Photon Scattering by Atoms and Dark Matter

1
Photon Scattering by Atoms (and Dark Matter?)

• Kris Sigurdson
• University of British Columbia
• Particle Astrophysics Seminar
• Fermilab
• September 24, 2007

2
Photon Interactions with Atoms (and Dark Matter?)

• Kris Sigurdson
• University of British Columbia
• Particle Astrophysics Seminar
• Fermilab
• September 24, 2007

3

• Part I Rayleigh Scattering of CMB photons and
  Baryon Acoustic Oscillations
• Part II Cosmic 21-cm Fluctuations from the
  Cosmic Dark Ages. Absorption of CMB at Radio
  Wavelengths.
• Part III The Shadow of Dark Matter - Resonant
  Scattering of Gamma Ray Photons by Dark Matter

4
Part I Rayleigh Scattering of the CMB and
Baryon Acoustic Oscillations
KS and Chris Hirata, in preparation

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Photon Acoustic Oscillations PAO

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Baryon Acoustic Oscillations BAO

Credit Daniel Eisenstein
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Acoustic Oscillations BAO

8
Origin of BAO

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Collision Term

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Collision Term With Rayleigh

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Rayleigh Scattering

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Rayleigh Scattering
Scattering of Long Wavelength Photons From Atoms.
For Cosmology H Atoms are most important.

Leading term p4
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Effects of Rayleigh Scattering

• Momentum dependence induces spectral
• distortions in the CMB temperature anisotropies.
• (Yu, Spergel, Ostriker 2001).
• 3 effect at high frequencies (550 GHz)
• Polarization Answer In progress.
• 2) Coupling between photons and baryons induces
• a drag force on the baryons. This will in
  principle
• modify the BAO signature in the matter power
• spectrum some level.

Mentioned by Peebles and Yu (1970)
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Effect in CMB Anisotropies

From Yu, Spergel, Ostriker 2001
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Effect on BAO Motivation

• Can use BAO (sound horizon) as a standard ruler
  to explore dark energy. Compare with CMB
  observables.
• Reference Target Precision on Acoustic Scale
  10-3
• Rayleigh scattering introduces a systematic
  effect.
• How big/small?

Assuming
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Rayleigh Drag

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Thermal Cross Section

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Hydrogen Atoms

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Change in Drag Coefficient

Few relative change
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Relative to Measured CMB

Momentum-weighted fraction of coupling arising
from CMB photons at today
Low-Energy CMB not significantly altered
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Power Spectrum

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Power Spectrum

3 x 10-3 effect
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Correlation Function

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Correlation Function

3 x 10-3 effect in amplitude
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Correlation Function

1.5 x10-4 shift in linear acoustic scale
relative to CMB
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FYI Equivalent w

holding everything else fixed
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Summary Part I

• 1) Rayleigh scattering has a 0.3 effect on the
  matter power spectrum and correlation function
  near the parameters of the SCM.
• 2) Rayleigh scattering only shifts the BAO scale
  by at most 15 of the target statistical errors
  on BAO dark-energy missions forthcoming.
• 3) Easy to account for. Real physics that is
  guaranteed to be there. Safe to ignore for now I
  bet. Nonlinear effects likely more troublesome.
• Complication if combined with other
  systematics??
• Future SuperBAO Missions??

28
Part II Cosmic 21-cm Fluctuations from Dark-Age
Gas

KS and Chris Hirata, MNRAS 375, 1241 (2007).
Matthew Kleban, KS, and Ian Swanson, JCAP 0708,
009 (2007).
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What are the properties of a gas of neutral
hydrogen atoms 100 million years after the big
bang? What are their detectable signatures?

30
Cosmic 21-cm Fluctuations

• The Epoch of Reionization (e.g. Furlanetto et. al
  2004). Measure the Primordial Power Spectrum at
  high redshift! 3D instead of a 2D CMB. (e.g. Loeb
  and Zaldarriaga 2004)
• Might help probe Exotic Effects, Inflation and
  particle physics effects on the Small Scale
  Matter Power Spectrum. (e.g. Kleban, KS, and
  Swanson 2007 KS and Cooray 2005 Profumo, KS,
  Ullio and Kamionkowski 2004)
• Observational Challenges Galactic and
  Extragalactic Foreground Removal, RFI, etc..
• If these fluctuations can be measured they will
  leave us with a 3D snapshot of our past
  lightcone! Best you can do short of waiting.

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Cosmic 21-cm Fluctuations
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What I am talking about.

• 21-cm fluctuations before reionization physics
  becomes important.
• Smooth, slightly lumpy Universe.
• Main Players Neutral Gas and the CMB
• Roughly Speaking 30 lt z lt 200

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21-cm Hyperfine Transition

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Calculate Atomic Distribution Function

• Determines the 21-cm line profile.
• The integrated line profile determines the
• total 21-cm emissivity.
• The 21-cm emissivity (and fluctuations in the
  emissivity) are needed when calculating the power
  spectrum of 21-cm fluctuations.

35
The Plan

• First Calculate the spin-resolved
• distribution function of atomic
• hydrogen.
• Then Calculate the 21-cm Line Profile, the
  21-cm Emissivity, and the 21-cm Power
  Spectrum.

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The Atomic H Distribution Function

• Statatistical Mechanics Basics

H atom distribution function
Maxwell-Boltzmann
Number Density
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The Spin Temperature
(Dalgarno 1961 Allison Dalgarno 1969)

• Radiative interactions with the CMB vs. Atomic
  Collisions

Collision Threshold
Thermal Spin-Change Cross Section
Einstein A Coefficient
Before Ly-? photons and the Wouthuysen-Field
Effect turns on
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Atomic Spin-Change Collisions

Schrödinger
Phase Shifts
Spin-Change Cross Section (Dalgarno 1961 Allison
and Dalgarno 1969)
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Spin-Change Cross Section

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Thermal Cross Section

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Spin-Temperature Evolution
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Whats Wrong?

• Some Clues

Thermal Spin-Change Cross Section
(Velocity Independent)
(A Velocity Independent Function of T)
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Thermal Cross Section

(A Velocity Independent Function of T)
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Spin-Change Cross Section

(A Velocity dependent Function of E)
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Whats wrong?

• Distribution does not factor!
• Collision time comparable to the radiative time
• Spin degrees of freedom are correlated with the
  kinetic degrees of freedom!

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Boltzmann

• Solve the Boltzmann equation

Dominant Terms
No Ly? Early
Mostly Neutral
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Boltzmann

• Steady State Solution

Radiative Term
Blackbody Formula
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Boltzmann

• Collision Term

Product of Cross Section and Relative Velocity
Scattering out of v
Scattering in to v
Probability of F
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Boltzmann

• Equations are nonlinear and nontrivial to solve
• However as
• May solve in a perturbation series in
• about the thermal equilibrium solution

Perturbation
Spins thermalized at Tk
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Boltzmann

• Expand in orthogonal modes

Smooth
Hermite
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The Solution

• The steady state solution is
• where

The Answer!!!!
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Ts(v)

• The spin-resolved distribution functions are
• For comparison define

Velocity-Dependent Spin Temperature
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Ts(v)

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The ObservableThe Brightness Temperature
A function of redshift, density, and
velocity (and direction on the sky)
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The ObservableThe Brightness Temperature
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The ObservableThe Brightness Temperature
Linear
Fourier Space
Power Spectrum
Direction cosine between wavevector and line of
sight
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The ObservableThe Brightness Temperature
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Power Spectra
(Naoz and Barkana, astro-ph/0503196)
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Cosmic 21-cm Fluctuations
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Power Spectra Change

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Power Spectra Change

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21-cm Line Profile

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Line Profile Width

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Fourier Transform of Profile

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Summary Part II

• The spin and velocity degrees of atomic hydrogen
  in primordial gas are correlated and the
  spin-resolved distribution function of atomic
  hydrogen is nonthermal.
• The 21-cm line profile is not Gaussian. Total
  emissivity altered.
• Redshift and projection dependent effect of up to
  5 on the large scale power spectrum, and an
  order unity effect on the small scale power
  spectrum of 21-cm fluctuations.
• Details (See C. Hirata and KS in MNRAS)

66
Part III The Shadow of Dark Matter

Stefano Profumo and KS, PRD 75, 023521 (2007).
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Motivation

• Cosmology of dark matter is well established.
• But we dont know very much about the physics of
  dark matter.
• Direct Detection. Indirect Detection. Production.
• Are there other avenues to learn about and
  detect dark matter?

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Dark Matter is Dark Matter
Not Dark Matter
Images Martin Whites Webpage
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Dark Matter is Dark Matter
?
Not Dark Matter
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Dark Matter is Dark Matter

• Very weak coupling to photons
• Strong Limits Charge (e.g. A. Gould et al. 1990)
• Milli-Charge (e.g. S. Davidson et al. 2000 S.
  Dubovsky et al. 2004)
• Magnetic/Electric Dipole (e.g. KS et al. 2004)
• CONCLUSION Can NOT appreciably scatter light
  because the coupling is so weak.

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Can Dark Matter Cast a Shadow?
?
g
g (?)
Dark Matter
Observer
Photon Source
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The Low-Energy Model

• Stable Neutral Dark Matter Particle
• Unstable Neutral Heavier Particle
• Coupled to Photons and each other via a
  Transition Magnetic/Electric Moment

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The Low-Energy Model

Atom-like interaction
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The Model Resonant Scattering

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Resonant Photon Scattering
Relativistic Breit-Wigner Cross Section

CM Energy Squared
CM Momentum
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The Parameters

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Constraints from Pair Processes

• The coupling can allow
  for
• production of pairs
• Existing astrophysical constraints on
  Milli-charge
• (fractional charge) particles (e.g. G. Raffelt
  1996)
• Can apply, but replace with

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Lyman-?

• Large-Scale Structure constraints from the
  Lyman-??forest on warm dark matter impose

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The Constraints

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SN1987A

• Excess production of pairs in
• SN1987A

SN Core Plasma Frequency
Excludes
(Too Much Energy Loss)
(Particles Trapped)
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The Constraints

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Big Bang Nucleosynthesis

• If thermalized in the early Universe around
• BBN and would contribute to the number
  of light degrees of freedom present during BBN

Excludes
83
The Constraints

84
Running of ?em

Modifies the Running of ? up to the Z-pole
Must Have
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The Constraints

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Accelerators

87
The Constraints

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Can Dark Matter Cast a Shadow?
?
g
g (?)
Dark Matter
Observer
Photon Source
89
Velocity Broadening

• Dark matter particles live in a halo with a
  nonzero velocity dispersion

Maxwell-Boltzmann
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Broadening in DM Halos

Coma-like
Broadened
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The Opacity

In Detail
DM Surface Density
The Optical Depth
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An Absorption Feature?

• The dynamics of the scattering process Compton
  scattering
• forward scattering is unlikely if a photon
  scatters, its lost to LOS

• Absorption occurs if t 1

Can ? be large enough?
93
An Absorption Feature?

• Consider a cluster like the Coma Cluster
• Estimate ? 5x1029 MeV/cm2 for a line of sight
  through cluster center
• Consider a source at the center of the cluster
  (e.g. a quasar) or perhaps behind the cluster.

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Absorption Feature?

Vary Intrinsic Width
LOS through Center
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Potentially Interesting Targets?

• Perhaps Active Galactic Nuclei (e.g. Centaurus A
  or M87). With a DM spike around the central
  black hole.
• Perhaps Gamma Ray Bursts?
• Statistical Detection?

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Summary The (?,m2) Plane
Coma reference surface density giving t 1
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Summary

For
Mass Range
Resonant Energy
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Annihilation?

• Through the same interaction dark matter
  particles could annihilate to monochromatic
  photons

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Annihilation Flux
Flux
For
From Galactic Center
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Annihilation Flux
Expected Flux
Diffuse Gamma from COMPTEL/EGRET
Unfortunately Difficult to detect such a line
from the Galactic center. Perhaps Dwarf
galaxies (e.g. Profumo and Kamionkowski 2006)
Dedicated line search by INTEGRAL-SPI also not
sensitive enough
(Teegarden and Watanabe 2006)
101
Supersymmetric?

• SUSY Neutralino Dark Matter
• In principle construct such a model in a SUSY
  setup with lightest neutralino and
  next-to-lightest neutralino

Number density too low for a detectable signal
102
Extended ?MSM?

• ?MSM DM abundance, neutrino masses, baryon
  asymmetry, potentially inflation
• (T. Asaka et al. 2005 M. Shaposhnikov 2006)
• 1-10 MeV mass dark-matter possible. High number
  density and (relatively) sizable cross sections!
• Extending a model like this with the
  transition-moment interaction could lead to the
  phenomenology discussed here

103
Part III Conclusions

• Dark Matter is Dark Matter. But for special
  energies resonant scattering is possible
• A range of the parameter space remains.
• Perhaps Observable Black Hole Accretion (AGN)
• Not SUSY. Perhaps model with MeV dark matter.

Stefano Profumo and KS Phys. Rev. D75 023521
(2007) astro-ph/0611129
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End