dataesr/scientific-paragraphs-categorization huggingface dataset:
The spectral resolution of the combined PdBI+30m dataset is limited by the 30m dataset at 1. 3 mm (0. 27 km s -1 ) and the PdBI one at 3 mm (0. 13 km s -1 ). We produced the N 2 H + (1-0) combined datacubes in such a way to have a synthesized beam size < 2 and a noise level <10 mJy beam -1. As the N 2 H + emission traces preferably the outer protostellar envelope, we used a natural weighting to build the combined maps to minimize the noise rather than to maximize angular resolution. The C 18 O (2-1) combined maps were produced using a robust weighting scheme, in order to obtain synthesized beam sizes close to the PdBI ones, and to minimize the side-lobes. In all cases, the deconvolution was carried out using the Hogbom algorithm in MAPPING. A&A proofs: manuscript no. main Table  1. Sample of CALYPSO Class 0 protostars considered for this analysis.
Properties of the analyzed maps Following the procedure described above, we have obtained, for each source of the sample, a set of three cubes for each of the two molecular tracers C 18 O (2-1) and N 2 H + (1-0), probing the emission at different spatial scales (PdBI map, com-bined PdBI+30m map, and 30m map). In order to build maps with pixels that contain independent dataset and avoid oversampling, we inversed visibilities from the PdBI and the combined PdBI+30m datasets using only 4 pixels per synthesized beam, and we smoothed the resulting maps afterwards to obtain 2 pixels per element of resolution.
Integrated intensity maps To identify at which scales of the protostellar envelopes the different datasets are sensitive to, we produced integrated intensity maps by integrating spectra of each pixel for the molecular lines C 18 O (2-1) and N 2 H + (1-0) from the PdBI, combined, and 30m datasets for each source. For C 18 O (2-1), we integrated each spectrum on a velocity range of ± 2. 5 km s -1 around the velocity of the peak of the mean spectrum of each source. The 1-0 line of N 2 H + has a hyperfine structure with seven components (see Fig. 2 ). We integrated the N 2 H + spectra over a range of 20 km s -1 encompassing the seven components. Figure  1  shows as an example the integrated intensity maps obtained for L1448-2A. The integrated intensity maps of the other sources are provided in Appendix H.
We used the integrated intensity maps to measure the average emission size of each tracer in each dataset above a 5σ threshold. The values reported in Tables B. 3 and B. 4 are the average of two measurements: an intensity cut along the equatorial axis and circular averages at different radii around the intensity peak position of the source. Only pixels whose intensity is at least 5 times higher than the noise in the map are considered to build these intensity profiles. The FWHM of the adjustment by a Gaussian function allows us to determine the average emission size of the sources. For both tracers and for all sources in our sample, the emission is detected above 5σ in an area larger in the combined datasets than in the PdBI datasets, and smaller than in the 30m ones (see  Tables B. 3 and B.
4). Our three datasets are thus not sensitive to the same scales and allow us to probe different scales within the 12 sampled protostellar envelopes: the 30m datasets trace the outer envelope, the PdBI datasets the inner part and the combined ones the intermediate scales. The C 18 O and N 2 H + molecules do not trace the same regions of the protostellar envelope either:  Anderl et al. (2016)  report from an analysis of the CALYPSO survey that the N 2 H + emission forms a ring around the central C18O emission in four sources. Previous studies  (Bergin et al. 2002; Maret et al. 2002 Maret et al. , 2007;; Anderl et al. 2016)  show that N 2 H + , which is abundant in the outer envelope, is chemically destroyed when the temperature in the envelope reaches the critical temperature (T 20K) at which CO desorbs from dust ice mantles.
Thus, while N 2 H + can be used to probe the envelope kinematics at outer envelope scales, C 18 O can be used as a complementary tracer of the gas kinematics at smaller radii where the embedded protostellar embryo heats the gas to higher temperatures. The C 18 O emission is robustly detected (>5σ) in our PdBI observations for most sources, except for L1521F and IRAM04191 which are the lowest luminosity sources of our sample (see Table  1 ), and for SVS13-B where the emission is dominated by its companion, the Class I protostar SVS13-A. For most sources, the interferometric map obtained with the PdBI shows mostly compact emission (r < 3 , see Table  B. 3). However, the C 18 O emission from the 30m datasets shows more complex structures (see Appendix H). Assuming that, under the hypothesis of spherical geometry, the emission from a protostellar envelope is compact (r 40 , i.
e. , 10000 au, see Table  1 ) and stands out from the environment in which it is embedded, the 30m emission of L1448-2A, L1448-C, and IRAS4A comes mainly from the envelope. The N 2 H + emission is detected in our combined observations for all sources. In the four sources studied by  Anderl et al. (2016) , they do not detect the emission at the 1. 3 mm continuum peak, but emission rings around the C 18 O central emission. From Table  B. 4, we noticed two types of emission morphologies based on the PdBI dataset: compact (r <7 , see Table  B. 4) or filamentary (r ≥9 ). In the same way as the C 18 O emission, the N 2 H + emission from the 30m datasets shows complex structures with radius r 40 for most sources, except for five sources (IRAM04191, L1521F, L1448-NB, L1448-C, and L1157) where the emission is consistent with the compact emission of the protostellar envelope.
Velocity gradients in protostellar envelopes To quantify centroid velocity variations at all scales of the protostellar envelopes, we produced centroid velocity maps of each Class 0 protostellar envelope by fitting all individual spectra (pixel by pixel) by line profile models in the CLASS program of the GILDAS software. We only considered the line intensity detected with a signal-to-noise ratio higher than 5. We fit the spectra to be able to deal with multiple velocity components. Indeed, because protostellar envelopes are embedded in large-scale clouds, multiple velocity components can be expected on some lines of sight where both the protostellar envelope and the cloud emit. For example,  Belloche et al. (2006)  find several velocity components in their 30m of the N 2 H + emission of IRAS4A (see Appendix H.
6). Except for IRAS4A and IRAS4B for which we fit two velocity components (see details in Appendix H), for most sources we used a Gaussian line profile to model the C 18 O (2-1) emission, with the line intensity, full width at half maximum (FWHM), and centroid velocity let as free parameters (see Fig. 2 ). In the case of N 2 H + (1-0), we used a hyperfine structure (HFS) line profile to determine the FWHM and centroid velocity of the molecular line emission (see Fig. 2 ). Figures 3 to 14 show the centroid velocity maps obtained for each source of the sample using the PdBI, combined, and 30m datasets for both the C 18 O and N 2 H + emission. For most sources in our sample, these centroid velocity maps reveal organized velocity patterns with blue-shifted and redshifted velocity components on both sides of the central stellar embryo, along the equatorial axis where such velocity gradients could be due to rotation of the envelopes.
A mean gradient oriented along the outflow axis could be due to jets and outflows or infall in a flattened geometry. The gradients were fit on the region of the velocity maps shown in Fig. 3 , namely 10 × 10 in the PdBI and combined datasets for the C 18 O emission (lower left and central panels), 40 × 40 for the N 2 H + emission from the PdBI and combined datasets (upper left and central panels), and 80 × 80 and 160 × 160 , respectively for the C 18 O and N 2 H + emission from the 30m datasets (right panels). Table  2  reports for each source the significant mean velocity gradients detected with an amplitude higher than 2σ. No significant velocity gradient is observed for IRAM04191, L1521F, and SVS13-B in C 18 O emission at scales of r <5 or for L1448-C and IRAS4B at r >30 (see Table  2 ).
The analysis described in detail in Appendix C allows us to build a PV rot diagram with a high dynamic range from 50 au up to 5000 au for each source as follows (see the example of L1527 in Fig. 15 ): • To constrain the PV rot diagram at the smallest scales   Absolute value, between 0 • and 90 • , of the difference between the angle of the mean gradient and the angle of the equatorial axis. The equatorial axis is defined perpendicularly to the direction of the outflows (see Table  1 ). (  ) For IRAM04191, the N 2 H + emission in the 30m dataset was fit ignoring the pixels close to the Class I protostar IRAS04191 in the field of view (see Appendix H). G v 0 Θ a ∆Θ b G v 0 Θ a ∆Θ b G v 0 Θ a ∆Θ b (km s -1 pc -1 ) (km s -1 ) ( • ) ( • ) (km s -1 pc -1 ) (km s -1 ) ( • ) ( • ) (km s -1 pc -1 ) (km s -1 ) ( • ) ( • ) L1448-2A C 18 O (2- A&A proofs: manuscript no.
main Fig. 2. Mean spectra of the N 2 H + (top) and C 18 O (bottom) molecular lines from the 30m datasets for L1448-2A. The best fits of the spectra, by a hyperfine structure and a Gaussian line profile models respectively, are represented in green solid lines. In the top panel, the velocity axis corresponds to the isolated HFS component 1 01 -0 12. The systemic velocity is estimated to be 4. 10 km s -1 for this source (see Table  E. 1). resolved by our dataset (∼0. 5 ), we use the PdBI C 18 O datasets that we analyze in the (u,v) plane to avoid imaging and deconvolution processes (see label "C 18 O PdBI" in Fig. 15 ). We only kept central emission positions in the channel maps at a position angle <|45 • | with respect to the equatorial axis (see Appendix C). • Since the C 18 O extended emission is filtered out by the interferometer, we used the combined C 18 O emission to populate the PV rot diagram at the intermediate scales of the protostellar envelopes (see label "C 18 O combined" in Fig.
15 ). The C 18 O molecule remains the most precise tracer when the temperature is higher than ∼20K because below, the C 18 O molecule freezes onto dust ice mantles. To determine the transition radius R trans between the two tracers, we calculate the C 18 O and N 2 H + column densities along the equatorial axis from the combined integrated intensity maps (see Appendix D and green points in Fig. 15 ). • At radii r > R trans , the N 2 H + emission traces better the envelope dense gas. We use the combined N 2 H + emission maps to analyze the envelope kinematics at larger intermediate scales. When the N 2 H + column density profile reaches a minimum value due to the sensitivity of the combined dataset, this dataset is no longer the better dataset to provide a robust information on the velocity (see label "N 2 H + combined" in Fig.
15 ). • Finally, we use the 30m N 2 H + emission map to populate the PV rot diagram at the largest scales of the envelope (see label "N 2 H + 30m" in Fig. 15 ). The CALYPSO datasets allow us to continuously estimate the velocity variations along the equatorial axis in the envelope over scales from 50 au up to 5000 au homogeneously for each protostar. Figure  16  shows the PV rot diagrams built for all sources of the sample. The systemic velocity used in the PV rot diagrams are determined in Appendix E. The method of building PV rot diagrams described above and in Appendix C corresponds to an ideal case with a detection of a continuous blue-red velocity gradient along the direction perpendicular to the outflow axis in the velocity maps. In practice, the direction of velocity gradients is not always continuous at all scales probed by our observations (see Table  2  and Figure  19 ).
Characterization of rotational motions We assume that the protostellar envelopes are axisymmetric around their rotation axes, and thus, the velocity gradients observed along the equatorial axis, and reported in the PV rot diagrams, are mostly due to the rotational motions of the envelopes. We model the rotational velocity variations by a simple powerlaw model v ∝ r α without taking the upper limits into account. This method has been tested with an axisymmetric model of collapsing-rotating envelopes by  Yen et al. (2013). As long as datasets for L1448-2A. The blue and red solid arrows represent the directions of the blue-and red-shifted outflow lobes, respectively. The white crosses represent the positions of the binary system determined from the 1. 3 mm dust continuum emission (see Table  1 ).
3, see Table  3 ). These flat PV rot diagrams (v rot ∼ constant) suggest differential rotation of the envelope with an angular velocity of Ω = v rot r ∝ r -1. For two other sources (IRAS4B and IRAM04191), the best indices are compatible with -0. 5, which could suggest Keplerian rotation at scales of r <1000 au. However, the reduced χ 2 are also satisfactory (∼1) when we fix the power-law index at α=-1 (see Table  3 ). Thus, for these two sources, our CALYPSO datasets only allow us to estimate a range of the power-law indices between -1 and -0. 5 (see Table  3 ). Rotational velocity variations along the equatorial axis between 50 and 5000 au in L1448-NB cannot be reproduced satisfactorily by any single power-law model (χ 2 >2, see Table  3 ). However, considering only the points at r <400 au for L1448-    3 , but for IRAS4A.
The black cross represents the position of the secondary protostar L1448-NB2 of the multiple system. Fig. 10. Same as Figure  3 , but for IRAM04191. The white cross represents the position of the Class I protostar IRAS04191. The black cross represents the position of IRAM04191 determined from the 1. 3 mm dust continuum emission (see Table  1 ). interpretation of the velocity field as tracing solid-body rotation in the envelope of IRAS4A is therefore unlikely to be correct. For the sources IRAS2A, IRAM04191, and L1157, the reduced χ 2 is also good (∼1) when the PV rot diagrams of these sources are ajusted by a model with a fixed index of α=-1 (see Table  3 ). We determine position and velocity from four different and independent methods and we did not consider the uncertainties of the connection between the different tracers and datasets.
The uncertainty on the indices reported in Table  3  may thus be underestimated. On the other hand, although we determined the systemic velocity by maximizing the overlap of the blue and red points, this method does not allow a more accurate determination than 0. 05 km s -1. The systematic error of 0. 05 km s -1 , added to previous velocity errors of the points in the PV rot diagrams to take this uncertainty on the systemic velocity into account (see Appendix E), can be overestimated and thus lead us to underestimate the χ 2. For these three sources, the CALYPSO dataset only allow us to estimate a range of power-law indices between  -1 and the α value reported in the fifth column of Table  3. The uncertainties on the indices reported in Table E are statistical errors and a systematic uncertainty of ±0.
6±0. 2 ) in the outer envelope. The radius of ∼1600 au therefore appears to be a critical radius which delimits two regimes of angular momentum in protostellar envelopes: the specific angular momentum decreases down to ∼1600 au and then tends to become constant. The change of behavior of j app above the break radius could be due to a change of tracer to study the kinematics in the outer envelope. However, we do not find any systematic consistency between r app,break and the transition radius R trans between the two tracers C 18 O and N 2 H +. Even if for SVS13-B, R trans is in the error bars of r app,break , for three sources (L1448-NB, L1448-C, and A&A proofs: manuscript no. main   (1997b). Panel (b): zoom on the region where the angular momentum profiles due to rotation of the CALYPSO sources lie.
Origin of the velocity gradients at r >1600 au At outer envelope scales, we detect velocity gradients (∼2 km s -1 pc -1 at ∼10000 au, see Table  2 ) in the CALYPSO single-dish maps. They may not be directly related to rotational motions of the envelopes but rather to other mechanisms. Indeed, we observe in the CALYPSO dataset a systematic evolution of the orientation of the gradients between the inner and outer scales in the envelope (see Table  2 ). Figure  19  shows the orientation of the mean velocity gradient observed at different scales of the envelope with respect to the position angle of the gradient observed at scales ∼100 au. The clear dispersion (∼100 • on average, see Fig. 19 ) of gradient position angle across scales within individual objects may be due to a change of dominant mechanisms responsible for the observed gradients from inner to outer scales of the envelope.
From the literature, velocity gradients are often measured in the outer protostellar envelopes along the equatorial axis and they are interpreted as due to rotational motions or infall from a filamentary structure at scales of 1500-10000 au  (Ohashi et al. 1997b; Belloche et al. 2002; Tobin et al. 2011). In this section, we explore the possible origins of the velocity gradients found at scales of r > 1600 au and used to build the | j app |(r) profiles (see Fig. 18 ). Fig. 19. Evolution of the orientation of the mean velocity gradient in the different datasets used to build the PV rot diagrams and angular momentum distributions with respect to the PA of the velocity gradient observed at small scales Θ small (PdBI C 18 O emission). The error bars of the orientation Θ are given in Table  2. They are smaller than 10 • except for 7 of the 67 gradient measurements.
2014). Indeed, the column density maps of the Herschel Gould Belt Survey program 5  (André et al. 2010 ) reveal that the CALYPSO protostars are embedded in or lie in the immediate vicinity of filamentary structures with N H 2 >10 21 cm -2. Thus, the large-scale kinematics in protostellar envelopes could be contaminated or dominated by the kinematics of the filaments. Kirk et al. (2013)  studied the velocity field of Serpens-South in the Aquila molecular cloud and showed a complex kinematics with longitudinal collapse along the main filament, radial contractions, and accretion streams from the cloud to the main filament. The longitudinal collapse of the filament could be responsible for the large-scale gradients observed in our protostellar envelopes as observed in the Serpens-Main region by  Dhabal et al.
C18O points N2H+ points 10 1 10 0 10 1 10 2 offset (arcsec) r > 470 = 0. 7 ± 0. 4 r > 470 = 0. 7 ± 0. 4 Fig. 20. Linewidth along the equatorial axis of the CALYPSO protostellar envelopes. Blue and red dots show the linewidths at positions that have blue-and red-shifted velocities, respectively. Dots and large dots show the C 18 O and N 2 H + data, respectively. The dashed curve shows the best fit with a power-law model leaving the index γ as a free parameter (Dv ∝ r γ ) in the outer envelope (see Appendix G). The radius of the outer envelope is given by the break radius of the j(r) or j app (r) profiles (see Tables F. 1 and F. 2) or the radius where we observe a reversal of the velocity gradients with respect to the inner envelope. The vertical dashed lines show the transition radii between the different datasets  (PdBI, combined, and 30m ) and the two tracers as given in Table  C.
1. Notes. ( a) r max value defined as the mean radius of the area where integrated molecular line emission is detected above a 5σ contour. ( b) rms noise levels per channel computed with a spectral resolution of 0. 27 km s -1 for all maps. ( c) Integrated fluxes computed inside the PdBI primary beam at 1. 3 mm (∼20 ) for the PdBI and combined PdBI+30m datasets and inside the primary beam (2 × HPBW ∼25 at 1. 3 mm) for the 30m datasets. Notes. ( a) r max value defined as the mean radius of the area where integrated molecular line emission is detected above a 5σ contour. ( b) rms noise levels per channel computed with a spectral resolution of 0. 13 km s -1 for all maps. ( c) Integrated fluxes computed inside the PdBI primary beam at 3 mm (∼50 ) for the PdBI and combined PdBI+30m datasets and inside the primary beam (2 × HPBW ∼60 at 3 mm) for the 30m datasets.
For most sources, R trans is smaller than the 30m HPBW. We used the combined C 18 O emission map to constrain the gas kinematics in the PV rot diagram up to R trans (see label "C 18 O combined" in Fig. 15 ). • At radii r > R trans , the N 2 H + emission traces better the envelope dense gas. We use the combined N 2 H + emission maps to analyze the envelope kinematics at intermediate scales, from R trans to the 30m HPBW (∼14 at the N 2 H + frequency, see Table  B. 2). However, the N 2 H + column density profile can reach a minimum value at radii R trans < r < 30m HPBW due to the sensitivity of the combined datasets. In this case, the combined dataset is no longer the better dataset to provide a robust information on the velocity. We defined R int the maximum radius up to which we use N 2 H + emission from the combined dataset (see Table  C.
1 and see label "N 2 H + combined" in Fig. 15 ). • Beyond R int , we use the 30m N 2 H + emission map to populate the PV rot diagram up to the largest scales of the envelope (see label "N 2 H + 30m" in Fig. 15 ). We note R out the maximum radius of the protostellar envelopes (see Table  C. 1). The sources in our sample show specific individual behaviors, therefore we adapted the method of building the PV rot diagram described above on a case-by-case basis. Nevertheless we respected the transition radii as closely as possible (see Table  C. 1). Notes. ( a) Outer radius of the C 18 O emission from the PdBI datasets. ( b) Transition radius between C 18 O and N 2 H + determined from column density profiles along the equatorial axis (see Appendix D). R trans is defined following criteria (i), (ii), (iii), and (iv) which are detailed in Sect.
C. 3. ( c) Intermediate radius in N 2 H + emission between the combined and 30m datasets. ( d) Envelope radius from PdBI or 30m dust continuum emission. See Table  1  for the references. ( ) For IRAS4A and IRAS4B, we used the N 2 H + emission from the PdBI datasets instead of the combined datasets to build the PV rot diagram. In these cases, R int is the maximum radius below which we used the PdBI dataset. ( ) For L1521F, we only used the C 18 O emission from the combined and 30m datasets to build the PV rot diagram (see Appendix H). For this case, we used the combined dataset up to R trans and we used the 30m dataset up to R out. We calculated the opacity on the spectra of each pixel from the combined dataset for both molecular transition. We used the excitation temperature values mentioned above and a standard value of the cosmic background temperature T bg =2.
(D. 1) to calculate the column density. Indeed, the column density determined in the optically thin hypothesis by Eq. (D. 1) is underestimated by more than 20% for a value of τ ν =0. 4. H. 5, H. 9, H. 13, H. 17, H. 19, H. 24, H. 28, H. 32, H. 36, H. 40, and H. 44). Notes. The mean column density of C 18 O and N 2 H + and the opacity of the transitions (2-1) and (1-0), respectively, are calculated within the central 5 ×5 and 20 ×20 respectively, from the combined datasets. The N 2 H + column density was determined from the isolated hyperfine component (1 01 -0 12 ). ( ) For IRAS4A and IRAS4B, the calculations were made from the PdBI datasets for the N 2 H + emission. If the reference velocity value is well chosen, blue-and red-shifted velocity points should overlap if the envelope is axisymmetric.