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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