Simple Halo Models for Small Weak Lensing Datasets

Notes in preparation for Summer 2015.

Update 7/6/2015

We are now able to plot convergence maps, shear maps, and foreground galaxy catalogs, as well as all three overlaid at once. Current work is to generate sufficient background sources that are uniformly distributed across the maps, each with an intrinsic shape and orientation. A short demo outlining the new features is given here. For more detailed demos, check out the \demos folder here.

Goals:

• Generate simulated weak lensing (galaxy ellipticity catalog) data given full density field ray-traced convergence and shear maps.
• Test the Pangloss halo model's ability to fit the (full density field ray-traced) weak lensing data in a 40x40arcmin Millennium Simulation (MS) field. If we know the halo positions, masses and redshifts, how well does this simple halo model (plus a simple void correction) fit the weak lensing data? We may need to test in multiple fields to increase our sensitivity.
• Report to the H0LICOW group on our prospects for analyzing the HE0435 weak lensing dataset, and predicting the external convergence at the lens position, with Pangloss.

Stretch goals:

• Produce a set of "posterior" (ie from LSST) sampled weak lensing + photometric catalogs for a 40x40 arcmin MS field. These will have to be separated into foreground and background galaxies for now. The foreground galaxies will need stellar masses and redshifts: these objects are already treated by the code, but we'll need to upgrade the catalog book-keeping.
• Write code to define a simple halo model, based on what is already there in Pangloss, that takes in hyper-parameters and generates halos attached to foreground galaxies.
• Compute the log probability of the catalogs given the halo model. This is what we will need in future for inferring the hyper-parameters.
• Compute posterior predictive distributions for convergence, assuming fixed hyper-parameters.
• Compare these with the PDF from the simple number counts procedure.

Tasks:

1) Weak Lensing Data Analysis Tools

• Select a Millennium Simulation analog lens galaxy, matched to HE0435 in lens redshift and velocity dispersion). Extract 40x40 arcmin shear and convergence maps, and galaxy catalog, centered on this Simulated HE0435 object.
• Write Pangloss code to generate mock ellipticity catalogs, given the SHE0435 convergence and shear maps. These will assume random background source positions, ns = 10 galaxies/square arcmin, and zs = 1.6 for all sources. This is all Millennium Simulation-specific, but ns and zs should be options. We'll need to upgrade Pangloss to work with a catalog class that we then sub-class for Millennium. (This is to make it easy for Matt to provide Dark Sky simulation data later.)
• Produce a mock weak lensing catalog, using the ray-traced shear and convergence maps, for SHE0435, using this new code.
• Extend the Pangloss Lightcone class with methods to predict the (reduced) shear at a given catalog of positions within its field, due to the halos in its field.
• Add a method to write out a mock ellipticity catalog given that set of halos (for functional testing).
• Code up (as ellipticity catalog class methods) and investigate various diagnostic summary statistics, to see how well the halo model can reproduce the ray-traced weak lensing maps. Tangential ellipticity averaged in annuli, ellipticity correlation functions will both be interesting.

The first three steps could be adapted to work with Matt's new mocks instead. Comparing Millennium with one or more different cosmology simulations is a long-standing goal of the H0LiCOW group.

2) Towards Hierarchical Inference with Weak Lensing Data

• Upgrade Pangloss to generate N mock MCMC sample catalogs of stellar mass and photo-z (as if from LSST level 2)
• Upgrade Pangloss to draw interim N halo mass sample catalogs to match the Mstar and zp catalogs
• Extend Pangloss to compute the log probability for the Mstar, zp and ellipticity catalog, given all the halo parameters. This log prob will depend on the current values of various hyper-parameters, so this task could be pretty involved)
• Compute log likelihood for each sample catalog, and use them to weight the Pangloss predictions of convergence at the lens analog position (at the centre of the field).
• Compare with the results of an N45 number counts analysis