[Paper Review] Distance, reddening and three dimensional structure of the SMC - I: Using RRab stars

Sukanta Deb|arXiv (Cornell University)|Jul 11, 2017

Stellar, planetary, and galactic studies3 references3 citations

TL;DR

This study uses simultaneous V and I-band photometry of 3,522 RRab stars from the OGLE-IV survey to simultaneously determine the true distance modulus and reddening to the Small Magellanic Cloud (SMC), yielding a mean distance modulus of μ₀ = 18.909 ± 0.148 mag and E(B−V) = 0.066 ± 0.036 mag. It further models the 3D structure of the SMC as an ellipsoid, deriving axes ratios of 1.000 ± 0.001, 1.113 ± 0.002, and 2.986 ± 0.023, consistent with recent independent studies.

ABSTRACT

We present a study of simultaneous determination of mean distance and reddening to the Small Magellanic Cloud (SMC) using the two photometric band RR Lyrae data. Currently available largest number of highly accurate and precise light curve data of the fundamental mode RR Lyrae stars (RRab) with better areal coverage released by the Optical Gravitational Lensing Experiment (OGLE)-IV project observed in the two photometric bands $(V,I)$ were utilised simultaneously in order to determine true distance and reddening independently for each of the individual RRab stars. Different empirical and theoretical calibrations leading to the determination of absolute magnitudes of RRab stars in the two bands, $V$ and $I$ along with their mean magnitudes were utilised to calculate the apparent distance moduli of each of these RRab stars in these two bands. Decomposing the apparent distance moduli into true distance modulus and reddening in each of these two bands, individual RRab distance and reddening were estimated solving the two apparent distance moduli equations. Modeling the observed distributions of the true distance moduli and reddenings of the SMC RRab stars as Gaussian, the true mean distance modulus and mean reddening value to the SMC were found to be {\bf $μ_{0}=18.909\pm0.148$ mag and $E(B-V)=0.066\pm0.036$ mag, respectively. This corresponds to a distance of $D = 60.506\pm 4.126$~kpc to the SMC. The three dimensional distribution of the SMC RRab stars was approximated as ellipsoid. Then using the principal axes transformation method \citep{deb14} we find the axes ratios of the SMC: $1.000\pm0.001,1.113\pm 0.002, 2.986\pm0.023$ with $i=3^{\circ}.156\pm0^{\circ}.188$ and $θ_{ ext{lon}}=38^{\circ}.027\pm0.577$.} These results are in agreement with other recent independent previous studies using different tracers and methodologies.

Motivation & Objective

• To simultaneously determine the true distance modulus and reddening to the Small Magellanic Cloud (SMC) using multi-band photometry of RRab stars.
• To model the three-dimensional spatial distribution of SMC RRab stars as an ellipsoid to infer the galaxy's intrinsic shape and orientation.
• To validate empirical period-colour relations for RRab stars using a large, high-precision dataset from OGLE-IV.
• To produce a high-resolution reddening map of the SMC based on individual RRab star reddening estimates.

Proposed method

• Simultaneous analysis of V and I-band light curves from 3,522 RRab stars in the OGLE-IV database to derive apparent distance moduli in both bands.
• Decomposition of apparent distance moduli into true distance modulus and reddening using empirical and theoretical calibrations of RRab absolute magnitudes.
• Modeling the distribution of true distance moduli and reddenings as Gaussian to estimate the mean distance and mean reddening to the SMC.
• Applying the principal axes transformation method (Deb & Singh, 2014) to the 3D spatial distribution of RRab stars to determine the ellipsoidal axes ratios and orientation angles.
• Constructing a 10×10 grid reddening map by averaging individual reddening values to visualize spatial variations in extinction across the SMC.
• Deriving a period-colour relation (V−I)₀ = (1.255 ± 0.003)logP + (0.787 ± 0.001) using intrinsic colours from E(V−I) corrections.

Experimental results

Research questions

• RQ1 What is the simultaneous, self-consistent determination of distance and reddening to the SMC using RRab stars in two photometric bands?
• RQ2 How does the three-dimensional spatial distribution of RRab stars in the SMC deviate from spherical symmetry, and what are the axes ratios of its ellipsoidal structure?
• RQ3 What is the spatial variation of reddening across the SMC, and does it correlate with observed stellar density or morphology?
• RQ4 How robust is the period-colour relation for RRab stars derived from a large, high-precision OGLE-IV dataset?
• RQ5 How do the derived structural parameters of the SMC compare with those from other tracers and methodologies?

Key findings

• The mean true distance modulus to the SMC is μ₀ = 18.909 ± 0.148 mag, corresponding to a distance of D = 60.506 ± 4.126 kpc.
• The mean reddening to the SMC is E(B−V) = 0.066 ± 0.036 mag, with a corresponding E(V−I) = 0.088 ± 0.049 mag.
• The three-dimensional structure of the SMC RRab stars is best described as an ellipsoid with axes ratios of 1.000 ± 0.001, 1.113 ± 0.002, and 2.986 ± 0.023.
• The inclination angle i = 3.156° ± 0.188° and longitude of the line of nodes θ_lon = 38.027° ± 0.577° indicate a nearly face-on, elongated structure.
• A period-colour relation was derived: (V−I)₀ = (1.255 ± 0.003)logP + (0.787 ± 0.001), with a residual standard error of 0.108 per degree of freedom.
• The derived period-colour relation was validated on 27,138 LMC RRab stars, yielding a mean reddening of E(V−I) = 0.096 ± 0.067 mag, consistent with independent measurements.