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Simulating the 4% Universe Hydro-cosmology simulations and data analysis Michael L. Norman SDSC/UCSD Lecture Plan Lecture 1: Hydro-cosmology simulations of baryons in the Cosmic Web Lyman alpha forest (LAF) Baryon Acoustic

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Simulating the 4% Universe

Hydro-cosmology simulations and data analysis

Michael L. Norman SDSC/UCSD

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Lecture Plan

  • Lecture 1: Hydro-cosmology simulations of

baryons in the Cosmic Web

– Lyman alpha forest (LAF) – Baryon Acoustic Oscillation (BAO)

  • Lecture 2: Radiation hydro-cosmology

simulations of Cosmic Renaissance

– Epoch of Reionization (EOR) – First Galaxies

ISSAC 2012 SDSC, San Diego, USA 2 7/17/2012

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Motivation

  • It’s the part of the Universe we can see
  • Involves real astrophysics which is complicated

and interesting

  • Can place constraints on the dark universe
  • Computational discoveries

Norman (1997)

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Computational Discoveries

  • Physical nature of Lyman alpha forest

absorption systems

Cen+1994, Zhang+1995, Hernquist+1996

  • Existence of the warm-hot intergalactic

medium

Cen & Ostriker 1999

  • Mass scale of Pop III stars

Abel+2001, Bromm+2002

ISSAC 2012 SDSC, San Diego, USA 4 7/17/2012

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What is Hydro-cosmology?

+ =

dark matter + gravity ideal gas dynamics + “microphysics” hydrodynamic cosmology

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1990

adiabatic gas dynamics

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1990

adiabatic gas dynamics

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1991

gas dynamics + radiative cooling

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Baryons!

(not the Bolshoi simulation)

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http://enzo-project.org

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http://hipacc.ucsc.edu/html/2010SummerSchool_archive.html

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LECTURE 1 Hydro-cosmology simulations of baryons in the cosmic web *** (Lyman α forest)

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Q: Where are the baryons? A: In the IGM mostly

Cen & Ostriker (1999) IGM

ISSAC 2012 SDSC, San Diego, USA 13 7/17/2012

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Observing the intergalactic medium in quasar absorption line spectra

Source: M. Murphy

Lyman α forest

ISSAC 2012 SDSC, San Diego, USA 14 7/17/2012

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Kirkman & Tytler (1997)

High Resolution Spectrum

virtually every absorption line is H Ly α at a different redshift along the LOS

ISSAC 2012 SDSC, San Diego, USA 15 7/17/2012

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Physical Origin of the Lyman Alpha Forest

Cen et al. 1994, Zhang et al. 1995, Hernquist et al. 1996

  • intergalactic medium

exhibits cosmic web structure at high z

  • models explain
  • bserved hydrogen

absorption spectra

N=1283 Zhang, Anninos, Norman (1995) 5 Mpc/h

“The Cosmic Web”

ISSAC 2012 SDSC, San Diego, USA 7/17/2012

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Ly α absorption directly probes DM distribution

Zhang et al. (1998)

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Cosmology from the Ly α Forest

  • What is measured
  • The standard model
  • Observations vs. simulations I:

– spectacular agreement at the ~10% level

  • DM power spectrum estimation
  • Observations vs. simulations II:

– discrepancies at the 1-2% level

ISSAC 2012 SDSC, San Diego, USA 18 7/17/2012

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The Standard Model

  • Your favorite cosmological model (Ωdm, Ωb , ΩΛ,

H0, σ8, ns)

  • IGM of primordial H and He photoionized by

homogeneous but evolving UVB due to GALS and QSOs (JUVB(z))

  • Ly α forest due to optically thin absorption in

highly ionized gas in intergalactic filaments tracing the DM distribution

  • LLS and DLAs due to optically thick absorption in

denser ionized gas in halos

ISSAC 2012 SDSC, San Diego, USA 19 7/17/2012

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Kirkman & Tytler (1997)

What is Observed

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And hundreds more…

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Simulated Spectra and Fitting

Zhang et al. (1997)

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Observations vs. Simulations I.

Remarkable Agreement on Line Statistics

<b> = 23 σ = 14

Zhang, Anninos, Norman (1995) Kirkman & Tytler (1997)

23 7/17/2012

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What is a Ly α Forest Absorber?

Zhang, Anninos, Meiksin & Norman (1998)

LAF

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What is a Ly α Forest Absorber?

Zhang, Anninos, Meiksin & Norman (1998) Z=3

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What is a Ly α Forest Absorber?

  • Sheet or filament of low
  • verdensity relative to

the local mean

  • Not gravitationally

bound in 3D

  • Unbiased WRT to dark

matter

  • Photo-ionized gas at

~104 K

  • D ~ λJeans ~ 100 kpc

Zhang, Anninos, Meiksin & Norman (1998) λJeans λJeans

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Resolving the Ly α Forest

Bryan, Machacek, Anninos, Norman (1999)

  • Observed linewidths

reflect

– Thermal broadening – Hubble broadening (redshift, LOS, and NHI dependent) – Possibly turbulent broadening

  • Simulated linewidths

reflect above plus

– Numerical resolution broadening

ISSAC 2012 SDSC, San Diego, USA 28 7/17/2012

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Higher resolution simulations predict lines that are too narrow

Bryan et al. (1999)

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Higher resolution simulations predict lines that are too narrow

  • Possible reasons

– Cosmological model wrong – UV background model wrong – Box too small (large scale power missing) – Missing heat sources (He II reionization, X-rays, …) – Missing turbulent broadening (galactic winds?) – Magnetic support?

13 years later, this discrepancy has not been resolved Opportunity for a fundamental contribution

ISSAC 2012 SDSC, San Diego, USA 30 7/17/2012

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N=10243 L = 80 Mpc

Baryon Overdensity, z=3

Jena et al. (2005)

  • 40 fully hydrodynamic simulations* varying

– Cosmological parameters – Box size – Numerical resolution – UV background intensity – Extra heating put in by hand

  • Sensitivity analysis and uncertainty

quantification

  • ObservationsConcordance model @z=1.95

*Data available at http://lca.ucsd.edu/data/concordance/

ISSAC 2012 SDSC, San Diego, USA 31 7/17/2012

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Sensitivity analysis and uncertainty quantification

  • Derive simple parametric fits that connect key inputs to
  • utput
  • Key inputs

– σ8: amplitude of matter fluctuations – γ912: normalized HI photoionization rate – X228: normalized HeII photoheating rate – L: simulation box size – C: cell resolution

  • Key outputs

– <F>=exp(-τeff): mean transmitted flux – bσ: median Doppler width – P-2, P-1.5, P-1: flux power at log k=10-2, 10-1.5, 10-1 s/km

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Flux Power

) (

  • f

FT 1D is ) ( ); ( * ) ( ) ( spectrum for flux mean is ; ) ( ) ( υ δ δ δ δ υ υ δ

f f f f f f

k k k k P f f f f = − ≡

P-2 P-1.5 P-1 Jena et al. (2005) SIMS OBS

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Table of Simulations

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Table of Simulations, cont’d

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Scaling Relations

before scaling after scaling Jena et al. (2005)

τeff bσ

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Findings

  • After scaling out boxsize and

resolution effects, a wide range of σ8 (0.8< σ8 <1.1) fit

  • bservations (<F>, bσ, P-1) by

adjusting γ912 and X228

  • Using only <F>, bσ, P-1 cannot

uniquely determine σ8, γ912, X228 because bσ and P-1 are correlated

  • Using <F> to fix γ912, then σ8

and X228 degenerate

Jena et al. (2005)

ISSAC 2012 SDSC, San Diego, USA 37 7/17/2012

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Findings (cont’d)

  • Can potentially remove degeneracy using large scale

flux power P-2

  • This was not explored in Jena+(2005)

– box sizes too small – observational uncertainties at low k

  • Based on scalings, need at least 100 Mpc boxes and

at least 50 kpc resolution20003 but preferably 25 kpc40003

  • Comparable to largest N-body simulations, but

without the need to resolve halo substructure

– Eulerian simulations on uniform grids are adequate

ISSAC 2012 SDSC, San Diego, USA 38 7/17/2012

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a 40963 hydro-cosmology simulation

L=614 Mpc, Cell=150 kpc

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  • Key ansatz:
  • Where bias b(k) is determined from hydro simulations

(Croft et al. 1998, 2002)

  • Difficulty with SDSS spectra is that lines are not resolved,

and therefore PF(k) needs to be corrected for many systematics errors

– Continuum level – Metal line contamination – High column density absorbers

  • In practice, b(k) is estimated on large scales from non-

hydrodynamic simulations of the LAF that model the absorption phenomenologically

  • UPSHOT: lots of systematic uncertainties

) , ( ) ( ) , (

2

z k P k b z k P

M F

=

Estimating P(k) from SDSS Quasars

McDonald et al. (2005)

  • - Noise
  • - UVB fluctuations

ISSAC 2012 SDSC, San Diego, USA 41 7/17/2012

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  • Revisit Jena et al. (2005) suite of simulations with

more analysis on the effect of box size on LAF

  • bservables, incl. PF(k)
  • All parameters except L kept constant (incl.

resolution)

  • Bigger box means:

– More total power – Higher peak densities – Higher peculiar velocities – Hotter gas

Observations vs. Simulations II.

Tytler et al. (2009)

ISSAC 2012 SDSC, San Diego, USA 42 7/17/2012

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Effect of Box Size

Tytler et al. (2009) IN: 1D Matter Power OUT: 1D Flux Power 76.8 Mpc

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Effect of Box Size

Tytler et al. (2009)

  • Simulated spectra are

visibly different for given path length

  • As L increases:

– Deeper absorption – Longer gaps – Wider lines

L L/2 L/4 L/8 L/16 L/32

ISSAC 2012 SDSC, San Diego, USA 44 7/17/2012

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Have we converged?

  • Largest box has

– Converged <F> – Essentially converged for PM(k) and PF(k) – Approaching convergence for f(b), f(NHI)

10243

ISSAC 2012 SDSC, San Diego, USA 45 7/17/2012

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Does it agree with observations?

  • Mean flux, line

widths can be made to agree to 5% for suitable choices of parameters

  • Flux power

underestimated

  • n large scales by

50-100%

ISSAC 2012 SDSC, San Diego, USA 46 7/17/2012

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Baryon acoustic oscillations in the Lyman alpha forest

  • r

What can intergalactic gas tell us about dark energy?

Michael L. Norman Pascal Paschos Robert Harkness SDSC and UCSD

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Standard rulers to measure dark energy

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Baryon Acoustic Oscillations (BAO) in the Cosmic Microwave Background

(148 Mpc)

ISSAC 2012 SDSC, San Diego, USA 50 7/17/2012

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BAO: Origin of Standard Ruler

Overdense perturbations launch a spherical acoustic wave in the photon-baryon fluid which moves at speed c/sqrt(3) in a frame comoving with the expanding universe

rec

t c D 3 =

Eisentstein & Bennett Physics Today 2008

ISSAC 2012 SDSC, San Diego, USA 51 7/17/2012

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Evolution of Point Perturbation

Eisentstein & Bennett Physics Today 2008

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BAO in Galaxy LSS

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Detection of BAO in SDSS luminous red galaxy LSS (Eisenstein et al. 2005)

Galaxy 2–pt correlation function Existence proof

  • f BAO technique

ISSAC 2012 SDSC, San Diego, USA 54 7/17/2012

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Baryon Oscillation Spectroscopic Survey (BOSS)

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BAO in the Ly α Forest

  • Not yet detected
  • BAO method more powerful at higher redshift

where survey volumes are larger

  • BAO modes are long wavelength (150 Mpc) and

in the linear part of the CDM spectrum

  • Ly α absorption arises near mean density of the

IGM and should show BAO modulation with minimal redshift space distortion

  • Large numbers of absorbers per LOS, and large

number of quasars makes for a very large statistical sample

ISSAC 2012 SDSC, San Diego, USA 56 7/17/2012

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Simulating BAO in the Lyman Alpha Forest

Technical Difficulty: Range of Scales

  • Wavelength of BAO is 150 Mpc

– Need a box at least 4 x this to contain enough modes

  • Absorption filaments are 100 Kpc thick
  • Ncell=4 x 150,000 Kpc/100 Kpc = 6000
  • Need 3D grid of size 60003

– 216 BILLION CELLS – 216 BILLION DARK MATTER PARTICLES

ISSAC 2012 SDSC, San Diego, USA 57 7/17/2012

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Simulation Campaign

Grid Box size (Mpc) Cell size (kpc) ICs 10243 614 600 WMAP5 no BAO 20483 307, 614 150, 300 WMAP3 WMAP5 40963 614 150 WMAP5

ISSAC 2012 SDSC, San Diego, USA 58 7/17/2012

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40963 = 68.7 billion cells and particles 16,384 processors 2 million CPU-hrs NICS Kraken 614 Mpc ENZO Hydrodynamic Cosmology code

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Correlation Analysis:

5,000 random lines-of-sight ~12.5 million pairs

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Flux autocorrelation 20483

Log(NHI)>16 Log(NHI)<16 All lines

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Flux cross-correlation 20483

All lines

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Flux cross-correlation 20483

Log(NHI)>16 Log(NHI)<16 All lines

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Cross-correlation of matter properties along LOS

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Findings and Implications

  • Detecting the BAO in the Lyman alpha forest is

feasible

  • based on synthetic observations of fully

hydrodynamic simulations

– Signal is statistically significant in flux cross- correlation but not in the auto-correlation – Higher column density systems show signal better, but are rarer and hence have higher statistical error – Signal more sensitive to spectroscopic resolution than numerical resolution of simulation

ISSAC 2012 SDSC, San Diego, USA 68 7/17/2012

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Future Simulation Work

  • Need to understand why auto-correlation

signal is so weak (signal should be there!)

– Redshift space distortion? – Masking by high column systems?

  • Need to investigate reality of satellite peaks in

cross-correlation

  • Quantify effects of

– spatial resolution (40963) – redshift evolution – a variety of astrophysical effects

ISSAC 2012 SDSC, San Diego, USA 69 7/17/2012