cmb and cluster lensing

CMB and cluster lensing Antony Lewis Institute of Astronomy, Cambridge Lewis & Challinor, Phys. Rept. 2006 : astro-ph/0601594 Lewis & King, PRD 2006 : astro-ph/0512104

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CMB and cluster lensing. Antony Lewis Institute of Astronomy, Cambridge Lewis & Challinor, Phys. Rept. 2006 : astro-ph/0601594. Lewis & King, PRD 2006 : astro-ph/0512104. Weak lensing of the CMB. Last scattering surface. Inhomogeneous universe - PowerPoint PPT Presentation


Page 1: CMB and cluster lensing

CMB and cluster lensingAntony Lewis

Institute of Astronomy, Cambridge

Lewis & Challinor, Phys. Rept. 2006 : astro-ph/0601594

Lewis & King, PRD 2006 : astro-ph/0512104

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Lensing order of magnitudes


Newtonian argument: β = 2 Ψ General Relativity: β = 4 Ψ


Potentials linear and approx Gaussian: Ψ ~ 2 x 10-5

β ~ 10-4

Characteristic size from peak of matter power spectrum ~ 300Mpc

Comoving distance to last scattering surface ~ 14000 MPc

pass through ~50 lumps

assume uncorrelated

total deflection ~ 501/2 x 10-4

~ 2 arcminutes

(neglects angular factors, correlation, etc.)

(β << 1)

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So why does it matter?

• 2arcmin: ell ~ 3000

- on small scales CMB is very smooth so lensing dominates the linear signal

• Deflection angles coherent over 300/(14000/2) ~ 2°

- comparable to CMB scales

- expect 2arcmin/60arcmin ~ 3% effect on main CMB acoustic peaks

Page 5: CMB and cluster lensing

LensPix sky simulation code:

Full calculation: deflection angle on sky given in terms of lensing potential

Lensed temperature given by

Lewis 2005,astro-ph/0502469

Page 6: CMB and cluster lensing

Lensed temperature Cl

Analogous results for CMB polarization. Essentially exact to order of weak lensing – very well understood effect on power spectra.Non-linear Pk 0.2% on TT, ~5% on BB

Lewis, Challinor Phys. Rept. 2006 : astro-ph/0601594

and linear in lensing potential power spectrum

Full-sky fully non-perturbative generalization of method by Seljak 1996

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Lensing effect on CMB temperature power spectrum: smoothing of acoustic peaks; small scale power

Full-sky calculation accurate to 0.1%: Fortran code CAMB (

Page 8: CMB and cluster lensing

Polarization lensing: Cx and CEImportant ~ 10% smoothing effect

Page 9: CMB and cluster lensing

Polarization lensing: CB

Nearly white BB spectrum on large scales

Lensing effect can be largely subtracted if only scalar modes + lensing present, but approximate and complicated (especially posterior statistics).Hirata, Seljak : astro-ph/0306354, Okamoto, Hu: astro-ph/0301031

Lewis, Challinor : astro-ph/0601594

Page 10: CMB and cluster lensing

Current 95% indirect limits for LCDM given WMAP+2dF+HST

Polarization power spectra

Lewis, Challinor : astro-ph/0601594; Lewis Moriond 2006

Page 11: CMB and cluster lensing

Non-Gaussianity• Unlensed CMB expected to be close to Gaussian• With lensing:

• For a FIXED lensing field, lensed field also Gaussian

• For VARYING lensing field, lensed field is non-Gaussian

Three point function: Bispectrum < T T T >

- Zero unless correlation <T Ψ>

• Large scale signal from ISW-induced T- Ψ correlation• Small scale signal from non-linear SZ – Ψ correlation

Zaldarriaga astro-ph/9910498, Goldberg&Spergel, etc…

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Trispectrum: Connected four-point < T T T T>c

- Depends on deflection angle and temperature power spectra- ‘Easily’ measurable for accurate ell > 1000 observations

Other signatures

- correlated hot-spot ellipticities- Higher n-point functions- Polarization non-Gaussianity

Zaldarriaga astro-ph/9910498; Hu astro-ph/0105117

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Confusion with primordial non-Gaussianity?

• 1-point function

- SZ-lensing correlation can dominate on very small scales

- On larger scales oscillatory primordial signal should be easily distinguishable with Planck if large enough

Komatsu: astro-ph/0005036

- ISW-lensing correlation only significant on very large scales

• Bispectrum

- lensing only moves points around, so distribution at a point Gaussian- But complicated by beam effects

Kesden, Cooray, Kamionkowski: astro-ph/0208325

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• Trispectrum (4-point)

Basic inflation:- most signalin long thin quadrilaterals

Lensing:- broader distribution, lesssignal in thin shapes

Can only detect inflation signal from cosmic variance if fNL >~ 20

Komatsu: astro-ph/0602099 Hu: astro-ph/0105117

No analysis of relative shape-dependence from e.g. curvaton??

Lensing probably not main problem for flat quadrilaterals if single-field non-Gaussianity

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Cluster CMB lensinge.g. to constrain cosmology via number counts


Last scattering surface What we see

Following: Seljak, Zaldarriaga, Dodelson, Vale, Holder, etc.

CMB very smooth on small scales: approximately a gradient

Lewis & King, astro-ph/0512104

0.1 degrees

Need sensitive ~ arcminute resolution observations

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Unlensed Lensed Difference

RMS gradient ~ 13 μK / arcmindeflection from cluster ~ 1 arcmin Lensing signal ~ 10 μK

BUT: depends on CMB gradient behind a given cluster

can compute likelihood of given lens (e.g. NFW parameters) essentially exactly

Unlensed CMB unknown, but statistics well understood (background CMB Gaussian) :

Page 17: CMB and cluster lensing

Unlensed T+Q+U Difference after cluster lensing

Add polarization observations?

Less sample variance – but signal ~10x smaller: need 10x lower noise

Note: E and B equally useful on these scales; gradient could be either

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• Temperature - Thermal SZ, dust, etc. (frequency subtractable) - Kinetic SZ (big problem?) - Moving lens effect (velocity Rees-Sciama, dipole-like) - Background Doppler signals - Other lenses

• Polarization - Quadrupole scattering (< 0.1μK)- Re-scattered thermal SZ (freq)- Kinetic SZ (higher order)- Other lenses

Generally much cleaner

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Is CMB lensing better than galaxy lensing?

• Assume background galaxy shapes random before lensing• Measure ellipticity after lensing by cluster


• On average ellipticity measures reduced shear

• Shear is γab = ∂<a αb>

• Constrain cluster parameters from predicted shear• Assume numerous systematics negligible…

Page 20: CMB and cluster lensing

CMB polarization only (0.07 μK arcmin noise)

Optimistic Futuristic CMB polarization lensing vs galaxy lensingLess massive case: M = 2 x 1014 h-1 Msun, c=5

Galaxies (500 gal/arcmin2)

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Summary• Weak lensing of the CMB very important for precision cosmology

- changes power spectra

- potential confusion with primordial gravitational waves for r <~ 10-3

- Non-Gaussian signal, but well known and probably not main problem

• Cluster lensing of CMB

- Temperature lensing difficult because of confusions

- CMB polarisation lensing needs high sensitivity but potentially useful at high redshift

- galaxy lensing expected to be much better for low redshift clusters

- CMB lensing has quite different systematics to galaxy lensing

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Planck (2007+) parameter constraint simulation (neglect non-Gaussianity of lensed field)

Important effect, but using lensed CMB power spectrum gets ‘right’ answer

Lewis 2005,astro-ph/0502469

Parameters can be improved using BB/lensing reconstruction; non-Gaussianity important in the future; c.f. Wayne Hu’s talk

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Full calculation: Lensed temperature depends on deflection angle:

Lensing PotentialDeflection angle on sky given in terms of lensing potential

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Toy model: spherically symmetric NFW cluster




M200 ~ 1015 h-1 Msun

c ~ 5, z ~ 1 (rv ~ 1.6Mpc)Deflection ~ 0.7 arcmin

(approximate lens as thin, constrain projected density profile)

assume we know where centre is