Complete Reionization Constraints from Planck 2015 Polarization

Chen He Heinrich University of Chicago

Oct. 2016 UC Berkeley - Cosmology Seminar

Heinrich, Miranda & Hu arXiv:1609.04788

Outline• Intro: Probing reionization with CMB polarization

• Advantages of principal components (PCs)

• Probing high-z ionization with Planck 2015

• Fast model testing with our effective likelihood code

Image credit: https://en.wikipedia.org/wiki/Reionization

Recombination

Inflation

z ~1000

z ~10

z = 0

e� e�

CMB

Reionizatione�

• Astrophysical interest

• Cosmology: (optical depth) error propagates to other cosmological parameters

• leading source of error for neutrino mass from gravitational lensing

• growth of structure and cosmic acceleration [Hu & Jain 04]

Reionization

Image credit: https://en.wikipedia.org/wiki/Reionization

⌧

• Astrophysical interest

• Cosmology: (optical depth) error propagates to other cosmological parameters

• leading source of error for neutrino mass from gravitational lensing

• growth of structure and cosmic acceleration [Hu & Jain 04]

Reionization

Image credit: https://en.wikipedia.org/wiki/Reionization

Image Credit: http://www.staff.uni-mainz.de/wurmm /wurm-home/mass-hierarchy.png

⌧

Probes of reionization• Gunn-Peterson effect (in quasar spectra):

conclude that Universe is fully ionized by z=6.

• CMB anisotropies: signatures on the temperature and polarization power spectra.

• Galaxy luminosity function: well measured for z < 8, ~10s of galaxies at z > 9.

• 21cm experiments (underway): map the distribution of neutral hydrogen with redshift. (PAPER, LOFAR, MWA, MITEoR, HERA, SKA …)

Cosmic microwave background (CMB)

angular wavenumber

Image Credit: http://www.esa.int/spaceinimages/Images/2013/03/Planck_CMB

(mean = 2.7K)

temperature anisotropies

Fourier Transform

Temperature power spectrum

101 102 103

l

102

103

104

l(l+

1)C

TT

l/2

⇡[µ

K2]

Cosmic microwave background (CMB)

angular wavenumber

Image Credit: http://www.esa.int/spaceinimages/Images/2013/03/Planck_CMB

101 102 103

l

10�3

10�2

10�1

100

101

102

l(l+

1)C

EE

l/2

⇡[µ

K2]

E-mode polarization power spectrum

CMB photons Thomson scatter with free electrons

⌧ =

Z ⌘

0d⌘0�Tnea

�T

e� e�

e� + � ! e� + �

ne� �

Optical depth:

e�

⌧ =

Z ⌘

0d⌘0�Tnea

1.Suppress anisotropies (both temp. and pol.)

Thomson scattering optical depth

e�2⌧

angular wavenumber

101 102 103

l

102

103

104

l(l+

1)C

TT

l/2

⇡[µ

K2 ]

⌧

101 102 103

l

10�3

10�2

10�1

100

101

102

l(l+

1)C

EE

l/2

⇡[µ

K2 ]

Power spectrum suppressed as ,

temperature power spectrum

Effects of reionization on the CMB

angular wavenumber

E-mode polarization power spectrum

Effects of reionization on the CMB

Quadrupole Anisotropy

Thomson Scattering

e–

Linear Polarization

ε'

ε'

ε

Image Credit: Wayne Hu’s Tutorials

Temperature quadrupole —> polarization

101 102 103

l

10�3

10�2

10�1

100

101

102

l(l+

1)C

EE

l/2

⇡[µ

K2]

E-mode polarization power spectrum

angular wavenumber

Reionization bump

2. Create polarization anisotropies on large scales

0.00

0.05

0.10

0.15

0.20

CMB measurements of ⌧

⌧

WMAP9Planck dust

cleaned

Planck

Planck

Planckw/ LFI

TT+ lensing

w/ HFIWMAP9

WMAP1TE

Outline• Intro: Probing reionization with CMB polarization

• Advantages of principal components (PCs)

• Probing high-z ionization with Planck 2015

• Fast model testing with our effective likelihood code

Standard approach: tanh

0.0

0.2

0.4

0.6

0.8

1.0

1.2

xe(

z)

tanh ML

5 10 15 20 25 30z

0.00

0.02

0.04

0.06

0.08

⌧(z

,zm

ax)

xe(z) =ne

nH

optical depth

simple tanh

ionization fraction

0.0

0.2

0.4

0.6

0.8

1.0

1.2

xe(

z)

tanh ML

fiducial

5 10 15 20 25 30z

0.00

0.02

0.04

0.06

0.08

⌧(z

,zm

ax)

x

fide = 0.15

Our model independent approach: +

X

a

maSa(z)xe(z) = x

fide

optical depth

ionization fraction

(Hu & Holder 03)

Eigenfunctions ranked by contribution to observables

Contribution to from each eigenfunction

~ high vs low z

~ weighted

optical depth

ionization fraction

a = 1

a = 2

⌧

⌧

�2�1

01234

Sa(z

)a = 1

a = 2

a = 3

a = 4

a = 5

10 15 20 25 30z

�0.1

0.0

0.1

0.2

0.3

⌧(z

,zm

ax)

5 10 15 20 25 30 35 40

l

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08l(

l+

1)C

EE

l/2

⇡[µ

K2]

tanh ML

1 PC

5 PCs completely describe E-mode power spectrum

5 10 15 20 25 30 35 40

l

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08l(

l+

1)C

EE

l/2

⇡[µ

K2]

tanh ML

2 PCs

5 PCs completely describe E-mode power spectrum

5 10 15 20 25 30 35 40

l

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08l(

l+

1)C

EE

l/2

⇡[µ

K2]

tanh ML

3 PCs

5 PCs completely describe E-mode power spectrum

5 10 15 20 25 30 35 40

l

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08l(

l+

1)C

EE

l/2

⇡[µ

K2]

tanh ML

4 PCs

5 PCs completely describe E-mode power spectrum

5 10 15 20 25 30 35 40

l

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08l(

l+

1)C

EE

l/2

⇡[µ

K2]

tanh ML

5 PCs

reionization bump matches to cosmic variance precision!

5 PCs completely describe E-mode power spectrum

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

xe(

z)

tanh ML

tanh ML PC

5 10 15 20 25 30z

0.00

0.02

0.04

0.06

0.08

⌧(z

,zm

ax)

Project ionization fraction model onto PCs

5PCs designed for observables, not model reconstruction (remove fiducial)

not well constrained

by data

data reflects better this integrated quantity

ionization fraction

optical depth

Outline• Intro: Probing reionization with CMB polarization

• Advantages of principal components (PCs)

• Probing high-z ionization with Planck 2015

• Fast model testing with our effective likelihood code

⌦bh2,⌦ch

2, ✓MCMC, As, ns

⌧

m1 ,…, m5 LCDM (modify CAMB)PCs

tanh

+(corresponds to step time)

sampled with COSMOMC 10 parameters

Method: Apply MCMC to Planck 2015

Constraints on 5PC

parameters• Constraints on the

PC amplitude in the space of physical models (edge of box)

• First two PCs best constrained, third to fifth still constrained!

• tanh trajectory not favored by data

tanh ML

tanh 68, 95% CL

PC 68, 95% CL

0 0.3

-0.3

0

0.3

-0.3

0

0.3

-0.3

0

0.3

-0.6

-0.3

0

0.6 -0.6 -0.3 0 -0.3 0 0.3 -0.3 0 0.3 -0.3 0 0.3

0 < xe < 1 + fHe

xe(z) = x

fide +

X

a

maSa(z)

CH, Miranda, Hu 2016

Tanh less favoured in PC space

• tanh ML ~2 away from PC mean

−0.1 0.0 0.1 0.2

m1

−0.4

−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

m2

Gaussian

unph

ysic

al

* PC ML vs tanh ML:

CH, Miranda, Hu 2016

�

2�log Like = 5.3

• shift is 1 up

• consequence on cosmo parameters (show as

• what is the origin of higher ?0.02 0.04 0.06 0.08 0.10 0.12 0.14

⌧ (0, zmax)

P(⌧

|dat

a)

tanh

PC

Model

PC

tanh

⌧(0, zmax

)

0.079± 0.017

0.092± 0.015⌧ � shifts by 1

CH, Miranda, Hu 2016

High redshift ionization shifts tau

0 5 10 15 20 25 30

z

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

τ(z

,zm

ax)

tanh ML PC

PC mean

PC 68, 95% CL

Planck 2015

• Standard tanh misses this by assumption of form

2 preference for ionization by z = 15

�

CH, Miranda, Hu 2016

Removing effects of lensing

0 5 10 15 20 25 30

z

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

τ(z

,zm

ax)

tanh ML PC

PC mean

PC 68, 95% CL

Planck 2015 lensing AL marginalized

High redshift ionization is not due to lensing effects

AL

⌧

As

More smoothing

Less initial power

Ase�2⌧

Fixed

goes down

Marginalize over AL

CH, Miranda, Hu 2016

still 2�

High z ionization only found in Planck

• Planck pol —> WMAP pol: preference dropped to 1 • High redshift ionization: origin is Planck polarization (LFI)

�

Data

P15

P13 +WMAP(P)

0.033± 0.016

0.022± 0.018

⌧(15, zmax

)

Extended ionization broadens bump

• PC ML: broader bump —> extended ionization to higher z. • E-mode polarization 8 < l < 20. Tanh fails to pick this out.

5 10 15 20 25 30 35 40l

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

l(l+

1)C

EE

l/2

π[µ

K2]

tanh ML

tanh ML PC

PC ML

High redshift ionization

CH, Miranda, Hu 2016

Sources

• Foregrounds or systematics (Planck 2017 will clarify)

• Possible high redshift reionization sources:

• DM annihilation

• POP II + POP III stars (metal-poor stars), etc …

• Running MCMC vs PC effective likelihood

Outline• Intro: Probing reionization with CMB polarization

• Advantages of principal components (PCs)

• Probing high-z ionization with Planck 2015

• Fast model testing with our effective likelihood code

Effective Likelihood Code

• Easily tests any models of ionization model xe(z) between 6 < z < 30.

• Projection unto PCs:

• Kernel density estimate:

Gaussian kernel (zero mean, covariance a fraction f of the chain covariance)

P (⌧ |data) / LPC [data|m(⌧)]P (⌧)

p ! xe(z) ! m

LPC (data|m) =NX

i=1

wiKf (m�mi)

Example: tanh

• Cutoff due to full ionization by z = 6

• f = 0.14 smoothing suffices for tanh (should work better for models favoured by data)

0.03 0.06 0.09 0.12τ (tanh model)

P(τ|d

ata)

tanhtanh LPC

Gaussian

P (⌧ |data) / LPC[data|m(⌧)]P (⌧)

5min vs 24 hours!

⌧ ! xe(z) ! {ma} ! LPC

CH+16, submitted to PRD

High z ionization: Pop-III stars?

Type of star Metal Content Cooling Host halos

Pop-III Metal-free Molecular hydrogen Minihalos

Pop-II Metal-poor Atomic line emission More massive halos

105 � 106M�

Tanh

Pop-II

Pop-III

Pop-III, self-regulated

Ionization fraction

Miranda, Lidz, CH, Hu 2016

Regularization mechanism needed

plateau from regularization

Tanh

P15 68%, 95% CL

Pop-II

Pop-III

Pop-III, self-regulated

regularization mechanism needed

Miranda, Lidz, CH, Hu 2016

Pop-III, self-regulated

Miranda, Lidz, CH, Hu 2016

Conclusion• We probed reionization using CMB polarization data

• With the principal component analysis, we can extract all information available in the observable

• Planck 2015 polarization data allows us to constrain an additional mode: high redshift polarization.

• Optical depth shifts by 1 (compared to tanh)

• z >15 optical depth preferred at ~ 2

• Use PC analysis!

�

�

Effective Likelihood Code

• Use our effective likelihood code for efficient and unbiased testing of any ionization history models.(tanh: 5min vs 24 hours MCMC ).

• When applied on Planck 2017 polarization data — better constraints on high redshift ionization component.

(Code available on request)

Thank you!

Back-up slides

⌧ = 0.089± 0.014 (WMAP9)

⌧ = 0.075± 0.013 (WMAP9 dust cleaned with Planck 353)

⌧ = 0.078± 0.019 (Planck LFI low l + high l TT )

⌧ = 0.070± 0.024 (Planck TT + lensing)

⌧ = 0.17± 0.04 (WMAP1, TE)

⌧ = 0.055± 0.009 (Planck HFI low l)

⌧CMB measurements of

• shifts up by 1

• consequence on other cosmo parameters

0.02 0.04 0.06 0.08 0.10 0.12 0.14

⌧ (0, zmax)

P(⌧

|dat

a)

tanh

PC

65 66 67 68 69 70 71

H0

0.78

0.80

0.82

0.84

0.86

0.88

�8

PC

tanh

Model

PC

tanh

⌧(0, zmax

)

0.079± 0.017

0.092± 0.015

⌧ �

Parameter shifts

End of Back-up slides