Isolated sector production from primordial BHs Hannah Tillim Oxford - - PowerPoint PPT Presentation

Isolated sector production from primordial BHs

Hannah Tillim

Oxford University (supervisors J. March-Russell & S. M. West)

YTF Durham, December 2018

Dark Matter from Primordial Black Holes

• O. Lennon, J. March-Russell, R. Petrossian-Byrne, H. Tillim,

Black Hole Genesis of Dark Matter, JCAP 1804 (2018), arXiv:1712.07664

Hannah Tillim Isolated sectors from primordial black holes December 19, 2018 1 / 13

Isolated sector DM

• The WIMP paradigm - requires couplings

between sectors - much of the parameter space now explored

• Important to explore alternatives

“Isolated” Interactions with SM purely gravitational

• Production mechanisms

(freeze-out, freeze-in) not applicable to isolated sectors

• Coupling to gravity →

Hawking radiation

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Hawking radiation

Hawking temperature: TBH = M2

Pl

8πMBH Hawking radiation rate: d dNs,i dt

• =
• ℓ,h

(2ℓ + 1) 2π Γi,s,ℓ,h(ω) exp(ω/T(t)) + (−1)(2s+1) dω

• S. Hawking, Commun.Math.Phys. 43 (1975) 199-220
• D. Page, Phys. Rev. D13 (1976) 198206

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Hawking radiation

→ Ns,i ≃ fs,igs,i 2eT M0 MPl 2 1 (T0 > mi/ds) d2

sT 2 0 /m2 i

(T0 < mi/ds) eT =

• i,s

gi,sei,s

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Setup

• Model:
• Population of micro pBHs with near-uniform initial density n0
• Any other initial energy density is SM radiation (no DM)
• DM is single species, long-lived, sub-Planckian massive

particles, spin ≤ 2

• Simplifying assumptions:
• All Schwarzschild
• All masses = M0
• T0 > vW

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Setup

dρBH dt + 3HρBH = −eT M4

Pl

M2 n dρrad dt + 4Hρrad = +eT M4

Pl

M2 n H(t)2 = 8π(ρBH + ρrad)/3M2

Pl

dM dt = −M4

Pl

M2

• s,i

es,igs,i ≡ −eT M4

Pl

M2

• Fast vs. slow evaporation
• Light vs. heavy DM
• Yield Yi ≡ ni/stot

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Light DM results

Y slow

i

≃ 1 2 fs,igs,i g

1 4

∗ e

1 2

T

MPl M0 1

2

Y fast

i

≃ 1 2 fs,igs,i g

1 4

∗ eT

n0 M3

Pl

1

4 M0

MPl 5

4

• Y × mDM = 0.43 eV

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Light DM constraints

Constraints for single real s = 0 dof before free-streaming constraint is imposed.

• red line: B0 = 1
• blue line: one pBH per initial Hubble

patch

• blue shaded regions: TRH < 3 MeV
• pink, dotted line: TRH = 200 GeV.
• upper purple region: ρBH(0) > M4

Pl.

Free streaming: excludes most of light region (for s < 3/2)

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Thermalisation

Ongoing work with J. March-Russell, S. M. West

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Thermalisation

• Emitted with non-thermal spectrum and very high energy tail
• Underpopulated compared to equilibrium density
• Require redistribution of energy (2 → 2) and particle creation

(2 → 3 ...) Kinetic f(p) = 1/(exp[−(E − µ)/T] ± 1) Thermal Ti = T Chemical µin

i = µfin j

• Other studies in this direction: S. Davidson & S. Sarkar arXiv:0009.078v3; M.

Garny et. al. arXiv:1810.01428, S. Heeba; F. Kahlhoefer & P. St¨

• cker arXiv:1809.04849, ....

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Thermalisation

• Kinetic, thermal and ‘partial chemical’ → evolution to full

chemical

• Boltzmann equation governs evolution - depends on a collision

term ˙ n + 3Hn = g π2

• d3pC[f]

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Thermalisation: interim results

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What’s next

• Robust model-independent framework for estimating

thermalisation timescales

• Concrete pheno of permanently underpopulated sectors
• Application to pBH production model to reopen light DM case

Thank you!

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