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## John Wheeler

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**The non-linear power spectrumof the Lyα**forest.Collaborators: Andreu Arinyo-Prats (PhD thesis), Matteo Viel, Renyue Cen Jordi Miralda Escudé ICREA, Institut de Ciències del CosmosUniversity of Barcelona, CataloniaTrieste, May 12th 2015**John Wheeler**“The real reason universities have students is to educate the professors” 1911-2008**Patrick McDonald**“The Lyα forest ought to be like the CMB: a theory predicting the power spectrum accurately that can be compared with observations, with error bars that are believable.” PhD student at Upenn and OSU 1997-2001**Lyα absorption spectra in photoionized medium:fluctuating**Gunn-Peterson optical depth Without thermal broadening:**Bias factors of the Lyα forest**• In every quasar spectrum pixel: • On small scales, the variations in δF are large and strongly affected by non-linear evolution and complex physical processes. But the 3-D average over a large scale should behave linearly. • Galaxy number density fluctuation in redshift space: • Same for Lyα forest, except that a peculiar velocity gradient bias factor different from 1 is induced by the non-linear relation :**Whatweexpect: linear theory**• For a single Fourier mode, peculiar velocity gradient: • Galaxies: • Lyα forest: • Power spectrum in redshift space: • In one dimension: Kaiser 1987; Hamilton 1998; Croft et al. 1998, 1999, McDonald et al. 2000; McDonald 2003**Physical bias factors**• The transmission bias factors we have defined tell us how transmission varies with δ and η, but F is not zero when there is no gas. The physical bias factors are related to the variations in the absorption effective optical depth. • These bias factors are interpretable as we are used to and reflect the biased distribution of the underlying gas structures in the IGM: a value of 1 means that Lyα absorption varies with the same amplitude as mass density fluctuation.**Simulations in Arinyo-Prats et al. 2015: Gadget-II,**CDMΛ.Ωm=0.3, σ8=0.88, ns=1 (fiducial model) • At a given redshift output, choose one axis as the line of sight and compute simulated Lyα spectra of transmission fraction F along all simulation rows. • Compute 3-D FFT of the F field. • Compute power spectrum PF(k,μk), divide by linear power PL(k) • Fit formula for the non-linear power spectrum (McDonald 2003): Ansatz from perturbation theory:**The μ-dependence of log(D) is very close to a power-law**(why?) PF/PL is nearly flat at a value of k where the non-linear anisotropy just cancels the linear one (all curves of different μ cross each other)**Linear biasfactors**• Density bias factor is nearly flat at ~ 60%. • Velocity gradient bias is close to 1 at z ≈ 2.3 , decreases with z. • β ≈ 1.4 at z ≈ 2.3, decreases with redshift. • There is some dependence on the fitting function, which can only be resolved with more simulations to reduce uncertainties.**Bias factors for different σ8**• Transmission power varies weakly with mass power, so density bias factor is nearly inversely proportional to σ8. • β increases with σ8.**Redshiftevolution**• The redshift evolution is a combination of the effect of changing <F> and the variation of the power spectrum amplitude with redshift. • These two effects fortuitously cancel for the density bias factor, resulting in a constant bτδ.arly inversely proportional to σ8. • β decreases with z owing to the decrease of bτη.**First year results: redshift distortions (Slosar et al.**2011) Clearly detected anisotropy, consistent with Kaiser’s linear formula. • Fitting model: • Also, from quasar-Lyα cross-correlation, β ≈ 1.2. • But continuum fitting distortion effects prevented more reliable fits.**Blomqvist et al. 2015: DR11 data**withanimprovedmethodtodealwith continuum fittingdistortion. These linear bias factors agree with our results for a model consistent with Planck, although with substantial errors in the theory prediction at the level of 10-20% that can only be improved from the analysis of more simulations on large boxes.**Conclusions**• We can use numerical hydrodynamic simulations of the Lyα forest to predict the non-linear form of the transmission power spectrum and the values of the linear bias factors. • These can be measured from observations and compared to the theoretical predictions. • At the moment we have only made a preliminary comparison of the linear bias factors, and they are consistent but still with large errors. • We should be able to greatly improve the reliability of the theoretical predictions for the Lyα forest power spectrum, and measure it in detail from BOSS, eBOSS and upcoming surveys (WEAVE, 4-MOST, DESI), as well as the sample of luminous quasar pairs observed at high S/N for very small scales.