A Malmquist-like bias in the inferred areas of diamond caustics and the resulting bias in inferred time delays for gravitationally lensed quasars

Kavli Affiliate: Paul L. Schechter

| First 5 Authors: Derek Baldwin, Paul L. Schechter, , ,

| Summary:

Quadruply lensed quasars are visible only when the source quasar lies within
the diamond caustic of the lensing galaxy. This condition creates a
Malmquist-like selection effect in the population of observed quadruply lensed
quasars, increasing the true caustic area. The inferred areas are therefore
biased low by an amount proportional to the square of the uncertainty in the
natural logarithm of the area, $sigma_{ln{A}}$. The inferred time delays,
$tau$, vary with the caustic area of the lensing galaxy as $sqrt{A}$. As a
consequence, model time delays are biased low, leading to underestimates of the
Hubble constant. Classical Malmquist bias also plays a role, with inferred
magnifications biased low. As magnification is strongly anti-correlated with
the area of the caustic, this classical Malmquist bias has an effect opposite
to, but smaller than, the effect of the area bias. The overall effect is
estimated to be small (median bias of less than 1%), but has the potential to
be larger. Current posterior plots do not include caustic area, which limits
the capability to accurately estimate the bias. With anticipated increases in
sample sizes (in particular with the completion of LSST), correction for these
biases becomes increasingly important.

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