New constraints on small-scale primordial magnetic fields ...
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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 L52(2018)] S.S, A.Ota, H.Tashiro, and S.Yokoyama in prep.
Transcript of New constraints on small-scale primordial magnetic fields ...
Newconstraintsonsmall-scaleprimordialmagneticfieldsfromMagneticReheating
ShoheiSaga(YITP,KyotoUniversity)Basedon
S.S,H.Tashiro,andS.Yokoyama[MNRAS475L52(2018)]S.S,A.Ota,H.Tashiro,andS.Yokoyamainprep.
Outline1. IntroductiontoPMFs
2. ReheatingoftheCMBphoton
3. MagneticReheating
4. Summary
Outline1. IntroductiontoPMFs
2. ReheatingoftheCMBphoton
3. MagneticReheating
4. Summary
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1. IntroductiontoPMFs PrimordialMagneticFields(PMFs)
generatedbycosmologicalphenomenaintheearlyuniverse
WhyweconsiderPMFs?
Observed(large-scale)magneticfields• Galaxy(~kpc) ~10-5 - 10-6 Gauss• Cluster(~Mpc) ~10-6 Gauss• Intergalactic(void) >10-16 - 10-21 Gauss
SettingseedfieldsintheearlyuniverseandamplifyingCosmologicalconstraintonPMFs
• CMBanisotropy• CMBdistortion• BigBangNucleosynthesis(BBN)
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1.1 Example(1)CMBanisotropy PMFsgenerateCMBtemperatureandpolarizationanisotropies.
101 102 103
`
10�
610�
310�
110
110
310
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`(`+
1)C
`/2
⇡⇥ µ
K2⇤
TTTTTTTTTTTT
Primary
Scalar magnetic
Vector magnetic
Passive tensor magneticnB = -2.9 B1Mpc = 4.5 nGauss
Planck2015[1502.01549]
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A.Lewis[astro-ph/0406096]
PB(k) / knB
~O(nGauss)
1.2 Example(2)CMBdistortion
z
~ 2.0 × 106
~ 4.0 × 104
DoubleComptonscattering
Comptonscattering#ofCMBphotonfixBose-Einsteindistribution
Non-equilibriumstate
μera
yera
DoubleComptonera
DecayingofPMFsgeneratesμ andydistortionèFromtheobservationofCOBE,B < O(nG).
Chemicalpotential
y-parameter
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e� + � ! e� + � + �
J.GancandM.S.Sloth[1404.5957]K.K.KunzeandE.Komatsu[1309.7994]
1.3 ConstraintonPMFs Inthecosmologicalobservations,
PMFsonmuchsmallerscales?
n GaussPMFsonLargeScale(≳Mpc)
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Outline1. IntroductiontoPMFs
2. ReheatingoftheCMBphoton
3. MagneticReheating
4. Summary
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2. ReheatingoftheCMBphoton Beforeμera,i.e.,2.0 × 106 ≲ 1 + z,
DoubleComptonscatteringisefficient.• Thermalequilibrium• Planckdistribution
Anenergyinjectionincreases#ofCMBphotonswhile#ofbaryonsdoesnotchange.
Thebaryon-photonnumberratioηdecreases. ⌘ =nb
n�
z
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~ 2.0 × 106
~ 4.0 × 104
ComptonscatteringDoubleComptonscatteringPlanckdistribution
Comptonscattering#ofCMBphotonfixBose-Einsteindistribution
Non-equilibriumstate
μera
yera
DoubleComptonera
2.1 Baryon-photonratioη Baryon-photonratioisindependentlyconstrainedbyBBNandCMB.
ConstrainedvaluebyBBN
⌘BBN = (6.19± 0.21)⇥ 10�10
K.M.NolletandG.Steigman[1312.5725]
η determinesè photon dissociationrate,reactionrate,andsoon.è abundance of light element generated in BBN era
R.H.Cyburt,B.D.Fields,andK.A.Olive[astro-ph/0503065]
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⌘ =nb
n�
2.2 Baryon-photonratioη Baryon-photonratioisdeterminedindependentlybyBBNandCMB.
ConstrainedvaluebyCMB(aftertheonsetoftheμ-era)
⌘CMB = (6.11± 0.08)⇥ 10�10
Planck2013[1303.5076]
FromCMBobservations,• TemperatureofCMBphotons:TCMB• Densityofbaryons:Ωb0
Wecandirectlydetermineη
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2.3 Baryon-photonratioη
⌘BBN = (6.19± 0.21)⇥ 10�10
⌘CMB = (6.11± 0.08)⇥ 10�10
@BBN @CMB
η
Standardmodel
z
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Energyinjection
Outline1. IntroductiontoPMFs
2. ReheatingoftheCMBphoton
3. MagneticReheating
4. Summary
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3 MagneticReheating
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kD(z) ⇡ 7.44⇥ 10�6(1 + z)3/2 Mpc�1 ⇠ kSilk(z)
k kD kD
MHDmodeanalysisExample:Fast-magnetosonicmode
Largescale← →Smallscale
SpectrumofPMFs:
Reheatingphotons
Energyinjectionsource=DiffusionofPMFsàincreasingnγ(i.e.,reheating)
3.1 Delta-functiontype
101
102
103
104
102 103 104 105 106 107 108 109
B del
ta [n
G]
kp [Mpc-1]
Magnetic reheatingBBN
CMB distortion
PB(k) = B2delta�D(ln (k/kp))
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M.KawasakiandM.Kusakabe[1204.6164]K.Jedamziketal.[astro-ph/9911100]
3.2 Power‐lawtype(Upperbound)
10-30
10-25
10-20
10-15
10-10
10-5
100
105
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
B [n
G]
nB
Fast modeAlfven mode
Planck constraint
k0 = 1 Mpc�1
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PB(k) = B2
✓k
k0
◆nB+3
Scale-invariant
Planck2015[1502.01549]
3.3 Anisotropicreheating(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
-3.0 -2.0 -1.0 0.0 1.0 2.0
B [n
G]
nB
Anisotropic reheatingzini = 1014
Uniform reheating (Fast)Uniform reheating (Alfven)
Planck constraint
Preliminary
Outline1. IntroductiontoPMFs
2. ReheatingoftheCMBphoton
3. MagneticReheating
4. Summary
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4. Summary MagneticReheatingisthenovelmechanismtoexploresmall-scalePMFs.
forexample,B ≲ 10−17 nG fornB = 1.0
10−23 nG fornB = 2.0ó Planck ~ O(1.0 nG) !!!
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Inthecaseofpower-lawtypespectrum,bluertiltisstronglyconstrained:
+Magneticanisotropicreheating?
