# Presentation: 486302

## Photon Scattering by Atoms (and Dark Matter?)

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

## Photon Interactions with Atoms (and Dark Matter?)

- Photon Interactions with Atoms (and Dark Matter?)

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

- 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

## Part I: Rayleigh Scattering of the CMB and Baryon Acoustic Oscillations

*KS** and Chris Hirata, in preparation*

## Photon Acoustic Oscillations: PAO

## Baryon Acoustic Oscillations: BAO

*Credit: Daniel Eisenstein*

## Acoustic Oscillations: BAO

## Origin of BAO

## Collision Term

## Collision Term: With Rayleigh

## Rayleigh Scattering

## Rayleigh Scattering

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

*Leading term: p**4*

## 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)*

## Effect in CMB Anisotropies

*From Yu, Spergel, Ostriker 2001*

## 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:*

## Rayleigh Drag

## Thermal Cross Section

## Hydrogen Atoms

## Change in Drag Coefficient

*Few % relative change*

## Relative to Measured CMB

*Momentum-weighted fraction of coupling*
*arising from CMB photons at*
*today**	**	**	** *

*Low-Energy CMB not significantly altered*

## Power Spectrum

## Power Spectrum

*~3 x 10**-3  **effect*

## Correlation Function

## Correlation Function

*~3 x 10**-3  **effect in amplitude*

## Correlation Function

*~1.5 x10**-4  **shift in **linear** acoustic scale **relative to CMB** *

## FYI: “Equivalent w”

** holding everything else fixed*

## 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??

## 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). *

**Notes:**
Gr
Atomic Physics/Kinetic Theory
Cosmology
Apologies total number.  Density is OK.
Result. Interesting. Details. 

## What are the properties of a gas of neutral hydrogen atoms 100 million years after the big bang? What are their detectable signatures? 

**Notes:**
Gr
Atomic Physics/Kinetic Theory
Cosmology
Apologies total number.  Density is OK.
Result. Interesting. Details. 

## 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”.

## Cosmic 21-cm Fluctuations

## 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 < z < 200

## 21-cm Hyperfine Transition

**Notes:**
What are the properties of neutral hydrogen atoms during the cosmic dark ages  

## 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.

## 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.

## The Atomic H Distribution Function

- Statatistical  Mechanics Basics:

*Maxwell-Boltzmann*

*Number Density*

*H atom distribution function*

## The Spin Temperature*

- Radiative interactions with the CMB vs. Atomic Collisions:

** Before Ly-**** photons and the Wouthuysen-Field Effect turns on*

*Collision Threshold*

*Thermal Spin-Change Cross Section*

*Einstein A Coefficient*

*(Dalgarno 1961; Allison & Dalgarno 1969)*

## Atomic Spin-Change Collisions

*Schrödinger*

*Phase Shifts*

*Spin-Change Cross Section *(Dalgarno 1961; Allison and Dalgarno 1969)

## Spin-Change Cross Section

## Thermal Cross Section

## Spin-Temperature Evolution

## What’s Wrong?

- Some Clues:

***Thermal ****Spin-Change Cross Section*

*(Velocity Independent)*

*(A Velocity Independent Function of T)*

## Thermal Cross Section

*(A Velocity Independent Function of T)*

## Spin-Change Cross Section

*(A Velocity **dependent** **Function of E)*

## What’s wrong?

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

## Boltzmann

- Solve the Boltzmann equation:

*Dominant Terms*

*No Ly**** Early*

*Mostly Neutral*

**Notes:**
Redshift 20 and 80 

## Boltzmann

- Steady State Solution:

*Radiative Term*

*Blackbody Formula*

## Boltzmann

- Collision Term:

*Product of Cross Section and Relative Velocity*

*Scattering out of **v*

*Scattering in to **v*

*Probability of F*

## 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 T**k*

## Boltzmann

- Expand      in orthogonal modes:

*Smooth*

*Hermite*

## The Solution

- The steady state solution is
- where

*The Answer!!!!*

## Ts(v)

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

*Velocity-Dependent Spin Temperature*

## Ts(v) 

**Notes:**
Gas Temperature in Green
Photon Temperature in Red
Old Calculation in Black 

## The Observable:The Brightness Temperature

*A function of redshift, density, and velocity*
*(and direction on the sky)*

## The Observable:The Brightness Temperature

## The Observable:The Brightness Temperature

*Linear*

*Power Spectrum*

*Direction cosine between wavevector and line of sight*

*Fourier Space*

## The Observable:The Brightness Temperature

## Power Spectra

*(Naoz and Barkana, astro-ph/0503196)*

## Cosmic 21-cm Fluctuations

## Power Spectra Change

## Power Spectra Change

**Notes:**
Redshift and Angular Projection Dependent Change in the Power Spectrum.
Must be included if trying to use 21-cm observations to constrain cosmology. 

## 21-cm Line Profile

## Line Profile Width

## Fourier Transform of Profile

## 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)

## Part III: The Shadow of Dark Matter

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

## Motivation

- 	Cosmology of dark matter is well established.
- But... we don’t 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?

## ‘Dark’ Matter is Dark Matter 

- ‘Dark’ Matter is Dark Matter

*Not Dark Matter *

*Images: Martin White’s Webpage*

**Notes:**
Ignore gravitational lensing  

## ‘Dark’ Matter is Dark Matter 

*Not Dark Matter *

*?*

## ‘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.

**Notes:**
Defining Property

## ?

**Can Dark Matter Cast a Shadow?**

**Photon Source**

**Dark Matter**

**Observer**

****

**?**

********

## 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

**Notes:**
Dark Sector: Unknown 

## The Low-Energy Model

*“**Atom-like interaction”*

## The Model: Resonant Scattering

**Notes:**
Lyman-Alpha

## Resonant Photon Scattering

*Relativistic Breit-Wigner Cross Section*

*CM Energy Squared*

*CM Momentum *

## The Parameters

## 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:

## Lyman-

- Large-Scale Structure constraints from the Lyman-**forest on warm dark matter impose:

## The Constraints

## SN1987A

- Excess production of                 pairs in

*SN Core Plasma Frequency*

*Excludes:*

*(Too Much Energy Loss)*

*(Particles Trapped)*

## The Constraints

## 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:*

## The Constraints

## Running of em

*Modifies the Running of **** up to the Z-pole*

*Must Have:*

**Notes:**
Mz 91.188Gev

## The Constraints

## Accelerators

**Notes:**
Free quark searches
Vector-Meson Decays

## The Constraints

**Notes:**
The Lay of the Land 

## ?

**Can Dark Matter Cast a Shadow?**

**Photon Source**

**Dark Matter**

**Observer**

****

**?**

********

## Velocity Broadening

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

*Maxwell-Boltzmann:*

## Broadening in DM Halos

*Coma-like*

*Broadened*

## The Opacity

*In Detail:*

*DM Surface Density*

*The Optical Depth*

## An Absorption Feature?

** ****The dynamics of the scattering process ~ Compton scattering**
**    ***forward scattering is unlikely: if a photon scatters, it’s lost to LOS *

** ****Absorption occurs if ********~ 1**

*Can **** be large enough?*

## 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.

## Absorption Feature?

*LOS through Center*

*Vary Intrinsic Width*

## 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?

## Summary: The (,m2) Plane

**“****Coma”**
**reference**
**surface**
**density**
**giving **
****** ****~ 1**

## Summary

*For:*

*Mass Range: *

*Resonant Energy:*

## Annihilation?

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

## Annihilation: Flux

*Flux:*

*For:*

*From Galactic Center*

## 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)*

## 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*

## 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

**Notes:**
3 Sterile Neutrinos

## 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*

## End