1. Light-cone data format and ray-tracing tools
Euclid CSWG Task 2
Light-cone data format and ray-tracing tools
Coordinators: S. Colombi & S. Hilbert
K. Benabed, IAP

2. CSWG Tasks Task 1: Large N-body runs and coordinated access to
supercomputing facilities
Task 3: Halo, sub-halo and smooth background decomposition,
mass function, merger tree
Task 4: Indexing and database of simulation products, data types
Task 5: Covariance estimation of various observables
Task 6: Tools for non-standard models
Task 7: Beyond 1% accuracy in dark matter statistics
Task 8: The impact of baryons on cosmic statistical indicators
Task 9: Generation of galaxy catalogs
Task 10: Simulation output comparison/validation
Task 2: Light-cone data format and ray-tracing tools

3. Task 2 Goals
Light-cones: to define a common data format for light-cone N-body data, with possible extension beyond pure particle data type such as dark matter halos or mock galaxies.
Weak lensing: to set up the suite of tools that will be used to perform ray-tracing simulations of weak lensing, using various approximations and input data, with increasing level of complexity and realism.

4. Light-cone techniques I: from snapshots of a single “small” simulation
(< ~ 1Gpc)
From Blaizot et al. 2005
Using the same simulation induces some replica effects
Random translations and rotations allow one to reduce these effects. Potential issues: discontinuities
If the light-cone is small, it is possible to give to it the right direction to avoid replica
These methods are often used e.g. for generating galaxy catalog from semi-analytic methods which require high mass resolution N-body simulations, e.g. moderate box size.

5. Light-cone techniques II: The tiling technique of White & Hu (2000) from a set of “small” simulations (<~ 1 Gpc)
One performs a set of simulations of decreasing size when approaching the observer:
Photon plane
This handy method, valid for small enough light-cones (small angle approximation and flat sky) is particularly appreciated by weak lensing simulators, due to the approximate conservation of angular resolution and the simplicity of the approach (usage of periodicity in the transverse direction to derive easily the lensing potential).
Issues : discontinuity effects

6. Light-cone techniques III: runtime output and full sky
huge runs (>~ 1Gpc)
Runtime Light-cone:
Note that for best accuracy, it is best to generate the light-cone data during runtime at coarse time-steps sufficiently small to avoid discontinuity effects such as e.g. halo replica problems.
Spherical photon surface:
For large simulations (> 1Gpc) it becomes interesting to produce a large angular coverage with a photon surface being spherical or part of a sphere.
Teyssier et al. 2009; Fosalba et al. 2008

7. Light-cone outputs I: compression techniques
How to reduce the huge size of the light-cones during runtime?
Random dilution of dark matter particles
Extraction of dense structures such as halos and their sub-halos
The onion approach: projected quantities on spherical shells: e.g. the projected mass density and the 3D force on (adaptive resolution) Healpix spheres: best for weak lensing?
The onions from a MICE simulation (Fosalba et al. 2008)

8. Light-cone outputs II: what do we need?
What do we need in the light-cones?
For dark matter (macro)-particles, the mass, the position, the velocity and the 3D gravity field (gravitational potential/force).
For the onions/sampled planes, the projected density and the 3D/transverse gravity field
What kind of light-cones do we need?
High resolution light-cones with small angular coverage, no compression: e.g. to understand the effects of the baryons on the small scale clustering. Flat sky approximation/tiling methods probably most handy.
Lower resolution light-cones with large angular coverage extracted from huge simulations, with compression if needed: e.g. to be able to produce large mock surveys for cosmic covariance estimates.

9. Weak lensing techniques available in CSWG I: standard methods
(list not yet exhaustive)
From Hilbert et al. 2009
Backwards algorithms based on standard multiple lenses approximation using the gravity field of the projected mass distribution on successive slices (either flat or spherical): can be used in any of the light-cone methods described previously
Traditional flat sky approximation implementation on small light-cones with backwards ray-tracing calculating ray deflections: Hilbert et al. (2009)
Onion approach: ray-tracing performed backwards on successive HEALPix spheres
- MICE: Fosalba et al. (2008) current implementation: Born approximation
- Teyssier et al. 2009: similar as MICE but with actual deflection of rays calculated backwards in time

10. Weak lensing techniques available in CSWG II: alternative methods
- RATANA: Li et al. (2001)
On a 3D grid: calculations are performed along each line of sight using an analytic method after calculating intersections with the computational grid. The method can be run on the fly within the Born approximation or as a post-treatment for more accurate backwards ray-tracing with actual deflections calculated.
Advantage/disadvantage : requires a sampling on a grid. Good for RAMSES, bad for GADGET.
SUNGLASS: Kiessling et al. (2011)
On the particle distribution: ray-tracing method working on lines of sight but on particles instead of a grid, which allows one to avoid radial binning. The current implementation uses flat sky approximation and the tiling method of White & Hu.
Disadvantage: this method is applicable only within the Born approximation (straight light rays).
Question: Is the Born approximation good enough at least for some applications?

11. A non exhaustive list of current available very large simulations
The MICE simulations (Fosalba et al. 2008) with full-sky lensing maps in the lightcone
The Horizon 4PI simulation and its full sky light-cone up to z=1 and a 400 square degrees light-cone up to z=10 (Teyssier et al. 2009)
The Millennium XXL simulation (Angulo et al. 2012)
The DEUS simulations including the Guinness book one , with full sky light-cones

12. Example: the two largest simulations from DEUS consortium
Box Size
Force Resolution
Mass
Resolution
Number of Particles
Initial Redshift
Cosmological Models
Calculateur
(Nb of Proc)
10368 h-1 Mpc
40 h-1 kpc
~ h-1 M⦿
40963
~100
ΛCDM
Curie (9728)
20736 h-1 Mpc
81923
100
Curie (38016/76032)
Currently the largest DM simulation ever performed!
Both simulations have a full sky light-cone (position, velocity and force for each DM particle) up to z=3.5 for the one and to z=30 for the one and 30 snapshot saved up to z=50.

13. Working plan Adopt a format for pure particle lightcone outputs.
Adopt a format for onion outputs if thought useful: HEALPix?
Compare various weak lensing algorithms. Adopt one “official” method? Is the Born approximation sufficient at least for some applications?
Coordinate with others CSWG tasks for setting a common set of N-body simulations in order to have coherent mock data.
Prepare a set of preliminary light-cone data/weak lensing maps available and useful to other members of the Euclid community.