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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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