We present VLT near-IR spectroscopic observations of three X-ray sources characterized by extremely high X-ray–to–optical ratios ( X/O > 40 ) , extremely red colors ( 6.3 < R–K < 7.4 , i.e .
EROs ) and bright infrared magnitudes ( 17.6 < K < 18.3 ) .
These objects are very faint in the optical , making their spectroscopic identification extremely challenging .
Instead , our near-IR spectroscopic observations have been successful in identifying the redshift of two of them ( z=2.08 and z=1.35 ) , and tentatively even of the third one ( z=2.13 ) .
When combined with the X-ray properties , our results clearly indicate that all these objects host obscured QSOs ( 4 \times 10 ^ { 44 } < L _ { 2 - 10 keV } < 1.5 \times 10 ^ { 45 } ~ { } erg~ { } s ^ { -1 } , 2 \times 10 ^ { 22 } < N _ { H } < 4 \times 10 ^ { 23 } cm ^ { -2 } ) at high redshift .
The only object with unresolved morphology in the K band shows broad H \alpha emission , but not broad H \beta , implying a type 1.9 AGN classification .
The other two objects are resolved and dominated by the host galaxy light in the K band , and appear relatively quiescent : one of them has a LINER-like emission line spectrum and the other presents only a single , weak emission line which we tentatively identify with H \alpha .
The galaxy luminosities for the latter two objects are an order of magnitude brighter than typical local L _ { K } ^ { * } galaxies and the derived stellar masses are well in excess of 10 ^ { 11 } ~ { } M _ { \sun } .
For these objects we estimate black hole masses higher than 10 ^ { 9 } ~ { } M _ { \odot } and we infer that they are radiating at Eddington ratios L / L _ { Edd } \leq 0.1 .
We discuss the implications of these findings for the coevolution of galaxies and black hole growth .
Our results provide further support that X-ray sources with high X/O ratios and very red colors tend to host obscured QSO in very massive galaxies at high redshift .