SMASHing the LMC: A Tidally Induced Warp in the Outer LMC and a Large-scale Reddening Map

In each SMASH field catalog, we first select point-like sources using the DAOPHOT "chi" and "sharp" parameters: chi <3 (<5 for Fields 36 and 41 in the center) and $| \mathrm{sharp}|$ < 1 (<2 for Fields 36 and 41). Inside the LMC main body, contamination by background galaxies is negligible, especially within the magnitude range of interest in this study.

Figure 3 describes our RC selection in each SMASH field. Selecting the RC stars based on their color and magnitude is straightforward. First, we define a large initial box (red dashed line) around the RC along the reddening vector and use it as a guiding boundary. The maximum color (g − i = 2) is set in order to limit the contamination by MW foreground stars. To further minimize the contaminants in the RC selection, we carefully adjust the initial RC selection box by eye for each field, excluding stellar populations other than the main RC. The determined color range varies for each field mainly according to their relative dust extinction, while the slope is almost parallel to the reddening vector. Traditionally, other studies have used simple square selection boxes around the RC. For our CMDs, we found that such an approach led to an unacceptably high contamination of RGB stars and did not capture the entire RC in areas with high internal differential extinction. Once we select RC stars in each observing field, we remove duplicates in the overlapping regions among fields. The number of unique RC stars in our final catalog is ∼2.2 million.

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Figure 4 shows the number count map of the selected RC stars at 10' (150 pc) spatial resolution. We keep the same 10' × 10' spatial cell size for all subsequent analysis. We also conduct the same analysis at a much higher resolution of 40'' (10 pc) and conclude that our main results are robust against the choice of spatial resolution. In general, the RC stars show an extended spatial distribution with smoothly decreasing number density with galactic radius, compared to the more concentrated and patchy distribution of young stars (e.g., Zaritsky et al. 2004)—their star count map of young MS clearly shows a star-forming bar and one-armed spiral pattern. We note that high dust extinction makes our RC selection slightly incomplete only in the very central region (ρ < 05). In the rest of the disk with low crowding and low extinction, our RC selection is almost 100% complete. The observed number count map itself already shows some interesting structures. We investigate the LMC disk structure for various stellar populations, such as RC and young MS, by modeling their observed star count map as a 2D projection of a tilted elliptical disk model in a separate paper (Choi et al. 2018).

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Because the RGB usually overlaps with the RC in an observed optical CMD, it is impossible to completely remove RGB contaminants from the RC sample without extra information from spectroscopic data on surface gravity and effective temperature (e.g., Bovy et al. 2014; Nidever et al. 2014). Infrared (IR) color information could be helpful to distinguish the RC from RGB to some degree (e.g., Majewski et al. 2011). However, there are no publicly available IR survey data comparable with our optical data in terms of depth, photometric precision, and areal coverage even for the RC brightness level.

Fortunately, measuring extinction and distance does not depend significantly on the small fraction of RGB contaminants because they might induce only a small bias in the RC color and magnitude due to their similar color and magnitude compared to those of the RC, especially in each small 10' cell. Nevertheless, we estimate the fraction of possible RGB contaminants in our RC sample in each SMASH field.

In Figure 3, we also show histograms of the color and magnitude for a given CMD. A Gaussian profile can describe the main RC distribution, and a second-order polynomial can describe the underlying distribution of contaminants including RGB stars (e.g., Stanek & Garnavich 1998; Olsen & Salyk 2002). We fit the magnitude distribution of stars near the RC with a Gaussian profile combined with a second-order polynomial and find that the bright and faint end magnitudes of our selected RC stars are mostly within 2σ from the Gaussian mean, except for high-extinction fields. We calculate the RGB contamination fraction within our RC selection polygon based on the second-order polynomial terms. On average, the RGB contamination fraction in our sample is ∼10%. If one uses a simple square box for the RC selection, the contamination fraction can be as high as ∼30%–40% by including additional populations on the bluer side (i.e., HB, SRC, and VS) as well as more RGB stars. This high contamination fraction would result in significant systematic errors in extinction and distance measurement by shifting the average color and magnitude from those of true RC stars.

We first produce maps of the median observed color and magnitude at each 10' cell, from which we will derive the reddening and distance. While the mean RC color and magnitude have typically been calculated by fitting the distributions with a Gaussian profile combined with a second-order polynomial, we take the median magnitude and color for each cell. Due to our conservative RC selection, we found no significant contribution from second-order polynomial terms when describing the selected RC's magnitude distribution in each 10' cell. Thus, there is no significant difference between the geometric median and the Gaussian mean, except for cells at the edge of the maps that suffer from small number statistics where the geometric median provides more robust measurements.

Figure 5 presents the maps of observed (i.e., undereddened) median g − i color and i-band magnitude, which is less affected by dust than the bluer DECam filters and more complete than the z-band. The observed color map traces the dust emission in the inner disk (see Figure 6 in Gordon et al. 2014) as well as the MW galactic cirrus in the outer disk (Schlegel et al. 1998). In addition, the observed magnitude map shows a spatial gradient with magnitude increasing from the northeast to the southwest. The LMC disk is known to be tilted in a way such that the northeast is closer (brighter) to us and the southwest is farther away (fainter) from us (e.g., Caldwell & Coulson 1986; van der Marel & Cioni 2001; Olsen & Salyk 2002; Mackey et al. 2016). We measure the inclination (i) and line-of-nodes position angle (θ) of the LMC disk using the RC in Section 6.

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4.1.1. Derived Intrinsic RC Color from a "Clean" RC Subsample

To derive the intrinsic color distribution of the RC, we first construct a subsample of the RC in the regions with no or negligible internal dust. Because dust in front of these RC stars comes solely from the MW foreground, which acts as a dust screen, it is easy to break the degeneracy between the internal line-of-sight dust and the effect of stellar populations on their observed color. Using those RC stars enables us to derive their intrinsic colors after correcting for MW foreground dust.

To construct the RC subsample, we start by selecting 18 SMASH fields that do not show noticeable reddened RC "streaks" in their CMDs after correcting for MW foreground dust,²² indicating zero or a negligible amount of internal dust. It is highly unlikely that all RC stars in one SMASH field (a field of view of ∼3 deg²) experience the same amount of internal dust, and thus do not develop a streak. For the MW dust correction in these 18 observing fields, we use the Schlegel et al. (1998, hereafter SFD98) reddening map, which was derived from infrared dust emission. To convert SFD98 $E(B-V)$ to $E(g-i)$, we use updated reddening coefficients²³ with R_V = 3.1 for the DECam standard bandpasses that reflect Schlafly & Finkbeiner's (2011) calibration adjustment (Abbott et al. 2018). Although the above 18 fields are located outside the regions where the emission from the LMC dominates FIR emission, a tiny fraction of 3 fields out of 18 overlaps with the inner region of the LMC where the internal dust becomes dominant. We first exclude RC stars residing in these overlapping regions. From the remaining RC stars in the 18 observing fields, we further exclude stars with SFD98 $E(B-V)$ values larger than 0.099 (outside 1σ of the mean) to minimize potential contamination by RC stars that might be slightly reddened by a small amount of internal dust without developing a clear streak feature in a CMD. We designate this internal-dust-free RC sample as the "clean" RC sample, which accounts for ∼4% of our RC star catalog. The clean RC sample is distributed over the regions that are outlined in pink in Figure 4. The median SFD98 $E(B-V)$ value of the clean RC sample is 0.065 mag, which is consistent with a typical reddening value of 0.075 mag within uncertainty toward the LMC that was estimated based on the median dust emission arising from surrounding annuli (SFD98).

Using only the clean RC sample, we compute the median intrinsic color for each 10' cell over the clean RC region outlined by the pink line in Figure 4. In Figure 6, we present their median intrinsic color distribution (left) as well as the intrinsic color distribution of individual clean RC stars (right) for completeness. Both distributions are well described as a Gaussian profile with an identical mean ${(g-i)}_{0}$ of ∼0.82, but with different widths, with narrower width for the cells' median color distribution, as expected. The median RC color distribution of 10' cells reflects the cell-to-cell variation in SFH and chemical enrichment (i.e., global variations in stellar populations). The color distribution of individual clean RC stars, on the other hand, reflects both the full SFH and chemical enrichment history sampled in each cell (i.e., the local distribution of stellar populations) and their spatial variation. Almost all of the 10' cells exhibit standard deviations larger than ∼0.02 in their intrinsic color distribution of individual clean RC stars. The fact that the median color distribution of 10' cells in the clean RC region is narrower than the color distribution of individual clean RC stars per cell suggests that global variations in stellar populations across the LMC are moderate, at least for those populations that produce RC stars.

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4.1.2. Intrinsic Color Radial Profile

In Figure 7, we investigate a radial profile of the intrinsic color using the clean RC sample. Because the clean RC sample consists of stars selected in the restricted area (see Figure 4), it covers a limited range of galactic radius (ρ in degrees) from ∼27 to ∼85. The grayscale shows the distribution of the intrinsic colors of individual cells as a function of galactic radius from the LMC center, and the blue solid line presents a mean color with an associated error in each 02 width radial bin. The red shaded line shows the best fit to the gray data characterizing the overall radial profile of the observed intrinsic RC color. We find no statistically meaningful radial dependence of the intrinsic RC color between 4° and 7°. In this radial range, there is basically no change in the mean color with galactic radius, but there is a larger scatter around the median colors at larger radius. On the other hand, the intrinsic RC color tends to be slightly bluer both toward the center, with a slope of 0.024 dex deg⁻¹, and the outer galaxy, with a slope of −0.033 dex deg⁻¹.

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This RC color radial trend can be interpreted as a result of more metal-rich, but younger, populations in the inner region and older, but more metal-poor, populations in the outer region. An outside-in formation has been suggested for the LMC, supported by the observational evidence that old and metal-poor stars are preferentially found in the outer disk, whereas young and metal-rich stars are found in the inner disk (e.g., Gallart et al. 2008; Meschin et al. 2014). Although deriving full SFHs can provide a complete picture for the intrinsic RC properties across the LMC disk, this is beyond the scope of this paper. In a future paper, we will map the full SFHs using the SMASH data (C. Gallart et al. 2018, in preparation).

To verify whether the detected radial color trend is physically reasonable, we conduct a simple comparison of the intrinsic RC colors with PARSEC isochrones (Bressan et al. 2012; Marigo et al. 2017) by using previously reported metallicity gradients and age–metallicity relations (AMRs) in the LMC disk (Carrera et al. 2008, 2011; Piatti & Geisler 2013; Choudhury et al. 2016; Pieres et al. 2016) as a guide. These previous studies reported a shallow metallicity gradient with the mean [Fe/H] decreasing from −0.4 in the star-forming bar region to −0.8 to ∼−1.0 in the outer region (≥7°). There is no solid metallicity measurement for stars in the southern regions of the LMC outer disk yet. However, our CMDs can provide a loose constraint on it. For example, low-metallicity populations develop an extended horizontal branch feature in the CMD. We found no prominent extended HB features in any of our CMDs across the LMC disk, indicating that the minimum metallicity of the dominant stellar populations cannot be lower than [Fe/H] ≃ −2 even in the outer disk. Therefore, we set the minimum average [Fe/H] as −1.0, which is the minimum average [Fe/H] in the northern regions of the the LMC outer disk (Carrera et al. 2008).

We first compute the mean absolute g- and i-band magnitude as well as the mean g − i color only for core He-burning stars from an isochrone at a given age and metallicity by following Girardi & Salaris (2001; see their Equations (3) and (4)). The age is in steps of Δlog(age) = 0.5, and the metallicity ranges from [Fe/H] = −0.4 to −1.0 in steps of 0.1 dex. We use the Chabrier initial mass function to be consistent with the PARSEC isochrones used in this study. The calculated model RC colors and magnitudes show the same behavior presented in Girardi & Salaris (2001) and Girardi (2016). In short, the RC stars older than ∼2 Gyr behave in a simple way—they become fainter and slightly bluer (redder) as the age (metallicity) increases. However, the colors and magnitudes for RC stars younger than ∼1.5 Gyr vary rapidly with age and behave differently for different metallicities. We refer the readers to Girardi & Salaris (2001) and Girardi (2016) for the detailed discussion about population effects on the RC photometric properties.

We compare these calculated model mean colors for a given age and metallicity with the clean RC sample's intrinsic colors in each radial range: (i) 27–4°, (ii) 4°–7°, and (iii) 7°–85. For these three radial bins, we adopt representative [Fe/H] values of −0.5, −0.7, and −0.8, respectively, which reflect the reported metallicity gradient in the LMC (Carrera et al. 2008, 2011; Piatti & Geisler 2013; Pieres et al. 2016). Combining these three representative metallicities with the known AMR (Carrera et al. 2008; Piatti & Geisler 2013), we derive stellar ages of ∼1.6 Gyr, ∼5.6 Gyr, and ∼6.3 Gyr for these radial bins by finding models that best match our observed intrinsic colors. The best model colors in each radial bin are marked as yellow stars in Figure 7.

For the innermost radial bin (0°–27), we adopt the intrinsic RC color at ρ = 27 as a default color, and for the outermost radial bin (85–105), we adopt the intrinsic RC color at ρ = 85 as a default color rather than introducing additional color gradients in these radial bins.

We, however, can attempt to infer physically reasonable intrinsic RC colors both inside ρ = 27 and outside ρ = 85. For example, we can rule out the possibility of extrapolating the inner color gradient (∼0.024 dex deg⁻¹) to the innermost radial bin. This is because the metallicity gradient in the central bar region has been known to be shallow with a mean [Fe/H] of about −0.4 dex (e.g., Carrera et al. 2008, 2011; Choudhury et al. 2016). If we extrapolate the inner color gradient of ∼0.024 dex deg⁻¹ to the very center of the LMC, this predicts a g − i color of ∼0.73. However, none of the metal-rich ([Fe/H] > −0.5) isochrones have colors that blue and, in fact, all of the extrapolated colors for ρ < 27 are too blue (which are bluer than $g-i\simeq 0.8$) for the metal-rich isochrones, even with very young ages. Therefore, this color extrapolation to smaller radii does not appear physically reasonable.

In Section 7.2, we will investigate physically reasonable intrinsic RC colors in the innermost and outermost radial bins, and fully discuss the dependence of the 3D structure determination on the choice of the intrinsic RC colors.

Girardi & Salaris (2001) measured the effect of stellar population variations in the mean RC magnitude for some fields across the LMC disk based on spatially resolved SFHs and AMRs, and reported the maximum difference of 0.036 mag in the I-band magnitude among different regions. Using the clean RC sample, we also derive the intrinsic magnitude of the RC after correction for both MW dust and its gradual variation across the inclined LMC disk by assuming that the relative distances (due to the inclined disk) are the primary cause of the magnitude differences observed among the cells (van der Marel & Cioni 2001).

First, we compute the median i-band magnitude for all 10' cells in the clean RC region after correcting for the extinction by the foreground MW dust. We then adopt the median MW extinction-corrected i-band magnitude as a "fiducial" RC magnitude to obtain the relative distances to each other. These relative distances are converted to the absolute distances by putting the LMC center at D₀ = 49.9 kpc (de Grijs et al. 2014). We use the absolute distances (D) and celestial coordinates (right ascension α, declination δ) of each cell to compute their Cartesian coordinates (X, Y, Z).

To perform the coordinate transformation from the celestial coordinates and distance to Cartesian coordinates, we adopt the LMC disk's photometric center, (α₀, δ₀) = (8225, −695), as the origin (van der Marel 2001; van der Marel & Kallivayalil 2014).

Cartesian coordinates (X, Y, Z) with the origin (α₀, δ₀) are defined as follows:

$$\begin{eqnarray}\begin{array}{rcl}X & = & -D\sin (\alpha -{\alpha }_{0})\cos (\delta ),\\ Y & = & D\sin (\delta )\cos ({\delta }_{0})-D\sin ({\delta }_{0})\cos (\alpha -{\alpha }_{0})\cos (\delta ),\\ Z & = & {D}_{0}-D\sin (\delta )\sin ({\delta }_{0})-D\cos (\delta )\cos ({\delta }_{0})\cos (\alpha -{\alpha }_{0}),\end{array}\end{eqnarray} \tag{ 1 }$$

where the X-axis is antiparallel to the right ascension axis, the Y-axis is parallel to the declination axis, and the Z-axis is toward the observer.

We fit a plane to the (X, Y, Z) positions of all clean RC cells by minimizing their distances to the plane using an optimization algorithm (scipy.optimize.leastsq). The fitting yields an inclination angle of 2781 ± 023 and position angle of 14637 ± 037. From this fitted plane for the clean RC sample, we compute the expected magnitude gradient across the LMC disk and correct the extinction-corrected i-band magnitude for this expected geometric effect. This MW dust and inclination correction yields the intrinsic RC magnitude. We note that the inclination and position angle measured based on only the clean RC sample is not our final measurement (see Section 6.1 for the final measurement), but there is no significant change in the resulting intrinsic RC magnitude with our final measurements of the inclination angle (∼26°) and position angle (∼149°). Between these two sets of the inclination and position angles, the maximum geometric effect in magnitude is found to be ∼0.03 mag, and the magnitude differences in most areas are comparable to our photometric uncertainty.

Because we assume that the relative distance is the primary cause of the relative magnitude difference among cells, the residuals in the inclination-corrected magnitudes might allow us to characterize the "marginal" population effects in the intrinsic RC magnitude distribution. In fact, assuming that the inclination is the primary cause is physically reasonable in terms of the expected mild stellar population gradient across the disk. Thus, the residual differences in the magnitudes after correction for first-order inclination should contain information on the effect of variation in stellar populations across the LMC on the RC intrinsic magnitudes.

In Figure 8, we present the intrinsic RC magnitude distributions of the cells (left) and individual stars (right). Although both distributions roughly follow a Gaussian profile with the same mean magnitude of ∼18.47, the distribution of individual stars is slightly skewed to brighter magnitudes. Bright stars contributing to this skewness are confined into the end of the prominent spiral arm, suggesting these bright stars might be younger on average. Since RC brightness responds to stellar age more sensitively than color for a given metallicity, a lack of skewness in the color distribution of individual stars can be understood. Nevertheless, the width (∼0.1 mag) of the individual stars' magnitude distribution is consistent with the theoretical dispersion in magnitude due to local age and metallicity spread (e.g., Girardi & Salaris 2001; Yanchulova Merica-Jones et al. 2017). Furthermore, we find an excellent agreement between the width (0.031 mag) of the cells' distribution, which reflects a global variation in stellar population effect across the LMC disk, and the maximum I-band magnitude difference of 0.036 mag that is measured among different regions in the LMC (Girardi & Salaris 2001).

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Figure 9 presents the radial profile of the intrinsic RC magnitude in the i-band. In contrast to the radial color dependence, the radial profile of the intrinsic RC magnitude is rather flat across the entire observed radial range, with only a slightly brighter (∼0.03 mag) magnitude in the radial bin, 27 < ρ < 4°, which is likely due to younger populations toward the central region. This magnitude radial profile shows excellent agreement with the expected magnitudes (marked as yellow stars) from the same age, metallicity models that explain the measured intrinsic RC color radial profile (see Section 4.1.2). Thus, we adopt the mean magnitude of 18.476 as a constant intrinsic RC magnitude between 4° < ρ < 85, and adopt a slope of 0.019 mag deg⁻¹ between 27 < ρ < 4°. As with the color radial profile, we set the magnitudes at ρ = 27 and 85 as the default values in the innermost (ρ < 27) and outermost (ρ < 85) radial bins, respectively. We will also discuss how the choice of different magnitudes affects the resulting 3D structures in Section 7.2.

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In this section, we constrain the LMC disk's (i, θ) using RC stars selected from the data covering a wide area of the unexplored southern part of the disk. First, we measure relative distances with respect to the LMC center using the extinction-corrected relative i-band magnitudes for each subregion. With a distance to each subregion, the subregion positions are expressed in Cartesian coordinates (X, Y, Z).

To characterize the properties of the LMC disk, we define a galaxy plane relative to the sky plane based on the 3D distribution of all cells by minimizing their distances to the plane using scipy.optimize.leastsq again. The unit normal vector ($\hat{n}$), defined in Cartesian coordinates, of the best-fit plane is (n_x, n_y, n_z) = (0.375, −0.223, 0.899). From this normal vector, we derive $i={\cos }^{-1}({n}_{z})$ and $\theta =\pi +{\tan }^{-1}({n}_{y}/{n}_{x})$. The fitted plane has an inclination of 2586 ± 0.19 and the position angle (θ) of 14923 ± 0.49. The uncertainties reported here are random errors, associated with the plane fitting, calculated using the MCMC sampler emcee (Foreman-Mackey et al. 2013). We allow each of the 100 walkers to take 2000 steps and compute the 68% confidence interval as the 1σ uncertainty of each fitting quantity after discarding the burn-in phase of the first 500 steps. These errors do not include any systematic uncertainties associated with stellar population effects. The systematic uncertainties in our (i, θ) measurements are provided in Section 7.

The LMC disk has been found to be twisted (varying line of nodes with galactic radius), warped (not a single plane), and flared (increasing scale height with galactic radius) likely due to tidal interactions with both the SMC and the MW (van der Marel & Cioni 2001; Olsen & Salyk 2002; Nikolaev et al. 2004; Subramanian & Subramaniam 2009b; Balbinot et al. 2015). Therefore, the inclination (i) and the position angle of the line of nodes (θ; the intersection of the galaxy plane and the sky plane) depend on the spatial coverage of the survey data. Indeed, it has been shown that these two parameters vary with both angular distance from the galactic center and measurement techniques even for a given stellar tracer because of the complicated shape of the LMC disk (van der Marel & Cioni 2001; Subramanian & Subramaniam 2013; Jacyszyn-Dobrzeniecka et al. 2017). Furthermore, it has been found that the determined LMC disk properties depend significantly on the choice of stellar populations to trace the disk structure (e.g., Balbinot et al. 2015).

In Figure 13, we explore the effect of twists and warps on (i, θ) measurement. We first define eight 1° wide radial annuli between 2° and 10° on the tangent plane (ξ, η), and then (1) measure (i, θ) from all RC cells in each annulus and (2) measure (i, θ) for all RC cells enclosed within a circular area that defines the outer edge of each annulus. Each annulus fitting reflects the local geometry better than the circular area fitting. Black dashed lines present how the (i, θ) measurements change for each annulus, while black solid lines show the dependence of (i, θ) on areal coverage (i.e., each circular area for a given angular distance from the LMC center). Like van der Marel & Cioni (2001), we also find a strong radial dependence of (i, θ)—in general, both (i, θ) rapidly (slowly) decrease with galactic radius in the inner (outer) disk. The inclination and position angle are large in the central region (<4°), where the bar is dominant. This indicates that the bar itself is likely tilted more than the rest of the disk (see Section 6.3). Inno et al. (2016) studied the 3D distribution of Cepheids and also found a strong radial dependence of (i, θ) in the inner LMC disk. The inclination angle from annulus fitting significantly increases in the very outer region (>8°), where the warp is dominant.

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Both measuring methods (annulus versus circular area) produce similar radial trends, except for the outer region (ρ > 8°). The inferred inclination angle dramatically decreases from ∼40° to ∼25° with angular distance until ρ ≃ 7° and then almost converges or slightly increases beyond that radius. On the other hand, the θ values are rather flat with a slight decrease after a sharp drop at ρ < 35–45, ranging between ∼140° and ∼160°. This trend is found in both measuring schemes, although the measured θ values from the annulus fitting are slightly smaller, and there is a drop to ∼120° in the outer region.

We also investigate the radial dependence of (i, θ) values for the case in which a constant intrinsic RC color of 0.82 is used across the disk. The red lines in Figure 13 show (i, θ) results for the case of constant intrinsic RC color and circular area fitting. The inclination angles behave in an almost identical way to those from the radially varying intrinsic RC color case in all different areal coverages. There are only a few degree differences along the galactic radius. The position angles for the constant intrinsic RC color case also behave in a similar way to the radially varying intrinsic RC color case. For the (i, θ) measurements in each annulus, the constant color case follows almost the same pattern as the radially varying color case, and thus we do not overplot them for clarity.

For the LMC, its previously reported inclination angle ranges from ∼7° to ∼40°, and its reported position angle also widely ranges from ∼100° to ∼180° (e.g., van der Marel & Cioni 2001; Olsen & Salyk 2002; Koerwer 2009; Subramanian & Subramaniam 2010, 2013; Inno et al. 2016; Jacyszyn-Dobrzeniecka et al. 2017). Our measured i and θ values, both from the best-fit plane and from the annulus/circular area fitting, fall well within these ranges. Specifically, the measured position angle is in good agreement with the reported values based on the RC (e.g., Olsen & Salyk 2002). On the other hand, the measured i is smaller than reported values based on the RC. This discrepancy from face-value comparison is likely due to our larger areal coverage of the southern disk than previous studies. If we consider the smaller areal coverage of the different data sets based on Figure 13, the measured i agrees well with the previous measurements. Our inclination is also similar to that measured in the northern outer disk by modeling the star number count map as an elliptical disk (i = 2518 ± 0.71; Mackey et al. 2016). Furthermore, our results are consistent with the measured (i, θ) based on combined information of line-of-sight velocities and proper motions (van der Marel & Kallivayalil 2014). They measured (i, θ) = (303 ± 5.9, 1537 ± 5.4) for their young star sample (red super giant stars) and (340 ± 7.0, 1391 ± 4.1) for their old star sample (a mix of carbon stars, AGB stars, and RGB stars).

We measure the thickness of the LMC's stellar disk from the distribution of distances of individual stars to the fitted plane. The distribution of distances to the fitted disk plane roughly follows a Gaussian distribution with a σ of ∼1.0 kpc, leading to the FWHM thickness of ∼2.35 kpc. The LMC disk has been known to be thicker than the MW thick disk.

The line-of-sight depth of the LMC disk has been measured in the literature (e.g., Subramanian & Subramaniam 2009b; Jacyszyn-Dobrzeniecka et al. 2017; Yanchulova Merica-Jones et al. 2017). We also measure a line-of-sight depth by looking at the distribution of individual stars along the Z-axis. We use stars only at ρ > 2° to obtain a robust measurement by avoiding the artificial broadening along the line of sight due to the bias in our dust correction from using the median reddening values (see bottom panels in Figure 11). The measured line-of-sight depth is ∼7 kpc, which is larger than previous measurements by 1–2 kpc. This larger depth might be due to our larger areal coverage with the outer warp. As expected, including stars in the central region (ρ < 2°) increases the line-of-sight depth by ∼0.5 kpc.

The left panel of Figure 14 shows the 3D structure of the LMC disk in projected Cartesian coordinates (X, Y, Z) along the maximum distance gradient, which is perpendicular to the line of nodes. The grayscale reflects the stellar number counts along the viewing direction. The LMC disk is tilted against the sky plane, with the northeast (southwest) closer to (farther from) us. As shown, the LMC disk is clearly not a simple plane, which is consistent with previous studies—it has multiple ripples like the MW or other spiral galaxies (e.g., Gómez et al. 2013). Similar ripples in the inner region can be also found in the near-infrared photometric data of the RC (Figure 9 in Subramanian & Subramaniam 2013). A rippled disk is a common feature in a galaxy with close encounters with its satellite galaxies (Gómez et al. 2017).

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In the LMC inner disk, Olsen & Salyk (2002) detected a warp feature in the southwest (between 2° and 4° from the center along the maximum gradient). We reproduce their warp in our data as well by looking at cells corresponding to their observing fields (red circles Figure 14). These cells coincide with the highest stellar density. We mark their warp the "Olsen & Salyk warp" in Figure 14, which turns out to be a portion of the rippled disk. Its amplitude (∼2 kpc) and direction (toward us) are in excellent agreement with the findings in Olsen & Salyk (2002). The Olsen & Salyk warp corresponds to the feature seen between −2.5 kpc and −4 kpc along the maximum gradient. Its direction toward us makes the warp tilted opposite to the rest of the southwest disk. van der Marel & Cioni (2001) suggested a warped disk based on decreasing inclination angle with angular radius between 27 and 7°, indicating that the Olsen & Salyk warp indeed affected their inclination and position angle measurements. We also detect such a decrease in inclination until ∼7° from the center (see Figure 13). When measuring the disk inclination using the cells in the Olsen & Salyk (2002) observing fields, but excluding the cells that form the Olsen & Salyk warp, the fitting yields i = 3442, which is consistent with i = 358 ± 24 measured by Olsen & Salyk (2002).

In the right panel of Figure 14, we present the edge-on view of the disk. The red line shows the average distance to the fitted plane weighted by stellar number count in each 0.2 kpc bin along the x-axis. With our large areal coverage for the southern disk, we find a new prominent warp in the southwest that starts at about −5.5 kpc from the center (or ∼7° southwest from the center on the sky). The warp departs from the fitted disk plane up to ∼4 kpc in a direction away from the Sun, which is in the opposite direction to the Olsen & Salyk warp. This is the first detection of this outer warp, made possible by the large areal coverage of the SMASH data for the southern LMC disk. The warp feature is robust against the choice of the intrinsic RC color radial profile. Also, we do believe that the warp is not an artifact resulting from the edge of our observing area, which is imprinted as a sharp drop in stellar number density that is coincidentally parallel to the direction of the new warp. This is because the average distance from the galaxy plane starts to increase negatively (i.e., away from the observer) between −5 and −6.5 kpc, where the effect of the observing edge does not kick in yet.

The bar stands out as a high density in the central region in Figure 4. The 3D spatial distribution of cells around the bar—it is non-trivial to identify only bar stars—shows a wide dispersion along the vertical direction (i.e., perpendicular to the plane). Thus, quantifying the bar structure as a plane is not reasonable. Instead, we can interpret the larger (i, θ) of the inner disk (ρ < 4°), which encompasses the bar, as evidence of a highly tilted bar. If the central bar significantly affects the determination of the geometry of the inner disk, the bar seems to be tilted relative to the fitted plane at least by ∼5°–15°. Although the origin and the geometry of the off-centered bar in the LMC remains to be fully understood (e.g., Zhao & Evans 2000; Zaritsky 2004; Bekki 2009; Subramaniam & Subramanian 2009a), an off-centered and tilted bar naturally forms in Besla's Model 2 due to a recent direct collision with the SMC.

The SMASH data enable us to constrain the 3D structure of the LMC disk and detect its interesting features. The LMC disk is found to be twisted and warped with ripples, and to have a tilted bar. These features were previously found in other studies, and are mainly associated with the inner LMC disk. With our SMASH data, which includes a large unexplored area of the southern disk, we also detect these features, confirming that the LMC is indeed significantly disturbed. Furthermore, we reveal a prominent warp in the outer southwest disk (ρ > 7°) for the first time. This warp departs ∼4 kpc from the LMC disk plane toward the SMC.

The current space velocities of the MCs favor their first infall into the MW halo, suggesting interactions with the SMC as the primary cause of the disturbed LMC disk rather than MW tides. Thus, morphological studies of the MCs are one of the keys to constraining their interaction history. Under the first infall scenario, Besla et al. (2012) investigated the role of tidal interactions between the MCs in their evolution using two different orbital histories between the MCs: (1) Model 1—the SMC completes two passages around the LMC without getting closer than 20 kpc, and (2) Model 2—the SMC completes three passages around the LMC including the recent (∼100–300 Myr ago) direct collision. Each model successfully reproduces some properties of the Magellanic system, and while Model 1 better reproduces the large-scale gaseous structures, Model 2 performs significantly better at reproducing the detailed morphology and kinematics of the LMC disk.

The edge-on view in Figure 14 is comparable to the galaxy y–z plane shown in the bottom panels of Figures 12 and 13 from Besla et al. (2012). For convenience, we show a modified version of an edge-on view stellar density map for Model 2 from Besla et al. (2012) in Figure 15. Their Model 2 clearly shows the outer warps in both the stellar and gaseous disks.

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Although Besla et al. (2012) tried to connect their outer warp with the Olsen & Salyk warp, which was the only prominent observed warp at that time, our study makes it clear now that the Olsen & Salyk warp is one of the inner disk features. Thus, their predicted outer warp, starting at ∼5 kpc from the disk center in their Model 2, actually has not had an observed counterpart until now. Based on the very similar position and size of the warp we find in the outer southwest disk, we argue that our new warp is the one corresponding to the outer warp presented in Model 2. Indeed, the position and amplitude of the warp is surprisingly similar to those predicted in their Model 2.

By contrast, the big warp in the outer disk does not appear in their Model 1, in which the SMC completed only two passages with large separations around the LMC. Because this outer warp is not created in Model 1, which has no direct collision between the MCs, our finding of the new warp (in addition to the tilted bar) supports a recent direct collision of the LMC with the SMC. The observed relative velocities of the SMC and LMC measured using new HST proper motions of the SMC (Zivick et al. 2018) further support this direct collision scenario.

More importantly, this new morphological feature might provide better constraints on model parameters for future theoretical modeling, not just for the MCs themselves but possibly also for other dwarf–dwarf pair systems (e.g., Stierwalt et al. 2015; Pearson et al. 2016). To provide a more complete picture of the outer warp, future studies should attempt to identify and quantify its counterpart in the northeast disk. If the warp originates owing to the tidal field of the MW, we expect an "integral" shape (e.g., Mackey et al. 2016; Gómez et al. 2017). If the structure originates from a collision with the SMC, the warp in the northeast is expected to be weaker than the outer warp we find (Besla et al. 2016).

Although the RC is a good probe of extinction and distance, it suffers from stellar population effects in its color and magnitude. In the previous section, we measured the radial profiles of the intrinsic color and magnitude using only stars from the clean RC regions across the LMC disk to take population variations into account as much as possible. This analysis uncovered a radial variation both in color and magnitude. However, the limited areal coverage (27 < ρ <85) of the clean RC regions prevents us from obtaining complete color and magnitude radial profiles that fully cover the innermost region (ρ < 27) to the outer region (ρ > 85).

The (i, θ) and amplitude of the warp might depend on our choice of the intrinsic RC color in the innermost and outermost radial bins. The amount of the extinction correction is determined by the choice of the intrinsic colors, and a larger extinction correction to the observed magnitude leads to a brighter intrinsic magnitude (i.e., closer to us), and vice versa. If we adopt a redder (bluer) intrinsic color for the outermost radial bin, then the distances to the regions associated with the warp feature would become larger (smaller), making the warp more (less) prominent. Furthermore, variations in the intrinsic magnitude in the innermost and outermost radial bins also affect the relative shape of the disk, probably leading to a change in the warp amplitude.

In this section, we attempt to adopt reasonable extremes of the assumed intrinsic color and magnitude for those regions based on both our own measurements in the rest of the radial range and the results of previous studies on the LMC's metallicity gradient and AMR. We discuss how our choice of the intrinsic color and magnitude in the central and outer regions can affect the 3D structural measurements. We also discuss the case for a single intrinsic color and magnitude across the disk to compare with the traditional RC method.

Case I: For the innermost radial bin (ρ < 27), if we adopt [Fe/H] = −0.4 and a ∼1 Gyr old²⁴ population, the predicted mean RC color is ∼0.84, which is redder than the rest of the disk, and the corresponding mean RC magnitude is ∼18.76 mag, which is ∼0.3 mag fainter than the default magnitude in the innermost radial bin.

This fainter intrinsic magnitude in the innermost region induces a structure protruding from the disk by 4–5 kpc, making the outer warp slightly less prominent than the default case (by ∼10%). For the main disk (i.e., excluding the protruding structure), we obtain the inclination of 2656 and position angle of 14702 with respect to the results for our default case.

An elevated bar above the disk in the LMC has been suggested by some studies (e.g., Zhao & Evans 2000; Nikolaev et al. 2004; Haschke et al. 2012). For example, Haschke et al. (2012) found evidence that the bar is ∼5 kpc closer to us than the disk in their RR Lyrae sample, but no evidence was found in their Cepheid sample. On the other hand, Jacyszyn-Dobrzeniecka et al. (2017) interpreted the protruding structure seen in their OGLE-IV RR Lyrae stars as an artifact due to blending and crowding effects. In addition, Subramaniam & Subramanian (2009a) analyzed the OGLE-III RC stars and concluded that the bar is located within the disk. We also do not take this protruding structure seriously because the inferred reddening from this color choice is lower than the previous measurements for the central region (e.g., Haschke et al. 2011; Tatton et al. 2013).

Although it might be reasonable to adopt this combination of age and metallicity for the innermost radial bin, the intrinsic RC color and magnitude vary significantly in the young age regime (<1.5 Gyr; see Figure 1 in Girardi & Salaris 2001). This means that it is impossible to determine representative ages from our own clean RC sample without detailed SFH measurements in the central region. Stellar populations in the central region might be too complex to be described as one representative color and magnitude.

Case II: For the outermost radial bin (ρ > 85), if we extrapolate with the outer radial bin's slope of −0.033dex deg⁻¹, the expected color at ρ = 105 is ∼0.7. This color can be reasonably explained with a slightly lower metallicty ([Fe/H] = −0.9 or −1.0) and older age (∼10 Gyr or ∼8 Gyr) compared to the previous radial bin, which is also consistent with the LMC's smooth and shallow metallicity and age gradients. If we adopt the population of [Fe/H] = −0.9 and 10 Gyr, the corresponding model magnitude at ρ = 105 is ∼18.6 mag, which requires a magnitude profile slope of 0.059 dex deg⁻¹ in the outermost radial bin. With these modified color and magnitude radial profiles, we measure the inclination of 2447 and position angle of 15566. The outer warp becomes more prominent; its amplitude increases by ∼10% with respect to the results for our default case.

Case III: If we combine the changes in these two radial bins (i.e., Cases I and II), both the inclination and position angle are consistent with the results for our default case within uncertainties. This might be because the net effect from the bar region and the warp region compensate each other. The warp shows no noticeable change in its shape and amplitude.

Case IV: Adopting a constant intrinsic RC color and magnitude is the simplest way to derive line-of-sight extinctions and distances to RC stars. Previously, many studies measured the LMC structure in this way, and then discussed possible uncertainties due to population effects. If we assume no radial dependence of the intrinsic RC color and magnitude throughout our analysis, the inclination and position angle are 2659 (∼1° larger than the default case) and 14088 (∼9° smaller than the default case). In this case, the Olsen & Salyk warp becomes stronger, making the outer warp launch from below the fitted plane. This results in a decrease in an amplitude of the outer warp, which is measured from the fitted plane, by up to ∼25%. If we make a fairer comparison with the other cases where the outer warp launches from the fitted plane by measuring its amplitude from where it actually starts, the amplitude is ∼10% smaller than the default case.

In conclusion, the systematic uncertainties due to population effects on the inclination are −5.4%/+2.8% (corresponding to −139 and 073) and −5.6%/+4.3% (corresponding to −835 and 643) on the position angle. The shape and the presence of the outer warp are robust against the choice of radial profiles of the intrinsic RC color and magnitude. The amplitude of the warp is marginally sensitive (up to ∼10%) to the choice of the intrinsic color and magnitude in the innermost and outermost radial bins. Although there are small variations in the (i, θ) measurements with the population effects, the general trends of these parameters do not change: (1) the disk is tilted with respect to the sky plane (the northeast is closer to us, whereas the southwest is farther away from us), (2) the LMC has a well-developed warp toward the SMC in the southwestern region, and (3) the central bar is tilted relative to the rest of the disk. We also find that the disk thickness is robust against the variation in stellar populations (Cases I–IV) regardless of whether the central disk where our RC-derived median reddening map can cause the bias is included. The line-of-sight depth is also robust against the variation in stellar populations when excluding the protruding structure in the central region.