# The ALMA Legacy survey of Class 0/I disks in Corona australis, Aquila,
chaMaeleon, oPhiuchus north, Ophiuchus, Serpens (CAMPOS). I. Evolution of
Protostellar disk radii

Cheng-Han Hsieh (謝承翰) Department of Astronomy, Yale University, New Haven, CT
06511, USA  Héctor G. Arce Department of Astronomy, Yale University, New
Haven, CT 06511, USA  María José Maureira Max Planck Institute for
Extraterrestrial Physics, Gießenbachstraße 1, 85748, Garching bei München,
Germany  Jaime E. Pineda  Max Planck Institute for Extraterrestrial Physics,
Gießenbachstraße 1, 85748, Garching bei München, Germany  Dominique Segura-Cox
Department of Astronomy, The University of Texas at Austin, 2515 Speedway,
Stop C1400 Austin, Texas 78712-1205, USA  Diego Mardones Departamento de
Astronomía, Universidad de Chile, Camino El Observatorio 1515, Las Condes,
Chile  Michael M. Dunham Physics department, State University of New York at
Fredonia, 280 Central Ave. Fredonia, NY 14063, USA  Aiswarya Arun
Departamento de Astronomía, Universidad de Chile, Camino El Observatorio 1515,
Las Condes, Chile

###### Abstract

We surveyed nearly all the embedded protostars in seven nearby clouds (Corona
Australis, Aquila, Chamaeleon I & II, Ophiuchus North, Ophiuchus, Serpens)
with the Atacama Large Millimeter/submillimeter Array at 1.3mm observations
with a resolution of 0$\farcs$1\. This survey detected 184 protostellar disks,
90 of which were observed at a resolution of 14–18 au, making it one of the
most comprehensive high-resolution disk samples across various protostellar
evolutionary stages to date. Our key findings include the detection of new
annular substructures in two Class I and two Flat-spectrum sources, while 21
embedded protostars exhibit distinct asymmetries or substructures in their
disks. We find that protostellar disks have a substantially large variability
in their radii across all classes. In particular, the fraction of large disks
with sizes above 40 au decreases with the protostellar evolutionary stage.
Compiling the literature data, we discovered an increasing trend of the gas
disk radii to dust disk radii ratio ($R_{\rm gas,Kep}/R_{\rm mm}$) with
increasing bolometric temperature (${\rm T}_{\rm bol}$). Our results indicate
that the dust and gas disk radii decouple during the early Class I stage. We
find that Class 0 dust disk size resembled the gas disk size, enabling a
direct comparison between models and observational data at the earliest stages
of protostellar evolution. We show that the distribution of radii in the 52
Class 0 disks in our sample is in high tension with various disk formation
models, indicating that protostellar disk formation remains an unsolved
question.

star formation – disks – methods: observational – stars: low-mass –techniques:
interferometric

††journal: ApJ††facilities: ALMA††software: Astropy (Greenfield et al., 2013;
Astropy Collaboration et al., 2018), CASA (McMullin et al., 2007)

##  1 Introduction

Circumstellar disks play an important role in star and planet formation. Disks
mediate the transfer of mass and angular momentum facilitating the accretion
of material onto protostars. Their physical structure and chemical conditions
also determine the resulting planetary systems. Circumstellar disks are formed
from the gravitational collapse of molecular cloud cores. However, the details
of their formation are complicated by the presence of magnetic fields,
turbulence, and rotation.

Theoretical studies suggested magnetic fields play an important role in disk
formation (Li et al., 2014b; Machida et al., 2016). Highly pinched magnetic
fields thread the protostellar disks and remove the angular momentum in a
process known as magnetic braking (Allen et al., 2003). In the ideal
magnetohydrodynamics (MHD) approximation, the magnetic braking effect is very
efficient and this leads to the suppression of disk formation (Mellon & Li,
2008; Hennebelle & Ciardi, 2009). This problem is softened by the realization
of the importance of non-ideal MHD effects (Ohmic diffusion, Hall effect, and
ambipolar diffusion) caused by the low conductivity of the gas during the disk
formation process (e.g., Mellon & Li 2009; Machida et al. 2014; Tomida et al.
2015; Masson et al. 2016; Krasnopolsky et al. 2011; Li et al. 2011; Wurster et
al. 2016; Tsukamoto et al. 2015, 2017). Additional explanations have been
proposed for reducing the magnetic braking effects, for example, misalignment
between the disk rotation axis and the magnetic field (Ciardi & Hennebelle,
2010) and turbulence (Santos-Lima et al., 2012; Joos et al., 2013; Seifried et
al., 2013; Matsumoto et al., 2017).

One way to progress in our understanding of disk formation is to find
observables that test different disk formation models. Gas disk radii can
provide useful insights because disk sizes are a good tracer of their angular
momentum. Many non-ideal MHD models offer distinct predictions for the initial
distribution of protostellar gas disk sizes, for example, a bimodal
distribution in disk sizes due to the Hall effect (Tsukamoto et al., 2015),
and the small variation of disk size centered at 18 au predicted by the
ambipolar diffusion (e.g., Hennebelle et al. 2016). While the advance of
Atacama Large Millimeter/submillimeter Array (ALMA) with an order of magnitude
increase in sensitivity and angular resolution compared to earlier radio
interferometers has led the way for the characterization of disk properties,
the molecular line observation towards the youngest Class 0 protostellar disks
remains limited to a small sample in nearby clouds (Murillo et al., 2013;
Ohashi et al., 2014; Sakai et al., 2014a; Codella et al., 2014; Lindberg et
al., 2014; Aso et al., 2017; Yen et al., 2017; Alves et al., 2018; Hsieh et
al., 2020). This is due to the large observational time required to resolve
the small rotating disk. Recently, the ALMA large program Early Planet
Formation in Embedded Disks (eDisk) observed 12 Class 0 and 7 Class I
protostellar disks in great detail, significantly increasing the number of
young protostellar disks with line observations (Ohashi et al., 2023; Lin et
al., 2023; van’t Hoff et al., 2023; Kido et al., 2023; Sai et al., 2023a).
Even so, the total number of observed young protostellar disks with molecular
lines falls significantly short of a population study.

In contrast, the sample size of dust continuum observation towards
protostellar disks has improved significantly over the last decade. The
Protostellar Submillimeter Array Campaign (PROSAC) surveyed 20 Class 0/I disks
at 2$\farcs$0 ($\sim 250-650$ au) resolution at 0.85 mm and 1.3 mm wavelength
using the Submillimeter Array (SMA) (Jørgensen et al., 2009). Subsequent
efforts, such as the IRAM-PdBI survey, observed 21 Class 0 sources at
0$\farcs$3 ($\sim 120$ au) resolution (Maury et al., 2010, 2019) at 1.3 mm
wavelength. The Combined Array for Research in Millimeter-wave Astronomy
(CARMA) observed 9 more Class 0 sources in the Serpens molecular cloud at
1$\farcs$0 ($\sim 415$ au) resolution at 1.3 mm wavelength (Enoch et al.,
2011). Additionally, the Very Large Array (VLA) observed 18 Class 0/I disks in
the Perseus molecular cloud at $\sim$0$\farcs$05 (12 au) resolution at 8 mm
wavelength (Segura-Cox et al., 2016, 2018). These early surveys mostly focused
on selected sources, and either had a relatively low angular resolution
($>100$ au resolution) or a limited sample size.

The advent of ALMA marked a revolutionary leap forward in the field. The
recent VLA/ALMA Nascent Disk and Multiplicity (VANDAM) survey of the Orion
molecular clouds stands out, detecting a total of 379 protostellar disks out
of 421 surveyed at an excellent angular resolution of $\sim$0$\farcs$07 (40
au) at 0.87 mm wavelength (Tobin et al., 2020). To complete the sample of
protostellar disks in nearby molecular clouds within 450 pc at 0$\farcs$1
angular resolution, we initiated the ALMA Legacy survey of Class 0/I disks in
Corona australis, Aquila, chaMaeleon, oPhiuchus north, Ophiuchus, Serpens
(CAMPOS). We surveyed nearly all the Class 0/I protostellar disks in seven
molecular clouds: Chamaeleon I at a distance of 179 pc (Voirin et al., 2018),
Chamaeleon II at 181 pc (Voirin et al., 2018), Corona Australis at a distance
of $149$ pc (Galli et al., 2020), Ophiuchus and Ophiuchus North at a distance
of 144 pc (Zucker et al., 2019). We also include the Serpens and Aquila
molecular clouds at a distance of $436$ pc (Ortiz-León et al., 2018) which is
similar to Orion, allowing us to compare with the Orion Class 0/I disk survey
(Tobin et al., 2020).

To compare our CAMPOS dust disk observation with different protostellar disk
formation models, we compiled the literature data and discovered an increasing
trend of the gas disk radii to dust disk radii ratio with the protostar’s
evolutionary stage. In particular, for Class 0 sources, the dust disk size is
similar to the gas disk size, allowing a direct comparison between models with
observational data. We found the size distribution of 52 Class 0 disks is in
high tension with both the pure hydrodynamical models and the Hall effect
models, and it is also inconsistent with the ambipolar diffusion models.

This paper is organized as follows: In section 2, we give an overview of the
CAMPOS observation. In section 3, we describe the detailed self-calibration
tests, data reduction, imaging, and source detection for the project. In
section 4, we present the main result of this paper: sources detection
statistics, distribution of dust disk radii, the discovery of new disk
substructures, streamer candidates, and edge-on protostellar disks. We discuss
our results in section 5, and present our conclusion in section 6.

##  2 Observation

###  2.1 Sample Selection

Our protostellar sample is derived from the Dunham et al. (2015) catalog,
which originated from two Spitzer Space Telescope Legacy Projects: the “From
Molecular Cores to Planet-forming Disks” (c2d) and its successor, the “Spitzer
Gould Belt (GB) Legacy Survey”. An overview of the c2d survey was given by
Evans et al. (2003) with major results for major star-forming clouds
highlighted in Evans et al. (2009). The combined survey targeted nearly all
the molecular clouds within 500 pc of the Sun.

We selected the Class 0, Class I, flat-spectrum sources, and early Class II
protostars with bolometric temperatures ($T_{\rm bol}\leq 1900\,$K) in seven
molecular clouds: Serpens, Aquila, Ophiuchus, Ophiuchus North, Chamaeleon I,
and Chamaeleon II. All sources are associated with dense cores detected via
submillimeter or millimeter continuum emission (wavelength $>$ 350 $\mu$m) as
noted in Table 2 of Dunham et al. (2015). By employing sources with
established dense cores, our protostar sample is robust, avoiding reliance on
assumptions regarding infrared protostar colors.

However, while our stringent criteria in dust continuum selection assure
sample reliability, there’s a trade-off with incompleteness. Our sample lacks
representation of protostars nestled within low-mass cores, leading to a bias
against the lowest-mass (luminosity) protostars. The recent complete results
from the Herschel and James Clerk Maxwell Telescope Submillimetre Common-User
Bolometer Array (SCUBA)-2 Legacy GB surveys allow the detection of dense cores
in all GB clouds down to 0.1 $M_{\odot}$ (e.g., Pattle et al. (2015); Könyves
et al. (2015)). Pokhrel et al. (2023) published an updated protostar catalog
for the Serpens and Aquila molecular clouds, incorporating both Herschel and
SCUBA data, while compiling a complete list of protostars encompassing other
clouds covered by our CAMPOS survey remains pending.

Despite the trade-off for reliability at the expense of completeness, our
sizable sample ensures a fairly uniform sampling of sources within the ranges
of $25\,K<T_{\rm bol}<1900\,K$ and $0.1\,L_{\odot}<L_{\rm bol}<10\,L_{\odot}$.
Our sample is only completed up to 1900 K and is incomplete for Class II. In
fairness, while we include the early Class II sources in this data release
paper, they are excluded from the analysis.

###  2.2 ALMA 1.3 mm Continuum Observations

Table 1: ALMA Observations summary RegionaaCloud name of the ALMA observations. The characters represent the name of the cloud (eg. CorAus: Cor Australis, ChamI: Chamaeleon I, ChamII: Chamaeleon II, Oph: Ophiuchus, OphN: Ophiuchus North, Serp: Serpens. If multiple executions were carried out for a cloud, then they are labeled with A, B, C…etc in parenthesis.  | Observed | DurationbbTotal duration of the observation per field includes time used for calibration. | Baseline | Number of | MRSccMaximum recoverable scale. | PWVddPercipitable water vapor. | Calibrators
---|---|---|---|---|---|---|---
| Date | (minutes) | Range (m) | Antennas | (arcsec) | (mm) | Bandpass, Flux, Phase
Aquila | 2021 Jul 6 | 32.0 | $29-3638$ | 45 | 2.3 | 0.54 | J1924-2914, J1924-2914, J1834-0301
ChamI (A) | 2021 Jul 20 | 22.4 | $15-3697$ | 39 | 1.5 | 1.68 | J1617-5848, J1617-5848, J1058-8003
ChamI (A) | 2021 Jul 22 | 16.1 | $43-3697$ | 22 | 1.2 | 0.58 | J0635-7516, J0635-7516, J1058-8003
ChamI (B) | 2021 Jul 20 | 24.7 | $15-3697$ | 42 | 1.5 | 1.56 | J1617-5848, J1617-5848, J1058-8003
ChamI (B) | 2021 Oct 24 | 23.8 | $47-8548$ | 34 | 0.9 | 0.18 | J1107-4449, J1107-4449, J1058-8003
ChamII | 2021 Jul 20 | 22.9 | $15-3697$ | 44 | 1.5 | 1.63 | J1617-5848, J1617-5848, J1058-8003
CrAus | 2021 Jul 10 | 23.6 | $29-3638$ | 46 | 1.9 | 0.66 | J1924-2914, J1924-2914, J1925-3401
Oph (A) | 2021 Jul 6 | 48.1 | $29-3638$ | 45 | 2.3 | 0.50 | J1427-4206, J1427-4206, J1633-2557
Oph (B) | 2021 Jul 7 | 24.6 | $29-3638$ | 45 | 2.1 | 0.50 | J1517-2422, J1517-2422, J1650-2943
OphN-01 | 2021 Jul 7 | 18.7 | $29-3638$ | 45 | 2.1 | 0.51 | J1550+0527, J1550+0527, J1643-0402
OphN-02 | 2021 Jul 7 | 21.9 | $29-3638$ | 45 | 2.1 | 0.57 | J1517-2422, J1517-2422, J1653-1551
OphN-03 | 2021 Jul 6 | 22.0 | $29-3638$ | 45 | 2.3 | 0.50 | J1517-2422, J1517-2422, J1653-1551
Serp (A) | 2021 Jul 6 | 34.4 | $29-3638$ | 45 | 2.3 | 0.51 | J1924-2914, J1924-2914, J1851+0035
Serp (B) | 2021 Jul 6 | 32.7 | $29-3638$ | 45 | 2.3 | 0.57 | J1924-2914, J1924-2914, J1830+0619

Observations for the CAMPOS project were taken between 2021 July-October
(Project ID: 2019.1.01792). The project consists of 2 parts: the molecular
line component and the high-resolution continuum component. For the molecular
line component, a single pointing using the 12 m array (with a resolution of
1$\farcs$0) was used to study the morphology and kinematics of the molecular
outflows and envelopes associated with the protostars in our sample. We will
present the result from the line observations in future papers.

In this paper, we focus on the high-resolution continuum component. A single
pointing with the ALMA 12 m array in configuration C43-7 (which provided a
resolution of 0$\farcs$1) was used for each target. Band 6 dual polarization
mode was used for the ALMA observation. The continuum was sampled in four
spectral windows (SPW) centered at 224, 226, 240, and 242 GHz. Our observation
was divided into 14 scheduling blocks, with four scheduling blocks for the
Chamaeleon I molecular clouds, three scheduling blocks for the Ophiuchus
North, two scheduling blocks each for Ophiuchus and Serpens molecular clouds,
and one scheduling block each for Aquila, Chamaeleon II, and Cor Australia
molecular cloud. The date of each observation, the duration (including the
calibration time), the baseline range, the number of antennas, the maximum
recoverable scales (MRS), the precipitable water vapor (PWV), and the
Bandpass, Flux, and Phase calibrators used are summarized in
LABEL:table:observation. The total time on each source was $\sim$ 0.6 minutes.
All data were calibrated using the Common Astronomy Software Application
(CASA) version 6.1.1.15 (McMullin et al., 2007).

##  3 Data

###  3.1 Self-calibration and Imaging processing

We used a modified version of `auto_selfcal`111This self-calibration pipeline
developed by J. Tobin can be found at:
https://github.com/jjtobin/auto_selfcal. to conduct the self-calibration of
the entire sample. The most significant modification was to change the mask
used for cleaning from being created automatically by CASA `tclean`
(`automasking`) task to a manually-inputted mask created before the self-
calibration process. In Appendix A we provide more details on the procedure
and the different tests we performed. We first ran the self-calibration
pipeline with `automasking` to obtain the first round of self-calibrated
measurement sets. We then applied `tclean` to image these measurement sets
with “uniform”, “briggs 0.5”, and “natural” weighted models with the “mtmfs”
deconvolver. We then identified local peaks in these 3 maps and used them as a
guide to create self-calibration masks centered on sources with clear
detection. With the self-calibration masks ready, we ran the modified self-
calibration pipeline three times with “uniform”, “briggs 0.5”, and “natural”
weighted models with the “mtmfs” deconvolver.

Once the self-calibration was completed, we started to create clean masks for
the imaging process. We applied `tclean` on the final self-calibrated
measurement sets, and cleaned down to $2\sigma$ using the same mask used for
self-calibration. We then drew new clean masks on the naturally weighted maps,
including all the sources that were detected with a signal-to-noise (S/N)
greater than or equal to 4 in all three maps (“uniform”, ”briggs0.5”, and
“natural” weighted maps), and detected with S/N $\geq 5$ in at least one of
the three maps. We also drew clean masks on possible candidate sources on the
position of the known protostars or visually identified local peaks with sizes
greater than the beam near other protostars.

We applied the clean masks for our final imaging. For the final imaging, the
deconvolver was set to “multi-scale” in order to better recover the large-
scale emission (1–2″). We cleaned down to $2\sigma$ using three different
weighting parameters (“natural”, “briggs0.5”, and “uniform”) to produce three
different images with different sensitivity and angular resolution. For each
weighting scheme, we used the visibilities self-calibrated with the same
weighting scheme to achieve the best signal-to-noise ratio. In Appendix B, we
summarize all the image properties of each field before and after the self-
calibration.

###  3.2 Source Detection process

We applied the Scipy Maximum Filter to the final cleaned images to identify
the sources. The maximum filter replaces each pixel value of an image with the
maximum value of its neighborhood pixels. It is used to find the brightest
points in an image and to filter out structures smaller than the beam size. We
then identified all the local maxima in the maps with S/N $\geq 4$ in all 3
maps (“uniform”, ”briggs0.5”, and “natural” weighted maps), or have S/N $\geq
5$ in at least one of the maps. Lastly, we also added one more source that has
S/N $\geq 4$ in two of the 3 maps. While many continuum surveys use S/N $\geq
3$ as a detection threshold (eg. Tobin et al. (2020)), we adopted a more
conservative detection threshold S/N $\geq 5$. For ALMA Band 6 observations,
the 0.2 primary beam cutoff (i.e., the radius at which the map reaches a
sensitivity that is 20% of that of the phase center) results in a field of
view of 37$\farcs$0\. For a beam size of 0$\farcs$1, there are $1.1\times
10^{5}$ beams in each map. Adopting $3\sigma,\,4\sigma,\,5\sigma$, based on
the random statistics we would expect around 290, 6, and 0.06 artificial
sources in each map respectively. All the sources detected in our survey
except one are detected at least above $5\sigma$.

##  4 Results

Our ALMA continuum images revealed the detailed disk structures on scales
between 0$\farcs$1 and 1$\farcs$1\. This corresponds to a physical scale of
15–163 au for sources in Cor Australis, 14–158 au for sources in Ophiuchus and
Ophiuchus North, and 18–197 au for sources in Chamaeleon. As for the Serpens
and Aquila molecular clouds, these clouds are located at a distance of 420 pc
and 440 pc respectively (Ortiz-León et al., 2018). Thus, our ALMA survey
targeted sources in these clouds at scales of 42–462 au, and 44–484 au similar
to the scales probed by the Orion and Perseus Class 0/I disk surveys (Tobin et
al., 2018, 2020). In this section, we present all the high-resolution
continuum images and sources detected in our survey.

Table 2: Fields and detection of sources per cloud CloudaaThe Cloud name of the ALMA observations. The names show the names of the cloud as in LABEL:table:observation | Targeted | DetectedbbNumber of fields with detection. | Sources DetectedccTotal number of sources detected.
---|---|---|---
Aql | 18 | 18 | 32
CorAus | 11 | 10 | 19
Cham I | 13 | 11 | 13
Cham II | 3 | 3 | 3
Oph | 41 | 38 | 52
OphN | 3 | 3 | 3
Serp | 36 | 35 | 62
Total | 125 | 118 | 184

###  4.1 Source Detection Statistics

Out of the 125 embedded protostellar systems initially targeted from Dunham et
al. (2015), our ALMA CAMPOS survey detected protostars in 118 fields.
Including multiple systems and all sources within the field of view, we
detected a total of 184 embedded protostars. Among these, 53 were associated
with Class 0 systems, 71 with Class I systems, 33 with flat-spectrum systems,
and 27 with early Class II systems. The evolutionary Class and estimate of
${\rm T}_{\rm bol}$ for all sources was derived from the latest eHOPS survey
(Pokhrel et al., 2023) for the Aquila and Serpens molecular clouds. For the
remaining clouds, we utilized unpublished eHOPS results through private
communication. In instances where CAMPOS sources lacked corresponding entries
in the eHOPS survey, we relied on the ${\rm T}_{\rm bol}$ and classification
from Dunham et al. (2015).

The evolutionary stage classification and estimate of ${\rm T}_{\rm bol}$ for
each source was obtained by constructing Spectral Energy Distribution (SED)
plots using photometry and spectra across from 1 to 850$\,\mu m$ (Pokhrel et
al., 2023). This involved data from various catalogues and telescopes such as
the Two Micron All Sky Survey (2MASS) point source catalog (Skrutskie et al.,
2006), observations by the Spitzer Space Telescope (Rieke et al., 2004; Fazio
et al., 2004), the Herschel Space Observatory (Pilbratt et al., 2010), and the
James Clerk Maxwell Telescope (Kirk et al., 2018). The SEDs were constructed
using telescopes with diverse apertures, ranging from the Infrared Array
Camera (IRAC) for Spitzer with a FWHM of 2$\farcs$0 to Herschel-SPIRE 500
$\mu$m detector with an FWHM of 37$\farcs$4\. In situations where the eHOPS
data could not resolve close binaries or multiples, we adopted the same ${\rm
T}_{\rm bol}$ and evolutionary class measured for sources within the ALMA
field. For detailed detection statistics in each molecular cloud, please refer
to LABEL:table:dection_stat.

We cross-referenced all 184 protostars identified in our ALMA survey with
established literature catalogs, listing the detected sources and alternative
names used in the literature in Appendix C, while presenting their images in
Appendix D. Remarkably, our survey unveiled 30 previously undetected
protostellar sources at submillimeter wavelengths. Among these, ten were part
of close binary systems, namely IRAS 18278-0158 b, eHOPS-aql-139 b, V* HO Cha
a, ChamI-9 mm, V* VV CrA B, Oph-emb 26b, Oph-emb 10b, Ser-emb 15B, eHOPS-
aql-86B, and Ser-emb 24A. Additionally, five new protostars were associated
with triple systems (eHOPS-oph-20c, Ser-emb 12A, Ser-emb 12C, Ser-emb 30C,
Ser-emb 30A). Fifteen others were linked with complex multiple systems
harboring at least 4 protostars each (SSTgbs J1829381-015100, SerpS-MM2 b,
SSTgbs J1829386-015100, SSTgbs J1829419-015011, MIRES G028.6593+03.8185,
SerpS10-mm, IRAS 18278-0158 b, eHOPS-aql-139 b, CrAus7-mm, CrAus8-mm1, CXO 34,
SSTc2d J182907.1+003043, Ser-emb 8B, Ser-emb 8C, Ser-emb 6B). A comprehensive
analysis of protostar multiplicity will be presented in forthcoming
publications.

Within our CAMPOS survey of 125 fields, 5 fields exhibited non-detections. The
Class I protostar, ChamI-03 (J110658.0-772248) and Class II protostar,
CrAus-06 (J190153.7-370033) were not detected. As for the flat-spectrum
systems, Oph-24 (J162721.8-242727), Serp-32 (J183000.3+010944), and ChamI-04
(J110716.1-772306) were not detected in our survey. However, the Spitzer Space
Telescope (Dunham et al., 2015) clearly detected these sources, suggesting
their continuum are below our sensitivity limits. Additionally, two sources,
Class 0 protostar Oph-04-0 (J162614.6-242507) and Class I protostar Oph-37-0
(J163152.0-245726), exhibited faint emission ($\leq 3\sigma$) corresponding to
the known sources identified by the Spitzer Space Telescope.

We also identified 4 potential candidates. These sources exhibited a signal-
to-noise ratio of $\geq 3\sigma$ in at least one of three maps (natural
weighted, Briggs 0.5, uniform weighted), or represented a local peak connected
to a known protostar. Assuming the sources are coeval with the nearby sources,
the Class 0 candidate is CrAus-04-1, the Class I candidate is ChamI-02-1, and
the Class II candidates are Serp-14-1 and Serp-26-3. While ChamI-02-1 and
Serp-14-1 were detected at $11\sigma$ and $5\sigma$ respectively, additional
higher resolution observations are essential to confirm these candidates’
nature, as some may represent extended emission from the surrounding dusty
envelope. Detailed images showing (and a table listing) all the candidate
sources and faint emission sources are provided in Appendix E.

###  4.2 Distribution of Protostellar Dust Disk Radii

####  4.2.1 Measuring disk radii

Figure 1: Comparison of disk major axis (Rmaj), minor axis (Rmin), and
position angle (PA) for naturally weighted and Briggs 0.5 weighted maps.
Unresolved sources are not included. The red line represents identical
measurements from the two maps. The gray shaded region represents a $\pm
10^{\circ}$ spread in the position angle measurements. Figure 2: Dust disk
major axis (Rmaj) versus bolometric temperature (${\rm T}_{\rm bol}$) of the
source. The blue, orange, green, and red represent Class 0, Class I, Flat-
spectrum, and Class II sources respectively. We exclude the circumbinary disks
in our samples: SMM 2, IRAS16293-2422 A, and the VLA1623A circumbinary disk.
The triangles represent the upper limit radius of unresolved disks, which
corresponds to half the beam size.  Table 3: Dust Disk Radii Distribution
Properties

Sample | Mean ${\rm R}_{\rm disk}$ | $\sigma\left(log_{10}\left(\frac{R_{disk}}{1au}\right)\right)$ | Median ${\rm R}_{\rm disk}$ | References
---|---|---|---|---
| (au) |  | (au) |
All Sources |  |  |  |
Class 0 | $59.3\pm 7.4$ | $0.33_{-0.17}^{+0.02}$ | $41.4_{\;26.4}^{\;67.8}$ | 1
Class I | $46.0\pm 4.0$ | $0.36_{-0.16}^{+0.02}$ | $39.9_{\;22.9}^{\;61.4}$ | 1
Flat | $41.6\pm 7.2$ | $0.38_{-0.06}^{+0.03}$ | $27.8_{\;19.3}^{\;50.8}$ | 1
Class II | $66.9\pm 8.4$ | $0.37_{-0.32}^{+0.05}$ | $56.7_{\;31.0}^{\;94.2}$ | 1
Subsample by cloud and ClassaaWe only reported values with a sample size greater than 5 disks. |  |  |  |
Ophiuchus (Class 0) | $35.4\pm 8.0$ | $0.26_{-0.01}^{+0.01}$ | $31.2_{17.9}^{42.0}$ | 1
Ophiuchus (Class I) | $26.4\pm 6.4$ | $0.41_{-0.06}^{+0.03}$ | $12.0_{\;7.2}^{\;33.4}$ | 1
Ophiuchus (Flat) | $38.4\pm 12.9$ | $0.41_{-0.07}^{+0.04}$ | $27.4_{\;13.9}^{\;40.2}$ | 1
Ophiuchus (Class II) | $89.6\pm 15.6$ | $0.33_{-0.12}^{+0.05}$ | $83.4_{\;49.8}^{\;126.2}$ | 1
Serpens (Class 0) | $77.3\pm 11.7$ | $0.25_{-0.06}^{+0.03}$ | $54.9_{\;40.6}^{\;88.3}$ | 1
Serpens (Class I) | $48.6\pm 7.4$ | $0.25_{-0.19}^{+0.05}$ | $44.2_{\;25.7}^{\;55.3}$ | 1
Serpens (Flat) | $51.0\pm 5.7$ | $0.15_{-0.04}^{+0.01}$ | $54.7_{\;40.1}^{\;62.9}$ | 1
Serpens (Class II) | $72.0\pm 11.5$ | $0.25_{-0.04}^{+0.02}$ | $82.3_{\;39.9}^{\;100.3}$ | 1
Aquila (Class 0) | $49.9\pm 17.6$ | $0.37_{-0.07}^{+0.08}$ | $24.6_{\;20.8}^{\;65.8}$ | 1
Aquila (Class I) | $61.8\pm 7.3$ | $0.23_{-0.07}^{+0.03}$ | $57.3_{\;36.6}^{\;78.8}$ | 1
Cor Australia (Class 0) | $36.8\pm 9.3$ | $0.3_{-0.02}^{+0.02}$ | $25.1_{\;17.9}^{\;43.3}$ | 1
Chamaeloeon (Class I) | $51.4\pm 7.5$ | $0.16_{-0.02}^{+0.02}$ | $50.9_{\;34.1}^{\;61.5}$ | 1
Chamaeloeon (Class II) | $39.3\pm 11.9$ | $0.44_{-0.02}^{+0.1}$ | $36.2_{\;15.4}^{\;54.1}$ | 1
Orion (Class 0) | $44.9_{-3.4}^{+5.8}$ | $0.38_{-0.004}^{+0.002}$ | $48.1_{\;24.5}^{\;79.6}$ | 2
Orion (Class I) | $37.0_{-3.0}^{+4.9}$ | $0.42_{-0.005}^{+0.001}$ | $38.1_{\;17.5}^{\;64.0}$ | 2
Orion (Flat) | $28.5_{-2.3}^{+3.7}$ | $0.38_{-0.007}^{+0.001}$ | $30.9_{\;13.0}^{\;51.3}$ | 2

††footnotetext: References: (1) This Work. (2) Tobin et al. (2020). Note: The
sub- and superscripts on the median values correspond to the ﬁrst and third
quartiles of the distributions and are absolute values, not relative to the
median. In addition, circumbinary disks are excluded from the sample.

Figure 3: Cumulative distributions of the dust disk radii for the CAMPOS
survey sample. The cumulative distributions reveal the fraction of large disks
with sizes above 40 au decreases with evolution (left panel) and a large
variation of disk radii between different molecular clouds (right panel). The
blue, orange, and red shaded regions mark the Class 0, Class I, and Flat
Spectrum Sources respectively. The shaded region marks the $1\sigma$
uncertainty. The disk size for unresolved sources is adopted to be half of the
beam size. The right panel shows the cumulative distributions of dust disk
radii for different clouds in the CAMPOS sample. The names shown in the legend
correspond to the names of the cloud as in LABEL:table:observation. For both
panels, circumbinary disks (SMM2, IRAS16293-2422 A and VLA1623A) are excluded.
We include the deconvolved radii calculated for the resolved or marginally
resolved disks. For sources without a deconvolved radius (point source), we
adopted half of the beam size as their disk size.

We characterized the protostellar disk radii using CASA imfit to fit a 2D
Gaussian to the continuum data. The simple Gaussian fitting enables us to
quantify the size of the emission and its corresponding orientation. It is
important to note that the 2D Gaussian fitting might not reflect the exact
radius of the disks, potentially due to contamination with envelope material
(Tung et al., 2024). This concern is more significant for the most embedded
sources and those observed with lower resolution due to their greater
distances (See §5.2 for the detailed discussion). However, this approach has
been used in previous large surveys (e.g, Orion: Tobin et al. (2020), Perseus:
Tobin et al. (2016)). Thus for easier comparison between younger protostellar
disks, we adopted the same definition and methods employed in the Orion Class
0/I disk survey by (Tobin et al., 2020). We adopted the $2\sigma$ size of the
deconvolved major axis as disk radius. We multiplied the FWHM of the Gaussian
deconvolved radius by a factor of 2/2.355 to obtain the disk radius (${\rm
R}_{\rm 95}$), which includes $\sim 95\%$ of the total flux density within the
fitted Gaussian222The FWHM of a Gaussian roughly equals 2.355$\sigma$..

We used CASA imfit to fit an elliptical Gaussian on the 3 sets of images:
naturally weighted, briggs0.5 weighted, and uniformly weighted images. Despite
the different S/N ratios and angular resolutions of the 3 sets of images,
measurements from the 3 maps are generally consistent for most sources.
Measurements from the uniform and Briggs 0.5 weighted maps are nearly
identical, with the major differences observed between the naturally weighted
and Briggs 0.5 weighted maps, as illustrated in the comparison plots for the
disk major axis (${\rm R}{\rm maj}$), minor axis (${\rm R}{\rm min}$), and
position angle (PA) in Figure 1.

In Figure 1, the red line represents the identical measurements from the 2
maps. For some sources with sizes close to the beam size (0$\farcs$1), we
found that the naturally weighted maps tend to yield larger deconvolved major
and minor axes due to the larger angular beam size. Unresolved point sources
with CASA-fitted deconvolved major and minor radius sizes of 0 are excluded
from this plot. Regarding the position angle, the majority of the sources fall
within the gray-shaded region, representing a $\pm 10^{\circ}$ spread in the
position angle measurements. Most of the sources with significant differences
in position angle measurements have small disk sizes comparable to the beam
size.

We constructed the final disk size table by first adopting the measurements
from the Uniform weighted maps which have the smallest beam size. For sources
without a CASA imfit measurement in their uniform weighted image (CASA imfit
failed due to low S/N or unresolved), we adopted the measurements from the
Briggs 0.5 weighted maps and, if necessary, using the results from the
naturally weighted maps as a final resort.

For sources that exhibit emission profiles that deviate significantly from
Gaussian, potentially due to disk substructures, edge-on configurations, or
have poor CASA imfit results due to low S/N, we used the 5$\sigma$ contour in
the Briggs 0.5 weighted maps to measure the radius. These sources are ISO Oph
2a, DoAr 20, ISO-Oph 17, DoAr 25, Elias 2-24, Oph-emb 22, Elias 2-27, DoAr 29,
Oph-emb-20, CFHTWIR-Oph 79, EDJ 1013, IRAS 16459-1411, IRS 2, SMM 2, ISO-ChaI
101, ISO-ChaI 207, eHOPS-oph-20a, Ser-emb 2, Ser-emb 13, Ser-emb 6D, Ser-emb
12C, Ser-emb 15B, eHOPS-aql-86B, and MIRES G028.6593+03.8185. The measured
dust disk sizes for all the sources detected are listed in Appendix C.

####  4.2.2 Evolution of disk radii

Our results indicated that protostellar disks have substantially large
variability in disk radii across all evolutionary classes. In Figure 2, we
plotted the disk’s major axis with respect to the bolometric temperature,
which is commonly used as an indicator of the protostellar evolutionary stage
(Myers & Ladd, 1993; Chen et al., 1995), with certain caveats (Fischer et al.,
2013). The blue, orange, green, and red represent Class 0, Class I, Flat-
spectrum, and Class II sources respectively. Triangular markers denote the
upper limit of unresolved point sources, set at half the beam size. A notable
observation is that early Class II disks tend to be larger and exhibit less
variability in disk size. This phenomenon arises because our sample is only
completed up to $T_{\rm bol}\sim$ 1900 K and is incomplete for Class II. To
maintain fairness, we have omitted Class II sources from our analysis.

In particular, we found the fraction of large disks with sizes above the
median of 40 au decreases with the evolutionary stage. In
LABEL:table:disk_radii, our survey shows that the median radii for Class 0,
Class I and Flat-spectrum sources are always smaller than the mean radii,
indicating the presence of large disks in the population. Between Class 0 and
Class I, the mean radii decreased between 59.3$\pm 7.4$ au to 46.0$\pm 4.0$
au, while the median radius stayed roughly constant only decreasing from 41.4
au to 39.9 au. This suggests a significant decrease in the fraction of large
disks with sizes above the median radii between Class 0 and Class I. To
highlight the evolution of disk radii distribution between different Class, we
plotted the protostellar disk radii cumulative distribution in Figure 3 and
the corresponding probability density function in Figure 4. In both figures,
we excluded the circumbinary disks (SMM 2, IRAS16293-2422 A and VLA1623A) and
Class II disks. The sizes of the unresolved point sources are adopted to be
half of the beam size. In Figure 3 (left panel), the blue, orange, and red
shaded regions represent the Class 0, Class I, and Flat Spectrum sources
respectively. While the three distributions overlap for disk radii less than
40 au, a clear separation between the three classes can be seen for larger
disk radii (see Figure 3). The Class 0 stage has the highest fraction of disks
with radii greater than $40\,$au, followed by Class I and Flat-spectrum
sources respectively. The data shows a decreasing trend in the fraction of
large disks with sizes above the median of 40 au as the protostar evolves. In
addition, we found that for disks with radii less than 40 au, Class 0 sources
tend to be slightly larger than Class I and Flat-spectrum sources.

We computed the kernel density distribution of disk radii with a Gaussian
Kernel shown in Figure 4 to compare the disk radii distribution between each
Class. The crosses mark the disk size measurements for each source. We also
labeled the most probable radii for each Class. The probability density
functions of protostellar disk radii in Figure 4 are composed of positive
tails in addition to Gaussian components. To quantify the radii distribution,
we fit the distribution with an exponentially modified Gaussian distribution
(EMG), which is composed of the sum of independent normal and exponential
random variables. The function is given as:

$f(x;\mu,\sigma,\lambda)=\frac{\lambda}{2}e^{\frac{\lambda}{2}\left(2\mu+\lambda\sigma^{2}-2x\right)}{\rm
erfc}\left(\frac{\mu+\lambda\sigma^{2}-x}{\sqrt{2}\sigma}\right),$ (1)

where $\mu$, $\sigma^{2}$ represent the Gaussian mean and variance,
respectively, and $\lambda$ represents the exponential rate. We found that for
Class 0: $\mu=16.4\pm 0.2$, $\sigma=12.5\pm 0.3$, and $\lambda=0.030\pm
0.001$; Class I: $\mu=13.6\pm 0.3$, $\sigma=19.8\pm 0.3$, and
$\lambda=0.037\pm 0.001$; Flat-spectrum sources: $\mu=9.2\pm 0.2$,
$\sigma=11.7\pm 0.3$, and $\lambda=0.036\pm 0.002$. Overall, the disk dust
radius decreases significantly for the Gaussian component ($\mu$) and the most
probable radius (marked peaks in Figure 4). Between Class 0 and the flat-
spectrum phase, the most probable radius decreases from 39 au to 23 au or by
41 %, and the Gaussian component ($\mu$) also decreases by 44 %. The
exponential rate parameter ($\lambda$) increases as the protostar evolves,
which indicates a shortening of the positive tail at a larger radius. The
general increasing trend of $\lambda$ is consistent with the drop of the large
disk fraction with size above 40 au over time.

Lastly, we conducted the Anderson-Darling test to assess the statistical
differences among the disk radii distributions of each evolutionary class. As
indicated in LABEL:table:disk_radii_stat, we found that the likelihood of
Class 0 and Class I sources, Class 0 and Flat spectrum sources, Class I and
Flat spectrum sources to be being drawn from the same distribution are 0.23,
0.06, and $>$0.25, respectively. Although there is no statistical evidence
suggesting Class I and Flat-spectrum sources are drawn from different
distributions, there is a weak statistical significance (p-value: 0.06)
suggesting Class 0 and Flat-spectrum sources are drawn from distinct
distributions. The high p-value is consistent with Figure 2 showing the large
scatter in disk radii across all classes.

Table 4: Dust Disk Radii Sample Comparisons (Anderson-Darling Tests) Sample | Disk Radius | Number of
---|---|---
| Probability | Sources
All Sources |  |
Class 0 vs. Class I | 0.23 | (52, 70)
Class 0 vs. Flat-spectrum | 0.06 | (52, 33)
Class I vs. Flat-spectrum |  $>$0.25 | (70, 33)
Ophiuchus only |  |
Class 0 vs. Class I | 0.09 | (8, 20)
Class 0 vs. Flat-spectrum |  $>$0.25 | (8, 16)
Class I vs. Flat-spectrum |  $>$0.25 | (20, 16)
Serpens only |  |
Class 0 vs. Class I | 0.03 | (27, 20)
Class 0 vs. Flat-spectrum |  $>$0.25 | (27, 7)
Class I vs. Flat-spectrum |  $>$0.25 | (20, 7)
Aquila only |  |
Class 0 vs. Class I | 0.03 | (7, 21)
Class 0 onlyaaAbbreviation of cloud names are the same as in LABEL:table:observation |  |
Aql vs. Serp | 0.004 | (7, 27)
Aql vs. CrAus |  $>$0.25 | (7, 10)
Aql vs. Oph & OphN |  $>$0.25 | (7, 8)
CrAus vs. Serp | 0.002 | (10, 27)
CrAus vs. Oph & OphN |  $>$0.25 | (10, 8)
Serp vs. Oph & OphN | 0.01 | (27, 8)
Class I only |  |
Aql vs. Serp | 0.13 | (21, 20)
Aql vs. Cham I & II |  $>$0.25 | (21, 6)
Aql vs. Oph & OphN | 0.001 | (21, 20)
Serp vs. Cham I & II |  $>$0.25 | (20, 6)
Serp vs. Oph & OphN | 0.002 | (20, 20)
Cham I & II vs. Oph & OphN | 0.02 | (6, 20)
Flat-spectrum only |  |
Serp vs. Oph & OphN | 0.02 | (7, 16)
Figure 4: Dust disk radius distribution for the protostellar disks detected in
the CAMPOS survey at different evolutionary stages. Note that circumbinary
disks are excluded and half of the beam size is adopted for the radii of the
unresolved disks. The radius distribution is computed with a kernel density
estimation with a Gaussian Kernel. The cross marks the disk size measurements
for each source. We also labeled the radius for the peak of the distribution
for Class 0, Class I, and flat-spectrum sources. Overall, the peak disk dust
radius decreases significantly from 39 au to 23 au (or 41 %) between Class 0
and the flat-spectrum phase. Figure 5: Evolution of mean disk major axis
(Rmaj) at the different evolutionary stages of the protostars. The blue,
green, orange, red, black, and purple represent sources from the Serpens,
Ophiuchus, Aquila, Cor Australis, Chamaeleon, and Orion respectively. The
number behind the labels represents the sample size. Circumbinary disks (SMM
2, IRAS16293-2422 A, and VLA1623A) are excluded. We include the deconvolved
radii calculated for the marginally resolved disks. For sources without a
deconvolved radius (point source), we adopted half of the beam size as their
disk size.

####  4.2.3 Disk radii comparison across molecular clouds

Our data shows that even within the same Class, protostellar disks show
substantially large variability in disk radii. One possible source of this
large variability is cloud variation (See Figure 3 right panel). The blue,
orange, red, green, and black-shaded regions represent the cumulative
distribution of dust disk radii for Ophiuchus & Ophiuchus North (hereafter
Ophiuchus), Serpens, Aquila, Cor Australis, and Chamaeleon I & II (hereafter
Chamaeleon), respectively. The mean and median dust disk radii and the log
dispersion for each cloud and evolutionary stage are shown in
LABEL:table:disk_radii. Since our survey is only complete up to ${\rm T}_{\rm
bol}\leq 1900\,$K, we excluded the Class II sources in Figure 3. We found that
Ophiuchus has the smallest disks followed by Cor Australis. In contrast, disks
in Serpens, Aquila, and Chamaeleon molecular clouds are generally larger.

We conducted the Anderson-Darling test between clouds that have more than 5
disks and found 2 distinct radii distributions at different evolutionary
stages. For Class 0 disks, disk sizes in Aquila, Ophiuchus, and Cor Australis
are consistent with being drawn from the same distribution. Class 0 disks in
Serpens are generally larger and seem to be drawn from a different population
than the above 4 clouds. For Class I disks in the Serpens, Aquila, and
Chamaeleon molecular clouds, the sizes are consistent with being drawn from
the same distribution. Class I disks in Ophiuchus in contrast are much smaller
and appear to be drawn from a different distribution. For Flat-spectrum
sources, disks in Serpens and Ophiuchus molecular clouds are consistent with
being drawn from different distributions. The p-values, and sample sizes are
tabulated in LABEL:table:disk_radii_stat.

Significant variation in disk radii for sources at a similar evolutionary
stage, in different clouds (LABEL:table:disk_radii_stat), instead of a
universal trend, highlights the influence of local environments on disk radii
evolution. The mean radii distribution for each cloud evolves differently as
illustrated in Figure 5. The error bars represent the $1\sigma$ dispersion of
the disk radii distribution. The number following the name of the cloud shown
in the legend indicates the sample size for that cloud. For comparison, we
also included the sources from the Orion Class 0/I disk survey (Tobin et al.,
2020). From our CAMPOS survey, we find that the Serpens and Ophiuchus
molecular cloud, which represents more than 60% of our entire CAMPOS samples,
show statistically significant evidence suggesting the decrease of dust disk
radii between Class 0 and Class I. In contrast, for the Aquila molecular
cloud, there is tentative evidence that the dust disk radii increase between
Class 0 and Class I sources. Between the Class I and the Flat-spectrum phase,
the radii stays constant for the Serpens molecular cloud, but for Ophiuchus it
appears that the disk radii increase to sizes similar to the Class 0 disks.
For other clouds, the sample sizes are too small to be statistically
significant.

###  4.3 Streamer Candidates

Figure 6: Possible streamers detected in our ALMA Band 6 CAMPOS dust continuum
survey. The green crosses mark the position of the protostars in the multiple
systems. The cyan-filled ellipse represents the synthesized beam size. The
white line marks a scale of 100 au. The red arrows show the direction of the
protostellar outflow traced by our 1$\farcs$0 CO data. When multiple
protostars are present in the field of view, they are marked by a green cross.
Note that Ser-emb-12A does not show a clear CO outflow at 1 $\farcs$0
($\sim$420 au) resolution. White contours are added to each image to highlight
the extended dust emission.

Past observation of embedded protostar envelopes (e.g., L1157, L1165, TMC-1A,
Per-bolo 58 and CB230) has revealed complex velocity structures (Tobin et al.,
2012a; Aso et al., 2015; Maureira et al., 2017; Sai et al., 2023b). Detailed
Position-velocity (PV) diagram modeling of these envelopes shows that their
velocity structures are inconsistent with an axisymmetric collapse or solid-
body rotation. Some of these envelope kinematics can be well described by an
infalling filament model, suggesting that the accretion in envelopes is non-
axisymmetric (Tobin et al., 2012a).

Many of the protostellar envelopes that showed evidence of non-axisymmetric
infall reveal flow-like structures that appear to be funneling cloud material
from large scales to the inner envelope or disk. These “accretion flows” or
“streamers” have been discovered around some Class 0 systems (Lupus3-MMS:
Thieme et al. (2022), Per-emb-2: Pineda et al. (2020), IRAS16293 binary:
Murillo et al. (2022), VLA1623A: Cheong & Lai (2018); Hsieh et al. (2020)), as
well as Class I systems like Per-emb-50 (Valdivia-Mena et al., 2022), and
SVS13A binary (Hsieh et al., 2023b)). Additionally, similar features have been
observed in more evolved Class I/II systems such as HL Tau (Garufi et al.,
2022; Yen et al., 2019), and DR Tau (Garufi et al., 2022; Huang et al., 2023).

The discovery of these accretion flows or streamers provided evidence of
asymmetric accretion from the envelope. Streamers link the small 100 au scale
disks with the larger 10,000 au scale core (Pineda et al., 2020; Valdivia-Mena
et al., 2022). The collision between the streamer material and the disk can
form accretion shocks, traced by the enhancement of SO, which can cause the
outer disk to deviate from Keperian rotation (Hsieh et al., 2020). The
connection between streamers and disks has not been fully explored.

Our CAMPOS continuum survey revealed extended structures around 6 possible
“streamer candidates” shown in Figure 6. Out of the 6 candidates, 3 of them
are Class 0 systems (Ser-emb 6, Ser-emb 7, Ser-emb 8) and 3 are Class I
systems (Ser-emb 12A, IRAS 12553-7651, IR Cha INa4). The white line marks the
100 au scalebar. The cyan ellipse marks the beam resolution. The red arrows
marks the direction of the protostellar outflow traced by our 1$\farcs$0 CO
data (Arce et al., in perp.). We did not detect a clear outflow for Ser-emb
12A. Note that these 6 sources are only candidates and line observations are
needed to analyze the kinematics of these structures to determine whether
these trace materials moving towards the sources or outflow cavity walls.

The emission that extends beyond the disk structure for two of the 6 sources
that we labeled as being candidate streamers (IRAS 12553-7651 and IR Cha INa4)
is considerably more compact than the extended structure in the other four
sources. In the case of IRAS 12553-7651, a minor dust tail south of the
protostellar disk aligns closely with the protostellar outflow axis, which has
a position angle around $-15^{\circ}$. The alignment with the protostellar
outflow axis suggests the dust tail might be tracing the walls of the outflow
cavity rather than infalling gas. Conversely, the dusty tail in IR Cha INa4 is
perpendicular to the outflow direction. However, due to the modest signal-to-
noise (S/N) ratio for sources in the Chamaeleon molecular cloud, the tail
could potentially be residual artifacts from the deconvolution process.
Suboptimal observational conditions—characterized by fewer antennas and
elevated water vapor levels relative to observations of sources in other
molecular clouds, limit our confidence in the streamer detection in the
Chamaeleon molecular cloud.

Ser-emb 6 system is a complex Class 0 system with 5 embedded protostars. 3
protostars are located within the embedded filament structure shown in Figure
6. The brightest source in the field, Ser-emb 6A, drives a clear CO outflow
with a position angle of $\sim 140^{\circ}$ perpendicular to the filament
structure marked by the red arrow in Figure 6. We compared our CO outflow data
and the CARMA observations by Francis et al. (2019) and found that the
extended continuum breaks into 2 parts separated by the Ser-emb 6A
protostellar outflow. The northern part includes 2 sources (not shown in the
figure) while the 3 protostars lie in the southern filament shown in Figure 6.

Ser-emb 7, a Class 0 source with a bolometric temperature of 57 K (Pokhrel et
al., 2023), is surrounded by complex filamentary structures. While the “$<$”
shaped dust structure is perpendicular to the outflow direction, the
protostellar outflow traced by CO is very wide and shows an “X” shape that
overlaps with the dusty structure. The “$<$” shaped dust structure might be a
protostellar outflow cavity wall rather than infalling streamers. Molecular
line data is needed to determine the nature of this dust filamentary
structure. In addition, the “$<$” shaped structure is part of a much larger
tilted “k” shaped structure that extends about 4$\farcs$0 ($\sim 1800$ au)
towards the north, as revealed by CARMA observations (Francis et al., 2019).

Ser-emb 8A also known as S68N (McMullin et al., 1994) is a Class 0 protostar
with a bolometric temperature of 33 K (Pokhrel et al., 2023). 3 protostars
including the Ser-emb 8A (brightest central source) are marked by green
crosses in Figure 6. Another protostar, Class 0 protostar Ser-emb 8(N)
(McMullin et al., 1994), not shown in the field of view is located north of
Ser-emb 8A. From the large-scale CARMA observation, an extended filament can
be seen connecting all 4 protostars (Francis et al., 2019). Ser-emb 8 drives a
molecular outflow in the southwest-northeast direction marked in red, which is
perpendicular to the filament direction (Hull et al., 2014).

###  4.4 Annular Substructures

Table 5: Disk Substructure Table

Source | $T_{\rm bol}$ | Class | Detected
---|---|---|---
Name | (K) |  | by
Circumbinary Disks |  |  |
VLA 1623A | 30 | 0 | (1)
IRAS 16293-2422 A | 31 | 0 | (2)
SMM 2 | 72 | IaaClassification updated using the latest e-HOPS survey (See Pokhrel et al. 2023, and Pokhrel, private communication. | This work
Annular Substructures |  |  |
CFHTWIR-Oph 79 | 112 | I | eDiskbbAlso known as GY263, observed by the eDisk survey at 5 au resolution (Narayanan et al., 2023).
Oph-emb 22 | 224 | I | ODISEAccObserved by the ODISEA survey at 5 au resolution (Cieza et al., 2021).
IRS 2 | 235 | I | This work
ISO-Oph 17 | 290 | II | ODISEA
Oph-emb-20 | 310 | FlataaClassification updated using the latest e-HOPS survey (See Pokhrel et al. 2023, and Pokhrel, private communication. | This work
Elias 2-27 | 410 | FlataaClassification updated using the latest e-HOPS survey (See Pokhrel et al. 2023, and Pokhrel, private communication. | DSHARPddObserved by the DSHARP survey at 5 au resolution (Andrews et al., 2018).
ISO-ChaI 101 | 650 | Flat | This work
DoAr 29 | 840 | II | ODISEA
Elias 2-24 | 980 | II | ODISEA
ISO Oph 2a | 1100 | II | ODISEA
DoAr 20 | 1100 | II | DSHARP
IRAS 16459-1411 | 1400 | II | DSHARP
EDJ 1013 | 1500 | II | ODISEA
DoAr 25 | 1500 | II | ODISEA
Asymmetric disk |  |  |
IRAS 16293-2422 B | 31 | 0 | (2)
Ser-emb 6A | 42 | 0 | (3)
eHOPS-aql-86A | 46 | 0 | (3)
Ass Cha T 1-15 | 1400 | II | This work

††footnotetext: References: (1) Harris et al. 2018 (2) Oya & Yamamoto 2020;
Maureira et al. 2022 (3) Enoch et al. 2009b.

Figure 7: Sources with a clear detection of disk annular substructures or
spirals in our ALMA Band 6 CAMPOS dust continuum survey. The cyan-filled
ellipse represents the synthesized beam size. The white scale bar marks a
scale of 100 au. The sources are arranged in an increasing order of
evolutionary sequence based on Bolometric temperature ($T_{\rm bol}$) from
left to right and from top to bottom. Detailed analysis of substructures will
be included in forthcoming papers.

One of the major problems in planet formation is understanding the formation
and growth of planetesimals (e.g. Johansen et al. (2014)). ALMA has been a
game changer in this field with resolved observations of continuum emission
directly tracing how millimeter/centimeter-sized particles are distributed in
protoplanetary disks. In particular, many evolved Class II and Class III
protoplanetary disks are observed with unprecedented sensitivity and
resolution revealing single or multiple dust rings/ gaps and spirals (Andrews
et al., 2016, 2018; Isella et al., 2016; Tsukagoshi et al., 2016; Fedele et
al., 2017; Long et al., 2018; Clarke et al., 2018; Pérez et al., 2019;
Tsukagoshi et al., 2019; Cieza et al., 2021). Interestingly, these
substructures are also detected in young Class I disks ($\leq 1\,Myr$) (e.g.
HL Tau: ALMA Partnership et al. (2015), WL 17: Sheehan & Eisner (2017), Elias
42: Dipierro et al. (2018), GY 91: Sheehan & Eisner (2018), IRS 63: Segura-Cox
et al. (2020)). Studies have shown that gaps in these young disks ($\leq
1\,Myr$) are consistent with the existence of fully formed planets (ALMA
Partnership et al., 2015; Cieza et al., 2017). In addition, simulations have
shown that planets with mini-Neptune-mass (Pérez et al., 2019) or Earth mass
(Dong et al., 2017) can produce detectable disk substructures with the minimum
gap opening mass depending on the viscosity and the scale height of the disk
(Crida et al., 2006; Duffell & MacFadyen, 2013). If yet-undetected planets are
responsible for the gaps and rings observed in Class I disks, then rapid
planet formation (within $1\,$Myr) is needed to reach the minimum gap opening
mass (e.g., Sheehan & Eisner (2018); Segura-Cox et al. (2020)). In addition,
the dust masses of embedded disks are a factor of 3 to 5 times larger than
Class II disks indicating that the core of the giant planets may need to begin
their formation during the protostellar phase (Tychoniec et al., 2020).
However, rapid planet formation within $\sim 1$ Myr remains a challenge for
the core accretion model (Mizuno, 1980; Pollack et al., 1996) due to the long
time scales required to form planetary cores with a mass larger than the
critical mass needed for runaway gas accretion at radii $\geq 10\,$au
(Kobayashi et al., 2011).

While embedded protoplanets can create disk substructures, they are not the
only way to form the observed substructures. Recent planet formation
simulation with migrations shows that large amounts of pebbles ($\sim
2000\,M_{\earth}$) are needed to reproduce all the gap structures in the
DSHARP survey (Andrews et al., 2018), thus showing that not all gaps and rings
in observed disks are caused by protoplanets (Ndugu et al., 2019). Many
different mechanisms have been proposed to explain the disk substructures (See
Bae et al. (2023) for the review), such as the sintering of dust aggregates
near the snow line (Zhang et al., 2015), reconnection of toroidal magnetic
fields in the disk-wind system (Suriano et al., 2018, 2019; Riols & Lesur,
2019), secular gravitational instability (e.g. Youdin 2011; Takahashi &
Inutsuka 2014; Tominaga et al. 2019, 2020), eccentric instability (Li et al.,
2021), irradiation instability (Wu & Lithwick, 2021) and viscous ring-
instabilities (Dullemond & Penzlin, 2018). However, the dominant mechanism
behind substructure formation remains unclear, and it is debated whether the
observed substructure morphology results from the combined effects of multiple
processes.

While the origins of disk substructures remain debated, investigating their
presence in young Class 0/I systems holds particular significance. These
substructures represent localized pressure bumps, which slow or trap drifting
solids and can facilitate planetesimal formation via gravitational or
streaming instabilities (Youdin & Shu, 2002; Youdin & Goodman, 2005). If such
substructures are common in young Class 0/I disks, then planetesimals or
planetary systems are created much more efficiently (Andrews et al., 2018).
Currently, the search for disk substructures in Class 0/I disks remains
limited (e.g., Segura-Cox et al. 2020; Sheehan et al. 2020; Zamponi et al.
2021; Ohashi et al. 2023). Out of the 300 protostellar disks observed at a
$\sim$40 au spatial resolution, the Orion survey only found 7 Class 0/I
protostellar disks associated with substructures (Tobin et al., 2020; Sheehan
et al., 2020). However, the detected rings and cavities have sizes larger than
50 au, possibly representing close-separation binary formation at early times
instead of planet formation (Sheehan et al., 2020). In a different approach,
the eDisk collaboration conducted observations of Class 0/I disks at $\sim$7
au (0$\farcs$04) resolution, but the sample size was limited to 19 sources
(Ohashi et al., 2023). Out of the 19 sources, only 3 sources (L1489IRS,
IRAS04169+2702, and OphIRS 63), show visually identified ring-like structures
possibly suggesting that disk substructures are rare in the Class 0 and early
Class I stage (Ohashi et al., 2023).

Our CAMPOS survey is designed to balance between angular resolution and sample
size. Among the 184 disks in our survey, 74 have been observed with a
resolution of 15 au, and 16 with a resolution of 18 au, making it the most
extensive high-resolution ($\leq$ 18 au) and uniform search for disk
substructures around young Class 0/I protostars. Our findings, including all
sources with clear disk substructure detections, are presented in Figure 7,
Figure 8, and Figure 9. Out of the 21 disks discovered with substructures or
asymmetric flux distribution, 5 of them are newly discovered. Cross-matching
them with the Dunham et al. (2015) and eHOPS (private communication) reveals
that two of them belong to Class I, two are Flat-spectrum sources, and one is
a Class II source. A comprehensive summary of the discovered disk
substructures is provided in LABEL:table:disk_substructure. Detailed modeling
of these newly discovered disk substructures will be presented in future
papers.

###  4.5 Circumbinary disks

In the CAMPOS survey we detected 3 circumbinary disks, VLA1623 A, IRAS
16293-2422A, and SMM 2 as shown in Figure 8. These circumbinary disks are
associated with Class 0 or extremely young Class I systems. The absence of
circumbinary disks around more evolved Flat-spectrum sources or Class II
sources suggests that the lifetime of circumbinary disks is shorter than that
of circumstellar disks. In what follows, we will provide comments on the 3
young circumbinary disks detected in the survey.

Figure 8: Circumbinary disks detected in the CAMPOS survey. The cyan-filled
ellipse represents the synthesized beam size. The white line marks a scale of
100 au.

VLA 1623A is a well-known Class 0 multiple system and has been considered to
be the prototype of Class 0 objects (Andre et al., 1993; Looney et al., 2000;
Ward-Thompson et al., 2011; Murillo et al., 2013; Santangelo et al., 2015;
Murillo et al., 2018; Hsieh et al., 2020; Codella et al., 2022; Ohashi et al.,
2022; Codella et al., 2024). Recent ALMA observation by Hara et al. (2021)
revealed misaligned twin protostellar outflows from VLA 1623A. The outflow
axes of these 2 outflows are inclined by 70∘ to each other, suggesting a
misalignment of 70∘ between the 2 protostellar disks within the circumbinary
system (Hara et al., 2021).

In contrast, our new 0$\farcs$1 ($\sim$14 au) resolution CAMPOS data
challenges the misaligned protostellar disk interpretation proposed by Hara et
al. (2021). As depicted in Figure 8, the resolved circumstellar disks around
VLA 1623Aa and VLA 1623Ab in the center of the circumbinary disks are aligned.
We used CASA imfit to constraint their position angles to be $40.1\pm
8.8^{\circ}$ and $48.0\pm 9.7^{\circ}$. As for the inclination angle, assuming
thin circular disks, the major-to-minor axis ratio gives inclination angles of
$56.5\pm 8.1^{\circ}$ and $59.0\pm 9.0^{\circ}$ respectively. The larger
circumbinary disk has an inclination angle of $55^{\circ}$ (Murillo et al.,
2013). From our data, we conclude that the individual circumstellar disks
around VLA1623Aa and VLA1623Ab are co-planer with each other as well as the
circumbinary disk. This alignment is a natural consequence of angular momentum
conservation, with the circumbinary disk serving as the mass reservoir for the
2 smaller circumstellar disks.

Our high-resolution continuum data suggest that the misaligned protostellar
outflows reported by Hara et al. (2021) are not caused by the misalignment of
the circumstellar disks around VLA1623Aa and VLA1623Ab. Instead, a more
natural explanation is that one of the misaligned protostellar outflows
originated from the neighboring protostar VLA 1623B (Hsieh et al., 2020). An
alternative interpretation is that the protostellar outflows must be
misaligned to the 2 circumstellar disks. Future higher angular resolution with
optical thin tracer is needed to determine the origin of the misaligned
protostellar outflows.

SMM 2 is an early Class I source with a bolometric temperature of 72 K. With
our high-resolution ALMA continuum data, we discovered the presence of two
substantial holes within the SMM 2 disk shown in Figure 8. Higher angular
resolution dust continuum data indicates that tat he center of the disk lies
two distinct sources connected by a dusty stream (Maureira, private
communication). The SMM2 disk is therefore a protostellar circumbinary disk.

IRAS16293-2422 A1 and IRAS16293-2422 A2 are Class 0 protostars member of a
binary system that are separated by a plane-of-sky distance of 54 au (Pineda
et al., 2012; Dzib et al., 2018; Maureira et al., 2022). This system is a
well-known prototypical hot corino (Jørgensen et al., 2016; Coutens et al.,
2016; Oya et al., 2018; Drozdovskaya et al., 2019). Three-dimensional modeling
of dust and gas shows that the extended 4 $M_{\odot}$ envelope around
IRAS16293-2422 A is connected to the nearby protostar, IRAS16293-2422 B, by a
dust filament (Jacobsen et al., 2018). Within the extended IRAS16293-2422 A
circumbinary envelope, Maureira et al. (2022) discovered multiple 10 au dust
hot spots. These emission peaks do not show strong variation in the spectral
index, indicating that they are due to high-temperature spots instead of
optical depth variation. Detailed analysis and comparison with complex organic
molecular emission show these substructures are due to mechanical heating from
shocks (Maureira et al., 2022).

###  4.6 Asymmetries in disks

Figure 9: Asymmetric disks or embedded disk systems detected in the CAMPOS
survey. The cyan-filled ellipse represents the synthesized beam size. The
white line marks a scale of 100 au.

The CAMPOS survey detected 4 highly nebulous sources with asymmetric flux
distribution, Ass Cha T 1-15, IRAS 16293-2422B, Ser-emb 6A, and eHOPS-aql-86A
shown in Figure 9. All sources except Ass Cha T 1-15 are young Class 0
protostars. Ass Cha T 1-15 also known as 2MASS J11074366-7739411 is a 1.01
$M_{\odot}$ Class II M0 pre-main sequence star (Olofsson et al., 2013). The
dust continuum emission of ChamI-06-0 in Figure 9 has a size expected for a
disk ($\sim$100 au). It remains unclear why the disk appears asymmetric with
the peak of the dust continuum shifted to one side.

The other 3 sources all show extended dust continuum emission resembling
embedded envelopes. Ser-emb 6A also known as SMM 1a (Casali et al., 1993; Hull
et al., 2017a; Francis et al., 2019) is the brightest Class 0 source in the
Serpens Main molecular cloud. SMM 1a powers a one-sided high-velocity
molecular jet ($\sim 80$ km s-1) inside an ionized outflow cavity (Hull et
al., 2016). Previous ALMA observations identified this system as a Class 0
protobinary system (Francis et al., 2019), however from our high-resolution
ALMA observation, we found this region has 5 embedded protostars. In
particular, the nebulous dust emission around the intermediate mass Class 0
source, SMM 1a, was previously identified as an unusually massive disk ($\sim
1\,M_{\odot}$) (Hogerheijde et al., 1999; Enoch et al., 2009a). The source
also shows significant brightness variation in submillimeter wavelengths.
Archival data of the James Clerk Maxwell Telescope (JCMT) Gould Belt Survey
and the JCMT Transient Survey data shows that the brightness of SMM 1a
increased by $\sim 2\%$ yr-1 from 2012 to 2016 (Mairs et al., 2017). Its
brightness further increased by $\sim 5\%$ yr-1 during the 18 months of the
JCMT Transient Survey from 2017 December to 2018 June (Johnstone et al.,
2018). The huge brightness variations and the amorphous shape of the continuum
emission as seen in our high-resolution map suggest the source is deeply
embedded within an infalling envelope.

eHOPS-aql-86A also known as Ser-SMM3 is a single source Class 0 protostar
first identified by (Casali et al., 1993). Early observation by Herbst et al.
(1997) found molecular hydrogen knots that arise from the bow shocks of Ser-
SMM3 jets. Ser-SMM3 is a well-known source for astrochemistry studies
(Dionatos et al., 2013; Mirocha et al., 2021; Wurmser & Bergner, 2022;
Kushwahaa et al., 2023). The source is surrounded by an extended 800 au
envelope similar to IRAS 16293-2422A, and the flux peak is off-centered within
the envelope. Future observation at longer (optically thin) wavelengths and
dust modeling similar to Maureira et al. (2022) is needed to search for
possible substructures within the extended envelope.

###  4.7 Edge-on Disks

Figure 10: Edge-on disks with inclination angle greater than $75^{\circ}$
detected in the CAMPOS survey. The cyan-filled ellipse represents the
synthesized beam size. The white line marks a scale of 100 au. The 3 disks
(eHOPS-oph-20a, Ser-emb 13, and Ser-emb 2) show possible signs of
substructures as evidenced by the asymmetric intensity profiles along their
major axis.  Table 6: Edge-on disks with inclination angle greater than
$75^{\circ}$ detection summary

Source Name | inc [∘] |  | CAMPOS ID | inc [∘]
---|---|---|---|---
TIC 454329229 | 77.9 $\pm$4.8 |  | SMM1C | 77.4 $\pm$0.3
VLA1623W | 80.5 $\pm$0.7 |  | eHOPS-oph-20a | 85.0 $\pm$0.4
Ser-emb 13 | 85.1 $\pm$0.4 |  | Ser-emb 2 | 75.1 $\pm$2.5

††footnotetext: Note: Column title inc represents the disk inclination angle.
$90^{\circ}$ is edge-on and $0^{\circ}$ is face-on. Inclination angle derived
from disk major and minor axis measured by DS9. The inclination angle error is
derived by assuming 10 % error in the disk major and minor axis measurements.

Edge-on circumstellar disks are particularly interesting for optical and
infrared surveys, due to their distinctive orientation. The disk occults the
central star, enhancing contrast for scattering light imaging (Stapelfeldt et
al., 2014). This configuration allows ice signatures to be observed in
absorption against the continuum produced by the warmer central disk region.
This makes the edge-on disks a perfect laboratory for constraining the
abundance and distribution of ice in circumstellar disks (Terada & Tokunaga,
2017; Sturm et al., 2023a).

At longer millimeter or sub-millimeter wavelengths, edge-on disks can be used
to measure the thickness of disks, trace their vertical structure, and
determine the degree of dust settling in the disk mid-plane (Villenave et al.,
2020; Sturm et al., 2023b). Understanding dust settling sets constraints on
the vertical shear instability (VSI) of disks (Dullemond et al., 2022).
Observation of edge-on disks is also important for studying whether or not the
VSI is commonly inhibited or quenched in circumstellar disks. VSI arises from
the vertically sheared angular velocity profile coupled with rapid cooling of
the gas. It produces upward and downward vertical streams of gas that slowly
oscillate, which stirs up the dust particles in the mid-plane (Lehmann & Lin,
2022; Dullemond et al., 2022). Edge-on disks are the perfect targets to test
for the vertical mixing of dust particles and compare them with the VSI
prediction. Furthermore, these disks serve as optimal candidates for exploring
rotational features in protostellar jets, a key element in discerning jet
launching models (Lee et al., 2018b).

Despite their significant research appeal, edge-on disks are scarce.
Demographic studies of edge-on disks identified by their SEDs have shown that
edge-on disks are underrepresented in low-mass star-forming regions observed
by Spitzer (Stapelfeldt et al., 2014; Angelo et al., 2023). In our CAMPOS
survey of 184 disks in seven nearby molecular clouds, we discovered six edge-
on disks with an inclination angle greater than $75^{\circ}$. The 3.3%
detection rate is consistent with the 3.4 % prediction based on simple
geometric arguments. While the edge-on-disk occurrence rate is
underrepresented in SED modeling, it is fully recovered in our resolved
submillimeter continuum disk observations.

We list the detected edge-on disks in LABEL:table:edge-on_disk. The
inclination angle is derived from the major and minor axis of the disk
assuming a circular flat disk. $90^{\circ}$ signifies an edge-on view and
$0^{\circ}$ denotes face-on orientation. Among the six edge-on disks, eHOPS-
oph-20a, Ser-emb 13, and Ser-emb 2, show signs of substructure that cannot be
identified as either ring or spiral. eHOPS-oph-20a shows an intensity dip at
the position of the protostar with one side significantly brighter than the
other. This raises the possibility that eHOPS-oph-20a comprises two closely
orbiting disks, potentially separated by a mere 20 au in the plane of the sky.
The true nature awaits clarification through future line observations.

Similarly, Ser-emb 2 also shows asymmetric brightness with one side much
brighter than the other. Interestingly, Ser-emb 13 shows 3 bright spots evenly
spaced along the disk’s major axis. Doi & Kataoka (2021) shows that for an
inclined thin ring with a vertical dust scale height, due to the optical
depth, the major axis would be brighter than the minor axis. It is possible
that the 3 bright spots of Ser-emb 13 can be explained by an inclined ring
with the central bright spot corresponding to the central protostar. Higher
resolution observation and detailed modeling are needed to determine the
nature of these sources.

##  5 Discussion

###  5.1 Evolution of Dust disk radii: Observational Trends

(a)  (b)

Figure 11: _Left_ : Inclination angle distribution of the protostellar disks
detected in the CAMPOS survey. The inclination angles are derived from the
deconvolved disk’s major and minor axes assuming a flat circular disk. The
inclination distribution is computed with a kernel density estimation with a
Gaussian Kernel. Note that 0∘ is face-on, and 90∘ is edge-on. The blue,
orange, and green lines represent Class 0, Class I, and flat-spectrum sources
respectively. The distribution drops significantly for edge-on sources due to
the intrinsic disk scale height and the breakdown of the flat disk assumption.
The cross marks the inclination angle for each source. We also labeled the
peak of the distribution. _Right_ : The inclination angle uncertainty
distribution. Considering the uncertainty (right panel), the inclination angle
distribution between the Class 0, Class I, and flat-spectrum sources (left
panel) are consistent with each other.

Instead of a universal trend, our CAMPOS survey found significant variation in
disk radii among the same Class between different clouds, which highlights the
influence of local environments on disk radii evolution (See
LABEL:table:disk_radii). For a combined sample of disks in all 7 clouds, the
Anderson-Darling Test shows that Class 0 and Class I disk radii distributions
are consistent with being drawn from the same distribution. The large p-value
is a result of dust disk radii varying significantly among the same Classes
for different molecular clouds. This suggests that the study of disk radii
evolution should take into account cloud variation (Figure 3 right panel).

For each molecular cloud, we separated the disks by Class and conducted
Anderson-Darling Tests to compare the evolution of disk radii distribution.
The tests show that out of the 7 molecular clouds, only Serpens, Ophiuchus,
and Aquila have statistically distinct Class 0 and Class I disk radii
distribution with p-values of 0.03, 0.09, and 0.03 respectively. Between Class
0 and Class I, disk radii cumulative distribution shows that the fraction of
large disks with sizes above the median of 40 au decreases with evolution
(Figure 3). Separating the disks by both cloud and Class shows that this trend
is dominated by disks in Serpens and Ophiuchus molecular cloud (Figure 5). The
decreasing of the dust continuum radii between Class 0 and Class I is
consistent with the VANDAM survey which observed more than 300 protostars in
the Orion region with the same angular resolution (0$\farcs$1) as our CAMPOS
survey (Tobin et al., 2020). On the other hand, the average disk size in the
Aquila molecular cloud increased between the Class 0 and Class I stages.

For Class I and flat-spectrum sources, the evolutionary trend for disk radii
is unclear. Anderson-Darling Tests of Serpens and Ophiuchus and Ophiuchus
North molecular clouds show Class I and flat-spectrum disk radii are drawn
from the same distribution. All other clouds do not have statistically
significant samples.

Conflicting evolutionary trends can be observed across different clouds. The
disk radii in Aquila and Cor Australis decreased over time, but the disk radii
in Ophiuchus increased over time. In contrast, the disk radii in Serpens and
Chamaeleon molecular clouds stay roughly constant. Interestingly, Hendler et
al. (2020) found the 58 evolved Class II/III (age of 2–3 Myr old) disks in the
Chamaeleon I have a $R_{\rm 90}$ median radius of 43.1 au, which is consistent
with the Class I $R_{\rm 90}$ median radius of 42.0 au ($R_{\rm 90}\sim
0.825R_{\rm 95}$) measured from our CAMPOS survey. This indicates little
evolution of dust radii in the Chamaeleon I molecular cloud.

The different disk radii evolutionary trends between the clouds might be
attributed to the imperfect protostellar age tracers, bolometric temperature
and spectral index, used in the classification of protostars. Bolometric
temperature and spectral index are both inclination-dependent and sources with
a face-on disk or pole-on outflow have an outflow cavity wall along the line-
of-sight of the observer, allowing more infrared emission to be detected and
thus classified as more evolved sources. This effect is more prominent in
Class I and flat-spectrum sources, as these have significantly larger outflow
cavities compared to Class 0 sources (Hsieh et al., 2023a). To test this
interpretation, we plot the protostellar disk inclination distribution for
different evolutionary stages in Figure 11. Considering the uncertainty of the
inclination angle measurements (right panel of Figure 11), the inclination
angle distribution for Class 0, Class I, and flat-spectrum sources are
consistent with each other. The lack of inclination dependence between
evolutionary stages implies Class misclassification due to the inclination
effect being minimal and not significantly affecting the distribution. Thus,
the data suggests that instead of a universal trend, local cloud environments
play an important role in shaping the disk radii evolution.

###  5.2 Evolution of Dust disk radii: Comparison with theory

We found that disk radii decrease between Class 0 and Class I for Serpens and
Ophiuchus molecular cloud, but increase for sources in the Aquila molecular
cloud.

For Aquila disks, the increase of dust disk radii as protostar evolves between
Class 0 and Class I is consistent with the prediction of non-magnetized
hydrodynamic models with inside-out collapse. For a collapsing and rotating
dense core, if magnetic fields are neglected, then centrifugal radius will
grow with $t^{3}$ (Ulrich, 1976; Cassen & Moosman, 1981; Terebey et al.,
1984). In addition, the standard models of viscosity-driven disk evolution
involving the $\alpha$-prescription also naturally predict the growth of disk
radii (Shakura & Sunyaev, 1973). In the context of non-ideal
magnetohydrodynamics (MHD) simulations, the influence of non-ideal MHD effects
(e.g. ambipolar diffusion) diminishes the magnetic braking effects over time
and results in disk radii growth (Machida et al., 2014; Tsukamoto et al.,
2015; Masson et al., 2016; Hennebelle et al., 2016). Consequently, regardless
of the presence or absence of magnetic fields, an expansion in disk radii is
anticipated, which is consistent with the evolutionary trend shown in the
Aquila molecular cloud.

For the Serpens and Ophiuchus molecular cloud, the dust disk radii decrease
between Class 0 and Class I seems to contradict the theoretical models.
However, it is important to point out that the theoretical models give
predictions in gas disk radii, not dust disk radii as measured in our
observation. Dust disk radii are expected to be smaller than the gas disk
radii due to the radial drift of dust grains. The decreasing dust disk radii
in Serpens and Ophiuchus molecular cloud as the protostar evolves could be
explained by the following:

  1. 1.

Class 0 protostellar disks are contaminated by the envelope resulting in
larger disk radii.

  2. 2.

Radial drift of dust resulting in smaller dust radii over time.

  3. 3.

Disk winds and protostellar outflows removing the angular momentum of the disk
(Bai et al., 2016).

Our ALMA observations are sensitive only to compact structures with sizes
smaller than 2$\farcs$0\. Thus we expect minimal envelope contamination, as
large envelope emission would be resolved out in our observations. In
addition, if the dense inner envelope contaminated the emission, the emission
would be more isotropic on the plane of the sky. Thus creating inclination
angle distribution peaks towards face-on disks. We found the distribution of
inclination angles for Class 0 sources is consistent with the envelope-
depleted flat-spectrum sources as shown in Figure 11. Both inclination
distributions are nearly consistent with the random distribution of disk
inclinations, and we did not detect an overabundance of face-on disks in our
sample. This implies that most of the continuum structures detected in our
survey are not contaminated by the isotropic dense inner envelope.

While the inclination angle distribution rules out possible contamination by
an isotropic dense inner envelope as a cause for larger disks in more embedded
sources, it does not rule out the possibility of overestimating disk sizes for
young sources due to the contamination of asymmetric large-scale structures
such as streamers, filaments, or outflow cavity walls. These sources with
extended dust emission are shown in Figure 6 and Figure 9. The boundaries of
protostellar disks are sometimes connected with accreting streamers or
protostellar outflow cavity walls. These sources with extended emission may be
contaminated by accreting streamers (Figure 6) or compact inner envelopes
(Figure 9). Even so, sources with extended emissions are infrequent in our
sample. More importantly, Orion, Aquila, and Serpens molecular clouds are
located at a similar distance and observed at similar angular resolution
($\sim 40\,au$), but show distinct disk radii distributions or evolutionary
trends. This indicates that the protostellar disk emission dominates the dust
continuum emission.

Another possible explanation for the decrease of dust disk radii between Class
0 and Class I in the Ophiuchus and Serpens molecular clouds is dust radial
drift. If radial drift is responsible for the decrease in dust disk radii,
then its timescale should be smaller or comparable to the half-life of the
Class 0 stage. We conducted an order of magnitude analysis and compared the
two timescales to assess this scenario. The drift timescale
($\tau_{\mathrm{drift}}$) is given by

$\tau_{\mathrm{drift}}=\frac{rV_{\mathrm{k}}}{\mathrm{St}c_{\mathrm{s}}^{2}}\gamma^{-1}$
(2)

, where $V_{k}$ is the Keplerian velocity, $r$ is the distance the dust moves
due to radial drift, $c_{s}$ is the sound speed, $St$ is the stokes number of
the dust particle, and

$\gamma=\left|\frac{\mathrm{d}\ln P}{\mathrm{~{}d}\ln r}\right|$ (3)

is the absolute value of the power-law index of the gas pressure profile
(Birnstiel et al., 2012). Between Class 0 and Class I, the Ophiuchus mean
protostellar disk radii decreased $\sim 25\%$ from 35.4 au to 26.4 au between
Class 0 and Class I (See LABEL:table:disk_radii). Therefore, we assume $r\sim
10\,$au. We estimate the Keplerian velocity at the outer disk boundary of 40
au. For this, we assume a typical Class 0 mass of 0.1 $M_{\odot}$ (Jhan & Lee,
2021), which gives us a Keplerian velocity of $V_{k}\sim 1.5$ km s-1 at the
radius of interest. Assuming an isothermal midplane temperature of 10 K, the
corresponding sound speed is 0.2 km s-1. Supposing an equation of state of
$P=\rho c_{s}^{2}$, and a disk density profile of $\rho(r)\propto r^{-1}$,
this gives $\gamma\sim 1$.

The Stokes number ($St$) is given by the ratio of the particle stopping time
($t_{stop}$) to the turn-over time of the largest turbulent eddy ($t_{L}$).
Assuming Epstein drag law, compact spherical particles, an isothermal gas
density profile, and $t_{L}=\Omega_{K}^{-1}$ (Keplerian angular frequency),
then the particles near the disk mid-plane have Stokes number of:

$\mathrm{St}=\frac{a\rho_{\mathrm{s}}}{\Sigma_{\mathrm{g}}}\frac{\pi}{2}$ (4)

, where $a$ is the particle radius, $\rho_{s}$ is the internal density of dust
grains which is adopted to be 1.6 g cm-3 (Birnstiel et al., 2012), and
$\Sigma_{g}$ is the gas surface density. Our ALMA 1.3 mm continuum maps mostly
trace millimeter dust grains, so we adopt$a\sim 10^{-3}$ m. Assuming a typical
protostellar disk column density of $\Sigma_{g}\sim 10$ g cm-2 (Tanaka &
Tsukamoto, 2019), we estimate $St\sim 0.025$. This gives us a dust drift
timescale ($\tau_{\rm drift}$) of $\sim 1.3\times 10^{5}$ years for the
Ophiuchus molecular cloud. This timescale is a factor of 3 longer than the
half-life of the Class 0 stage (5 $\times 10^{4}$ years) derived from the
Spitzer Space Telescope “cores to disks” (c2d) and “Gould Belt” (GB) Legacy
surveys (Kristensen & Dunham, 2018).

While simulations show that radial drift is possible in protostellar disks
(Birnstiel et al., 2010), the lifetime for Class 0 is too short compared to
the dust drift timescales. In addition, it takes time for the dust to grow
from small $\sim 0.1\mu m$ grains inherited from the ISM to roughly
millimeter-sized grains that are affected by gas drag (Powell et al., 2019).
Moreover, the high accretion rate in the Class 0 phase indicates that the gas
and dust in the protostellar disk are constantly replenished (Lee, 2020), thus
a much shorter dust radial drift timescale is needed to offset the dust
accreted from outside the disk.

The mean radius of protostellar disks in the Serpens molecular cloud decreases
$\sim 37\%$ (from 77.3 au to 48.6 au) between Class 0 and Class I, more than
the decrease in disk size seen in the Ophiuchus molecular cloud. Therefore,
the decrease in dust disk size between Class 0 and Class I in the Ophiuchus
and Serpens molecular clouds cannot be explained by radial drift alone.

Another possible explanation for the decrease of disk dust radii is the impact
of MHD disk winds on the disk. Removal of angular momentum by a disk wind can
keep the disk radii small (e.g., Bai et al. 2016), and possibly cause the disk
radii to decrease with time. However, it is important to point out that such
predictions are for gas radii. Thus, only gas disk radii can be tested against
predictions from theory and simulations. In the next section, we will
investigate the evolution of disk gas radii to disk dust radii ratio, and show
that dust and gas radii decouple during the early Class I stage. Because of
the decoupling of dust and gas radii at early Class I, it remains unclear
whether or not disk winds are responsible for the decrease in disk radii
between Class 0 and Class I for sources in the Serpens and Ophiuchus molecular
cloud.

###  5.3 The decoupling of dust and gas disk in early Class I phase: Evolution
of gas disk radius to dust disk radius ratio

Figure 12: The evolution of gas disk radius to dust disk radius ratio ($R_{\rm
gas,Kep}/R_{\rm mm}$) for young stellar objects as a function of evolutionary
stages traced by the bolometric temperature ($T_{\rm bol}$), using data from
the literature. We separate the data into Class 0 (blue circle), Class I
(orange square), and Class II (green triangle). The green dashed line shows
the best-fitted power-law Bayesian model with $y=a\times x^{b}$, where
$a=0.42\pm 0.12$, and $b=1.7\pm 0.2$. The gray region marks the $2\sigma$
uncertainty. Note that the Class 0 outlier, IRAS 15398-3359 (in the upper part
of the plot), is excluded from the fit.

Most measurements of disk sizes around the youngest embedded protostars come
from (sub)-millimeter dust continuum observations (e.g., Maury et al. 2019;
Tobin et al. 2020 or see subsection 4.2). These continuum observations probe
the distribution of millimeter-sized dust grains and reveal the evolution of
disk solids. The dust particles might be aerodynamically decoupled from the
gas and migrate inwards due to radial drift. On the other hand, molecular line
observations encode important information about the disks’ gaseous content
evolution, especially the angular momentum transport (Bai et al., 2016;
Pudritz & Ray, 2019; Tabone et al., 2022a)). The predictions of hydrodynamic
models (Yorke & Bodenheimer, 1999; Bate & Bonnell, 2005; Stamatellos &
Whitworth, 2009; Kratter et al., 2010; Bate, 2018), non-ideal
magnetohydrodynamical (MHD) models (Galli et al., 2006; Hennebelle & Fromang,
2008; Mellon & Li, 2008; Hennebelle & Ciardi, 2009; Terebey et al., 1984) and
the latest MHD disk-wind-driven disk accretion models (Pudritz & Ray, 2019;
Tabone et al., 2022a) should be compared to gas disks, which require
significantly more time to observe (compared to dust continuum measurements).
Besides several case studies of individual sources and a few surveys with a
relatively small sample of less than 20 sources, large systematic high-
resolution CO disk surveys of the youngest Class 0/I protostars remain limited
(e.g., Ohashi et al. (2023)).

Currently, the sample size of existing high-resolution CO disk surveys is too
small to conduct a population study and conclude the disk formation mechanism.
In contrast, the CAMPOS survey and the Orion VANDAM survey (Tobin et al.,
2020) in total cover more than 500 Class 0/I and flat-spectrum phase
protostellar disks in nearby star-forming regions at 0$\farcs$1 resolution.
This extensive dataset holds the key to conducting a comprehensive demographic
study, shedding light on the intricate processes governing the formation and
evolution of protostellar disks. It is therefore important to understand when,
in disks, do millimeter-sized dust grains decouple from the gas and how
reliably dust traces the gas in disks in order to determine how protostellar
disks form and evolve.

Detailed comparisons between the gas disk radii and dust disk radii have been
done for more evolved Class II disks (Long et al., 2022), however, this has
never been done for younger Class 0/I sources. As a result, the evolutionary
trend of how the gas disk radii to dust disk radii ratio evolves has never
been studied. We compiled the existing literature for disks with both a
measurement of the gas disk radius, defined by the Keplerian rotation radius
($R_{\rm gas,Kep}$), and the dust disk radius ($R_{\rm mm}$) measured by the
millimeter continuum data in LABEL:table:disk_RgasRdust. We list both the
methods and lines used to determine the radii in LABEL:table:disk_RgasRdust.
If the disk radii uncertainty is not given in the literature, we adopted half
of the beam size as the uncertainty in the disk radius measurement. We cross-
matched the sources with Dunham et al. (2015) to obtain their bolometric
temperature ($T_{\rm bol}$), which is an indicator of the protostellar age
(Chen et al., 1995).

Table 7: Disk properties from literature

Source | $T_{\rm bol}$ | $R_{\rm gas,Kep}$ | $R_{\rm mm}$ | ratio | Ref | Note
---|---|---|---|---|---|---
ID | (K) | (au) | (au) |  |  |
L1489 IRS | 213 | 600 $\pm$ 62 | 230 $\pm$ 3 | 2.61 $\pm$ 0.27 | 1, 2 |  $R_{\rm gas}$: C18O PV fitaaGas disk radius derived using the Position-velocity (PV) diagram method. Here Keplerian rotation ($v\propto r^{-0.5}$) is fitted to the PV diagram. The gas disk radius is determined by the radius at which the velocity profile changes from $v\propto r^{-0.5}$ to $v\propto r^{-1}$ (consistent with an infalling envelope with the conservation of angular momentum)., $R_{\rm mm}$: Visibility fit
IRAS 04302+2247 | 88 | 620 $\pm$ 62 | 310 $\pm$ 10 | 2.00 $\pm$ 0.21 | 3 |  $R_{\rm gas}$: By eye, $R_{\rm mm}$: By eye
L1527 IRS | 41 | 102 $\pm$ 6 | 85 $\pm$ 6 | 1.20 $\pm$ 0.11 | 4, 5 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: 5$\sigma$ contour
CB 68 | 50 | 25.7 $\pm$ 0.5 | 31.3 $\pm$ 2.5 | 0.82 $\pm$ 0.07 | 6 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: CASA imfit
Ced110 IRS4A | 68 | 120 $\pm$ 5 | 91.7 $\pm$ 0.2 | 1.31 $\pm$ 0.05 | 7 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: COGbbRadius derived from the Curve-of-growth (COG) method by Ansdell et al. (2016).
IRS5N | 59 | 77.0 $\pm$ 2.3 | 62.0 $\pm$ 0.5 | 1.24 $\pm$ 0.04 | 8 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: CASA imfit
IRAS 16253-2429 | 42 | 16 $\pm$ 3 | 14.9 $\pm$ 0.3 | 1.08 $\pm$ 0.20 | 9 |  $R_{\rm gas}$: UCMccDetermine the disk centrifugal radius from the UCM envelope model (Ulrich, 1976; Cassen & Moosman, 1981) with the specific angular momentum of $j\sim 45\,$km s-1 au (Hsieh et al., 2019), and central stellar mass of 0.14 $M_{\odot}$., $R_{\rm mm}$: CASA imfit
IRAS 15398-3359 | 50 | 31.2 $\pm$ 2.4 | 3.82 $\pm$ 0.09 | 8.17 $\pm$ 0.66 | 10 |  $R_{\rm gas}$: SO PV fit, $R_{\rm mm}$: CASA imfit
Oph IRS63 | 348 | 265 $\pm$ 9 | 62 $\pm$ 2 | 4.27 $\pm$ 0.21 | 11 |  $R_{\rm gas}$: 13CO PV fit, $R_{\rm mm}$: GoFishdd2$\sigma$ radius from the GoFish fit code developed by Teague (2019). fit
VLA1623A CB | 10 | 210 $\pm$ 45eeMurillo et al. (2013) reported a Keplerian rotation radius of 180 au assuming a distance of 120 pc. Sadavoy et al. (2018) also report a dust radius of 180 au assuming the same 120 pc distance. We adjusted the radius by using the latest Gaia distance estimate for Ophiuchus (144 pc) (Zucker et al., 2019). | 215 $\pm$ 15 | 0.98 $\pm$ 0.22 | 12, 13 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: By eye
HH211 | 33 | 10 $\pm$ 30 | 30 $\pm$ 6 | 0.33 $\pm$ 1.00 | 14 |  $R_{\rm gas}$: SO diskffThe radius of the rotating disk atmosphere detected in SO. SO PV modeling was shown in Figure 4 of Lee et al. (2018a), but a break-point between infall and Keplerian rotation is not detected. We assume a factor of 3 error in the derived gas disk radii due to the lack of break-point between infall and Keplerian rotation., $R_{\rm mm}$: CASA imfit
HH212 | 48 | 44 $\pm$ 9ggCentrifugal Barrier is adopted to be the gas disk radius. | 68 $\pm$ 4 | 0.65 $\pm$ 0.14 | 15 |  $R_{\rm gas}$: HCO+ PV fit, $R_{\rm mm}$: Intensity profilehhHalf width half maximum of the intensity profile.
Lupus 3 MMS | 39 | 100 $\pm$ 53 | 82 $\pm$ 49 | 1.22 $\pm$ 0.97 | 16 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: CASA UVmodelfit
TMC-1A | 118 | 90 $\pm$ 74 | 70 $\pm$ 4 | 1.29 $\pm$ 1.06 | 17 |  $R_{\rm gas}$: C18O PV fit, $R_{\rm mm}$: CASA imfit
L1551 IRS 5 | 94 | 64 $\pm$ 64 | 80 $\pm$ 5 | 0.80 $\pm$ 0.80 | 18 |  $R_{\rm gas}$: CS PV fit, $R_{\rm mm}$: CASA imfit
Sz 65 | 3300 | 178 $\pm$ 25 | 66 $\pm$ 2 | 2.70 $\pm$ 0.39 | 19 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COGiiFor all the Class II sources with $T_{\rm bol}>1400$ K, the sources are from Table 2 of Long et al. (2022).
Sz 91 | 2900 | 358 $\pm$ 64 | 123 $\pm$ 3 | 2.91 $\pm$ 0.53 | 19 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
Sz 98 | 1900 | 279 $\pm$ 41 | 148 $\pm$ 3 | 1.89 $\pm$ 0.28 | 19 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
Sz 100 | 2400 | 121 $\pm$ 8 | 56 $\pm$ 2 | 2.16 $\pm$ 0.16 | 19 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
Sz 123A | 2300 | 118 $\pm$ 10 | 60 $\pm$ 2 | 1.97 $\pm$ 0.18 | 19 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
MY Lup | 2800 | 192 $\pm$ 7 | 77 $\pm$ 3 | 2.49 $\pm$ 0.13 | 20 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
SR 4 | 1400 | 82 $\pm$ 7 | 29 $\pm$ 2 | 2.83 $\pm$ 0.31 | 20 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
DoAr 25 | 1700 | 233 $\pm$ 6 | 147 $\pm$ 2 | 1.59 $\pm$ 0.05 | 20 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
DoAr 33 | 1800 | 64 $\pm$ 6 | 25 $\pm$ 2 | 2.56 $\pm$ 0.32 | 20 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG
WaOph 6 | 1700 | 297 $\pm$ 7 | 91 $\pm$ 4 | 3.26 $\pm$ 0.16 | 20 |  $R_{\rm gas}$: CO Moment 0, $R_{\rm mm}$: COG

††footnotetext: References: (1) Sai et al. (2020) (2) Yamato et al. (2023) (3)
Lin et al. (2023) (4) van’t Hoff et al. (2023) (5) Tobin et al. (2012b) (6)
Kido et al. (2023)(7) Sai et al. (2023a) (8) Sharma et al. (2023) (9) Aso et
al. (2023) (10) Thieme et al. (2023) (11) Yamato et al. (2023) (12)Murillo et
al. (2013) (13) Sadavoy et al. (2018) (14) Lee et al. (2018a) (15) Lee et al.
(2017) (16) Yen et al. (2017) (17) Aso et al. (2015) (18) Chou et al. (2014)
(19) Ansdell et al. (2018) (20) Andrews et al. (2018)

We found that the gas disk radius to dust disk radius ratio ($R_{\rm
gas,Kep}/R_{\rm mm}$) increases as a protostar evolves (See Figure 12). We
separated the data into Class 0 (blue circles), Class I (orange squares), and
Class II (green triangles). Excluding the outlier IRAS 15398-3359, the Class 0
source with the highest $R_{\rm gas,Kep}/R_{\rm mm}$ ratio, we found the
average $R_{\rm gas,Kep}/R_{\rm mm}$ for Class 0, Class I, and Class II are
$1.0\pm 0.3$, $2.2\pm 1.2$, and $2.4\pm 0.5$, respectively. To quantify the
relationship between $R_{\rm gas,Kep}/R_{\rm mm}$ and $T_{\rm bol}$, we
adopted a simple Bayesian power-law model and used the emcee package (Foreman-
Mackey et al., 2013) to draw 2,000 posterior samples in 50 sampling chains to
conduct the Monte Carlo Markov chain (MCMC) modeling. We set the burn-in
period to be 1,000 and from the MCMC modeling we found:

$\frac{R_{\rm gas,Kep}}{R_{\rm mm}}=(0.4\pm 0.1)\times\left(\frac{T_{\rm
bol}}{\rm K}\right)^{1.7\pm 0.2},$ (5)

shown as the green solid line in Figure 12. The gray-shaded region represents
the $2\sigma$ uncertainty.

Note that we strongly caution that the evolutionary trend shown in Figure 12
is not robust due to different angular resolutions, different line tracers,
and a variety of methods used to obtain $R_{\rm gas,Kep}$ and $R_{\rm mm}$
(LABEL:table:disk_RgasRdust). For example, the Keplerian disks of Lupus 3 MMS,
TMC-1A, and L1551 IRS 5 are not well resolved, and this resulted in higher
uncertainties in the gas disk radius measurements (Yen et al., 2017; Aso et
al., 2015; Chou et al., 2014). In addition, we noticed that gas-to-dust disk
radii ratios derived from SO significantly deviate from the results derived
from C18O. The Class 0 sources IRAS 15398-3359 and HH211 have gas-to-dust disk
radii ratios of 8.2 and 0.3 respectively. This significantly deviates from the
Class 0 average of 1. This indicates that SO, a well-known shock tracer, is
not a good line tracer for gas disk radius. Furthermore, the Class II gas
radii traced by the integrated intensity map (Moment 0) of CO might be more
extended than the Keperlian rotation modeling with C18O. As a result, we do
not know whether the trend in $R_{\rm gas,Kep}/R_{\rm mm}-T_{\rm bol}$ seen in
Figure 12 between Class I and Class II is due to the evolution of disk radii
or the systematic error from using different methods and tracers.

In contrast to the Class II sources, most Class 0/I gas disk radii in Figure
12 are traced by the same method (Keplerian rotation modeling) and the same
molecular line tracer (C18O). The Class 0/I gas radius is defined as the
transition radius between the Keplerian rotation and infall in the C18O
position-velocity diagram (PV). With the consistent method and line tracer,
the current data suggests that for Class 0 protostellar disks, the C18O
Keplerian rotating gas disk is comparable in size with the submillimeter dust
disk. This allows a direct comparison of our submillimeter dust disk
observation with different hydrodynamical and non-ideal MHD disk formation
models to constrain the main mechanisms behind the Class 0 disk formation.

Class 0 sources have gas disk to dust disk radii ratio much smaller than early
Class I protostellar disks with bolometric temperature between 70 and 400 K
($R_{\rm gas,Kep}/R_{\rm mm}\sim 2.2$). This implies that the dust and gas
disk radii rapidly decouple around early Class I. The evolution of $R_{\rm
gas,Kep}/R_{\rm mm}$ ratio cannot be explained by the evolution of dust disk
radius alone. The $R_{\rm gas,Kep}/R_{\rm mm}$ ratio increases by a factor of
2.2 between Class 0 and the early Class I, while the dust radii only decrease
by $\sim$30 % (e.g., Ophiuchus molecular cloud). Nevertheless, the rapid
evolution of $R_{\rm gas,Kep}/R_{\rm mm}$ and $R_{\rm mm}$ during the early
Class I phase highlights an important timescale for the decoupling of gas disk
radius and dust disk radius. The underlying mechanism for setting this
timescale is unclear and should be explored by future studies.

###  5.4 Class 0 protostellar disks are small

Our CAMPOS survey found that for the Aquila, Corona Australia, Ophiuchus
North, Ophiuchus, and Serpens molecular clouds, the median Class 0 dust disk
radius is 41.5 au, which is consistent with the median Class 0 dust disk
radius of 48.1 au in the Orion molecular cloud (Tobin et al., 2020). Together
with our CAMPOS survey, a large majority of Class 0 disks in at least 8
molecular clouds (Aquila, Corona Australia, Ophiuchus North, Ophiuchus,
Serpens, Orion A, Orion B, and Perseus) have been fully sampled333Based on the
Dunham et al. (2015) and Furlan et al. (2016) catalog. (Tobin et al., 2018,
2020). It is now well established that Class 0 disks have a typical disk
radius of 40–50 au (Tobin et al., 2018).

While there is a consensus that the majority of Class 0 disks are small with
disk radii of 40–50 au, it remains debated whether or not the distribution is
skewed with a long positive tail towards larger disks. The CALYPSO survey of
16 Class 0 protostars shows that less than 25 % of Class 0 disks are larger
than 60 au (Maury et al., 2019), and from this, the authors concluded that
large Class 0 disks are rare. In contrast, the Orion protostellar disk survey
shows that 46% of Class 0 protostars have dust radius greater than 50 au, and
argues that Class 0 disks larger than 50 au are not rare (Tobin et al., 2020).
From our CAMPOS survey, we found that out of 52 Class 0 circumstellar disks in
the 7 nearby clouds, only 14 disks (27 %) are larger than 60 au, this is in
strong agreement with Maury et al. (2019). Interestingly, 21 disks (40 %) are
larger than 50 au, this is also in agreement with Tobin et al. (2020). From
our CAMPOS survey, the distribution of Class 0 dust radii shows the existence
of a long tail towards the larger radii as shown in Figure 4.

###  5.5 The formation of protostellar disks: Tension with hydrodynamic, Hall
effect and ambipolar diffusion models

The study of gas disk radii offers a robust test for different disk formation
models. From our results, we see that Class 0 gas disk radii can be traced by
the dust disk radii ($R_{\rm gas,Kep}/R_{\rm mm}\sim 1$), allowing a direct
comparison between our observational data and the model predictions (See
subsection 5.3). Hydrodynamical models of infalling rotating cores with
angular momentum conservation predict that rotation-supported disks can
quickly grow to sizes larger than $100\,$au in only a few thousand years
(Yorke & Bodenheimer, 1999; Matsumoto & Hanawa, 2003; Bate & Bonnell, 2005;
Stamatellos & Whitworth, 2009; Kratter et al., 2010; Bate, 2018). These
hydrodynamical models are in strong tension with the much smaller $\sim$40 au
Class 0 disk radii found in our CAMPOS survey. In order to form a 50 au disk
from a uniformly rotating core with a size of 0.1 pc, density profile
($\rho\propto r^{-2}$), and $\beta=0.02$ (Goodman et al., 1993), more than 75
% of the initial angular momentum needs to be removed (Maury et al., 2019).
Without an additional mechanism to remove initial core angular momentum, disks
formed in infalling rotating cores are a factor of 2.5 times larger than the
Class 0 disks typically observed.

Currently, the only known mechanism that can effectively remove angular
momentum in infalling rotating cores is magnetic torques (Li et al., 2014a).
In particular, the evolution of magnetic fields is determined by non-ideal
effects like ambipolar diffusion. Hennebelle et al. (2016) developed an
analytical model for the protostellar disk radius. Assuming the magnetic
braking timescale is similar to the rotation timescale, and a Keplerian
rotating disk in vertical hydrostatic equilibrium, then according to
Hennebelle et al. (2016) the disk radius ($r_{\mathrm{d},\mathrm{AD}}$) can be
written as:

$\displaystyle r_{\mathrm{d},\mathrm{AD}}\simeq$ $\displaystyle 18\mathrm{au}$
(6)
$\displaystyle\times\delta^{2/9}\left(\frac{\eta_{\mathrm{AD}}}{0.1\mathrm{~{}s}}\right)^{2/9}\left(\frac{B_{z}}{0.1\mathrm{G}}\right)^{-4/9}\left(\frac{M_{\mathrm{d}}+M_{*}}{0.1M_{\odot}}\right)^{1/3},$

where $\eta_{\mathrm{AD}}$ is the ambipolar diffusion timescale, $\delta$ is a
scaling factor on the order of a few, and $M_{\mathrm{d}}+M_{*}$ is the sum of
the disk and the protostar mass. This model predicts a weak disk radius
dependence on all parameters, suggesting that even in environments with
different magnetic field strengths or protostars with different masses, Class
0 disks should not vary much in size. In contrast, the observed Class 0 disk
size distribution has a large variation in disk radii and the disk radii is a
factor of 2.2 times larger than the ambipolar diffusion model (Hennebelle et
al., 2016). One possible explanation for the disk radii difference is the lack
of small dust grains due to the grain coagulation process (Hirashita, 2012).
Small grains ($<0.1\mu m$) are the main charge carriers, responsible for the
coupling of neutral matter to the magnetic field at densities below $10^{10}$
cm-3 (Hennebelle et al., 2016). The depletion of very small grains with size
10-100 Å can enhance the ambipolar diffusion by 1 to 2 orders of magnitude and
trigger the early formation of larger rotationally supported disks (Zhao et
al., 2018). In addition, a weaker magnetic field combined with turbulence can
also explain the disk radii differences between the ambipolar model and our
observation.

In addition to the ambipolar diffusion, another non-ideal MHD effect, the Hall
effect, predicts a bimodal distribution of Class 0 disk radii (Tsukamoto et
al., 2015). When the disk rotation vector and the disk magnetic field are
anti-parallel, the Hall effect weakens the magnetic braking effect and allows
a 20 au disk to form. Likewise, when they are parallel, the magnetic braking
effect is enhanced, resulting in a very small ($<$1 au) disk (Tsukamoto et
al., 2015). Given that the Hall effect does not play a role during cloud core
formation (Wardle, 2004), the probability of having an anti-parallel versus a
parallel configuration should be the same. Thus the Hall effect predicts
bimodality in Class 0 disk size (Tsukamoto et al., 2015). If the Hall effect
would be an important factor in disk formation, then we would expect half of
the Class 0 disks to have radii of less than 1 au, thus unresolved. In our
CAMPOS results, only 1 out of 52 Class 0 sources are unresolved and we do not
see a bimodal distribution of Class 0 disk radii. The discovery of B335, a
Class 0 source with a disk radius much smaller than 10 au (Yen et al., 2015;
Bjerkeli et al., 2019) is an exception rather than the norm. Recent analytical
and numerical studies by Zhao et al. (2020) and Lee et al. (2021) show that
the bimodal distribution from the Hall effect is transient and only lasts a
few thousand years. Our observation is in high tension with the bimodal
distribution of Class 0 disk sizes predicted by the Hall effect and suggests
that the Hall effect is not the dominant factor in protostellar disk
formation. Furthermore, even in the anti-parallel case, the 20 au disk radii
is still a factor of 2 smaller than the observed Class 0 disk radii of 40 au.
Thus our Class 0 disk observation is in high tension with the Hall effect
model (Tsukamoto et al., 2015).

In summary, our work reveals that protostellar disk formation is magnetically
regulated. Hydrodynamical models without consideration of magnetic fields
cannot explain the disk radii distribution of Class 0 protostars. Our
observation is in high tension with the bimodal disk size distribution
predicted by the Hall effect (Tsukamoto et al., 2015). The large spread of
Class 0 disk radii centered at 40 au is also inconsistent with the small disk
radii (18 au) and the small variation of disk radii predicted by models that
include ambipolar diffusion (e.g., Hennebelle et al. 2016). Additional
parameters such as turbulence, dust distribution (Zhao et al., 2018), and the
inclination angle between the magnetic field and the angular momentum axis
(Lee et al., 2024) might also play a role in shaping disk radii sizes. Future
studies are needed to explain the Class 0 disk radii distribution.

##  6 Conclusion

We have conducted an ALMA high-resolution (0$\farcs$1) continuum survey of
nearly all known Class 0, Class I, and flat-spectrum protostars in 7 nearby
molecular clouds, Corona Australis, Aquila, Chamaeleon I & II, Ophiuchus,
Ophiuchus North, and Serpens. We also include young Class II sources still
surrounded by their natal envelopes, with ${\rm T}_{\rm bol}\sim 1900$ K. In
total, we detected 184 protostellar disks. In this paper, we present the first
paper of the CAMPOS survey, which covers the self-calibration and imaging of
all continuum sources; the first data release of the project. Our main results
are summarized as follows.

  1. 1.

The mean dust radii for the Class 0, Class I, and flat-spectrum protostars are
$59.3\pm 7.4$, $46.0\pm 4.0$, and $41.6\pm 7.2$ au. Using a kernel density
estimation with a Gaussian Kernel (See Figure 4), we found that the most
probable radii for Class 0, Class I, and flat-spectrum protostars are 39, 27,
and 23 au. The difference between the mean dust radii and the most probable
radii is attributed to the tail in the disk radii distribution. In particular,
we found the fraction of large disks with sizes above 40 au decreases with the
protostellar evolutionary stage.

  2. 2.

We conducted Anderson-Darling tests and found significant variation in disk
radii among the same Class between different clouds, which highlights the
influence of local environments on disk radii evolution (See
LABEL:table:disk_radii_stat and Figure 5).

  3. 3.

We found a statistically significant correlation (p-value $<$0.06) suggesting
that the dust disk radii decrease between Class 0 and Class I phase for the
Serpens and Ophiuchus molecular clouds (See LABEL:table:disk_radii_stat). We
showed that the dust drift timescale is longer than the Class 0 half-life, and
the 30 % decrease in dust disk radii between Class 0 and Class I cannot be
explained by radial drift alone (See Figure 4).

  4. 4.

For Class 0 sources the dust disk radii are similar in size to the gas disk
radii (See conclusion point 8), allowing a direct comparison between the gas
disk radii from simulations and our observed dust disk radii. Our work reveals
that protostellar disk formation is magnetically regulated. Hydrodynamical
models without consideration of magnetic fields cannot explain the disk size
distribution of Class 0 protostars. In addition, the CAMPOS data is in high
tension with the bimodal disk size distribution predicted by disk formation
models that include the Hall effect (Tsukamoto et al., 2015). Our data is also
inconsistent with the small disk size and the small variation of disk sizes
predicted by models that include the ambipolar diffusion (e.g., Hennebelle et
al. 2016).

  5. 5.

From our CAMPOS survey, we found 21 protostellar disks with substructures or
asymmetries as shown in Figure 7, Figure 8 and Figure 9. Out of the 21 disks
with substructures, 5 of them are newly discovered. Two of them are Class I
(SMM 2, IRS 2), two are Flat-spectrum sources (Oph-emb-20, ISO-ChaI 101), and
one is a Class II source (Ass Cha T 1-15). The discovered disks with
substructures are summarized in LABEL:table:disk_substructure.

  6. 6.

We cross-matched all protostars identified in our ALMA survey with the known
literature catalogs. In total, we found 30 protostellar sources that had not
been previously detected in the submillimeter wavelength. All the ALMA
protostellar sources detected by our ALMA survey are organized in Appendix C
with images shown in Appendix D.

  7. 7.

We highlight the sources with many large-scale extended structures in our
CAMPOS survey as possible “streamer candidates”, shown in Figure 6. In
addition, we report the detection of edge-on sources (Figure 10), which will
be interesting for follow-up study.

  8. 8.

We compiled the literature data and discovered a strong increasing trend of
the gas disk radii to dust disk radii ratio ($R_{\rm gas,Kep}/R_{\rm mm}$) as
a function of bolometric temperature (${\rm T}_{\rm bol}$) as shown in Figure
12. We found that Class 0 protostellar disks have $R_{\rm gas,Kep}/R_{\rm
mm}\sim 1.0$. Early Class I protostellar disks ($70\leq T_{\rm bol}\leq 400$)
have $R_{\rm gas,Kep}/R_{\rm mm}\sim 2.2$. Class II disks have $R_{\rm
gas,Kep}/R_{\rm mm}\sim 2.4$. The $R_{\rm gas,Kep}/R_{\rm mm}$ ratio increases
rapidly during the early Class I stage ($T_{\rm bol}\sim$ few 100 K). This
sets the important timescale for the decoupling of dust and gas disk radii.
Future studies are needed to precisely capture the rapid evolution of $R_{\rm
gas,Kep}/R_{\rm mm}$ in early Class I, and reveal the mechanism behind the
decoupling of gas and dust radii. However, we strongly caution that the
results from the literature we used to find the evolutionary trend may suffer
from large uncertainties due to the variety of methods used to obtain $R_{\rm
gas,Kep}$, different line tracers, and sensitivity limits.

## Acknowledgments

C.H.H. and H.A acknowledge the support from the National Radio Astronomy
Observatory (NRAO) with grant XXX. C.H.H. and H.A are supported in part by
NASA grants XXX and NSF grants XXX. D.S.C. is supported by an NSF Astronomy
and Astrophysics Postdoctoral Fellowship under award AST-2102405. Special
thanks to e-HOPS group, Riwaj Pokhrel, and Thomas Megeath for providing the
unpublished e-HOPs catalog for protostar classification. This paper makes use
of the following ALMA data: ADS/JAO. #2019.1.01792.S. ALMA is a partnership of
the ESO (representing its member states), NSF(USA), and NINS (Japan), together
with the NRC (Canada), NSC and ASIAA(Taiwan), and KASI(Republic of Korea),
incooperation with the Republic of Chile. The Joint ALMA Observatory is
operated by the ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy
Observatory is a facility of the National Science Foundation operated under a
cooperative agreement by Associated Universities, Inc.

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