Controlling intrinsic alignments in weak lensing statistics Benjamin Joachimi, Peter Schneider joachimi@astro.uni-bonn.de Bonn University, Germany ADA6, Monastir, Tunisia May 6th 2010
Outline Intrinsic alignments a challenge for cosmic shear What are intrinsic alignments (IA) and why are they important? The nulling technique How to remove intrinsic alignments from the cosmic shear signal in a model-independent way The boosting technique How to extract intrinsic alignments from cosmic shear data in a model-independent way Conclusions
Correlations in cosmic shear i γi + si i γi si measured ellipticity gravitational shear intrinsic ellipticity 2pt correlation: h i j i = hγi γj i + si sj + γi sj + h si γj i {z } {z } {z } GG GG II GI II GI lensing signal intrinsic ellipticity correlations gravitational shear-intrinsic ellipticity correlations Intrinsic alignments The nulling technique The boosting technique Conclusions B. Joachimi
Intrinsic alignments on the sky II: GI: (e.g. Catelan et al. 00) (Hirata & Seljak 04) 2pt correlation: ɛ i ɛ j = γ i γ j }{{} + ɛ s i ɛs j }{{} + γ i ɛ s j + ɛ s i γ j }{{} GG II GI GG II GI lensing signal intrinsic ellipticity correlations gravitational shear-intrinsic ellipticity correlations
Intrinsic alignments line of sight II: GI: 2pt correlation: ɛ i ɛ j = γ i γ j }{{} + ɛ s i ɛs j }{{} + γ i ɛ s j + ɛ s i γ j }{{} GG II GI GG II GI lensing signal intrinsic ellipticity correlations gravitational shear-intrinsic ellipticity correlations
Redshift dependence vs. modelling II has distinctive z-dependence easy to remove, e.g.: (King & Schneider 02,03) (Heymans & Heavens 03) Alignments of haloes with the surrounding large-scale structure of galaxy shapes or spins with halo shape of satellite positions and orientations w.r.t. host halo etc. 3D IA power spectra depend on formation and evolution of galaxies in their dark matter environment, including baryonic physics. Simple model: (Catelan et al. 00) Intrinsic ellipticity is linear function of tidal quadrupole field at the time of galaxy formation
Why bother? major astrophysical systematic of cosmic shear models crude; analytical progress difficult (e.g. Schneider & Bridle 10) simulations of limited use since alignments depend on both large-scale structure and baryonic physics (e.g. Heymans et al. 06) both II & GI detected e.g. in SDSS (Mandelbaum et al. 06, Hirata et al. 07) strong dependence on galaxy colour and luminosity: low for blue galaxies (Mandelbaum et al. 09); strong for LRGs (Hirata et al. 07) dark energy equation of state can be biased by 50 % or worse if intrinsic alignments are ignored (Bridle & King 07) need for model-independent removal of intrinsic alignments: Nulling need for intrinsic alignment measurement directly on the cosmic shear galaxy sample: Boosting
Projected power spectra Observable: P (ij) GG (l) = 9H4 0 Ω2 m 4c 4 P (ij) GI (l) = 3H2 0 Ω m 2c 2 P (ij) obs χhor 0 χhor 0 (l) = P(ij) GG (l) + P(ij) GI (l)+p(ij) II (l) dχ g(i) (χ) g (j) ( ) (χ) l a 2 P δ (χ) χ, χ dχ p(i) (χ) g (j) (χ) + g (i) (χ) p (j) (χ) a(χ) χ P δi ( l χ, χ ) p (i) (χ): g (i) (χ) = = χhor χ Dds D s d χ p (i) ( χ) ( 1 χ χ ) redshift/ com. distance distribution lensing efficiency
Principle of nulling Π (i) [q] (l) = Nz j=i+1 T (i) [q] j P (ij) obs (l) T (i) [q] has unit length ) = 0 for all r q ( T (i) [q] T (i) [r] T is rotation of data vector weighting of power spectra Choose P (ij) GI (l) 3H2 0 Ω m 2c 2 T (i) [0] j 1 χ(z i) χ(z j ) Π (i) [q](l) with q 1 free of GI contamination ( 1 χ(z ) ( ) i) 1 + zi l χ(z j ) χ(z i ) P δi χ(z i ), χ(z i)
Performance of nulling Fisher matrix analysis Euclid-like cosmic shear survey, z med = 0.9 20 redshift bins photo-z scatter 0.03(1 + z) modified linear alignment model for GI signal 2 σ contours bias due to GI signal largely reduced significant info loss: DETF FoM 1/10
Dependence on redshift quality using p (i) (z) to place nulling z placing nulling z at photo-z bin centre nulling is robust against photo-z uncertainty strong GI suppression requires high photo-z accuracy
Principle of boosting Observable: P (ij) obs (l) = P(ij) GG (l) + P(ij) GI (l)+p(ij) II (l) Can one extract the GI signal instead of GG? GI contains information about galaxy formation & evolution GI from the survey itself useful for modelling IA contamination Π (i) (l) = G (i) (χ) = χhor 0 χhor χ dχ B (i) (χ) P obs (χ i, χ, l) ( d χ B (i) ( χ) 1 χ χ ) Π (i) GI (l) scales with G(i) (χ i ) χi ) ( ) GG (l) dχ (1 χχi G (i) (χ) {1 + z(χ)} 2 lχ P δ, χ Π (i) 0
Performance of boosting Euclid-like survey z-bin width 0.01(1 + z) photo-z scatter 0.03(1 + z) modified linear alignment model for GI signal GI/GG 0.06, 0.24, 0.31 Boosting-transformed power spectra GI/GG 20.5
Constraints via boosting Fit GI model: (e.g. Hirata et al. 07) PδI model (k, z) = A PδI def (k, z) ( 1 + z 1 + z piv ) γ S: spectroscopic data w/o scatter; n g = 1 arcmin 2 P1: photo-z with scatter 0.03(1 + z); n g = 10 arcmin 2 P2: photo-z with scatter 0.05(1 + z); n g = 40 arcmin 2 1 σ constraints; use z i [0.4; 1.4] bias due to residual GG Nulling from Boosting: subtract boosted signal from original observable! poor constraints from boosting related to information loss due to nulling
Conclusions Nulling & Boosting constitute effective, model-independent, and purely geometrical methods that remove/extract intrinsic alignments They make use of the typical redshift dependence of the intrinsic alignment signal, hence depend on accurate redshift information For realistic photo-z quality Nulling & Boosting extract the desired signals with negligible residual contamination Nulling causes considerable information loss; Boosting yields relatively large errors limited capability of separating GG and GI Both techniques can serve as robust sanity checks for ambitious future cosmic shear surveys References: Joachimi & Schneider 2008, A&A, 488, 829 Joachimi & Schneider 2009, A&A, 507, 105 Joachimi & Schneider 2010, A&A, accepted