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...

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

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.

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.

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

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

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.

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.

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)

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)

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 ?

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 ?

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

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

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 10 000 times by every cosmic ray ~ 10 g cm-2 Mean grammage is determined by L/D

Propagation If the galactic disk was flattened, it would look like a sheet of usual paper, crossed about 10 000 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 10 000 times by every cosmic ray ~ 10 g cm-2 Mean grammage is determined by L/D

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

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

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

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

Propagation Results from a Monte Carlo Markov Chain analysis (MCMC) Putze, Derome, Maurin, astro-ph/1001.0551 Putze et al. 2010

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.

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

Propagation – Local Bubble The presence of the local bubble strongly affects the fluxes of radioactive species Putze, Derome, Maurin, astro-ph/1001.0551

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)  

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

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

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

Positrons from spallations Example of results for secondary positrons

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

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

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

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

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