O(NlogN) Curved-sky Weak Lensing Simulations · 2011-12-15 · Weak Lensing Simulations •...
Transcript of O(NlogN) Curved-sky Weak Lensing Simulations · 2011-12-15 · Weak Lensing Simulations •...
O(NlogN) Curved-sky Weak Lensing Simulations
Matthew R. Becker and Andrey V. KravtsovUniversity of Chicago
1Monday, June 14, 2010
Why should you care about weak lensing (and simulating it)?Weak lensing measurements are an essential component of all current and upcoming large-area optical imaging surveys (e.g. DES, LSST, JDEM, etc.) aimed (at least partially) at understanding dark energy.
Specifically, weak lensing will be used for both cosmic shear measurements and to measure the masses of galaxies and clusters of galaxies.
Unfortunately, there are a number of systematic effects associated with the interpretation of weak lensing signals.
Large-area simulations of weak lensing applied to mock galaxy catalogs and based on N-body structure formation models are needed to address these issues.
2Monday, June 14, 2010
Multiple-plane Ray Tracing
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No.1,
2002
CLUSTERS
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13
observer &
lensed galaxy
sourcegalaxy
image from Evrard et al. 2002
Pseudocode for a multiple-plane ray tracing algorithm:
initialize ray locations at the observerFOR i=1,# of lens planes DO
compute 2D mass density of the lens planesolve 2D Poisson equation for the lensing potential compute ray deflections and lensing Jacobian at ray positions from the lensing potentialusing ray deflections and the lensing Jacobian advance rays to next lens plane
ENDFOR
light cone from N-body simulation is divided into a set of nested shells to form lens planes
rays are traced from observer to source
3Monday, June 14, 2010
Computational Challenges in Weak Lensing Simulations
• requirements for weak lensing simulations (in order to make mock galaxy catalogs):
1) self-consistently handle large, contiguous areas of sky (e.g. DES, LSST, JDEM, etc. will cover ≥5000 deg2)
2) resolve both the relevant physical (~50 kpc/h) and angular (5-10 arcsecond) scales
3) produce proper redshift dependence of shear and magnification bias effects
• current algorithms either scale nicely with resolution (e.g. O(NlogN) as opposed to O(N3/2)) or handle a curved-sky, but cannot do both
• distributed or shared memory computers are a must - a full-sky map of the shear, convergence, and lensed positions at 12.9 arcsecond resolution in single precision takes up 60 GB of RAM
4Monday, June 14, 2010
The Essential Idea We want to divide the sphere into a union of patches which can be ray traced in parallel using the flat-sky approximation.
Why?
• flat-sky patches can be divided evenly between all of the processors
• thus the code can handle as many rays and N-body particles as you have RAM/processors for
• as I will show later, this scheme can reduce algorithmic complexity of the Poisson solver to approximately O(NlogN) from O(N3/2)
Potential problem:
How do you maintain continuity in the lensing quantities between the flat-sky patches and also resolve larger-scale modes in the shear power spectrum?
Order 4 HEALPix Map w/ Patches
5Monday, June 14, 2010
A Hybrid SHT+FFT Poisson Solver
Key Idea:Solution from SHT (via HEALPix) encodes the large-scale modes in the lensing potential, enforces the boundary conditions over the sphere, and enforces continuity across the flat-sky patches. The FFTs on the flat-sky patch resolve the small scale modes.
Other advantages:• SHT is expensive O(N3/2) and here
we only have to do 1 analysis + 1 synthesis operation as opposed to 1 analysis + 5 synthesis operations
• very easy to parallelize on distributed memory systems
• can use any adaptive finite-volume Poisson solver - I have chosen a set of nested FFTs which is approximately O(NlogN).
flat-sky potentialflat-sky density
HEALPix density HEALPix potential
BCs from SHT
Point Mass Test of the Poisson Solver
6Monday, June 14, 2010
Code Validation: A Point Mass
fractional error ≤ 0.2%
angle [arcsec]
fractional error
fractional error
deflection angle
tangential shear
discontinuities across patches exist but are
small
7Monday, June 14, 2010
Code Scaling with Resolution (extrapolated to a full-sky)
8Monday, June 14, 2010
Summary and Applications• Summary:
• this new algorithm enables accurate, efficient, high-resolution, full-sky lensing calculations on moderate sized machines (~100 processors/cores)
• very portable - written in C with MPI and standard libraries like HDF5, GSL, and FFTW
• Some example applications:
• code will first be used for the DES Blind Cosmology Challenge - will test if the DES can recover input cosmology from realistic mock galaxy catalogs
• optical sky survey simulations with realistic weak lensing information - cosmic shear, galaxy-galaxy lensing, cluster lensing, etc.
• also could be used for high-resolution CMB lensing calculations
9Monday, June 14, 2010