HII Case A Recombination Coefficients

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Alpha A HII.png

Comparison of Case A Recombination Coefficient αHII for Seaton59, HG97, Cen92, Sherman79, AAZN97, Spitzer78, Hummer94 and Ferland92.

Spitzer78, Hummer94 and Ferland92 are tabular data. The others are approximate fits to the tabular data.

Contents

Seaton59

Seaton, MNRAS 119, 81 (1959)

\alpha^A_{HII} = 2.065\times 10^{-17} T^{-1/2} (6.414 - \ln T /2 + 8.68\times 10^{-3} T^{1/3}) \mathrm{m}^3 \mathrm{s}^{-1}

Error < 3% for T < 106K

HG97

Hui & Gnedin 1997 MNRAS 292, 27

\alpha^A_{HII} = 2.337\times 10^{-11} T^{-1.503} (1 + 521.6 T^{-0.470})^{-1.923}\mathrm{m}^3 \mathrm{s}^{-1}

Error < 2% for 3K < T < 109K

Cen92

Cen 1992 ApJS 78, 341

\alpha^A_{HII} = 8.40\times 10^{-17} T^{-1/2} (T/10^3)^{-0.2}\left[1+(T/10^6)^0.7\right]^{-1}\mathrm{m}^3 \mathrm{s}^{-1}

Error < 2% for T < 16000 K
Error < 10% for T < 106 K

Sherman79

Sherman 1979 ApJ 232, 1

\alpha^A_{HII} = 2.08\times 10^{-17} T^{-1/2} (1.45 - \ln T /2 + 5.21\times 10^{-7} T) \mathrm{m}^3 \mathrm{s}^{-1}


AAZN97

Abel, Anninos, Zheng, Norman 1997 New Astronomy 2, 181

\begin{matrix} \alpha^A_{HII} & = & \exp( -28.61 - 0.7241 x - 2.026\times 10^{-2} x^2 - 2.381\times 10^{-3} x^3 - 3.213\times 10^{-5} x^4 \\ & & - 1.422\times 10^{-5} x^5 + 4.989\times 10^{-6} x^6 + 5.756\times 10^{-7} x^7 \\ & & - 1.858\times 10^{-8} x^8 - 3.071\times 10^{-9} x^9 ) \times 10^{-6} \mathrm{m}^3 \mathrm{s}^{-1} \end{matrix}
where x = ln(T / 11604.45K)

Spitzer78

\alpha^A_{HII} = 2.066e-17 T^{-1/2} \phi \mathrm{m}^3 \mathrm{s}^{-1}

T φ
31.3 4.68
62.5 4.36
125 4.04
250 3.71
500 3.38
1000 3.05
2000 2.73
4000 2.40
8000 2.09
16000 1.79
32000 1.50
64000 1.22
128000 0.96
256000 0.73
512000 0.52
1e6 0.36
1e7 0.074
1e8 0.011

Hummer94

Hummer 1994 MNRAS 268, 109

log(T) α1 [10-17 m3 s-1] αB [10-17 m3 s-1]
1.0 1.646 9.283
1.2 1.646 8.823
1.4 1.646 8.361
1.6 1.646 7.898
1.8 1.646 7.435
2.0 1.646 6.973
2.2 1.645 6.512
2.4 1.645 6.054
2.6 1.644 5.599
2.8 1.642 5.147
3.0 1.640 4.700
3.2 1.636 4.258
3.4 1.629 3.823
3.6 1.620 3.397
3.8 1.605 2.983
4.0 1.582 2.584
4.2 1.548 2.204
4.4 1.499 1.847
4.6 1.431 1.520
4.8 1.341 1.226
5.0 1.227 0.9696
5.2 1.093 0.7514
5.4 0.9454 0.5710
5.6 0.7920 0.4257
5.8 0.6427 0.3117
6.0 0.5058 0.2244
6.2 0.3866 0.1590
6.4 0.2877 0.1110
6.6 0.2089 0.07642
6.8 0.1485 0.05199
7.0 0.1036 0.03498

αAHII = α1 + αB

Ferland92

log(T) α1 [m3 s-1] αB [m3 s-1]
0.5 9.258\times 10^{-18} 5.758\times 10^{-17}
1.0 5.206\times 10^{-18} 2.909\times 10^{-17}
1.5 2.927\times 10^{-18} 1.440\times 10^{-17}
2.0 1.646\times 10^{-18} 6.971\times 10^{-18}
2.5 9.246\times 10^{-19} 3.282\times 10^{-18}
3.0 5.184\times 10^{-19} 1.489\times 10^{-18}
3.5 2.890\times 10^{-19} 6.430\times 10^{-19}
4.0 1.582\times 10^{-19} 2.588\times 10^{-19}
4.5 8.255\times 10^{-20} 9.456\times 10^{-20}
5.0 3.882\times 10^{-20} 3.069\times 10^{-20}
5.5 1.545\times 10^{-20} 8.793\times 10^{-21}
6.0 5.058\times 10^{-21} 2.245\times 10^{-21}
6.5 1.383\times 10^{-21} 5.190\times 10^{-22}
7.0 3.276\times 10^{-22} 1.107\times 10^{-22}
7.5 7.006\times 10^{-23} 2.221\times 10^{-23}
8.0 1.398\times 10^{-23} 4.267\times 10^{-24}
8.5 2.665\times 10^{-24} 7.960\times 10^{-25}
9.0 4.940\times 10^{-25} 1.457\times 10^{-25}
9.5 9.001\times 10^{-26} 2.636\times 10^{-26}
10 1.623\times 10^{-26} 4.737\times 10^{-27}

αAHII = α1 + αB

See Also

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