FAUST. XIV. Probing the Flared Disk in L1527 with Sulfur-bearing Molecules

IRAS04368+2557 in L1527 is a Class 0/I protostar with a clear disk-envelope system revealed by previous Atacama Large Millimeter/submillimeter Array (ALMA) observations. In this paper, we discuss the flared structure of this source with observed sulfur-bearing molecules included in the FAUST ALMA large program. The analyses of molecular distributions and kinematics have shown that CS, SO, and OCS trace different regions of the disk-envelope system. To evaluate the temperature across the disk, we derive rotation temperature with the two observed SO lines. The temperature profile shows a clear, flared “butterfly” structure with the higher temperature being ∼50 K and the central lower temperature region (<30 K) coinciding with the continuum peak, suggesting dynamically originated heating rather than radiation heating from the central protostar. Other physical properties, including column densities, are also estimated and further used to demonstrate the vertical structure of the disk-envelope system. The “warped” disk structure of L1527 is confirmed with our analyses, showing that sulfur-bearing molecules are not only effective material probes but also sufficient for structural studies of protostellar systems.


Introduction
Understanding the physical and chemical processes during low-mass star formation is not only one of the principal goals of general astronomy studies but also crucial for unfolding the origin of our solar system.Studies on the chemistry of protostellar sources have enhanced our knowledge of the chemical composition and evolution of protostars and demonstrated that chemical compounds are advantageous probes of physical conditions.For instance, sulfur-bearing species (e.g., CS, SO, and SO 2 ) are often observed in the heated regions, such as outflow cavity walls and shocked gas due to accretion, around Class 0/I sources (Harsono et al. 2014;Sakai et al. 2014b;Oya et al. 2016;Zhang et al. 2018;Tychoniec et al. 2021;Garufi et al. 2022).The injection of dust mantle products into the gas phase lead to the enhancement of sulfur-bearing species.SO, in particular, is proven to be an effective tracer for weak shocks due to its preferable sublimation temperature (∼50 K) and volatility (Hartquist et al. 1980;Pineau des Forets et al. 1993;Miura et al. 2017;Oya et al. 2019).In recent years, many observations toward low-mass protostellar sources have Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
been conducted in the effort to reveal the detailed disk structure, including Atacama Large Millimeter/submillimeter Array (ALMA; Wootten & Thompson 2009) projects such as ALMA chemical survey of disk-outflow sources in Taurus (Garufi et al. 2021).These surveys have helped uncover the chemical complexity and characterize the evolution of protostellar disks.The vertical chemical structure of the disks is especially of interest as it shows the origins of different molecules with resolved layers (Sakai et al. 2017;Podio et al. 2020;Paneque-Carreño et al. 2023).Such structures with rich chemical diversities of both low-and high-mass edge-on disks have been observed in recent studies, such as the stratified molecular layers in the disk atmosphere (HH 212, Codella et al. 2018) and edge-on disks (the Flying Saucer and IRAS 04302 +2247 Dutrey et al. 2017;Ruíz-Rodríguez et al. 2021;Lin et al. 2023), as well as the salty disk of Orion Source I (Wright et al. 2020).
IRAS 04368+2557 in L1527 (hereafter referred to as L1527) is a low-mass Class 0/I protostar that has been thoroughly studied in previous works (e.g., Fuller et al. 1996;Ohashi et al. 1997;Sakai et al. 2014b;Li et al. 2017;Nakatani et al. 2020;Cacciapuoti et al. 2023).Located in one of the closest star-forming regions, the Taurus molecular cloud, the protostar presents a bolometric luminosity of 1.6−2.75L e and a bolometric temperature of 41−79 K (Kristensen et al. 2007;Tobin et al. 2008;Karska et al. 2018;Ohashi et al. 2023).It has been reported that the distance of L1527 is 131-144 pc (e.g., Torres et al. 2007;Gaia Collaboration et al. 2018;Roccatagliata et al. 2020).Here we adopt 137 pc as its distance to be consistent with other studies.This source is nearly edge on with a clear disk-envelope system (Tobin et al. 2012;Sakai et al. 2014bSakai et al. , 2017)), which enables the study of its vertical structure.High-resolution ALMA and Karl G. Jansky Very Large Array (VLA; Perley et al. 2011) observations have revealed that its ∼100 au radius scale disk, being embedded in a ∼2000 au scale infalling-rotating envelope (IRE; Ohashi et al. 2014;Oya et al. 2015;Aso et al. 2017), is flared and slightly warped (Sakai et al. 2019;Ohashi et al. 2022b;Sheehan et al. 2022).Shown in the schematic structure of L1527 adapted from previous studies (Figure 1), the inner disk is misaligned with the outer disk by ∼3°-5°, while the extended infall flows have a wider offset along the northeast-southwest stretch.
In this paper, we discuss the flared vertical structure of L1527 with observed sulfur-bearing molecules included in the ALMA large program Fifty AU Study of the Chemistry in the Disk/Envelope System of Solar-like Protostars (FAUST; Bianchi et al. 2020;Codella et al. 2021Codella et al. , 2022;;Okoda et al. 2021;Imai et al. 2022;Ohashi et al. 2022a;Vastel et al. 2022).We briefly describe the observation in Section 2 and focus on the analyses of its disk structure in Section 3. The conclusions are summarized in Section 4.

Observation
Table 1 lists the observation details for L1527 in the FAUST program (ALMA project code: 2018.1.01205.L; PI: Satoshi Yamamoto) used in this study.Observations for the two setups were conducted between 2018 November and 2019 August, centering at α(2000) = 04 h 39 m 53 87 and δ(2000) = 26 03 09.60 +  ¢  .For both setups, 13 spectral windows (spws) were configured.Molecular lines are included in the 12 narrow spws that have a spectral resolution of 122 kHz (∼0.17 km s −1 for Setup 1 and ∼0.15 km s −1 for Setup 2).The 1.3 mm continuum is extracted from the wide spws that are set to a spectral resolution of 488 kHz (∼0.63 km s −1 ) in Setup 1 and 977 kHz (∼1.19 km s −1 ) in Setup 2. Here, we focus on the emission of sulfur-bearing molecules listed in Table 2: SO, CS, 13 CS, OCS, and H 2 CS.Data calibration is performed with the Common Astronomy Software Applications (CASA; CASA Team et al. 2022) using a modified version of the ALMA calibration pipeline.The data are further renormalized with an additional in-house routine for system temperature correction, improving the dynamical range of the continuum data up to 1 order of magnitude. 25Spectral image cubes are prepared with a Briggs robustness of 0.5 through the CLEANing algorithm, while the continuum is prepared with a robustness of 2.0 to highlight the extended features around the disk.Overall, an estimated uncertainty of 10% for flux density is achieved.The 1.3 mm continuum (Setup 2) emission is shown in Figure 2.
The emission from the disk region within 100 au radius is compact, and the extended structure is associated with the protostellar envelope.Such continuum distribution is consistent with previous ALMA band 6 and 7 observations (Aso et al. 2017;Sakai et al. 2017;Ohashi et al. 2022b;Cacciapuoti et al. 2023).

Line Emission of the Observed Sulfur-bearing Molecules
Four molecular lines of sulfur-bearing molecules are detected in our observations (Table 2), and the line emissions are presented in Figure 3. SO emission is concentrated in the disk region within 100 au while being enhanced toward the west and stretched to the south.It has been previously reported that the disk of L1527 is slightly inclined ∼5°with the western side facing the observer and warped with two zones (Tobin et al. 2008;Sakai et al. 2014aSakai et al. , 2014bSakai et al. , 2019;;Oya et al. 2015;Ohashi et al. 2022b).Therefore, protostellar heating from the central star could be responsible for the east-west asymmetric intensity distribution of SO lines.CS emission is extended to the envelope, while OCS is concentrated in the center near the continuum peak.With the highest upper-state energy (110.90K), OCS mainly traces the heated gas near the central star at 30-50 au.

Kinematics
The kinematics of the disk-envelope system of L1527 has been thoroughly studied previously, and the centrifugal barrier of the IRE is determined to be ∼100 au in radius (Sakai et al. 2014a(Sakai et al. , 2014b(Sakai et al. , 2017;;Oya et al. 2022).In Figure 4, the position-velocity (PV) diagrams of SO and CS along the midplane are demonstrated.As both SO transitions show similar distributions and velocity gradients, here we only include 6 6 − 5 4 in the figure.PV slices are 0 3 in width, comparable to the beam size, and the zero-offset position is fixed to the continuum peak.Both SO and CS show clear rotation features, with CS being more extended and enhanced around 100 au.SO is concentrated inward from ∼150 to 100 au where CS emission shows a cavity.The velocity extent of SO (Δv ∼ 2.5 km s −1 ) is slightly larger than that of CS (Δv ∼ 2 km s −1 ).Such velocity gradients of CS and SO are consistent with the previous observations (Sakai et al. 2014a(Sakai et al. , 2014b;;Oya et al. 2015;Maret et al. 2020;van't Hoff et al. 2023).
A simple IRE model is overlaid in Figure 4 to analyze the motion of the envelope.Such a model is constructed with the conservation of both angular momentum and mechanical energy, describing the motion in two components: the rotation velocity v CB stands for the centrifugal velocity, r is the radius, and r CB is the centrifugal barrier radius where the infall motion cuts off (the Keplarian disk within r CB is not included in the model).The envelope is slightly inclined (i = 5°) and with a scale height of h(r)/r = 0.2 (thin disk with no z-axis dependence).The outer radius, the centrifugal barrier, and the projected centrifugal velocity (v i cos

CB
) are fitted to be 1000 au, 100 au, and 2.0 km s −1 , respectively, based on the observation of PV diagrams (also consistent with literature values; Sakai et al. 2014a;Oya et al. 2022).Molecular emission is optically thin and gas density follows a power-law profile (ρ(r) ∝ r α , α = 1.5).Although the model is simplified without the consideration of various important factors, such as hydrodynamics and magnetic field (Stahler et al. 1994;Machida et al. 2010;Zhao et al. 2016;Jones et al. 2022;Shariff et al. 2022), it has been utilized to confirm the dynamics of infalling-rotating materials in protostars Notes.
a Line information taken from the Cologne Database of Molecular Spectroscopy (Clark & De Lucia 1976;Dubrulle et al.1980;Müller et al. 2001Müller et al. , 2005Müller et al. , 2019;;Gottlieb et al. 2003;Endres et al. 2016).b Not detected.previously and proven to be sufficient (Sakai et al. 2014b(Sakai et al. , 2016;;Oya et al. 2016Oya et al. , 2022;;Zhang et al. 2019Zhang et al. , 2023)).The reasonable agreement of CS emission with the IRE model suggests that CS mainly traces the 1000 au scale envelope and enhances around the 100 au scale centrifugal barrier, while SO exists inwards from ∼100 au (suggesting strong chemical effects at the centrifugal barrier; Sakai et al. 2014aSakai et al. , 2014bSakai et al. , 2017)).
Figure Integrated maps of observed sulfur-bearing molecules in both color scale and contours.Continuum peak is marked with a white cross as a reference.The integrated velocity range is 0.9-10.9km s −1 .The two SO transitions and CS are masked below 3σ, while OCS is masked below 1.5σ (σ values are listed in Table 2).
The increments for SO, OCS, and CS are 3σ, 0.5σ, 1σ, respectively.To estimate the temperature across the disk-envelope system, we derived rotation temperature with the two observed SO lines.The derivation, assuming the LTE and optically thin conditions, is shown in Equations (1) and (2), with k being the Boltzmann constant, ν being frequency, W being intensity, h being the Planck constant, c being the speed of light, and A being the Einstein A coefficient (Goldsmith & Langer 1999).SO J N = 6 5 − 5 4 and J N = 6 6 − 5 6 transitions are denoted by 1 and 2, respectively: For both of the SO lines, the emission intensity is masked under 3σ.The rotation temperature profile in Figure 5 shows a flared "butterfly" structure along the midplane within ∼100 au, with the highest rotation temperature being ∼49.4 K.Note that the uncertainty for detected SO emission in the disk region is <10%; hence, the rotation temperature could suffer from an absolute uncertainty up to ∼14%, and the relative uncertainty in different positions should be smaller.The temperature profile is roughly symmetric with respect to the east-west direction and the "wings" on the east are slightly wider due to disk inclination.Asymmetric enhancement of rotation temperature is seen along the northeast-to-southwest stretch.Along the midplane, there are three low-temperature cavities: two inwards from the centrifugal barrier at ∼50-100 au and one around the center.The continuum peak coincides with the central lowtemperature "hollow" region (∼30-50 au), which indicates that such a temperature distribution is not a result of thermal/ radiation heating from the central star.The "flared" temperature structure is further discussed in Section 3.3.3.

Column Density
In Table 3, we summarize the observed intensities and the derived column densities of observed sulfur-bearing molecules (upper limits are listed for nondetection).For three regions (envelope, centrifugal barrier, and disk), the flux density is evaluated over a circular area centered at the offset location along the midplane with a radius of 50 au.The integrated intensities obtained from moment-zero maps are referred to as "total," and the velocity range is 0.9-10.9km s −1 .The emissions with the velocity-shift ranges of −1.5 to −5 km s −1 and 1.5 to 5 km s −1 are listed as blue-and redshifted (also see Figure 7).Molecules are considered as detected with emissions over 3σ, while intensities around 1.5σ are given as references.Column densities are derived with the non-local thermal equilibrium (NLTE) code RADEX (van der Tak et al. 2007) by minimizing χ 2 over a temperature range of 20-140 K and H 2 density range of 10 6 -10 10 cm −3 , which are typical for low-mass star-forming regions (references for collisional data are listed in Table 2).Overall, SO is more concentrated in the disk, and CS is enhanced around the centrifugal barrier.
With the high spatial resolution of the FAUST survey, molecular emission could be partially resolved, resulting in lower integrated flux density than reported in Sakai et al. (2014a).The largest angular scale is ∼4 6-5 2 for our observations and ∼6 6 in Sakai et al. (2014a).Therefore, column densities could be partially underestimated in this study due to the missing flux beyond ∼630 au.Nonetheless, we compare the blue-and redshifted components with the total molecular abundances in Table 4. High-velocity SO abundance (−1.5 to −5 km s −1 and 1.5 to 5 km s −1 ) increases by ∼10%-20% from the centrifugal barrier to the disk, while highvelocity CS shows a small decrease in abundance only at the blueshifted.Although the ratios suffer from considerable uncertainties, such ratio trends hint that SO could be a better tracer for the activities in the disk (within ∼100 au).

Nature of the Disk Temperature Profile
It is generally considered that gas in the disk is heated by either radiation from the protostar or viscous accretion, both of which would predict a power-law disk temperature profile (T ∝ r −3/7 and T ∝ r −1/2 for radiation heating, T ∝ r −9/10 for viscous heating; Shakura & Sunyaev 1973;Chiang & Goldreich 1997;Chiang et al. 2001;Baumann & Bitsch 2020).The disk temperature of L1527 has been analyzed comprehensively in Ohashi et al. (2022b) with much higher angular-resolution dust-continuum data from both ALMA and VLA.The temperature is found to be determined by radiation heating within ∼20 au, while it drops steeply in the outer region due to the shadowing effect.In Figure 6, we overlay the power-law temperature structure from an irradiation model (Ohashi et al. 2022b; similar structures would be also predicted by viscous accretion models) on the SO rotation temperature profile.The modeled higher-temperature center (>25 K) coincides with the central "hollow"-showing that the "butterfly" is not induced by radiation or viscous accretion.Moreover, the central low rotation temperature region is ∼30-50 au in radius, consistent with the radius of the inner disk (∼40-60 au) of the warped structure, which is suggested by Sakai et al. (2019).Such a correlation might indicate that the central region is radiation dominated, making the LTE temperature estimation invalid.The vertically symmetric low-temperature regions (∼50-100 au) along the midplane near the centrifugal barrier are heated by vigorous accretion shocks, also unfit for the LTE estimation.With the derived disk column density (1.2 × 10 13 cm −2 ), the optical depth for SO J N = 6 5 − 5 4 and J N = 6 6 − 5 6 are estimated to be 4.2 × 10 −4 -7.8 × 10 −3 and 4.1 × 10 −4 -3.1 × 10 −3 , respectively, over the temperature range of 20-140 K and H 2 density range of 10 6 -10 10 cm −3 .Therefore, the rotation temperature profile is not a result of optical effect.Previously, "X-shape" molecular emission, such as CS and H 2 CO, were observed in other edge-on disks (Podio et al. 2020;Villenave et al. 2022), tracing the warm molecular layer at disk height.The angles between the disk midplane and molecular-emitting layer of these sources-IRAS 04302+2247 and Oph 163131-are ∼30°.Meanwhile, the angle of the temperature profile in this work is measured to be much wider -∼50°-further eliminating the possibility of heating from the penetration of inner stellar radiation typically seen in the flattened disks of class I/II sources.
The distributions of the detected sulfur-bearing molecules are overlaid with the rotation temperature profile in Figure 7 as references.The temperature profile shows high correlation with the outer-disk velocity components of SO (Δv = 1.5-1.8km s −1 , Figures 7(B), (C)) and no correlation with moment-zero maps (Figures 7(A), (D)), indicating that the heating is indeed dynamically originated from the outer disk.The anisotropic accretion onto the misaligned outer disk heats up the gas with minor shocks.Previous studies (e.g., van't Hoff et al. 2023) also suggest that SO mainly exists in the outer disk, or the disk surface layer, consistent with our conclusion.The higher-velocity components of SO (Δv = 1.8-5.0km s −1 ), which corresponds to the inner disk at 30-50 au, shows Notes.
a Offset is defined with respect to continuum peak.b Intensity is obtained by integrating over a circular area centered at the offset location along the midplane with a radius of 0 365 (50 au).Uncertainty is labeled in parentheses in the unit of the last digit.c Column densities are derived by minimizing the χ 2 value over a range of temperature and density.The upper limits for the column densities of 13 CS and H 2 CS are 6.5 × 10 11 cm −2 and 2.4 × 10 12 cm −2 , respectively.Note.
a Uncertainty is labeled in parentheses in the unit of the last digit.emission from the innermost part while stretched along the northeast-southwest direction.Such a distribution of highvelocity SO also suggests that the low-temperature "hollow" is not due to the high opacity of the dust-continuum emission.
Considering SO mainly exists in the outer disk, the inner higher-velocity components could be delivered from the outer disk and heated by protostellar heating (30 K is comparable with the model prediction shown in Figure 6), suffering from NLTE effects.Both the rotation temperature and the highvelocity SO are enhanced along the northeast-southwest infall stretch (Figure 1).CS, which traces the envelope, is concentrated in the symmetric cavities along the midplane.The OCS emission is slightly offset along the northeast high-temperature stretch of the profile.OCS could be originated either via gas-phase/ surface reactions or from ice mantles (Charnley 1997;Charnley et al. 2004).Experimental studies have also suggested that photon or electron irradiation is essential for OCS formation (Ferrante et al. 2008;Maity & Kaiser 2013;Chen et al. 2015).Therefore, the offset location of OCS, closer to the protostar, may imply the necessity of such irradiation.Moreover, the enhancement of OCS, with the highest binding energy (2325 ± 95 K, desorbed at 78 K; Penteado et al. 2017) among the three molecules, could possibly be a temperature effect from having hotter dust closer to the protostar (Charnley et al. 2001).
Previously, the disk temperature has been probed with muchhigher-resolution continuum observations (e.g., Ohashi et al. 2022b;van't Hoff et al. 2023).The flared temperature profile in this work has demonstrated that representative molecular emission could be effective diagnostics for the disk temperature with moderate spatial resolutions.Although the current results are satisfactory, it is recognized that a more accurate estimation of temperature could be obtained with multiple SO transitions from a wider energy range, other temperature tracing molecular species (e.g., CO minor isotopologues), and NLTE analysis; thus, our analysis is still limited.

Conclusion
With the observed sulfur-bearing molecules included in the FAUST program, we analyze the flared disk in the class 0/I protostar IRAS 04368+2557 in L1527.The molecular distributions and the kinematics both show that CS, SO, and OCS trace different regions of the disk-envelope system, such as the IRE and the disk.OCS is concentrated near the protostar, hinting high stellar radiation.Physical properties, such as temperature and column density, of different regions of the source are derived and compared.In particular, a clear, flared "butterfly" structure in the disk is revealed with SO rotation temperature, suggesting weak accretion shocks heating at the outer disk rather than irradiation/viscous accretion.Our analyses have further confirmed the "warped" disk structure of L1527 and disentangled the inner/outer disks with the rotation temperature profile.Sulfur-bearing molecules are effective diagnostics of the physical properties of protostellar materials, and our finding has demonstrated their sufficiency in structural studies with moderate spatial resolutions.D), (E), and (F): rotation temperature profile with moment-zero maps overlaid as white contours; the integrated velocity range is 0.9-10.9km s −1 .Two SO lines and CS are masked below 3σ, while OCS is masked below 1.5σ.The increments for SO, OCS, and CS are 3σ, 0.5σ, 1σ, respectively.(B) and (C): rotation temperature profile with SO velocity maps overlaid.The contours are in 3σ increments, starting from 6σ.

Figure 2 .
Figure 2. The 1.3 mm continuum of L1527 in both color scale and contours.Contour levels are as marked.The beam size is ∼0 38 × 0 26, and 1σ is 0.065 mJy beam −1 .

Figure 4 .
Figure 4. PV diagrams of CS and SO.IRE model is overlaid as contours with 20% peak intensity increments.The envelope inclination is set as 5°.System velocity and center position are marked with white dashed lines, while 100 au in radius is marked with gray dashed lines.

Figure 6 .
Figure 6.Color scale: rotation temperature profile derived from the two observed SO transitions (SO emission from both transitions is masked below 3σ).The modeled temperature structure due to protostellar heating is overlaid as white contours (Ohashi et al. 2023).

Figure 7 .
Figure 7. (A), (D), (E), and (F): rotation temperature profile with moment-zero maps overlaid as white contours; the integrated velocity range is 0.9-10.9km s −1 .Two SO lines and CS are masked below 3σ, while OCS is masked below 1.5σ.The increments for SO, OCS, and CS are 3σ, 0.5σ, 1σ, respectively.(B) and (C): rotation temperature profile with SO velocity maps overlaid.The contours are in 3σ increments, starting from 6σ.

Table 2
Line List a

Table 3
Observed Intensities and Physical Properties

Table 4
Column Density Ratios a N Blue /N Total N Red /N Total N Blue /N Total N Red /N