David Spergel, Paul Bode and Chris Hirata Simulating Gravitational Lensing of the CMB Sudeep Das with David Spergel, Paul Bode and Chris Hirata Princeton University June 8, 2007

Outline Why is CMB Lensing interesting? Some basics Why large sky? The simulation Results Future directions February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions The three R’s of the CMB Redshift Remoteness Randomness February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions The three R’s of the CMB A source at a well known Redshift. For lensing of the CMB the source redshift is accurately known. One of the main uncertainties in conventional weak lensing studies is the lack of accuracy in source redshifts. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions The three R’s of the CMB A source which is most Remote. CMB can act as a source for lensing by high redshift objects. Lensing of the CMB by quasars and sub-mm galaxies have the potential of telling us about the less understood halo properties of these objects. Mention distance ratio February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions The three R’s of the CMB A source which is Random. The hot and cold patches of the CMB are featureless. They have no intrinsic shape. In conventional weak lensing with galaxies, their intrinsic ellipticity is a source of systematic noise. Intrinsic galaxy ellipticities can also be correlated. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Detectable 3.4  detection with WMAP+NVSS. [Smith et al. arXiv:0705.3980v1] With upcoming surveys like ACT, PLANCK, SPT the effect should be detectable at high significance in cross correlation with large scale structure tracers. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Lensing remaps points Typical deflection is non-trivial (~ 2.7 arcmin) Deflections are coherent over few degrees. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Lensing smoothes features Power from large scales (l~60) in the deflection field gets aliased into smaller scales (l~1000) in the CMB. Tell how degree scale deflection patches change the size distribution of CMB patches. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Catching all those modes … A lot of power from large scale modes in the deflection field couples to small scale modes in the CMB. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Large Scale Structure Simulation For z < 4.0 • We use a Tree Particle Mesh (TPM) light-cone simulation. [Bode, P., & Ostriker, J.P. 2003, ApJS, 145, 1] Lbox = 1000 h−1 Mpc N = 10243 (mp = 6.72 × 1010Msun /h). Epsilon=16.3 Kpc/h For z > 4.0 LSS planes are generated as Gaussian random realizations from a theoretical power spectrum. February 22, 2019 Sudeep Das - Princeton University

Large Scale Structure Cosmology Why interesting? Some basics Why curved sky? Simulation Future directions Large Scale Structure Cosmology The cosmological parameters used are: = 0.044, m = 0.216, = 0.74, h = 0.72, ns = 0.95 and 8 = 0.77. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Large Scale Structure Projection onto sphere At each TPM step, Particles in a z- slice are projected onto the octant of a HEALpix sphere. Euler rotated and centroided on the North Pole. A disc is taken out and the surface mass density () on it saved. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University ~100 TPM discs are further binned up into ~10 planes. Both an effective and a multiple plane ray tracing are performed. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Connecting   Multiple Planes Effective Approximation February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Power Spectrum of  February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Getting the deflection field  The Poisson equation is inverted to get the lensing potential, Then the deflection angle, =r is then calculated as, February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Remapping points Given the deflection angle field, rays are propagated using the curved sky remapping equations, [Lewis, A. Phys. Rev. D71 (2005) 083008] February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions The Need to Interpolate Rays will end up off-centered on subsequent slices and on the CMB. Both r  and TCMB have to be sampled on an irregular grid. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Non-Isolatitude Spherical Harmonic Transform (NISHT) Hirata et al., PRD, 70, 103503, (2004). February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Unlensed CMB Gnomonic Projection NSIDE=4096. 0.856 arcmin. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Lensed CMB Gnomonic Projection NSIDE=4096. 0.856 arcmin. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Difference Map Gnomonic Projection NSIDE=4096. 0.856 arcmin. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Power Spectra Power Spectra The theory curves are spectra from CAMB* with mode-coupling due to a tapered polar cap window. * www.camb.info February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Power Spectra Power Spectra Structure at z>4 has a nontrivial contribution to the lensed signal. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions Utility Most of the forthcoming surveys will concentrate on the cross- correlation between gravitational lensing of the CMB and tracers of large scale. The current method provides a natural way to simulate such studies. The halos can be saved and populated with tracers (LRGs, SZ clusters etc.) Optical lensing (galaxy shear) studies can be simulated with the same LSS and cross correlated with the lensed CMB. February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions LRG Maps In collaboration with Charlie Conroy we are populating the simulation with LRGs with an HOD based approach. [Conroy et. al, Astrophys. J. 647 (2006) 201-214] February 22, 2019 Sudeep Das - Princeton University

Sudeep Das - Princeton University Why interesting? Some basics Why curved sky? Simulation Future directions The Atacama Cosmology Telescope. Achieved first light on June 8, 2007 pointing at Jupiter. ACT will be looking at the SDSS stripe 82 where we have LRG data. Stripe 82; 300 sq degees. Z<0.6 LRGs photometric down to L*. 1. This map was the simplest possible combination of 71 detectors. Maps were made with each detector alone (not shown) and then rescaled so the Jupiter peak on all maps was of unit amplitude. No other calibration info of any kind was used (e.g., IV curves). The rescaled maps were then averaged (with weighting appropriate to their noise).2. The averaged map was then smoothed by 1 map pixel (0.4 arcminutes).3. The pointing model was derived from these same observations and is far from complete. Any error in the model tends to make us stack the separate detectors incorrectly, smearing out the point source.4. Jupiter was 46 arcseconds in diameter this week. The beamwidth is estimated to be 100 arcseconds FWHM. Jupiter is more or less in the unresolved point source regime. February 22, 2019 Sudeep Das - Princeton University

Internally consistent LRG and SZ maps. Shear Maps for the same LSS. Why interesting? Some basics Why curved sky? Simulation Future directions Final Words… Extension to full sky. Internally consistent LRG and SZ maps. Shear Maps for the same LSS. Use them as training sets for detection algorithms. Thanks to… David Spergel (advisor), Paul Bode, Chris Hirata, Charlie Conroy. February 22, 2019 Sudeep Das - Princeton University

Maximum Error in each Fourier Mode Why interesting? Some basics Why curved sky? Simulation Future directions NISHT Errors K=1 K=10 In the simulation we sample at 4 times the Nyquist rate and use a Polynomial of order K=10. 1e-2 1e-5 Maximum Error in each Fourier Mode Lnyq = 3*nside Lsampling=6*lmax=12*nside =4 lnyq Phi=0.25 1e-8 LNyquist/LSampling Hirata et al., PRD, 70, 103503, (2004). February 22, 2019 Sudeep Das - Princeton University