Distance, reddening and three dimensional structure of the SMC - I:
  Using RRab stars
  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 $\mu_{0}=18.909\pm0.148$ 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
$\theta_{\text{lon}}=38^{\circ}.027\pm0.577$.} These results are in agreement
with other recent independent previous studies using different tracers and
methodologies.
