Your Name and Collaborators Statistical challenges in the Lyman- α forest Andreu Font-Ribera Graphic: Anze Slozar STFC Ernest Rutherford Fellow at University College London In collaboration with Pat McDonald (LBL) and An ž e Slosar (BNL) 1
Redshift Surveys BOSS Ly α forest Underdensity 160k spectra Overdensity 2.0 < z < 3.5 Look back time (billion years) BOSS galaxies 1.3M spectra 0.2 < z < 0.7 Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 2
Redshift Surveys BOSS Ly α forest Underdensity 160k spectra Overdensity 2.0 < z < 3.5 Look back time (billion years) BOSS galaxies 1.3M spectra 0.2 < z < 0.7 Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 3
Outline • Baryon Acoustic Oscillations in the Lyman- α (Ly α ) forest • Introduction to Ly α surveys • BAO results from BOSS Ly α • BAO forecasts for DESI Ly α • Small scale clustering of the Ly α forest • Opportunities (neutrinos, running, warm dark matter) • State of the art (one-dimensional power spectrum) • Statistical challenges (three-dimensional clustering) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 4
The Lyman- α forest Credits: Andrew Pontzen Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 5
The Lyman- α forest 1st step: from observed flux to cosmological fluctuations Observed flux Transmitted fraction 20 flux [10 ! 17 erg s ! 1 cm ! 2 A ! 1 ] Method 1 Method 2 15 f q ( λ ) = C q ( λ ) F q ( λ ) Quasar Continuum x Mean Flux 10 Quasar continuum 5 Absorption redshift Observed wavelength 0 λ = λ α (1 + z ) ! 5 440 460 480 500 520 540 LyaF wavelength (121.6 nm) ! (nm) δ F ( x ) = F ( x ) − ¯ F Flux fluctuations in pixels trace the density ¯ along the line of sight to the quasar F Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 6
Outline • Baryon Acoustic Oscillations in the Lyman- α (Ly α ) forest • Introduction to Ly α surveys • BAO results from BOSS Ly α • BAO forecasts for DESI Ly α • Small scale clustering of the Ly α forest • Opportunities (neutrinos, running, warm dark matter) • State of the art (one-dimensional power spectrum) • Statistical challenges (three-dimensional clustering) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 7
BOSS Lyman- α BAO Two independent ways of measuring the BAO scale A ∼ 70 km s − 1 ∼ 0 . 7 h − 1 Mpc 1˚ Quasar Quasar 1 deg ∼ 70 h − 1 Mpc r Gas Gas r Quasar Quasar Gas Ly α auto-correlation Ly α -quasar cross-correlation Bautista et al. (2017) —— DR12 —— du Mas des Bourboux (2017) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 8
BOSS Lyman- α BAO Two independent ways of measuring the BAO scale Ly α auto-correlation Ly α -quasar cross-correlation Bautista et al. (2017) —— DR12 —— du Mas des Bourboux (2017) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 9
Combined BOSS BAO Dark Energy is now detected from BAO data alone BAO In a flat Λ CDM model Planck Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 10
Outline • Baryon Acoustic Oscillations in the Lyman- α (Ly α ) forest • Introduction to Ly α surveys • BAO results from BOSS Ly α • BAO forecasts for DESI Ly α • Small scale clustering of the Ly α forest • Opportunities (neutrinos, running, warm dark matter) • State of the art (one-dimensional power spectrum) • Statistical challenges (three-dimensional clustering) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 11
Dark Energy Spectroscopic Instrument • 5000 fibers in robotic actuators • 10 fiber cable bundles • 3.2 deg. field of view optics • 10 spectrographs Mayall 4m Telescope Kitt Peak (Tucson, AZ) Readout & Control Increase BOSS dataset by an order of magnitude Scheduled to start in 2019 Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 12
Dark Energy Spectroscopic Instrument • 5000 fibers in robotic actuators • 10 fiber cable bundles • 3.2 deg. field of view optics • 10 spectrographs Mayall 4m Telescope Kitt Peak (Tucson, AZ) Readout & Control Increase BOSS dataset by an order of magnitude Scheduled to start in 2019 Lens in cell, UCL, March 2018 Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 13
Dark Energy Spectroscopic Instrument Planck prediction Acceleration Deceleration Expansion rate Redshift Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 14
Dark Energy Spectroscopic Instrument DESI projections (Font-Ribera++ 2014b) Planck prediction Acceleration Deceleration Expansion rate Redshift Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 15
Outline • Baryon Acoustic Oscillations in the Lyman- α (Ly α ) forest • Introduction to Ly α surveys • BAO results from BOSS Ly α • BAO forecasts for DESI Ly α • Small scale clustering of the Ly α forest • Opportunities (neutrinos, running, warm dark matter) • State of the art (one-dimensional power spectrum) • Statistical challenges (three-dimensional clustering) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 16
Small scale clustering Large scales Small scales Early time 0 1 2 Redshift 5 1100 CMB Lyman- α forest offers a unique window to study small scale clustering CMB Lyman- α Forest Lensing Combined with CMB, it Photometric allows us to study: • shape of primordial P(k) Galaxies Future 21cm Late time • dark matter properties • neutrino mass Spectroscopic Weak Galaxies Lensing 1000 100 Mpc 10 1 Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 17
Small scale clustering Quasar Flux correlations Estimator spectra (P1D or P3D) Hydrodynamical Likelihood simulations Cosmo params Density MCMC (neutrino mass) power spectrum Planck (+ others) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 18
Small scale clustering Quasar Flux correlations Estimator spectra (P1D or P3D) Hydrodynamical Likelihood simulations Cosmo params Density MCMC (neutrino mass) power spectrum Planck (+ others) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 19
Outline • Baryon Acoustic Oscillations in the Lyman- α (Ly α ) forest • Introduction to Ly α surveys • BAO results from BOSS Ly α • BAO forecasts for DESI Ly α • Small scale clustering of the Ly α forest • Opportunities (neutrinos, running, warm dark matter) • State of the art (one-dimensional power spectrum) • Statistical challenges (three-dimensional clustering) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 20
Estimators: 1D P(k) 1D correlations, one skewer at a time (Palanque-Delabrouille et al. 2013) ~ 0.1 h/Mpc Line of sight (1D) wavenumber ~ 2 h/Mpc Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 21
Outline • Baryon Acoustic Oscillations in the Lyman- α (Ly α ) forest • Introduction to Ly α surveys • BAO results from BOSS Ly α • BAO forecasts for DESI Ly α • Small scale clustering of the Ly α forest • Opportunities (neutrinos, running, warm dark matter) • State of the art (one-dimensional power spectrum) • Statistical challenges (three-dimensional clustering) Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 22
Estimators: 3D P(k) Motivation • Good to have an alternative way to study BAO • Constraint cosmology from the Ly α clustering, beyond BAO (DESI Ly α forecasts dominated by P3D, not P1D) 1D analyses have used both FFT / Pseudo-Cl and Maximum Likelihood However, current 3D studies in BOSS/eBOSS only try to measure BAO Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 23
Estimators: 3D P(k) � � 1 L ( � | p ) / det ( C ) − 1 / 2 exp Likelihood-based 2 � t C − 1 � = exp L , d 2 L L ( p ) ' L ( p 0 ) + d L � p i + 1 � p i � p j + ... ⌘ L ( p 0 ) + L ,i � p i + 1 2 L ,ij � p i � p j + ... 2 dp i dp i dp j Optimal Quadratic Estimator L ,i = 1 2 � t C − 1 S ,i C − 1 � � 1 ⇥ C − 1 S ,i ⇤ 2Tr L i � L − 1 p max = p 0 ,ij L ,j , i F ij ⌘ � h L ,ij i = 1 ⇥ C − 1 S ,i C − 1 S ,j ⇤ 2Tr • Can’t evaluate by brute force (roughly a billion correlated pixels) • We need to make controlled approximations for speed • Assume uncorrelated skewers (block-diagonal covariance) • Rotate data into eigenvectors of response matrices • Use special parameterization, change variables later Andreu Font-Ribera - Statistical challenges with the Lyman- ⍺ forest Oxford, April 19th 2018 24
Recommend
More recommend
