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We reformulate the gain correction problem of the radio interferometry as an optimization problem with regularization, which is solved efficiently with an iterative algorithm. Combining this new method with our previously proposed imaging method, PRIISM, the whole process of the self-calibration of radio interferometry is redefined as a single optimization problem with regularization. As a result, the gains are corrected, and an image is estimated. We tested the new approach with ALMA observation data and found it provides promising results., Comment: 18 pages, 13 figures, accepted for publication in PASJ

We report the development of Ruri, a series of Japanese general text embedding models. While the development of general-purpose text embedding models in English and multilingual contexts has been active in recent years, model development in Japanese remains insufficient. The primary reasons for this are the lack of datasets and the absence of necessary expertise. In this report, we provide a detailed account of the development process of Ruri. Specifically, we discuss the training of embedding models using synthesized datasets generated by LLMs, the construction of the reranker for dataset filtering and knowledge distillation, and the performance evaluation of the resulting general-purpose text embedding models.

Gas giant planets are formed by gas accretion onto planetary cores in protoplanetary disks. However, direct evidence of this process is still lacking, limiting our understanding of planetary formation processes. During mass accretion, planet-driven outflows may be launched, which could be observable by shock tracers such as sulfur monoxide (SO). We report the detection of SO gas in the protoplanetary disk around TW Hya in archival Atacama Large Millimeter/sub-millimeter Array (ALMA) observations. The $\rm SO\ J=8_7 - 7_6\ $ emission line is detected at a $6\sigma$ significance and localized to the southeast region of the disk with an arc-like morphology. The line center is red-shifted with respect to the systemic velocity by $\sim5\ \rm km\ s^{-1}$. The starting point of the SO emission is located at a planet-carved dust gap at $42$ au. We attribute this to an outflow driven by an embedded protoplanet. Indeed, the observed morphology is well reproduced by a ballistic outflow model. The outflow velocity suggests that the outflow launching source has a mass of $\sim 4 M_\oplus\ (0.012 M_{\rm Jup})$ and the mass-loss rate is $3\times10^{-8} - 1\times10^{-6}\ M_{\rm Jup}\ {\rm yr^{-1}}$. With the relation of mass-loss and mass-accretion rates established for protostars, we estimated the mass-accretion rate onto the protoplanet to be $3\times10^{-7} - 1\times10^{-5}\ M_{\rm Jup}\ {\rm yr^{-1}}$, which matches theoretical predictions for a $\sim 4 M_\oplus$ planet at this separation. The detection of planet-driven outflow provides us a unique opportunity to directly probe the earliest phase of gas giant planet formation., Comment: 13 pages, 8 figures, accepted for publication in ApJL

In the past decade, ALMA observations of protoplanetary disks revealed various substructures including gaps and rings. Their origin may be probed through statistical studies on the physical properties of the substructures. We present the analyses of archival ALMA Band 6 continuum data of 43 disks (39 Class II and 4 Herbig Ae) in the Taurus-Auriga region. We employ a novel 2D super-resolution imaging technique based on sparse modeling to obtain images with high fidelity and spatial resolution. As a result, we have obtained images with spatial resolutions comparable to a few au ($0''.02 - 0''.1$), which is two to three times better than conventional CLEAN methods. All dust disks are spatially resolved, with the radii ranging from 8 to 238 au with a median radius of 45 au. Half of the disks harbor clear gap structures, whose radial locations show a bimodal distribution with peaks at $\lesssim20$ au and $\gtrsim30$ au. We also see structures indicating weak gaps at all the radii in the disk. We find that the widths of these gaps increase with their depths, which is consistent with the model of planet-disk interactions. The inferred planet mass-orbital radius distribution indicates that the planet distribution is analogous to our Solar System. However, planets with Neptune mass or lower may exist in all the radii., Comment: 44 pages, 24 figures, 7 tables, accepted for publication in PASJ

The task of Split and Rephrase, which splits a complex sentence into multiple simple sentences with the same meaning, improves readability and enhances the performance of downstream tasks in natural language processing (NLP). However, while Split and Rephrase can be improved using a text-to-text generation approach that applies encoder-decoder models fine-tuned with a large-scale dataset, it still suffers from hallucinations and under-splitting. To address these issues, this paper presents a simple and strong data refinement approach. Here, we create WikiSplit++ by removing instances in WikiSplit where complex sentences do not entail at least one of the simpler sentences and reversing the order of reference simple sentences. Experimental results show that training with WikiSplit++ leads to better performance than training with WikiSplit, even with fewer training instances. In particular, our approach yields significant gains in the number of splits and the entailment ratio, a proxy for measuring hallucinations., Comment: Accepted at LREC-COLING 2024

Recent measurements of carbon isotope ratios in both protoplanetary disks and exoplanet atmospheres have suggested a possible transfer of significant carbon isotope fractionation from disks to planets. For a clearer understanding of the isotopic link between disks and planets, it is important to measure the carbon isotope ratios in various species. In this paper, we present a detection of the $^{13}$CN $N=2-1$ hyperfine lines in the TW Hya disk with the Atacama Large Millimeter/submillimeter Array. This is the first spatially-resolved detection of $^{13}$CN in disks, which enables us to measure the spatially resolved $^{12}$CN/$^{13}$CN ratio for the first time. We conducted non-local thermal equilibrium modeling of the $^{13}$CN lines in conjunction with previously observed $^{12}$CN lines to derive the kinetic temperature, ${\rm H_2}$ volume density, and column densities of $^{12}$CN and $^{13}$CN. The ${\rm H_2}$ volume density is found to range between $ (4 - 10)\times10^7 \ {\rm cm^{-3}}$, suggesting that CN molecules mainly reside in the disk upper layer. The $^{12}$CN/$^{13}$CN ratio is measured to be $ 70^{+9}_{-6}$ at $30 < r < 80$ au from the central star, which is similar to the $\rm ^{12}C/^{13}C$ ratio in the interstellar medium. However, this value differs from the previously reported values found for other carbon-bearing molecules (CO and HCN) in the TW Hya disk. This could be self-consistently explained by different emission layer heights for different molecules combined with preferential sequestration of $\rm ^{12}C$ into the solid phase towards the disk midplane. This study reveals the complexity of the carbon isotope fractionation operating in disks., Comment: 16 pages, 7 figures, accepted for publication in ApJ

Decoder-based large language models (LLMs) have shown high performance on many tasks in natural language processing. This is also true for sentence embedding learning, where a decoder-based model, PromptEOL, has achieved the best performance on semantic textual similarity (STS) tasks. However, PromptEOL requires a manually annotated natural language inference (NLI) dataset for fine-tuning. We aim to improve sentence embeddings without using large manually annotated datasets by automatically generating an NLI dataset with an LLM and using it for fine-tuning of PromptEOL. To achieve this, we explore methods of data generation suitable for sentence embedding learning in this study. Specifically, we will focus on automatic dataset generation through few-shot learning and explore the appropriate methods to leverage few-shot examples. Experimental results on the STS tasks demonstrate that our approach outperforms existing models in settings without large manually annotated datasets.

We report the development of Japanese SimCSE, Japanese sentence embedding models fine-tuned with SimCSE. Since there is a lack of sentence embedding models for Japanese that can be used as a baseline in sentence embedding research, we conducted extensive experiments on Japanese sentence embeddings involving 24 pre-trained Japanese or multilingual language models, five supervised datasets, and four unsupervised datasets. In this report, we provide the detailed training setup for Japanese SimCSE and their evaluation results.

Layer number-dependent band structures and symmetry are vital for the electrical and optical characteristics of two-dimensional (2D) transition metal dichalcogenides (TMDCs). Harvesting 2D TMDCs with tunable thickness and properties can be achieved through top-down etching and bottom-up growth strategies. In this study, we report a pioneering technique that utilizes the migration of in-situ generated Na-W-S-O droplets to etch out one-dimensional (1D) nanotrenches in few-layer WS$_2$. 1D WS$_2$ nanotrenches were successfully fabricated on the optically inert bilayer WS$_2$, showing pronounced photoluminescence and second harmonic generation signals. Additionally, we demonstrate the modulation of inkjet-printed Na$_2$WO$_4$-Na$_2$SO$_4$ particles to switch between the etching and growth modes by manipulating the sulfur supply. This versatile approach enables the creation of 1D nanochannels on 2D TMDCs. Our research presents exciting prospects for the top-down and bottom-up fabrication of 1D-2D mixed-dimensional TMDC nanostructures, expanding their use for photonic and optoelectronic applications., Comment: 37 pages, 16 figures

Characterizing the physical properties of dust grains in a protoplanetary disk is critical to comprehending the planet formation process. Our study presents ALMA high-resolution observations of the young protoplanetary disk around DG Tau at a 1.3 mm dust continuum. The observations, with a spatial resolution of $\approx 0.04''$, or $\approx5$ au, revealed a geometrically thin and smooth disk without substantial substructures, suggesting that the disk retains the initial conditions of the planet formation. To further analyze the distributions of dust surface density, temperature, and grain size, we conducted a multi-band analysis with several dust models, incorporating ALMA archival data of the 0.87 mm and 3.1 mm dust polarization. The results showed that the Toomre $Q$ parameter is $\lesssim2$ at a 20 au radius, assuming a dust-to-gas mass ratio of 0.01. This implies that a higher dust-to-gas mass ratio is necessary to stabilize the disk. The grain sizes depend on the dust models, and for the DSHARP compact dust, they were found to be smaller than $\sim400$ $\mu$m in the inner region ($r\lesssim20$ au), while exceeding larger than 3 mm in the outer part. Radiative transfer calculations show that the dust scale height is lower than at least one-third of the gas scale height. These distributions of dust enrichment, grain sizes, and weak turbulence strength may have significant implications for the formation of planetesimals through mechanisms such as streaming instability. We also discuss the CO snowline effect and collisional fragmentation in dust coagulation for the origin of the dust size distribution., Comment: 29 pages, 21 figures, 5 tables. Accepted for publication in ApJ

Magnetic skyrmions are particle-like spin-swirling objects ubiquitously realized in magnets. They are topologically stable chiral kinks composed of multiple modulation waves of spiral spin structures, where the helicity of each spiral is usually selected by antisymmetric exchange interactions in noncentrosymmetric crystals. We report an experimental observation of a distorted triangular lattice of skyrmions in the polar tetragonal magnet EuNiGe$_3$, reflecting a strong coupling with the lattice. Moreover, through resonant x-ray diffraction, we find that the magnetic helicity of the original spiral at zero field is reversed when the skyrmion lattice is formed in a magnetic field. This means that the energy gain provided by the skyrmion lattice formation is larger than the antisymmetric exchange interaction. Our findings will lead us to a further understanding of emergent magnetic states., Comment: 9 pages, 3 figures, supplemental material (6 pages, 12 figures)

The capability to finely tailor material thickness with simultaneous atomic precision and non-invasivity would be useful for constructing quantum platforms and post-Moore microelectronics. However, it remains challenging to attain synchronized controls over tailoring selectivity and precision. Here we report a protocol that allows for non-invasive and atomically digital etching of van der Waals transition-metal dichalcogenides through selective alloying via low-temperature thermal diffusion and subsequent wet etching. The mechanism of selective alloying between sacrifice metal atoms and defective or pristine dichalcogenides is analyzed with high-resolution scanning transmission electron microscopy. Also, the non-invasive nature and atomic level precision of our etching technique are corroborated by consistent spectral, crystallographic and electrical characterization measurements. The low-temperature charge mobility of as-etched MoS$_2$ reaches up to $1200\,$cm$^{2}\cdot$V$^{-1}\cdot$s$^{-1}$, comparable to that of exfoliated pristine counterparts. The entire protocol represents a highly precise and non-invasive tailoring route for material manipulation., Comment: 46 pages, 4 figures, with SI

The magnetic helicities of the cycloidal ordering in EuIrGe$_3$, with a noncentrosymmetric tetragonal structure, have been studied by circularly polarized resonant X-ray diffraction. It is shown that the helicity of each cycloidal domain is uniquely determined and satisfies the symmetry relations of the $C_{4v}$ point group of the crystal structure. The result shows that the cycloidal helicity is determined by the Dzyaloshinskii-Moriya type antisymmetric exchange interaction. The domain selection and the phase transition by the external magnetic field along [100] and [110] have also been studied. It is shown that the cycloidal plane prefers to be perpendicular to the field and the transverse conical state is realized., Comment: 6 pages, 4 figures, 5 figures in the supplemental material, accepted for publication in J. Phys. Soc. Jpn

We have performed magnetic susceptibility, magnetization, and specific heat measurements on a chiral magnet GdNi$_3$Ga$_9$, belonging to the trigonal space group $R32$ (\#155). A magnetic phase transition takes place at $T_{\rm N}$ = 19.5 K. By applying a magnetic field along the $a$ axis at 2 K, the magnetization curve exhibits two jumps at $\sim$ 3 kOe and = 45 kOe. To determine the magnetic structure, we performed a resonant X-ray diffraction experiment by utilizing a circularly polarized beam. It is shown that a long-period antiferromagnetic (AFM) helical order is realized at zero field. The Gd spins in the honeycomb layer are coupled in an antiferromagnetic manner in the $c$ plane and rotate with a propagation vector $q$ = (0, 0, 1.485). The period of the helix is 66.7 unit cells ($\sim 180$~nm). In magnetic fields above 3~kOe applied perpendicular to the helical $c$ axis, the AFM helical order changes to an AFM order with $q$ = (0, 0, 1.5)., Comment: 7 pages, 12 figures

Recent progress in sentence embedding, which represents the meaning of a sentence as a point in a vector space, has achieved high performance on tasks such as a semantic textual similarity (STS) task. However, sentence representations as a point in a vector space can express only a part of the diverse information that sentences have, such as asymmetrical relationships between sentences. This paper proposes GaussCSE, a Gaussian distribution-based contrastive learning framework for sentence embedding that can handle asymmetric relationships between sentences, along with a similarity measure for identifying inclusion relations. Our experiments show that GaussCSE achieves the same performance as previous methods in natural language inference tasks, and is able to estimate the direction of entailment relations, which is difficult with point representations., Comment: Accepted to EACL 2024 (Main)

Crystal field level scheme of a uniaxial chiral helimagnet YbNi$_3$Al$_9$, exhibiting a chiral magnetic soliton lattice state by Cu substitution for Ni, has been determined by inelastic neutron scattering. The ground and the first excited doublets are separated by 44 K and are simply expressed as $\alpha|\pm 7/2\rangle + \beta |\mp 5/2\rangle$ with $\alpha$ and $\beta$ nearly equal to $\pm 1/\sqrt{2}$. The easy axis of the crystal field anisotropy is the $c$ axis when the excited levels are populated at high temperatures and high magnetic fields. On the other hand, the magnetism at low temperatures and low magnetic fields, where only the ground doublet is populated, is described by an easy plane anisotropy which may be treated as an $S=1/2$ system with an anisotropic $g$-factor, $g_{xy}=3.02$ and $g_z=1.14$. An orbital dependent exchange interaction is also discussed to explain the temperature dependence of the magnetic susceptibility based on this level scheme., Comment: 9 pages, 7 figures, 2 figures in the supplemental material, accepted for publication in Phys. Rev. B

Crescent-like asymmetric dust structures discovered in protoplanetary disks indicate dust aggregations. Thus, the research on them helps us understand the planet formation process. Here we analyze the ALMA data of the protoplanetary disk around the T-Tauri star SR 21, which has asymmetric structures detected in previous sub-millimeter observations. Imaged at ALMA Band 6 (1.3 mm) with a spatial resolution of about 0.$\arcsec$04, the disk is found to consist of two rings and three asymmetric structures, with two of the asymmetric structures being in the same ring. Compared to the Band 6 image, the Band 3 (2.7 mm) image also shows the three asymmetric structures but with some clumps. The elongated asymmetric structures in the outer ring could be due to the interactions of a growing planet. By fitting the Band 3 and Band 6 dust continuum data, two branches of solutions of maximum dust size in the disk are suggested: one is larger than 1 mm, and the other is smaller than 300 $\mu m$. High-resolution continuum observations at longer wavelengths as well as polarization observations can help break the degeneracy. We also suggest that the prominent spiral previously identified in VLT/SPHERE observations to the south of the star at 0.$\arcsec$25 may be the scattered light counterpart of the Inner Arc, and the structure is a dust-trapping vortex in nature. The discovered features in SR 21 make it a good target for studying the evolution of asymmetric structures and planet formation., Comment: Accepted by The Astrophysical Journal

Inspired by the dexterous handling ability of an elephant's trunk, we propose a pneumatic actuator that generates diverse bending and extension motions in a flexible arm. The actuator consists of two flexible tubes. Each flexible tube is restrained by a single string with variable length and tilt angle. Even if a single tube can perform only three simple types of motions (bending, extension, and helical), a variety of complex bending patterns can be created by arranging a pair of tubes in parallel and making the restraint variable. This performance takes advantage of the effect of the superposition of forces by arranging two tubes to constructively interfere with each other. This paper described six resulting pose patterns. First, the configuration and operating principle are described, and the fabrication method is explained. Next, two mathematical models and four finite element method-based analyses are introduced to predict the tip position changes in five motion patterns. All the models were validated through experiments. Finally, we experimentally demonstrated that the prototype SEMI-TRUNK can realize the action of grabbing a bottle and pouring water, verifying the effectiveness of the proposed method., Comment: 8 pages, 11 figures, submitted to the IEEE Robotics and Automation Letters (RA-L)

In this study, we reported the results of high-resolution (0.14 arcsec) Atacama Large Millimeter/submillimeter Array (ALMA) observations of the 225 GHz dust continuum and CO molecular emission lines from the transitional disk around SY Cha. Our high-resolution observations clearly revealed the inner cavity and the central point source for the first time. The radial profile of the ring can be approximated by a bright narrow ring superimposed on a fainter wide ring. Furthermore, we found that there is a weak azimuthal asymmetry in dust continuum emission. For gas emissions, we detected $\rm{}^{12}CO$(2$-$1), $\rm{}^{13}CO$(2$-$1) and $\rm{}C^{18}O$(2$-$1), from which we estimated the total gas mass of the disk to be $2.2\times10^{-4}M_\odot$, assuming a CO/H$_2$ ratio of $10^{-4}$. The observations showed that the gas is present inside the dust cavity. The analysis of the velocity structure of the $\rm{}^{12}CO$(2$-$1) emission line revealed that the velocity is distorted at the location of the dust inner disk, which may be owing to warping of the disk or radial gas flow within the cavity of the dust disk. High-resolution observations of SY Cha showed that this system is composed of a ring and a distorted inner disk, which may be common, as indicated by the survey of transitional disk systems at a resolution of $\sim$0.1~arcsec., Comment: 33 pages, 22 figures

High spatial resolution observations of CO isotopologue line emission in protoplanetary disks at mid-inclinations (${\approx}$30-75{\deg}) allow us to characterize the gas structure in detail, including radial and vertical substructures, emission surface heights and their dependencies on source characteristics, and disk temperature profiles. By combining observations of a suite of CO isotopologues, we can map the 2D (r, z) disk structure from the disk upper atmosphere, as traced by CO, to near the midplane, as probed by less abundant isotopologues. Here, we present high angular resolution (${\lesssim}$0."1 to ${\approx}$0."2; ${\approx}$15-30 au) observations of CO, $^{13}$CO, and C$^{18}$O in either or both J=2-1 and J=3-2 lines in the transition disks around DM Tau, Sz 91, LkCa 15, and HD 34282. We derived line emission surfaces in CO for all disks and in $^{13}$CO for the DM Tau and LkCa 15 disks. With these observations, we do not resolve the vertical structure of C$^{18}$O in any disk, which is instead consistent with C$^{18}$O emission originating from the midplane. Both the J=2-1 and J=3-2 lines show similar heights. Using the derived emission surfaces, we computed radial and vertical gas temperature distributions for each disk, including empirical temperature models for the DM Tau and LkCa 15 disks. After combining our sample with literature sources, we find that $^{13}$CO line emitting heights are also tentatively linked with source characteristics, e.g., stellar host mass, gas temperature, disk size, and show steeper trends than seen in CO emission surfaces., Comment: 31 pages, 15 figures, accepted for publication in ApJ. Image cubes available at https://zenodo.org/record/7430257

The mass distribution of dense cores is a potential key to understand the process of star formation. Applying dendrogram analysis to the CARMA-NRO Orion C$^{18}$O ($J$=1--0) data, we identify 2342 dense cores, about 22 \% of which have virial ratios smaller than 2, and can be classified as gravitationally bound cores. The derived core mass function (CMF) for bound starless cores which are not associate with protostars has a slope similar to Salpeter's initial mass function (IMF) for the mass range above 1 $M_\odot$, with a peak at $\sim$ 0.1 $M_\odot$. We divide the cloud into four parts based on the declination, OMC-1/2/3, OMC-4/5, L1641N/V380 Ori, and L1641C, and derive the CMFs in these regions. We find that starless cores with masses greater than 10 $M_\odot$ exist only in OMC-1/2/3, whereas the CMFs in OMC-4/5, L1641N, and L1641C are truncated at around 5--10 $M_\odot$. From the number ratio of bound starless cores and Class II objects in each subregion, the lifetime of bound starless cores is estimated to be 5--30 free-fall times, consistent with previous studies for other regions. In addition, we discuss core growth by mass accretion from the surrounding cloud material to explain the coincidence of peak masses between IMFs and CMFs. The mass accretion rate required for doubling the core mass within a core lifetime is larger than that of Bondi-Hoyle accretion by a factor of order 2. This implies that more dynamical accretion processes are required to grow cores., Comment: 58 pages, 33 figures, 21 tables, accepted by ApJS

We report a promising InSiO film that allows simultaneous observation of sample morphology and Kikuchi patterns in raster scan mode of scanning electron microscopy. This new experimental observation suggests potential mechanism beyond existing diffraction theories. We find by simulation that this material has a novel cylindrically symmetric rotational crystalline structure that can control the diffraction direction of electrons through a specific rotational distribution of crystal planes, while being independent of the angle and energy of incident electrons within a certain range.

The gas surface density profile of protoplanetary disks is one of the most fundamental physical properties to understand planet formation. However, it is challenging to determine the surface density profile observationally, because the H$_2$ emission cannot be observed in low-temperature regions. We analyzed the Atacama Large Millimeter/submillimeter Array (ALMA) archival data of the \co line toward the protoplanetary disk around TW Hya and discovered extremely broad line wings due to the pressure broadening. In conjunction with a previously reported optically thin CO isotopologue line, the pressure broadened line wings enabled us to directly determine the midplane gas density for the first time. The gas surface density at $\sim5$ au from the central star reaches $\sim 10^3\ {\rm g\ cm^{-2}}$, which suggests that the inner region of the disk has enough mass to form a Jupiter-mass planet. Additionally, the gas surface density drops at the inner cavity by $\sim2$ orders of magnitude compared to outside the cavity. We also found a low CO abundance of $\sim 10^{-6}$ with respect to H$_2$, even inside the CO snowline, which suggests conversion of CO to less volatile species. Combining our results with previous studies, the gas surface density jumps at $r\sim 20$ au, suggesting that the inner region ($3

Successive magnetic phase transitions at $T_{\text{N}}$=12.2 K, $T_{\text{N}}^{\;\prime}$=7.0 K, and $T_{\text{N}}^{\;*}$=5.0 K in EuIrGe$_3$, an intermetallic compound with a body centered tetragonal lattice belonging to a polar space group $I4mm$, has been investigated by neutron diffraction and resonant X-ray diffraction. It is shown that EuIrGe$_3$ exhibits an incommensurate longitudinal sinusoidal order with $q\sim (0, 0, 0.792)$ and $m_{q} \parallel c\text{-axis}$ in the high temperature phase ($T_{\text{N}}^{\;\prime}< T < T_{\text{N}}$), which changes to a cycloidal order with $q=(\delta', 0, 0.8)$ ($\delta'\sim 0.017$) and $m_{q} \parallel ac\text{-plane}$ in the intermediate phase ($T_{\text{N}}^{\;*} < T < T_{\text{N}}^{\;\prime}$). In the low temperature phase ($T < T_{\text{N}}^{\;*}$), the cycloidal plane rotates by $45^{\circ}$ to have $q=(\delta, \delta, 0.8)$ ($\delta\sim 0.012$). It is also pointed out that the X-ray scattering amplitude from odd-parity magnetic quadrupole due to the polar environment interfere with that from normal even-parity magnetic dipole in the magnetic ordered phase., Comment: 5 pages, 6 figures, 7 figures in the supplemental material, accepted for publication in J. Phys. Soc. Jpn

The Kikuchi bands arise from Bragg diffraction of incoherent electrons scattered within a crystalline specimen and can be observed in both the transmission and reflection modes of scanning electron microscopy (SEM). Converging, rocking, or grazing incidence beams must be used to generate divergent electron sources to obtain the Kikuchi pattern. This paper report the observation of Kikuchi pattern from SEM images of an exceptional rotating crystal with continuous rotation in the local crystal direction and satisfying cylindrical symmetry, named a cylindrically symmetric rotating crystal. SEM images of cylindrically symmetric rotating crystals reflect the interactions between electrons and the sample in both the real- and momentum-space. Furthermore, we identify an unexpected mathematical relationship between the electron backscattered diffraction (EBSD) Kikuchi pattern matrix map and the SEM image of the present sample which can be rationalized as a concrete example of the Banach fixed-point theorems in the field of EBSD technique.

The radial extent of millimetre dust in protoplanetary discs is often far smaller than that of their gas, mostly due to processes such as dust growth and radial drift. However, it has been suggested that current millimetre continuum observations of discs do not trace their full extent due to limited sensitivity. In this Letter, we present deep (19 $\mu$Jy beam$^{-1}$) moderate resolution (0.37") ALMA observations at 1 mm of the nearest protoplanetary disc, TW Hya. Using the visibility analysis tool `frank', we reveal a structured millimetre intensity distribution out to 100 au, well beyond previous estimates of 60-70 au. Our analysis suggests the presence of a new millimetre continuum gap at 82 au, coincident with similar features seen in optical/near-infrared scattered light and millimetre molecular line observations. Examination of the fit residuals confirms the presence of the previously reported au-scale continuum excess at 52 au (P.A. = 242.5 degrees). Our results demonstrate the utility of combining deep, moderate resolution observations with super-resolution analysis techniques to probe the faintest regions of protoplanetary discs., Comment: 6 pages, 4 figures, accepted for publication in MNRAS Letters

High spatial resolution CO observations of mid-inclination (30-75{\deg}) protoplanetary disks offer an opportunity to study the vertical distribution of CO emission and temperature. The asymmetry of line emission relative to the disk major axis allows for a direct mapping of the emission height above the midplane, and for optically-thick, spatially-resolved emission in LTE, the intensity is a measure of the local gas temperature. Our analysis of ALMA archival data yields CO emission surfaces, dynamically-constrained stellar host masses, and disk atmosphere gas temperatures for the disks around: HD 142666, MY Lup, V4046 Sgr, HD 100546, GW Lup, WaOph 6, DoAr 25, Sz 91, CI Tau, and DM Tau. These sources span a wide range in stellar masses (0.50-2.10 M$_{\odot}$), ages (${\sim}$0.3-23 Myr), and CO gas radial emission extents (${\approx}$200-1000 au). This sample nearly triples the number of disks with mapped emission surfaces and confirms the wide diversity in line emitting heights ($z/r\approx0.1$ to ${\gtrsim}0.5$) hinted at in previous studies. We compute radial and vertical CO gas temperature distributions for each disk. A few disks show local temperature dips or enhancements, some of which correspond to dust substructures or the proposed locations of embedded planets. Several emission surfaces also show vertical substructures, which all align with rings and gaps in the millimeter dust. Combining our sample with literature sources, we find that CO line emitting heights weakly decline with stellar mass and gas temperature, which, despite large scatter, is consistent with simple scaling relations. We also observe a correlation between CO emission height and disk size, which is due to the flared structure of disks. Overall, CO emission surfaces trace ${\approx}2$-$5\times$ gas pressure scale heights (H$_{\rm{g}}$) and could potentially be calibrated as empirical tracers of H$_{\rm{g}}$., Comment: 31 pages, 17 figures, accepted for publication in ApJ. Image cubes available at https://zenodo.org/record/6410045

Planetary systems are thought to be born in protoplanetary disks. Isotope ratios are a powerful tool for investigating the material origin and evolution from molecular clouds to planetary systems via protoplanetary disks. However, it is challenging to measure the isotope (isotopologue) ratios, especially in protoplanetary disks, because the emission lines of major species are saturated. We developed a new method to overcome these challenges by using optically thin line wings induced by thermal broadening. As a first application of the method, we analyzed two carbon monoxide isotopologue lines, $^{12}$CO $3-2$ and $^{13}$CO $3-2$, from archival observations of a protoplanetary disk around TW Hya with the Atacama Large Millimeter/sub-millimeter Array. The $^{12}$CO/$^{13}$CO ratio was estimated to be ${ 20\pm5}$ at disk radii of ${ 70-110}$ au, which is significantly smaller than the value observed in the local interstellar medium, $\sim69$. It implies that an isotope exchange reaction occurs in a low-temperature environment with $\rm C/O>1$ . In contrast, it is suggested that $^{12}$CO/$^{13}$CO is higher than $\sim{ 84}$ in the outer disk ($r > { 130}$ au), which can be explained by the difference in the binding energy of the isotopologues on dust grains and the CO gas depletion processes. Our results imply that the gas-phase $^{12}$CO/$^{13}$CO can vary by a factor of ${ > 4}$ even inside a protoplanetary disk, and therefore, can be used to trace material evolution in disks., Comment: 17 pages, 13 figures, accepted for publication in ApJ