Star-formation rates of two GRB host galaxies at z~2 and a [CII] deficit
  observed with ALMA
  Event rate of long Gamma-Ray Bursts (GRBs) is expected to be an useful tracer
of the cosmic star-formation history. For this purpose, it is necessary to
understand what kind of star formations/galaxies are traced by GRBs. Here we
report rest-frame far-infrared (FIR) continuum detections of GRB 070521 and
080207 host galaxies at $z\sim2$ with ALMA band 8 and 9. The FIR photometries
provide the reliable star-formation rates (SFRs), because FIR emission is free
from dust extinction and possible radio contamination from long-lived
afterglows of GRBs. The spectral energy distribution fittings indicate
49.85$^{+72.33}_{-2.86}$ and 123.4$^{+25.19}_{-21.78}$ $M_{\odot}$ yr$^{-1}$
for the 070521 and 080207 hosts, respectively. The derived SFRs place them on
the \lq \lq main sequence\rq \rq\ of normal star-forming galaxies at $z\sim2$.
The derived SFRs are significantly lower than that of radio observations. It is
inferred that the observed radio fluxes in a previous study are contaminated by
the afterglows. ALMA marginally detected [C~{\sc ii}]\,158\,$\mu$m emission
line from the GRB 080207 host galaxy with S/N $\sim$ 4. This is the first
detection of [C~{\sc ii}]\,158\,$\mu$m of a GRB host at $z>2$, and the second
detection among known GRBs. The luminosity ratio of [C~{\sc~ii}]\,158$\mu$m to
FIR is 7.5$\times 10^{-4}$, which is one of the smallest values among galaxies
at $z\sim 1-2$ with the same FIR luminosity. The \lq \lq [C~{\sc ii}]
deficit\rq \rq\ could be a new physical property to characterise GRB hosts at
$z\sim1-2$. Possible parameters controlling the deficit include the
metallicity, initial mass function, and gas density.
