We present the average metallicity and star-formation rate of Ly \alpha emitters ( LAEs ) measured from our large-area survey with three narrow-band ( NB ) filters covering the Ly \alpha , [ O ii ] \lambda 3727 , and H \alpha + [ N ii ] lines of LAEs at z = 2.2 .
We select 919 z = 2.2 LAEs from Subaru/Suprime-Cam NB data in conjunction with Magellan/IMACS spectroscopy .
Of these LAEs , 561 and 105 are observed with KPNO/NEWFIRM near-infrared NB filters whose central wavelengths are matched to redshifted [ O ii ] and H \alpha nebular lines , respectively .
By stacking the near-infrared images of the LAEs , we successfully obtain average nebular-line fluxes of LAEs , the majority of which are too faint to be identified individually by narrow-band imaging or deep spectroscopy .
The stacked object has an H \alpha luminosity of 1.7 \times 10 ^ { 42 } erg s ^ { -1 } corresponding to a star formation rate ( SFR ) of 14 M _ { \odot } yr ^ { -1 } .
We place , for the first time , a firm lower limit to the average metallicity of LAEs of Z \gtrsim 0.09 Z _ { \odot } ( 2 \sigma ) based on the [ O ii ] / ( H \alpha + [ N ii ] ) index together with photo-ionization models and empirical relations .
This lower limit of metallicity rules out the hypothesis that LAEs , so far observed at z \sim 2 , are extremely metal poor ( Z < 2 \times 10 ^ { -2 } Z _ { \odot } ) galaxies at the 4 \sigma level .
This limit is higher than a simple extrapolation of the observed mass-metallicity relation of z \sim 2 UV-selected galaxies toward lower masses ( 5 \times 10 ^ { 8 } M _ { \odot } ) , but roughly consistent with a recently proposed fundamental mass-metallicity relation when the LAEs ’ relatively low SFR is taken into account .
The H \alpha and Ly \alpha luminosities of our NB-selected LAEs indicate that the escape fraction of Ly \alpha photons is \sim 12 - 30 % , much higher than the values derived for other galaxy populations at z \sim 2 .