Simulating Maps of the Rees-Sciama
Effect and the Lens Deformations of
the Cosmic Microwave Background
JENAM, Granada, September-04
Diego Sáez
diego.saez@uv.es
L. Antón, P. Cerdá-Durán, J.V. Arnau, and M. Fullana
Departamento de Astronomı́a y Astrofı́sica, Universidad de Valencia
46100 Burjassot, Valencia, Spain.
JENAM, Granada, September-04– p.1/14
ABSTRACT
Small maps of both the Rees-Sciama effect and the lens effect produced by strongly
nonlinear cosmological structures are built up. Appropriate techniques based on ray-tracing
through N-body simulations are used. A certain statistical analysis of the simulated maps is
designed with the essential aim of looking for deviations from Gaussianity.
BASIC IDEAS:
RAY-TRACING THROUGH N-BODY SIMULATIONS
DEVIATIONS FROM GAUSSIANITY DUE TO GRAVITY (LENS AND REES-SCIAMA
EFFECTS)
PREVIOUS PAPERS:
1.- CMB anisotropy: deviations from Gaussianity caused by nonlinear gravity, A.M. Aliaga, V.
Quilis, J.V. Arnau, and D. Sáez, MNRAS, 330, 2002, 625.
2.- Non Gaussian signatures in the lens deformations of the CMB sky: A new ray-tracing
procedure, P. Cerdá-Durán, V. Quilis, and D. Sáez, Phys. Rev. 69D, 2004, 043002
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PROBLEMS WITH RAY-TRACING
There are preferable directions (angle
, distance
Space and time periodicity effects
)
Only small enough spatial scales are well simulated
2D SKETCH OF A PERIODIC UNIVERSE
(1) circles and lines represent clusters
Φ
and photon trajectories, respectively
(2) trajectories parallel to edges are not
L
(3) for large enough
(or
appropriate (accumulative effect)
) values
photons cross different boxes through
O
statistically independent regions
(too large spatial scales must be eliminated)
Directions around the preferred one –used to cover a certain map– should not spread too
much in the periodic universe to avoid space-periodicity effects
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RAY-TRACING METHODS
MAIN FEATURES OF THE PROPOSED METHOD :
Only one N-body simulation
No discontinuities at crossing points
Preferred direction
Appropriate cutoff in the spatial scales
THE STANDARD RAY-TRACING METHOD :
Only one N-body simulation
Multiple plane projections
Roto-traslations
Discontinuities at crossing points
THE TILING RAY-TRACING METHOD (White & Hu, 2001:
A different N-body simulation in each box
Large computational cost
No continuity at crossing points
JENAM, Granada, September-04– p.4/14
Box size: ————————————
travelled distance : ————————
or
Separation between crossed regions in neighbouring boxes: ————-
Number of boxes : ————————-
Number of particles : ——————— either
or
Cell size : ———————————— either
Map size : ———————————–
,
Preferred direction: ———————–
Initial redshift: ——————————
CHOOSING FREE PARAMETERS AND N-BODY CODE
!
maximum spatial scale in the peculiar gravitational potential (not in the N-body
simulation)——-
PM N-body code designed by V. Quilis and D. Sáez (ver V. Quilis, J.M. Ibáñez, and D. Sáez,
ApJ, 502, 518 (1998) and references cited therein)
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REES-SCIAMA SIMULATION—1
map
(5) minimum temperature contrast
(4) maximum temperature contrast
(3)
(2) maximum spatial scale
(1) spatial resolution
REES-SCIAMA SIMULATION-1
JENAM, Granada, September-04– p.6/14
REES-SCIAMA SIMULATION—2
map
(5) minimum temperature contrast
(4) maximum temperature contrast
(3)
(2) maximum spatial scale
(1) spatial resolution
REES-SCIAMA SIMULATION-2
JENAM, Granada, September-04– p.7/14
LENS SIMULATION—1
(5) minimum temperature contrast
(4) maximum temperature contrast
map
(3)
(2) maximum spatial scale
(1) spatial resolution
LENS SIMULATION-1
JENAM, Granada, September-04– p.8/14
LENS SIMULATION—1: SPECTRUM
Left panel: Angular Power Spectrum (APS)
Right panel: Ratio between the APS of the lens
deformations and the APS of the dominant unlensed CMB
anisotropy
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LENS SIMULATION—2
(5) minimum temperature contrast
(4) maximum temperature contrast
map
(3)
(2) maximum spatial scale
(1) spatial resolution
LENS SIMULATION-2
JENAM, Granada, September-04– p.10/14
LENS SIMULATION—2: SPECTRUM
Left panel: Angular Power Spectrum (APS)
Right panel: Ratio between the APS of the lens
deformations and the APS of the dominant unlensed CMB
anisotropy
JENAM, Granada, September-04– p.11/14
Solid line: averaged APS from 20 simulations with
cells and
particles
Dotted line: averaged APS from 20 simulations with
cells and
particles
LENS SIMULATIONS: AVERAGED SPECTRUM
JENAM, Granada, September-04– p.12/14
LOOKING FOR DEVIATIONS FROM GAUSSIANITY
α
-direction correlation functions of the form
are
), where
. The chosen sets of
calculated from our maps (for
directions draw –on the Last Scattering Surface– the figures displayed above
!
In GAUSSIAN statistics,
functions vanish for odd m values, whereas in the even
.
case, all these functions can be written in terms of function
For GAUSSIAN statistics and sets of directions with the above relative positions one
, which implies
obtains the relation:
. The relation correponding to
is more complicated and it is
, it leads to
.
not written. For
or violations of
Non-Gaussianity implies either non vanishing correlations for odd
.
the above relations between the even correlations and
the lens effect has vanishing odd correlations (ver F. Bernardeau, AA, 324, 15, 1997).
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CONCLUSIONS AND PERSPECTIVES
CONCLUSIONS:
A ray-tracing procedure based on a preferred direction and an appropriate cutoff has
been designed. It has been used to get maps of the Rees-Sciama and lens effects.
The APS of the lens effect has been estimated for
PERSPECTIVES:
Deviations from Gaussianity are being studied with the method described above
The growing of the APS is being studied for different values of
. This will allow us
to answer the following question: How much and when are the different scales
contributing to the effects under consideration?
We are preparing a new code based on the AP3M N-body designed and used by the
HYDRA consortium. Greater resolutions will be considered with the new N-body.
The effect produced by complementary spatial scales (
) must be studied in
detail. If possible, this study would be developed by using linear and mildly nonlinear
techniques.
The resulting maps and their superimposition to other CMB components could be
studied by using sophisticated mathematical methods designed to detect deviations
from Gaussianity (wavelets, .....).
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