Using deep narrow-band H _ { 2 } S 1 and K _ { s } -band imaging data obtained with CFHT/WIRCam , we identify a sample of 56 \Ha emission-line galaxies ( ELGs ) at z = 2.24 with the 5 \sigma depths of H _ { 2 } S 1 = 22.8 and K _ { s } = 24.8 ( AB ) over 383 arcmin ^ { 2 } area in the Extended Chandra Deep Field South .
A detailed analysis is carried out with existing multi-wavelength data in this field .
Three of the 56 \Ha ELGs are detected in Chandra 4 Ms X-ray observations and two of them are classified as active galactic nuclei .
The rest-frame UV and optical morphologies revealed by HST /ACS and WFC3 deep images show that nearly half of the \Ha ELGs are either merging systems or have a close companion , indicating that the merging/interacting processes play a key role in regulating star formation at cosmic epoch z = 2 - 3 ; About 14 % are too faint to be resolved in the rest-frame UV morphology due to high dust extinction .
We estimate dust extinction from spectral energy distributions .
We find that dust extinction is generally correlated with \Ha luminosity and stellar mass .
Our results suggest that \Ha ELGs are representative of star-forming galaxies .
Applying extinction corrections for individual objects , we examine the intrinsic \Ha luminosity function ( LF ) at z = 2.24 , obtaining a best-fit Schechter function characterized by a faint-end slope of \alpha = -1.3 .
This is shallower than the typical slope of \alpha = \sim - 1.6 in previous works based on constant extinction correction .
We demonstrate that this difference is mainly due to the different extinction corrections .
The proper extinction correction is thus the key to recovering the intrinsic LF as the extinction globally increases with \Ha luminosity .
Moreover , we find that our \Ha LF mirrors the stellar mass function of star-forming galaxies at the same cosmic epoch .
This finding indeed reflects the tight correlation between star formation rate and stellar mass for the star-forming galaxies , i.e. , the so-called main sequence .