The Possible Impact of GRB Detector Thresholds on Cosmological Standard
  Candles
  GRB satellites are relatively inefficient detectors of dim hard bursts
because they trigger on photon counts, which are number-biased against hard
photons. Therefore, for example, given two bursts of identical peak luminosity
near the detection threshold, a dim soft burst will be preferentially detected
over a dim hard burst. This detector bias can create or skew an apparent
correlation where increasingly hard GRBs appear increasingly bright. Although
such correlations may be obfuscated by a middle step where GRBs need to be
bright enough to have their actual redshifts determined, it is found that the
bias is generally pervasive. This result is derived here through simulations
convolving a wide variety of possible GRB brightnesses and spectra with the
BATSE Large Area Detectors (LAD) detection thresholds. The presented analyses
indicate that the rest-frame $\nu F_{\nu}$ spectrum peak energy of
long-duration GRBs, $\epi$, is not a good cosmological standard candle without
significant corrections for selection effects. Therefore, the appearance of
$\epi$ in seeming correlations such as the Amati ($E_{iso}-\epi$), Ghirlanda
($E_{\gamma}-\epi$), and $L_{iso}-\epi$ relations is statistically real but
strongly influenced by so far uncalibrated GRB detector thresholds.
