GeneralConstraintsonDarkMatterDecayFromCMB

1

Chih-LiangWu

Aug112017TeVPA

TracySlatyer,Chih-LiangWuPhys.Rev.D95(2017)no.2,023010

(arXiv:1610.06933)

EnergyinjectioninthedarkagesHow?

• DMannihilatesordecaysintoSMparticles→betweenrecombinationandreionization (darkage)→newsourcesofenergyinjectionintoCMB→additionalheatingandionization→increaseopticaldepth,changeCMBpowerspectrum…

2

DM SMCascadedecay

H 𝑒$

EnergyinjectioninthedarkagesWhy?

1.Physicsinthedarkagesarewellunderstood2.CMBpowerspectrummeasuredprecisely3.DoeNotdependonlocalDMdensityanddistributionnowadays

3

EnergyinjectioninthedarkagesWhy?

1.Physicsinthedarkagesarewellunderstood2.CMBpowerspectrummeasuredprecisely3.DoeNotdependonlocalDMdensityanddistributionnowadays4.StronglimitbetweenMeV– GeV energyfor𝑒%𝑒$ channel

4

Energyinjectionhistory

• HowmuchenergyactuallydepositintotheCMBbydifferentchannel?

5

Compton,pairproduction…

Ionization

Heating...

Energyinjectionhistory

• HowmuchenergyactuallydepositintotheCMBbydifferentchannel?

• pa (𝑧',𝐸))=depositedinjected ,a:ionization,heating...(bysimulation)

• Injectionrate:∝< 𝜎𝑣 > (1 + 𝑧)3 forann;∝ 456/8 9⁄ (1 + 𝑧); fordecay

• Needtimetodeposit:delayeddeposition

6

CMBchange• Boltzmanncode(ex: :studyspecificenergyinjectionprofile

• DecayingDMInjecting30MeV𝑒%𝑒$ :

• Moreinformationandmodel-independentwaytoconstrainDM?

7

Principalcomponentanalysis• Determinenumbersofrelevantparameters

• PCA:

−Basis𝑀) forinjectionprocessex:10keV-1TeVphoton,find𝛿Ｃℓ

− ConstructFishermatrix,marginalizedoverstandardparameters

− Eigenvectors𝑒)= ∑ (𝛼))C C 𝑀Cwitheigenvalues𝜆)

− If𝜆E>>𝜆) , 𝑒E = ∑ (𝛼E)CC 𝑀C dominate

− 2𝜎 constraint:FGHIJK,E9 <

L(MN)O PN

*Inlinearregime,whereenergyinjectionissmall

*Gaussianlikelihood

8

𝑒E

PCA– Energy• Basis𝑀C:10Kev- 1Tev𝑒%𝑒$&10Kev- 1Tevphoton

9

4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12Log10[Energy (eV)]

0.01

0.10

1.00WMAP

PLANCKCVL

e++e- photonsAnnihilation

4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12Log10[Energy (eV)]

0.01

0.10

1.00WMAP

PLANCKCVL

e++e- photonsDecay

PCA– Energy• Basis𝑀C:10Kev- 1Tev𝑒%𝑒$&10Kev- 1Tevphoton

1.𝑒E = ∑ (𝛼E)CC 𝑀C dominate

2.𝜆Econtributes>99.9%ofvariance forann,>97%fordecay

3.Upperlimitatdifferentenergies𝐸) scalesasL

(MN)O PN

10

4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12Log10[Energy (eV)]

0.01

0.10

1.00WMAP

PLANCKCVL

e++e- photonsAnnihilation

4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12Log10[Energy (eV)]

0.01

0.10

1.00WMAP

PLANCKCVL

e++e- photonsDecay

PCA– Redshift• Basis𝑀C:redshift(Delta-likeenergyinjectionateachredshift)

11

Annihilation

PCA– Redshift• Basis𝑀C:redshift(Delta-likeenergyinjectionateachredshift)

• Theweightingfunctionforannihilationpeaksatz~600whilefordecaybroadlypeaksatz~300

• Theprocesscanbecapturedbyasingle parameter

12

Annihilation Decay

MCMC• GobeyondlinearityandGaussianlikelihood

• UseMCMCcode(ex:Montepython):sixstandardcosmologicalparameters+DMdecaylifetime

• PerformMCMCtocheckPCAresult

13

4 5 6 7 8 9 10 11 12 4 5 6 7 8 9 10 11 12Log10[Energy (eV)]

1023

1024

1025

1026

τ (

s)

e++e- photons

Comparewithobservation• ConstraintsfromobservationsofdiffuseX-rayorgamma-rayemission

• DependontheDMlocaldensityanddistributioninthepresent day

• Decaytophotons(usuallystronger)orelectronswithFSR

• DMdecayto𝑒%𝑒$:

14

ConstraintonDecayingDM• Short-lifetimeDMcouldbeafractionofDM

• Constraintonmassfractionasafunctionoflifetime:

15

1014 1016 1018 1020 1022 1024 1026

Lifetime (s)

10-12

10-10

10-8

10-6

10-4

10-2

100

Maxi

mum

allo

wed m

ass

fra

ctio

n

Summary• PCAprovidesamethodtoquicklyestimatetheCMBlimitfor

arbitraryenergyinjectionspectra,consistentwithMCMC

• ForannihilatingDMandDMdecayingwithalonglifetime,theeffectontheCMBcanbeapproximatelydescribedbyasingleparameter

• Constraintsondecayto𝑒%𝑒$ arestrongbetweenMeV– GeV

• Thelimitwouldimprovebyafactorof~5 withanexperimentthatiscosmicvariancelimiteduptol=2500

• AnExampleofMathematica notebookisgivenathttp://nebel.rc.fas.harvard.edu/epsilon/

• Future:exploremoregeneralenergyinjectionmodels,withdifferentredshiftdependence

16

BonusSlides

17

Energyinjectionhistory

• fa (𝑧),𝑧',𝐸))=depositedinjected ,a=excitation,ionization,heating…

◦ injectiontime(𝑧)),deposittime(𝑧'),injectionspecies&energy(𝐸))

• Energydeposited intoCMB:◦ pa(𝑧',𝐸))~∑ fa(𝑧) ,𝑧',𝐸))×injectionrate) (𝑧))

• Injectionrate:◦ ∝< 𝜎𝑣 > (1 + 𝑧)3 forannihilation◦ ∝ 456/8 9⁄ (1 + 𝑧); fordecay

pionization(𝑧',𝐸))

• Photon:ionizationefficiencyishighforlowenergyphoton

• Electron:30MeVupscatter CMBbyComptonscattering,producelowenergyphoton

TracySlatyer et.alarXiv:0906.197

pionization(𝑧',𝐸)) - Decay

• transparentatlowredshift?needtimetodeposit(delayeddeposition)

• Highefficiencywindow:30MeVfor𝑒%𝑒$and10keV forphoton

20

𝑒%𝑒$ photons

pionization(𝑧',𝐸)) - Annihilation

• transparentatlowredshift?->delayeddeposition

• Highefficiencywindow:◦ 30MeVforelectronand10keV forphoton

𝑒%𝑒$ photons

Short-lifetimedecayingDM• Short-lifetimedecayingDMcouldalsobeafractionofDM

• PCA:

basis:fixed30MeVelectronsbutdifferentlifetimes

1. 𝜆E(first PC) dominate > 98%

2. Short-lifetime DM has little weightInjection rate ∝ 456/8 9⁄ (1 + 𝑧);

18 17 16 15 14 13Log10[Lifetime (s)]

0.01

0.10

WMAPPLANCK

CVL

MCMC• Forexample:decayingDM,30MeVelectroninjection

0.0217 0.0223 0.0228

⌦bh2=0.0223+0.000184�0.000159

0.116 0.12 0.124

⌦ch2=0.119+0.00147�0.00152

1.04 1.04 1.04

100✓s=1.04+0.00035�0.000326

2.99 3.06 3.13

ln1010As=3.07+0.026�0.0252

0.952 0.965 0.979

ns=0.965+0.00482�0.00524

0.0203 0.0599 0.0996

⌧reio=0.0594+0.0142�0.0153

0 0.281 0.505

1025 ⇤ (1/⌧ )=0.133+0.0284�0.133

0.116

0.12

0.124

⌦ch

2

1.04

1.04

1.04

100✓

s

2.99

3.06

3.13

ln10

10A

s

0.952

0.965

0.979

ns

0.0203

0.0599

0.0996⌧ r

eio

0 0.281 0.505

1025 ⇤ (1/⌧ )0.0217 0.0223 0.0228

⌦bh20

0.281

0.505

1025⇤(

1/⌧)

0.116 0.12 0.124⌦ch2

1.04 1.04 1.04100✓s

2.99 3.06 3.13ln1010As

0.952 0.965 0.979ns

0.0203 0.0599 0.0996⌧reio

Generalconstraint• DMdecaytoStandardModelparticles:

PPPC4DMIDpackage:

28decaychannelsinthegalaxy,electron&photonenergyspectra

101 102 103 104

DM mass (GeV)

1022

1023

1024

1025

1026

τ (

s)

e+L e

-L

e+R e

-R

e+ e-

µL+ µL

-

µR+ µR

-

µ+ µ-

τL+ τL

-

τR+ τR

-

τ+ τ-

qq-

cc-

bb-

tt-

WL+ WL

-

WT+ WT

-

W+ W-

ZL+ ZL

-

ZT+ ZT

-

Z0 Z0

ggγ γh hνeνe

-

νµνµ

-

ντντ

-

VV → 4eVV → 4µ

VV → 4τ

FisherMatrix

• 6cosmologicalparameter:baryondensity,ωb,CDMdensity,ωc,theprimordialscalarspectralindexns,thenormalizationAs(k=0.002/Mpc),theopticaldepthtoreionization τ andtheHubbleparameterH0

25

Reionization• StudiedbyHongwan Liuet.al (arXiv:1604.02457)

• Usingdifferentreionizationmodels,includingstructureformation

• Lessthan10%totheionizationfractionatreionization isfromannihilatingDM

26