OGLE-ing the Magellanic System: Optical Reddening Maps of the Large and Small Magellanic Clouds from Red Clump Stars

The Large and Small Magellanic Clouds (LMC and SMC, respectively) are a pair of irregular galaxies that, due to their proximity to the Milky Way (MW) and their mutual interactions, are the most studied nearby galaxies. They serve as a local laboratory for investigating galaxy structure, evolution, and interactions, as well as stellar populations and interstellar medium distribution. The Magellanic Clouds (MCs) are also used to calibrate the cosmological distance scale.

The majority of stellar population studies require accounting for interstellar extinction in order to acquire precise distances; thus, it is very important to have accurate reddening maps of the Magellanic System. Previous efforts to construct reddening maps employed various tracers such as Red Clump (RC) stars (Udalski et al. 1999a, 1999b; Subramaniam 2005; Subramanian & Subramaniam 2009, 2013; Haschke et al. 2011; Tatton et al. 2013; Choi et al. 2018; Górski et al. 2020), classical Cepheids (Inno et al. 2016; Joshi & Panchal 2019), or RR Lyrae–type variables (Pejcha & Stanek 2009; Haschke et al. 2011; Deb 2017). Interstellar reddening has also been inferred from equivalent widths of spectral lines (Munari & Zwitter 1997), stellar atmosphere fitting (Zaritsky et al. 2002, 2004), and through the analysis of spectral energy distributions of background galaxies (Bell et al. 2019).

RC stars are low-mass red giants in the core He-burning stage of the evolution that occupy a well-defined region in the color–magnitude diagram (CMD). This property allows for these stars to be used as standard candles for determining distances (Paczyński & Stanek 1998) and by measuring shifts between the observed and theoretical RC color, can be successfully used to measure reddening to these stars. For details on RC stars and their applications with possible limitations, see the review by Girardi (2016).

In this study, we present the most detailed and extensive reddening maps of the MCs to date, based on RC stars. Section 2 provides details on observations and data preparation. In Section 3, we describe the process of determining RC color, and in Section 4, we analyze the intrinsic RC color distribution in the MCs. Section 5 describes the final reddening maps and compares them with previous reddening maps of the MCs. We summarize the paper in Section 6.

2.1. OGLE-IV Observations

The 1.3 m telescope of the OGLE survey is located at the Las Campanas Observatory in Chile and has been observing the southern sky since 1996 on a nightly basis. The fourth phase of the project started in 2010, when a new 32 chip mosaic CCD camera with a 1.4 deg² total field of view was installed on the telescope. Since then, OGLE-IV has been observing the Magellanic System in the I and V bands with a cadence of 1–4 days, later reduced to about 10 days in the sparsely populated regions of the Magellanic Bridge and the outskirts of the MCs. The OGLE-IV fields covering approximately 670 deg² in the Magellanic System are pictured in Figure 1. For technical details on the OGLE-IV survey, please refer to Udalski et al. (2015).

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The magnitude range of regular OGLE-IV images is 12–21 mag in the I band and 12.5–21.5 mag in the V band. In order to increase the effective depth of the survey, deep OGLE-IV images were constructed from 2 to 100 high-quality frames (depending on the field), with a median of 8 images in the V band and 88 in the I band. The resulting magnitude limit of the deep images is approximately 23 mag in the I band and 23.5 mag in the V band. Even though the use of the deep images is not necessary for this particular study, because the mean magnitude of RC stars in the MCs is much brighter than the regular survey limit, it is useful due to their cleanness—stacking multiple images removes practically all artifacts and spurious detections from the final frame, which are hard to fully account for otherwise (see discussion in Skowron et al. 2014).

2.2. Data Preparation

For each subfield (and in each of the six subfield sizes), we construct a (V − I, I) CMD and bin it in both magnitude and color to obtain a Hess diagram, using bin sizes of 0.04 and 0.02 mag in I and V − I, respectively. The value of each bin is the number of stars that fell into that bin. Figure 2 shows an example of the Hess diagram in the LMC (left) and in the SMC (right), with a well visible RC and the red giant branch (RGB). The location of the RC on the CMD depends on distance and metallicity, and so it is different for the two galaxies. The elongation of the RC in the SMC has been known for a long time (Hatzidimitriou & Hawkins 1989; Udalski et al. 2008b), and it has been shown that it is caused by the large depth of the SMC along the line of sight, rather than a presence of blue-loop stars (Nidever et al. 2013).

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The first step in determining the RC color is to define the initial CMD region occupied by RC stars, which will be used for a more detailed analysis. Its location and extent change with extinction—the more reddened the region, the more dispersed and shifted toward fainter magnitudes and redder colors the RC is. There are two main approaches: (a) to define a generous CMD region, which would cover all possible RC locations, and deal with disentangling the RC in a subsequent algorithm; and (b) to define a small box in (V − I) and magnitude and modify its position and size iteratively (or by hand) for each line of sight, and then use a simple algorithm such as a mean or median to calculate the final RC color. The disadvantage of the first approach is that the contamination from other stars within the region forces the algorithm to be much more complex. However, in the second approach, in order to remove the majority of contamination (e.g., the RGB) and outliers (from the MW foreground), one has to reduce the size of the box and potentially remove some of the genuine RC stars. This leads to biases in the final measurement.

Within the discussed scenarios, the box can be "rectangular" or "slanted", i.e., the CMD region can be defined only by specifying a range in color and magnitude, or it can follow the extinction vector. In the second case, the area of the box can be safely reduced, which in effect lowers the contamination from the RGB stars. We see no obvious disadvantages of the latter choice, which can be simply viewed as a definition of the magnitude axis using a Wesenheit index (W).

In this study we choose the generous CMD region approach and the "slanted" magnitudes (left panel of Figure 3):

$$\begin{eqnarray}&&W=I-1.67\,(V-I\,)\,\,\,\mathrm{for}\ \mathrm{LMC},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&W=I-1.74\,(V-I\,)\,\,\,\mathrm{for}\ \mathrm{SMC}.\end{eqnarray} \tag{ 2 }$$

We restrict our investigation to a conservative range in color of 0.65 < (V − I) < 1.7 mag and a magnitude range that falls within 17 < I < 20 mag at (V − I) ≈ 1, which is typical for the RC. In the center of the LMC, due to the large differential reddening, we extend the color range to (V − I) = 2.1 mag. In our approach, the final results are not sensitive to the exact choice of the extinction slope and magnitude range.

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First, we determine a luminosity function of the RC in W, which is fairly narrow (typical dispersion of 0.23 mag) even for highly extincted fields. There are two main components in the luminosity function: a distinct distribution of stars belonging to the RC and a smooth contribution of the RGB. The first is well approximated by the Gaussian distribution and the second can be modeled with an exponent or, in this narrow magnitude range, even with a straight line (see the right panel of Figure 3). Our aim is not to make a precise model of the luminosity function but to determine the most likely region in W where the RC stars are located, and then, with the measurement of the standard deviation, assign the probability of belonging to the RC for each star.

We tested various fitting scenarios, in particular the normal distribution plus the exponent, and found that the biggest obstacle in determining the RC magnitude region is the unstable nature of the fits in regions with lower star counts. Concurrently, we noticed that the scale parameter of the exponent is rather consistent between various lines of sight. Hence, the exact value of this parameter is not crucial, and we decide to fix it to 2.5 mag, which makes the fits more stable. The luminosity function then becomes

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{LF}(W) & = & {\mathrm{LF}}_{\mathrm{RC}}(W)+{\mathrm{LF}}_{\mathrm{RGB}}(W)\\ & \sim & \exp \left(-\displaystyle \frac{1}{2}{\left(\displaystyle \frac{W-\overline{W}}{{\sigma }_{W}}\right)}^{2}\right)+A\,\exp \left(\displaystyle \frac{W}{2.5}\right),\end{array}\end{eqnarray} \tag{ 3 }$$

where $\overline{W}$ is the mean, σ_W is the standard deviation of the Gaussian, and A reflects the relative amplitudes of the two components. The luminosity function is marked with a black solid line in the right panel of Figure 3.

In the second step, we fit the (V − I) distribution where we weigh each star with its probability of belonging to the RC sample based on the luminosity function:

$$\begin{eqnarray}&&{p}_{\mathrm{LF}}(W)={\mathrm{LF}}_{\mathrm{RC}}(W)/\mathrm{LF}(W).\end{eqnarray} \tag{ 4 }$$

This approach is analogous to choosing a box in magnitude W but avoids imposing sharp limits, which could bias the RC sample, or conversely, leave too many unrelated stars within the sample. Even though this approach minimizes the contamination of the RGB in the RC sample, it does not remove it completely—there is still an RGB component visible in the color distribution. The majority of MC regions have moderate differential reddening, and both components can be well approximated using the normal distribution ${ \mathcal N }(\,\overline{V-I},\sigma )$ (see upper panels of Figure 4).

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In order to properly model the RC color distribution in all lines of sight, even those with a large differential reddening, we expand the basic model of ${ \mathcal N }(\,\overline{V-I},\sigma )$ by allowing the σ parameter to be different for the low (L) and high (H) side of $\overline{V-I}$:

$$\begin{eqnarray}&&\begin{array}{l}{{ \mathcal N }}_{2}(\,\overline{V-I},{\sigma }_{{\rm{L}}},{\sigma }_{{\rm{H}}})\\ \quad \ =\ \left\{\begin{array}{cc}\displaystyle \frac{2{\sigma }_{{\rm{L}}}}{{\sigma }_{{\rm{L}}}+{\sigma }_{{\rm{H}}}}{ \mathcal N }(\overline{V-I},{\sigma }_{{\rm{L}}}), & \mathrm{for}\ (V-I\,)\lt \overline{V-I}\\ \displaystyle \frac{2{\sigma }_{{\rm{H}}}}{{\sigma }_{{\rm{L}}}+{\sigma }_{{\rm{H}}}}{ \mathcal N }(\overline{V-I},{\sigma }_{{\rm{H}}}), & \mathrm{for}\ (V-I\,)\gt \overline{V-I}\end{array}\right..\end{array}\end{eqnarray} \tag{ 5 }$$

This modification was introduced after the visual inspection of hundreds of fields with various models of the color fit. The most typical situation in the inner parts of the MCs is that some fraction of stars lie between the observer and the bulk of dust—this fraction has a characteristic color scatter of σ_L. The rest of the stars lie within or behind the dust and are affected by the differential reddening, and for these stars, a better approximation is to use a different, higher value of σ_H. Such a hybrid model also allows for a reasonable approximation of many atypical RC distributions, but at the same time defaults to a Gaussian-like profile for the majority of well-behaved lines of sight. Figure 5 presents four examples of atypical RC color distributions, where this hybrid model (${{ \mathcal N }}_{2}$) proves useful.

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In general, Gaussian fitting is very sensitive to outliers, which can introduce a large bias in the fit parameters. Here we model the outliers with the constant background component added to the components of the RC and the RGB. Our model in principle has eight parameters: ${(\overline{V-I})}_{\mathrm{RC}}$, ${(\overline{V-I})}_{\mathrm{RGB}}$, four σ components (L and H, for both RC and RGB), and A_RGB and A_BKG, where the last two parameters are the relative amplitudes of the RGB to RC and the background to the RC, respectively. Fitting of such model to the data is inherently unstable because the RGB and RC regions overlap. Also the number of parameters is too large for many areas with low star counts. But because we are interested in determining the color of the RC only, and the RC component is dominant, we can determine other fit parameters approximately. This is sufficient to reduce the impact of the RGB and the MW foreground on the RC and reduces the systematic error of the RC color measurement. In order to do so, we fix the color offset between the RGB and RC, i.e., we fix ${O}_{\mathrm{RGB},\mathrm{RC}}={(\overline{V-I})}_{\mathrm{RGB}}-{(\overline{V-I})}_{\mathrm{RC}}$ to 0.07 in the LMC and 0.09 in the SMC. These values were determined with a simple algorithm that estimates the RGB color at the RC brightness using a ±1 magnitude range around the RC (with the narrow ±2 σ_W region around the RC magnitude removed). In other words, the algorithm uses parts of the RGB immediately above and below the RC. It then measures the median RGB color in 0.2 mag (or no less than 50 stars) bins, and using a linear fit, estimates the median RGB color at the RC position. The reported color offsets between the median RC and RGB colors (O_RGB,RC) are practically constant across the galaxies, with a typical scatter of 0.01 mag. In order to assess how such scatter influences the measured RC color, we performed RC color calculations with O_RGB,RC changed by −0.01 mag and +0.01 mag and found that it causes only a −0.001 mag and +0.001 mag difference, respectively, in the calculated RC color. This shows, that assuming a constant RGB-RC color offset in the entire galaxy is reasonable, especially when other sources of error are an order of magnitude larger.

We also found that it is sufficient to use a single width of the Gaussian components for the RC and the RGB (σ_L,RGB = σ_L,RC and σ_H,RGB = σ_H,RC) to model the observed distribution, as a higher differential reddening affects both groups of stars in the same way. This was verified by comparing standard deviations of the RC and RGB distributions in all LMC and SMC sight lines. They are equal to within a few percent.

Finally, we optimize the algorithm by estimating the relative number of stars within the RGB and RC groups in the previous step by integrating the RGB luminosity function with appropriate weights (p_LF(W) × LF_RGB(W)).

The four-parameter model:

$$\begin{eqnarray}&&\begin{array}{l}f\left({\left(\overline{V-I}\right)}_{\mathrm{RC}},{\sigma }_{{\rm{L}}},{\sigma }_{{\rm{H}}},{A}_{\mathrm{BKG}}\right)(V-I\,)\\ \qquad \ =\ {f}_{\mathrm{RC}}(V-I\,)+{f}_{\mathrm{RGB}}(V-I\,)+{f}_{\mathrm{BKG}}(V-I\,)\\ {f}_{\mathrm{RC}}(V-I\,)=\,{{ \mathcal N }}_{2}\left({\left(\overline{V-I}\right)}_{\mathrm{RC}},{\sigma }_{{\rm{L}}},{\sigma }_{{\rm{H}}}\right)(V-I\,)\\ {f}_{\mathrm{RGB}}(V-I\,)=\,{A}_{\mathrm{RGB}}\,{{ \mathcal N }}_{2}\left({\left(\overline{V-I}\right)}_{\mathrm{RC}}\right.\\ \qquad \ +\ \left.{O}_{\mathrm{RGB},\mathrm{RC}},{\sigma }_{{\rm{L}}},{\sigma }_{{\rm{H}}}\right)(V-I\,)\\ {f}_{\mathrm{BKG}}(V-I\,)=\,{A}_{\mathrm{BKG}}\end{array}\end{eqnarray} \tag{ 6 }$$

(where A_RGB is calculated from the LF and O_RGB,RC is fixed) is fitted to the color distribution of stars expected to lie within the RC region based on the luminosity function fit, i.e., to the distribution of all stars multiplied by the probability p_LF(W).

We calculate a median value (50th percentile) of the first component of the fitted model (f_RC, representing only the RC distribution), as well as ±34.1% intervals from the median, as an analog of a typical σ value of a Gaussian distribution, providing the final color estimation as

$$\begin{eqnarray}&&\mathrm{median}{\left(V-I\,\right)}_{\,-{\sigma }_{1}}^{\,+{\sigma }_{2}}=\mathrm{median}{\left(V-I\,\right)}_{\mathrm{centile}(50-34.1)-\mathrm{median}}^{\mathrm{centile}(50+34.1)-\mathrm{median}}.\end{eqnarray} \tag{ 7 }$$

The probability that a given star belongs to the RC sample can be assessed with

$$\begin{eqnarray}&&{p}_{\mathrm{RC}}(V-I\,)={f}_{\mathrm{RC}}(V-I\,)/f(V-I\,).\end{eqnarray} \tag{ 8 }$$

The black histograms in Figures 4 and 5 show the final RC sample. The mode of the histogram (or the most likely color value) is equal to the median for symmetric Gaussian profiles and is typically smaller for asymmetric profiles, because for the majority of lines of sight, the differential reddening makes σ_H > σ_L. We estimate the modal value by fitting a constant level with a small Gaussian bump to the final RC sample, across the entire color range. The mean and sigma of the Gaussian component are fitted, but the area under the Gaussian is fixed and set to one-sixth of the total area of the model. That way, we avoid noise in the mode, which is typically imposed by arbitrary binning. In the final table, we provide both the median and the mode of the RC color distribution and leave it to the user to decide which is more suitable for their needs. One can imagine that depending on the scientific question asked, either the mode or the median reddening for a given line of sight will give a better answer. However, in the subsequent analysis, we will use the median RC color and hence the median reddening value. We also provide ±34.1% percentile values from the median as a measure of confidence intervals and of differential reddening.

Previous studies of reddening in the Magellanic Clouds typically used a combination of a Gaussian and a polynomial to fit the RC distribution (e.g., Haschke et al. 2011; Choi et al. 2018; Górski et al. 2020). However, this has a tendency to miss the RGB contamination entirely and focus the polynomial on the smooth stellar background instead. In effect, in fields with low differential reddening, this overestimates the RC color due to the RGB contamination, and in fields with high differential reddening, it chooses the most likely value. Additionally, in regions with lower star counts—either in the outskirts of the galaxies or in areas with large reddening, a simpler fit (with fewer parameters) is generally more stable because it does not require a large number of stars to converge. This allows for retaining high resolution in such areas.

3.1. The Age-related Complexity of the Red Clump

The RC observed in some parts of the LMC is rich in various substructures: a distinct secondary RC (SRC), which is about 0.4 mag fainter and slightly bluer than the main RC and is composed of younger, ∼1 Gyr stars (Girardi 1999); a vertical structure (VS), which is made of brighter and more massive RC stars; and a horizontal branch (HB) composed of low-mass metal-poor stars at the same evolutionary stage (see the review by Girardi 2016). Figure 6 shows an example of these substructures in one of many such sight lines in the LMC. The SRC is the second most pronounced feature in the CMD, and its origin is well depicted in Figure 11 of Girardi (2016), which shows the age structure of RC stars—the younger the stars within the 1–2 Gyr range, the bluer they are. Also, as shown in Figure 6 of Girardi (2016), their luminosity varies by ∼0.5 mag within this age range, which is the reason why the SRC is elongated in magnitude. However, for stars older than 2–3 Gyr, both magnitude and color change very slightly with age (see Figure 1 of Girardi & Salaris 2001), resulting in a very compact RC. In other words, the (V − I) of older RC stars remains almost constant with age.

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The presence of the SRC and/or VS significantly widens the observed distribution of RC stars in magnitude (σ_W) and influences our estimation of the number of stars in the RC (N_RC) based on the LF. In order to trace regions of the LMC where these additional structures are visible, we calculate the N_RC/N parameter, which is the relative number of RC stars to all stars in the ±1 mag range around the measured RC brightness (W_RC). In other words, it is the ratio of the number of stars in the green histogram to the number of stars in the blue histogram shown in the right panel of Figure 3, but limited to the ±1 mag range around W_RC. In regions where this parameter is above ∼50%, we observe the additional RC structures, which are significant enough, that may influence the color measurement of the older, main RC. The two-dimensional distribution of N_RC/N is shown in Figure 7 and will be discussed in detail in a forthcoming paper (J. Skowron et al. 2021, in preparation).

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The presence of an additional young (<2 Gyr) RC population, whose intrinsic color is bluer by a couple of hundredths of a magnitude (∼0.04 mag) than that of a regular RC, has an effect on the measurement of (V − I). The resulting offset is of the order of 0.01 mag and depends on the relative number of the young to old RC population. Because the regular RC is more numerous and its intrinsic color is more stable across the galaxy, we decide to use only the regular, older RC to derive the reddening. The detailed modeling of a complex RC structure, including a star formation history, would be a very challenging task itself and is beyond the scope of this paper. However, the influence of the young RC on the measured color of the main RC can be estimated empirically using the ${N}_{\mathrm{RC}}/N$ parameter as a proxy for the severity of the effect, and this is done in Section 4.

In the SMC, the RC is largely elongated in magnitude. Some of this dispersion may be explained by the RC age and metallicity distribution (Girardi 1999), although the majority of this effect is caused by a large depth of the SMC along the line of sight, rather than population effects (Nidever et al. 2013). Hence, even though the distribution of ${N}_{\mathrm{RC}}/N$ is not entirely uniform throughout this galaxy, this is caused mainly by geometrical, not population, effects and does not need to be taken into account.

3.2. Discussion of (V − I) Uncertainties

The intrinsic color of the RC depends on both age and metallicity (Girardi & Salaris 2001). The widely used reddening maps of Haschke et al. (2011) adopted a theoretical value of 0.92 mag and 0.89 mag for (V − I)₀ in the center of the LMC and SMC, respectively. Górski et al. (2020) measured (V − I)₀ = 0.838 mag for the LMC and (V − I)₀ = 0.814 mag for the SMC, which are a mean of four distinct methods. Nataf et al. (2020) employed a hybrid theoretical and empirical approach and derived (V − I)₀ = {0.89, 0.92, 0.88} mag for the LMC, using three different methods, and (V − I)₀ = {0.84, 0.84} mag for the SMC. All of the above studies were limited to the inner parts of the MCs and assumed a constant metallicity, and thus the RC color value.

In order to determine the intrinsic unreddened (V − I)₀ color of the RC in the MCs, we correct the median measured (V − I) values for the foreground dust of the MW, for which we use the all-sky reddening map of Schlegel et al. (1998) based on dust infrared emission (hereafter SFD). The map provides E(B − V) values that can be converted to E(V − I), taking into account the recalibration of the SFD dust map by Schlafly & Finkbeiner (2011). The recalibration recommends a 14% decrease of E(B − V) and the use of the R_V = 3.1 Fitzpatrick (1999) reddening law. We use the convenient conversion coefficients provided by Schlafly & Finkbeiner (2011):

$$\begin{eqnarray}&&{A}_{V}/E{\left(B-V\right)}_{\mathrm{SFD},\mathrm{original}}=2.742\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{A}_{I}/E{\left(B-V\right)}_{\mathrm{SFD},\mathrm{original}}=1.505\end{eqnarray} \tag{ 10 }$$

that give

$$\begin{eqnarray}&&E{\left(V-I\right)}_{\mathrm{SFD}}={A}_{V}-{A}_{I}=1.237\,E{\left(B-V\right)}_{\mathrm{SFD},\mathrm{original}}.\end{eqnarray} \tag{ 11 }$$

The SFD galactic reddening map is shown in Figure 8(a). The dust temperature and reddening values in the LMC and SMC centers are not reliable because their temperature structure is not sufficiently resolved (Schlegel et al. 1998), therefore we cut out the central regions of the MCs from further analysis of (V − I)₀. In the case of the LMC, we remove the inner 41 radius circle centered at (05^h20^m00^s, −68°48'00''). This region contains the inner disk of the LMC, which is abundant in gas, dust, and young stars. The dust content is clearly seen in SFD emission maps (Figure 8(a)) and will be apparent in our maps of differential reddening. The majority of Classical Cepheids in the LMC (Jacyszyn-Dobrzeniecka et al. 2016) are located in this region (with a sharp decline in density outside). This is also the center of rotation of H i gas measured using the 21 cm line (de Vaucouleurs 1960) and was also shown to be an acceptable center for the optical rotation curve (Feast et al. 1961). Thus, we adopt this "radio center" coordinates as a center of the excluded region, which is offset by over 1° from the LMC optical disk center at (05^h29^m00^s, −68°30'00'') from van der Marel (2001).

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In the case of the SMC, we remove measurements within an ellipse centered at (00^h58^m00^s, −72°12'00''), which was selected by eye to encompass the affected central region of the galaxy (r_a = 20, r_b = 13, r_PA = 40°) and is also different from the optical center of the SMC at (00^h52^m125, −72°49'43'') from de Vaucouleurs & Freeman (1972). See black circle/ellipse in Figure 8, with their centers marked with black dots and optical centers marked with crosses.

The middle panel of Figure 8 shows the median (V − I) colors of the RC in the MCs measured in this work, while panel (c) shows the RC colors corrected for the MW reddening (the difference between panels (a) and (b)), i.e., the intrinsic color (V − I)₀. Once again, it is clear that SFD reddening values within the central regions of the MCs are not real and only the values outside the marked areas can be used to determine the intrinsic color of the RC. Panels (b) and (c) also illustrate that the outskirts of the galaxies (the areas outside white ellipses) are not suitable for determining (V − I)₀—the color determination in these regions is erratic and the visual investigation of color fits in these lines of sight confirms that they are not reliable. The main reason is that we reach the edge of the galaxies where the RC star counts are so low that the RC is not well defined. This is well depicted in Figure 9(a), where we see a significant increase in σ₁ in the outskirts of the MCs (panel (a)). The highest values of σ₁ coincide with the increased MW extinction in the southern part of the LMC. This is caused by the reddened population of MW stars interfering with the RC of the LMC in the CMD. As a result, the region occupied by RC stars in the CMD is dominated by the MW foreground and the Gaussian fit generates a very wide peak across the entire fitting box defined in Section 3. This is also reflected in a very high value of σ_W (panel b), where the outskirts of the MCs reach σ_W = 0.5 mag, which reflects the fact that the LF is dominated by the background contamination and there is no distinct RC component visible.

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We therefore assume that all measurements that fall outside the white ellipses (Figures 8 and 9) are unreliable and reject them from the intrinsic RC color analysis. The ellipses were chosen based on the surface density of RC stars—about 1000 stars deg⁻². Then, after visual inspection of CMDs on both sides of the ellipses, the ellipse parameters were slightly adjusted to ensure that the bad measurements are outside the ellipse, while the majority of the good ones fall inside the ellipse.

As discussed in Section 3.1, there is a bias in the measurement of the (V − I) of the RC in some parts of the LMC that is caused by the presence of additional RC structures, mainly the younger SRC. The additional, bluer SRC is composed of stars younger than about 2 Gyr, while the majority of RC stars are older, and their intrinsic color (V − I)₀ remains fairly constant with age. Figure 7 shows the distribution of N_RC/N that reveals sight lines, where the measured (V − I) is affected by the young SRC. Figure 10 shows how our measurement of the intrinsic color is as a result biased with the growing value of N_RC/N. Even though the color difference between the regular RC and the SRC is a few hundredths of a magnitude, typically ∼0.04 mag, its influence on the measured color is on average only of the order of 0.01 mag. We apply this small correction (0.1 × (N_RC/N − 0.5) for N_RC/N ≥ 0.5) to the final value of (V − I), based on Figure 10. The detailed modeling of the RC in individual sight lines is not necessary, because the correction is small compared to other sources of uncertainty.

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4.1. Metallicity Gradient in the MCs

As was already discussed, the RC color depends on both the age and metallicity of the RC. Because we are using only the intermediate- and old-age RC stars (approximately >2–3 Gyr), the color change with age is negligible in this age range, but the change with metallicity is not (Figure 1 of Girardi & Salaris 2001).

The presence of the metallicity gradient in the LMC has long been a subject of discussion (Choudhury et al. 2016 and references therein), although recent studies support a shallow metallicity gradient, e.g., −0.047 ± 0.003 dex kpc⁻¹ out to ∼8 kpc (Cioni 2009), −0.029 ± 0.002 dex kpc⁻¹ in the inner 5 kpc (Skowron et al. 2016), and from −0.049 ± 0.002 to −0.066 ± 0.006 dex kpc⁻¹ up to a radius of 4 kpc (Choudhury et al. 2016). The distribution of [Fe/H] among the LMC clusters also shows a radial dependence (Pieres et al. 2016).

In the case of the SMC, the existence of the metallicity gradient has also been questioned, although a number of most recent results do report a shallow metallicity gradient: −0.075 ± 0.011 dex/deg within the inner 5° (Dobbie et al. 2014), −0.08 ± 0.08 dex/deg out to 4° (Parisi et al. 2016), from −0.045 ± 0.004 to −0.067 ± 0.006 dex/deg within the radius of 25 (Choudhury et al. 2018), and −0.031 ± 0.005 within the inner 2° (Choudhury et al. 2020).

Nataf et al. (2020) used [Fe/H] metallicities of bright and faint red giants, derived by the ASPCAP pipeline (García Pérez et al. 2016) from high-resolution spectra taken for the APOGEE survey (Majewski et al. 2017), which is part of the Sloan Digital Sky Survey (Blanton et al. 2017), and found a mean metallicity value for the inner LMC [Fe/H] = −0.64 dex (within the inner LMC disk, i.e., inside the black circle), and [Fe/H] = −0.88 dex for the inner SMC. Following Nataf et al. (2020), we select bright and faint red giants (K > 12.25 mag and 0.55 < J − K < 1.3 mag) as defined by Nidever et al. (2020), from APOGEE LMC fields 1–17, encompassing both the central parts and the outskirts of the LMC, and from SMC APOGEE fields 1–7 (see their Figure 1). We then remove foreground stars (log(g) ≥ 2) and very metal-poor stars ([Fe/H] ≤ −1.3 dex in the LMC and [Fe/H] ≤ −1.6 dex in the SMC). This leaves 2134 red giants in the LMC and 957 in the SMC. Their distribution is shown in Figures 11(a) and (b), for the LMC and SMC, respectively, and their metallicity values against distance from the LMC/SMC optical center are plotted in panels (c) and (d). In the case of the SMC, we adopt an elliptical system with the major to minor axis ratio of 1.5 and a position angle of 553 east of north, in order to account for the elongation of the SMC and to be consistent with previous metallicity studies (e.g., Piatti et al. 2007; Dobbie et al. 2014; Parisi et al. 2016). The line fit to the data gives a metallicity gradient of −0.026 ± 0.002 dex deg⁻¹ in the LMC. In the majority of the SMC, the gradient is consistent with −0.033 ± 0.005 dex deg⁻¹, but there is a clear change in the slope at about 15 distance (in elliptical coordinates), and the gradient can be described by −0.118 ± 0.027 dex deg⁻¹ in the central part of the SMC.

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Because the locations of the APOGEE fields are sparse across the galaxies and the scatter of [Fe/H] values is large, it is difficult to investigate the metallicity gradient in more detail, i.e., to verify whether it is uniform in all radial directions. However, if the metallicity gradient was variable, it would not significantly alter the results of this paper due to a very shallow dependence of (V − I)₀ on [Fe/H] within the metallicity range of the MCs, which is discussed below.

The relation between the intrinsic color of the RC and its metallicity is supported by both theory and observations (Girardi 2016; Nataf et al. 2020). In an attempt to calibrate this dependence, we selected a sample of 17 star clusters from the LMC and SMC, which are older than 3 Gyr and younger than 9.5 Gyr, as their RC color does not change with age over this age range (see Figure 1 of Girardi & Salaris 2001). The selection also required that the clusters are located in areas with low reddening (E(V − I)_SFD < 0.12 mag). We use their [Fe/H] values available in the literature (Da Costa & Hatzidimitriou 1998; Bica et al. 1998; Grocholski et al. 2006; Glatt et al. 2008; Parisi et al. 2009; Dias et al. 2016), with the preference for spectroscopically determined metallicities over the photometric ones, if both were available. The spectroscopically determined metallicities are based on the calcium triplet technique and have typical uncertainties of ∼0.05 dex. The photometric estimations are based on comparing the observed and synthetic CMDs and have much larger errors, usually >0.20 dex. The RC colors of the 17 clusters are measured using OGLE-IV data within the cluster radius, with a typical error <0.02 mag, and dereddened with the SFD maps. Because MC star clusters meeting these criteria are rather metal poor, we supplement the above data set with data for NGC 6791 and the solar neighborhood (Nataf et al. 2020) and for the Galactic Bulge (Bensby et al. 2017).

Figure 12 shows the dependence of the intrinsic RC color (V − I)₀ on metallicity [Fe/H] for the above sample. The top panel includes the theoretical relation between (V − I)₀ and [Fe/H] from Nataf et al. (2020), which was limited to [Fe/H] ∼ −1.0 dex at the low-metallicity end (the purple line). The red line shows a line fit to the data points, within the metallicity range considered in this work (−1.2 < [Fe/H] < −0.4 dex). The estimated slope is 0.080 ± 0.016 mag dex⁻¹ and the zero point is 0.925 ± 0.016 mag. The fit takes into account both [Fe/H] and (V − I)₀ uncertainties, marked in the bottom panel of Figure 12. The intrinsic color change in this metallicity range is nonnegligible but small, and the estimated slope may change with the availability of new cluster data. The calculated slope of 0.08 mag dex⁻¹, combined with the metallicity gradient⁴ in both galaxies (as estimated in Figure 11), predicts an intrinsic color change with the distance from the galaxy center of the order of −0.002 mag deg⁻¹ in the LMC, −0.003 mag deg⁻¹ in the outer SMC, and −0.009 mag deg⁻¹ in the inner SMC.

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4.2. (V − I)₀ of the Red Clump in the LMC

The distribution of E(V − I)_SFD reddening in the MW around the LMC is presented again in Figure 13(a), while panel (b) shows the distribution of the unreddened RC color, i.e., the difference between the measured median (V − I) color of RC and the E(V − I)_SFD reddening in the MW around the LMC. The MW dust distribution in the LMC region is not uniform—its southern part is highly affected by dust, the northeastern part is moderately affected, whereas the northwestern part is almost unaffected by Galactic extinction. We therefore subdivide the LMC into four quadrants (Figure 13, panels (a)–(b)), along constant R.A. and decl., that cross in the center of the LMC disk (05^h29^m00^s, −68°30'00'', from van der Marel 2001). Note that the center of dust emission is offset from the center of the LMC disk by over one degree. Each of Figures 13(c)–(f) contains three plots: the MW reddening E(V − I)_SFD (top, blue points), the measured median RC color (V − I) (middle, red points) and their difference, i.e., the inferred intrinsic RC color (V − I)₀ = (V − I) − E(V − I)_SFD (bottom, cyan points), against the distance from the center of the LMC disk. They represent data within the four quadrants of the LMC: northeast (panel (c)), northwest (panel (d)), southeast (panel (e)), and southwest (panel (f)). Black points in all plots show spurious measurements that either fall inside the black circle (where E(V − I)_SFD is wrong) or outside the white ellipse (where RC color measurements are spurious) pictured in panels (a) and (b). The dark-gray shaded area marks the central region entirely excluded from the analysis, while the light-gray shaded area marks the region partially excluded from the analysis (the black circle crosses a range of distances due to the difference in coordinates of the LMC dust and stellar disks).

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The line fit to (V − I)₀ versus distance from the LMC center (cyan points) is shown with a dashed line in the bottom plots of panels (c)–(f). The fit is based on joined data from the NE, SE, and SW quadrants and accounts for the fixed metallicity gradient and the resulting RC color change of −0.002 mag deg⁻¹. The different behavior of (V − I)₀ in the NW is unlikely to be caused by the actual intrinsic color difference in this LMC quadrant but is very likely to be a systematic effect originating from the calibration of SFD extinction maps. This effect becomes most prominent in LMC regions with the lowest MW extinction, probably because the contribution of the LMC internal dust is higher than that of the MW foreground dust, for which the relation between dust temperature and reddening was calibrated. Another possibility is that E(V − I)_SFD is underestimated in regions with very low dust density. For these reasons, we did not use the NW quadrant, where the reddening is the lowest, when fitting the intrinsic color.

The median value of (V − I)₀ in the investigated area, between the black circle and the white ellipse, is 0.877 mag. The scatter of individual lines of sight around the fitted line is 0.014 mag. The predicted intrinsic color in the LMC center from the color gradient is 0.886 mag, which is consistent with the results of Nataf et al. (2020).

4.3. (V − I)₀ of the Red Clump in the SMC

The MW extinction around the SMC is lower, and its distribution is more uniform than around the LMC (see Figure 14(a)), with only a slight difference between the MW dust distribution in the northern and southern parts of the SMC. The distribution of the unreddened RC color, i.e., the difference between the measured median (V − I) color of RC and the E(V − I)_SFD reddening in the MW around the SMC is presented in Figure 14(b). Similarly to the case of the LMC, panel (c) shows the MW reddening E(V − I) (top, blue points), the measured RC color (V − I) (middle, red points) and the inferred intrinsic RC color (V − I)₀ (bottom, cyan points) against the elliptical distance from the center of the SMC at (00^h52^m125, −72°49'43'') from de Vaucouleurs & Freeman (1972), with the major to minor ellipse axis ratio of 1.5 and a position angle of 553 east of north (e.g., Piatti et al. 2007; Dobbie et al. 2014; Parisi et al. 2016). Black points in all plots of panel (c) show spurious measurements that either fall inside the black ellipse (where E(V − I)_SFD is wrong) or outside the white ellipse (where RC color measurements are spurious) pictured in panels (a) and (b). The dark-gray shaded area marks the central region entirely excluded from the analysis, while the light-gray shaded area marks the region partially excluded from the analysis (the black ellipse crosses a range of distances from the SMC center).

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The line fit to (V − I)₀ versus elliptical distance from the SMC center (cyan points) is shown in the bottom plot of panel (c) with a dashed line. The fit accounts for the fixed metallicity gradient and the resulting RC color change of −0.003 mag deg⁻¹ for distances larger than ∼15 (black line) and −0.009 mag deg⁻¹ for distances smaller than ∼15 (orange line).

The median value of (V − I)₀ in the investigated area, between the black and white ellipses, is 0.853 mag. The scatter of individual measurements around the fitted line is 0.018 mag. The predicted intrinsic color in the SMC center is 0.877 mag, which is much higher than the 0.84 mag estimated by Nataf et al. (2020) and is a result of the steepening of the metallicity gradient in the inner SMC. If we assumed that the gradient does not change and follows the black dashed line (panel (c) of Figure 14), then the predicted intrinsic color in the SMC center would be 0.865 mag. Another reason for the high central value of (V − I)₀ may be due to the underestimation of E(V − I)_SFD in areas with very low reddening. Similarly to the NW quadrant of the LMC, where increasing E(V − I)_SFD by a few hundredths would shift the reddening estimates to fit the (V − I)₀ gradient estimated from other quadrants, in the SMC (where the extinction is generally much lower than in the LMC), it would cause the lowering of (V − I)₀.

The final E(V − I) reddening map of the MCs was obtained by subtracting the intrinsic RC color (Sections 4.2 and 4.3) from the measured one. The resolution of the map is 17 × 17 in the central parts of the MCs and decreases down to approximately 27' × 27' in the outskirts.

Figure 15 shows the distribution of reddening (panel (a)) and its standard deviation: σ₁ (panel (b)) and σ₂ (panel (c)). Both σ₁ and σ₂ are measures of internal reddening in the MCs and inform of the distribution of dust within the galaxies along the line of sight—high σ₁ indicates increased amounts of dust in the near parts, while high σ₂ in the central and far parts of the galaxy. It is well represented in panel (c), where σ₂ reflects the distribution of dust within the LMC inner disk (see Section 3 for details).

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The mean reddening is E(V − I) = 0.100 ± 0.043 mag in the LMC and E(V − I) = 0.047 ± 0.025 mag in the SMC. This is lower than all previous measurements but is expected—this is the first reddening map of the MCs that encompasses all areas where the RC is visible, including the outskirts of the galaxies, where the reddening is very low.

The reddening data are available from http://ogle.astrouw.edu.pl/cgi-ogle/get_ms_ext.py both for download (in TEXT and FITS formats, for the users' convenience) and in the form of an interactive interface. A subset of the data is presented in Table 1.

5.1. Comparison with Previous Large-scale Reddening Maps Based on RC Stars

Here we compare our reddening maps with other large-scale reddening maps of the MCs based on RC stars. Instead of comparing reddening values themselves, which highly depend on the adopted intrinsic color of the RC, we instead compare maps of measured RC color and the adopted intrinsic RC color separately.

5.1.1. Haschke et al. (2011)

Large-scale reddening maps of the LMC and SMC published by Haschke et al. (2011) were based on RC stars from the OGLE-III data (Udalski et al. 2008a, 2008b). Authors found a mean reddening E(V − I) = 0.09 ± 0.07 mag in the LMC and E(V − I) = 0.04 ± 0.06 mag in the SMC. When taking into account only the area investigated by Haschke et al. (2011), we find mean reddening values of E(V − I) = 0.122 ± 0.048 mag in the LMC and E(V − I) = 0.056 ± 0.020 mag in the SMC. The difference is 0.032 and 0.016 mag for LMC and SMC, respectively, and is mostly a result of the adopted zero color of the RC. Haschke et al. (2011) used theoretical values that depend on metallicity, adopting (V − I)₀ = 0.92 mag and (V − I)₀ = 0.89 mag for the LMC and SMC, respectively (Girardi & Salaris 2001), while we use empirical values, which together with accounting for a metallicity gradient give mean intrinsic colors within the area investigated by Haschke et al. (2011) of (V − I)₀ = 0.884 (LMC) and (V − I)₀ = 0.862 mag (SMC).

Figure 16 presents a comparison between color measurements from this work and the work of Haschke et al. (2011). Panels (a) and (b) show a two-dimensional map of RC color differences that are color coded. The histogram of differences between (V − I) color values from this work and from Haschke et al. (2011) is shown in panel (c) for the LMC and in panel (d) for the SMC. In the case of the LMC, the mean difference is $\langle {(V-I)}_{\mathrm{Skowron}}-{(V-I)}_{\mathrm{Haschke}}\rangle =-0.004\pm 0.018$ mag. There are some expected larger discrepancies in the central region of the LMC, where the differential reddening is high, but the overall agreement is reasonable and falls within one σ value. This is further pictured in panel (e), where a comparison of color differences divided by the σ of the color is shown.

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In the case of the SMC, there is a mean difference of $\langle {(V-I)}_{\mathrm{Skowron}}-{(V-I)}_{\mathrm{Haschke}}\rangle =-0.011\pm 0.014$ mag, but there is also a systematic difference between the eastern and western parts, due to small offsets between the OGLE-III and OGLE-IV calibrations (panel (b)). As seen in panel (f), there is an agreement within one σ value for the majority of the area, although larger differences are observed at the edges, and these result from the differences in an algorithm calculating (V − I).

5.1.2. Choi et al. (2018)

More recently, Choi et al. (2018) released the E(g − i) reddening map of a large part of the LMC based on RC stars observed by the Survey of the MAgellanic Stellar History (SMASH; Nidever et al. 2017). They postulated that there is a radial dependence of the intrinsic color of the RC, such that it is practically constant in the range between 4° and 7° from the galaxy center, with (g − i)₀ = 0.822, but follows a slope of 0.024 dex deg⁻¹ between 27 and 4° and a slope of −0.033 dex deg⁻¹ between 7° and 85 from the center of the LMC (see their Figure 7). This finding is not supported by our data. Figure 17(a) shows the distribution of (V − I)₀ from this work. The black circle marks the central region of the LMC, where the SFD map is not reliable, while the white ellipse cuts off the rejected outer region of the galaxy, unsuitable for color measurements. In Section 4, we demonstrated that only the region between the black circle and white ellipse can be reliably used for determining the intrinsic color of the RC. In Figure 17(a), we use pink contours to overplot regions used by Choi et al. (2018) to determine the intrinsic RC color, which are identical to their Figure 4. It can immediately be seen that the pink contours in the southern and western part of the LMC partially cover the outskirts of the LMC, where the (V − I) determination is not reliable. Similarly, eastern and western contours close to the galaxy center enter the region within the black circle, in which SFD reddening values, and so the (V − I)₀ determination, are not realistic.

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The plots in Figures 17(b) and (c) show the change of (V − I)₀ measured in this work, with distance from the LMC disk center. Panel (b) (cyan points) presents intrinsic color values in the "safe" region, between the black circle and the white ellipse, while panel (c) (pink points) shows the intrinsic color values within pink contours used by Choi et al. (2018). It is apparent that the (V − I)₀ gradient in the range 27–4° and 7°–85, visible in panel (c), originates solely from the choice of regions to determine (V − I)₀. However, when we use data from the reliable area only, we only see a slight gradient of (V − I)₀ in the entire range 35–9° from the LMC center (panel (b)), originating from the metallicity gradient in the LMC.

When working with the reddening map of Choi et al. (2018), which is provided in FITS format, we found that their map departs from the WCS convention. The FITS-WCS standard (Greisen & Calabretta 2002, Section 2.1.4) states that the "integer pixel numbers refer to the center of the pixel in each axis, so that, for example, the first pixel runs from pixel number 0.5 to pixel number 1.5 on every axis". From our tests, it appears that the reddening values of Choi et al. (2018) are for the area of the sky between the coordinates calculated for the integer pixel numbers, e.g., the first pixel represents the area between the WCS coordinates calculated for positions 1 and 2. This half-pixel offset in both axes translates to the typical offset of 7' in their published map and is clearly visible when comparing with our maps, especially in the center, where the resolution is 17' × 17. We account for this offset in further analysis.⁵

In order to compare RC color values from this work and from Choi et al. (2018), we use the provided (g − i) color maps and transform them to (V − I) with

$$\begin{eqnarray}&&{\left(V-I\right)}_{\mathrm{Choi}}=0.765\,(g-i\,)+0.242.\end{eqnarray} \tag{ 12 }$$

The constant 0.242 was chosen arbitrarily so that the mean color difference is zero, as the exact value of the constant term is not known without a detailed comparison of individual stars in both samples.

In Figure 18, we plot a color-coded 2D map (panel (a)) and a histogram (panel (b)) of the differences between (V − I) measured in this work and obtained by Choi et al. (2018). Panels (c) and (d) show a comparison of color differences divided by the σ of the color distribution. Even though there is a moderately good overall agreement between the two maps, there are multiple regions with significant differences, which originate from Choi et al. (2018) adopting the median value of the color distribution of all stars in the selection box, as the RC color. This is especially seen in areas with the higher scatter in color, i.e., in the center and in the outskirts. We investigated the nature of this discrepancy by looking by eye at the CMDs of regions with the largest color differences. We found that in these cases, the measurements of Choi et al. (2018) fall either on the blue or on the red side of the actual RC color peak. This is caused by the manual selection of the box containing RC stars. In the case where the RC is in the region of low extinction, their selection box omits some of the RC stars on the red side when trying to minimize the RGB contribution. This is well depicted in Figure 3 of Choi et al. (2018)—the red part of the top histogram in panel (a) is quite sharply cut off. The median of such a distribution will underestimate the real color of the RC, falling on the blue side of the maximum of the RC color histogram. In the other case, when the RC is in the region of high extinction, their selection box contains mostly all RC stars on the red side, but there is a sharp cutoff on the blue side in order not to include other features that might contain stars from different populations. (see the red part of the top histogram in Figure 3(b) of Choi et al. 2018). The median of such a distribution will overestimate the real RC color, falling on the red side of the maximum of the RC color histogram.

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5.1.3. Górski et al. (2020)

Most recently, Górski et al. (2020) published an update of the reddening maps of Haschke et al. (2011) based on OGLE-III RC stars, with a new calibration of the intrinsic RC color based on independently measured reddening of late-type eclipsing binary systems and blue supergiants and reddening derived from Strömgren photometry of B-type stars. They calculated the intrinsic RC color separately for each tracer and then averaged the results to find (V − I)₀ = 0.838 ± 0.034 in the LMC and (V − I)₀ = 0.814 ± 0.034 in the SMC. This is disturbingly lower than the values obtained in this work. If we average our intrinsic color estimates within the region investigated by Górski et al. (2020), we obtain a mean (V − I)₀ of 0.883 mag for the LMC and 0.862 mag for the SMC. The difference is 0.045 and 0.048 mag for the LMC and SMC, respectively. While it is true that our estimated central value of (V − I)₀ is based on the RC color measurements in the outer disk, beyond 3° from the LMC center, while the (V − I)₀ of Górski et al. (2020) is based on the central part of the LMC, the difference is nevertheless larger than expected. Because we have accounted for the metallicity, and hence color gradient, in the LMC, it is unlikely that our estimated intrinsic color in the inner parts of the LMC differs by as much as 0.045 mag.

This is further supported by a comparison of RC color measurements in this work and in Górski et al. (2020). Figure 19 presents a comparison of measured (V − I) in the MCs, where panels (a) and (c) show a two-dimensional map of differences that are color coded. The histogram of differences between (V − I) color values from this work and from Górski et al. (2020) is shown in panel (b) for the LMC and in panel (d) for the SMC. In the case of the LMC, the mean difference is only −0.005 ± 0.021, and in the SMC it is −0.004 ± 0.018, which shows that color estimates are consistent. Significant discrepancies in the galaxy centers are largely due to large differential reddening and disappear in panels (e) and (f), where the RC color differences are divided by the σ of the color distribution. On the other hand, panels (e)–(f) highlight discrepancies in areas where the different approach to estimating the RC color plays a role.

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Tables 5 and 6 in Górski et al. (2020) list separate (V − I)₀ values for each of the tracers used to estimate the final intrinsic color. The method using Na i line in eclipsing binaries (from Graczyk et al. 2014, 2018) has the smallest standard deviation of all four methods and gives consistent results in terms of the intrinsic color difference between LMC and SMC of 0.023 mag, which is a reasonable number and is confirmed with our data. Remaining methods tend to show smaller values of (V − I)₀, which can be caused either by the additional reddening or a different reddening law in the case of blue supergiants, or by systematic errors affecting reddening determinations from effective temperature for eclipsing binaries or Strömgren photometry (M. Górski, private communication). It is also worth mentioning that the standard deviation of (V − I)₀ obtained from the effective temperature of eclipsing binaries and atmospheric models of blue supergiants is higher compared to the standard deviation of (V − I)₀ obtained from Na i line. Additionally, the intrinsic color difference between the LMC and SMC obtained from effective temperature of eclipsing binaries is zero, for blue supergiants it is only 0.01 and is as much as 0.068 mag for the Strömgren photometry, which is inconsistent with values obtained from Na i line analysis and our results. Thus, none of these values seem realistic, and combined with the high standard deviation of these methods, seem untrustworthy. Given that the method using the Na i line in eclipsing binaries gives the most reliable results, one can assume that the intrinsic color in the MCs obtained by Górski et al. (2020) should rather be 0.854 and 0.831, than 0.838 and 0.814, in the LMC and SMC, respectively. This is closer to our (V − I)₀ averaged within the region investigated by Górski et al. (2020), with the difference of 0.029 in the LMC and 0.031 in the SMC.

The remaining question is whether this difference between the intrinsic RC color in the outer (this work) and inner (work of Górski et al. 2020) MCs is of physical nature or is some sort of a statistical/calibration effect. The argument in favor of it being real is that we observe a dip in E(V − I) in the most central part of the LMC—see Figure 15(a), where the color of the densest regions of the LMC bar is bluer than the surrounding area, which may indicate a change in the RC intrinsic color.

After verifying that our RC color measurements are consistent with those of Górski et al. (2020), we also verified our RC color measurements at the locations of eclipsing binaries from Graczyk et al. (2014, 2018) and found very similar values as Górski et al. (2020), thus ultimately concluding that this is not a matter of some calibration error between OGLE-III and OGLE-IV data or significant differences in methods of RC color determination.

We then compared our E(V − I) reddening values (assuming an intrinsic color gradient as determined in Sections 4.2 and 4.3) at the locations of eclipsing binaries with E(B − V) reddening values for these binaries estimated using the Na i line (Graczyk et al. 2018), as was done by Górski et al. (2020). We convert E(B − V) to E(V − I) with E(V − I) = 1.318 E(B − V). The average difference is −0.040 both in the LMC and SMC, such that our reddening is lower than that of Graczyk et al. (2018). This is fairly consistent with the difference in the intrinsic color between Górski et al. (2020) and this work (0.045 and 0.048 for the LMC and SMC, respectively). However, we found that the reddening of eclipsing binaries in the LMC estimated by Graczyk et al. (2018) should not be averaged as it depends on the density of stars, and so does the difference between reddening from Graczyk et al. (2018) and this work. Figure 20 shows the surface density of stars in the centers of the LMC (panel (a)) and SMC (panel (c)). White dots mark the locations of eclipsing binaries from Graczyk et al. (2018). Panels (b) and (d) show the change of the E(V − I) difference with the surface density of giant stars. In the case of the LMC (panel (b)), our reddening measurements are similar to those of Graczyk et al. (2018) in low-density areas but become lower with growing surface density. This can be explained in two ways: either there is a decrease of (V − I)₀ within the very center of the LMC bar, or there is a problem with the calibration of the equivalent width of the Na i line and the reddening.

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In the latter case, the potential caveat is the use of an empirical relation between gas and dust content in our Galaxy. This relation may be different in the LMC and/or change with the gas metallicity, and thus could be the source of error, although the detailed analysis of this problem is beyond our area of expertise.

In the former case, we have already shown that there is an increase of (V − I)₀ in the LMC that results from the metallicity gradient. The decrease of (V − I)₀ is possible for RC stars younger than 2 Gyr, which have been excluded from our analysis. However, we can compare reddening from RC stars with reddening from another tracer to see if there is a similar behavior in the bar of the LMC. If there is no dip in E(V − I) in the LMC bar from another tracer, then it would mean that our E(V − I) values are underestimated, i.e., the intrinsic RC color is overestimated. Figure 21 shows such a comparison between the reddening of RC stars and RR Lyrae–type variable stars. The RC sample (panel (a)) is presented in lower resolution to match the one of the RR Lyrae sample (panel (b)), where each bin contains an averaged reddening value of at least 10 stars. The RR Lyrae data were taken from Soszyński et al. (2016), the photometric metallicity values from Skowron et al. (2016) and (V − I)₀ was calculated with the theoretical metallicity-dependent relations from Catelan et al. (2004). It is clearly visible that the central bar area with lower reddening is also present in the reddening distribution of RR Lyrae stars. We therefore conclude that this is caused by the actual dust distribution in front of the bar region and is not a result of the change of intrinsic color.

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In the case of the SMC, the (V − I)₀ obtained by Górski et al. (2020) is lower by 0.048 mag (or 0.031 mag if we exclude results from dubious tracers) than our intrinsic color averaged in the area investigated by Górski et al. (2020). Figures 20(c) and (d) show how the difference in reddening between Graczyk et al. (2014) and this work depends on the density of RC stars. The sample of eclipsing binaries is very small and does not span a sufficient range of stellar densities, so it is hard to draw explicit conclusions. With the available data, it seems that E(V − I) is almost independent of the surface density of stars. This may be due to lower extinction in the SMC, lower star densities, and a small number of eclipsing binaries that could trace the potential change of their reddening with star surface density.

In this paper, we present the most detailed and extensive E(V − I) reddening map of the MCs based on RC stars from the OGLE-IV survey (Udalski et al. 2015) that provides reddening information for 180 deg² in the LMC and 75 deg² in the SMC, with a resolution of 17 × 17 in the central parts of the MCs, decreasing to approximately 27' × 27' in the outskirts. The mean reddening in the LMC is 0.100 ± 0.043 mag in the LMC and 0.047 ± 0.025 mag in the SMC.

We refine methods of calculating the RC color to obtain the highest possible accuracy of reddening maps based on RC stars. In particular, we account for the age-related additional RC structures that influence the measurement of RC color.

From the spectroscopy of red giants (Nidever et al. 2020), we find that there is a small metallicity gradient with distance from the galaxy center in both the LMC and SMC. Based on cluster data, we find a shallow dependence of intrinsic RC color on cluster metallicity. By combining the two relations, we show that there is a slight decrease of the intrinsic RC color with distance from the center. In the LMC, (V − I)₀ = 0.886 − d × 0.002, where d is the distance from the galaxy center. In the SMC, (V − I)₀ = 0.865 − d × 0.003 for d > 15, and (V − I)₀ = 0.877 − d × 0.009 for d < 15, where d is the elliptical distance from the galaxy center. This is consistent with the results of Nataf et al. (2020), but contrary to the findings of Choi et al. (2018) and Górski et al. (2020). We also argue that the low value of (V − I)₀ obtained by Górski et al. (2020) is a result of using unreliable tracers, combined with possible calibration errors.

The reddening map is available from the OGLE website at http://ogle.astrouw.edu.pl/cgi-ogle/get_ms_ext.py both for download (in TEXT and FITS formats, for the users' convenience) and in the form of an interactive interface.

The presented map covers the entire area where the RC is detectable and where the spatial resolution it provides is better than that of the SFD reddening map, thus exhausting the possibility of extending the detailed reddening map of the MCs with the future RC data.

We thank Marek Górski and David Nataf for fruitful discussions on reddening in the MCs. We also thank the referee for their valuable suggestions that led to many improvements of this paper. The OGLE project has received funding from the NCN grant MAESTRO 2014/14/A/ST9/00121 to A.U. D.M.S. has received support from the NCN grant 2013/11/D/ST9/03445.

This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is www.sdss.org.

SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics ∣ Harvard & Smithsonian (CfA), the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

This work has made use of NASA's Astrophysics Data System Bibliographic Services.