Outline 1. Introduction to PMFs 2. Reheating of the CMB photon 3. - - PowerPoint PPT Presentation
New constraints on small-scale primordial magnetic fields from Magnetic Reheating Shohei Saga (YITP, Kyoto University) Based on S.S, H.Tashiro, and S.Yokoyama [MNRAS 475 L 52(2018)] S.S, A.Ota, H.Tashiro, and S.Yokoyama in prep. Outline 1.
New constraints on small-scale primordial magnetic fields from Magnetic Reheating
Based on S.S, H.Tashiro, and S.Yokoyama [MNRAS 475 L52(2018)] S.S, A.Ota, H.Tashiro, and S.Yokoyama in prep.
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1. Introduction to PMFs
Primordial Magnetic Fields(PMFs) generated by cosmological phenomena in the early universe Why we consider PMFs? Observed (large-scale) magnetic fields
~ 10-5 - 10-6 Gauss
~ 10-6 Gauss
> 10-16 - 10-21 Gauss Setting seed fields in the early universe and amplifying Cosmological constraint on PMFs
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1.1 Example(1) CMB anisotropy
PMFs generate CMB temperature and polarization anisotropies.
101 102 103
` 10−6 10−3 10−1 101 103 106 `(` + 1)C`/2⇡ ⇥ µK2⇤
TT TT TT TT TT TT
Primary Scalar magnetic Vector magnetic Passive tensor magnetic
nB = -2.9 B1Mpc = 4.5 nGauss Planck 2015 [1502.01549]
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PB(k) ∝ knB ~ O(nGauss)
1.2 Example(2) CMB distortion
z
~ 2.0 × 106 ~ 4.0 × 104 Double Compton scattering Compton scattering # of CMB photon fix Bose-Einstein distribution Non-equilibrium state μ era y era Double Compton era
Decaying of PMFs generates μ and y distortion è From the observation of COBE, B < O(nG).
Chemical potential y-parameter
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e− + γ ← → e− + γ + γ
1.3 Constraint on PMFs
In the cosmological observations,
PMFs on much smaller scales ?
n Gauss PMFs on Large Scale (≳ Mpc)
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2. Reheating of the CMB photon
Before μ era, i.e., 2.0 × 106 ≲ 1 + z, Double Compton scattering is efficient.
An energy injection increases # of CMB photons while # of baryons does not change. The baryon-photon number ratio η decreases. η = nb
nγ
z
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~ 2.0 × 106 ~ 4.0 × 104 Compton scattering Double Compton scattering Planck distribution Compton scattering # of CMB photon fix Bose-Einstein distribution Non-equilibrium state μ era y era Double Compton era
2.1 Baryon-photon ratio η
Baryon-photon ratio is independently constrained by BBN and CMB. Constrained value by BBN ηBBN = (6.19 ± 0.21) × 10−10
K.M.Nollet and G.Steigman [1312.5725]
η determines è photon dissociation rate, reaction rate, and so on. è abundance of light element generated in BBN era
R.H.Cyburt, B.D.Fields, and K.A.Olive [astro-ph/0503065]
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η = nb nγ
2.2 Baryon-photon ratio η
Baryon-photon ratio is determined independently by BBN and CMB. Constrained value by CMB (after the onset of the μ-era) ηCMB = (6.11 ± 0.08) × 10−10
Planck 2013 [1303.5076]
From CMB observations,
We can directly determine η
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2.3 Baryon-photon ratio η
ηBBN = (6.19 ± 0.21) × 10−10 ηCMB = (6.11 ± 0.08) × 10−10
@BBN @CMB
η Standard model
z
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Energy injection
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3 Magnetic Reheating
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kD(z) ≈ 7.44 × 10−6(1 + z)3/2 Mpc−1 ∼ kSilk(z)
k
kD kD MHD mode analysis Example: Fast-magnetosonic mode
Large scale ← → Small scale
Spectrum of PMFs: Reheating photons Energy injection source = Diffusion of PMFs à increasing nγ (i.e., reheating)
3.1 Delta-function type
101 102 103 104
102 103 104 105 106 107 108 109
Bdelta [nG]
kp [Mpc-1]
Magnetic reheating BBN CMB distortion
PB(k) = B2
deltaδD(ln (k/kp))
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M.Kawasaki and M.Kusakabe [1204.6164] K.Jedamzik et al. [astro-ph/9911100]
3.2 Power‐law type (Upper bound)
10-30 10-25 10-20 10-15 10-10 10-5 100 105
0.0 1.0 2.0 3.0
B [nG]
nB
Fast mode Alfven mode Planck constraint
k0 = 1 Mpc−1
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PB(k) = B2 ✓ k k0 ◆nB+3
Scale-invariant
Planck 2015 [1502.01549]
3.3 Anisotropic reheating(Preliminary)
k0 = 1 Mpc−1
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PB(k) = B2 ✓ k k0 ◆nB+3
Scale-invariant
10-25 10-20 10-15 10-10 10-5 100 105
0.0 1.0 2.0
B [nG]
nB
Anisotropic reheating zini = 1014 Uniform reheating (Fast) Uniform reheating (Alfven) Planck constraint
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4. Summary Magnetic Reheating is the novel mechanism to explore small-scale PMFs. for example, B ≲ 10−17 nG for nB = 1.0 10−23 nG for nB = 2.0 ó Planck ~ O(1.0 nG) !!!
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In the case of power-law type spectrum, bluer tilt is strongly constrained: + Magnetic anisotropic reheating?