Table 6
Parameters of the best-fit Plummer envelope models (Pl models) and Plummer + Gaussian models (PG models) that best reproduce the observed dust continuum emission radial profiles.
| Plummer | Plummer | Plummer | Inner | Gaussian | Gaussian | Reduced | PG better | ||
|---|---|---|---|---|---|---|---|---|---|
| Source | Model | radius | index | flux | radius | FWHM | flux | χ2 | than Pl? |
| (Rout) | (p + q) | (Ri) | |||||||
| (′′) | (mJy) | (′′) | (′′) | (mJy) | |||||
| [1] | [2] | [3] | [4] | [5] | [6] | [7] | [8] | [9] | [10] |
| L1448-2A | Pl231 | 18 ± 4 | 2.3 ± 0.1 | 527 ± 30 | 0.01 ± 0.01 | – | – | 1.0 | – |
| Pl94 | 25 ± 5 | 2.2 ± 0.2 | 58 ± 5 | 0.01 ± 0.01 | – | – | 1.0 | – | |
| PG231 | 20 ± 10 | 2.2 ± 0.1 | 526± 100 | 0.09 ± 0.01 | <0.15 | 12 ± 3 | 1.0 | No | |
| PG94 | 22 ± 2 | 2.0 ± 0.1 | 60 ± 30 | 0.01 ± 0.01 | <0.3 | 2.2 ± 0.5 | 0.9 | No | |
| L1448-NB1 | Pl231 | 25 ± 5 | 2.2 ± 0.2 | 3373 ± 200 | 0.01 ± 0.01 | – | – | 3.0 | – |
| Pl94 | 19 ± 3 | 2.7 ± 0.3 | 226 ± 110 | 0.2 ± 0.1 | – | – | 7.0 | – | |
| PG231 | 23 ± 3 | 2.2 ± 0.2 | 3176 ± 380 | 0.06 ± 0.02 | <0.15 | 38 ± 11 | 3.2 | No | |
| PG94 | 23 ± 3 | 2.7 ± 0.2 | 243 ± 18 | 0.94 ± 0.1 | 0.94 ± 0.1 | 39 ± 4 | 5.0 | No | |
| L1448-C | Pl231 | 12 ± 3 | 2.5 ± 0.2 | 660 ± 40 | 0.01 ± 0.01 | – | – | 6.8 | – |
| Pl94 | 17 ± 7 | 2.7 ± 0.2 | 53 ± 10 | 0.01 ± 0.01 | – | – | 9 | – | |
| PG231 | 14 ± 4 | 1.7 ± 0.2 | 860 ± 70 | 0.14 ± 0.05 | 0.16 ± 0.05 | 130 ± 5 | 0.7 | Yes | |
| PG94 | 14 ± 1 | 1.4 ± 0.2 | 79 ± 2 | 0.05 ± 0.03 | <0.3 | 18 ± 1 | 0.1 | Yes | |
| IRAS2A1 | Pl231 | 5.7± 1 | 2.5 ± 0.2 | 600 ± 50 | 0.01 ± 0.01 | – | – | 1.3 | – |
| Pl94 | 10 ± 5 | 2.6 ± 0.2 | 65 ± 2 | 0.01 ± 0.01 | – | – | 0.9 | – | |
| PG231 | 7.7 ± 1 | 2.5 ± 0.2 | 600 ± 40 | 0.05 ± 0.02 | <0.15 | 52 ± 5 | 1.3 | No | |
| PG94 | 10 ± 5 | 2.4 ± 0.2 | 56 ± 2 | 0.06 ± 0.02 | <0.3 | 9 ± 1 | 0.5 | Yes | |
| SVS13B | Pl231 | 14 ± 7 | 2.9 ± 0.2 | 446 ± 15 | 0.06 ± 0.02 | – | – | 2.5 | – |
| Pl94 | 6.7 ± 2 | 2.6 ± 0.2 | 52 ± 4 | 0.01 ± 0.01 | – | – | 0.45 | – | |
| PG231 | 9 ± 3 | 2.5 ± 0.3 | 636 ± 88 | 0.2 ± 0.1 | 0.19 ± 0.1 | 80 ± 7 | 4.6 | Yesa | |
| PG94 | 10 ± 3 | 2.4 ± 0.2 | 58 ± 4 | 0.1 ± 0.05 | <0.3 | 10 ± 1 | 0.6 | No | |
| IRAS4A1 | Pl231 | 3.7 ± 0.5 | 2.48 ± 0.1 | 3489 ± 106 | 0.1 ± 0.05 | – | – | 1.6 | – |
| Pl94 | 5.4 ± 0.8 | 2.8 ± 0.2 | 363 ± 12 | 0.07 ± 0.02 | – | – | 2.2 | – | |
| PG231 | 3.8 ± 0.6 | 2.69 ± 0.2 | 3155 ± 60 | 0.4 ± 0.1 | 0.32 ± 0.1 | 348 ± 25 | 1.7 | No | |
| PG94 | 4.5 ± 0.3 | 2.3 ± 0.1 | 363 ± 30 | 0.5 ± 0.1 | 0.5 ± 0.1 | 130 ± 9 | 4.3 | No | |
| IRAS4B | Pl231 | 4 ± 2 | 2.9 ± 0.4 | 1448 ± 40 | 0.14 ± 0.1 | – | – | 3.3 | – |
| Pl94 | 3.9 ± 0.4 | 2.9 ± 0.4 | 141 ± 6 | 0.14 ± 0.05 | – | – | 0.8 | – | |
| PG231 | 3.8 ± 1 | 2.9 ± 0.4 | 841 ± 80 | 1.0 ± 0.2 | 0.53 ± 0.1 | 645 ± 35 | 2.5 | Yes | |
| PG94 | 7.8 ± 0.5 | 2.9 ± 0.4 | 131 ± 11 | 0.3 ± 0.1 | 0.29 ± 0.15 | 24 ± 7 | 1.8 | No | |
| IRAM04191 | Pl231 | 27 ± 2 | 1.6 ± 0.2 | 410 ± 60 | 0.01 ± 0.01 | – | – | 2.37 | – |
| Pl94 | 29 ± 2 | 1.4 ± 0.3 | 44 ± 9 | 0.01 ± 0.01 | – | – | 0.86 | – | |
| PG231 | 28 ± 2 | 1.4 ± 0.3 | 539 ± 10 | 0.2 ± 0.3 | 0.17 ± 0.1 | 3.6 ± 1 | 0.84 | Yes | |
| PG94 | 29 ± 4 | 1.54 ± 0.2 | 32.8 ± 9 | 1.28 ± 1 | <0.3 | 0.2 ± 0.1 | 1.0 | No | |
| L1521F | Pl231 | 32 ± 2 | 1.7 ± 0.2 | 1100 ± 100 | 3.0 ± 3.0 | – | – | 2.4 | – |
| Pl94 | 37 ± 8 | 2.0 ± 0.2 | 53 ± 30 | 3.0 ± 2.0 | – | – | 1.35 | – | |
| PG231 | 32 ± 3 | 1.6 ± 0.4 | 1100 ± 100 | 2.6 ± 0.8 | 0.13 ± 0.1 | 1.3 ± 0.4 | 0.79 | Yes | |
| PG94 | 39 ± 10 | 1.65 ± 0.5 | 53 ± 30 | 1.8 ± 0.8 | 0.16 ± 0.2 | <0.5 ± 0.1 | 5.0 | No | |
| L1527 | Pl231 | 35 ± 5 | 2.57 ± 0.2 | 1080 ± 100 | 0.01 ± 0.01 | – | – | 19 | – |
| Pl94 | 35 ± 10 | 2.6 ± 0.2 | 85 ± 20 | 0.01 ± 0.01 | – | – | 4 | – | |
| PG231 | 28 ± 4 | 1.68 ± 0.4 | 1275 ± 320 | 0.4 ± 0.2 | 0.4 ± 0.1 | 215 ± 14 | 2.9 | Yes | |
| PG94 | 35 ± 10 | 1.78 ± 0.3 | 85 ± 20 | 0.28 ± 1.0 | 0.3 ± 0.1 | 23 ± 1 | 0.6 | Yes | |
| SerpM-S68N | Pl231 | 15 ± 2 | 2.28 ± 0.1 | 800 ± 80 | 0.01 ± 0.01 | – | – | 1.67 | – |
| Pl94 | 22 ± 5 | 2.56 ± 0.2 | 35 ± 10 | 0.03 ± 0.03 | – | – | 1.2 | – | |
| PG231 | 13.9 ± 3 | 2.1 ± 0.2 | 800 ± 80 | 0.1 ± 0.1 | 0.11 ± 0.1 | 28 ± 11 | 2.1 | No | |
| PG94 | 15 ± 2 | 2.08 ± 0.2 | 35 ± 10 | 0.5 ± 0.1 | 0.5 ± 0.1 | 6.5 ± 1 | 3.4 | No | |
| SerpM-SMM4 | Pl231 | 25 ± 5 | 2.8 ± 0.4 | 1700 ± 200 | 0.06 ± 0.05 | – | – | 2.7 | – |
| Pl94 | 15 ± 4 | 2.8 ± 0.4 | 105 ± 6 | 0.01 ± 0.01 | – | – | 3.7 | – | |
| PG231 | 22 ± 5 | 1.8 ± 0.5 | 1305 ± 500 | 0.70 ± 0.1 | 0.70 ± 0.2 | 595 ± 35 | 0.14 | Yes | |
| PG94 | 25 ± 5 | 1.6 ± 0.3 | 103 ± 20 | 0.6 ± 0.1 | 0.62 ± 0.1 | 61 ± 3 | 0.39 | Yes | |
| SerpS-MM18 | Pl231 | 16 ± 2 | 2.24 ± 0.2 | 2208 ± 190 | 0.01 ± 0.01 | – | – | 1.8 | – |
| Pl94 | 20 ± 5 | 2.4 ± 0.2 | 114 ± 20 | 0.015 ± 0.05 | – | – | 0.87 | – | |
| PG231 | 15.5 ± 6 | 2.17 ± 0.2 | 2327 ± 55 | 0.13 ± 0.07 | 0.128 ± 0.08 | 76 ± 4 | 0.68 | Yes | |
| PG94 | 11 ± 2 | 2.24 ± 0.2 | 114 ± 20 | 0.04 ± 0.02 | <0.1 ± 0.1 | <1 ± 0.5 | 2.78 | No | |
| SerpS-MM22 | Pl231 | 11 ± 2 | 2.56 ± 0.2 | 135 ± 30 | 0.01 ± 0.01 | – | – | 1.8 | – |
| Pl94 | 25 ± 5 | 2.7 ± 0.3 | 10 ± 5 | 0.01 ± 0.01 | – | – | 1.16 | – | |
| PG231 | 10 ± 4 | 2.0 ± 0.3 | 148 ± 9 | 0.26 ± 0.08 | 0.25 ± 0.08 | 31 ± 4 | 1.1 | Yes | |
| PG94 | 19 ± 3 | 1.98 ± 0.3 | 10 ± 5 | 0.31± 0.07 | 0.31± 0.07 | 3.2 ± 0.5 | 0.59 | Yes | |
| L1157 | Pl231 | 12 ± 10 | 2.68 ± 0.2 | 520 ± 170 | 0.01 ± 0.01 | – | – | 1.29 | – |
| Pl94 | 16 ± 5 | 2.65 ± 0.2 | 61 ± 10 | 0.01 ± 0.01 | – | – | 1.4 | – | |
| PG231 | 6.8 ± 2 | 2.5 ± 0.2 | 494 ± 35 | 0.05 ± 0.04 | <0.1 ± 0.1 | 56 ± 6 | 0.76 | Yes | |
| PG94 | 8.2 ± 2 | 2.24 ± 0.3 | 61 ± 10 | 0.05 ± 0.04 | <0.3 ± 1 | 9 ± 1 | 2.5 | No | |
| GF9-2 | Pl231 | 40 ± 7 | 2.36 ± 0.2 | 179 ± 20 | 0.01 ± 0.01 | – | – | 5 | – |
| Pl94 | 40 ± 10 | 2.2 ± 0.2 | 27 ± 7 | 0.01 ± 0.01 | – | – | 1.8 | – | |
| PG231 | 37 ± 3 | 1.67 ± 0.3 | 407 ± 80 | 0.18 ± 0.05 | 0.18 ± 0.05 | 11.8 ± 2 | 0.55 | Yes | |
| PG94 | 34 ± 5 | 1.71 ± 0.3 | 39 ± 20 | 0.15 ± 0.07 | <0.3 ± 0.1 | 1.3 ± 0.5 | 0.45 | Yes |
Notes. Column 1: name of the primary protostar. Column 2: type of model used (Pl or PG plus the frequency of the modeled visibility profile): for each source, the first two lines report the parameters of the best Plummer envelope (Pl) models and the two following lines report the parameters of the best Plummer + Gaussian (PG) models. Columns 3–8: parameters of the best-fit model: the size of the Plummer envelope (Col. 3), the value of the (p + q) brightness radial distribution index (Col. 4), the total flux of the Plummer envelope component emission at the considered frequency (Col. 5), the FWHM of the Gaussian component (Col. 6), the inner radius (Col. 7), and the flux of the Gaussian component (Col. 8). Column 9: reduced χ2 value associated with this best-fit model, and Col. 10 indicates whether the result of the F-test suggests that the PG model is a better model than the Pl model. (a)For SVS13B, although the reduced chi square of the PG model is not statistically better than the one obtained for the Pl model, the more reasonable value of the p + q parameter makes the PG model a satisfactory model at 231 GHz as well. The fact that the visibilities at 231 GHz might need an additional unresolved component to be properly reproduced while the 94 GHz visibility profile is fine without this might suggest that the additional component might be due to an optically thick component at 231 GHz that is not seen at 94 GHz and is embedded in the otherwise optically thin envelope.
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