arXiv subjects

Mikito Kohno

Publications and source records attributed to Mikito Kohno.

At least 19 recordsLinked to original sources

arXiv2026

The trigonometric parallax of IRAS 23385+6053 and physical properties of molecular clouds based on the VLBI astrometry

We performed very long baseline interferometry (VLBI) observations to measure the trigonometric parallax of H$_2$O maser sources in the outer massive star-forming region IRAS 23385+6053 using the VLBI Exploration of Radio Astrometry (VERA) in Japan. The annual parallax is $\pi=0.460 \pm 0.086$~mas, which corresponds to a distance of $2.17^{+0.50}_{-0.34}$ kpc, roughly half the kinematic distance of 4.9 kpc reported in previous studies. The proper motion of IRAS 23385+6053 is obtained to be ($\mu_{\alpha}\cos{\delta}$,$\mu_{\delta}$)=($-3.73\pm0.53$, $-2.0{7}\pm0.73$) mas yr$^{-1}$. Based on VLBI astrometry result, we derived the physical properties of molecular clouds in which H$_2$O masers have been detected, including IRAS 23385+6053 in the Cepheus and Cassiopeia region. We discuss the line-of-sight structures of the giant molecular clouds using the trigonometric distances obtained from the H$_{2}$O maser sources. Our results suggest that molecular clouds in the Perseus arm extend over approximately $2$ kpc at the Cepheus and Cassiopeia region.

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arXiv2025

Head-tail molecular clouds falling onto the Milky Way disk

We report discovery of two CO clouds which are likely falling down to the Galactic plane at more than $35$ km s$^{-1}$. The clouds show head-tail distributions elongated perpendicular to the Galactic plane at $l=331.6^{\circ}$ and $b=0^{\circ}$ as revealed by an analysis of the Mopra CO $J=$1-0 survey data. We derived the distance of the clouds to be $2.46 \pm 0.18$ kpc based on the Gaia Data Release 3. The CO clouds have molecular masses of $4.8\times 10^3\ M_{\odot}$ and $3.5\times 10^3\ M_{\odot}$, respectively, and show kinetic temperature of 30-50 K as derived from the line intensities of the $^{13}$CO $J$=2-1, $^{12}$CO $J$=1-0, and $^{13}$CO $J$=1-0 emission. The temperature in the heads of the clouds is significantly higher than 10 K of the typical molecular clouds, although no radiative heat source is found inside or close to the clouds. Based on the results, we interpret that the present clouds are falling onto the Milky Way disk and are significantly heated up by the strong shock interaction with the disk HI gas. We suggest that the clouds represent part of the HI intermediate velocity clouds falling to the Galactic plane which were converted into molecular clouds by shock compression. This is the first case of falling CO clouds having direct observed signatures of the falling motion including clear directivity and shock heating. Possible implications of the CO clouds in the evolution of the Galactic interstellar medium are discussed.

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arXiv2025

A catalog of molecular clouds possibly associated with Galactic infrared bubbles I. The Southern Galactic plane

We have carried out a morphological search for molecular clouds possibly associated with 48 Galactic infrared bubbles with angular radii of $>1'$ in the southern Galactic plane of $295^\circ \le l\le 350^\circ$ and $|b|\le 1^\circ$ presented by Hanaoka et al. (2019). 116 molecular clouds in the $(l,b,V_{\rm LSR})$ space are identified from the archival $^{12}$CO~$J$~=~1--0 line data obtained by the Mopra Southern Galactic plane survey, where $V_{\rm LSR}$ is the CO-line radial velocity. The kinematic distances are derived from $V_{\rm LSR}$ using the most accurate rotation curve of the Milky Way. We also present measurements of velocity dispersion, size parameter, molecular mass, and virial mass of 116 molecular clouds. This catalog is presented to investigate star formation and the origin of molecular shells and cavities, possibly associated with infrared bubbles. CO line intensity maps and position-velocity diagrams of the molecular clouds are available online as supplementary data.

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arXiv2025

Giant Molecular Clouds in RCW 106 (G333): Galactic Mini-starbursts and Massive Star Formation Induced by Supersonic Cloud-Cloud Collisions

To reveal the origin of the mini-starbursts in the Milky Way, we carried out large-scale CO observations toward the RCW 106 giant molecular cloud (GMC) complex using the NANTEN2 4-m radio telescope operated by Nagoya University. We also analyzed the Mopra Southern Galactic plane CO survey and Herschel infrared continuum archival data. The RCW 106 GMC complex contains the radial velocity components of $-68$ km s$^{-1}$ and $-50$ km s$^{-1}$ reported by Nguyen et al. (2015). Focusing on the RCW 106 East and West region with the massive star formation having the bright infrared dust emission, we found that these regions have three different velocity components with $\sim 10$ km s$^{-1}$ differences. The two out of three velocity components show morphological correspondence with the infrared cold dust emission and connect with the bridge feature on a position-velocity diagram. Therefore, two molecular clouds (MCs) with $\sim 10$ km s$^{-1}$ differences are likely to be physically associated with massive star-forming regions in the GMC complex. Based on these observational results, we argue that mini-starbursts and massive star/cluster formation in the RCW 106 GMC complex are induced by supersonic cloud-cloud collisions in an agglomerate of molecular gas on the Scutum-Centaurus arm.

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arXiv2024

The CO-to-H$_2$ Conversion Factor in the Central Molecular Zone of the Milky Way using CO isotopologues

We performed correlation analyses between the $^{12}$CO and $^{13}$CO $J=$1-0 line intensities in order to derive the variability of the CO-to-H$_2$ conversion factor ($X_{\rm CO, iso}$) in the central molecular zone (CMZ) of our Galaxy. New high-resolution $X_{\rm CO, iso}$ maps at a resolution of $\sim 30$" and the longitude-velocity diagram (LVD) at resolution $\sim 30$" $ \times\ 2$ km s$^{-1}$ are presented using the $^{12}$CO and $^{13}$CO archival survey data obtained by the Nobeyama 45 m telescope. We revealed the variation of $X_{\rm CO, iso}$ in the CMZ within the range of $X_{\rm CO, iso} \sim (0.2-1.3) \times 10^{20}\ {\rm cm^{-2}\ (K\ km\ s^{-1})^{-1}}$, if we assume the normalization value of $0.59 \times 10^{20}\ {\rm cm^{-2}\ (K\ km\ s^{-1})^{-1}}$. The mean value is obtained as $X_{\rm CO, iso} = (0.48 \pm 0.15) \times 10^{20}\ {\rm cm^{-2}\ (K\ km\ s^{-1})^{-1}}$ in the CMZ of our Galaxy.

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arXiv2023

The CO-to-H$_2$ Conversion Factor of Galactic Giant Molecular Clouds using CO isotopologues: High-resolution $X_{\rm CO}$ maps

We investigated the correlation between intensities of the $^{12}$CO and $^{13}$CO ($J=1$-0) lines toward the Galactic giant molecular clouds (GMCs) W51A, W33, N35-N36 complex, W49A, M17SW, G12.02-00.03, W43, and M16 using the FUGIN (FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope) CO line data. All the GMCs show intensity saturation in the $^{12}$CO line when the brightness temperature of $^{13}$CO is higher than a threshold temperature of about $\sim 5$ K. We obtained high-resolution ($\sim 20"$) distribution maps of the $X_{\rm CO}$ factor ($X_{\rm CO, iso}$) in individual GMCs using correlation diagrams of the CO isotopologues. It is shown that $X_{\rm CO, iso}$ is variable in each GMC within the range of $X_{\rm CO, iso} \sim (0.9 {\rm -} 5) \times 10^{20}$ cm$^{-2}$ (K km s$^{-1})^{-1}$. Despite the variability in the GMCs, the average value among the GMCs is found to be nearly constant at $X_{\rm CO, iso} = (2.17 \pm 0.27) \times 10^{20}$ cm$^{-2}$ (K km s$^{-1})^{-1}$, which is consistent with that from previous studies in the Milky Way.

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arXiv2023

Multi log-normal density structure in Cygnus-X molecular clouds: A fitting for N-PDF without power-law

We studied the H$_2$ column density probability distribution function (N-PDF) based on molecular emission lines using the Nobeyama 45-m Cygnus X CO survey data. Using the DENDROGRAM and SCIMES algorithms, we identified 124 molecular clouds in the $^{13}$CO data. From these identified molecular clouds, an N-PDF was constructed for 11 molecular clouds with an extent of more than 0.4 deg$^2$. From the fitting of the N-PDF, we found that the N-PDF could be well-fitted with one or two log-normal distributions. These fitting results provided an alternative density structure for molecular clouds from a conventional picture. We investigated the column density, dense molecular cloud cores, and radio continuum source distributions in each cloud and found that the N-PDF shape was less correlated with the star-forming activity over a whole cloud. Furthermore, we found that the log-normal N-PDF parameters obtained from the fitting showed two impressive features. First, the log-normal distribution at the low-density part had the same mean column density ($\sim$ 10$^{21.5}$ cm$^{-2}$) for almost all the molecular clouds. Second, the width of the log-normal distribution tended to decrease with an increasing mean density of the structures. These correlations suggest that the shape of the N-PDF reflects the relationship between the density and turbulent structure of the whole molecular cloud but is less affected by star-forming activities.

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arXiv2023

Ammonia mapping observations of the Galactic infrared bubble N49: Three NH$_3$ clumps along the molecular filament

We have carried out the NH$_3$ $(J,K)=(1,1),(2,2),$ and $(3,3)$ mapping observations toward the Galactic infrared bubble N49 (G28.83-0.25) using the Nobeyama 45 m telescope. Three NH$_3$ clumps (A, B, and C) were discovered along the molecular filament with the radial velocities of $\sim$ 96, 87, and 89 km s$^{-1}$, respectively. The kinetic temperature derived from the NH$_3$ (2,2)/NH$_3$ (1,1) shows $T_{\rm kin} = 27.0 \pm 0.6$ K enhanced at Clump B in the eastern edge of the bubble, where position coincides with massive young stellar objects (MYSOs) associated with the 6.7 GHz class II methanol maser source. This result shows the dense clump is locally heated by stellar feedback from the embedded MYSOs. The NH$_3$ Clump B also exists at the 88 km s$^{-1}$ and 95 km s$^{-1}$ molecular filament intersection. We therefore suggest that the NH$_3$ dense gas formation in Clump B can be explained by a filament-filament interaction scenario. On the other hand, NH$_3$ Clump A and C at the northern and southern side of the molecular filament might be the sites of spontaneous star formation because these clumps are located $\sim$5$-$10 pc away from the edge of the bubble.

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arXiv2022

Distance determination of molecular clouds in the 1st quadrant of the Galactic plane using deep learning : I. Method and Results

Machine learning has been successfully applied in varied field but whether it is a viable tool for determining the distance to molecular clouds in the Galaxy is an open question. In the Galaxy, the kinematic distance is commonly employed as the distance to a molecular cloud. However, there is a problem in that for the inner Galaxy, two different solutions, the ``Near'' solution, and the ``Far'' solution, can be derived simultaneously. We attempted to construct a two-class (``Near'' or ``Far'') inference model using a Convolutional Neural Network (CNN), a form of deep learning that can capture spatial features generally. In this study, we used the CO dataset toward the 1st quadrant of the Galactic plane obtained with the Nobeyama 45-m radio telescope (l = 62-10 degree, |b| < 1 degree). In the model, we applied the three-dimensional distribution (position-position-velocity) of the 12CO (J=1-0) emissions as the main input. The dataset with ``Near'' or ``Far'' annotation was made from the HII region catalog of the infrared astronomy satellite WISE to train the model. As a result, we could construct a CNN model with a 76% accuracy rate on the training dataset. By using the model, we determined the distance to molecular clouds identified by the CLUMPFIND algorithm. We found that the mass of the molecular clouds with a distance of < 8.15 kpc identified in the 12CO data follows a power-law distribution with an index of about -2.3 in the mass range of M >10^3 Msun. Also, the detailed molecular gas distribution of the Galaxy as seen from the Galactic North pole was determined.

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arXiv2022

Ammonia mapping observations toward the Galactic massive star-forming region Sh 2-255 and Sh 2-257

We performed NH$_3\ (J,K)=(1,1),(2,2),$ and $(3,3)$ mapping observations toward the Galactic massive star-forming region Sh 2-255 and Sh 2-257 using the Nobeyama 45-m telescope as a part of the KAGONMA (KAgoshima Galactic Object survey with the Nobeyama 45-metre telescope by Mapping in Ammonia lines) project. NH$_3$ (1,1) has an intensity peak at the cluster S255 N, is distributed over 3 pc $\times$ 2 pc and is located between two HII regions. The kinetic temperature derived from the NH$_3 (2,2)/(1,1)$ ratio was $\sim 35$ K near the massive cluster S255 IR. These clusters also show emission with a large line width of $\sim$ 3-4 km s$^{-1}$. Based on the reported data we suggest that NH$_3$ gas in these regions is affected by stellar feedback from embedded YSO clusters in S255 IR and S255 N. We also detected NH$_3$ (1,1) emission in a region west of the main gas clump at the location of a concentration of Class II YSOs adjacent to the HII regions Sh 2-254. The presence of Class II YSOs implies $\sim$ 2 Myr of star formation, younger than Sh 2-254 ($\sim 5$ Myr), thus we suggest that star formation in the western region could be influenced by the older HII region Sh 2-254.

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arXiv2022

Velocity structure of the 50 pc-long NGC 6334 filamentary cloud: Hints of multiple compressions and their impact on the cloud properties?

[Abridged] The interstellar medium is observed to be organised in filamentary structures, as well as neutral (HI) and ionized (HII) bubbles. The expanding nature of these bubbles makes them shape their surroundings and possibly play a role in the formation and evolution of interstellar filaments. We present APEX $^{13}$CO and C$^{18}$O(2-1) observations of the NGC 6334 molecular cloud. We investigate the gas velocity structure along and across the 50 pc-long cloud and towards 75 identified velocity-coherent-filaments (VCFs). We measure a wealth of velocity gradients along the VCFs. We derive the column density and velocity power spectra of the VCFs. These power spectra are well represented with power laws showing similar slopes for both quantities (with a mean of about -2), albeit some differ by up to a factor of two. The position velocity diagrams perpendicular to three VCFs show the V-shaped velocity pattern, corresponding to a bent structure in velocity space with the filament at the tip of the V surrounded by an extended structure connected to it with a velocity gradient. This velocity structure is qualitatively similar to that resulting from numerical simulations of filament formation from large-scale compression from propagating shock fronts. In addition, the radial profiles perpendicular to these VCFs hint to small-scale internal impacts from neighbouring HII bubbles. The observed opposite curvature in velocity space towards the VCFs points to various origins of large-scale external compressions from propagating HI bubbles. This suggests the plausible importance of multiple HI compressions, separated in space and time, in the formation and evolution of molecular clouds and their star formation history. These latter atomic compressions due to past and distant star formation events are complemented by the impact of HII bubbles from present time and local star formation activity.

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arXiv2021

Nobeyama 45 m Local Spur CO survey. I. Giant molecular filaments and cluster formation in the Vulpecula OB association

We have performed new large-scale $^{12}$CO, $^{13}$CO, and C$^{18}$O $J=$1-0 observations toward the Vulpecula OB association ($l \sim 60^\circ$) as part of the Nobeyama 45 m Local Spur CO survey project. Molecular clouds are distributed over $\sim 100$ pc, with local peaks at the Sh 2-86, Sh 2-87, and Sh 2-88 high-mass star-forming regions in the Vulpecula complex. The molecular gas is associated with the Local Spur, which corresponds to the nearest inter-arm region located between the Local Arm and the Sagittarius Arm. We discovered new giant molecular filaments (GMFs) in Sh 2-86, with a length of $\sim 30$ pc, width of $\sim 5$ pc, and molecular mass of $\sim 4\times 10^4\ M_{\odot}$. We also found that Sh 2-86 contains the three velocity components at 22, 27, and 33 km s$^{-1}$. These clouds and GMFs are likely to be physically associated with Sh 2-86 because they have high $^{12}$CO $J =$ 2-1 to $J =$ 1-0 intensity ratios and coincide with the infrared dust emission. The open cluster NGC 6823 exists at the common intersection of these clouds. We argue that the multiple cloud interaction scenario, including GMFs, can explain cluster formation in the Vulpecula OB association.

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arXiv2021

Massive star formation in the Carina nebula complex and Gum 31 -- II. a cloud-cloud collision in Gum 31

We present the results of analyses of the 12CO (J=1-0), 13CO (J=1-0), and 12CO (J=2-1) emission data toward Gum 31. Three molecular clouds separated in velocity were detected at -25, -20, and -10 km/s . The velocity structure of the molecular clouds in Gum 31 cannot be interpreted as expanding motion. Two of them, the -25 km/s cloud and the -20 km/s cloud, are likely associated with Gum 31, because their 12CO (J=2-1)/12CO (J=1-0) intensity ratios are high. We found that these two clouds show the observational signatures of cloud-cloud collisions (CCCs): a complementary spatial distribution and a V-shaped structure (bridge features) in the position-velocity diagram. In addition, their morphology and velocity structures are very similar to the numerical simulations conducted by the previous studies. We propose a scenario that the -25 km/s cloud and the -20 km/s cloud were collided and triggered the formation of the massive star system HD 92206 in Gum 31. This scenario can explain the offset of the stars from the center and the morphology of Gum 31 simultaneously. The timescale of the collision was estimated to be ~1 Myr by using the ratio between the path length of the collision and the assumed velocity separation. This is consistent with that of the CCCs in Carina Nebula Complex in our previous study.

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arXiv2020

Development of the new multi-beam receiver and telescope control system for NASCO

We report the current status of the NASCO (NAnten2 Super CO survey as legacy) project which aims to provide all-sky CO data cube of southern hemisphere using the NANTEN2 4-m submillimeter telescope installed at the Atacama Desert through developing a new multi-beam receiver and a new telescope control system. The receiver consists of 5 beams. The four beams, located at the four corners of a square with the beam separation of 720$''$, are installed with a 100 GHz band SIS receiver having 2-polarization sideband-separation filter. The other beam, located at the optical axis, is installed with a 200 GHz band SIS receiver having 2-polarization sideband-separation filter. The cooled component is modularized for each beam, and cooled mirrors are used. The IF bandwidths are 8 and 4 GHz for 100 and 200 GHz bands, respectively. Using XFFTS spectrometers with a bandwidth of 2 GHz, the lines of $^{12}$CO, $^{13}$CO, and C$^{18}$O of $J$=1$-$0 or $J$=2$-$1 can be observed simultaneously for each beam. The control system is reconstructed on the ROS architecture, which is an open source framework for robot control, to enable a flexible observation mode and to handle a large amount of data. The framework is commonly used and maintained in a robotic field, and thereby reliability, flexibility, expandability, and efficiency in development are improved as compared with the system previously used. The receiver and control system are installed on the NANTEN2 telescope in December 2019, and its commissioning and science verification are on-going. We are planning to start science operation in early 2021.

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arXiv2020

Atlas of CO-Line Shells and Cavities around Galactic Supernova Remnants with FUGIN

A morphological} search for molecular shells and cavities was performed around 63 Galactic supernova remnants (SNR) at $10^\circ \le l \le 50^\circ$, $|b|\le 1^\circ $using the FUGIN (FOREST Unbiased Galactic Imaging survey with the Nobeyama 45-m telescope) CO line data at high angular ($20''$) and velocity (1.3 km s$^{-1}$) resolutions. The results are presented as supplementary data for general purpose for investigations of the interaction between SNRs and interstellar matter in the form of an atlas of CO-line maps superposed on radio continuum maps at 20 cm along with a list of their kinematic distances determined from CO-line radial velocities. (Full atlas including all figures is available in this URL: https://nro-fugin.github.io/2020-apjs-CO-Shell-Atlas-SNR-FUGIN-IX.pdf)

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arXiv2020

Massive star formation in the Carina nebula complex and Gum 31 -- I. The Carina nebula complex

Herein, we present results from observations of the 12CO (J=1-0), 13CO (J=1-0), and 12CO (J=2-1) emission lines toward the Carina nebula complex (CNC) obtained with the Mopra and NANTEN2 telescopes. We focused on massive-star-forming regions associated with the CNC including the three star clusters Tr14, Tr15, and Tr16, and the isolated WR-star HD92740. We found that the molecular clouds in the CNC are separated into mainly four clouds at velocities -27, -20, -14, and -8 km/s. Their masses are 0.7x10^4Msun, 5.0x10^4 Msun, 1.6x10^4 Msun, and 0.7x10^4 Msun, respectively. Most are likely associated with the star clusters, because of their high 12CO (J=2-1)/12CO (J=1-0) intensity ratios and their correspondence to the Spitzer 8 micron distributions. In addition, these clouds show the observational signatures of cloud--cloud collisions. In particular, there is a V-shaped structure in the position--velocity diagram and a complementary spatial distribution between the -20 km/s cloud and the -14 km/s cloud. Based on these observational signatures, we propose a scenario wherein the formation of massive stars in the clusters was triggered by a collision between the two clouds. By using the path length of the collision and the assumed velocity separation, we estimate the timescale of the collision to be ~1 Myr. This is comparable to the ages of the clusters estimated in previous studies.

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arXiv2020

FOREST unbiased Galactic plane imaging survey with the Nobeyama 45 m telescope (FUGIN): Possible evidence of cloud-cloud collisions triggering high-mass star formation in the giant molecular cloud M16 (Eagle Nebula)

M16, the Eagle Nebula, is an outstanding \HII \ region which exhibits extensive high-mass star formation and hosts remarkable "pillars". We herein obtained new $^{12}$CO $J=$1-0 data for the region observed with NANTEN2, which were combined with the $^{12}$CO $J=$1-0 data obtained using FUGIN survey. These observations revealed that a giant molecular cloud (GMC) of $\sim 1.3 \times 10^5$ \Msun \ is associated with M16, which is elongated by over 30 pc and is perpendicular to the galactic plane, at a distance of 1.8 kpc. This GMC can be divided into the northern (N) cloud, the eastern (E) filament, the southeast (SE) cloud, the southeast (SE) filament, and the southern (S) cloud. We also found two velocity components (blue and red shifted component) in the N cloud. The blue-shifted component shows a ring-like structure, as well as the red-shifted component coincides with the intensity depression of the ring-like structure. The position-velocity diagram of the components showed a V-shaped velocity feature. The spatial and velocity structures of the cloud indicated that two different velocity components collided with each other at a relative velocity of 11.6 \kms. The timescale of the collision was estimated to be $\sim 4 \times 10^5$ yr. The collision event reasonably explains the formation of the O9V star ALS15348, as well as the shape of the Spitzer bubble N19. A similar velocity structure was found in the SE cloud, which is associated with the O7.5V star HD168504. In addition, the complementary distributions of the two velocity components found in the entire GMC suggested that the collision event occurred globally. On the basis of the above results, we herein propose a hypothesis that the collision between the two components occurred sequentially over the last several $10^{6}$ yr and triggered the formation of O-type stars in the NGC6611 cluster.

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arXiv2020

CO-to-H$_2$ Conversion and Spectral Column Density in Molecular Clouds: The Vriability of $X_{\rm CO}$ Factor

Analyzing the Galactic plane CO survey with the Nobeyama 45-m telescope, we compared the spectral column density (SCD) of H$_2$ calculated for $^{12}$CO line using the current conversion factor $X_{\rm CO}$ to that for $^{13}$CO line under LTE in M16 and W43 regions. Here, SCD is defined by $dN_{\rm H_2}/dv$ with $N_{\rm H_2}$ and $v$ being the column density and radial velocity, respectively. It is found that the $X_{\rm CO}$ method significantly under-estimates the H$_2$ density in a cloud or region, where SCD exceeds a critical value ($ \sim 3\times 10^{21}\ [{\rm H_2 \ cm^{-2} \ (km \ s^{-1})^{-1}}]$), but over-estimates in lower SCD regions. We point out that the actual CO-to-H$_2$ conversion factor varies with the H$_2$ column density or with the CO-line intensity: It increases in the inner and opaque parts of molecular clouds, whereas it decreases in the low-density envelopes. However, in so far as the current $X_{\rm CO}$ is used combined with the integrated $^{12}$CO intensity averaged over an entire cloud, it yields a consistent value with that calculated using the $^{13}$CO intensity by LTE. Based on the analysis, we propose a new CO-to-\Htwo conversion relation, $N_{\rm H_2}^* = \int X_{\rm CO}^*(T_{\rm B}) T_{\rm B} dv$, where $X_{\rm CO}^*=(T_{\rm B}/T_{\rm B}^*)^βX_{\rm CO}$ is the modified spectral conversion factor as a function of the brightness temperature, $T_{\rm B}$, of the ${12}$CO ($J=1-0$) line, and $β\sim 1-2$ and $T_{\rm B}^*=12-16$ K are empirical constants obtained by fitting to the observed data. The formula corrects for the over/under estimation of the column density at low/high-CO line intensities, and is applicable to molecular clouds with $T_{\rm B} \ge 1$ K (rms noise in the data) from envelope to cores at sub-parsec scales (resolution). (Full resolution copy available at http://www.ioa.s.u-tokyo.ac.jp/~sofue/news/2020_mn_Xco12co13_fugin.pdf)

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