Transcript z-space distortions
Disentangling dynamic and geometric distortions
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
Bologna cosmology/clustering group
Carmelita Carbone : N-body with DE and neutrinos + forecasts Victor Vera (PhD): BAO with new statistics Fernanda Petracca (PhD): DE and neutrino constraints from ξ (r p , π ) Carlo Giocoli : HOD and HAM (Halo Abundance Matching) Roberto Gilli : AGN clustering Michele Moresco : P(k) Lauro Moscardini : clustering of galaxy clusters Andrea Cimatti : galaxy/AGN evolution Federico Marulli : RSD + Alcock-Paczynski test + clustering of galaxies/AGN
Redshift space distortions How to constract a 3D map Ra, Dec, Redshift comoving coordinates Geometric distortions the real comoving distance is:
c z
dz c
(
M z c
Dynamic distortions the observed galaxy redshift:
z obs = z c + v || c
v c
Observational distortions z c : cosmological redshift due to the Hubble flow v || : component of the galaxy peculiar velocity parallel to the line-of-sight
Dynamic and geometric distortions The two-point correlation function geometric distortions ( 2 ) 2
n
galaxy
DM
no distortions 1 2 geometric distortions dynamic + geometric distortions dynamic distortions dynamic + geometric distortions
Modelling the dynamical distortions The “dispersion” model (
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|| )
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linear model 0 (
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Statistical errors on the growth rate
bias
δβ β
Cb 0.7
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exp
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2 0
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Bianchi et al. 2012
Effect of redshift errors on β and σ 12 Only dynamic distortions Dynamic distortions + δz Dynamic distortions + δz δz small sistematic error on β δβ ~ 5% for all δz
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
The Alcock-Paczynski test Steps of the method 1. Choose a cosmological model to convert redshifts into comoving coordinates 2. Measure ξ 3. Model only cosmology the dynamical distortions 4. Go back to 1. using a different test
…next future 10 N-body simulations with massive neutrinos (L=2 Gpc/h) (1e6 CPU hours at CINECA) for:
all-sky mock galaxy catalogues via HOD and box-stacking
all-sky shear maps via box-stacking and ray-tracing
all-sky CMB weak-lensing maps
end-to-end simulations for BAO and RSD statistics
reference skies for future galaxy/shear/CMB-lensing probes
ISW/Rees-Sciama implementation/analysis PI Carmelita Carbone
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 (σ v >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 Ω M
Mock halo catalogues
BASICC simulation by Raul Angulo
GADGET-2 code • ~ 1448^3 DM particles with mass 5.49e10 Msun/h • periodic box of 1340 Mpc/h on a side • Λ CDM “concordance” cosmological framework (Ω m =0.25, Ω b =0.045, Ω Λ =0.75, h=0.73, n=1, σ 8 =0.9) • DM haloes: FOF M>1e12 Msun/h • Z=1
Systematic errors on the growth rate
Errors on β on different mass ranges • Small masses [M<5e12 Msun/h] systematic error on β ~ 10% • Intermediate masses [5e12
Statistical errors vs Volume
Effect of redshift errors on β and σ 12
Effect of geometric distortions 1D correlation function deprojected correlation
Effect of redshift errors on 1D ξ