# Presentation: 453756

## Searching for CMB lensing with ACBAR

- Chao-Lin Kuo
- Observational Cosmology, JPL/Caltech

## Outline

- Brief introduction
- Theory/methodology – adapted for ACBAR analysis/data
- ACBAR & Lensing – instrument, data, expected S/N

## Lensing

** Lensing is a way of probing large scale matter distribution using smaller objects with known (statistical) shape*
** For CMB lensing, these “small objects” are the small scale CMB anisotropy (z~1000).*

## Science of lensing

- Lensing as a cosmological probe ---
-    Deflection power spectrum/reconstructed potential:
- 	M, neutrino mass, dark energy, dark matter tomography, ISW...
- Lensing is a foreground to B-mode polarization: this might set the ultimate limit for our ability to see primordial B-mode
- Upcoming high resolution experiments (SPT, ACT, Planck, ..) will revolutionize this field. Our modest goal is to get a detection before these experiments come online.
- We are trying to extract lensing using CMB temperature anisotropy alone – no cross correlation, galaxy bias, gastronomy, feedback,... involved.

## Lensing power spectrum: Beyond Cl

- C**l**

- The deflection power spectra for two cosmological models
- with the *same* CMB power spectrum (1a&1c from Stompor & Efstathiou)

- Cmbfast
- WMAP CDM

## Lensing as foreground to GW B-mode

- Task force on CMB research
- , a.k.a. the “Weiss report” (2005)

## Effect of weak-lensing on the CMB temperature power spectrum

- Weak lensing has a tiny effect on the power spectrum of the CMB:
- Need to go beyond the power spectrum (2-point correlation)

- Cmbfast
- WMAP CDM

- Solid: unlensed
- Dashed: lensed

## Lensing: theoretical work

- Effects on polarization & temperature power spectra (*Seljak & Zaldarriaga, 1998*)
- Lensing potential reconstruction (*Seljak & Zaldarriaga, 1999*)
- Hu derived a optimal quadratic estimator for lensing reconstruction (*Hu 2001*)
- Hirata & Seljak reformulate the problem in terms of maximum likelihood analysis (*Hirata& Seljak 2003*)
- Impact on the detectability of primordial B-mode evaluated (*Knox/Song, Kesden/Cooray/Kamionkowski 2002*)
- Lensing reconstruction with CMB polarization (*Hu/Okamoto & Hirata/Seljak 2003*)
- Hirata et al. performed a search with 1st year WMAP map (*Hirata et al. 2004*)

## The effect of weak lensing on CMB

- 5’ resolution, r.m.s.=5 K

- 3.2

- Maximum deflection=5’

## Lensing potential reconstruction

*Ref: Hu, 2001 ApJL*

## The limit of quadratic estimator

- Implemented in Fourier space – irregular map coverage becomes a problem
- Assuming uniform, uncorrelated noise, symmetrical beams
- Filtering treatment
- (Ignores higher order effects)

## Lensing with maximum likelihood estimator

**CMB**

**Observer**

**Intervening**
**Dark matter**

- * Parameterize the lensing potential with ....
- * Maximize the likelihood L(,....) to find the lensing potential
- * From  to the lensing power spectrum
- * The science products are the lensing potential and the lensing power spectrum
** Hirata & Seljak reproduce the quadratic estimator using this method*

- (Hirata & Seljak 2003)

## Mode reconstruction

- Up to the second order, the likelihood function is given by
- To find the maxima, we take the derivative and set it to zero:
- The solution to the equation is
- With the Fisher matrix *F* defined to be

## Mode reconstruction

- From Bond, Jaffe, Knox (98), the Fisher matrix is
- And the first derivatives (of likelihood) are
- Together with                                  these are the familiar iterative quadratic estimation formulae for C**l**
*The only difference: the parameters are not the CMB “band powers” , but the “lensing modes”*

## Lensing power spectrum

*<****>=C**** , however, we can’t just “square the lensing potential” to get the lensing power spectrum – (instrument + reconstruction) noise bias*
- For given data ,  L() is the likelihood for having the lensing potential 
- For given lensing potential , P(C) is the likelihood for having lensing power spectrum Cgiven by
- We define the *grand* likelihood function to be the product of the two, *marginalized* over 
- This process is again very similar to the angular power spectrum analysis:
-         maximum likelihood map

- (Hirata & Seljak 2003)

## Lensing power spectrum

- Define
- The integral can be done if we approximate the *integrand (joint likelihood)* as a Gaussian near the extrema
- The result of the integral gives the likelihood function for C

## Lensing power spectrum

- Now we convert these equations into their parameterized version: we parameterize the potential with *p*, and the power spectrum with *q*
-           *<****>=C***

## Lensing power spectrum

- This is the final result:
-       for a given *q*, find L*, p, K,* and L,  go to a new *q* and repeat....

**^**

## ACBAR & Lensing

## ACBAR Collaborators

- J.B. Peterson
- Sussex:
- A.K. Romer
- Laura Valkonen

- U.C. Berkeley:
- W.L. Holzapfel (co-PI)
- M.D. Daub

- JPL/Caltech:
- J.J. Bock
- C.L. Kuo
- A.E. Lange
- C. Reichardt

- Cardiff:
- P.A. Ade
- Chicago
- M.C. Runyan

- Case-Western:
- J. Ruhl (co-PI)
- J. Goldstein

**ACBAR is funded by the NSF Office of Polar Programs**

**ACBAR Collaborators**

## Cooled to 240mK

**Cooled to 240mK**
**He3/He3/He4**
**Fridge**

- Arcminute  Cosmology Bolometer Array Receiver (2001-2005)

**Bolometers**

**corrugated **
**feed horns**

**2 meter Telescope**
**@ South Pole**

- In 2005, ACBAR is equipped with 16 150GHz bolometers, i.e.,
- 1⁄2 the mapping speed of QuaD in temperature (31 feeds).

## ACBAR sees the damping tail

-  Confirmation of the damping tail (caused by photon diffusion)
-  Consistency check of the standard cosmology: flat, low baryon, CDM, with 
-  Improving constraints on M, b, ns
-  Barely any foreground

**C*****l*****(*****l*****+1)*****l*****/2******

**2002**

- I

## ACBAR expanded sky coverage in 2004 & 2005

- *700 square degrees in low dust regions
- *The lensing fields r.m.s. ~ 3-5 K, 60 square degrees- comparable or slightly
- deeper than *Planck*

**Published C*****l***** results**

**lensing **
**analysis**

## Dramatic Improvements to be expected

- ACBAR 2002 – LMT (published)

- ACBAR 2002 - No LMT (to be published)

- Full ACBAR Data set – No LMT (being analyzed)

- Expected error bar reductions

**l=650**

**2000**

**1550**

**2700**

**1050**

**Reduced **
**by 7**

**Reduced **
**by 5**

**Reduced **
**by 4**

- Calibration to be obtained from WMAP
- (expect 3% uncertainty)

- Power Spectrum forecast

**2****nd**

**3****rd**

**4****th**

**5****th**

## ACBAR power spectrum analysis

- ACBAR theory matrix

- The Fourier transform
- of the filter functions

- A typical ACBAR filter
- function

## ACBAR power spectrum analysis

- =

- The Fourier transform
- of the *de-lensed* filter functions

**~**

**~**

- Lensing distorts the line of sight:
- The de-lensed theory matrix

*if*

## E-mode and B-mode lensing

- From the lensing potential , how do we calculate the deflection field?
- E-mode lensing (true lensing): take the gradient of 
*	**	*
*	**          *(*d**x *, *d**y*) =  (         ,        )
- B-mode lensing: (treat  as the vector potential and) take the curl of 
-                 (*d**x *,* d**y*) =  (-        ,         )

*This B-mode lensing should be zero *
*for scalar lensing field- the inflationary *
*tensor perturbation is too small to be detected*
*this way (Dodelson et al.).*

## Expected signal-to-noise

- From Hu 2001

- Total signal to noise

- From Hu 2003, two models
- are w=-1 & w=-2/3

- CMB5: ~3 K, 20 square degrees; w-1/2 =5.5 , f1/2=2.2x10-2   ~2-3 
- BOOM: ~5 K, 40 square degrees; w-1/2 =9.2 , f1/2=3.2x10-2  ~2-3 

*****

*****

- ACBAR??

## end

## Summary of ACBAR’s CMB Observations

| Field |  | Est Depth
(K-beam) | Area
Deg2 | 2001
4-150s | 2002
8-150s | 2004
8-150s | 2005
16-150s |
| --- | --- | --- | --- | --- | --- | --- | --- |
| CMB2/4 |  | 4.1* | 36 | 348 | 98 |  |  |
| CMB6 |  | 5.5* | 23 |  | 241 |  |  |
| CMB7 |  | 5.3* | 25 |  | 289 |  |  |
| CMB5 |  | 1.8* | 23 |  | 1130 | 767 | 607 |
| BOOM |  | 3.3 | 56 |  |  | 765 | 1192 |
| CMB7ext |  | 9 | 102 |  |  |  | 456 |
| CMB5ext |  | 10 | 102 |  |  |  | 342 |
| WM1 |  | 10 | 95 |  |  |  | 294 |
| WM5 |  | 12 | 95 |  |  |  | 209 |
| WM2 |  | 13 | 95 |  |  |  | 190 |
| WM4 |  | 12 | 95 |  |  |  | 218 |
| Total: |  | - | 700 | 348 | 1469 | 1532 | 3508 |

## Improved analysis

- CMB5 field, M-(L+T)/2

- CMB5, un-differenced

- Guiding quasar

- 2