Disentangling dynamic and geometric distortions

1. Disentanglingdynamic and geometricdistortions Federico Marulli Dipartimento di Astronomia, Università di Bologna • Marulli, Bianchi, Branchini, Guzzo, Moscardini and Angulo • 2012, arXiv:1203.1002 Bianchi, Guzzo, Branchini, Majerotto, de la Torre, Marulli, Moscardini and Angulo 2012, arXiv:1203.1545

2. Bologna cosmology/clusteringgroup Carmelita Carbone: Victor Vera (PhD): Fernanda Petracca (PhD): Carlo Giocoli: • Roberto Gilli: • Michele Moresco: Lauro Moscardini: Andrea Cimatti: Federico Marulli: N-body with DE and neutrinos + forecasts BAO with new statistics DE and neutrino constraints from ξ(rp,π) HOD and HAM (Halo Abundance Matching) AGN clustering P(k) clustering of galaxy clusters galaxy/AGN evolution RSD + Alcock-Paczynski test + clustering of galaxies/AGN

3. Redshift space distortions How to constract a 3D map Ra, Dec, Redshift  comoving coordinates • the real comoving distance is: the observed galaxy redshift: zc : cosmological redshift due to the Hubble flow v||: component of the galaxy peculiar velocity parallel to the line-of-sight Geometric distortions Dynamic distortions Observational distortions

4. Dynamic and geometric distortions The two-point correlation function geometric distortions geometric distortions no distortions dynamic+geometric distortions dynamic+geometric distortions dynamic distortions

5. Modelling the dynamical distortions The “dispersion” model non-linear model linear model model parameters

6. Statistical errors on the growth rate δβ/β density bias Bianchi et al. 2012

7. Effect of redshift errors on β and σ12 Dynamic distortions + δz Only dynamic distortions Dynamic distortions + δz δz  small sistematic error on β δβ ~ 5% for all δz

8. Effect of geometric distortions Error on the bias Error on β Spurious scale dependence in b(r) Error on ξ(s)/ξ(r) GD  δβ is negligible

9. The Alcock-Paczynski test Steps of the method • Choose a cosmological model to convert redshifts into comoving coordinates • Measure ξ • Model onlythe dynamical distortions • Go back to 1. using a different test cosmology

10. …next future 10 N-bodysimulationswith massive neutrinos (L=2 Gpc/h) (1e6 CPU hours at CINECA) for: • all-sky mockgalaxycatalogues via HOD and box-stacking • all-skyshearmaps via box-stacking and ray-tracing • all-sky CMB weak-lensingmaps • end-to-endsimulationsfor BAO and RSD statistics • referenceskiesfor future galaxy/shear/CMB-lensingprobes • ISW/Rees-Sciamaimplementation/analysis PI Carmelita Carbone

11. Conclusions • systematic error on β of up to 10%, for small bias objects • small systematic errors for haloes with more than ~1e13 Msun • scaling formula for the relative error on β as a function of survey parameters • the impact of redshift errors on RSD is similar to that of small-scale velocity dispersion • large redshift errors (σv >1000km/s) introduce a systematic error on β, that can be accounted for by modelling f(v) with a gaussian form • the impact of GD is negligible on the estimate of β • GD introduce a spurious scale dependence in the bias • AP test  joint constraints on β and ΩM

12. Mockhalocatalogues BASICC simulation by Raul Angulo GADGET-2 code • ~1448^3 DM particles with mass 5.49e10 Msun/h • periodic box of 1340Mpc/h on a side • ΛCDM “concordance” cosmological framework (Ωm=0.25, Ωb=0.045, ΩΛ=0.75, h=0.73, n=1, σ8=0.9) • DM haloes: FOF M>1e12 Msun/h • Z=1

13. Systematic errors on the growth rate ~10%

14. Errors on β on different mass ranges • Small masses [M<5e12 Msun/h]  systematic error on β ~ 10% • Intermediate masses [5e12<M<2e13 Msun/h]  systematic error is small  the linear model works accurately • Large masses [M>2e13 Msun/h]  large random errors

15. Statistical errors vs Volume

16. Effect of redshift errors on β and σ12

17. Effect of geometric distortions 1D correlation function deprojected correlation

18. Effect of redshift errors on 1D ξ