FAUST - XXVI. The dust opacity spectral indices of protostellar envelopes bridge the gap between interstellar medium and disks

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Volume 700 (August 2025)

A&A, 700 (2025) A188

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Table 2

Best-fit parameters as obtained with galario for each source, ALMA band, and model.

Source	Band	Gauss f0 (Jy/sr)	Gauss σ(^′′)	Gauss inc (deg)	Gauss PA (deg)	Plummer 0 (Jy/sr)	Plummer R_i	Plummer R_out	Plummer p+q	χ²
IRAS1538-3359	3	${10.22}_{- 0.19}^{+ 0.13}$ $10.22_{-0.19}^{+0.13}$	${0.03}_{+ 0.001}^{- 0.001}$ $0.03_{+0.001}^{-0.001}$	$44_{+ 4}^{- 3}$ $44_{+4}^{-3}$	$- 73_{+ 8}^{- 4}$ $-73_{+8}^{-4}$	${8.02}_{- 0.01}^{+ 0.02}$ $8.02_{-0.01}^{+0.02}$	${0.1}_{- 0.01}^{+ 0.01}$ $0.1_{-0.01}^{+0.01}$	$8_{- 0.3}^{+ 0.5}$ $8_{-0.3}^{+0.5}$	${1.84}_{- 0.01}^{+ 0.01}$ $1.84_{-0.01}^{+0.01}$	1.0
–	6	${10.95}_{- 0.01}^{+ 0.02}$ $10.95_{-0.01}^{+0.02}$	${0.03}_{+ 0.001}^{- 0.001}$ $0.03_{+0.001}^{-0.001}$	$41_{+ 1}^{- 1}$ $41_{+1}^{-1}$	$- 79_{+ 1}^{- 1}$ $-79_{+1}^{-1}$	${8.65}_{- 0.01}^{+ 0.01}$ $8.65_{-0.01}^{+0.01}$	${0.5}_{- 0.01}^{+ 0.02}$ $0.5_{-0.01}^{+0.02}$	${7.9}_{- 0.3}^{+ 0.1}$ $7.9_{-0.3}^{+0.1}$	${1.92}_{- 0.01}^{+ 0.02}$ $1.92_{-0.01}^{+0.02}$	1.2
CB68	3	${10.32}_{- 0.02}^{+ 0.02}$ $10.32_{-0.02}^{+0.02}$	${0.07}_{- 0.01}^{+ 0.01}$ $0.07_{-0.01}^{+0.01}$	${58.5}_{- 1.4}^{+ 1.3}$ $58.5_{-1.4}^{+1.3}$	${46.2}_{- 2}^{+ 2}$ $46.2_{-2}^{+2}$	${8.35}_{- 0.22}^{+ 0.35}$ $8.35_{-0.22}^{+0.35}$	${0.04}_{- 0.02}^{+ 0.02}$ $0.04_{-0.02}^{+0.02}$	${9.7}_{- 0.4}^{+ 0.4}$ $9.7_{-0.4}^{+0.4}$	${2.35}_{- 0.09}^{+ 0.08}$ $2.35_{-0.09}^{+0.08}$	1.0
–	6	${11.21}_{- 0.03}^{+ 0.01}$ $11.21_{-0.03}^{+0.01}$	${0.08}_{- 0.01}^{+ 0.01}$ $0.08_{-0.01}^{+0.01}$	${67.9}_{- 0.25}^{+ 0.25}$ $67.9_{-0.25}^{+0.25}$	${43.5}_{- 0.1}^{+ 0.1}$ $43.5_{-0.1}^{+0.1}$	${9.98}_{- 0.01}^{+ 0.01}$ $9.98_{-0.01}^{+0.01}$	${0.03}_{- 0.001}^{+ 0.001}$ $0.03_{-0.001}^{+0.001}$	${6.34}_{- 0.04}^{+ 0.03}$ $6.34_{-0.04}^{+0.03}$	${2.45}_{- 0.01}^{+ 0.01}$ $2.45_{-0.01}^{+0.01}$	1.1
L483	3	${9.61}_{- 0.01}^{+ 0.01}$ $9.61_{-0.01}^{+0.01}$	${0.07}_{- 0.01}^{+ 0.01}$ $0.07_{-0.01}^{+0.01}$	${31.9}_{- 1.4}^{+ 1.3}$ $31.9_{-1.4}^{+1.3}$	$- 37_{- 0.04}^{+ 0.1}$ $-37_{-0.04}^{+0.1}$	${8.13}_{- 0.07}^{+ 0.1}$ $8.13_{-0.07}^{+0.1}$	${0.02}_{- 0.001}^{+ 0.001}$ $0.02_{-0.001}^{+0.001}$	${13.9}_{- 0.5}^{+ 0.1}$ $13.9_{-0.5}^{+0.1}$	${1.92}_{- 0.02}^{+ 0.02}$ $1.92_{-0.02}^{+0.02}$	1.1
–	6	${10.54}_{- 0.01}^{+ 0.01}$ $10.54_{-0.01}^{+0.01}$	${0.08}_{- 0.01}^{+ 0.02}$ $0.08_{-0.01}^{+0.02}$	$50_{- 0.1}^{+ 0.1}$ $50_{-0.1}^{+0.1}$	$- 38_{- 0.3}^{+ 0.3}$ $-38_{-0.3}^{+0.3}$	${8.22}_{- 0.01}^{+ 0.01}$ $8.22_{-0.01}^{+0.01}$	${0.5}_{- 0.01}^{+ 0.01}$ $0.5_{-0.01}^{+0.01}$	${6.75}_{- 0.01}^{+ 0.01}$ $6.75_{-0.01}^{+0.01}$	${2.02}_{- 0.01}^{+ 0.01}$ $2.02_{-0.01}^{+0.01}$	1.1
Elias 29	3	${10.61}_{- 0.09}^{+ 0.11}$ $10.61_{-0.09}^{+0.11}$	${0.03}_{- 0.001}^{+ 0.003}$ $0.03_{-0.001}^{+0.003}$	$50_{- 15}^{+ 14}$ $50_{-15}^{+14}$	$15_{- 14}^{+ 13}$ $15_{-14}^{+13}$	${8.09}_{- 0.06}^{+ 0.09}$ $8.09_{-0.06}^{+0.09}$	${0.02}_{- 0.001}^{+ 0.001}$ $0.02_{-0.001}^{+0.001}$	${6.11}_{- 0.13}^{+ 0.14}$ $6.11_{-0.13}^{+0.14}$	${1.88}_{- 0.04}^{+ 0.04}$ $1.88_{-0.04}^{+0.04}$	1.3
–	6	${10.70}_{- 0.01}^{+ 0.01}$ $10.70_{-0.01}^{+0.01}$	${0.05}_{- 0.002}^{+ 0.005}$ $0.05_{-0.002}^{+0.005}$	$40_{- 0.03}^{+ 0.01}$ $40_{-0.03}^{+0.01}$	$- 30_{- 0.01}^{+ 0.02}$ $-30_{-0.01}^{+0.02}$	${8.55}_{- 0.01}^{+ 0.01}$ $8.55_{-0.01}^{+0.01}$	${0.05}_{- 0.003}^{+ 0.001}$ $0.05_{-0.003}^{+0.001}$	${5.40}_{- 0.01}^{+ 0.004}$ $5.40_{-0.01}^{+0.004}$	${1.72}_{- 0.04}^{+ 0.05}$ $1.72_{-0.04}^{+0.05}$	1.0
VLA1623A	3	${9.70}_{- 0.01}^{+ 0.01}$ $9.70_{-0.01}^{+0.01}$	${0.37}_{- 0.002}^{+ 0.003}$ $0.37_{-0.002}^{+0.003}$	${76.8}_{- 0.2}^{+ 0.2}$ $76.8_{-0.2}^{+0.2}$	$90_{- 0.01}^{+ 0.00}$ $90_{-0.01}^{+0.00}$	${10.49}_{- 0.03}^{+ 0.03}$ $10.49_{-0.03}^{+0.03}$	${0.01}_{- 0.001}^{+ 0.001}$ $0.01_{-0.001}^{+0.001}$	${5.97}_{- 0.03}^{+ 0.03}$ $5.97_{-0.03}^{+0.03}$	${2.38}_{- 0.01}^{+ 0.01}$ $2.38_{-0.01}^{+0.01}$	1.1
–	6	${10.54}_{- 0.001}^{+ 0.001}$ $10.54_{-0.001}^{+0.001}$	${0.34}_{- 0.002}^{+ 0.002}$ $0.34_{-0.002}^{+0.002}$	${76.2}_{- 0.04}^{+ 0.03}$ $76.2_{-0.04}^{+0.03}$	$90_{- 0.01}^{+ 0.0}$ $90_{-0.01}^{+0.0}$	${10.59}_{- 0.003}^{+ 0.002}$ $10.59_{-0.003}^{+0.002}$	${0.13}_{- 0.01}^{+ 0.01}$ $0.13_{-0.01}^{+0.01}$	${7.9}_{- 0.1}^{+ 0.1}$ $7.9_{-0.1}^{+0.1}$	${2.73}_{- 0.01}^{+ 0.02}$ $2.73_{-0.01}^{+0.02}$	2.0
IRAS4A1	3	${10.17}_{- 0.01}^{+ 0.01}$ $10.17_{-0.01}^{+0.01}$	${0.12}_{- 0.002}^{+ 0.001}$ $0.12_{-0.002}^{+0.001}$	${38.5}_{- 0.2}^{+ 0.2}$ $38.5_{-0.2}^{+0.2}$	$20_{- 0.2}^{+ 0.1}$ $20_{-0.2}^{+0.1}$	${10.54}_{- 0.02}^{+ 0.01}$ $10.54_{-0.02}^{+0.01}$	${0.13}_{- 0.03}^{+ 0.02}$ $0.13_{-0.03}^{+0.02}$	${3.31}_{- 0.03}^{+ 0.04}$ $3.31_{-0.03}^{+0.04}$	${2.98}_{- 0.02}^{+ 0.02}$ $2.98_{-0.02}^{+0.02}$	25
–	6	${11.18}_{- 0.01}^{+ 0.01}$ $11.18_{-0.01}^{+0.01}$	${0.14}_{- 0.02}^{+ 0.01}$ $0.14_{-0.02}^{+0.01}$	$45_{- 1}^{+ 1}$ $45_{-1}^{+1}$	$- 66_{- 2}^{+ 1}$ $-66_{-2}^{+1}$	${10.93}_{- 0.03}^{+ 0.01}$ $10.93_{-0.03}^{+0.01}$	${0.20}_{- 0.02}^{+ 0.02}$ $0.20_{-0.02}^{+0.02}$	${2.94}_{- 0.02}^{+ 0.01}$ $2.94_{-0.02}^{+0.01}$	${2.53}_{- 0.02}^{+ 0.01}$ $2.53_{-0.02}^{+0.01}$	35
IRAS4A2	3	−	−	−	−	${10.08}_{- 0.001}^{+ 0.02}$ $10.08_{-0.001}^{+0.02}$	${0.07}_{- 0.006}^{+ 0.001}$ $0.07_{-0.006}^{+0.001}$	${3.88}_{- 0.3}^{+ 0.1}$ $3.88_{-0.3}^{+0.1}$	${2.48}_{- 0.01}^{+ 0.01}$ $2.48_{-0.01}^{+0.01}$	25
–	6	−	−	−	−	${10.89}_{- 0.02}^{+ 0.01}$ $10.89_{-0.02}^{+0.01}$	${0.05}_{- 0.002}^{+ 0.001}$ $0.05_{-0.002}^{+0.001}$	$8_{- 0.4}^{+ 0.5}$ $8_{-0.4}^{+0.5}$	${2.30}_{- 0.02}^{+ 0.02}$ $2.30_{-0.02}^{+0.02}$	35
L1551-IRS5	3	${10.84}_{- 0.01}^{+ 0.01}$ $10.84_{-0.01}^{+0.01}$	${0.06}_{- 0.001}^{+ 0.001}$ $0.06_{-0.001}^{+0.001}$	$41_{- 0.2}^{+ 0.1}$ $41_{-0.2}^{+0.1}$	$- 20_{- 0.1}^{+ 0.2}$ $-20_{-0.1}^{+0.2}$	${10.46}_{- 0.01}^{+ 0.02}$ $10.46_{-0.01}^{+0.02}$	${0.07}_{- 0.002}^{+ 0.001}$ $0.07_{-0.002}^{+0.001}$	$14_{- 0.10}^{+ 0.02}$ $14_{-0.10}^{+0.02}$	${3.18}_{- 0.02}^{+ 0.02}$ $3.18_{-0.02}^{+0.02}$	11
–	6	${11.61}_{- 0.001}^{+ 0.002}$ $11.61_{-0.001}^{+0.002}$	${0.09}_{- 0.001}^{+ 0.001}$ $0.09_{-0.001}^{+0.001}$	$55_{- 0.1}^{+ 0.3}$ $55_{-0.1}^{+0.3}$	$- 29_{- 0.1}^{+ 0.05}$ $-29_{-0.1}^{+0.05}$	${11.05}_{- 0.001}^{+ 0.001}$ $11.05_{-0.001}^{+0.001}$	${0.12}_{- 0.001}^{+ 0.001}$ $0.12_{-0.001}^{+0.001}$	${9.97}_{- 0.05}^{+ 0.09}$ $9.97_{-0.05}^{+0.09}$	${2.85}_{- 0.02}^{+ 0.02}$ $2.85_{-0.02}^{+0.02}$	12
IRAS4C^∗	3	${10.00}_{- 0.004}^{+ 0.004}$ $10.00_{-0.004}^{+0.004}$	${0.13}_{- 0.02}^{+ 0.02}$ $0.13_{-0.02}^{+0.02}$	${62.3}_{- 0.2}^{+ 0.2}$ $62.3_{-0.2}^{+0.2}$	${14.2}_{- 0.2}^{+ 0.2}$ $14.2_{-0.2}^{+0.2}$	−	−	−	−	13
–	6	${10.38}_{- 0.05}^{+ 0.05}$ $10.38_{-0.05}^{+0.05}$	${0.15}_{- 0.02}^{+ 0.02}$ $0.15_{-0.02}^{+0.02}$	${70.2}_{- 1.3}^{+ 1.4}$ $70.2_{-1.3}^{+1.4}$	${16.3}_{- 0.3}^{+ 0.3}$ $16.3_{-0.3}^{+0.3}$	${10.36}_{- 0.04}^{+ 0.04}$ $10.36_{-0.04}^{+0.04}$	${0.07}_{- 0.01}^{+ 0.004}$ $0.07_{-0.01}^{+0.004}$	${5.7}_{- 0.02}^{+ 0.02}$ $5.7_{-0.02}^{+0.02}$	${2.28}_{- 0.01}^{+ 0.01}$ $2.28_{-0.01}^{+0.01}$	12
Source	Band	Gauss f0 (Jy/sr)	Gauss σ(^′′)	Gauss inc (deg)	Gauss PA (deg)	δ f 0(Jy/sr)	−	−	−	χ²
GSS30^∗	3	${10.07}_{- 0.01}^{+ 0.01}$ $10.07_{-0.01}^{+0.01}$	${0.23}_{- 0.005}^{+ 0.005}$ $0.23_{-0.005}^{+0.005}$	${68.7}_{- 0.09}^{+ 0.1}$ $68.7_{-0.09}^{+0.1}$	$- 70_{- 0.11}^{+ 0.11}$ $-70_{-0.11}^{+0.11}$	${14.58}_{- 0.01}^{+ 0.01}$ $14.58_{-0.01}^{+0.01}$	−	−	−	1.1
–	6	${10.34}_{- 0.01}^{+ 0.02}$ $10.34_{-0.01}^{+0.02}$	${0.28}_{- 0.02}^{+ 0.01}$ $0.28_{-0.02}^{+0.01}$	$62_{- 0.12}^{+ 0.12}$ $62_{-0.12}^{+0.12}$	$- 69_{- 0.15}^{+ 0.13}$ $-69_{-0.15}^{+0.13}$	${14.84}_{- 0.01}^{+ 0.01}$ $14.84_{-0.01}^{+0.01}$	−	−	−	13
IRS63^∗	3	${9.79}_{- 0.01}^{+ 0.01}$ $9.79_{-0.01}^{+0.01}$	${0.22}_{- 0.004}^{+ 0.003}$ $0.22_{-0.004}^{+0.003}$	$49_{- 0.12}^{+ 0.1}$ $49_{-0.12}^{+0.1}$	$- {27.4}_{- 0.17}^{+ 0.16}$ $-27.4_{-0.17}^{+0.16}$	15.02	−	−	−	1.5
–	6	${10.72}_{- 0.01}^{+ 0.01}$ $10.72_{-0.01}^{+0.01}$	${0.24}_{- 0.002}^{+ 0.002}$ $0.24_{-0.002}^{+0.002}$	$47_{- 0.12}^{+ 0.1}$ $47_{-0.12}^{+0.1}$	$- 28_{- 0.2}^{+ 0.3}$ $-28_{-0.2}^{+0.3}$	15.57	−	−	−	12
Source	Band	Gauss₁ f0 (Jy/sr)	Gauss₁σ(^′′)	Gauss₁ inc (deg)	Gauss₁ PA (deg)	Gauss₂ f0 (Jy/sr)	Gauss₂ σ(^′′)	Gauss₂ inc (deg)	Gauss₂ PA (deg)	χ²
BHB07-11	3	${9.08}_{- 0.02}^{+ 0.02}$ $9.08_{-0.02}^{+0.02}$	${0.32}_{- 0.02}^{+ 0.01}$ $0.32_{-0.02}^{+0.01}$	$53_{- 2}^{+ 2}$ $53_{-2}^{+2}$	$89_{- 1}^{+ 1}$ $89_{-1}^{+1}$	${8.07}_{- 0.05}^{+ 0.11}$ $8.07_{-0.05}^{+0.11}$	${1.62}_{- 0.01}^{+ 0.02}$ $1.62_{-0.01}^{+0.02}$	$52_{- 4}^{+ 8}$ $52_{-4}^{+8}$	$- 24_{- 3}^{+ 5}$ $-24_{-3}^{+5}$	1.3
−	6	${10.37}_{- 0.002}^{+ 0.001}$ $10.37_{-0.002}^{+0.001}$	${0.25}_{- 0.02}^{+ 0.02}$ $0.25_{-0.02}^{+0.02}$	${40.3}_{- 0.1}^{+ 0.1}$ $40.3_{-0.1}^{+0.1}$	$- 60_{- 0.2}^{+ 0.2}$ $-60_{-0.2}^{+0.2}$	${9.31}_{- 0.001}^{+ 0.002}$ $9.31_{-0.001}^{+0.002}$	${1.59}_{- 0.01}^{+ 0.01}$ $1.59_{-0.01}^{+0.01}$	${53.0}_{- 0.2}^{+ 0.2}$ $53.0_{-0.2}^{+0.2}$	$- {21.6}_{- 0.1}^{+ 0.2}$ $-21.6_{-0.1}^{+0.2}$	1.2
RCra IRS7B	3	${10.55}_{- 0.0}^{+ 0.02}$ $10.55_{-0.0}^{+0.02}$	${0.16}_{- 0.02}^{+ 0.01}$ $0.16_{-0.02}^{+0.01}$	${67.7}_{- 0.2}^{+ 0.2}$ $67.7_{-0.2}^{+0.2}$	$- {64.3}_{- 0.4}^{+ 0.4}$ $-64.3_{-0.4}^{+0.4}$	${10.18}_{- 0.01}^{+ 0.01}$ $10.18_{-0.01}^{+0.01}$	${0.07}_{- 0.001}^{+ 0.001}$ $0.07_{-0.001}^{+0.001}$	${62.3}_{- 0.7}^{+ 0.7}$ $62.3_{-0.7}^{+0.7}$	$- 75_{- 0.85}^{+ 0.85}$ $-75_{-0.85}^{+0.85}$	15
−	6	${11.28}_{- 0.002}^{+ 0.003}$ $11.28_{-0.002}^{+0.003}$	${0.18}_{- 0.01}^{+ 0.01}$ $0.18_{-0.01}^{+0.01}$	${68.6}_{- 0.01}^{+ 0.03}$ $68.6_{-0.01}^{+0.03}$	$- {64.8}_{- 0.1}^{+ 0.1}$ $-64.8_{-0.1}^{+0.1}$	${11.33}_{- 0.001}^{+ 0.001}$ $11.33_{-0.001}^{+0.001}$	${0.06}_{- 0.01}^{+ 0.01}$ $0.06_{-0.01}^{+0.01}$	${84.3}_{- 1}^{+ 0.3}$ $84.3_{-1}^{+0.3}$	$- 66_{- 0.20}^{+ 0.24}$ $-66_{-0.20}^{+0.24}$	16

Notes. Sources with a (^∗) apex lack envelope continuum excess at either 3.1 mm or both wavelengths, and they were modelled using one or more compact components (see Section 3 for more details). The cases in which the χ² value is significantly higher than one are those for which high signal-to-noise ratio asymmetries highlight the limitation of a spherically symmetric model (e.g. IRAS4A, VLA1623A, and L1551-IRS5) or where secondary sources in the FOV are left in the residuals (IRS7B, GSS30, and IRAS4C; see text in Section 3).

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