dataesr/scientific-paragraphs-categorization huggingface dataset:
b rms noise in the maps of total intensity I and polarized intensity P. c Typical H2 column densities probed in the protostellar envelope by the ALMA observations, selecting the pixels with total intensity values greater than 5 times the rms noise in the Stokes I map. The column density of each pixel was derived following the method described in Section 2. 2. Each pointing in BHR 71 contains both of the components of the wide binary. Thus, the corresponding ranges in column density include all emission from both BHR 71 IRS1 and IRS2. d The maximum value of polarization fraction in the core, selecting the pixels with total intensity values greater than 5 times the rms noise in the Stokes I map. e Maximum recoverable scale. f Reference of the publication(s) presenting the corresponding ALMA polarization dataset(s).
g  Takahashi et al. (2019)  presented the ALMA observations of OMC3 MMS6 in two separate datasets, as the angular resolutions of the two datasets were very different, and thus probe distinct regions of the envelope. values of polarization fraction P frac can be affected significantly when dividing by Stokes I values that are uncertain. Here, we compute the rms noise values in each of the three Stokes maps I, Q, and U (σ I , σ Q , and σ U respectively) by measuring the root mean square in an area without strong emission. We notice that typically σ Q ≈ σ U , so we use a single value σ P ≡ σ Q ≈ σ U. We present in Figure  1  the distribution of P frac and polarization position angles φ in the region where the Stokes I is > 5 σ I , from all individual maps of all sources at each wavelength. In these histograms, the uncertainties in P frac , and φ (in radians) are showed as shaded areas, and are calculated as follows: σ P frac = P frac σ P P 2 + σ I I 2 , (2) σ φ = 1 2 σ P P.
We follow the method introduced in Planck Collaboration et al. (2018)  to compute a pixel-selection criterion in order to test appropriately the correlation between S and P frac in our objects. This pixel-selection is a cutoff based on Stokes I, which allows us to remove the noise-biased data. We obtain this cutoff by analyzing the average S/N of the polarized intensity P , which typically increases with increasing Stokes I. When this average S/N of P , plotted as a function of the total intensity Stokes I for each dataset, meets the value S/N = 5, we use the corresponding value of Stokes I as the pixel-selection cutoff for the given dataset. We show an example in Figure  2  (top panel ), where we plot the S/N of the polarized intensity map as a function of the total intensity for the 1. 3 mm observations of the B335 core.
The vertical dotted line, which denotes this cutoff value of Stokes I, thus corresponds to the value of Stokes I where P/σ P I ≥ 5. We then take all points lying above this cutoff in Stokes I and form the sample to which we will apply our statistical method. Note that if this method provides a threshold limit of Stokes I below 5 σ I , we chose 5 σ I as the cutoff for the dataset. As shown in the lower panel of Figure  2 , the values of S × P frac diverge at Stokes I values lower than the aforementioned threshold, as a consequence of the noise-bias of S and P frac at low values of Stokes I. It is important to note that we have not performed any selection based on the P values; we select only on the I values in order to keep the pixels exhibiting low polarized intensity that contain the information of depolarization, which is essential for our statistical analysis.
79 ± 0. 03, which is flatter than the results and the analytical correlation found with Planck observations at larger scales, where S ∝ P frac -1. Merging all the ALMA data does not enable us to investigate the relation between S and P frac with respect to Stokes I because of the heterogeneous properties of the sources and observations (e. g. , the wavelength of the observations). Thus, we use the column density (calculated as described Top: Evolution of the S/N of the polarized intensity, i. e. , P/σP , as a function of the total intensity Stokes I in Jy str - 1. The dot-dashed horizontal black line is at the value of P/σP = 5. The dotted vertical line is the selected cutoff in Stokes I described in Section 3. 1. The dot-dashed vertical line is the 5σI value. The solid line is the running mean, which is calculated along the Stokes I; the shaded area represents ± the standard deviation of the Gaussian fit performed on each bin.
Comparing the statistical properties of the polarized dust emission in protostellar cores with those in star-forming clouds The statistical analysis of the polarized dust emission from the sample of 15 datasets analyzed (see Table  1 ) reveals a significant correlation between the dispersion of polarization angles S observed in the plane of the sky and the polarization fraction P frac measured in each line of sight in these 11 protostellar envelopes. However, the S ∝ P frac -0. 79 relationship we find at core scales is shallower than the S ∝ P frac -1 relationship found at larger scales in the Planck observations of star-forming clouds  (Planck Collaboration et al. 2018). Moreover, we obtain on average higher values of S and P frac than those found in the lower density molecular clouds probed by Planck.
What physics governs the disorganized component of the magnetic field? The correlation between S and P frac is governed by the level of disorganization of the apparent magnetic field lines projected on the plane of the sky. The magnetic field is also linked with the kinematics of the gas, assuming the gas is Article number, page 8 of 38 angles S as a function of the polarization fraction P frac from all of the datasets merged together. The points were selected according the method developed in Section 3. 1. The color scale represents the number density of points in the plot. The solid black line and black points represent the running mean of P frac ; the associated black error bars are ± the standard deviation of each bin. We plot the linear fit in purple, which is a linear regression. We take into account the saturation of S in the derivation of the linear fit by applying a threshold in polarization fraction, indicated by the vertical dot-dashed grey line.
Nevertheless, if the magnetic field is highly complex at smaller scales than the ones we probe, then indeed P frac drops and conversely S rises toward its highest values. The spatial distributions of both the polarized and unpolarized emission in the plane of the sky show characteristics that are likely to affect the polarization fraction toward protostellar cores, and thus the statistical results we present in this paper. A qualitative view of typical ALMA maps of the dust emission from cores often reveals that the emission in Stokes Q and U looks sharper and more extended that in Stokes I. We have therefore examined the spatial power spectra, which quantify the power present at each spatial scale, of the Stokes I, Q, and U emission in each of our 15 datasets (see Appendix C). Each spectrum is normalized to its maximum value, which allows us to compare the relative power of the emission as a function of spatial scale.
On the effect of spatial filtering on statistical polarization properties One major issue we face with the ALMA dust polarization observations is spatial filtering by the interferometer, which removes the scales of emission that are not included in the uvcoverage of the dataset. In contrast to the statistical analysis of dust polarization performed with single dish instruments such as Planck  (Planck Collaboration et al. 2015a ,b, 2018) , BLASTPOL in  (Fissel et al. 2016) , and SCUPOL  (Poidevin et al. 2013) , our analysis of interferometric data requires us to characterize how the filtering alters the polarization quantities we use in our statistics. With this aim, we use a set of synthetically observed non-ideal MHD simulations computed with RAMSES  (Teyssier, R. 2002; Fromang et al. 2006 ) that follow the gravitational collapse of cores whose range of initial mass and turbulence reproduce the main characteristics of the sources from our sample.
In addition, a case where the grains are perfectly aligned is only taking into account the source-specific geometrical effects governing the resulting polarization maps, and thus is useful to understand where alignment drops or is suppressed. We present all the details of the simulations and the radiative transfer calculations in Appendix D. In order to produce realistic synthetic observations to compare with the ALMA datasets, we use the CASA simulator (with the typical ALMA uv-coverage of these observations) to implement the effects of interferometric filtering and atmospheric noise on the POLARIS synthetic emission maps. In Figure  7  we present the histograms of S and P frac (where all simulations have been merged) before and after filtering, assuming RATs or PA 3. Note that if no spatial 3 Note that merging all the simulations does not change the result, as each simulation of the six we present in Appendix D sees their values of S and P frac increase.
In addition, note that the statistical weights (in terms of number of independent points, see Table  2 ) of each observation are very different. Therefore, averaging all the observations may cause observations with larger weights to mask the results of those with lower weights. Hence, to examine in more detail some of these physical processes that are thought to cause the efficiency of RATs to vary, we perform two separations in our datasets. First, we separate the "low" and "high" luminosity cores (i. Observed cores Highluminosity core models implementing RAT Highluminosity core models implementing RAT and filtering Lowluminosity core models implementing RAT Lowluminosity core models implementing RAT and filtering Fig. 8 : Observed distributions of the mean values of S × P frac as a function of the column density NH 2 (normalized by its maximum value, N H 2 ,peak ) of all the ALMA cores (triangles) and of all the models (crosses).
e. , outflow cavity and envelope emission), as well as the trend seen when all the datasets are merged together. On the other hand, the distribution from the low-luminosity cores shows a clear decrease in S × P frac as a function of column density, which indicates less efficient grain alignment in the highest density regions of these cores. As the product S × P frac is also dependent on the function f m (δ) (see Section 4. 1. 1), this may indicate that these low-luminosity cores are subject to different amounts of the gravo-turbulent motions responsible for the correlation between S and P frac. However, while this would modify the average values of S and P frac , it is unclear that this would result in such a strong decrease of S × P frac with the column density, and there are no obvious reasons why only the low-luminosity cores would be affected.
g. ,  Valdivia et al. 2019; Le Gouellec et al. 2019; Galametz et al. 2019; Hull et al. 2020). The radiation field resulting from the radiative transfer, impinging on the dust grains in the protostellar envelope, comprises low-energy submillimeter photons whose wavelength need to be comparable to the size of dust grains in order to efficiently align the grains via RATs. We synthetically observe the MHD simulations with PO-LARIS at 870 µm, at a distance of 400 pc, in maps 8000 au in size with pixel sizes of 8 au. We observed each of the six simulations along two independent, orthogonal lines of sight. As a result, we analyse twelve different POLARIS synthetic observations, each of which was produced assuming grain alignment via either RATs or PA. Thus, this sample of twelve models and our fifteen ALMA datasets yield a similar numbers of cases to which we can apply our statistical analysis.
Histograms of polarization fraction P frac (left) and polarization position angle φ (right) for all the sources of our sample. The histogram lines have been smoothed with a 1D-Gaussian kernel of a size of 0. 2% in P frac and 2 • in φ. The shaded areas correspond to the mean of the uncertainty in the values of P frac and φ within each bin of the histograms. Note that among the two datasets we have toward OMC3 MMS6, "OMC3 MMS6 H" and "OMC3 MMS6 L" denote the high and low resolution observations, respectively.
Acknowledgments V. J. M. L. G. acknowledges the support of the  ESO Studentship Program. A. J. M. acknowledges support from the  Joint ALMA Observatory Visitor Program , and  ESO   Visitor program. J. M. G. is supported by the  Spanish  grant  AYA2017-84390-C2-R (AEI/FEDER, UE ). C. L. H. H. acknowledges the support of both the  NAOJ  Fellowship as well as  JSPS KAKENHI  grants  18K13586  and  20K14527. This work has benefited from the support of the  European Research Council  under the  Horizon 2020 Framework Programme  ( Starting Grant MagneticYSOs  with grant agreement no. 679937 ). V. J. M. L. G. thanks  Maud Galametz  and  Javier Abril  for the precious help they offered for the statistical analysis. This paper makes use of the following ALMA data: ADS/JAO. ALMA# 2013. 1. 00726. S, ADS/JAO.
Histograms of polarization fraction P frac (left) and polarization position angle φ (right) for all the sources of our sample. The histogram lines have been smoothed with a 1D-Gaussian kernel of a size of 0. 2% in P frac and 2 • in φ. The shaded areas correspond to the mean of the uncertainty in the values of P frac and φ within each bin of the histograms. Note that among the two datasets we have toward OMC3 MMS6, "OMC3 MMS6 H" and "OMC3 MMS6 L" denote the high and low resolution observations, respectively. Le Gouellec et al. : Polarization statistics of ALMA observations of Class 0 cores 200 Histogram of P frac values B335 B3 B335 B5 90 Histogram of φ values B335 B3 B335 B5 175 IRAS 16293 IRAS4A B7 B335 B6 Serpens Emb6 Serpens Emb8 Serpens Emb8N BHR71 IRS1 80 B335 B6 Serpens Emb6 Serpens Emb8 Serpens Emb8N BHR71 IRS1 BHR71 IRS2 BHR71 IRS2 150 IRAS 16293 VLA 1623 L1448 IRS2 OMC3 MMS6 H 70 IRAS 16293 VLA 1623 L1448 IRS2 OMC3 MMS6 H Numer of points 75 100 125 Serpens Emb6 OMC3 MMS6 H OMC3 MMS6 L OMC3 MMS6 L IRAS4A B6 IRAS4A B7 Numer of points 40 50 60 OMC3 MMS6 L IRAS4A B6 IRAS4A B7 B335 B6 30 50 B335 B5 VLA 1623 Serpens Emb8 BHR71 IRS2 20 IRAS4A B6 25 L1448 IRS2 Serpens Emb8N BHR71 IRS1 10 B335 B3 0.
c Thickness of outflow cavity walls, fit by eye. d We show the average values of e and c obtained from the observations at the three different wavelengths. e Both outflows are from IRAS 16293A; IRAS 16293B does not have any detected outflow. The parameters e and c have been determined by eye thanks to the previously published CO emission. Furthermore, IRAS 16293B lies within one of the outflow cones of IRAS 16293A; however, we consider it to be envelope emission. f g We report e and c for the two datasets separately, as they have very different angular resolutions. h We report values separately for the two protostars in this core, IRAS4A1 and IRAS4A2.
Note that our sources are at different distances and have been observed at different resolutions. Therefore, the variation of the lag δ among all of our 15 datasets causes the parameter fm(δ) to vary. However, this variation does not affect our results as the dependence of the variations of fm(δ) caused by the different values of δ fall within the uncertainty of our ALMA correlation (the standard deviation of all the extrapolated values of fm(δ) from the fifteen datasets is 0. 004). Nevertheless, all the processes responsible for the disorder in the magnetic field are not necessarily associated with a peculiar physical scale, but rather are phenomena that act across a range of scales, from the envelope to the disk. In consequence, the lag does not represent any intrinsic turbulent length scale within a core.
Bennu is an ~500-m-diameter rubble-pile asteroid that is the target of detailed study by the Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer (OSIRIS-REx) mission. Here we use data from the OSIRIS-REx Laser Altimeter to assess depth-to-diameter ratios (d/D) of 108 impact craters larger than 10 m in diameter. The d/D of craters on Bennu ranges from 0. 02 to 0. 19. The mean is 0. 10 ± 0. 03. The smallest craters show the broadest range in d/D, consistent with d/D measurements on other asteroids. A few craters have central mounds, which is interpreted as evidence that a more competent substrate lies a few meters beneath them. The range of d/D narrows as crater size increases, with craters larger than 80 m tending toward smaller d/D. At large scales, increases in target strength with depth, combined with target curvature, may affect crater morphometry.
Impact Crater Selection Impact craters on Bennu were found by examining images acquired by the OSIRIS-REx Camera Suite (OCAMS)  (Golish et al. , 2020; Rizk et al. , 2018)  during the Approach, Preliminary Survey, and Detailed Survey phases of the OSIRIS-REx mission  (Lauretta et al. , 2017). OCAMS imaged Bennu globally at a range of illumination and viewing geometries  (DellaGiustina et al. , 2019) , and multiple OSIRIS-REx team members searched the images for craters  (Walsh et al. , 2019). Identified craters were combined into a global crater database  (Bierhaus, Barnouin, Walsh, et al. , 2019; Bierhaus, Barnouin, McCoy, et al. , 2019; Bierhaus et al. , 2020; Walsh et al. , 2019). Craters analyzed here were selected from the October 2019 version of the crater database, which contained 135 crater candidates larger than ~10 m in diameter.
This size cutoff was chosen based on the horizontal ground-sample distance of topographic data products developed in the first few months of Bennu arrival and to keep the total number of craters manageable for this initial study. Of these, 108 craters were included in the d/D analyses. The remaining candidates were excluded because they lacked a topographic expression (i. e. , no depressed interior with a discernable rim around at least part of the crater circumference), substantially overlapped another crater, or had a large boulder in their center.
Depth and Diameter Measurements We measured impact crater depths and diameters using digital terrain models (DTMs) derived from data collected by the OSIRIS-REx Laser Altimeter (OLA)  (Barnouin et al. , 2020; Daly et al. , 2017). Supporting information Text S1 details the OLA data set and DTM creation. From each crater DTM, we extracted topographic elevation profiles at eight evenly spaced azimuths by means of a semiautomated IDL code. Rim-to-rim diameter and rim-to-floor depth were determined along each profile. The user specified the deepest point to be used (based on examination of images and the DTMs) so that the depths were not biased by features such as crevices between boulders. Using multiple topographic profiles is consistent with recommended best practices for d/D studies  (Robbins et al.
The remaining profiles were averaged to compute rim-to-rim diameter, rim-to-floor depth, and thereby d/D. The uncertainties reported here represent the standard deviation of the depths and diameters of all the profiles deemed useable for a given crater. The automated IDL code generated eight profiles for each crater; after human evaluation of the profiles, a crater could have as many as eight to as few as two profiles. In addition to the standard deviation, the number of profiles used for a crater can be a metric for how much weight one can give an individual crater when interpreting the data. Craters quantified using many profiles were easier to analyze than craters for which only a few profiles could be used. Small numbers of profiles can lead to small standard deviations, whereas the small number of profiles indicates the crater was challenging to evaluate.
Conclusions We measured the diameters and depths of impact craters on Bennu larger than 10 m using data from the OSIRIS-REx Laser Altimeter. The average d/D is 0. 10 ± 0. A few craters have central mounds, a trait that implicates the presence of competent material located a few meters beneath them. For craters >80 m, an increase in target strength with depth appears to affect crater morphometry, although target curvature likely also contributes. The results reported here highlight the role that impacts play in shaping the surfaces of rubble-pile asteroids and the how the physical properties of an asteroid can be inferred by studying its impact craters.
Data Availability Statement Data from OLA (Orbital B mission phase) and OCAMS (Approach, Preliminary Survey, and Detailed Survey mission phases) are publicly available in the Planetary Data System (PDS)  (Daly et al. , 2019; Rizk et al. , 2019). Data are delivered to the PDS according to the timeline described in the OSIRIS Data Management Plan  (Crombie & Selznick, 2019). The DTMs analyzed here are available in a permanent archive associated with this paper at http://lib. jhuapl. edu/papers/the-morphometry-of-impact-craters-on-bennu/ website.
16, 17 Low temperature CL was performed in a field emission gun SEM (Zeiss LEO DSM 982) equipped with custom-built liquid helium flow cryostage (CryoVac). The light was collected using a UV-enhanced glass fiber placed in close contact with the sample, dispersed with a 90 cm focal length monochromator (SPEX 1702), and detected using a liquid nitrogen-cooled, UV-optimized CCD. 18 In both microscopes, the CL was collected in hyperspectral imaging mode, where a spectrally-resolved luminescence spectrum is collected for every pixel in the image. The room temperature and low temperature (%12 K) measurements were acquired with a beam voltage of 5 kV. The images presented here are generated from the hyperspectral dataset by either least-squares peak fitting (using Gaussian and Voigt functions) or plotting intensity images of selected wavelength ranges.
The single vertical black line is the join of the bow-tie where the two opposing (0001) GaN growth fronts meet and coalesce. Figure  2 (b) shows an example CL spectrum, which consists of two emission peaks. One is associated with the near band edge (NBE) emission from the underlying GaN and the other arises from the 5-period MQW structure grown on the (10 11) surfaces. To generate two-dimensional CL images, each spectrum in the CL dataset was fitted with a Voigt and Gaussian function for the GaN NBE and MQW peaks, respectively. The integrated intensity and peak energy for the GaN NBE and MQW peaks are displayed in Figs. 2(c ) and 2(d) and Figs. 2(e ) and 2(f), respectively. The intensity distribution of the GaN NBE peak is fairly uniform except for the appearance of black spots and a dark line as seen in the GaN intensity image in Fig.
Closer examination of the individual CL spectra from the hyperspectral dataset revealed sharp peaks superimposed on the MQW emission, as seen in Fig. 3(a). The peak separation is approximately constant with a mean energy separation Δ E of 47 meV. An optical path length L of about 5:3 μm can be calculated using the simple equation L ¼ hc 2nΔE using a refractive index of n ¼ 2:45 for GaN, taken as a constant over this spectral range. This matches well with the stripe width of 5:5 μm in the patterned Si substrate, as also seen in the SE image in Fig. 1(b). The change in the refractive index between the GaN and the 111 f g Si sidewalls causes the width of the groove to act as an optical cavity giving rise to these Fabry-Pérot interference fringes. Alternatively, the cavity size can be calculated more accurately from the slope of the curve in Fig.
The actual width of the cavity could be smaller than the width of the patterned Si substrate due to slight differences in the patterning. Also, the light has to pass through the entire structure to reach either interface, which means that it has to pass through the center of the bow-tie. This is where the two c-plane growth fronts meet and coalesce, leading to an antiphase domain boundary as seen as a dark line in the top-view CL intensity images in Figs. 2(c ) and 2(e), where the join appears as a black line of reduced intensity. The generation of the modes is, therefore, most likely more complicated than the assumed internal reflection on the GaN/Si interface and the light propagation. Figure  4  displays example CL spectra extracted from the hyperspectral dataset recorded at low temperature (%12 K).