Important slides (Cosmological group at KASI) http://cosmology.kasi.re.kr/ Halo velocity bias - a first order systematic error in peculiar velocity cosmology ZHENG Yi (郑逸) Zhang, Zheng & Jing, 2014, arXiv: 1405.7125, PRD accepted Zheng, Zhang & Jing, 2014a, arXiv: 1409.6809, PRD accepted Zheng, Zhang & Jing, 2014b, arXiv: 1410.1256, PRD submitted Good evening everyone, today I would like to introduce our study about a first order systematic error in peculiar velocity cosmology, the halo velocity bias which is a key step to understand the galaxy velocity bias Sampling artifact Velocity bias YongPyong-High1 2015

Cosmological observations: galaxy velocity field (power spectrum) Cosmological observations: dark matter velocity field (power spectrum) YongPyong-High1 2015

Peculiar velocity: a window to the dark universe Matter distribution in our universe is inhomogeneous Gravitational attraction arising from inhomogeneity perturbs galaxies and causes deviation from the Hubble flow v=Hr v=Hr v v I would start from introducing the cosmological peculiar velocity field. Cosmological principle….primordial quantum ….gravitational attraction…..away from hubble flow…. peculiar velocity r r ZPJ’s PPT YongPyong-High1 2015

Peculiar velocity: unique probe of cosmology At scales larger than galaxy clusters, directly probes gravity (t-t component: In linear regime, honest tracer of matter distribution Necessary for the complete phase-space description of the universe The cosmological peculiar velocity field is important for cosmology at least for 3 reasons:….. ZPJ’s PPT YongPyong-High1 2015

Challenges However, accurate velocity measurement? In particular at cosmological distance, e.g. z~1? Conventional method: subtract the Hubble flow with distance indicators (FP, TF). E.g. SFI++, 6dF (e.g. Johnson et al. 1404.3799) Statistical errors blow up with redshift. Only applicable at z<0.1 Systematic errors (e.g. 6dF, Magoulas et al. 1206.0385). New methods Kinetic Sunyaev Zel’dovich effect: bias from baryon mass SNe Ia: statistical errors blow up with z; contamination from lensing Relativistic effects in galaxy number density: only detectable at horizon scales (e.g. Yoo et al. 2011 ) Relativistic effect in galaxy size/flux/magnification bias: only applicable at low z (e.g. Bonvin, 2008. But see ZPJ & Chen 2008) Redshift space distortion: very promising…. However it is challenging to measure velocity field in particular at cosmological distance, e.g. z~1. many methods…..have their own problems….focus on redshift space distortion… ZPJ’s PPT YongPyong-High1 2015

Measure peculiar velocity at cosmological distance heuristic approach A. J. S. Hamilton, astro-ph/9708102 Peculiar velocity can be reconstructed! Not only the average statistics, but also the 3D field Real space power spectrum Redshift space power spectrum Also directly measurable! Directly measurable Basically, RSD effect is the anisotropic properties of galaxy clustering induced by galaxy peculiar velocity. We determined line of sight distance by redshift, RSD additional … distort line of sight …. Reid et al. 2012 YongPyong-High1 2015

After layers of approximations, Through the anisotropy in the redshift space power spectrum, one can reconstruct the velocity power spectrum Has been applied to real data (Tegmark et al. 2002 on 2dF; Tegmark et al. 2004, on SDSS; etc. ) I will skip 3D velocity …..show here….RSD….velocity power spectrum….different angle dependence… ZPJ’s PPT YongPyong-High1 2015

Often further compressed into a single number Linear growth rate: 𝑓 Will be improved significantly by eBOSS To 1% by stage IV surveys such as DESI , Euclid and SKA In most cosmological data analysis, we further compress the velocity information into a single number f, linear growth rate, combined with ….broke the degeneracy …. Chuang et al. 1312.4889 ZPJ’s PPT YongPyong-High1 2015

Velocity bias or not? A fundamental problem in peculiar velocity cosmology In linear theory: Desjacques & Sheth 0909.4544 Cosmological observations: galaxy velocity field (power spectrum) Cosmological observations: dark matter velocity field (power spectrum) Since in observation we observe galaxy, in theoretical side we disrobe dark matter , so Where combine cosmological observation with theoretical prediction, we have a question to ask, is the same .at very large scales. One key intermediate step is to understand halo velocity bias .same….small scales… different. Transition scale? YongPyong-High1 2015

Velocity bias: potential systematic error and loophole in accurate cosmology A first order systematic error in cosmology Have to understand the velocity bias to 1% level accuracy at k~0.1h/Mpc. Galaxy velocity To make it more clear of the importance., we… 1% 𝛿𝑓 𝑓 =𝛾 𝛿 Ω 𝑚 (𝑎) Ω 𝑚 𝑎 +ln Ω 𝑚 𝑎 𝛿𝛾≈0.25×0.05𝛿𝑤(𝑧=1) 80%! Known Ω 𝑚 𝑎 YongPyong-High1 2015

What would be the velocity bias of halos in simulations? Peculiar velocity cosmology by default assumes no velocity bias at large scale: Environmental effect: halos/galaxies locate at special regions around density peaks. Proto-halos/linearly evolved density peaks (BBKS 1986; Desjacques & Sheth 2010) have velocity bias What would be the velocity bias of halos in simulations? Now in the literature, peculiar velocity cosmology ….. PJZ’s PPT YongPyong-High1 2015

Severe sampling artifact can be misinterpreted as a “velocity bias” PJZ’s PPT Severe sampling artifact can be misinterpreted as a “velocity bias” DM Halo Naive comparison between the raw measurements of halo velocity and DM velocity gives a apparent bv<1 Illusion caused by the sampling artifact Unphysical numerical effect. But can be misinterpreted as a “velocity bias” When we want to measure the velocity bias from simulation, one obst Yipeng’s P3M simulation: 1200 Mpc/h, 10243 particles Zheng, ZPJ, Jing, 2014b YongPyong-High1 2015

The sampling artifact Velocity field from most RSD models is volume weighted Where there is no particle, the velocity is usually non-zero. It can be large. The sampling on the volume weighted velocity field is biased/imperfect The sampling artifact: inevitable for inhomogeneously distributed objects. Severe for sparse populations. Persists for NP, Voronoi and Delaunay tessellation. The sampling and the signal are neither completely uncorrelated nor completely correlated. Hard to correct straightforwardly Can be fully described in the language of the D field (ZPJ, Zheng & Jing, 2014), similar to CMB lensing ? Theoretically, this equally important… PJZ’s PPT YongPyong-High1 2015

Understanding the sampling artifact Neglect v-D correlation. Neglect correlation in D Including the correlation in D.Not exact. ZPJ, Zheng & Jing, 2014 Zheng, ZPJ & Jing, 2014a Our model works. But improvements are needed Take correlation in D fully into account Take v-D correlation into account PJZ’s PPT YongPyong-High1 2015

Theory and simulation of the sampling artifact The measured velocity power spectrum The real velocity power spectrum Theory prediction: ZPJ, Zheng & Jing, 2014 Simulation verification Zheng, ZPJ & Jing, 2014a ZPJ’s PPT YongPyong-High1 2015

Sampling artifact: theory vs. simulation 1% accuracy <0.1h/Mpc YongPyong-High1 2015

Raw measurement Step one Correction Step two correction ZPJ’s PPT YongPyong-High1 2015

1. Velocity bias vanishes at k<0. 1 h/Mpc 1. Velocity bias vanishes at k<0.1 h/Mpc. Consolidates peculiar velocity cosmology 2. Velocity bias at k>0.1h/Mpc? Poses a challenge ZPJ’s PPT YongPyong-High1 2015

For discussions Needs theory explanation Needs more accurate quantification Need improved understanding of the sampling artifact Needs to extend to galaxies (mock catalog) Perhaps needs new velocity assignment (e.g. Jun Zhang’s idea) Cosmological applications Could be smoking guns of MG Promising tests of the equivalence principle (ongoing work with Zheng Yi, Yipeng, Baojiu Li & De-Chang Dai) ZPJ’s PPT YongPyong-High1 2015

(Cosmological group at KASI) http://cosmology.kasi.re.kr/ YongPyong-High1 2015

YongPyong-High1 2015

Detection of the sampling artifact in DM velocity field DM control samples: Randomly select a fraction of DM simulations particles. By construction, the control samples and the FULL sample should have identical velocity. Therefore any difference is the result of sampling artifact. We use simulation to detect and quantify this sampling effect Halo number density Zheng, ZPJ, Jing, 2014a YongPyong-High1 2015

Main cosmological research concern Fundamental physics: quantum mechanics, gravity…… Cosmological observations Nonlinear, nonGaussian structure growth, complicated astrophysical processes…… YongPyong-High1 2015