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### No evidence for departure from scale-invariance n=1, dn/dlnk=0

### No evidence for departure from scale-invariance n=1, dn/dlnk=0

Cosmology result

On simulation type

(in analysis, we marginalized over the differences between 3 Cen simulations)

Direct PCA analysis and power spectrum analysis of SDSS data agree, and agree with HIRES results.

Evolution of mean flux consistent with external constraints

No feature at z=3.2

parameters

True cosmological

parameters

Theory (simulations)

Observations

Statistics (power spectrum)

Statistics (power spectrum)

Compare (chi^2)

Scales of various LSS probes

The Ly forest is great for determining the running of the spectral index, ,

because it extends our knowledge to small scales

We only report an amplitude and slope no band powers

(out of date figure by

Max Tegmark)

Constraints in the natural LyaF plane from WMAP, minimal model, with and without running

3-fold reduction in errors on alpha_s

Very large running ruled out

Pre-SDSS LyaF power spectrum measurements: dn/dlnk=0

- Croft et al. (1999)
19 low resolution spectra

- McDonald et al. (2000)
8 Keck/HIRES spectra

- Croft et al. (2002)
30 Keck/HIRES, 23 Keck/LRIS spectra

- Kim et al. (2004)
27 VLT/UVES spectra

SDSS Data dn/dlnk=0

3300 spectra with zqso>2.3 (DR3 has 5767)

redshift distribution of quasars

1.4 million pixels in the forest

redshift distribution of Ly forest pixels

Measured Power dn/dlnk=0

- 2(k) = π-1 k P(k)
(0.01 s/km ~ 1 h/Mpc)

- Colors correspond to redshift bins centered at z = 2.2, 2.4, …, 4.2 (from bottom to top)
- 1041<rest<1185 Å
- Computed using optimal weighting
- Noise subtraction
- Resolution correction
- Background subtraction using regions with rest>1268 Å
- Error bars from bootstrap resampling
- Code tested on semi-realistic mock spectra
- HIRES/VLT data probes smaller scales
- Computationally only modestly challenging

Fractional Errors dn/dlnk=0

- Lines connect the fractional errors on PF(k) points
- Equivalent to an overall amplitude measurement to +-0.6%
- Logarithmic slope measurement to +-0.006

Noise Power dn/dlnk=0

- Ratio of noise power to signal power
- Important to subtract accurately, especially on small scales (in the future we won’t need noise subtraction because can cross-correlate multiple exposures)

Residual Noise Power dn/dlnk=0

- Power in measured from differences between exposures of the same quasar
- Should be zero
- Actually consistent with a 16% underestimate of the noise subtraction term
- Probably due to error in initial “gain”, maybe some sky subtraction noise

Bootstrap error estimates dn/dlnk=0

- Bootstrap resampling by quasar
- Tested using mock spectra
- Diagonal errors reasonably close to Gaussian

Resolution test dn/dlnk=0

- W2(k R) =
exp[-(k R)2]

I measured the power in the sky spectra near the 5577 Å line (a delta function), and divided by the resolution estimate.

Background Contamination dn/dlnk=0

- The top set of lines shows the Ly forest power
- The bottom set of lines shows the power in the region 1268<rest<1380Å

Background Fraction dn/dlnk=0

- Probably mostly metals (CIV), but not all.
- Error bars starting at zero show error on the forest power.

Difference Between two Background Estimates dn/dlnk=0

- Difference in power between the regions 1268<rest<1380Å and 1409<rest<1523Å

Our Simulations dn/dlnk=0

- Predict PF(k) using simulations of a large grid in parameter space and compare directly to the observed PF(k).
- Allow general relation PF(k) = f[PL(k)] (but only amplitude, slope, and curvature of PL(k)], no band powers).
- IGM gas in ionization equilibrium with a not necessarily homogeneous UV background (still assuming homogeneous reionization).
- Assume IGM not arbitrarily badly disturbed by feedback from galaxies (but allow for some winds).
- Fully hydrodynamic simulations near the best-fit cosmological model are used to calibrate approximate hydro-PM simulations which are used to explore parameter space.
- Marginalize over temperature density relation parameters, T=T0(1+)-1, mean absorption level, reionization history, etc.

HPM simulation grid dn/dlnk=0

Nuisance parameters dn/dlnk=0

Errors +-0.01 on both parameters if modeling uncertainty is ignored:

Noise/resolution

Mean absorption

Temperature-density

Damping wings

SiIII

UV background fluctuations

Galactic winds

reionization

Best fitted model dn/dlnk=0

- 2 ≈ 185.6 for 161 d.o.f.
- A single model fits the data over a wide range of redshift and scale
- Wiggles from SiIII-Ly cross-correlation
- Helped some by HIRES data

Theory now includes: dn/dlnk=0

- Rudimentary galactic superwinds (known to exist in starburst galaxies and LBGs)
- Ionizing background fluctuations from quasars
- Damped and lyman limit systems, which are not well modeled in simulations

Fluctuations in the ionizing background dn/dlnk=0

- Place quasars with a given luminosity function and lifetime in dark matter halos in a large (320 Mpc/h - Bode & Ostriker) N-body simulation (also try galaxies).
- Compute the radiation field produced by the sources, including attenuation by the IGM. (Uros Seljak)
- Fluctuations can be large at high redshift where the attenuation length is short.

Fluctuations in ionizing background dn/dlnk=0

Attenuation length is rapidly

decreasing with redshift,

so effect can be large at z>4,

negligible at lower redshifts

Fluctuations in ionizing background dn/dlnk=0

Correlation of galaxies with density leads to coherent fluctions - suppression of power

Galactic winds heat IGM to 100,000K and pollute IGM with metals

Temperature maps

No wind

wind

Cen, Nagamine, Ostriker 2004

Strong wind versus no wind simulations metals

Winds have no effect after simulations have been adjusted for temperature change

This is not conclusive and more work is needed to investigate other possible wind models

Effectively metals no effect from winds on the power spectrum

Damped and lyman limit systems metals

- When density of hydrogen is high photons get absorbed and do not ionize hydrogen (self-shielding)
- Simulations generally cannot simulate this accurately
- We have measurements of the number density of these systems as a function of column density and redshift
- We place these systems into densest regions of simulations
- Damping wings (Lorenzians) wipe out a large section of the spectrum
- This adds long wavelength power, removing it makes spectrum bluer
- Important effect which was not previously estimated

Can determine power law slope of the growth factor to 0.1 metals

Mandelbaum etal 2003

Comparison with theory (first try) metals

- Curves from simulations
- Fitted parameters: Amplitude and slope of the primordial power spectrum, mean absorption level, and temperature-density relation for the gas
- 2 ≈ 192 for 106 degrees of freedom!

SiIII-Ly metals cross-correlation bump

- SiIII absorbs at 1207 Å, corresponding to a velocity offset 2271 km/s
- Vertical line at 2271 km/s
- No other obvious bumps out to about 7000 km/s
- Dashed line shows
0.04 F(v-2271 km/s)/ F(0)

Best fitted model metals

- 2 ≈ 185.6 for 161 d.o.f.
- A single model fits the data over a wide range of redshift and scale
- Wiggles from SiIII-Ly cross-correlation
- Helped some by HIRES data

Self calibration metals

Errors +-0.01 on both parameters if modeling uncertainty is ignored:

Noise/resolution

Mean absorption

Temperature-density

Damping wings

SiIII

UV background fluctuations

Winds

reionization

Model uncertainties metals

If potential systematic errors were ignored, errors would be a factor of 5 smaller!

Model uncertainties metals

Uncertainties in the estimate of the noise and resolution of the SDSS data are allowed for

Model uncertainties metals

Evolving cross-correlation between Lyman-alpha and SiIII absorption is included in the model (no change at this point)

Model uncertainties metals

An evolving relation between temperature and density is included in the model (dotted line shows previous case)

Model uncertainties metals

UV background fluctuations are included in the model

Model uncertainties metals

Damping wings add power on large scales

Model uncertainties metals

Fully hydrodynamic simulations include three different treatments of energy and metal feedback from galaxies

Model uncertainties metals

Uncertainty in extrapolation of results from small-box simulations to larger scales

Model uncertainties metals

Redshift evolution of the mean level of absorption is assumed to follow a power law in effective optical depth

Model uncertainties metals

The overall normalization of the mean level of absorption is the most important nuisance parameter

Model uncertainties metals

The order of adding parameters matters. Here we include only uncertainty in the mean absorption level

Cosmological parameters metals

- Observations:
- WMAP
- SDSS LyaF
- HIRES LyaF (McDonald et al. 2000 observations)
- SDSS galaxy clustering (Tegmark et al. 2003)
- SDSS galaxy-galaxy lensing determination of bias (Seljak et al. 2004)
- SN1a (Riess et al. 2004)

- Parameters:
- Always:
- Sometimes:

- MCMC to generate probability distributions (Alexey Makarov)

3-fold reduction in errors on alpha_s

Very large running ruled out

Correlations with optical depth dn/dlnk=0

Basic six parameter model dn/dlnk=0

Basic six parameter model dn/dlnk=0

Time evolution of equation of state dn/dlnk=0

Individual parameters very degenerate

Time evolution of equation of state dn/dlnk=0

- w remarkably close to -1
- Robust against adding more terms
- Best constraints at z=0.3
- Lya helps because there is no evidence for dark energy at z>2

w is correlated with r dn/dlnk=0

Parameter dependence of the power spectrum at z=4 dn/dlnk=0

Early reionization leads to less small-scale power (more smoothing - Gnedin & Hui).

High-z structure formation dn/dlnk=0

- Primordial power spectrum constraint
- Mean level of absorption/ionizing background strength as a function of z
- Ionizing background fluctuations
- Smoothing (“Jeans”) scale of IGM
- Temperature-density relation of IGM
- Metal correlations
- Galactic winds
- Signatures of inhomogeneous reionization?
- Other?

Remaining to be done for power spectrum cosmology dn/dlnk=0

- Winds from galaxies (better)
- Inhomogeneous reionization (thermal history)
- Alternative hydro codes
- Anything else?

Is the result correct? dn/dlnk=0

To spoil the result the possible systematic must have very specific properties:

Must boost power on large scales in such a way to still give consistent slope derivative (ie, the results are consistent on large and small scales) and change slope and amplitude in a very specific way

Splits by redshift and scale give consistent results (one may imagine the systematic to be significantly redshift dependent between z=2-4 and to be more important on large or small scales); we see the same power spectrum

Ongoing/Future dn/dlnk=0

- SDSS is an enormous source of information.
- More spectra
- Bispectrum
- Correlation between absorption in pairs of quasars
- Evolution of mean absorption level, PDF
- Metal correlations
- Lyman-beta auto/cross correlation

- More high resolution spectra
- 3D observing programs (baryon wiggles?)