Exploring the dust grain size and polarization mechanism in the hot and massive Class 0 disk IRAS 16293-2422 B

Multiwavelength dust continuum and polarization observations arising from self-scattering have been used to investigate grain sizes in young disks. However, the polarization by self-scattering is low in face-on optically thick disks and puts some of the size constraints from polarization on hold, particularly for the younger and more massive disks. The 1.3 mm emission detected toward the hot ($\gtrsim$400 K) Class 0 disk IRAS 16293-2422 B has been attributed to self-scattering, predicting grain sizes between 200-2000 $\mu$m. We investigate the effects of grain size in the resultant flux and polarization fractions from self-scattering using a hot and massive Class 0 disk model and compare with observations. We compared new and archival high-resolution observations between 1.3 and 18 mm to a set of synthetic models. We have developed a new public tool to automate this process called Synthesizer. This is an easy-to-use program to generate synthetic observations from numerical simulations. Optical depths are in the range of 130 to 2 from 1.3 to 18 mm, respectively. Predictions from significant grain growth populations, including millimetric grains are comparable to the observations at all wavelengths. The polarization fraction produced by self-scattering reaches a maximum of $\sim$0.1% at 1.3 mm for a maximum grain size of 100 $\mu$m, being an order of magnitude lower than that observed with ALMA. From the comparison of Stokes I fluxes, we conclude that significant grain growth could be present in the young Class 0 disk IRAS 16293 B, particularly in the inner hot region ($<10$ au, $T>$ 300 K) where refractory organics evaporate. The polarization produced by self-scattering in our model is not high enough to explain the observations at 1.3 and 7 mm, and effects like dichroic extinction or polarization reversal of elongated aligned grains remain other possible but untested scenarios.


Introduction
Circumstellar disks, the sites of planet formation, are relatively well-studied in the more evolved Class II stage.However, in the earliest Class 0 phase, protostellar disks have only recently begun to be studied in detail (e.g., Maury et al. 2019;Segura-Cox et al. 2018;Tychoniec et al. 2020;Zamponi et al. 2021), and many of their properties such as mass, temperature and dust properties remain unknown, or highly debated.Since Class 0 protostellar disks set the initial conditions for planet formation, which could be underway already in the Class I phase (Sheehan & Eisner 2018;Segura-Cox et al. 2020), constraining the sizes of dust grains in disks at the earliest time possible is critical.This is usually done by constraining the variations of the spectral index at millimeter wavelengths, which can be related to the dust opacity index (Testi et al. 2014).In addition, polarization observations have proven to be a useful independent method to constrain the grain sizes in disks.This can be done if the origin of the polarized emission is self-scattering (Lazarian & Hoang 2007a,b;Kataoka et al. 2015;Andersson et al. 2015;Tazaki et al. ⋆ NSF Astronomy and Astrophysics Postdoctoral Fellow 2017).Self-scattering refers to the polarization of the dust thermal emission scattered by the dust itself, and produces emission polarized to a few percent, at millimeter wavelengths for grain sizes in the micro-and millimeter range (Kataoka et al. 2017).The amount of polarization depends on the level of anisotropy of the radiation field generated by the self-scattered photons of the dust emission, which in turns depends on the inclination of the disk and the size of the scattering dust particles (Yang et al. 2016).The relation between the size of the dust grains and the maximum polarization fraction turns this polarized emission into a tool to estimate the level of grain growth at different evolution stages.
In the more evolved (Class II) protoplanetary disks, optical and near-infrared observations of scattered flux usually trace the emission from small dust grains that scatter off the protostellar flux in the upper layers of the disk (Avenhaus et al. 2018;Garufi et al. 2018Garufi et al. , 2019Garufi et al. , 2020)).At millimeter wavelengths, the observed dust scattered emission is mainly originated from the dust thermal emission (Kataoka et al. 2015;Yang et al. 2016).
tions by dust self-scattering at millimeter wavelenghts.We use a model produced by a radiation-hydrodynamic (RHD) numerical simulation of core collapse.The disk formed is massive (∼0.3 M ⊙ ), hot (>300 K, within 10 au), and optically thick at millimeter wavelenths.This disk model successfully reproduced Stokes I fluxes from ALMA ∼6-10 au resolution observations, at 1.3 mm and 3 mm, for the very young Class 0 disk IRAS 16293 B (Zamponi et al. 2021).Thus we also aim to test whether we can reproduce the fluxes and levels of polarization fraction observed in this source when the polarization is produced by self-scattering of spherical grains in the Mie regime.We expand on our previous exploration on grain sizes in this young disk (Zamponi et al. 2021) by showing the effects of varying the maximum grain size (a max ) in the model from 10 µm to 1000 µm.Furthermore, as the disk is hot enough to evaporate solid organics, we show the effects of evaporating water and potentially some organics within the so-called sootline and having grain growth within this region, motivated by recent laboratory (Gundlach et al. 2018;Pillich et al. 2021) and observational (Liu et al. 2021) results.
IRAS 16293-2422 B is a well studied Class 0 protostar located in the star-forming region ρ-Ophiuchi, and it is one of the closest and brightest protostars at a distance of 141 pc (Dzib et al. 2018).The disk around the protostar is hot (T b ≳ 400 K) and massive, and likely subject to gravitational instabilities, as initially proposed by Rodríguez et al. (2005) and Dipierro et al. (2014), and recently confirmed by Zamponi et al. (2021).The source is very young (<10 4 yr, Andre et al. 1993) and its water snow line extends over a 20 au radius (Zamponi et al. 2021), making it an ideal laboratory to test the scenario proposed by recent laboratory experiments (Gundlach et al. 2018;Pillich et al. 2021;Li et al. 2021), that grain growth is boosted in dry conditions.The disk mass estimated by Zamponi et al. (2021) is 0.003 M ⊙ in solid material, which would be 33 times higher than the minimum mass solar nebula of 30M ⊕ (in solids; Weidenschilling 1977;Andrews 2020).This implies that IRAS 16293B contains enough mass to form super-Earth planetesimals.Because of all these conditions, IRAS 16293B represents one of the ideal sites to probe grain growth at the earliest stages.
In the younger Class 0 disks, although polarization by selfscattering at millimeter wavelengths have also been proposed (e.g., Sadavoy et al. 2018;Tsukamoto et al. 2022), studies simulating the feasibility of this mechanism in more realistic young disk models, such as those formed out of the collapse of a core using 3D numerical simulations have not been done.This is particularly important since the physical properties of deeply embedded disks appear different in numerical simulations (e.g., Zamponi et al. 2021;Xu & Kunz 2021a,b;Bate 2022) as compared to widely used analytical models for Class II disks (Ballering & Eisner 2019).
In IRAS 16293-2422 B, polarized light was initially observed by Rao et al. (2009Rao et al. ( , 2014) ) with the SMA at 0.87 µm, who detected polarization fractions of around ∼1.4%, distributed mostly azimuthally around the protostar location.The resolution of this detection was 0.6" (85 au) and likely traced envelope scales, which correspond to the bridge structure connecting the northern and southern protostars (Jørgensen et al. 2016;Maureira et al. 2020).Additional observations were presented by Liu et al. (2018) with the VLA at 7 mm, and a 1.5 times better resolution.These observations resolved down to 50 au and found a similar polarization pattern and fraction (≲2%).More recently, the survey of 1.3 mm polarization observations toward Class 0 protostars in ρ-Ophiucus, carried out by Sadavoy et al. (2019) at a 2 times better resolution (0.2"; 30 au), found polarization signatures associated to self-scattering in inner regions of most of their sources.The polarization in the disk of IRAS 16293 B was found to be azimuthal, similar to the SMA and VLA observations, however the authors associated the vector distribution to polarized self-scattering from an optically thick face-on disk, based on the models from Yang et al. (2017).The connection of a similar polarization pattern between 1.3 mm and 7 mm, being produced by self-scattering, implies that grains can have sizes between 200-2000 µm.In this work, we use a disk model from numerical simulations to test this hypothesis.
This paper is structured as follows: in section 2 we provide details on the archival and new observational data used in this work, in section 3 we describe the dust model and polarization scheme used for the radiative transfer analysis, in section 4 we present the results of the assessment of grains sizes through the stokes I fluxes and our self-scattering models, in section 5 we discuss grain growth and possible mechanisms responsible for the observed polarization and other scenarios, and finally, in section 6 we present the conclusions of this work.

ALMA & VLA archival data
We have compiled archival multiwavelength polarization observations of IRAS 16293-2422 B at 1.3 mm (ALMA Band 6), 3 mm (ALMA Band 3) and 7 mm (JVLA Band Q).The 1.3 mm data used in this work is twofold.For the analysis presented in section 4.1 we used high-resolution Stokes I continuum images, with a resolution of 0.114"×0.069"and a noise level of 104 µJy beam −1 (0.3 K; see colorscale from leftmost panel in Fig. 1).For the analysis of polarized data, we used publicly available Stokes I, Q and U images by Sadavoy et al. (2018), each with a resolution of 0.18"×0.09"and a noise level of 280 µJy beam −1 (0.4 K), 25 µJy beam −1 and 25 µJy beam −1 , respectively.Band 6 polarization vectors shown in Fig. 1 have been masked in regions were the stokes I flux is lower than 3σ I and the polarized intensity is lower than 3σ Q .The 3 mm data we used is only available in stokes I, but presented the highest resolution image of IRAS 16293 B currently available, with a beam size of 0.048"×0.046"and a noise level of 17 µJy beam −1 (0.95 K).The data used at 7 mm contains full polarization information, with a resolution of 0.39"×0.24"and a noise level of 35 µJy beam −1 (0.25 K).Polarization vectors have been masked following the same criteria as for Band 6 observations.We refer the reader to Zamponi et al. (2021) for more information about the high-resolution ALMA observations at bands 6 and 3 as well as their calibration and imaging.Similarly, we refer to Liu et al. (2018) for the details on the observations, calibration and imaging of the polarized data at the JVLA band Q.
For the band Ku observations, the absolute flux/passband and complex gain calibrators were 3C286 and J1625-2527.The projected baseline range is ∼1.15-36.50kilometers.We manually followed the standard data calibration strategy using CASA (release 5.6.2).We utilized the built-in image model for 3C286 during the calibrations.After implementing the antenna position corrections, weather information, gain-elevation curve, and opacity model, we bootstrapped delay fitting and passband calibrations, and then performed complex gain calibration.We applied the absolute flux reference to our complex gain solutions, and then applied all derived solution tables to the target source.Finally, we based our observations on 3C286 to solve the crosshand delay and absolute polarization position angles, and took J2355+4950 as a low polarization percentage calibrator when solving the leakage term (i.e., the D-term).We performed the zeroth order (i.e., nterm=1) multifrequency synthesis imaging.The Briggs Robust=0 weighted image achieved a noise level of 47 µJy beam −1 and a 0 ′′ .23×0′′ .094(P.A.=5.2 • ) synthesized beam.
Finally, since all the observations shown in Fig. 1 have been taken at different times, we have been corrected the images for the proper motion of the source calculated based on previous observations with the VLA (Hernández-Gómez et al. 2019) and the 3 mm observations presented here.The applied correction is RA: −11.8 ± 0.3 mas/yr and DEC: −19.7 ± 1.3 mas/yr.We have aligned the observations to the observing time of the most recent band Ka observation (2022/03/07).

Protostellar disk model
For comparison with the observations of the IRAS 16293-2422 B disk, we use a numerical simulation of the collapse of a prestellar core which results in a hot and gravitationally unstable protostellar disk.This simulation has been presented in Zamponi et al. (2021) and the resultant density and temperature structure is also shown in Fig. 2. In Zamponi et al. (2021) we showed that this disk can successfully reproduce both the 1.3 and 3 mm observed fluxes and the spectral index between both bands.This implies producing high brightness temperatures (e.g., T 3mm b ≳ 400 K at the peak) to match those from IRAS 16293B observed with ALMA.The disk is obtained from a simulation snapshot at a stage 18.2 kyr after the collapse of a 1 M ⊙ spherical and isothermal cloud, simulated using the smoothedparticle-hydrodynamics (SPH) code sphNG (Bate et al. 1995).This simulation setup included a radiation transport scheme.This helps to more accurately reproduce the cooling and heating source terms along its temporal evolution and to deliver more realistic gas temperature distributions.The mass in the disk at this point is ∼0.3 M ⊙ .The gas temperature is ≳300 K within the central 10 au and decreases to ∼200 K at the scales where two roughly symmetric spiral arms have formed (10-30 au; see Fig. 2).
To generate the radiative transfer model, we have set the dust temperature to be equal to the gas temperature from the RHD simulation.This is justified because of the high densities found within the disk, that allow the dust to be dynamically and thermally coupled with the gas (see also Zamponi et al. 2021).We assume a homogeneous gas to dust density ratio of 100.We have used the RADMC3D radiative transfer code (Dullemond et al. 2012) with a regular cartesian grid, generated by interpolating all particle positions.The particle interpolation and gridding was done with our newly developed tool, called Synthesizer (see section 3.2), which automates the generation and execution of radiative transfer models from numerical simulations.The resulting dynamic range and spatial distribution of the gas density and temperature between our gridding scheme and that from Zamponi et al. (2021) are in very good agreement.The former gridding scheme used in Zamponi et al. (2021) consisted on a Voronoi tessellation of the particle locations which was supported in POLARIS (Reissl et al. 2016), but it is not yet fully supported in RADMC3D (beta feature).

The Synthesizer: from simulations to synthetic observations
In order to automate the comparison of observational data and simulation outputs, we have developed a new tool called Synthesizer, which we have made publicly available 1 in the form of a python package2 .Synthesizer is a program to calculate synthetic images from either an analytical model or numerical simulations directly from the command-line.For SPH simulations, it interpolates the particle positions into a rectangular cartesian grid and then uses RADMC3D to do the Monte-Carlo and raytracing.Then it feeds the output image to CASA to generate a final synthetic observation.Support for polarization models, either by scattering or grain alignment, is also included.Additionally, the Synthesizer includes a module called the DustMixer.This is a tool to generate dust opacity tables and full scattering matrices from the optical constants of a given material, all from the command-line.DustMixer also allows to experiment with the mixing of different materials and different grain sizes.For further information about this dust module, see appendix A.

Grain sizes
In this work we have used a dust model similar to that used by Zamponi et al. (2021), corresponding to spherical grains with a minimum size of 0.1 µm.This lower end of the size distribution is chosen based on the prediction for removal of very small grains during the stage of protostellar disk formation (Zhao et al. 2018;Silsbee et al. 2020).In this work we explore maximum grain sizes in IRAS 16293B by showing the effect of a max on the resultant simulated fluxes.In Zamponi et al. (2021) we modeled the emission of IRAS16293B using a dust population with a max = 10µm only, which successfully reproduced the observed brightness temperatures.The millimeter scattering opacities in that case are negligible (see Fig. 3).The results in Zamponi et al. (2021)   The angular resolution of the observations are: 0.114"×0.069"at 1.3 mm (0.18"×0.09" for polarized data), 0.048"×0.046"at 3 mm, 0.39"×0.24"at 7 mm, 0.12"×0.05"at 9 mm and 0.23"×0.09"at 18 mm.the need for larger grains in which the scattering opacities are important.The reason for this was that the resultant disk from the numerical simulation is both hot toward the inner layers and optically thick at millimeter wavelengths, both necessary conditions to recover the low observed alpha (see Figure 9 in Zamponi et al. 2021).Here we extend the analysis by considering distributions with a max = 10, 100 & 1000 µm, and compare the resulting images to the observations presented in Fig. 1 (see section 4.1).
The dust opacities computed for different models are presented in Fig. 3 (silicates + graphites and silicates + graphites + organics).The figure shows three panels, one for each maximum grain size, and tabulated in Table 1 for the 4 observing wavelengths from Fig. 1.For each a max , three different linestyles represent absorption, scattering and extinction opacities for a given composition (colored lines).When comparing the three panels, we can see at a glance the relation between the albedo (κ sca /κ ext ) and the maximum grain size.The wavelength regime in which λ ∼ 2πa max is also where the albedo is the highest.Because of this, the millimeter scattering opacities can vary by orders of magnitude for maximum grain sizes between 10 and 1000 µm.These differences reflect also on the level of polarized scattered flux (produced by dust self-scattering) and turn it into a proxy of grain growth (Kataoka et al. 2016a,b;Yang et al. 2016;Stephens et al. 2017;Harris et al. 2018;Sadavoy et al. 2018;Ohashi et al. 2020;Lin et al. 2021).

Composition
Our fiducial dust mixture consists of 62.5% of astronomical silicates and 37.5% of graphite (Sil:Gra curve in Fig. 3).The optical constants3 for both materials were obtained from Draine (2003a) and Draine (2003b), respectively.However, carbonbearing species in the interstellar medium may be present in many forms and shapes, and may not necessarily be all crystallized as graphite.They can also be amorphous or ring-like (as in PAHs) carbonaceous.The predominant shape of carbonaceous material in space is hard to determine (Jager et al. 1998;Zubko et al. 2004;Birnstiel et al. 2018).According to Draine (2003a), molecules with sizes larger than 0.1 µm are likely to be crystallized.This is in fact the lower end of our size distribution (see section 3.3), hence, we assume graphite as a fiducial representation of the carbon budget in our dust model.
To consider the effects of carbon evaporation, we have also considered inclusions of refractory organics (Henning & Stognienko 1996) into the carbon mixture and studied the resulting differences in the overall opacity.Refractory organics have considerably lower sublimation temperature (∼300 K, Jager et al. 1998;van 't Hoff et al. 2020;Li et al. 2021) compared to that of graphite (∼2100 K).Taking into account the lower sublima-tion temperatures of certain carbonaceous materials is important because they decrease the dust mass in hot regions and results in an overall decrease in the dust opacity.This sublimation zone within which the amount of carbon in the grains is reduced, also called "soot-line" (Kress et al. 2010;van 't Hoff et al. 2020), is likely to be present in IRAS 16293B at a radius of ∼10 au, based on the high (T b ≳ 400 K) brightness temperatures observed (see Fig. 1).The spatial extension of this region in the simulated disk is illustrated by the white contour in the edge-on temperature projection in Fig. 2 which extends radially up to ∼10 au and vertically to ∼8 au.
The difference between opacities with and without organics can be seen in Fig. 3.In the two compositions with carbon, the total carbon fraction of 37.5% is kept constant.For the one including refractory organics, we replaced 50% of the graphite by refractory organics, meaning, both have mass fractions of 18.75%.At millimeter wavelengths, the opacity of a dust population with a max of 10 or 100 µm is largely dominated by graphite instead of silicate.When we compare the two different compositions, i.e., silicates-graphites versus silicates-graphites-organics, we see that a mixture with inclusions of organics has a lower opacity than a purely graphitic material.This is because the opacity of pure graphite is larger than that of pure organics and including organics into the mixture implies a partial removal of graphite, since our carbon budget is maintained constant 4 .When considering organics evaporation in our radiative transfer calculation we change the dust compositions accordingly.In regions where T dust < 300 K, the dust is a mixture of silicates, graphites and refractory organics, whereas in regions where T dust ≥ 300 K (∼10 au radius), we removed the organics from the mixture to mimic the sublimation of carbon and locally scaled down the dust-to-gas mass ratio by the corresponding mass-loss factor.Within the soot-line, the organics get sublimated and removed from the dust grains.This produces a reduction of the dust mass and opacity which results in a reduction of the optical depth.
Two major features can be concluded from Fig. 3: (I) for every a max the difference in opacity between both compositions is very small, and (II) in the regime where λ ∼ 2πa max , i.e., where the albedo is maximum (Mie regime), the dust opacity is highly insensitive to variations in the dust composition.This means that observations of polarized emission produced by scattering can serve as a tool to constrain grain sizes but not compositions.The small differences we find for different compositions are associated with the resulting extinction opacity and not with the polarization pattern or fraction.We acknowledge that in some cases, variations in the scattering polarization patterns can indeed be produced by different dust compositions, as it is shown by Yang & Li (2020).Their works show that compositions like those from Kataoka et al. (2015) or Yang et al. (2016) can produce polarization reversal (i.e., 90 degrees rotation of the vector angles) when elongated millimetric grains are present.

Polarization by dust self-scattering
We have performed radiative transfer calculations in all four Stokes components (I, Q, U, V) using the radiative transfer code RADMC3D (Dullemond et al. 2012) via the Synthesizer.To 4 We acknowledge that the presence of refractory organics in the icy mantles of dust grains should in principle not affect the content of core carbon (i.e., graphite) and that a proper sublimation model should evaporate the refractory carbon without affecting the graphitic core.However, the nature of the mixing process in our setup (see section 3.2), forces us to reduce the mass fractions of some materials to account for the inclusion of new others, while keeping the dust mass constant.model the Stokes I fluxes produced, we raytraced the dust thermal emission along the line-of-sight and included the emission scattered by the dust grains, both from stellar and dust thermal radiation.The dominant source of scattering at millimeter wavelengths is the scattered dust thermal emission, namely, selfscattering (Kataoka et al. 2015).Scattering of light in dusty media is commonly modeled as a stochastic process of absorption and re-emission of light (Bjorkman & Wood 2001) by means of a Monte-Carlo (MC) simulation (Steinacker et al. 2013).The scattering event is modeled as the re-emission of an absorbed photon in a new random direction.The likelihood for a given direction is not isotropically distributed, but rather follows the commonly used phase function from Henyey & Greenstein (1941).However, this kind of scattering model considers only information about the light intensity and not of the polarization state, i.e, stokes I only flux, without stokes Q and U. To calculate polarized flux, the scattering process has to be represented by a matrix rotation of all four Stokes components.This process is also called full Mie scattering (Mie 1908;Bohren & Huffman 1983;Wolf & Voshchinnikov 2004) and is significantly more computationally expensive than the case for the Stokes I only.To ensure both approaches (i.e., Stokes I only and Full Mie) deliver similar Stokes I fluxes, we tested the convergence of the scattering Monte-Carlo.The convergence was reached at about 10 10 photons.
The information associated with linear polarization of light is stored in the Q and U components of the Stokes vector.We estimate the total linearly polarized intensity PI, polarization degree P frac and polarization angle P angle as (1) and respectively.

Synthetic observations
We post-processed the output from the radiative transfer with a series of synthetic observations, using the observing setups of the ALMA and VLA observations shown in Fig. 1.This step was performed using the Synthesizer (see section 3.2).Synthesizer uses the CASA (v5.6.2) software and its simobserve and tclean tasks to produce a synthetic image from a model image, created by the output of RADMC3D.The CASA scripts for the setup at every band are available within the Synthesizer public repository5 .All synthetic maps include the thermal noise associated to the corresponding observing setup (time, bandwidth, cycle, etc.), and lead to noise levels comparable to the real observations.In regions of the images where Q and U are not well detected, equation (1) leads to a positive bias in the polarized intensity that must be removed (Simmons & Stewart 1985;Vaillancourt 2006).The polarized intensity must be then debiased by taking into consideration the thermal noise in the polarization map σ PI as where we assume that σ Q ∼ σ U ∼ σ PI (Vaillancourt 2006).
When producing maps of polarized emission and polarization vectors from synthetic observations, we mask out the vectors at locations where I/σ I < 3 and PI/σ PI < 3, same as we did for the real observations in Fig. 1.

Effects of different maximum grain sizes on the Stokes I fluxes
We At each wavelength, the flux decreases with increasing a max .This is because all the models are optically thick (see Fig. 5), and the larger the a max the higher the optical depth.This effect, along with the decreasing temperature as a function of the scale height, leads to colder dust temperatures being traced by the larger a max .For a max = 100 µm and 1000µm, the fluxes are further lowered from the dust temperature of the τ = 1 layer due to a significant albedo (Birnstiel et al. 2018).This also explain why for a given a max , the peak fluxes increase with wavelength as longer wavelength penetrate further within the disk where the temperatures are higher.We note that at 18 mm both the observed models and observations are affected by beam dilution.The net fluxes from both a max = 10 and 100 µm are similar because they are completely determined by the extinction optical depth, which is similar between these two models (see Fig. 5).The difference between these two models lies on the albedo, which is higher for a max = 100 µm.
When comparing our models to the observations (black profile in Fig. 4), a similar trend is seen.This is a feature of a optically thick disks with a positive temperature gradient toward the center.In this central regions, the observed Class 0 disk fluxes lie between the models with a max = 100 µm and 1000 µm, with differences between the observations and models within a factor of up to 2. On the outskirts, most models tend to overpredict fluxes up to a factor of 2 toward negative offsets and a factor of several for positive offsets.This east-west difference is because our disk model does not have such a marked east-west asymmetry as the one observed in IRAS 16293 B (see Fig. 1).Scenarios that can explain the observed asymmetry like the presence of asymmetric spiral arms or an off-center protostar were discussed in Zamponi et al. (2021).The comparison between models and observations suggest that grains could have grown significantly in this young Class 0 disk even up to millimeter grain sizes, provided that the vertical gradients of temperature and density are close to those in IRAS 16293 B.

Effect of carbon sublimation within the soot line
Because the observed brightness temperatures and model dust temperatures are high (≳ 400 K), it might be that some of the dust material gets evaporated at these early stages.Silicate sublimation temperature is around 1200 K, and for graphite it is 2100 K.Both well above the central disk temperatures.However, carbon can also exist in nongraphitic forms, like amorphous carbon or Polyciclyc Aromatic Hydrocarbons (PAHs) within ice layers.
To study the scenario of dust containing refractory carbon that can sublimate at the observed disk temperatures, we also produced synthetic observations with a dust model that includes amorphous carbon.For this we use the optical constants from amorphous carbon (CHON) from Henning & Stognienko (1996) and set a sublimation temperature of 300 K.This temperature is based on the analysis presented by Li et al. (2021) who estimate a temperature range between 200 and 650 K from meteoritic constraints.This range was further narrowed to 300 K by van 't Hoff et al. (2020) after analyzing the relation between sublimation, gas temperature and pressure at hot-core conditions.The thermodynamic relations they used were derived from PAHs characterized in the lab (Goldfarb & Suuberg 2008;Siddiqi et al. 2009).In our disk model, the soot-line at 300 K covers the inner 10 au in radius and ∼ 8 au in scale height (see Fig. 2).The extension of this region is also shown with a black scalebar at the bottom of Fig. 4. Details on the dust composition and radiative transfer setup for the inclusion of amorphous carbon are given in section 3.4.
The resulting brightness temperature profiles for the case with carbon sublimation are also shown in Fig. 4 in the form of dashed lines.In the sublimation case the grain size remains homogeneous but the composition does not.Outside of the sootline, grains are composed by silicate, graphite and refractory organics (opacity given by the purple line of Fig. 3).Inside the sootline, amorphous carbon is removed and the composition is the fiducial silicate and graphite mixture (turquoise line in Fig. 3), however, with a dust mass reduced by the factor of material sublimated.In Fig. 4 the dashed lines show the the case of 80% organics, meaning a dust composition whose carbon budget was split between 20% of graphite and 80% of amorphous carbon, while keeping the total carbon budget constant at 37.5%, i.e., with mass fractions of 0.675, 0.300 and 0.075 for silicate, graphite and amorphous carbon, respectively.We tried different percentages for organics but we show here only the one with the most significant differences from our fiducial composition.
The fluxes produced by sublimated grains are not significantly different to those without sublimation, regardless of the size and wavelength or particular amount of organics.As discussed in section 3.4, the sublimation has the effect of lowering the optical depth because of the mass reduction and the change in composition.This results in observed emission being produced by a slightly inner and hotter parcel of the disk, which leads to slightly higher fluxes toward the center than the fiducial model without organics evaporation.The difference in flux in the central region between models with and without evaporation is larger for the wavelenghts with higher resolution observations.
Our results indicate that detecting dust sublimation with continuum observations at a particular wavelength, even with very high-resolution, is challenging.Future observations that can obtain molecular line emission from this region, can probe whether an active carbon-rich chemistry exists or not in this source (van 't Hoff et al. 2020), providing independent robust constraints on the scenario of a sootline of about 10 au within this Class 0 disk.

Variation of the spectral index
Another observable piece of comparison between observations and models is the spectral index α produced between 1.3 and 3 mm, for which there are higher resolution and deeper observations available.We computed the spectral index between 1.3 and 3 mm for all a max models and for several percentages of organics, 10%, 30%, 50% and 80%.We present in Fig. 6, our results for models with our fiducial composition, where carbon does not sublimate, and representative sublimation models with 50% and 80% of organics with sublimation temperatures from 300 K.
Since the disk model is optically thick at 1.3 mm and 3 mm (see Fig. 5), the values of the spectral index will depend on the vertical distribution of temperature and opacity in the disk.The models in Fig. 6 have all the same temperature gradient but the opacity changes with a max and composition leading to the observed differences.The models with higher opacities toward the center show a more extended region with α < 2.5 values.
An important feature observed in the IRAS 16293 B spectral index is that central values go as low as 1.7, this means, lower than the threshold of α = 2 (indicated by the black contour in Fig. 6) for optically thick emission, first presented in Zamponi et al. (2021).The presence and extent of this feature in our models depend on having sufficient variations of temperature along the line of sight between the layers traced by the different wavelenghts (with T 1.3mm < T 3mm ).The larger the region for which these differences are present the more prominent and widespread these feature is.In the case of 100 µm the feature is more prominent because of the higher optical depths while in the case of 1000 µm sized grains with carbon sublimation, the feature is likely present because the reduced optical depth in the inner hot region allows flux to come from a region with a larger gradient in temperature than the same models with less amount of sublimation.Although none of our models reproduce the extent of this region, models with grain growth are able to reproduce small regions showing this feature (panels with 100 µm or 1000 µm considering carbon sublimation).

Polarization by self-scattering
Polarization observations toward embedded disks have been interpreted as caused by self-scattering, similar to that observed toward more evolved Class I sources (Kataoka et al. 2016a;Stephens et al. 2017;Lin et al. 2021).This interpretation is based on the morphology of the polarization observations.In this work, we test whether the disk model we use in this work, with a physical density and temperature structure representative of a Class 0 disk, can produce the few percent (2-4%) levels of polarization fractions as observed for IRAS 16293 B as well as other Class 0/I disk observations at millimeter wavelengths (Lee et al. 2021).We do so by generating radiative transfer models of polar- ization by scattering at 1.3 and 7 mm, meant to be compared with the available high-resolution polarization data shown in Fig. 1.Creating models of polarization by scattering requires the calculation of full Mie scattering (i.e., Monte-Carlo scattering in all four stokes components) and is highly computationally expensive.Hence, we produced models for all three maximum grain sizes, using only our fiducial and homogeneous dust composition of silicates and graphites.Given that the albedo between the different compositions used in this work are very similar, the results at each a max will not deviate significantly when considering the other compositions.Between the three models, the highest polarized intensity is produced by an a max of 100 µm, since the albedo of 10 µm grains is negligible and the extinction opacity of 1000 µm sized grains larger than for 100 µm sized grains (see Table 1) and produces lower scattered flux.Unlike for a max = 10 and 100 µm, the polarization fraction of millimetric grains is very similar at both 1.3 mm and 7 mm, both in polarization pattern and intensity (maxmimum P frac ∼ 0.2%).This is because their albedo is almost constant at all millimetric wavelengths (see Fig. 3).The results of our self-scattering models are presented in Fig. 7 at the disk model's native resolution.We present the resulting Stokes I, Q and U fluxes, along with the polarization fraction (and polarization E-vectors overlaid) at both wavelengths.The resulting Stokes Q and U fluxes at 1.3 mm are extremely low.The polarization fraction in the model reaches around a tenth of percent (P frac ≲ 0.1%) within the central 20 au where it shows an azimuthal polarization pattern for the E-vectors.This azimuthal distribution is expected from a centrally concentrated density distribution (Kataoka et al. 2015), in the spiral arms, the vectors become radial or rather perpendicular to these structures.These patterns are similar to those presented by Kataoka et al. (2015) for a ringed and lopsided disk.The fraction of polarization falls significantly at 7 mm as expected, since it is far from the λ ∼ 2πa max regime, and barely reaches 0.005% within the disk.We also tested the results for the case of an edge-on hot disk (Fig. B.1).In this case the polarization fraction remains the highest at 1.3 mm but consistently low (∼ 1%).
Previous ALMA Band 6 polarization observations of IRAS 16293 B from Sadavoy et al. (2018) show an azimuthal E-vector pattern, with polarization fractions as high as ∼ 2 − 4 %.The authors have associated this polarization emission to that produced by dust scattering from the dust thermal emission itself (i.e., selfscattering).To directly compare these models with IRAS 16293 B observations, we performed polarized synthetic observations at all three Stokes components, mimicking the corresponding observing setups presented in section 2, and the procedure described in sections 3.6.The resulting synthetic maps (in units of Jy/beam) are presented in Fig. 8 for both wavelengths and all three Stokes components.In this case, we have omitted the polarization fraction results from the layout because the polarized intensity is completely dominated by thermal noise.The resulting Stokes I fluxes are comparable to the original observations, confirming the analysis presented in section 4.1 but now with the inclusion of the polarized 1.3 mm data.However, the model Stokes Q and U fluxes are not detectable within the sensitivity levels achieved by these observing setups.We conclude from this analysis, that linear polarization produced by self-scattering from spherical grains in our model is not high enough to be consistent with the observations of IRAS16293B carried out at 1.3 and 7 mm by Sadavoy et al. (2018) and Liu et al. (2018), respectively.
Our resulting polarization fractions are in-line with the predictions for IRAS 16293 B discussed by Yang et al. (2016) from analytical models of polarized scattering in optically thick media.The millimeter optical depth in IRAS 16293 B is extremely high (τ ≳100), which reduces the degree of anisotropy in the radiation field and hence the percentage of polarized scattered light (Kataoka et al. 2015).

Grain growth in Class 0 disks
Grain growth in Class 0 protostars and their associated disks has been a subject of significant interest in recent years.Several recent studies, including Bate (2022), Kawasaki et al. (2022), Koga et al. (2022), Lebreuilly et al. (2023) and Marchand et al. (2023) have provided compelling evidence suggesting the possibility of grain growth up to at least few hundred microns in these environments.Bate (2022) conducted simulations of prestellar core collapse and followed them up to the formation of a rapidly rotating marginally gravitationally unstable first core.This represents a stage previous to the formation of a well defined protostellar disk, as the one in IRAS 16293 B, but shows similar physical properties.Bate (2022) demonstrated that the combination of enhanced collisional rates and efficient grain growth mechanisms can lead to the formation of substantial dust aggregates in Class 0 disks, growing up to 100 µm in this first core stage.These results are in line with our possibility to have 100 µm or even up to 1000 µm sized particles in a Class 0 disk.Similarly, Kawasaki et al. (2022) evolved one-zone non-ideal MHD models of the collapse of dense cores up to densities comparable to those found in our disk model (n g ≳ 10 12 cm −3 ).Their calculations focused on the evolution of the grain sizes along the collapse, including the effects of coagulation and fragmentation of silicate dust.Their models show that grains can coagulate up to a few 100 microns at the densities of our disk model, and therefore those ex-pected in IRAS 16293 B, and even up to millimetric sizes within the very inner dense regions of the disk.These results seem to also be in line with our grain size estimations for the disk in IRAS 16293 B. The similar recent work conducted by Koga et al. (2022) simulated the formation of a protostellar disk with mass, radius and age similar to our disk model, i.e., representative of a Class 0 disk.In this simulations, they did not include dust coagulation but rather fixed grain sizes over the whole evolution.Their results indicate that only the big grains (100-1000 µm) are tightly coupled to the gas within the disk, while small grains (≲10 µm) are partly depleted or swept out form the disk.More recently, Lebreuilly et al. (2023) presented hydrodynamical simulation of protostellar collapse and followed the evolution of the grain size distribution up until the formation of a first core, with densities similar to those found by Bate (2022) and in our disk.Their results also suggest that grains can coagulate up to a few tens of microns in the the protostellar envelope and up to a few 100 µm within the first core.The results from Marchand et al. (2023) similarly suggests that grain growth is extremely rapid once a disk is formed.Their simulations show how grain sizes can reach more than 100 µm in the inner disk within 1000 yr after disk formation.Older predictions for grain sizes in protostellar cores, such as those from Ormel et al. (2009), Hirashita & Yan (2009) and Hirashita & Li (2013), suggested that even isothermally collapsing dense cores can achieve coagulation up to 100 µm but only if the cloud's dynamical support slows down the collapse beyond its free-fall time and let the grains grow.In the case of a collapse faster than the free-fall time (≲10 5 yrs), grains should coagulate up to a most a few 10 µm.
It is also worth mentioning that a dust population with maximum grain sizes comparable to ISM values (≲ 1 µm; Mathis et al. 1977) was not consistent with IRAS 16293 B based on the model-observation comparison presented in Zamponi et al. (2021).
The size distribution is yet another source of uncertainty for comparing models to observations.Although all the theoretical works mentioned above predict significant grain growth in the envelope around Class 0 protostars and in particular in the highdensity material in the disks (e.g., Marchand et al. 2023), the resultant distribution of the grain sizes might be different among different studies (e.g., Bate 2022 andLebreuilly et al. 2023).While in Lebreuilly et al. (2023) the resultant distribution resembled a power-law, as the one used here, in Bate (2022) the resultant distribution resembled more of a log-normal.This differences can be attributed to how the collision velocities for the grains are calculated (see discussion in Lebreuilly et al. 2023 andMarchand et al. 2023).We find that, if we were to consider a lognormal distribution for the grain sizes, the opacities at millimeter wavelengths would slightly increase but still remain within the same order of magnitude as the ones in Fig. 3.Such limited variations cannot help in constraining the dust grain size distribution with our current model and thus, our conclusions regarding the maximum grain size remain the same regardless of the adopted size distribution.

Grain growth within the soot-line
The recent VLA observation of FU Ori presented by Liu et al. (2021) showed that within the inner 10 au, where T≳ 400 K, dust grains have grown to millimeter sizes.Since this region is hot enough for evaporation of the water icy mantles, this implies that grain growth was efficient in this "dry" conditions.This scenario of grain growth in the inner and hotter regions of protoplanetary disks is also supported by laboratory experiments (Kimura et al. 2020).They show that the stickiness of silicate and carbonaceous grains is enhanced after the removal of quasi-liquid layers of water.This process facilitates dust coagulation and supports the formation of planetesimals in dry environments (Pillich et al. 2021).
The possibility to have millimetric grains can potentially be explained by the high fragmentation velocity v frag found for water-ice-free grains ≳10 m s −1 (Kimura et al. 2015;Gundlach et al. 2018;Steinpilz et al. 2019;Pillich et al. 2021), larger than previously considered for rocky poorly-sticky grains of 1 m s −1 (Blum & Wurm 2000).These results on the fragmentation velocity have also been independently found by Liu et al. (2021) and more recently by Yamamuro et al. (2023).
Motivated by these recent laboratory experimental results, we reproduced synthetic brightness profiles at 1.3 and 3 mm (similar to Fig. 4), accounting for sublimation and grain growth when the temperature is over 300 K. Outside of the sublimation zone the maximum grain size is 100 µm and a mixture of silicates, graphites and refractory organics (80% of the carbon bud-get).Inside of it, we have increased the grain size to 1000 µm.The results of this test are shown in Fig. 9 for two different sublimation temperatures, 300 and 500 K, at 1.3 and 3 mm.We present the synthetic ALMA Stokes I maps, at the resolution of the observations for comparison with IRAS 16293 B. The resulting brightness profiles show that the combination of the overestimation in the case of a max = 100 µm is mitigated by the reduction of flux in the center when a max = 1000 µm within the sootline.We present the results for two different sootlines, to explore the effects of considering the range of sublimation temperatures presented by Lin et al. (2021).The fluxes from models with a 500 K sootline are higher than with 300 K.This happens because with a sootline of 500 K the region traced by millimetric grains is more compact than the case with 300 K, this means that the region with higher opacity is smaller in the 500 K case.Another feature observed in Fig. 9 is the appearance of a gap in the model with sootline at 300 K observed at 3 mm.This is caused by the reduction of the opacity, and is not seen in the model with 500 K because the region with reduced opacity is compact and less resolved by the observations.This shows that observations of such gaps for hot disks could then be the result of changes on the opacity.
Considering grain growth within the sootline results in a better match with the observations than the cases with homogeneous grain sizes.The comparison suggests that grain growth up to millimeter sizes could be enhanced within the sootline in this young Class 0 disk, provided the disk densities temperatures and densities in the model are close to the ones present in IRAS 16293B.

If not self-scattering, what is the polarization mechanism
in IRAS 16293-2422 B?
As we have shown in section 4.4, the emission from IRAS 16293B is too optically thick to produce detectable levels of polarization by self-scattering when considering spherical grains.This raises the question of what other mechanisms or grain properties can we consider to explain the observed polarization patterns and fractions.
Polarization observations are commonly associated with the optically thin emission of magnetically aligned grains (Lazarian & Hoang 2007a;Andersson et al. 2015).However, the emission detected from young embedded disks is likely optically thick (Galván-Madrid et al. 2018;Lin et al. 2020;Zamponi et al. 2021;Ohashi et al. 2023;Lin et al. 2023).In the context of optically thick emission, the polarization observed might also come from magnetically aligned grains, but produced in the form of extinction (Ko et al. 2020;Liu 2021).In this case, the differential attenuation of the two orthogonal components of the light E-vectors, results in an excess of polarization along a given axis (Wood 1997).This is known as dichroic extinction and occurs when the grains are elongated and the background light is optically thick and almost unpolarized.In the context of optically thick embedded disks, this can be produced by foreground (e.g., envelope) elongated grains aligned with their minor axis parallel to the magnetic field lines, which absorbs light preferentially along the grain's major axis and produce a net polarization parallel to the magnetic field lines, as opposed to the optically thin polarized emission.Such a polarization mechanism has actually been proposed and detected in a few other Class 0 sources and contradicts the current understanding of magnetic field structures within the optically thick inner regions of the disks (Liu 2021).Similarly, the multiwavelength polarization observations of NGC 1333 IRAS4A, presented by Ko et al. (2020), show a 3 mm Fig. 9. Models with grain growth within the sublimation zone.In these models, the maximum grain size is 100 µm outside of the sublimation zone (i.e., in regions where T > 300 K for the upper panels and T > 500 K for the lower panels) and 1000 µm within it, with a mixture of silicates, graphites and amorphous carbon (80% of the carbon).
transition between E-vectors parallel to the magnetic field, traced at 0.87-1.3mm, to E-vectors perpendicular to the magnetic field, traced at 6.9-14.1 mm.These results show evidence for a transition between extinction and emission of aligned grains which is determined by an optically thick to thin transition.Similarly, polarization by dichroic extinction has been detected within the inner 100 au of the Class 0 protostar OMC-3/MMS 6 (also known as HOPS-87) in Orion (Liu 2021), after comparing ALMA and VLA observations.Moreover, in the protostar HH212, the polarization observed at a resolution of 14 au, shows a possible combined contribution of both dichroic extinction and self-scattering (Lee et al. 2021).These studies support that dichroic extinction by aligned grains can be an important mechanism to explain the polarization pattern at or close to disks scales in several Class 0 protostars.As this mechanism requires that the region near disk scales is optically thick, it would be present preferentially in younger and more massive disks such as those in the Class 0 stage.
In the case of IRAS 16293B, the 1.3 mm polarization observations from Sadavoy et al. (2018) show azimuthal E-vectors between 30-50 au and uniform vectors within 30 au (see Fig. 1).In Zamponi et al. (2021) and this work we have shown that the emission is optically thick and can reach optical depths well above 100 at 1.3 mm within the central 10 au.If the polarized emission is produced by dichroic extinction of magnetically aligned grains, this pattern would indicate a toroidal magnetic field.Alternatively, the polarization pattern could still be related to the direct emission of magnetically aligned grains close to the disk.The magnetic field morphology (traced by B-vectors) could be associated with a poloidal field in that scenario.Future mod-eling and higher-resolution observations can help constraining the contribution of dichroic extinction as well as magnetic field configurations that can best explain the observations in Fig. 1.
Another possible scenario producing azimuthal E-vectors, as those in Fig. 1, is the polarization reversal effect, happening when millimetric elongated grains are present in the disk and observed in the Mie regime (i.e, millimetric wavelengths).This has been used by Guillet et al. (2020) to explain the azimuthal polarization pattern of [BHB 2007] 11 (the pretzel) in the Pipe nebula, where polarization E-vectors, and so B-vectors, could be aligned with the accretion streamers shown by Alves et al. (2019).
Another scenario is that the polarization can be produced by dust alignment, but not necessarily with the magnetic field only.Both emission and extinction of light from elongated particles lie on the assumption that dust grains are aligned with a given underlying field.This could be either the magnetic, radiation or the velocity field (Gold 1952;Wood 1997;Lazarian 2007).The most commonly accepted mechanisms responsible for the alignment of grains (see Andersson et al. 2015;Reissl et al. 2016or Hoang et al. 2022 for a review) can be either associated to Radiative Torques (RAT) (Lazarian & Hoang 2007a) or to supersonic motions, namely, mechanical alignment (MET) (Gold 1952;Lazarian & Hoang 2007b;Kataoka et al. 2019;Reissl et al. 2023;Hoang et al. 2022).In the case of RAT, this can lead to alignment with the radiation field (k-RAT; Tazaki et al. 2017) instead of the magnetic field (B-RAT).In the case of mechanical alignment this could result in alignment with the magnetic field (B-MET) or the velocity field (v-MET; Hoang et al. 2022).In the scenarios of alignment with the radiation (k-RAT) or the dust-gas drift velocity field (v-MET or MAT; Hoang et al. 2018), the resulting polarization pattern would be azimuthal, as long as the radiation field is assumed to be centrally concentrated and the disk to be Keplerian (e.g., around a protostar), respectively.However, the recent work presented by Le Gouellec et al. (2023) shows that k-RAT is not the main mechanism responsible for the observed polarization in Class 0 protostars, since it requires high protostellar luminosities radiating on large and rapidly rotating grains, and such grains are commonly settled toward the midplanes of Class 0 disks, shielded from protostellar radiation.The case of mechanical alignment depends strongly on the Stokes number, i.e., the degree of spatial coupling between the gas and the dust.Whether radiation or mechanical alignment are efficient in Class 0 disks requires further investigation.
Finally, given our suggestion of large (>100 µm) grains present in this Class 0 disk, we find interesting to consider the scenario of grain rotational disruption induced by radiative torques (RATD), introuduced by Hoang et al. (2019) and recently discussed by Le Gouellec et al. (2023) and Reissl et al. (2023).According to RATD, rapidly rotating large aligned grains might become rotationally disrupted when they exceed a certain critical angular momentum and would produce a depletion of grown dust.Le Gouellec et al. (2023) showed that RATD might be effective within the outflow cavity regions of Class 0 protostars, for protostellar luminosities above 20 L ⊙ , and that the densest regions of the disk are well protected against such intense radiative torques.These are the region where we suggest dust is grown to above 100 microns in IRAS 16293B.

Conclusions
In this work we have explored the effects the effects of different maximum grain sizes and carbon sublimation in the millimeter continuum emission from a hot and optically thick Class 0 disk, generated from numerical simulations of prestellar core collapse.The disk model has successfully reproduced the fluxes of the nearly face on Class 0 disk IRAS 16293 B (Zamponi et al. 2021).Hence, we produced synthetic observations of the different cases to compare with multiwavelength (1.3, 3, 9 and 18 mm) and high-resolution (6 to 44 au) observations of IRAS 16293 B, including polarization.In order to automate the generation of synthetic observations, we have developed a new publicly available tool called Synthesizer, that allows to generate synthetic models from numerical simulations directly from the command line.The conclusions of this work are summarized as follows: -For a dust mixture of silicates and graphites, we extended the results of Zamponi et al. (2021), that used maximum grain sizes a max of 1 µm and 10 µm, and generated opacity tables for maximum grain sizes of up to 100 µm and 1000 µm.Peak fluxes increase with wavelength and decrease with a max , a feature of hot and optically thick disks.Optical depths range between 130 to 2 from 1.3 to 18 mm, respectively.The high optical depths and positive temperature gradient toward the center also result in extended regions in the disk with α < 2.5 for all a max and even below 2 for a max = 100 µm and 1000 µm.Predictions from significant grain growth populations, including a max = 1000 µm are comparable to the observations from IRAS 16293 B at all observed wavelengths.Hence, significant grain growth could be present in this young Class 0 disk.-Motivated by the high brightness temperatures (≳400 K) observed toward IRAS 16293 B, we explored the scenario of sublimation of solid amorphous refractory carbon at temperatures above 300 K, the so-called sootline.The sublimation results in a local decrease of the optical depth, due to both the reduction of graphite within the grain carbon budget and the evaporated mass reduction.This decrease produces higher fluxes because the emission then traces deeper and hotter layers of the disk.The difference in the fluxes with and without sublimation are small (< 10%).-We also tested the hypothetical case of grain growth within the sootline, motivated by recent laboratory experiments suggesting that dry grains without ice mantes would enhance stickiness and coagulation.We modeled this scenario with an a max of 100 µm at all disk scales outside of the sootline, and with millimetric grains within it.Our results indicate that a combination of grain sizes can help to provide a better match to the ALMA observations of IRAS 16293 B. -We generated polarization models by self-scattering for three different maximum grain sizes, 10, 100 and 1000 µm.The millimetric polarized intensity is highest for the case with a max = 100 µm at 1.3 mm, thanks to the high albedo and not extremely high optical depth, as it happens for millimetric grains.However, the predicted polarization fraction produced by self-scattering are very low (≲0.5%), both for edge-on and face-on disks.These low levels of polarization by self-scattering are too low to be consistent with those observed for IRAS 16293 B at both 1.3 mm and 7 mm (2 − 4%).
Since self-scattering is unlikely to be at the origin of the high-polarization fractions observed toward the Class 0 disk IRAS 16293 B, future modeling is needed to constraint the mechanism responsible for the observed polarization.Similar studies toward other embedded disks would be useful to see if this is a general result for other Class 0 disks.Higher-resolution molecular observations will also help to probe if there is enriched carbon chemistry in the inner regions of the disk.

Fig. 2 .
Fig.2.Face-on gas density (top) and edge-on temperature (bottom) distributions across the midplane of the protostellar disk formed from the numerical simulations collapse of a core ans that we used to compare to the observations of IRAS 16293-2422 B. The white contour in gas temperature represents the extension of the soot-line at 300 K.This model is presented in greater detail inZamponi et al. (2021).
start our analysis by producing synthetic observations of the Stokes I fluxes from the simulated disk at 4 different wavelengths: 1.3, 3, 9 & 18 mm, corresponding to the ALMA bands 6 & 3 and VLA bands Ka & Ku (Fig.1).All Stokes I images and profiles presented in this paper represent net fluxes.This means thermal plus scattered flux.For each band we mimicked the observing setup of the real observations described in section 2 and presented in Fig.1.We extracted a cut of the brightness temperature maps along the east-west axis and plotted it as a function of physical offset from the peak, as shown in Fig.4.All brightness temperature cuts are taken along the position of the peak flux which correspond to offset zero in Fig.4.The black line in Fig.4represents the observed source brightness, and the three different colored solid lines represent the models with different a max .A black horizontal line in the upper right corner of each panel indicates the geometric mean between the major and minor axis of the beam.Dashed lines show models with carbon-sublimation (see section 4.2).

Fig. 4 .
Fig. 4. Cuts of the brightness temperature distribution along the east-west axis for real and synthetic observations at four wavelengths.The black solid line in each panel represents the ALMA and VLA observations shown in Fig. 1.Colored lines indicate models with different maximum dust grain size, taking values of a max = 10, 100 & 1000 µm.We have included models accounting for the sublimation of 80% of the carbonaceous material, in the form of refractory organics.The sublimation zone extends over a 10 au radius where the gas temperature exceeds 300 K.The black line under every wavelength label, indicates the angular resolution.

Fig. 5 .
Fig. 5. Similar to Fig. 4 but for the optical depth of every radiative transfer model at the ideal resolution, this is, at the resolution of the radiative transfer output before any beam convolution.

Fig. 6 .
Fig. 6.Spectral for the real observation (left) and models (right).Models are shown for a max of 10 (top) and 100 µm (center) 1000 µm (bottom).Columns represent the cases without sublimation and with 50% and 80% of carbon sublimation, from left to right, respectively.The black contour indicates α = 2.

Fig. 7 .
Fig. 7. Radiative transfer models of self-scattering at 1.3 (top) and 7 mm (bottom) for a max = 100 µm, shown in the upper and lower row, respectively.Panels illustrate the Stokes I, Q, U fluxes and polarization fraction (with constant-size polarization vectors overlaid) from left to right.
Dust opacities for different maximum grain sizes and compositions.The three panels show, from left to right, dust opacities for a maximum grain size of 10, 100 & 1000 µm, respectively.Each panel contains opacities generated for a mixture of silicates and graphite (0.625-0.375) and a mixture of silicates, graphites and refractory organics (0.627-0.300-0.075;80% of organics).The gray curve on every panel indicates the albedo of the fiducial composition (silicates and graphites).Four vertical gray lines indicate the observing wavelengths used in this study, corresponding to the observations from Fig.1.The exact opacity values used in this work are listed in Table1, for different a max and compositions, at all four wavelengths.