Abundance analysis of red clump stars in the old, inner disc, open
  cluster NGC 4337: a twin of NGC 752?
  Open star clusters older than ~ 1 Gyr are rare in the inner Galactic disc.
Still, they are objects that hold crucial information for probing the chemical
evolution of these regions of the Milky Way. We aim at increasing the number of
old open clusters in the inner disc for which high-resolution metal abundances
are available. Here we report on NGC 4337, which was recently discovered to be
an old, inner disc open cluster. We present the very first high-resolution
spectroscopy of seven clump stars that are all cluster members. We performed a
detailed abundance analysis for them. We find that NGC 4337 is marginally more
metal-rich than the Sun, with [Fe/H]=+0.12$\pm$0.05. The abundance ratios of
$\alpha$-elements are generally solar. At odds with recent studies on
intermediate-age and old open clusters in the Galactic disc, Ba is
under-abundant in NGC 4337 compared with the Sun. Our analysis of the iron-peak
elements (Cr and Ni) does not reveal anything anomalous. Based on these
results, we estimate the cluster age to be 1.6$^{+0.1}_{-0.1}$ Gyr, and derive
a reddening E(B-V)=0.23$\pm$0.05, and an apparent distance modulus
$(m-M)_{V}=12.80\pm0.15$. Its distance to the Galactic centre is 7.6 kpc. With
this distance and metallicity, NGC 4337 fits the metallicity gradient for the
inner Galactic disc fairly well. The age and metallicity we measured make NGC
4337 a twin of the well-known old open cluster NGC 752. The red clumps of these
two clusters bear an amazing resemblance. But the main sequence of NGC 752 is
significantly more depleted in stars than that of NGC 4337. This would mean
that NGC 752 is in a much more advanced dynamical stage, being on the verge of
dissolving into the general Galactic field. Our results make NGC 4337 an
extremely interesting object for further studies of stellar evolution in the
critical turn-off mass range 1.1-1.4 solar masses.
