  I investigate the origin of the observed correlation between a GRB's nuFnu
spectral peak Epk and its isotropic equivalent energy Eiso through the use of a
population synthesis code to model the prompt gamma-ray emission from GRBs. By
using prescriptions for the distribution of prompt spectral parameters as well
as the population's luminosity function and co-moving rate density, I generate
a simulated population of GRBs and examine how bursts of varying spectral
properties and redshift would appear to a gamma-ray detector here on Earth. I
find that a strong observed correlation can be produced between the source
frame Epk and Eiso for the detected population despite the existence of only a
weak and broad correlation in the original simulated population. The energy
dependance of a gamma-ray detector's flux-limited detection threshold acts to
produce a correlation between the source frame Epk and Eiso for low luminosity
GRBs, producing the left boundary of the observed correlation. Conversely, very
luminous GRBs are found at higher redshifts than their low luminosity
counterparts due to the standard Malquest bias, causing bursts in the low Epk,
high Eiso regime to go undetected because their Epk values would be redshifted
to energies at which most gamma-ray detectors become less sensitive. I argue
that it is this previously unexamined effect which produces the right boundary
of the observed correlation. Therefore, the origin of the observed correlation
is a complex combination of the instrument's detection threshold, the intrinsic
cutoff in the GRB luminosity function, and the broad range of redshifts over
which GRBs are detected. These simulations serve to demonstrate how selection
effects caused by a combination of instrumental sensitivity and the
cosmological nature of an astrophysical population can act to produce an
artificially strong correlation between observed properties.
