First Infrared-based implications for the dust attenuation and star
  formation of typical Ly$\alpha$ emitters
  By stacking publicly available deep Spitzer/MIPS 24 $\mu$m and Herschel/PACS
images for 213 $z \simeq 2.18$ Ly$\alpha$ Emitters (LAEs) in GOODS-South, we
obtain a strong upper limit to the IR luminosity of typical LAEs and discuss
their attenuation curve for the first time. The $3\sigma$ upper limit $L_{\rm
TIR}^{3\sigma}= 1.1 \times 10^{10} L_\odot$, determined from the MIPS data
providing the lowest limit, gives $IRX \equiv L_{\rm TIR}/L_{\rm UV} \leq 2.2$.
Here we assume that the local calibration between the 8 $\mu$m emission and the
dust SED shape and metallicity applies at high redshifts and that our LAEs have
low metallicities as suggested by previous studies. The inferred escape
fractions of Ly$\alpha$, $16$--$37%$, and UV continuum, $\ge 44%$, are higher
than the cosmic averages at the same epoch. The SMC attenuation curve is
consistent with the IRX and the UV slope $\beta = -1.4^{+0.2}_{-0.2}$ of our
stacked LAE, while the Meurer's relation (Calzetti curve) predicts a 3.8 times
higher IRX; we also discuss the validity of PACS-based $L_{\rm TIR}^{3\sigma}$
allowing the Meurer's relation. SED fitting using the Calzetti curve also gives
a $\sim 10$ times higher SFR than from the $L_{\rm TIR}^{3\sigma}$ and $L_{\rm
UV}$. With $M_{\star}=6.3^{+0.8}_{-2.0} \times10^8 \mathrm{M_{\odot}}$, our
LAEs lie on a lower-mass extrapolation of the star formation main sequence at
$z \sim 2$, suggesting that the majority of $z \sim 2$ LAEs are mildly star
forming with relatively old ages of $\sim 200$ Myr. The faint $L_{\rm
TIR}^{3\sigma}$ implies that LAEs contribute little to the faint ($\gtrsim 100
\mu$Jy) submm number counts by ALMA.
