A new non-parametric method to infer galaxy cluster masses from weak lensing

We introduce a new, non-parametric method to infer deprojected 3D mass profiles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of galaxy clusters from weak gravitational lensing observations. The method assumes spherical symmetry and a moderately small convergence, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>κ</mml:mi> <mml:mo>≲</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . The assumption of spherical symmetry is an important restriction, which is, however, quite common in practice, for example in methods that fit lensing data to an NFW profile. Moreover, with a mild assumption on the probability distributions of the source redshifts, our method relies on spherical symmetry only at radii larger than the radius <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>r</mml:mi> </mml:math> at which the mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>M</mml:mi> </mml:math> is inferred. That is, the method may be useful even for clusters with a non-symmetric inner region, since it correctly estimates the enclosed mass beyond the radius where spherical symmetry is restored. We discuss how to correct, statistically and approximately, for miscentering given that the probability distribution of miscentering offsets is known. We provide an efficient implementation in Julia code that runs in a few milliseconds per galaxy cluster. We explicitly demonstrate the method by using data from KiDS DR4 to infer mass profiles for two example clusters, Abell 1835 and Abell 2744, finding results consistent with existing literature.