We present the results of a survey for Extremely Red Objects ( EROs ) undertaken in the fields of ten massive galaxy cluster lenses at z \sim 0.2 , combining sensitive , high-resolution Hubble Space Telescope imaging with deep , half-arcsecond K –band imaging from UKIRT .
We detect 60 EROs with ( R - K ) \geq 5.3 , of which 26 have ( R - K ) \geq 6.0 in a total image plane survey area of 49 arcmin ^ { 2 } down to K = 20.6 , including one multiply-imaged ERO .
We use detailed models of the cluster lenses to quantify the lens amplification and thus correct the observed number counts and survey area for the effects of gravitational lensing .
After making these corrections , we estimate surface densities at K \leq 21.6 of ( 2.5 \pm 0.4 ) and ( 1.2 \pm 0.3 ) arcmin ^ { -2 } for EROs with ( R - K ) \geq 5.3 and 6.0 respectively .
These ERO number counts agree with previous shallower surveys at K \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 19 and flatten significantly at magnitudes fainter than K \sim 19 –20 .
This flattening may be due to a transition from an ERO population dominated by evolved galaxies at z \sim 1 –2 ( K \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 19.5 ) to one dominated by dusty starburst galaxies at z > 1 ( K \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 19.5 ) .
We also compare our results with various model predictions , including a model that attempts to explain EROs in terms of a single population of elliptical galaxies formed at high redshift .
We find that a formation epoch of z _ { f } \sim 2.5 for this population matches the observed surface density of ( R - K ) \geq 5.3 EROs quite well , and the ( R - K ) \geq 6.0 sample less well .
More sophisticated models , including semi-analytic prescriptions , under-predict the ERO surface density by approximately an order of magnitude , suggesting that these models produce insufficient stars and/or dust at high redshift .
This deficit of EROs appears to be a general problem with models that reproduce the median redshift from K –selected redshift surveys .
One possible explanation is that the current K – selected redshift distribution may be incomplete beyond z \sim 1 .