1. Important slides
(Cosmological group at KASI)
Halo velocity bias - a first order systematic error in peculiar velocity cosmology
ZHENG Yi (郑逸)
Zhang, Zheng & Jing, 2014, arXiv: , PRD accepted
Zheng, Zhang & Jing, 2014a, arXiv: , PRD accepted
Zheng, Zhang & Jing, 2014b, arXiv: , 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
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2. Cosmological observations: galaxy velocity field (power spectrum)
Cosmological observations: dark matter velocity field (power spectrum)
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3. 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
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4. 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

5. 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 )
Statistical errors blow up with redshift. Only applicable at z<0.1
Systematic errors (e.g. 6dF, Magoulas et al ).
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 )
Relativistic effect in galaxy size/flux/magnification bias: only applicable at low z (e.g. Bonvin, 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
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6. Measure peculiar velocity at cosmological distance heuristic approach
A. J. S. Hamilton, astro-ph/
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
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7. 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 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
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8. 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
ZPJ’s PPT
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9. Velocity bias or not? A fundamental problem in peculiar velocity cosmology
In linear theory:
Desjacques & Sheth
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?
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10. 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
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11. 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
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12. 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, particles
Zheng, ZPJ, Jing, 2014b
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13. 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
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14. 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
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15. 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
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16. Sampling artifact: theory vs. simulation
1% accuracy <0.1h/Mpc
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17. Raw measurement Step one Correction Step two correction ZPJ’s PPT
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18. 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
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19. 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
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20. (Cosmological group at KASI) http://cosmology.kasi.re.kr/
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21. YongPyong-High1 2015

22. 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
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23. Main cosmological research concern
Fundamental physics: quantum mechanics, gravity……
Cosmological observations
Nonlinear, nonGaussian structure growth, complicated astrophysical processes……
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