The photodissociation and chemistry of CO isotopologues: applications to interstellar clouds and circumstellar disks

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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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