Probing growth of cosmic structure using galaxy dynamics: a converging picture of velocity bias Hao-Yi Wu University of Michigan
Galaxies are not necessarily test particles
Probing dark energy with growth of structure Huterer et al. (arxiv:1309.5385) Snowmass white paper Simulation: Virgo Consortium Galaxy cluster counts Galaxy clustering (redshift-space distortions) Growth is the key to test modified gravity models!
Galaxies are not necessarily test particles Galaxy velocity bias b v = Velocity dispersion of galaxies (σ gal) Velocity dispersion of dark matter (σ DM ) How well do we need to understand b v in order to get unbiased cosmological parameters? How well can we understand b v with current simulations?
From galaxy surveys to parameter constraints Surveys Galaxy cluster abundance Galaxy clustering (power spectrum) Modeling Constraints Cosmic acceleration, modified gravity, primordial non- Gaussianity, etc. N cl (M obs, z) = Z Geometry dv c Z Growth dm n h (M, z)p(m obs M) Mass function Mass-observable relation
From galaxy surveys to parameter constraints Surveys Galaxy cluster abundance Galaxy clustering (power spectrum) Modeling Constraints Cosmic acceleration, modified gravity, primordial non- Gaussianity, etc. N cl (M obs, z) = P 1h gal(k) / Z Z Geometry dv c Z Growth Mass function Growth dm n h (M, z)p(m obs M) Mass function Number of galaxy pairs Mass-observable relation dm n h (M, z)hn gal (N gal 1)iu 2 profile(k)r(k, v) Density profile Velocities of galaxies
From galaxy surveys to parameter constraints Surveys Galaxy cluster abundance Galaxy clustering (power spectrum) Modeling Constraints Cosmic acceleration, modified gravity, primordial non- Gaussianity, etc. N cl (M obs, z) = P 1h gal(k) / Z Z Geometry dv c Z Growth Mass function Growth dm n h (M, z)p(m obs M) Mass function Number of galaxy pairs Mass-observable relation dm n h (M, z)hn gal (N gal 1)iu 2 profile(k)r(k, v) Density profile Velocities of galaxies
Small-scale redshift-space distortion (The Fingers-of-God effect) Real Space Redshift Space B A B A see e.g. Dodelson s textbook Virial motion of galaxies suppresses small-scale clustering
Small-scale clustering includes rich information 10 5 10 3 Solid: no prior; dashed: Planck prior no nuisance parameters 10 4 2-halo 10 2 5 Zheng HOD parameters 2 para for cen; 5 para for sat 10 3 10 1 k NL 1-halo dominated P(k ; z = 0.41) 10 2 10 1 10 0 1-halo p (w a) (wp) 10 0 10 1 10 1 10 2 without RSD with RSD 10 10 3 4 10 3 10 2 10 1 10 0 10 1 10 2 k[h/mpc] 10 2 10 3 10 4 Planck prior 10 1 10 0 10 1 k max [h/mpc] Wu and Huterer, MNRAS (1303.0835)
Velocity bias can potentially dominate the systematic error in galaxy power spectrum Fractional bias in P(k) scales used for cosmology Wu and Huterer MNRAS (1303.0835)
How well can we understand velocity bias using current simulations?
N-body simulation Rhapsody MHD simulation Magneticum (Wu, Hahn, Wechsler et al. 2013) (Klaus Dolag) used in this work Zoom-in simulations of clusters Mass resolution: 1.3x108 M /h 96 clusters of mass 6x1014 M /h (z=0), 8142 progenitors (0 z 2) Collisionless, gravity only Rich subhalo/galaxy statistics Limited input physics Full cosmological volume Mass resolution: 6.9x108 M /h 46 clusters above 1014 M /h Star formation, AGN feedback, magnetic fields, etc. Rich input physics Limited statistics (so far)
Galaxy tracers in N-body simulations M pk or V pk M 0 or V 0 accretion occurs Subhalo properties include: V max : maximum circular velocity (GM/r max ) 1/2 ; proxy for subhalo mass V 0 (z=0): affected by stripping V pk (peak): unaffected by stripping; correlated with galaxy luminosity and stellar mass
In N-body sims, using subhalos current mass leads to too high velocity bias bv = σgal/σdm bv = gal/ DM 1.1 1.0 0.9 0.8 N-body only DM-v 0 Massive/bright galaxies slow (dyn. friction) Low-mass/faint galaxies fast (stripping) Strong tidal stripping can remove slow galaxies and lead to higher velocity bias 0.7 DM-v pk Random 10 1 10 2 N brightest galaxies in a halo N brightest galaxies in a cluster Wu, Hahn, Evrard et al. (1307.0011, MNRAS)
Using v pk in N-body sims gives results similar to hydro simulations bv = σgal/σdm bv = gal/ DM 1.1 1.0 0.9 0.8 DM-v 0 DM-v pk Hydro-v 0 Galaxies in hydro simulations suffer less stripping less velocity bias v 0 in hydro sims behaves like v pk in N-body sims 0.7 Hydro-M star Random 10 1 10 2 N brightest galaxies in a halo N brightest galaxies in a cluster Wu, Hahn, Evrard et al. (1307.0011, MNRAS)
Using v pk in N-body sims gives results similar to hydro simulations Be careful when using subhalo mass in N-body simulations! bv = σgal/σdm bv = gal/ DM 1.1 1.0 0.9 0.8 DM-v 0 DM-v pk Hydro-v 0 Galaxies in hydro simulations suffer less stripping less velocity bias v 0 in hydro sims behaves like v pk in N-body sims 0.7 Hydro-M star Random 10 1 10 2 N brightest galaxies in a halo N brightest galaxies in a cluster Wu, Hahn, Evrard et al. (1307.0011, MNRAS)
Comparing with results from the literature bv = σgal/σdm bv = gal/ DM 1.1 1.0 0.9 0.8 0.7 N-body-v 0 N-body-v pk Hydro-v 0 Hydro-M star Random Lau 10 CSF 10 1 10 2 N brightest galaxies in a halo N brightest galaxies in a cluster Lau 10 Munari 13 Velocity bias is consistent among (1) subhalos with v pk in N-body sims and (2) galaxies in CSF+AGN sims. D04 F06 N-body SAM NR CSF AGN 1.1 1.066 ±0.027 1.0 0.9 0.8 0.7 A converging picture: b v = 1.065 ± 0.005 (stat) ± 0.027 (sys)
Summary Velocity bias of galaxies can cause systematics in the measurements of growth of structure. When using galaxy P(k), 10% uncertainty in b v can leads to 5% systematic bias in P(k) at k=0.3 We present a converging picture of velocity bias from simulations: b v = 1.07±0.03, which is a combined effect of dynamical friction and tidal stripping.