Detailed analysis of the poorly studied northern open cluster NGC 1348
  using multi-color photometry and GAIA EDR3 astrometry
  The membership determination for open clusters in noisy environments of the
Milky Way is still an open problem. In this paper, our main aim is provide the
membership probability of stars using proper motions and parallax values of
stars using Gaia EDR3 astrometry. Apart from the Gaia astrometry, we have also
used other photometric data sets like UKIDSS, WISE, APASS and Pan-STARRS1 in
order to understand cluster properties from optical to mid-infrared regions. We
selected 438 likely members with membership probability higher than $50\%$ and
G$\le$20 mag. We obtained the mean value of proper motion as
$\mu_{x}=1.27\pm0.001$ and $\mu_{y}=-0.73\pm0.002$ mas yr$^{-1}$. The cluster's
radius is determined as 7.5 arcmin (5.67 pc) using radial density profile. Our
analysis suggests that NGC 1348 is located at a distance of $2.6\pm0.05$ kpc.
The mass function slope is found to be $1.30\pm0.18$ in the mass range
1.0$-$4.1 $M_\odot$, which is in fair agreement with Salpeter's value within
the 1$\sigma$ uncertainty. The present study validates that NGC 1348 is a
dynamically relaxed cluster. We computed the apex coordinates $(A, D)$ for NGC
1348 as $(A_\circ, D_\circ)$ = $(-23^{\textrm{o}}.815\pm 0^{\textrm{o}}.135$,
$-22^{\textrm{o}}.228\pm 0^{\textrm{o}}.105)$. In addition, calculations of the
velocity ellipsoid parameters (VEPs), matrix elements $\mu_{ij}$, direction
cosines ($l_j$, $m_j$, $n_j$) and the Galactic longitude of the vertex have
been also conducted in this analysis.
