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

Intros to

• The EoR
• 21cm
• Telescope
• Bayesian Statistics

Talk Plan

• 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.

• Planck CMB optical depth

(Planck Collaboration XLVII 2016)

Current EoR Probes

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)

̅ 𝑦*+ = 0.434.56

74.89

(2σ).

The 21cm Signal

• the electron's spin-flip

emission from a Hydrogen atom. 𝑜9 𝑜4 = 3𝑓

<=> ?@AB

• Rayleigh-Jeans approximation

𝑈D ≈

+F GH 6?@I

The 21cm Signal

• We write 𝑈D in terms of the optical depth

𝑈D = 𝑈

J − 𝑈LMD 𝜐I

(1 + 𝑨)

And substitute

(Furlanetto, Oh & Briggs 2006)

• 200 > z > ~50 - As the universe

expands, concentrations of particles decrease – gas and T

spin cool

adiabatically

The 21cm Signal – milestones

• z < ~50 – collisional coupling stops à

T

spin returns to equilibrium with TCMB

(Loeb & Furlanetto 2012)

• z? - First stars cause a resonant

scattering of Ly-𝛽 photons (The Wouthuysen-Field effect)

• z > 10 - Brightness temperature dictated

by T

spin fluctuations

The 21cm Signal – milestones

• z ~ 10 – ‘post heating regime’

à T

spin >> TCMB

(Loeb & Furlanetto 2012)

• z ~ 6 Reionisation is complete

( ̅ 𝑦*+ à 0)

Post Heating Finish Epoch of Heating First Stars Tspin à TCMB (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)

• Collecting area 35,762 m2

LOFAR-48

• 13 Hours of published data

(Patil et al. 2017)

• 214 Independent UV bins

SKA-512

• 492 602 m2 in the central 296 stations (left)
• 87160 independent uv bins

• Configurations - 19, 61 (left), 127,

217, 331 (right), 469

• Collecting area (for 331)

à 50 953 m2

• Currently running with 91 Dipoles
• Only 25 uv bins

HERA

Intro to Bayesian Statistics

…Or ℒ U

𝒶 = 𝒬

• 21CMMC is a parameter estimation

code… (with uniform priors) à 𝒬 ∝ ℒ

𝑞( 𝜘|𝐸, ℳ)

• Parameters are estimated via MCMC – Markov Chain Monté Carlo

Intro to Bayesian Statistics

• Basic example (Metropolis algorithm):

Choose starting point (i) Guess trial point (ii) Accept if ℒnew > ℒold Repeat

Bayesian Model Selection

we want 𝒶 = 𝑞(𝐸|𝑁) – the Bayesian Evidence

• Conventionally tricky 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

The Jeffreys’ Scale (i) Strong –ℬ96 > 150

model 1 outperforms model 2 objectively.

(ii) Moderate – 10 < ℬ96 < 150

models ‘likely’ to be distinguishable by this method - Be careful!

(iii) Weak – ℬ96 < 10

models are likely to be indistinguishable by this method

Bayesian Model Selection – The Bayes Factor

The Savage-Dickey Density Ratio

• By ‘nesting’ parameter Θ∗
• The odds our model is better at Θ = Θ∗

• Semi-numerical simulation (21cmFAST)

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

• 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)

• Global inside-out Reionisation (3 parameters)

(FZH - Furlanetto, Zaldariaggan, Hernquist 2004)

TH THE STATE TE OF TH THE ART T - 21C 21CMMC (GRE REIG, MESINGER R ET AL. 2015) 2015)

• Excursion set formalism applied to reionisation bubbles

𝜂 - the ionising efficiency of galaxies. 𝑆mfp – mean free path of ionising photons log10[Tvir ] - the minimum virial temperature for star-forming galaxies.

• 𝑔

Gpqq = 9 rs ∫ Mtuv

Fuw

x

𝑛

z{ z| 𝑒𝑛

• Iterated from Rmfp 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~ > 𝜀pixel

Toy Models

+ Mathematical Inversions – FZHinv (global outside-in) 𝑔

Gpqq =

1 𝜍M

• Mtuv

Fuw

x

𝑛 𝑒𝑜 𝑒𝑛 𝑒𝑛 𝑔′Gpqq = 1 𝜍M

• 4

Mtuv

Fuw

𝑛 𝑒𝑜 𝑒𝑛 𝑒𝑛

‘

Toy Models

+ Mathematical Inversions Density Field Filters – MHRinv (local Inside-out) 𝑘 = 𝑂…~†‡q − 𝑗 Over density threshold 𝜀

‰ < 𝜀pixel

Gives pixel as ionised

+ Density Field Filters

Toy Models

• 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

Other toy models test the methodology Reality will be a combination of the two

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 Heatingà (Greig, Mesinger 2018a)
• Including UV luminosity functions (Park, Greig, Mesinger, Gillet 2018)

Introducing E4 - Minimum Energy of EoR X-rays 𝑀—˜6?‡™

• soft band X-ray Luminosity

𝑈𝑇𝑞𝑗𝑜 no longer ignored

Further Model Testing (in progress)

• X-ray heating Parameterisation

Mturn incorporates the duty cycle of Galaxies

Further Model Testing (in progress)

• UV Luminosity Function Parameterisation

𝑀›™ 𝛽

How much stuff is in the galaxy forms star? And over what time?

𝑇𝐺𝑆~ 𝑁∗ 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

Photo Credit: CSIRO Thanks for Listening! Questions?

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• PRINCETON UNIV. PRESS, PRINCETON, NJ

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