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## Code comparison

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**Code comparison**ENZO Hy Trac’s code Renyue Cen’s code GADGET VERY SOON: ENZO/Trac-only analysis**Code comparison**Blue: Cen Black: Trac Denominator: ENZO**Thermal histories**Red: Cen Black: Trac Green: ENZO Blue: GADGET**Dependence of**Cosmology result On simulation type (in analysis, we marginalized over the differences between 3 Cen simulations)**Mean absorption**Direct PCA analysis and power spectrum analysis of SDSS data agree, and agree with HIRES results.**PCA analysis of QSO spectra**Evolution of mean flux consistent with external constraints No feature at z=3.2**Ly-alpha forest**SDSS quasar spectrum Cen simulation of the IGM (neutral hydrogen) z = 3.7 quasar**Assumed cosmological**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index, , because it extends our knowledge to small scales We only report an amplitude and slope no band powers (out of date figure by Max Tegmark)**Constraints in the natural LyaF plane from WMAP, minimal**model, with and without running**No evidence for departure from scale-invariance n=1,**dn/dlnk=0 3-fold reduction in errors on alpha_s Very large running ruled out**Pre-SDSS LyaF power spectrum measurements:**• 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**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**• 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**• 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**• 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**• 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**• Bootstrap resampling by quasar • Tested using mock spectra • Diagonal errors reasonably close to Gaussian**Error Correlations**Inverted window function Un-inverted window function**Resolution test**• 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**• 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**• Probably mostly metals (CIV), but not all. • Error bars starting at zero show error on the forest power.**Difference Between two Background Estimates**• Difference in power between the regions 1268<rest<1380Å and 1409<rest<1523Å**Our Simulations**• 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.**Nuisance parameters**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**• 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:**• 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**• 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**Attenuation length is rapidly decreasing with redshift, so effect can be large at z>4, negligible at lower redshifts**Fluctuations in ionizing background**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**Neutral hydrogen maps show much less effect**No wind wind**Strong wind versus no wind simulations**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**Damped and lyman limit systems**• 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**Mandelbaum etal 2003**Comparison with theory (first try)**• 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 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**• 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**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**If potential systematic errors were ignored, errors would be a factor of 5 smaller!**Model uncertainties**Uncertainties in the estimate of the noise and resolution of the SDSS data are allowed for**Model uncertainties**Evolving cross-correlation between Lyman-alpha and SiIII absorption is included in the model (no change at this point)**Model uncertainties**An evolving relation between temperature and density is included in the model (dotted line shows previous case)