[PPT] - CMB Spectral Distortion Computations using the Greens function PowerPoint Presentation

SLIDE 1

CMB Spectral Distortion Computations using the Green’s function package of CosmoTherm

1 10 100 1000

ν [GHz]

3
2
1

1 2 3 4 5

Gth(ν, zh, 0) [ 10

18 W m
2 s
1 Hz
1 sr
1 ]

temperature-shift, zh > few x 10

6

µ-distortion at zh ~ 3 x 10

5

y-distortion, zh < 10

4

Primordial Distortions

Jens Chluba

Cosmology School in the Canary Islands Fuerteventura, Sept 21st, 2017

(∆⇤ ⌘ ∆ ∆f) Fiducial values: ∆f = 1.2 ⇥ 104 yre = 4 ⇥ 107 fann,s = 1022 eV sec1 fann,p = 1026 eV sec1

Distortion parameter estimation

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Physical mechanisms that lead to spectral distortions

Cooling by adiabatically expanding ordinary matter

(JC, 2005; JC & Sunyaev 2011; Khatri, Sunyaev & JC, 2011)

Heating by decaying or annihilating relic particles

(Kawasaki et al., 1987; Hu & Silk, 1993; McDonald et al., 2001; JC, 2005; JC & Sunyaev, 2011; JC, 2013; JC & Jeong, 2013)

Evaporation of primordial black holes & superconducting strings

(Carr et al. 2010; Ostriker & Thompson, 1987; Tashiro et al. 2012; Pani & Loeb, 2013)

Dissipation of primordial acoustic modes & magnetic fields

(Sunyaev & Zeldovich, 1970; Daly 1991; Hu et al. 1994; JC & Sunyaev, 2011; JC et al. 2012 - Jedamzik et al. 2000; Kunze & Komatsu, 2013)

Cosmological recombination radiation

(Zeldovich et al., 1968; Peebles, 1968; Dubrovich, 1977; Rubino-Martin et al., 2006; JC & Sunyaev, 2006; Sunyaev & JC, 2009)

Signatures due to first supernovae and their remnants

(Oh, Cooray & Kamionkowski, 2003)

Shock waves arising due to large-scale structure formation

(Sunyaev & Zeldovich, 1972; Cen & Ostriker, 1999)

SZ-effect from clusters; effects of reionization

(Refregier et al., 2003; Zhang et al. 2004; Trac et al. 2008)

more exotic processes

(Lochan et al. 2012; Bull & Kamionkowski, 2013; Brax et al., 2013; Tashiro et al. 2013)

„high“ redshifts „low“ redshifts

pre-recombination epoch post-recombination

Standard sources

f distortions

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Average CMB spectral distortions in ΛCDM

1 3 6 10 30 60 100 300 600 1000 3000

ν [GHz]

10

1

10 10

1

10

2

10

3

10

4

∆I [ Jy sr

1]

low redshift y-distortion for y = 2 x 10

6

relativistic correction to y signal Damping signal cooling effect CRR

negative branch n e g a t i v e b r a n c h PIXIE sensitivity negative branch negative branch Late time absorption

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dρe dτ = d(Te/Tγ) dτ = tT ˙ Q αhθγ + 4˜ ργ αh [ρeq

e − ρe] − 4˜

ργ αh HDC,BR(ρe) − H tT ρe.

kαh = 3 2k[Ne + NH + NHe] = 3 2kNH[1 + fHe + Xe]

ρeq

e = T eq e /Tγ

˜ ργ = ργ/mec2 Idc = Z x4f(1 + f) dx ≈ 4π4/15 T eq

e

= Tγ R x4f(1 + f) dx 4 R x3f dx ≡ h k R ν4f(1 + f) dν 4 R ν3f dν

Set of evolution equations for distortions

Photon field Ordinary matter temperature

∂f ∂τ ≈ θe x2 ∂ ∂xx4  ∂ ∂xf + Tγ Te f(1 + f)

+ KBR e−xe

x3

e

[1 − f (exe − 1)] + KDC e−2x x3 [1 − f (exe − 1)]+S(τ, x) KBR = α 2π λ3

e

√ 6π θ7/2

e

X

i

Z2

i Ni ¯

gff(Zi, Te, Tγ, xe), KDC = 4α 3π θ2

γ Idc gdc(Te, Tγ, x)

¯ gff(xe) ≈ ( √

3 π ln

⇣

2.25 xe

⌘ for xe ≤ 0.37 1

therwise

, gdc ≈ 1 + 3

2x + 29 24x2 + 11 16x3 + 5 12x4

1 + 19.739θγ − 5.5797θe . x = hν kTγ θe = kTe mec2

SLIDE 5

CosmoTherm: a new flexible thermalization code

Solve the thermalization problem for a wide range of energy release histories
several scenarios already implemented (decaying particles, damping of acoustic modes)
first explicit solution of time-dependent energy release scenarios
open source code
will be available at www.Chluba.de/CosmoTherm/
Main reference: JC & Sunyaev, MNRAS, 2012 (arXiv:1109.6552)

2 x 10

4

10

3

10

2

10

1

20 10 1 50

x

4×10
8
2×10
8

2×10

8

4×10

8

6×10

8

8×10

8

T(x) / TCMB - 1

z = 4.1 x 10

6

z = 2.4 x 10

6

z = 1.5 x 10

6

z = 8.8 x 10

5

z = 5.2 x 10

5

z = 3.1 x 10

5

z = 1.9 x 10

5

z = 1.1 x 10

5

z = 6.7 x 10

4

0.1 0.02 1 10 100 10

3

ν [GHz]

z = 4.0 x 10

4

z = 1.4 x 10

4

z = 2.4 x 10

4

z = 8.7x 10

3

z = 5.2x 10

3

z = 3.1x 10

3

z = 1.9x 10

3

z = 1.1x 10

3

z = 200

strong low frequency evolution at low redshifts

10

3

10

4

10

5

10

6

10

7

z

10

11

10

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10

1 - Te / Tz

no energy release zX = 3 x 10

6

zX = 5 x 10

5

zX = 1 x 10

5

zX = 5 x 10

4

zX = 1 x 10

4

End of HI recombination hotter than photons

Electron temperature evolution Evolution of distortion

SLIDE 6

Quasi-Exact Treatment of the Thermalization Problem

But: distortions are small ⇒ thermalization problem becomes linear!
Case-by-case computation of the distortion (e.g., with CosmoTherm, JC &

Sunyaev, 2012, ArXiv:1109.6552) still rather time-consuming

Simple solution: compute “response function” of the thermalization

problem ⇒ Green’s function approach (JC, 2013, ArXiv:1304.6120)

Final distortion for fixed energy-release history given by

∆Iν ≈ Z 1 Gth(ν, z0)d(Q/ργ) dz0 dz0

For real forecasts of future prospects a precise & fast method for

computing the spectral distortion is needed!

Thermalization Green’s function

Fast and quasi-exact! No additional approximations!

CosmoTherm available at: www.Chluba.de/CosmoTherm

SLIDE 7

1 10 100 1000

ν [GHz]

3
2
1

1 2 3 4 5

Gth(ν, zh, 0) [ 10

18 W m
2 Hz
1 sr
1 ]

temperature-shift, zh > few x 10

6

µ-distortion at zh ~ 3 x 10

5

y-distortion, zh < 10

4

hybrid distortion probes time-dependence of energy-release history

f u l l t h e r m a l i z a t i

n

Intensity signal for different heating redshifts

Response function: energy injection ⇒ distortion

JC & Sunyaev, 2012, ArXiv:1109.6552 JC, 2013, ArXiv:1304.6120

high-z SZ effect

What does the spectrum look like after energy injection?

SLIDE 8

y-distortion µ-distortion

1 10 100 1000

ν [GHz]

3
2
1

1 2 3 4 5

Gth(ν, zh, 0) [ 10

18 W m
2 Hz
1 sr
1 ]

temperature-shift, zh > few x 10

6

µ-distortion at zh ~ 3 x 10

5

y-distortion, zh < 10

4

µ+y + residual distortion

pre- post-recombination epoch y-distortion era µ-era T-era µ-y-era HI&He extra time-slicing at recombination New hybrid era

SLIDE 9

0.01 0.1 1 10 30 50

x = hν / kT

1.2
1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Intensity in units of I0(T)

Blackbody spectrum Temperature shift x 1/4

1 10 100 1000

ν [ GHz ]

300
200
100

100 200 300 400

Intensity [ MJy sr

1]

x3nbb(x) = x3 ex − 1 x3G(x) = x4ex (ex − 1)2 I0 = (2h/c2)(kT0/h)3 ≈ 270 MJy sr−1

Simplest spectral shapes

full thermalization

SLIDE 10

0.01 0.1 1 10 30 50

x = hν / kT

1.2
1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Intensity in units of I0(T)

Blackbody spectrum Temperature shift x 1/4 y-distortion x 1/4

1 10 100 1000

ν [ GHz ]

300
200
100

100 200 300 400

Intensity [ MJy sr

1]

x3YSZ(x) = x3G(x)  xex + 1 ex − 1 − 4

I0 = (2h/c2)(kT0/h)3 ≈ 270 MJy sr−1

Simplest spectral shapes

equivalent of th-SZ full thermalization

y → νc ≈ 217 GHz

SLIDE 11

0.01 0.1 1 10 30 50

x = hν / kT

1.2
1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Intensity in units of I0(T)

Blackbody spectrum Temperature shift x 1/4 y-distortion x 1/4 µ-distortion x 1.401

1 10 100 1000

ν [ GHz ]

300
200
100

100 200 300 400

Intensity [ MJy sr

1]

I0 = (2h/c2)(kT0/h)3 ≈ 270 MJy sr−1

x3M(x) = x3G(x)  π2 18ζ(3) − 1 x

≈ 0.4561

Simplest spectral shapes

y → νc ≈ 217 GHz µ → νc ≈ 124 GHz

SLIDE 12

Energy release histories

SLIDE 13

Energy release histories for some cases

d(Q/ργ) dz = 3 2 NtotkTγ ργ(1 + z) ⇡ 5.71 ⇥ 1010 (1 + z) "(1 Yp) 0.7533 #" Ωbh2 0.02225 # ⇥ "(1 + fHe + Xe) 2.246 #  T0 2.726 K 3

d(Q/ργ) dz = fann NH(z)(1 + z)2+λ H(z) ργ(z)

d(Q/ργ) dz ⇡ 4A2∂zk2

D

Z 1

kmin

k4 dk 2π2 Pζ(k) e2k2/k2

D,

y A2 ⇡ (1 + 4Rν/15)2 ⇡ 0.813,

ton damping scale (Weinberg 1971; kD ⇡ 4.048 ⇥ 10 (1 + z)3/2Mpc1 we have a heating e ciency A2

Rν ⇡ 0.409 for Neff kmin ⇡ 0.12 Mpc1, the recombination

d(Q/ργ ) dz

dec

≈ ϵX NH(z)(1 + zX)ŴX H(z)ργ (z) (1 + z) exp (−ŴX t)

Adiabatic cooling Annihilation Decay Dissipation of acoustic modes

SLIDE 14

Text

10

3

10

4

10

5

10

6

redshift z 10

8

10

7

10

6

effective heating rate (1+z) d(Q/ρ) / dz

zX = 2x10

4

zX = 8x10

4

zX = 3x10

5

µ - distortion y - distortion µ−y transition fX / zX = 1 eV

Decaying particle scenarios

JC & Sunyaev, 2011, Arxiv:1109.6552 JC, 2013, Arxiv:1304.6120

SLIDE 15

Text

1 10 100 1000 ν [GHz]

300
200
100

100 200 300 400 ∆Iν [ 10

26 W m
2 s
1 Hz
1 sr
1 ]

y-distortion with y = 2x10

7

zX = 2x10

4

zX = 8x10

4

zX = 3x10

5

Decaying particle scenarios

JC & Sunyaev, 2011, Arxiv:1109.6552 JC, 2013, Arxiv:1304.6120

Shape of the distortions depends

n the particle lifetime!

, 0) [ 10

18 W m
2 Hz
1 sr
1 ]

SLIDE 16

Simple analytic approximations for estimates

SLIDE 17

tK ' texp

Very simple way to estimate the spectral distortion for a given energy release history!

y ' 1 4 ∆ργ ργ ⌘ 1 4 Z zµy

zrec

d(Q/ργ) dz0 dz0 µ ≈ 1.4 Z 1

zµy

d(Q/ργ) dz0 Jµ(z0)dz0

Jµ(z) ≈ e

− ⇣

z 1.98×106

⌘5/2

SLIDE 18

Jy(z) ≈ 1 +  1 + z 6.0 × 104 2.58!−1 Jµ(z) ≈  1 − e

− h

1+z 5.8×104

i1.88

e

− h

z 2×106

i2.5

JC, 2013, ArXiv:1304.6120

y ' 1 4 ∆ργ ργ ⌘ 1 4 Z zµy

zrec

d(Q/ργ) dz0 dz0 µ ≈ 1.4 Z 1

zµy

d(Q/ργ) dz0 Jµ(z0)dz0

→ Obtained as simple fits to Green’s function → approximately models the transition era neglecting r-distortion

SLIDE 19

Using the Green’s function package

Green’s function package available at www.Chluba.de/CosmoTherm/
Depends on GSL library
Has python interface and python packages
PCA methods (not added yet…)
Green’s function method for photon injection too (JC 2015, ArXiv:1506.06582)

JC 2015, ArXiv:1506.06582 JC 2013, ArXiv:1304.6121

(∆⇤ ⌘ ∆ ∆f) Fiducial values: ∆f = 1.2 ⇥ 104 yre = 4 ⇥ 107 fann,s = 1022 eV sec1 fann,p = 1026 eV sec1

SLIDE 20

Some useful commands

Some other runmodes… ./run_Greens Greens runfiles/parameters.dat (Greens function output) ./run_Greens Mock runfiles/parameters.dat (band average for mock) Execute Greens-package like ./run_Greens runfiles/parameters.dat (default computation) Making and cleaning > make > make py > make clean > make tidy

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