Context : The optical and ultraviolet emission lines of galaxies are widely used to distinguish star-forming galaxies ( SF ) from active galactic nuclei ( AGNs ) .
However , this type of diagnostic has some associated uncertainties , because AGNs can be of low luminosity and/or heavily obscured , and the optical emission lines may be dominated by a stellar component .
On the other hand , and despite its limitations , X-ray emission can be used as a reliable tracer of luminous AGNs .
Several well-studied examples exist where the optical diagnostics are indicative of SF galaxy , but the X-ray properties reveal the presence of an AGN .

Aims : We aim to characterize the nature of galaxies whose optical emission line diagnostics are consistent with star formation , but whose X-ray properties strongly point towards the presence of an AGN .
Understanding these sources is of particular importance in assessing the completeness of AGN samples derived from large galaxy surveys , selected solely on the basis of their optical spectral properties .

Methods : We construct a large sample of 211 narrow emission line galaxies ( NELGs ) ( which have full widths at half maximum ( FWHMs ) H _ { \beta } emission line < 1200 km/s ) from the SDSS-DR7 galaxy spectroscopic catalogue , for which we are able to construct a classical diagnostic diagram , [ OIII ] /H _ { \beta } versus [ NII ] /H _ { \alpha } ( hence z < 0.4 ) , and that are also detected in the 2 - 10 keV X-ray band and present in the 2XMM X-ray source catalogue .
This sample offers a large database by which to investigate potential mismatches between optical diagnostics and X-ray emission .

Results : Among these 211 objects , which based on our selection criteria all are all at z < 0.4 , we find that 145 galaxies are diagnosed as AGNs , having 2 - 10 keV X-ray luminosities that span a wide range , from 10 ^ { 40 } erg/s to above 10 ^ { 44 } erg/s .
Out of the remaining 66 galaxies , which are instead diagnosed as “ star-forming ” , we find a bimodal distribution in which 28 have X-ray luminosities in excess of 10 ^ { 42 } erg/s , large thickness parameters ( T = F _ { 2 - 10 keV } / F _ { [ OIII ] } > 1 ) and large X-ray to optical flux ratios ( X / O > 0.1 ) , while the rest are consistent with being simply starforming galaxies .
Those 28 galaxies exhibit the broadest H _ { \beta } line widths ( FWHMs from \sim 300 to 1200 km/s ) , and their X-ray spectrum is steeper than average and often displays a soft excess .

Conclusions : We therefore conclude that the population of X-ray luminous NELGs with optical lines consistent with those of a starforming galaxy ( which represent 19 % of our whole sample ) is largely dominated by narrow line Seyfert 1s ( NLS1s ) .
The occurrence of such sources in the overall optically selected sample is small ( < 2 \% ) , hence the contamination of optically selected galaxies by NLS1s is very small .