Table 2
Estimated values and standard deviations of Te, ne, and EM for hyper-compact H II regions.
| σ/µ | 3% | 10% |  |
LTE temperature | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ne = 105 cm−3 | ne = 105 cm−3 | ne = 105 cm−3 | ne = 105 cm−3 | |||||||||
| EM cm−6 pc |  K |
 105 cm−3 |
 109 cm-6 pc |
 K |
 105 cm−3 |
 109 cm−6 pc |
H30α | H40α | H60α |  K |
 K |
 K |
| 1.0 × 109 | 10014 ± 146 | 1.10 ± 0.12 | 1.02 ± 0.01 | 10078 ± 352 | 1.22 ± 0.31 | 1.02 ± 0.01 | 0.83 | 1.32 | 3.02 | 11603 | 8136 | 4612 |
| 5.0 × 109 | 10017 ± 102 | 1.07 ± 0.09 | 5.03 ± 0.08 | 10012 ± 278 | 1.19 ± 0.23 | 5.03 ± 0.10 | 1.17 | 3.92 | 32.34 | 9080 | 3736 | <2000 |
| 1.0 × 1010 | 10002 ± 25 | 1.04 ± 0.04 | 9.90 ± 0.07 | 10067 ±124 | 1.09 ± 0.14 | 9.91 ± 0.07 | 1.82 | 7.81 | 204.22 | 6623 | 2417 | <2000 |
| 5.0 × 1010 | … | … | … | … | … | … | … | … | … | … | … | … |
| ne = 106 cm−3 | ne = 106 cm-3 | ne = 106 cm-3 | ne = 106 cm-3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| EM cm−6 pc |  K |
 106 cm-3 |
 109 cm-6 pc |
 |
 106 cm-3 |
 109 cm-6 pc |
H30α | H40α | H60α |  K |
 K |
 K |
| 1.0 × 109 | 10018 ±179 | 1.14 ± 0.26 | 1.02 ± 0.01 | 10157 ± 459 | 1.54 ± 1.83 | 1.02 ± 0.01 | 0.97 | 1.12 | 1.34 | 10307 | 9279 | 8839 |
| 5.0 × 109 | 10038± 147 | 1.01 ± 0.06 | 5.01 ± 0.09 | 10074 ± 456 | 1.14 ± 0.26 | 5.01 ± 0.11 | 1.29 | 1.88 | 3.76 | 8423 | 6531 | 6636 |
| 1.0 × 1010 | 10008 ± 76 | 1.00 ± 0.02 | 9.93 ± 0.14 | 10064 ± 340 | 1.06 ± 0.16 | 9.91 ± 0.18 | 1.80 | 3.38 | 12.04 | 6671 | 4464 | 5038 |
| 5.0 × 1010 | … | … | … | … | … | … | … | … | … | … | … | … |
| ne = 107 cm−3 | ne = 107 cm-3 | ne = 107 cm-3 | ne = 107 cm-3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| EM cm−6 pc |  K |
 107 cm−3 |
 109 cm-6 pc |
 K |
 107 cm−3 |
 109 cm-6 pc |
H30α | H40α | H60α |  K |
 K |
 K |
| 1.0 × 109 | 10036 ±191 | 2.46 ± 3.04 | 1.02 ± 0.01 | 10314 ± 536 | 3.22 ± 4.16 | 1.03 ± 0.02 | 1.00 | 1.02 | 1.05 | 10061 | 9952 | 10648 |
| 5.0 × 109 | 10029 ± 218 | 1.14 ± 0.33 | 5.01 ± 0.10 | 10152 ± 735 | 1.65 ± 1.71 | 5.00 ± 0.14 | 1.09 | 1.14 | 1.41 | 9526 | 9598 | 13451 |
| 1.0 × 1010 | 10030 ±197 | 1.06 ± 0.14 | 10.01 ± 0.23 | 10141 ± 617 | 1.17 ± 0.42 | 10.0 ± 0.25 | 1.23 | 1.31 | 2.43 | . 8896 | 9184 | 16844 |
| 5.0 × 1010 | 10006 ±149 | 1.05 ± 0.08 | 50.2 ± 1.37 | 10016 ± 429 | 1.15 ± 0.26 | 50.0 ± 1.8 | 3.18 | 3.88 | > 103 | 5103 | 6540 | >20000 |
Notes. The values and standard deviations of Te, ne, and EM estimated by using the line-to-continuum ratios (∫Iv,Ldv/Iv,C) of the H30α, H40α, and H60α lines and the continuum emission at 99.023 GHz from ionized gas with different electron densities and EMs. The actual electron temperature is 10 000 K. The relative uncertainties σ/µ of the line-to-continuum ratio are assumed to be 3 and 10%, and the corresponding relative uncertainties of the 99.023 GHz continuum is 3%. The ratios of the frequency-integrated intensity (∫Iv,Ldv) to the intensity calculated under the LTE assumption 
for the H30α, H40α, and H60α lines are given in the three columns below the heading 
. The LTE temperatures estimated by using a single line-to-continuum ratio of one of the three Hnα lines to the continuum emission at corresponding frequency are given in the three right-most columns.
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