Detectability of Cosmic Dark Flow in the Type Ia Supernova
  Redshift-Distance Relation
  We re-analyze the detectability of large scale dark flow (or local bulk flow)
with respect to the CMB background based upon the redshift-distance relation
for Type Ia supernovae (SN Ia). We made two independent analyses: one based
upon identifying the three Cartesian velocity components; and the other based
upon the cosine dependence of the deviation from Hubble flow on the sky. We
apply these analyses to the Union2.1 SN Ia data and to the SDSS-II supernova
survey. For both methods, results for low redshift, $z < 0.05$, are consistent
with previous searches. We find a local bulk flow of $v_{\rm bf} \sim 300$ km
s$^{-1}$ in the direction of $(l,b) \sim (270, 35)^{\circ}$. However, the
search for a dark flow at $z>0.05$ is inconclusive. Based upon simulated data
sets, we deduce that the difficulty in detecting a dark flow at high redshifts
arises mostly from the observational error in the distance modulus. Thus, even
if it exists, a dark flow is not detectable at large redshift with current SN
Ia data sets. We estimate that a detection would require both significant sky
coverage of SN Ia out to $z = 0.3$ and a reduction in the effective distance
modulus error from 0.2 mag to $\lesssim 0.02$ mag. We estimate that a greatly
expanded data sample of $\sim 10^4$ SN Ia might detect a dark flow as small as
300 km s$^{-1}$ out to $z = 0.3$ even with a distance modulus error of $0.2$
mag. This may be achievable in a next generation large survey like LSST.
