# Presentation: 004086

## Weak Lensing of the CMB 

- by Large-Scale Structures

- Alexandre Amblard

- University of California, Berkeley

- Santa Fe 2004

## How does it work

- LSS

- The light from the Last Scattering Surface is deflected by matter along the line of sight

- α

- DLS

- DL

**M**

- Effect depends on the mass of the lens
- M, and the distance DL(lens), DS (source),
- DLS (lens-source)

- z≈ 1100

- z=0

## If the deflection is small, one can relate the deflection angle

- α with the convergence κ :

- With the convergence κ representing the projected mass distribution :

- Contribution to the
- lensing effect of the CMB
- versus redshift :
- Efficiency * Growth factor

- From Bartelmann

## Convergence :

- Lensed

- Unlensed

- with

- Effect to detect

## Order of Magnitude

-  Size of the deflection : ~ 1’
-  Temperature difference : ~ 20μK
- ( 1 μK for E, B)

## What can we do with the CMB lensing ?

- On small scales to reconstruct
- the cluster density profile and mass
- Zaldarriaga & Seljak (2000)
- Holder & Kosowsky (2004)
- Vale et al. (2004)
- Dodelson (2004)

- On larger scales, measure the convergence power spectrum [Hirata et al. (2003), Okamoto et al. Kesden et al. (2003), Amblard et al. (2004)]

- 8’

- 7.5o

- 4% for 0.1 eV

- Kaplinghat et al. (2003)

## How to estimate of κ ?

- Basically 2 ways :

-  Quadratic Estimator :

-  Maximum Likelihood :

- Okamoto & Hu (PRD 67 - 2003)
- Kesden et al. (PRD 67 – 2003)

- Hirata & Seljak (astro-ph/0306354)

- use simplify likelihood and iterate to solve it

- lensed noisy map

- noise correlation matrix

- lensing operator

- CMB correlation matrix

## Assumptions 

-  Valid if the deflection angle is small (especially quadratic one)
-  Valid if the noise is uncorrelated
-  Valid if the convergence field is Gaussian
-  Valid in the absence of foreground

- But large scale structures
- are not Gaussian on small
- scales

- But at least the kinetic SZ is
- spectrally undistinguishable from
- the CMB.

- Assumptions

- Test with simulations to quantify the effect
- (work done with C. Vale & M. White)

## The simulations

- The simulations used in the following contained :

-  a lensed CMB map by :
-  an uniform Gaussian noise of 2 μK/arcmin
-  an estimated kinetic SZ with the same N-body simulation

- a combination of a Gaussian field for z>2 and a simulated
- convergence field from a N-body simulation for z<2

- Our test survey has the following characteristics :

-  0.8’ of angular resolution
-  2 μK/arcminute noise level
-  30x30 degrees sky coverage

## How to assess the results ? 

- regions lies,

-  The cross spectrum of the estimated map with the input one,
- which tell us how good statistically is the estimate :

-  The auto spectrum of the estimated map, which contains
- some cosmological information, and that should match our input one :

- Similarities in the map

- Bias in the estimated map κest

- Bias in the convergence
- power spectrum estimate

- How to assess the results ?

- Ratio :

- obtained

- expected

## Map reconstruction (no kSZ)

- 20’ smoothed maps :

- The two maps are very similar at 20 arcminutes, but the noise level is
- still quite high

- input

- Recovered
- (quadratic estimator)

## Power Spectrum

- The map is now bias
- by 10%

- The power-spectrum
- is now bias by 50%

- The non-Gaussianity of the convergence field bias the quadratic
- estimator even more.

## Adding a foreground

- input

- recovered

- Smoothed (20’)
- kSZ map

- Obvious contamination
- from the kSZ

- The estimated convergence map still look quite
- alike the input one but spurious fluctuations due
- to the kSZ appear.

## 20% of bias in the map, showing the correlation between the kSZ and the lensing

- 200% bias on the
- estimated spectrum
- , kSZ contributes to
- 150% level

- Correlated and uncorrelated kSZ structures bias our measurement
- of the convergence power spectrum.

## On the way to separate the kSZ

- Let’s assume we have a map at another frequency which allows to
- detect clusters via thermal SZ (S > 50 μK), 1.4% of the pixels are masked.

- Could we get rid of the kinetic SZ ?

- Mask used

- Interpolated Map
- (using Renka & Cline algorithm)

## Results

**input**

**output without kSZ**

**output with kSZ**

**output with masked kSZ**

-  the main kSZ spots have
- disappeared with the masking
- technique
-  the recovered map using the
- masking technique looks very
- similar to the ones which does
- not contain any kSZ

## Back to 70% extra power

- 20 % residuals

- 10% bias on the map

- Most of the correlated
- structures are gone

- The mask suppresses most of the correlated kSZ structures, does
- not affect much the convergence spectrum (less than 5%), and
- suppresses almost 90% of the bias linked to the kSZ.

## Bias and angular resolution : a solution ?

- Non-Gaussianity comes
- from small structures

- Small structures may
- create the bias

- A low angular resolution limits the coverage in l space but
- decreases the bias level.
- A mission with large coverage, good sensitivity, but moderate
- resolution may be the suitable one.

- From 4 to 0.8 arcminutes (FWHM)

- bias on the estimated map

- Estimated power
- spectrum bias

## What could we expect from forthcoming experiments

**input**

**APEX/ACT recovered**

**SPT recovered**

**Planck recovered**

- The 20’ features are quite
- recognizeable with APEX, ACT
- and SPT, but not with Planck
- as its noise will be at least 6
- times larger.
**APEX**** : 0.8’ resolution, 8 ****μ****K/arcmin, 15x15 degrees**
**(2004)**
**SPT**** : 1.1’ resolution, 10 ****μ****K/arcmin, 60x60 degrees**
**(2006)**
**PLANCK (1/10) : 5’ resolution, 65 ****μ****K/arcmin, 60x60 degrees – one tenth of Planck (2007)**

## Planck, SPT and APEX

- Bias on the power spectrum for
**Planck**, **SPT** and **APEX**
**with masking the kSZ **

- Thet bias is around 10% for APEX
- and SPT, Planck estimated power
- spectrum does not present
- a significant bias.

## Conclusions

-  CMB lensing is promising but it requires “great” data and robust detection algorithm.
-   The kinetic SZ and the non-Gaussianity create a bias on the      estimated convergence power spectrum, but could be both reduce (masking in real and Fourier space)
-  Other foreground effect need to be addressed, polarization
- (B-mode especially) measurement is maybe the way to go
-  Forthcoming experiments should be able to detect the lensing
- of the CMB