{'fraction_non_alphanumeric': 0.04285851181064635, 'fraction_numerical': 0.027166882276843468, 'mean_word_length': 4.068358426420592, 'pattern_counts': {'":': 0, '<': 2, '<?xml version=': 0, '>': 4, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Three-dimensional dust geometry of the LMC HI ridge region as revealed by the IRSF/SIRIUS survey

We present a new method to evaluate the dust extinction (AV) along the line of sight using the InfraRed Survey Facility (IRSF) near-infrared (NIR) data of the Large Magellanic Cloud (LMC) HI ridge region. In our method, we estimate an AV value for each star from the NIR color excess and sort them from bluer to redder in each line of sight. Using the percentile values of the sorted AV, we newly construct the three-dimensional AV map. We compare the resultant AV map with the total hydrogen column density N(H) traced by velocity-resolved HI and CO observations. In the LMC HI ridge region, Fukui et al. (2017, PASJ, 69, L5) find two velocity components and an intermediate velocity one bridging them. Comparing our three-dimensional AV maps with N(H) maps at the different velocities, we find that the dust geometry is consistent with the scenario of the on-going gas collision between the two velocities as suggested in the previous study. In addition, we find difference by a factor of 2 in AV/N(H) between the two velocity components, which suggests that inflow gas from the Small Magellanic Clouds (SMC) is mixed in this region. As a whole, our results support the triggered star formation in 30 Doradus due to the large-scale gas collision caused by tidal interaction between the LMC and the SMC.


Introduction
The Large Magellanic Cloud (LMC) represents an ideal laboratory for studying the interstellar medium (ISM) among external galaxies. Because of its proximity (≃ 50 kpc; Pietrzyński et al. 2019) and its nearly face-on orientation (i ∼ 35 • ; van der Marel & Cioni 2001), we can perform spatially well-resolved studies of the ISM in almost two dimensions. In addition, the LMC is a suitable site for studying massive star formation in low metallicity environments (Z ∼ 0.5 Z⊙; Westerlund 1997). In the LMC H I ridge region, several massive star formations have been reported in 30 Doradus (30 Dor; e.g., Fukui et al. 2017;Indebetouw et al. 2020) and N159 (e.g., Fukui et al. 2019;Tokuda et al. 2019). In particular, 30 Dor is the most extreme starburst in the Local Universe. 30 Dor harbors about 400 O-type/Wolf-Rayet stars, primarily powered by the central super star cluster R136 (Doran et al. 2013). R136 has the mass of 5.0 × 10 4 M⊙, 10 times larger than that of a super star cluster in our Galaxy and hosts the most massive stars heavier than 200 M⊙ (Crowther et al. 2010;Crowther et al. 2016;Schneider et al. 2018).
A recent study suggests that massive O-and B-type stars in R136 were formed by collision of H I clouds (Fukui et al. 2017). In their study, two velocity components of H I clouds and an intermediate velocity one bridging them are identified, from which they suggest that massive star formation in 30 Dor has been triggered by collision between these two velocity components. In addition, they compare the dust optical depth at 353 GHz, τ353, with the H I intensity W (H I), and find that τ353/W (H I) in the H I ridge region is lower than that outside the H I ridge region. They suggest that the lower τ353/W (H I) ratio is caused by the contamination of inflow gas from the Small Magellanic Cloud (SMC), which is known to have even lower metallicity gas than the LMC, based on the result of the numerical simulation (Bekki & Chiba 2007a;Bekki & Chiba 2007b;Yozin & Bekki 2014). Hence the massive star formation in the H I ridge region is likely to have been triggered by the galactic interaction, and thus studying the dust/gas ratios of the H I ridge region is important to identify such inflow gases from the SMC. One of the most reliable indicators of the dust column density is the near-infrared (NIR) dust extinction because it does not depend much on the dust temperature which is difficult to estimate since irrelevant components can be contaminated along the line of sight.
The method to evaluate the NIR dust extinction was originally introduced by Lada et al. (1994). In this method, the H − K color excess is estimated from the mean H − K color in a reference field (i.e., extinction-free region), which is so called Near-Infrared Color Excess (NICE) method. Lombardi & Alves (2001) developed the NICE method by combining the H − K and J − H colors, which is called the NICER (NICE revised) method. Furthermore, Dobashi et al. (2008) proposed the "X percentile metho". In this method, first, the colors are sorted from blue to red. Then the color excess is estimated from the difference between the X percentile of the color (X = 0-100%. X = 100% denotes the reddest star) and that of the reference field. The X percentile method has the advantage that it is less affected by the contamination of the foreground stars causing under-estimation of the dust extinction. By using these methods, NIR dust extinction maps in the LMC were constructed based on the 2MASS data (Imara & Blitz 2007 using the NICER method; Dobashi et al. 2008 using the X percentile method). Furuta et al. (2019) derived the NIR dust extinction map of the LMC HI ridge region from the difference between the mean observed color and intrinsic colors accounting for several stellar spectral types. They compared the spatial distribution of the dust extinction with that of the hydrogen column density of different velocity components, and revealed differences in the dust/gas ratios between multiple velocity components, indicating that inflow gas from the SMC is present in the LMC H I ridge region. In addition, three-dimensional dust geometry was suggested based on the spatial (anti-)correlation between the dust extinction and hydrogen column density, which supported the gas collisions around 30 Dor. In this way, Furuta et al. (2019) demonstrated that the NIR extinction is a powerful tool to evaluate not only the dust/gas ratio but also dust geometry. However, the dust extinction estimated by Furuta et al. (2019) should be more or less under-estimated unless all the stars are located behind the clouds, because the color excess is calculated from the mean observed colors.
In this paper, we develop the method used in Furuta et al. (2019) by adopting the X percentile method to evaluate the dust extinction more precisely along the line of sight and to reveal the three-dimensional dust geometry. Using the resultant dust extinction map and gas maps of different velocity components, we discuss the dust distributions and dust/gas ratios of the multiple cloud components with different velocities.

IRSF/SIRIUS point source catalog
We used the NIR (J, H and KS bands) photometric catalog for the Magellanic Clouds (hereafter the IRSF catalog) obtained with the SIRIUS camera on the InfraRed Survey Facility (IRSF) 1.4 m telescope (Kato et al. 2007). In the IRSF catalog, Furuta et al. (2019) found systematic photometric errors due to the reflection of the incident twilight sky illumination inside the SIRIUS camera, and therefore reprocessed the raw data of the IRSF catalog by using the corrected flat-field images (for details of the analysis, see Furuta et al. 2019). In the present study, we selected data from this newly calibrated IRSF catalog according to the following criteria: (1) the magnitudes of the J, H and KS bands are brighter than 18.8, 17.8 and 16.6 mag, respectively, corresponding to the 10σ limiting magnitudes of the original IRSF catalog, (2) "quality flag" in the original IRSF catalog is 1 in all the bands, indicating that the shapes of sources are "point like" and (3) the number of combined dithered images is larger than 8 in all the bands.

Sample selection
The IRSF catalog is contaminated with Galactic foreground stars, which causes under-estimation of the dust extinction. Thus, we identify stellar populations using a color-magnitude diagram (CM diagram) according to the method used in Furuta et al. (2019). The authors classi- fied stellar populations into three categories which mainly consist of main sequence stars, red giant branch (RGB) stars and Galactic foreground stars. The boundary lines between the three categories are determined on the CM diagram (J − K vs. K) in their study. By using the same boundary lines, we classify the stellar populations, and use only the objects classified as RGB stars from the CM diagram. Figure 1 shows the number density map of the selected RGB stars in the H I ridge region.

Method
We describe our new method to measure the dust extinction along the line of sight in the LMC. The key is to take percentile values of the AV distribution in each line of sight based on the X percentile method. In the following subsections, we explain our procedure step by step.

Measuring A V for each star
We measure the dust extinction (AV ) for each star according to the method used in Furuta et al. (2019). In this method, AV is calculated from the difference between the observed and intrinsic colors on a color-color diagram (CC diagram). In figure 2, we present a CC diagram (H −K vs. J − H). The line connected with the black squares is the Fig. 2. Example of the color-color (H − K vs. J − H) diagrams of the sources selected within a spatial bin of 1. ′ 6×1. ′ 6. Red circles and black squares are observed and intrinsic colors of RGB stars, respectively. The black arrow shows the reddening vector corresponding to AV = 3 mag. Blue solid lines show the separation length between the observed and intrinsic colors of each star along the reddening vector.
locus of the intrinsic colors of RGB stars (Bessell & Brett 1988). The black arrow in figure 2 is the reddening vector obtained from Cardelli, Clayton and Mathis (1989), which is determined by the NIR photometry in the Johnson system. To unify the photometric system, the observed and intrinsic colors are converted into the Johnson system according to the conversion equations suggested by Nakajima et al. (2005) and Elias et al. (1985). From the reddening law of Cardelli, Clayton and Mathis (1989), we have and where E(J − H) and E(H − K) are the color excess of the J − H and H − K colors, respectively. Using equations (1) and (2), we estimate AV for each star from the separation length between the intrinsic and observed colors of each RGB star along the reddening vector on the CC diagram. Some of the observed colors in figure 2 are bluer than the intrinsic colors. In this case, we assign negative extinction corresponding to the separation length between the observed and intrinsic colors. In case that no intersection point exists between the reddening vector and the locus of the intrinsic colors, "not a number" is assigned to the corresponding star.

Calculation of A V distribution
For each spatial bin, we sort the stars with respect to their AV values estimated in section 3.1. In figure 3a, we show an example of the CC diagram of the stars included in a spatial bin of 5 ′ ×5 ′ at (α, δ)J2000.0 = (5 h 32 m , −69 • 16 ′ ). This spatial bin (the position is plotted in figures 12 and 15) is located in the LMC stellar bar region and has a low hydrogen column density (< 5×10 20 cm −2 ). We select this region as an example for demonstrating the calculation of AV distribution where we expect that no appreciable dust cloud is located along the line of sight.
The estimated AV distribution in the bin is shown by the red histogram in figure 3b. To check the AV distribution quantitatively, we plot individual AV at every 5 stars as shown by the red circles in figure 3c. The slope of the AV distribution in figure 3c indicates the presence of dust along the line of sight. However, even when there is no dust cloud along the line of sight, the slope is not zero due to the AV scatter caused by photometric errors. To evaluate this effect, we simulate the AV scatter based on the photometric errors as shown by the blue histogram and blue squares in figures 3b and 3c, respectively. As can be seen in the figures, the simulated AV is scattered around zero due to the photometric errors, the distribution of which is quite similar to the observed AV distribution. Therefore, we eliminate this effect from the observed data to evaluate the intrinsic dust distributions along the line of sight. In the following subsection, we describe the method to simulate the AV scatter and to eliminate this effect.

A V scatter caused by photometric errors
3.3.1 Calibration of the measured photometric errors If the photometric errors in the IRSF catalog are overor under-estimated for some reason, we cannot appropriately evaluate the AV scatter caused by photometric errors. When photometric errors are appropriate values, the logarithm of χ 2 /N should be close to zero for stars observed N times (e.g., Kaluzny et al. 1998;Yao et al. 2015). Here, χ 2 is defined as wherem is the weighted mean value of the colors of m observed N times for a star (m = H − K or J − H), and σm is the photometric error. We calculate σH−K = √ σH 2 + σK 2 and σJ−H = √ σJ 2 + σH 2 , where σJ , σH and σK are the photometric errors of the J, H and K bands, respectively. By using the stars which are observed more than four times (i.e., N > 4 in equation 3), we plot χ 2 /N of the H − K and J − H colors as a function of their errors of σH−K and σJ−H in figures 4a and 4b, respectively. From figures 4a and 4b, we see that χ 2 /N becomes lower for higher σH−K and σJ−H, showing that photometric errors are over-estimated for stars which have large photometric errors. Likely causes of the over-estimation are imperfect Point Spread Function (PSF) photometry, and/or over-estimation of the zero-point uncertainty. To solve this problem, we calculate the scaling factor F which is applied to σH−K and σJ−H, following the method of Kaluzny et al. (1998).
More specifically, we binned the data of χ 2 /N at an interval of 0.005 mag in both σH−K and σJ−H. For each binned data at σH−K =0.018 to 0.103 mag and σJ−H =0.016 to 0.046 mag, we calculate the scaling factor F so that the logarithm of χ 2 /N becomes zero. Data points in figures 5a and 5b are the estimated scaling factors for each binned data of σH−K and σJ−H, respectively. We finally perform the second-order polynomial fitting to the estimated scaling factors, and determine the scaling factor F as a function of photometric errors as shown by the solid lines in figures 5a and 5b. Figures 4c and 4d are the logarithmic plots of χ 2 /N of the H − K and J − H colors, respectively, after applying the resultant scaling factor F to the photometric errors of each star. In the figures, we clearly see that the logarithm of χ 2 /N are now closer to zero in all the range of photometric errors.

Simulation of the AV scatter
In order to evaluate the AV scatter caused by photometric errors in each spatial bin of 5 ′ ×5 ′ , we perform a Monte Carlo simulation. We first generate a random set of colors for each star on the CC diagram in each bin assuming that the colors follow the two-dimensional Gaussian distribution, the center of which is fixed at the observed H − K and J − H colors. We here adopt the corrected σH−K and σJ−H (see sub-subsection 3.3.1) as the standard deviation of the Gaussian distribution. We estimate AV for each simulated star and subtract observed AV from simulated AV to exclude the dust extinction. The distribution of the simulated values are shown by the blue histogram and blue squares in figures 3b and 3c, respectively, which can be considered as the AV scatter caused by photometric errors alone (i.e., without dust extinction) in the spatial bin. We repeat this simulation 100 times and generate 100 sets of the simulated AV distribution for each spatial bin.

Extinction along the line of sight
In order to evaluate the intrinsic AV distributions along the line of sight, we calculate the percentile values of AV based on the X percentile method. In this method, AV is originally estimated from the difference in the X percentile of the color between the reference and observed field, which  enables us to infer the positions of dark clouds. In our study, we evaluate AV at each percentile by subtracting simulated AV (excluding dust extinction) from observed AV (including dust extinction). We first average observed AV in the range of X% to (X +10)% percentile in figure 3c, where X is 10% to 80% at every 10%. Red circles in figure  6a show the resultant mean observed AV as a function of X%. We perform this procedure to the simulated AV distribution and calculate the mean percentile values of AV simulated 100 times as shown by blue squares in figure 6a. We finally calculate the difference between the observed and simulated percentile AV at each percentile as shown in figure 6b. Here and hereafter, we define AV (X%) as the resultant values shown in figure 6b (e.g., AV (10%) is the mean AV from 10% to 20% percentile of observed AV after subtraction of simulated AV ). The uncertainties of AV (X%) are calculated in subsection 3.5.
The shape of the histogram of the simulated AV in figure 3b is consistent with that of the observed one, which demonstrates that our simulation using the scaling factor F works well. Indeed, AV (X%) in figure 6b is almost constant value at 0.15 mag for all X%. The constant AV is likely caused by the Galactic extinction across the LMC. Dobashi et al. (2008) find that the Galactic extinction is AV ≃ 0.2 mag from the H I column density N (H I), assuming AV /N (H I) = 5.34 × 10 −22 mag/cm −2 (Bohlin et al. 1978, for RV =3.1). In addition, the constant AV for all X% in figure 6b means that the dust associated with the corresponding region of the LMC is not detected significantly along the line of sight as expected from the low column density region.

Uncertainties of dust extinction
We first calculate the AV uncertainty of each star. When we perform the Monte Carlo simulation as described in subsection 3.3, the AV value of each star is estimated 100 times. We estimate the AV uncertainty of each star as the standard deviation of AV simulated 100 times. As a next step, we calculate the uncertainties in the mean values of AV included in X% to (X + 10)% percentile, σA V,X , as where NX and δAV i are the number of stars included in X% to (X + 10)% percentile, and the AV uncertainty of the ith star, respectively. σA V,X for each X% is shown in figure 6b as error bars.
When we compare AV (X%) with the hydrogen column density to evaluate detailed dust geometry (section 5), we additionally consider the uncertainty of the percentile virtually corresponding to the uncertainty of the distance along the line of sight by using a simple count uncertainty (i.e., √ N ). We calculate its uncertainty as σ d,X = (A V k − A V l )/2, where A V k and A V l are the AV values for the stars of the index of k and l defined as the integer part of (icenter + √ N ) and (icenter − √ N ), respectively. Here, icenter is the median index of stars included in X% to (X + 10)% percentile, and N is the total number of stars in the spatial bin. We finally calculate the total uncertainties of AV (X)% from the error propagation, ). In the former region, gas collision is suggested and thus the dust cloud is expected to be located in front of the LMC disk (Furuta et al. 2019).
In the latter region, there is relatively high column density gas of the LMC disk (see figure 12c), and the gas collision is not suggested.
In figure 7a, we recognize that the observed AV histogram is shifted to positive values and broader compared to the simulated one. AV (10%) of about 1.1 mag in figure 7c suggests that the dust cloud is located in front of almost all stars as expected from the gas colliding region and largely contribute to the dust extinction in this region. In addition, the broader AV histogram is likely to be caused by the diffuse extinction existing along the line of sight. The former trend is also suggested by Tatton et al. (2013) who estimated AV for each star around 30 Dor using a CM diagram (J − K vs. K) and found that almost all the stars around the region have large dust extinction (AV > 1.2 mag).
In figure 8a, we find two peaks around AV =0.0 mag and 1.0 mag in the observational histogram. AV (10%) of 0.2 mag in figure 8c is consistent with the Galactic foreground extinction, which suggests that the first peak in the AV histogram is attributed to stars not affected by the dust extinction in the LMC itself. On the other hand, the second peak of the AV histogram is likely attributed to stars behind the dust cloud in the LMC, causing a rapid increase of AV at X=30% and onward in figure 8c. This result is consistent with the existence of the high column density gas of the LMC disk.

Extinction map along the line of sight
In this subsection, we consider large-scale dust geometry. Figure 9 shows the AV (10%) to AV (80%) maps in the H I ridge region. As described in section 3, AV is calculated with 5 ′ ×5 ′ bins every 1. ′ 6 grid and thus the PSF of the AV map is of a rectangular shape with the spatial resolution of 5 ′ and the grid size of 1. ′ 6. Since AV (X%) is the cumulative dust extinction from an observer to X%, AV increases with X% as can be seen in the figure. The AV (80%) map is considered to trace almost all the dust in the LMC. We present the uncertainty map of each AV map in figure 10. The uncertainty is relatively large in the east of the H I ridge region due to the lower density of stars (see figure 1).
In order to evaluate the Galactic foreground extinction using the derived dust extinction map, we calculate the averaged AV in the AV (10%) map where the total hydrogen column density N (H) is lower than 5.0 × 10 20 cm −2 (the total hydrogen column density is defined in the next subsection). As a result, we obtain 0.15 mag, which is consistent with the foreground extinction towards the LMC (∼ 0.2 mag) estimated by Dobashi et al. (2008).
We compare the derived AV map with the previous one in Furuta et al. (2019). Since the previous AV map was estimated from the mean observed colors, we use the AV (40%) map (i.e., mean AV from 40% to 50% percentile AV ) for comparison after subtracting the Galactic foreground extinction. Figures 11a and 11b show the AV (40%)  map and our previous AV map, respectively, whose spatial resolution is reduced to be the same as that of the AV (40%) map. Figure 11c shows the AV (40%) map after subtraction of the previous map, from which we confirm that the AV (40%) map is consistent with the previous AV map, although local differences can be seen at high extinction regions.

Gas tracer
As an atomic gas tracer, we use the H I velocityintegrated intensity maps constructed by Fukui et al. (2017) and Tsuge et al. (2019), where the Australia Telescope Compact Array (ATCA) and Parkes H I 21 cm data (Kim et al. 2003) are used. They subtracted the galactic rotation velocity from the H I data, which is defined as V offset , and decomposed the H I map into three velocity components (see Tsuge et al. 2019 for details of the analysis). These velocity components are defined as the L-, I-and D-components with the integrated velocity ranges of V offset = −100 to −30, −30 to −10 and −10 to 10 km s −1 , respectively. A typical H I spectrum in the H I ridge region is shown in figure 1 of Tsuge et al. (2019) together with the velocity range of each velocity component (see also figure 8 of Tsuge et al. 2021 for examples of the H I spectra in the LMC H I ridge region). The L-, I-and D-components are named after the initial letters of "Low", "Intermediate" and "Disk" velocity, respectively. As a molecular gas tracer, we use the rotational transitions of 12 CO (J =1-0) observed with the NANTEN 4 m telescope (Fukui et al. 1999). The CO integrated intensity map is decomposed into the L-, I-and D-components according to the above velocity ranges of the H I integrated intensity maps.
The H I integrated intensity map is converted into the H I column density map by using the conversion factor, XH I = 1.82 × 10 18 cm −2 /(K km s −1 ) (Dickey & Lockman 1990). CO is used to trace H2 through the CO-to-H2 conversion factor, XCO. We reduce the spatial resolutions of the H I column density maps and CO maps to be the same as that of the AV map at a resolution of 5 ′ by convolving Fig. 9. Cumulative dust extinction map from an observer to stars included in X% to (X + 10)% percentile for X=10% to 80% at every 10%. The angular resolution of the maps is 5 ′ .  with a boxcar kernel of 5 ′ ×5 ′ . Thus the PSF of the gas maps is of the same rectangular shape with that of the AV map to make a comparison on a pixel-by-pixel basis (subsection 5.3). We calculate the total gas column density N (H) of each of the L-, I-and D-component as where N (H I) and N (H2) are the H I and the H2 column densities, respectively.

A V vs. N (H) correlation
To check the spatial correlation between AV and N (H), we present the AV (80%) maps with the contours of N (H) of the L-, I-and D-components in figure 12. Here, we adopt XCO = 7 × 10 20 cm −2 /(K km s −1 ) which is the averaged XCO in the LMC derived from Fukui et al. (2008). Because N (H) is the integrated value along the line of sight, the AV (80%) map is expected to correlate with the N (H) maps best among the AV (10%) to AV (80%) maps. Indeed, the I-and D-component gases correlate well with the dust extinction. On the other hand, the L-component correlates well with the dust extinction in the northern part but not in the southern part, as can be seen from figure 12a. This trend can also be seen in Furuta et al. (2019), who con-sider the gas distribution based on the scenario that the L-component gas is falling into the LMC disk and the collision is on-going in the H I ridge region (Fukui et al. 2017).

Decomposition of A V into different velocities
We estimate the fractions of AV due to the dust associated with the L-, I-and D-components for every percentile from 10% to 80%, applying the fitting method described in Furuta et al. (2019) to our newly constructed AV maps. The fitting function is expressed as the following equation: where a, b and c are the free parameters indicating the dust/gas ratios (i.e., AV /N (H)) of the L-, I-and Dcomponents, respectively, while N (H) k for k=L, I or D is the gas column density of the L-, I-or D-component. Here, y and y0 are the pixel coordinates along the Declination direction. θ(y − y0) is a step function and the free parameter y0 indicates that the L-component at y > y0 is located in front of the LMC disk, contributing to the dust extinc- As demonstrated by Furuta et al. (2019), we can decompose AV into the three different velocity components with the linear regression of equation (6) using δAV (X%) calculated in subsection 3.5. In this study, we newly apply this method to each AV (X%) map after subtraction of the Galactic foreground extinction, which enables us to decompose AV existing along the line of sight into different velocity components. In other words, we can evaluate the three-dimensional dust geometry associated with the L-, I-and D-components. We discuss the dust geometry and dust/gas ratios of them in the next section.
When we perform the linear regression, we use only the region where N (H)D is higher than 1.0 × 10 20 cm −2 assuming XCO = 7 × 10 20 cm −2 /(K km s −1 ). In addition, we mask the 30 Dor region where the surface brightness is higher than 20 MJy/sr in the Spitzer/MIPS 24 µm map from the SAGE program (Meixner et al. 2006), because De Marchi & Panagia (2014 suggested that the reddening law around the 30 Dor region does not follow that of Cardelli, Clayton and Mathis (1989), which causes the under-estimation of the dust/gas ratio around 30 Dor.
Here, we name the former and latter boundaries boundary 1 and boundary 2, respectively, and the three regions separated by boundaries 1 and 2 as regions 1 to 3 (figures 13a and 14b). The position of boundary 2 is consistent with that obtained by Furuta et al. (2019) using the averaged AV map (see table 1). We newly find the presence of boundary 1 owing to our new method evaluating the dust distribution along the line of sight. The resultant two boundary positions indicate that the L-component in region 1 is located from observers to X=20%, while the L-component in region 2 is located on the far side from X=20%. In addition, the L-component in region 3 is located behind the LMC. Furuta et al. (2019) only revealed that the L-component in region 3 is behind the LMC disk. The present study enables us to evaluate the three-dimensional geometry of the L-, I-and D-components using AV /N (H) for each X%. Note that AV in figure 13a is an integrated value towards X% (i.e., variable depending on X%), while N (H) is a constant value integrated over the entire range along the line of sight. Thus, in principle, AV /N (H) increases more or less with X% for a given line of sight. However, since the decomposition of AV to each velocity component is determined by the fitting, AV /N (H) can decrease with X% (e.g., the decrease in AV /N (H) of the L-component within the errors from X=10% to 20%). increases with X% as can be seen in figure 13a, which indicates that the L-component in region 2 is extended from X = 30% to X = 80% . On the other hand, AV /N (H) of the L-component at X=10% and 20% is constant within the errors, which is the same trend as the I-component, indicating that region 1 is located in front of almost all the stars. The significant decrease in AV /N (H) of the Lcomponent from X = 20% to 30% is caused by the change of y0 in equation 6, i.e., the difference of the N (H) distribution used for the fitting. The expected geometry of the L-component is shown by the blue disk in figure 14b, suggesting that the L-component is penetrating the LMC disk at region 2, and is decelerating through interaction with the D-component, which causes the I-component (i.e., intermediate velocity) located in front of almost all the stars in the LMC. 30 Dor and N159 are expected to be located behind the I-component as shown in figure 14b, whereas 30 Dor and N159 in figure 12b show good spatial correlation with the I-component. Since the I-component is considered to be evidence for gas collision, their spatial correlation supports that the massive star formation in these region may have been triggered by collisions of the LMC disk with clouds as seen in the I-component (Fukui et al. 2017Tokuda et al. 2019).
The geometry in figure 14b suggests that gas collision occurred in the north region prior to the south region. In order to verify such a difference in the timing of the gas collision, we compare the evolutionary stages of giant molecular clouds (GMCs) with the crossing timescale of the gas collision. Kawamura et al. (2009) classified GMCs in the LMC into four evolutionary stages, Type I -III and last stage (Type I is the youngest phase). They found the evolutionary sequence from the south (young) to the north (old) of the H I ridge region, i.e., Type-I GMCs in region 3, Type-III GMCs around N159 and last-stage GMCs near 30 Dor. The transition timescale from Type I to last stage is ∼ 25 Myr. Assuming that the velocity of the inflow gas (L-component) is 100 km/s and the thickness of the LMC disk is 2 kpc (Balbinot et al. 2015), it spends 20 Myr for the inflow gas to cross the LMC disk, which is consistent with the transition timescale (∼ 25 Myr) from Type-I GMCs in region 3 to last-stage GMCs near 30 Dor. Therefore, the colliding cloud geometry shown in figure 14b can reasonably explain the evolutionary sequence in the H I ridge region found by Kawamura et al. (2009).

Comparison of dust extinction with dust emission
In order to check the validity of the geometry that the Lcomponent in region 3 is located behind the LMC disk, we compare the dust extinction with the dust emission; the dust extinction is caused by only the dust in front of the stars while the emission can come from all dust. As a dust emission map, we use the map of the dust optical depth at 353 GHz, τ353, obtained from the Planck and IRAS far-infrared data (Planck Collaboration 2014). To estimate τ353 in the LMC, Tsuge et al. (2019) calculated the Galactic foreground dust optical depth from the foreground H I intensity (W (H I)) using the conversion factor from W (H I) to τ353 derived from Fukui et al. (2015). We use the τ353 map after subtraction of the foreground component. Figure 15a shows the τ353 map with the contours of AV (80%) detected with significance higher than 1σ and AV ≥ 0.6 mag, from which we find that the dust emission exists in region 3 while the dust extinction does not. In regions 1 and 2, the dust emission correlates well with the dust extinction. On the other hand, figure 15b shows the τ353 map with the contours of N (H) of the L-component, from which we find that the dust emission correlates well with the L-component gas. N (H) of the L-component traces the dust emission in region 3. Those results strongly support that the L-component in region 3 is located behind the LMC. Now that the dust clouds in regions 1 and 2 are likely located in front of almost all the stars, we can securely investigate the relation between the dust extinction and emission in those regions. In figure 16, we present the scatter plot of AV and τ353 for each pixel of regions 1 and 2 with τ353 > 1.0 × 10 −5 for both regions. The figure shows that there is no systematic difference in the AV -τ353 relation between regions 1 and 2. The black solid line is the result of the least-square fit to all the data points in regions 1 and 2, assuming that the relation between AV and τ353 has a zero-point intercept. The estimated slope is AV /τ353 = (1.86 ± 0.04) × 10 4 . Planck Collaboration (2014) gives E(B − V )/τ353 = 1.5 × 10 4 for the Galactic diffuse dust (τ353 < 5 × 10 −6 ). Assuming RV = 3.1, we have AV /τ353 = 4.6 × 10 4 for the Galactic diffuse dust, which is 2.4 times larger than our estimation of AV /τ353 = (1.86 ± 0.04) × 10 4 for the dust in regions 1 and 2 of the LMC H I ridge region. The same trend was reported for our Galaxy by Planck Collaboration (2014), who found that τ353/N (H) systematically increases by a factor of ∼ 2 from the diffuse to denser regions due to dust  aggregation to larger grains. Therefore, the relation between AV and τ353 estimated in this paper is consistent with that in the dense ISM in our Galaxy, which suggests that the properties of large grains in the clouds of the Iand L-components are similar to those in our Galaxy.

Dust/gas ratio and CO-to-H 2 conversion factor
The AV /N (H) values at X = 40% of the L-, I-and Dcomponents are 1/10, 1/4 and 1/5, respectively, of the Galactic AV /N (H) values of ∼ 5.3 × 10 −22 mag/(H cm −2 ), while those at X = 80% are 1/5, 1/4 and 1/3 of the Galactic values, respectively. AV /N (H) at X = 40% of all the components is consistent with that derived by Furuta et al. (2019) using the averaged dust extinction map (see table 1 and figure 13a in the present paper). On the other hand, AV /N (H) at X = 80% of the L-component is 2 times higher than that derived by Furuta et al. (2019). This result can be interpreted as follows: since the L-component is penetrating the LMC disk (figure 14b), the averaged dust extinction of Furuta et al. (2019) would not trace all the dust in the L-component existing along the line of sight, which leads to under-estimation of the dust extinction. AV /N (H) at X = 80% of the D-component is also 2 times higher than that derived by Furuta et al. (2019). This reasonably indicates that stars are randomly distributed between the foreground and background, and thus the averaged dust extinction would correspond to ∼1/2 of the total dust extinction.
Based on the scenario that the low metalliciy gas from the SMC is accreted to and mixed in the H I ridge region (Fukui et al. 2017;Furuta et al. 2019), we compare the resultant AV /N (H) at X = 80% of each velocity component with the gas-to-dust ratios (GDRs) of the LMC and the SMC. Using Spitzer far-infrared, ACTA+Parkes H I 21 cm and NANTEN CO data, Bernard et al. (2008) and Leroy et al. (2007) obtained the averaged GDR about 3 times higher for the LMC and ∼10 times higher for the SMC, respectively, as compared to the Galactic GDR. Planck collaboration (2011) calculated the dust optical depth from the Planck data and suggested that the GDRs of the LMC and the SMC are 2.4 times and 13 times higher than the Galactic GDR, respectively. Roman-Duval et al. (2014) evaluated the GDRs in the Magellanic Clouds from dust and gas surface densities based on Herschel far-infrared, H I 21 cm, CO and Hα observations, and obtained the GDRs 3 times higher for the LMC and 6 times higher for the SMC than the Galactic value. In summary, the previous studies based on the dust emission indicate that the GDR is 2-3 times higher for the LMC and 6-13 times higher for the SMC than the Galactic value.
The AV /N (H) value at X=80% estimated for the Dcomponent in the present study corresponds to ∼1/3 of the Galactic value (see figure 13a), which is consistent with the GDR of the LMC as mentioned above. This implies that our method works well to evaluate the dust extinction caused by the D-component gas. The AV /N (H) values estimated for the L-and I-components in the present study correspond to ∼1/5 of the Galactic value (figure 13a), which are intermediate values between the GDRs of the SMC and the LMC as mentioned above. Thus we suggest that the L-and I-component gases are mixed with the D-component gas due to the interaction between the LMC gas and the inflow gas from the SMC. Assuming that AV /N (H) of the inflow gas was originally 1/10 of the Galactic value, 1/5 of the Galactic AV /N (H) for the L-and I-components can be explained by a mixture of the inflow gas with the LMC gas having 1/3 of the Galactic AV /N (H) at a mass ratio of 1:1. This result is consistent with the mass fraction of the inflow gas (∼50%) in the H I ridge region expected from the ratio of τ353 to the H I intensity (Fukui et al. 2017).
As can be seen in figure 13b, the XCO factors of each velocity component stay constant within the errors over the whole range of X% and are consistent with those in Furuta et al. (2019) (see table 1). This result indicates that the abundance ratio of CO to H2 is relatively uniform within the clouds associated with each velocity component. The XCO factors of the I-and D-components are similar to that of the LMC ∼ 2.9 × 10 20 cm −2 /(K km s −1 ) obtained by Pineda et al. (2017), who correct the effect of the photodissociation of CO due to the lack of dust shielding. In addition, the XCO factor of the L-component is in the range from that of the LMC ∼ 2.9×10 20 cm −2 /(K km s −1 ) to that of the SMC ∼ 7.6×10 20 cm −2 /(K km s −1 ) obtained by Pineda et al. (2017), which also supports the above picture of the inflow gas mixed with the LMC.
As a whole, the dust geometry and the difference in AV /N (H) and XCO between the three velocity components suggest the galactic interaction between the LMC and the SMC in the H I ridge region. In our future work, we will apply this method to the entire LMC field to discuss a possibility of the overall massive star formation triggered by the galactic interaction.

Conclusion
We develop the method to evaluate AV used in Furuta et al. (2019) by taking percentile values based on the X percentile method proposed by Dobashi et al. (2008). Using our new method, we construct the three-dimensional AV map of the LMC H I ridge region. From comparison of AV along the line of sight with N (H) of different velocities, we decompose AV into three velocity components, and evaluate the three-dimensional dust geometry and dust/gas ratios of the three velocities. Our main results are as follows: 1. The resultant dust geometry suggests that the Lcomponent in the north region is penetrating the LMC disk, while that in the south region is located behind the LMC disk. In addition, the I-component (i.e., intermediate velocity) is located in front of almost all the stars in the LMC. This can be explained by the deceleration of the L-component through interaction with the D-component. These results indicate that the gas collision is on-going in the north prior to the south of the H I ridge region. Such a difference in the timing of the gas collision is consistent with the evolutionary sequence of molecular clouds in the H I ridge region found by Kawamura et al. (2009). 2. We compare the spatial distributions of the dust extinction AV (80%) and the dust emission τ353 in the H I ridge region. We find that they are correlated well in the north while they are not in the south. The dust extinction is not detected whereas the dust emission exists and is well traced by N (H) of the L-component in the south region. Those results strongly support the geometry that the L-component in the south region is located behind the LMC disk. The relation between AV and τ353 suggests the dominance of large dust grains in the clouds of the I-and L-components, as found in dense clouds in our Galaxy.
3. AV (80%)/N (H) of the D-component (Disk, see figure  14b) is ∼1/3 of the Galactic value, which is consistent with the gas-to-dust ratio (GDR) of the LMC estimated from the dust emission. On the other hand, AV (80%)/N (H) of the L-and I-components is ∼1/5 of the Galactic value, which is an intermediate GDRs between the SMC and the LMC. This result suggests that the inflow gas from the SMC is mixed with the LMC gas at a mass ratio of 1:1 through the interaction between Magellanic Clouds in the H I ridge region. The difference in the XCO factors of each velocity component suggests a result consistent with the above picture.
As a whole, our results support the scenario that massive star formation in 30 Dor has been triggered by the tidal interaction between the LMC and the SMC.