HOW FEASIBLY CAN WE DISTINGUISH MODELS OF THE EOR WITH UP AND - PowerPoint PPT Presentation

HOW FEASIBLY CAN WE DISTINGUISH MODELS OF THE EOR WITH UP AND COMING EXPERIMENTS? TOM BINNIE IMPERIAL COLLEGE LONDON

Who am I ? https://arxiv.org/abs/1903.09064

Talk Plan Intros to • The EoR • 21cm • Telescope • Bayesian Statistics • Toy EoR models • Better EoR models

The Epoch of Reionisation • The most recent phase change of the Universe. • Current observational techniques probe z ~ 1100 and z ~ 7. • Up and coming Telescopes e.g. LOFAR, HERA and SKA aim to improve this.

Current EoR Probes • Planck CMB optical depth (Planck Collaboration XLVII 2016) τ = ∫ 𝑜 𝜏 𝑒𝑚 τ = 0.058 ± 0.012

̅ ̅ Current EoR Probes -QSOs - Gunn Peterson Trough (z=5.9) (McGreer, Mesinger & D’Odorico 2015) – half gaussian 𝑦 *+ = 0.06, σ = 0.05 - Red Ly- 𝛽 Damping Wing (z=7.08) (Greig et al. 2017) 74.89 𝑦 *+ = 0.4 34.56 (2σ).

The 21cm Signal • the electron's spin-flip emission from a Hydrogen atom . < => 𝑜 9 = 3𝑓 ? @ A B 𝑜 4 • Rayleigh-Jeans approximation + F G H 𝑈 D ≈ 6? @ I

The 21cm Signal • We write 𝑈 D in terms of the optical depth 𝑈 D = 𝑈 J − 𝑈 LMD 𝜐 I (1 + 𝑨) And substitute (Furlanetto, Oh & Briggs 2006)

The 21cm Signal – milestones • 200 > z > ~50 - As the universe expands, concentrations of particles decrease – gas and T spin cool adiabatically • z < ~50 – collisional coupling stops à T spin returns to equilibrium with T CMB • z? - First stars cause a resonant scattering of Ly- 𝛽 photons (The (Loeb & Furlanetto 2012) Wouthuysen-Field effect)

The 21cm Signal – milestones • z > 10 - Brightness temperature dictated by T spin fluctuations • z ~ 10 – ‘post heating regime’ à T spin >> T CMB • z ~ 6 Reionisation is complete 𝑦 *+ à 0) ( ̅ (Loeb & Furlanetto 2012)

Epoch of Heating Post Heating Finish First Stars T spin à T CMB (Loeb & Pritchard 2012)

Experiments • Three Telescopes • Modelled with 21cmSense (Pober 2014) • Assumed all foregrounds can be constrained to the wedge • Assumed Baselines added coherently • Possible Noise reduction à increase integration time t à vary the basslines (~ i ) Figure credit (Greig, Mesinger, Koopmans 2015)

LOFAR-48 • Collecting area 35,762 m 2 • 214 Independent UV bins • 13 Hours of published data (Patil et al. 2017)

SKA-512 • 492 602 m 2 in the central 296 stations (left) • 87160 independent uv bins

HERA • Configurations - 19, 61 (left), 127, 217, 331 (right), 469 • Collecting area (for 331) à 50 953 m 2 • Currently running with 91 Dipoles • Only 25 uv bins

Intro to Bayesian Statistics …Or ℒ U 𝒶 = 𝒬 𝑞( 𝜘|𝐸, ℳ) • 21CMMC is a parameter estimation code… (with uniform priors) à 𝒬 ∝ ℒ

Intro to Bayesian Statistics • Parameters are estimated via MCMC – Markov Chain Monté Carlo • Basic example (Metropolis algorithm): Choose starting point (i) Guess trial point (ii) Accept if ℒ new > ℒ old Repeat

Bayesian Model Selection we want 𝒶 = 𝑞(𝐸|𝑁) – the Bayesian Evidence - Conventionally t ricky to calculate

NE NEST STED SA SAMPLING NG Evidence easily calculated à Nd integral becomes 1d X = fraction of prior volume

Nested Sampling - We use Multinest (Feroz, Hobson et al. 2006) Iso-likelihood contours à Ellipsoidal rejection sampling à Solves Multi-modal likelihoods

Bayesian Model Selection – The Bayes Factor The Jeffreys’ Scale (i) Strong – ℬ 96 > 150 model 1 outperforms model 2 objectively. (ii) Moderate – 10 < ℬ 96 < 150 models ‘likely’ to be distinguishable by this method - Be careful! (iii) Weak – ℬ 96 < 10 models are likely to be indistinguishable by this method

The Savage-Dickey Density Ratio • By ‘nesting’ parameter Θ ∗ • The odds our model is better at Θ = Θ ∗

The State of the Art - 21CMMC (Greig, Mesinger et al. 2015) • Semi-numerical simulation (21cmFAST) • In brief - the Zel’dovich approximation applied to a linear density field realization - Ionising photons are compared to the number of baryons in a given region

The State of the Art - 21CMMC (Greig, Mesinger et al. 2015)

TH THE STATE TE OF TH THE ART T - 21C 21CMMC (GRE REIG, MESINGER R ET AL. 2015) 2015) • Global inside-out Reionisation (3 parameters) (FZH - Furlanetto, Zaldariaggan, Hernquist 2004) 𝜂 - the ionising efficiency of galaxies. 𝑆 mfp – mean free path of ionising photons log10[Tvir ] - the minimum virial temperature for star-forming galaxies. • Excursion set formalism applied to reionisation bubbles

x 9 z{ • 𝑔 Gpqq = 𝑛 z| 𝑒𝑛 r s ∫ Fuw M tuv • Iterated from R mfp to Pixel size • Post-heating regime Ts >> TCMB • Neutral fraction is counted

21CMMC (blue) and Multinest (red) agree

Toy Models • Defined by scale and morphology – based on two models: • FZH (as in 21cmmc, global inside-out) • MHR (local outside-in) – 2 parameters Miralde-Escude, Haenelt, Rees (1999) • ‘i’th pixel defines neutral fraction • Underdensity threshold 𝜀 ~ > 𝜀 pixel

Toy Models + Mathematical Inversions – FZHinv (global outside-in) x Fuw 1 𝑛 𝑒𝑜 M tuv 1 𝑛 𝑒𝑜 𝑔 Gpqq = • 𝑒𝑛 𝑒𝑛 𝑔′ Gpqq = • 𝑒𝑛 𝑒𝑛 𝜍 M 𝜍 M Fuw M tuv 4 ‘

Toy Models + Mathematical Inversions Density Field Filters – MHRinv (local Inside-out) 𝑘 = 𝑂 …~†‡q − 𝑗 Over density threshold 𝜀 ‰ < 𝜀 pixel Gives pixel as ionised

Toy Models + Density Field Filters • Makes MHR and MHRinv Global models • Possibility of third parameter R - (top hat filter radius)

Toy Models - What physics do they capture? FZH (global in-out) - Dense IGM regions form stars - UV radiation dominates large regions MHR (local out-in) - Dense IGM regions recombine fast - UV radiation background eventually percolates Reality will be a combination of the two Other toy models test the methodology

Dotted line represents Inverse model

How do they compare in BMS? Bayes Factors per Model LOFAR-48 > = Global red = outside-in + = Local blue = inside-out

SKA > = Global red = outside-in + = Local blue = inside-out

HERA-331 > = Global red = outside-in + = Local blue = inside-out

Analysing Parameters of Models - SDDR • Cross checks our algorithm • Quantitatively reveals simulation redundancies

Quantifying Inference - Observational Priors are input as Neutral fraction checks Negligible deviation in blue!

Further Model Testing (in progress) • Newer prescriptions of 21CMMC - Coeval cubes à lightcones (Greig, Mesinger 2018b) - Inhomogeneous recombinations (Sobacchi, mesinger 2014) - The Epoch of Heating à (Greig, Mesinger 2018a) - Including UV luminosity functions (Park, Greig, Mesinger, Gillet 2018)

Further Model Testing (in progress) • X-ray heating Parameterisation Introducing E 4 - Minimum Energy of EoR X-rays 𝑀 —˜6?‡™ - soft band X-ray Luminosity M turn incorporates the duty cycle of Galaxies 𝑈 𝑇𝑞𝑗𝑜 no longer ignored

Further Model Testing (in progress) • UV Luminosity Function Parameterisation 𝑇𝐺𝑆~ 𝑁 ∗ How much stuff is in the galaxy forms star? 𝑀 ›™ 𝛽 And over what time? 𝑢 ∗

Breaking degeneracies • Exciting time for astrophysics with JWST, ELT, SPICA on the horizon • Current approximations work for ‘Ensemble of Galaxies’ • IR Luminosity Function Parameterisation (in progress) • How much do Galaxies really contribute to reionization?

The Future • Decisive disfavouring of Toy EoR models will be very feasible with HERA and The SKA (assuming foregrounds can be constrained to the wedge). • Model Selection on real EoR models • Quantifying the inference of Luminosity Functions • Pinning down 𝑔 ‡JG

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