1. Propagation of cosmic rays
Richard Taillet
Université de Savoie & LAPTH (Annecy-le-Vieux, France)
I am assistant professor at Univ. de Savoie, and I do my research in the astroparticle group in LAPTH, a theoretical physics lab located in Annecy-le-Vieux, France.
This talk will be about propagation of cosmic rays. It is a very large subject, and I will only focus on the points that may be relevant for the study of indirect detection of dark matter.
I work with several people involved in writing and using a propagation code named USINE (see the names below) and when I need an illustration, I will take it from works achieved with USINE.
& D. Maurin,  P. Salati,  F. Donato,  J. Lavalle, 
T. Delahaye, A. Putze, L. Derome, N. Fornengo...

2. Three points:
 Physics of propagation
Indirect detection through antimatter
 Clumps/boost factors

3. Context
dark matter particles can annihilate and create other particles 
→ indirect detection
neutral     : neutrinos and gamma-rays
charged   : electrons, positrons, protons, antiprotons
e.g.
To be able to perform indirect detection, one must be able to tell the signal from the background.
Each of these particles can also be created by standard processes.
Indirect detection : search for an excess of one of these species, with respect to the standard background.
Antimatter particles have a lower background and should be easier to detect in cosmic rays.

4. Context
In the context of Dark Matter indirect detection, three main uncertainties :
 existence/properties of the dark matter particle ?
 distribution in space and in velocity space ?
 propagation of the annihilation products
Propagation is important for two reasons :
 to predict the signal (antiprotons, positrons from DM annihilation)
 to understand the background (primaries + secondaries from spallation)
The two studies must be done in a consistent way !
same propagation model with same physical effects
same parameters
first uncertainty : cf particle physics
second uncertainty : cf astronomers and cosmologists
here we are only interested in the last one
The antiprotons do not carry a label “hey, you know, I’m special, I come frome dm annihilation, they don’t wear a tee-shirt stating “hey I’m exotic”. We wish they would, but they don’t -> need to know the background very well to be able to detect an excess.

5. Context The two studies must be done in a consistent way !
first uncertainty : cf particle physics
second uncertainty : cf astronomers and cosmologists
here we are only interested in the last one
The antiprotons do not carry a label “hey, you know, I’m special, I come frome dm annihilation, they don’t wear a tee-shirt stating “hey I’m exotic”. We wish they would, but they don’t -> need to know the background very well to be able to detect an excess.
The two studies must be done in a consistent way !
same propagation model with same physical effects
same parameters

6. Context The two studies must be done in a consistent way !
first uncertainty : cf particle physics
second uncertainty : cf astronomers and cosmologists
here we are only interested in the last one
The antiprotons do not carry a label “hey, you know, I’m special, I come frome dm annihilation, they don’t wear a tee-shirt stating “hey I’m exotic”. We wish they would, but they don’t -> need to know the background very well to be able to detect an excess.
The two studies must be done in a consistent way !
same propagation model with same physical effects
same parameters

7. Propagation
Propagation of charged particles (positrons, antiprotons) is determined by the structure of the Galactic magnetic field.
Regular component + stochastic component, probably associated with turbulence 
→ fluctuations of the magnetic field on every scale
→ energy-dependent diffusion : diffusion is more efficient at high energy
A particle of a given energy explores a region which size is given by the Larmor radius. The propagation is most sensitive to the variations of the magnetic field at this scale. The stochastic nature of the variations leads to diffusion, and <B^2> determines the diffusion coefficient.
Said differently : the power spectrum of the spatial distribution of B translates directly into energies and diffusion coefficient.

8. Propagation 1/ secondary/primary ratios (e.g. B/C)
1/ secondary/primary ratios (e.g. B/C)
→ grammage (column density ~ 10 g/cm2)
→ confinement (provided by diffusion).
2/ radioactive species : nuclear clocks
→ time spent in the diffusion zone
→ cosmic rays spend most of their time in a empty halo (diffusive halo).
Cosmic rays are confined inside a zone larger than the Galactic disk
when a primary CR (coming from a source) propagates, it may collide with nuclei of the ISM an create a secondary. The sec/prim ratio indicates the average quantity of (column density) of matter crossed by the primary : the grammage, which is found equal to about 10 g/cm2. This is about 100 times larger than the column density of the whole galaxy. Thus, the cosmic rays must be confined in a region containing matter, where spallations occur.
Some of the species contained in cr are radioactive, unstable. They give access to the time spent in the diffusion zone : this time is large and if cr were subject to spallation all the time, the grammage would be much higher. There is a diffusive halo, much thicker than the galactic disk.

9. Propagation solve a diffusion equation, taking into account:
side boundary not so important
solve a diffusion equation, taking into account:
diffusion (diffusion coefficient ? anisotropic ? inhomogeneous ?)
escape (boundary conditions, geometry of diffusion volume)
spallations (creation/destruction, cross-sections, interstellar medium)
Sources (distribution, spectra)
energy losses
diffusive reaccerelation
galactic wind (convection)
inelastic non annihilating reactions (for antiprotons)

10. Propagation spallation losses spallation t (Myr) escape Ek (GeV/nuc)
caracteristic times
spallation
losses
106
spallation
t (Myr)
103 1
escape 1 10
100
Ek (GeV/nuc)

11. Propagation Different approaches to model propagation:
Leaky Box : escape time, distribution of grammages
Diffusion equation : 
numerical resolution (GALPROP, Strong & Moskalenko)
semi-analytical resolution (USINE, Maurin et al.)
Note : USINE will be publicly released within a few months
Leaky Box : energy losses and reacceleration very tricky : need to know not only how much matter was crossed, but also what was the energy all allong the trajectory !
Typical values for D ?

12. Propagation Diffusion parameters Diffusion coefficient
Height of diffusive halo
Alfvèn velocity (reacc.)
Gal. wind velocity (convection)
Leaky Box : energy losses and reacceleration very tricky : need to know not only how much matter was crossed, but also what was the energy all allong the trajectory !
Typical values for D ?

13. Propagation Diffusion parameters
Diffusion coefficient
Height of diffusive halo
Alfvèn velocity (reacc.)
Gal. wind velocity (convection)
Leaky Box : energy losses and reacceleration very tricky : need to know not only how much matter was crossed, but also what was the energy all allong the trajectory !
Related to the kind of magnetic turbulence : no consensus

14. Propagation Diffusion parameters
Diffusion coefficient
Height of diffusive halo
Alfvèn velocity (reacc.)
Gal. wind velocity (convection)
Leaky Box : energy losses and reacceleration very tricky : need to know not only how much matter was crossed, but also what was the energy all allong the trajectory !
Related to the amplitude of turbulence

15. Propagation Diffusion parameters ~ 10 g cm-2
Diffusion coefficient
Height of diffusive halo
Alfvèn velocity (reacceleration)
Galactic wind velocity (convection)
Leaky Box : energy losses and reacceleration very tricky : need to know not only how much matter was crossed, but also what was the energy all allong the trajectory !
If the galactic disk was flattened, it would be a sheet of usual paper, crossed about times by every cosmic ray
~ 10 g cm-2
Mean grammage is determined by L/D

16. Propagation
If the galactic disk was flattened, it would look like a sheet of usual paper, crossed about times by every cosmic ray nucleus
Leaky Box : energy losses and reacceleration very tricky : need to know not only how much matter was crossed, but also what was the energy all allong the trajectory !
If the galactic disk was flattened, it would be a sheet of usual paper, crossed about times by every cosmic ray
~ 10 g cm-2
Mean grammage is determined by L/D

17. Propagation General facts about propagation
The range of propagation is limited by escape, spallation and decay
Propagation of nuclei and antiprotons can be studied at a given energy per nucleon, as a first approximation
Propagation of positrons is dominated by energy losses

18. Propagation
Taillet, Maurin, A&A 402 (2003) 971

19. Propagation
The propagation parameters can be determined (or at least constrained) by the study of cosmic ray nuclei:
For a given set of parameters,
compute B/C
compare to data
keep if good
Astrophysical uncertainties (assuming the model is correct):
distribution of sources
distribution of interstellar matter
energy losses (Lavalle & Delahaye 2010)
nuclear cross-sections

20. Propagation
Results from a systematic exploration of the parameter space
Maurin et al. 2001

21. Propagation Results from a Monte Carlo Markov Chain analysis (MCMC)
Putze, Derome, Maurin, astro-ph/
Putze et al. 2010

22. Propagation
This procedure gives regions of the parameter space which are consistent with CR nuclei, not a unique value for each parameter.
sub-Fe/Fe does not help much
radioactive species could, but actually do not really
\ell \sim 100 pc
Half-lives are
1.5 Myr for 10Be,
0.9 Myr for 26Al,
0.3 Myr for 36Cl.

23. Propagation - Local Bubble
Radioactive species could help determine L.
But they are very sensitive to the local structure of the interstellar medium (local bubble)

24. Propagation – Local Bubble
The presence of the local bubble strongly affects the fluxes of radioactive species
Putze, Derome, Maurin, astro-ph/

25. Antiprotons from spallation
Results for secondary antiprotons (background)
uncertainties : parameterizations of nuclear cross sections, influence of helium.
Uncertainty on the parameterizations of nuclear cross sections (but proton flux rather well measured)

26. Antiprotons from dark matter
Examples of results for antiprotons from exotic sources
Kaluza-Klein, m = 50 GeV/c2
neutralino m = 300 GeV/c2
Donato et al. 2004

27. Antiprotons from dark matter
Very sensitive to L, for two reasons: if L si higher,
 Confinement is more efficient
 More sources in the diffusive halo

28. Positrons from spallations
Created through decay of pions produced in p-p collisions
Propagation dominated by energy losses (synchrotron & inverse Compton upon CMB/starlight)

29. Positrons from spallations
Example of results for secondary positrons

30. positrons [make nasty remark here …  ]
Remark about some plots that can be found in the litterature : the solid line does not mean a lot !
Adriani et al., Nature 458 (2009) 607

31. Antimatter from dark matter
Results for positrons from DM annihilation
uncertainty larger when the spectrum is flat, because of reacceleration ?

32. Antimatter from dark matter
clumpiness
The Dark Matter distribution must be clumpy
→ enhancement of the indirect detection signal (boost factor)
<\rho ^2> > <\rho>^2
via lactea simulation of a galactic halo

33. Antimatter from dark matter
When the diffusion range is short, we are very sensitive to the graininess of the source distribution
→ larger variance of the predicted flux
This shows:
at low energy for antiprotons
at high energy for positrons
antiprotons
positrons
why so large for GCR min ?
Lavalle, Yuhan, Maurin & Bi, A&A 479 (2008) 427

34. Conclusions
Signal and background must be studied within the same framework
There is no « standard model » for propagation parameters
Clumpiness does not simply translates into a boost factor