Photometric redshifts and intrinsic alignments: Degeneracies and biases in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>×</mml:mo><mml:mn>2</mml:mn><mml:mi>pt</mml:mi></mml:math> analysis
Abstract
We present a systematic study of cosmological parameter bias in weak lensing and large-scale structure analyses for upcoming imaging surveys induced by the interplay of intrinsic alignments (IA) and photometric redshift (photo-z) model misspecification error. We first examine the degeneracies between the parameters of the tidal alignment–tidal torquing (TATT) model for IA and of a photo-z model including a mean shift (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi><a:mover accent="true"><a:mi>z</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>) and variance (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>σ</f:mi><f:mi>z</f:mi></f:msub></f:math>) for each tomographic bin of lenses and sources, under a variety of underlying true IA behaviors. We identify strong degeneracies between: (1) the redshift scaling of the tidal alignment amplitude and the mean shift and variances of source bins, (2) the redshift scaling of the tidal torquing amplitude and the variance of the lowest-<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>z</h:mi></h:math> source bin, and (3) the IA source density weighting and the mean shift and variance of several source bins. We then use this information to guide our exploration of the level of cosmological parameter bias which can be induced given incorrect modeling of IA, photo-z, or both. We find that marginalizing over all the parameters of TATT is generally sufficient to preclude cosmological parameter bias in the scenarios we consider. However, this does not necessarily mean that IA and photo-z parameters are themselves unbiased, nor does it mean that the best-fit model is a good fit to the data. We also find scenarios where the inferred parameters produce <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msubsup><j:mi>χ</j:mi><j:mrow><j:mi mathvariant="normal">d</j:mi><j:mo>.</j:mo><j:mi mathvariant="normal">o</j:mi><j:mo>.</j:mo><j:mi mathvariant="normal">f</j:mi><j:mo>.</j:mo></j:mrow><j:mn>2</j:mn></j:msubsup></j:math> values indicative of a good fit but cosmological parameter bias is significant, particularly when the IA source density weighting parameter is not marginalized over. Published by the American Physical Society 2024