tokens: locations of the clusters on the sky are used to correct the individual distances for the inclination of the disc, thereby obtaining a more accurate absolute distance for the LMC. By doing so, we obtain an estimate of the distance to the centre of the LMC that is more accurate by accounting for the geometry of the galaxy. This process is outlined in van der Marel Cioni ( 2001 ) and Grocholski et al. ( 2007 ), and also presented in the equations ( 2 ) through ( 5 ) below. The distance to the LMC centre is denoted by D 0 . D is the distance to any location on the disc plane; in our case, this is the distance to each cluster. We assume the LMC disc to be inclined to the plane of the sky by the angle i around an axis at the position angle θ. θ is measured anticlockwise from the west; to align with usual astronomical convention, Θ is defined the position angle from the north (Θ = θ – 90). These values are adopted from van der Marel Cioni ( 2001 ); we note that Grocholski et al. ( 2007 ) explored a variety of geometries from other past works, finding differences in the resulting distance of ≲0.2 kpc for varying i and Θ. The right ascension and declination are referred to, respectively, by α and δ in the equations below, To calculate the distance to the LMC centre (D 0 above), it is necessary to calculate ρ and sin (φ − θ). The former is calculated as in equation ( 3 ): Via a typical trigonometric expansion, sin (φ − θ) may be determined as sin (φ − θ) = sin (φ) cos (θ) – cos (φ) sin (θ). These components are detailed in equations ( 4 ) and ( 5 ): Through these equations, we determine an average, error-weighted distance modulus to the LMC centre of D 0 = 18.20 ± 0.06, equivalent to 46.42 ± 0.45 kpc. However, NGC 1841 is a clear outlier in these data, lying more than 3σ from the mean D 0 distance to the LMC centre, leading to several possibilities. One interpretation of these results suggests that NGC 1841 may not be a member of the LMC disc or may have been pulled out of the LMC disc (Grocholski et al. 2007 ). Another view is that an uncertain estimate of the reddening could be affecting the distance measurement; if the reddening of NGC 1841 is doubled from E ( B − V ) = 0.18, it is brought into agreement with the LMC mean distance. Regardless of the reason(s) for the discrepancy, we remove NGC 1841 as an anomaly and continue determining the distance to the LMC centre. Leaving out the extreme outlier of NGC 1841, the error-weighted mean is 18.41 ± 0.04 (48.29 ± 0.38 kpc). This is within the range of the result from Section 4.1 from the HB analysis, as seen in Fig. 9 , where the subdwarf distances and the subdwarf distances adjusted for the LMC geometry are compared to those derived from the HB analysis. The subdwarf distances tend to be shorter by 0.14 mag on average than those of the HB analysis; the adjusted subdwarf distances are also shorter than the HB distances by 0.12 (leaving NGC 1841 out). The offset appears to be consistent regardless of
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