  Here we report the localizations and properties of four short-duration GRBs
localized by the High Energy Transient Explorer 2 satellite (HETE-2): GRBs
010326B, 040802, 051211 and 060121, all of which were detected by the French
Gamma Telescope (Fregate) and localized with the Wide-field X-ray Monitor (WXM)
and/or Soft X-ray Camera (SXC) instruments. We discuss eight possible criteria
for determining whether these GRBs are "short population bursts" (SPBs) or
"long population bursts" (LPBs). These criteria are (1) duration, (2) pulse
widths, (3) spectral hardness, (4) spectral lag, (5) energy Egamma radiated in
gamma rays (or equivalently, the kinetic energy E_KE of the GRB jet), (6)
existence of a long, soft bump following the burst, (7) location of the burst
in the host galaxy, and (8) type of host galaxy. In particular, we have
developed a likelihood method for determining the probability that a burst is
an SPB or a LPB on the basis of its T90 duration alone. A striking feature of
the resulting probability distribution is that the T90 duration at which a
burst has an equal probability of being a SPB or a LPB is T90 = 5 s, not T90 =
2 s, as is often used. All four short-duration bursts discussed in detail in
this paper have T90 durations in the Fregate 30-400 keV energy band of 1.90,
2.31, 4.25, and 1.97 sec, respectively, yielding probabilities P(S|T90) = 0.97,
0.91, 0.60, and 0.95 that these bursts are SPBs on the basis of their T90
durations alone. All four bursts also have spectral lags consistent with zero.
These results provide strong evidence that all four GRBs are SPBs (abstract
continues).
