LARGE MAGELLANIC CLOUD DISTANCE AND STRUCTURE FROM NEAR-INFRARED RED CLUMP OBSERVATIONS

The Large Magellanic Cloud (LMC), our nearest neighbor of appreciable mass, has long been one of the most important objects in the sky. Determining the distance to and the structure of the LMC is important in both its role as a key rung on the cosmological distance scale and the search for MACHO microlensing events.

The core helium burning red clump (RC) stars provide an excellent standard candle; they are numerous, easily identified in color–magnitude diagrams (CMDs), and population corrections calculated on the basis of stellar evolution libraries reduce the systematic uncertainties to 0.03–0.05 mag- depending on the band used.

Several groups have used the RC to measure the distance to the LMC (Udalski et al. 1998; Cole 1998; Alves et al. 2002; Pietrzyński & Gieren 2002; Sarajedini et al. 2002). Alves (2004) reviews the distance determinations using the RC as well as those from Cepheid, RR Lyrae, and Mira variables, main-sequence fitting, SN1987A, and eclipsing binaries to produce a weighted average of 18.50 ± 0.02. More recently, Grocholski et al. (2007) have also applied near-infrared JHK photometry to the measurement of the RC in 17 LMC clusters. Identifying these clusters with the spatial location of the LMC disk, they arrive at a distance modulus of 18.40 ± 0.04_rand ± 0.08_sys.

Several investigators have measured the inclination and orientation of the LMC disk. By assuming the LMC disk is circular when viewed face-on, de Vaucouleurs & Freeman (1972) found a disk inclination of i = 27° ± 2° and a position angle of the line of nodes of ϕ = 170° ± 5° from the elliptical outer isophotes in red exposures. More recently van der Marel & Cioni (2001) have used asymptotic giant branch (AGB) stars from the Deep Near-Infrared Southern Sky Survey (DENIS) and Two Micron All Sky Survey (2MASS) to track the inclination of the disk between 25 and 6° from the LMC center, finding an inclination of i = 347 ± 62 and a position angle of the line of nodes ϕ = 1225 ± 83. Cepheids have also been used to trace the LMC disk and constrain its orientation. Most recently Nikolaev et al. (2004), using data from the MACHO project, found i = 307 ± 11 and ϕ = 1510 ± 24. Subramaniam (2003), using V and I data from the Optical Gravitational Lensing Experiment (OGLE) observations of the LMC bar produce a map of the I band apparent RC magnitude of the bar region; they did not infer i and ϕ because the map is restricted to the bar region.

Here, we investigate the LMC bar and inner disk within about 3° of the LMC center. This study is based on a new near-infrared catalog (Kato et al. 2007), which provides the necessary resolution and depth to probe the LMC luminosity function (LF) across the whole survey region. We find that the mean of the RC magnitude traces a complex structure about a best-fitting plane with orientation comparable to that found previously. We also find it vital to include the AGB bump in our model and identify several regions that appear to have no significant AGB bump populations.

The Infrared Survey Facility (IRSF) Magellanic Clouds Point-Source Catalog (MCPSC; Kato 2006; Kato et al. 2007) was constructed from a survey of 55 deg² in the LMC, Small Magellanic Cloud, and the Magellanic Bridge in the J(1.25 μm), H(1.63 μm), and K_s(2.14 μm) bands and was conducted at the South African Astronomical Observatory at Sutherland with the IRSF 1.4 m telescope and the Simultaneous Infrared Imager for Unbiased Surveys (SIRIUS) three-color camera. The catalog's JHK_s magnitudes are calibrated to the 2MASS system using those sources bright enough to be included in the 2MASS catalog; Kato et al. (2007) found good agreement between the calibrated IRSF and the 2MASS systems. Here, we utilize the ∼40 deg² covered in the LMC.

The survey has a pixel scale of 045, a seeing limited resolution of ∼12, and 10σ limiting magnitudes of 18.8, 17.8, and 16.6 mag in the J, H, and K_s bands, respectively. Due to crowding, the survey is shallowest in the LMC bar, where, based on artificial star tests, Kato et al. (2007) found 90% completeness limits of 17.8, 17.6, and 16.9 mag in J, H, and K_s, respectively.

The K_s-band magnitude limits are too shallow to reliably detect RC stars in the LMC; Alves et al. (2002) found a mean magnitude RC magnitude of K = 16.97 and Sarajedini et al. (2002) found K-band magnitudes of 16.90 and 17.03 for the LMC clusters Hodge 4 and NGC 1651, respectively. The deeper J- and H-band limits, on the other hand, are ⩾ 0.5 mag deeper than the observed RC peak. In the disk, the completeness limits are more than 1.5 mag deeper than the RC, and thus have no effect on the measured RC magnitude. In the bar, the decreasing completeness with magnitude may have the effect of enhancing the brightness of the RC. This is further compounded by population effects; the young bar will have an inherently brighter RC than the disk.

To estimate the possible contribution of crowding, we model its effect on the derived RC magnitude. If the crowding effects are negligible in the most crowded bar regions, they can safely be ignored throughout the survey region. To test this hypothesis, we assume that the probability of detection follows an error function, P(m) = 1/2(erf(22.578 − 1.23m) + 1), where the two constants are chosen to make 90% detection probability at the 90% completion limit H = 17.6, and the 99% detection probability occur at H = 17.0. This is a pessimistic estimate. We divide the luminosity function of the next section by the detection probability to produce a "corrected" luminosity function, and reperform the fit described below. We find that even with this conservative estimate, the RC magnitude shifts by less than 0.01 mag. We therefore conclude that completeness effects are negligible throughout the survey region.

From J and H, we can construct the reddening-free magnitude

$$\begin{eqnarray} &&H_{J-H} = H - \frac{A_H}{E(J-H)} [(J-H) - (J-H)_0]\hbox{.}\nonumber \end{eqnarray}$$

Several sources give conflicting values for the ratio of total to selective extinction, A_H/E(J − H). Table 1 lists three such determinations in the IRSF system as given by Nishiyama et al. (2006). We adopt the mean and standard deviation of these values to estimate the ratio of total to selective extinction and its uncertainty, 1.65 ± 0.16. From Salaris & Girardi (2002) and the accompanying data (see Section 4.1), we estimate (J − H)₀ = 0.47 ± 0.06. To estimate the overall reddening correction uncertainty, we set a conservatively large value of the selective extinction J − H − (J − H)₀ ≈ 0.05, corresponding to A_V ∼ 0.5 mag of reddening. Writing R for A_H/E(J − H), we arrive at

$$\begin{eqnarray} \sigma _{H_{J-H}}^2 &\approx & \sigma _R^2\left(\partial H_{J-H} \over \partial R\right)^2 + \sigma _{(J-H)_0}^2\left(\partial H_{J-H} \over \partial (J-H)_0\right)^2 \nonumber\\ &\approx & 2.5\times 10^{-3}\hbox{, or} \\ \sigma _{H_{J-H}} &\approx & 0.05. \nonumber \end{eqnarray} \tag{ 1 }$$

The MCPSC contains a mixture of sources from various stellar populations. Figure 1 shows the H versus (J − H) CMD of all LMC sources in the MCPSC down to H = 17.5. The catalog contains 4.6 × 10⁶ sources within the CMD's bounds. To the left of H = 0.25 and to the right of H = 1.0, lie several easily separated populations: the LMC OB stars at H ≈ 0, unresolved galaxies with J − H ≳ 1 and H ≳ 15, and the highly reddened AGB stars forming a horizontal feature with J − H ≳ 1 and H ≈ 12. The center of the CMD contains several populations, which are not so clearly separated. The densest region, at ((J − H), H) ∼ (0.5, 17), is the RC. The red giant branch (RGB) extends brightward and redward of the RC toward (0.75, 12.5), and the foreground of Galactic main-sequence stars extends toward (0.25, 11). Additional "finger-like" features are visible between the RGB and the Galactic foreground; see Kato et al. (2007) for further discussion of these populations. We select the region between the two dashed lines for further investigation; in addition to the RC it contains the RGB and Galactic foreground, which converge toward the RC's position.

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Figure 2 shows the H_{J − H} luminosity function for the 4.2 × 10⁶ sources lying within the selection region in Figure 1 and having 13 < H_{J − H} < 17.5. The error bars due to counting statistics would barely be perceptible if shown. The data are well fit by a simple model (dashed curve) made from summing three components (dotted curves). Between 13 and 15 mag, the background populations (LMC red giant branch, Galactic foreground, etc.) are well described by a single exponential, the straight dotted line in the figure. The AGB bump, which is not apparent in Figure 1, is well fit by a Gaussian component centered at 15.70 ± 0.01 and containing 4.2 × 10⁴ ± 4 × 10³ stars. The RC is represented by the Gaussian at 17.026 ± 0.002 and contains 1.4 × 10⁶ ± 2 × 10⁵ stars as revealed by the model fit. The uncertainty of the RC apparent magnitude is dominated by that of the reddening correction (Equation (1)); therefore, we use H_{J − H} = 17.03 ± 0.05 as our final apparent magnitude estimate.

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4.1. LMC Distance

From the apparent magnitude of the RC, we can calculate the LMC distance modulus,

$$\begin{eqnarray} &&\mu = H_{J-H} - M_H \hbox{,}\nonumber \end{eqnarray}$$

where M_H is the H-band absolute magnitude of the RC in the LMC. Girardi & Salaris (2001) and Salaris & Girardi (2002) find that the RC magnitude depends on both age and metallicity in a complicated way. Using the Padova isochrones and recent LMC star formation history determinations, they calculate the RC absolute magnitudes in the V, I, and K bands for the LMC population and list them as corrections (ΔM_V, etc.) to the solar neighborhood RC magnitudes found by Alves (2000) using Hipparcos parallaxes. Girardi & Salaris (2001) uses star formation rates (SFRs) from Holtzman et al. (1999) along with the age–metallicity relation (AMR) of Pagel & Tautvaisiene (1998) to derive several V- and I-band RC magnitudes for both the bar and outer regions. They find that the bar RC is less than 0.02 mag brighter than the disk RC in the I band. Similarly, Olsen & Salyk (2002) find that same procedure applied to the Smecker-Hane et al. (2002) SFHs gives an RC magnitude difference of less than 0.03 in I.

Referring to Figure 2 of Holtzman et al. (1999) we see that the SFR is more or less constant over the clouds history, except for a recent burst starting less than 1 Gyr ago. Furthermore, Girardi & Salaris (2001) state that a young cutoff to the SFR of at least 0.5 Gyr is appropriate because young, massive core helium burning stars, though they are few, skew the mean due to their extreme brightness.

Accordingly, and in order to obtain conservative bounds on the systematic population errors, we use a simple model with the Pagel & Tautvaisiene (1998) AMR and constant star formation starting either 10, 12, or 15 Gyr ago, and continuing until a cutoff of either 0.5 or 1 Gyr ago. From these six model SFRs, method 1 from Girardi & Salaris (2001), and the J and H-band version¹ of their Table 1, we have calculated means and standard deviations of RC magnitudes of M_H = −1.51 ± 0.03 and M_J = −1.04 ± 0.05 and M_H = −1.51 ± 0.03. This also gives our estimate (J − H)₀ = 0.47 ± 0.06. Finally, we arrive at a distance modulus of

$$\begin{equation*} \mu = (17.03\pm 0.05) - (-1.51\pm 0.03) = 18.54\pm 0.06,\nonumber \end{equation*}$$

corresponding to a distance of 51.1 ± 1.4 kpc, which is in excellent agreement with the review of Alves (2004), who gives μ = 18.50 ± 0.02. After calculating population corrections similar to Girardi & Salaris (2001), Salaris & Girardi (2002) found 18.53 ± 0.07 from the K-band data of Alves et al. (2002).

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Table 2 shows our result in the context of several other distance determinations.

Table 2. Distance Modulus Measurements

Reference	μ
Salaris & Girardi (2002)	18.53 ± 0.07
Alves et al. (2002)	18.493 ± 0.033rand ± 0.03sys
Alves (2004)	18.50 ± 0.02
Grocholski et al. (2007)	18.40 ± 0.04rand ± 0.08sys
This work	18.54 ± 0.06

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4.2. Spatial Variation of RC Distance

With such a large sample of RC stars, we can investigate the variation of the RC distance modulus across the survey region. We extract a subsample of stars in a region and fit the same model luminosity function we used above to obtain a local RC distance modulus. Instead of dividing the survey region into a grid having very few sources and high uncertainties in low-density regions, we chose to extract samples of a given size (20,000 sources) about centers arranged in a grid. Figure 3 makes this concept clear. The origin is the LMC location given by the NASA/IPAC Extragalactic Database (NED), (α, δ) = (05^h23^m345, −69°45^m22^s). The thin contours show the source density. The thick circles show a subset (121 out of 2601) of the sample extraction regions. Only every fifth region is shown along each axis for clarity. Clearly there is overlap between adjacent regions, with points in low-density regions having an effectively larger smoothing radius.

The luminosity functions show a large amount of variation. Figure 4 shows two extreme examples along with their model fits. The upper histogram appears to completely lack an AGB bump and has a broad and dim RC. The lower histogram has a prominent AGB bump and a sharp and bright RC. Note that both histograms contain 20,000 sources; the lower histogram was shifted down by a factor of 2 for clarity, but its error bars are the correct size for its unshifted position. Because our model LF includes the AGB bump magnitude and dispersion as free parameters, we do not expect its presence and variability to affect the RC magnitude determinations. The variation does, however, indicate that further investigation of population effects on the RC magnitude across the LMC may be fruitful avenues for future work, thought as noted above, these effects are of the order of several hundredths of a magnitude.

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From the local histogram we can infer a local RC magnitude and therefore a local distance modulus, μ_local = H_{J − H,local} + 1.51 ± 0.06, where the uncertainty remains the same as for the whole survey because the dereddening and absolute magnitude uncertainties dominate in all cases. Figure 5 shows the local RC distance map. Note that the horizontal and vertical scales give kpc in the plane of the sky. The heavy solid line indicates the LMC distance as derived above, 51.1 kpc. The thin solid lines indicate contours 0.5, 1.0, 1.5, and 2.0 kpc closer to the observer, and the dashed lines indicate 0.5, 1.0, 1.5, 2.0, and 2.5 kpc farther away. Both reddening uncertainty and population effects, which we expect to vary across the LMC, are of the order of hundredths of a magnitude. To illustrate, an error of 0.01 mag corresponds to an offset of 470 pc, or slightly less than one contour level.

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Generally, there is a clear trend in which the northeast corner is nearest to us and the southwest corner farthest away. There is a "depression" in the northwestern corner from (X, Y) = (3, 1) to (1, 3) in our coordinate system. In addition, the bar, stretching along a northwest–southeast line through the origin, appears to be floating above the disk by about 1 kpc, nearer to us. This corresponds to brightness enhancement of 0.04 mag, and thus could be caused strictly by population (a few hundredths of a magnitude) and crowding effects (one hundredth of a magnitude), acting in concert to brighten the bar's RC. As such, we cannot conclude to what extent the enhanced brightness is due to each of the geometric, population, and crowding effects. The structure within the bar is less susceptible to these effects. We also confirm that the bar itself shows warps and structure as found by Subramaniam (2003, 2004), and find height variations within the bar of amplitude ∼1 kpc as in Figure 2 of Subramaniam (2004). The nature of the warps does not agree, however; whereas Subramaniam (2004) shows a clear large-scale warp of amplitude ∼5 kpc, our map shows variations on a much smaller scale, and only deviating by ∼1.5 kpc.

By fitting a plane to the binned region data in Figure 5, we can estimate the inclination, i, and position angle of the line of nodes, ϕ, of the inner disk. A least-squares fit to the data yields i = 235 ± 04 and ϕ = 1546 ± 12. As noted above, the errors in relative distance are uncertain on the order of a hundredth of a magnitude. Accordingly, when the data points are assigned uncertainties of 0.5 kpc (0.01 mag as above) the resulting fit has χ² = 1.32. Table 3 shows this result compared to several from the literature. Figure 6 shows the local distance map in three dimensions with the best-fitting plane for context. Note that up is nearer to the observer (smaller distance). This figure emphasizes the depression in the northwest corner and the fact that the bar appears to float above the plane.

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Table 3. Plane Orientation Measurements

Reference	i	ϕ
de Vaucouleurs & Freeman (1972)	27° ± 2°	170° ± 5°
van der Marel & Cioni (2001)	347 ± 62	1215 ± 83
Olsen & Salyk (2002)	358 ± 14	145° ± 4°
Nikolaev et al. (2004)	307 ± 11	1510 ± 24
This work	235 ± 04	1546 ± 12

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4.3. Effect of Smoothing on Derived Distances

Olsen & Salyk (2002) find that fields in the southwest are systematically brighter than the best fitting plane of their data. We find a less striking trend, and in the opposite direction: a region of RCs dimmer than the best-fitting plane in the southwest.

First, we note that our southwesterly deviation is of a much smaller magnitude than that of Olsen & Salyk (2002). Second, the deviation is of a much smaller extent on the sky. Compare the size of the region around (1, −1) in Figure 6 with Figure 3 of Olsen & Salyk (2002).

Following Olsen & Salyk (2002) we note the presence of a dust lane crossing the southwestern extremity of our survey area. This presumably galactic dust will have different selective reddening properties than the reddening in other regions. We note that the deviation from the best-fitting plane is within our estimated reddening error. We conclude that the southwestern depression is not statistically significant. Our result contradicts the warp found by Olsen & Salyk (2002), but does not suggest a warp in the opposite direction.

We also note the locations of young populations in the LMC: the massive star formation regions, and the super giant shells (SGSs). 30 Dor, at (−1.20, 0.55) appears farther away, though this can be attributed to being next to the apparently floating bar. N11 at (2.57, 2.82) shows a departure from the best-fitting plane of about 1 kpc nearer to us. Table 4 reproduces the locations and sizes of the nine LMC SGSs given in Book et al. (2008) along with their coordinates in our figures. Of particular note is LMC 4, which coincides with the apparently nearby region around (−1.5, 3), although that feature's peak appears to lie outside the survey region. The southern extreme of LMC 1 may be associated with the ridge extending from (2.2, 3), which is the same feature noted around N11 above. The association of LMC 1, LMC 4, and N11 with local brightness enhancements probably indicates the level of uncertainty in the reddening correction, or possibly population effects due to small-scale variations in star formation history. The other SGSs do not coincide with significant deviations from the best-fitting plane.

From the IRSF MCPSC, we measured the apparent H-band magnitude of the LMC RC stars to be 17.03 ± 0.05 mag. Adopting a theoretical calibration of the H-band absolute magnitude of −1.51 ± 0.03, we obtain a distance modulus to the LMC of μ = 18.54 ± 0.06.

The catalog's large area coverage allowed us to measure the variation of the RC apparent magnitude across the bar and inner disk region and produce a distance map. The best-fitting plane of the inner LMC region has an inclination of i = 235 ± 04 and a line of nodes position angle 1546 ± 12. The inferred distance map shows considerable structure about the best-fitting plane.

Our main results, the LMC distance, inclination, and angle of the line of nodes, are consistent with previous results. In particular, our distance determination is in excellent agreement with previous results. This is not surprising because our calibration is based on the work of Girardi & Salaris (2001) and Salaris & Girardi (2002), and our result, although using a different procedure and much simplified star formation history, is nearly identical to theirs.

Our best-fitting plane generally agrees with previous values, but we note the possible influence of crowding and population effects in the bar, the SGSs LMC 1 and LMC 4, and the galactic dust present in the LMC field. Our results do not reflect the warp detected by Olsen & Salyk (2002). Above all, we reiterate their call for further studies of the star formation history of the southwestern LMC.