Investigating H$\alpha$, UV, and IR star-formation rate diagnostics for
  a large sample of z ~ 2 galaxies
  We use a sample of 262 spectroscopically confirmed star-forming galaxies at
redshifts $2.08\leq z\leq 2.51$ to compare H$\alpha$, UV, and IR
star-formation-rate diagnostics and to investigate the dust properties of the
galaxies. At these redshifts, the H$\alpha$ line shifts to the $K_{s}$-band. By
comparing $K_{s}$-band photometry to underlying stellar population model fits
to other UV, optical, and near-infrared data, we infer the H$\alpha$ flux for
each galaxy. We obtain the best agreement between H$\alpha$- and UV-based SFRs
if we assume that the ionized gas and stellar continuum are reddened by the
same value and that the Calzetti attenuation curve is applied to both. Aided
with MIPS 24$\mu$m data, we find that an attenuation curve steeper than the
Calzetti curve is needed to reproduce the observed IR/UV ratios of galaxies
younger than 100 Myr. Furthermore, using the bolometric star-formation rate
inferred from the UV and mid-IR data (SFR$_{IR}$+SFR$_{UV}$), we calculated the
conversion between the H$\alpha$ luminosity and SFR to be $(7.5\pm1.3) \times
10^{-42}$ for a Salpeter IMF, which is consistent with the Kennicutt (1998)
conversion. The derived conversion factor is independent of any assumption of
the dust correction and is robust to stellar population model uncertainties.
