~10^{-10}$ s-1
0 1.000 9.974(-1) 9.777(-1) 8.519(-1) 5.060(-1) 1.959(-1) 2.764(-2) 1.742(-3)
19 8.571(-1) 8.547(-1) 8.368(-1) 7.219(-1) 4.095(-1) 1.581(-1) 2.224(-2) 1.618(-3)
20 7.554(-1) 7.532(-1) 7.371(-1) 6.336(-1) 3.572(-1) 1.372(-1) 1.889(-2) 1.383(-3)
21 3.559(-1) 3.549(-1) 3.477(-1) 3.035(-1) 1.948(-1) 7.701(-2) 1.071(-2) 6.863(-4)
22 1.214(-2) 1.212(-2) 1.199(-2) 1.105(-2) 8.233(-3) 3.324(-3) 6.148(-4) 3.225(-5)
23 4.251(-7) 4.251(-7) 4.251(-7) 4.251(-7) 4.249(-7) 4.233(-7) 4.180(-7) 4.142(-7)
13CO: unattenuated rate $k_{0,i}=2.595~\times~10^{-10}$ s-1
0 1.000 9.824(-1) 9.019(-1) 6.462(-1) 3.547(-1) 9.907(-2) 1.131(-2) 7.591(-4)
19 8.447(-1) 8.276(-1) 7.502(-1) 5.113(-1) 2.745(-1) 7.652(-2) 8.635(-3) 6.747(-4)
20 7.415(-1) 7.266(-1) 6.581(-1) 4.451(-1) 2.360(-1) 6.574(-2) 7.187(-3) 5.429(-4)
21 3.546(-1) 3.502(-1) 3.270(-1) 2.452(-1) 1.398(-1) 3.750(-2) 3.973(-3) 2.703(-4)
22 1.180(-2) 1.177(-2) 1.153(-2) 1.023(-2) 6.728(-3) 1.955(-3) 2.665(-4) 1.471(-5)
23 2.385(-7) 2.385(-7) 2.385(-7) 2.384(-7) 2.379(-7) 2.348(-7) 2.310(-7) 2.292(-7)
13C17O: unattenuated rate $k_{0,i}=2.598~\times~10^{-10}$ s-1
0 1.000 9.979(-1) 9.820(-1) 8.832(-1) 5.942(-1) 3.177(-1) 1.523(-1) 3.885(-2)
19 8.540(-1) 8.520(-1) 8.374(-1) 7.469(-1) 4.901(-1) 2.677(-1) 1.302(-1) 3.135(-2)
20 7.405(-1) 7.387(-1) 7.254(-1) 6.439(-1) 4.198(-1) 2.333(-1) 1.142(-1) 2.607(-2)
21 3.502(-1) 3.494(-1) 3.434(-1) 3.076(-1) 2.214(-1) 1.386(-1) 6.941(-2) 1.195(-2)
22 1.279(-2) 1.278(-2) 1.267(-2) 1.198(-2) 1.045(-2) 7.743(-3) 4.088(-3) 4.581(-4)
23 2.370(-7) 2.370(-7) 2.370(-7) 2.370(-7) 2.369(-7) 2.368(-7) 2.359(-7) 2.312(-7)
13C18O: unattenuated rate $k_{0,i}=2.503~\times~10^{-10}$ s-1
0 1.000 9.988(-1) 9.900(-1) 9.329(-1) 7.253(-1) 3.856(-1) 1.524(-1) 2.664(-2)
19 8.744(-1) 8.734(-1) 8.656(-1) 8.164(-1) 6.403(-1) 3.441(-1) 1.347(-1) 2.491(-2)
20 7.572(-1) 7.562(-1) 7.492(-1) 7.047(-1) 5.518(-1) 3.006(-1) 1.185(-1) 2.224(-2)
21 3.546(-1) 3.542(-1) 3.506(-1) 3.283(-1) 2.638(-1) 1.666(-1) 6.887(-2) 1.149(-2)
22 1.561(-2) 1.560(-2) 1.550(-2) 1.475(-2) 1.235(-2) 7.850(-3) 3.416(-3) 5.290(-4)
23 2.490(-7) 2.490(-7) 2.490(-7) 2.489(-7) 2.487(-7) 2.482(-7) 2.471(-7) 2.421(-7)
a These shielding functions were computed for the Draine (1978) radiation field ($\chi =1$) and the following set of parameters: $b({{\rm CO}})=0.3$ km s-1, $b({{\rm H}}_2)=3.0$ km s-1 and $b({{\rm H}})=5.0$ km s-1; $T_{{\rm ex}}({{\rm CO}})=5$ K and $T_{{\rm ex}}({{\rm H}}_2)=5^{1.5}$ K; $N({{\rm H}})=5~\times~10^{20}$ cm-2; $N(^{12}{{\rm CO}})/N(^{13}{{\rm CO}})=69$, $N(^{12}{{\rm CO}})/N({{\rm C}}^{18}{{\rm O}})=N(^{13}{{\rm CO}})/N(^{13}{{\rm C}}^{18}{{\rm O}})=557$ and $N({{\rm C}}^{18}{{\rm O}})/N({{\rm C}}^{17}{{\rm O}})=N(^{13}{{\rm C}}^{18}{{\rm O}})/N(^{13}{{\rm C}}^{17}{{\rm O}})=3.6$. Self-shielding is mostly negligible for the heavier isotopologues, so all shielding functions are expressed as a function of the 12CO column density. Continuum attenuation by dust is not included in this table (see Eq. (2)).

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