Nature and chemical abundances of a sample of Lyman-$\alpha$ emitter
  objects at high redshift
  We built a grid of photoionization models and compiled already available
observational emission line intensities ($\rm 1000 \: < \: \lambda(\AA) \: < \:
2000$) of confirmed star formation regions and Active Galactic Nucleus (AGNs)
in order to classify five Ly$\alpha$ emitter (LAE) objects at high redshift
$(5.7 \: < \: z \: < \:7.2)$. We selected objects for which at least one metal
emission-line was measured. The resulting sample is composed by the objects
RXCJ2248.7-4431-ID3, HSCJ233408+004403, COSY, A1703-zd6, and CR7 (clump C). The
photoionization models were built assuming a Power Law (associated with the
presence of an AGN), a Direct Collapse Black Hole (DCBH), and Population II
stars for the ionizing source. The resulting models were then compared with
observational emission-line ratios in six diagnostic diagrams to produce a
spectral classification of the sample. We found that CR7 (clump C),
HSCJ233408+004403 and COSY probably have a non thermal ionizing source (AGN or
DCBH) while the RXC J2248.7-4431-ID3 and A1703-zd6 seem to host a stellar
cluster. Detailed photoionization models were constructed to reproduce
observational emission line ratios of the sample of LAEs, and to derive
chemical abundances and number of ionizing photons $Q(\rm H)$ of these objects.
From these models, we found metallicities in the range $(Z/Z_{\odot})=0.1-0.5$
and $\log Q(\rm H) \: > \: 53$. Values for C/O abundance ratio derived for the
LAEs seem to be consistent with those derived for local star forming objects
with similar metallicities, while an overabundance of N/O was found for most of
the LAEs.
