International School for Advanced Studies SISSA/ISAS Properties of Interstellar Medium and Cosmic Ray Propagation, Impacts on Dark Matter Indirect Searches Thesis submitted for the degree of Doctor Philosophiae Candidate: Supervisor: Maryam Tavakoli Prof. Piero Ullio Trieste, September 2012 2 Abstract In this thesis the properties of the interstellar medium and cosmic rays prop- agation are studied in the light of unprecedented data from the Fermi γ-ray telescope. A combined analysis of cosmic rays and γ-rays spectra constrain the thickness of the diffusion zone and the gas distribution in the Galaxy. In- deed, there is a tight correlation between the distribution of gas in the Galaxy and the spectra of diffuse γ-rays. Small scale features in high angular res- olution diffuse γ-ray sky maps of the Fermi can be interpreted by detailed models for gas distribution. A new model for three dimensional distribution of atomic hydrogen gas, which is the major ingredient of the interstellar gas, is constructed. Based on established propagation models which account for astrophysical contribution to diffuse γ-rays, limits on possible contributions from dark matter are derived. Inspired by indications for a γ-ray line at en- ergy of about 130 GeV towards the Galactic center, limits on the continuous spectrum which accompanies the γ-ray line are extracted. Extending the win- dow of observation, the bounds on the morphological shape of a dark matter signal associated with the line is discussed. For this purpose, the standard templates for the dark matter profile, such as an Einasto or a NFW profile, and a new more general parametrization are applied. Upper limits on dark matter annihilation cross sections in the Galactic halo are also derived for a broader range of dark matter mass. 3 4 Contents 1 Introduction7 2 Interstellar Medium 11 2.1 Atomic Hydrogen Gas............................. 12 2.1.1 Derivation of Atomic Hydrogen Number Density........... 15 2.1.2 Large Scale Features.......................... 18 2.2 Molecular Hydrogen Gas............................ 20 2.3 Ionized Hydrogen Gas............................. 24 2.4 Galactic Magnetic Field............................ 25 3 Cosmic Rays 27 3.1 Primary Sources................................. 28 3.2 Diffusion..................................... 30 3.3 Energy Losses.................................. 31 3.4 Propagation................................... 33 4 Diffuse Gamma Rays 39 4.1 Impact of Cosmic Rays Diffusion....................... 42 4.1.1 Diffusion Spectral index........................ 42 4.1.2 Diffusion Radial Scale......................... 43 4.1.3 Diffusion Scale Height......................... 43 4.1.4 Convection............................... 48 4.2 Rigidity Break in Injection or Diffusion.................... 50 4.3 Influence of Supernova Remnants Distribution................ 53 4.4 γ-ray Yields from pp-Collision Parametrization............... 57 4.5 Significance of the Interstellar Gas Distribution............... 58 4.5.1 2D vs 3D Gas Distribution....................... 64 4.6 Reference Model for Diffuse γ-Ray Background............... 68 5 6 CONTENTS 5 Dark Matter Indirect Detection 73 5.1 Galactic Center................................. 74 5.1.1 Limits on WIMPs Annihilation Cross Section in the inner 10◦ 10◦ 74 × 5.1.2 Limits on WIMPs Annihilation Profile................ 79 5.1.3 A Specific Example........................... 84 5.2 Galactic Halo.................................. 85 5.2.1 Dark Gas................................ 86 5.2.2 Minimal non-DM Extragalactic Background............. 86 5.2.3 Limits on WIMPs Annihilation Cross Section in the Halo...... 92 6 Conclusion 97 Chapter 1 Introduction There are convincing pieces of evidence from cosmological and astrophysical observations that non-baryonic dark matter is the dominating matter component in the Universe and the building block for all visible structures [1,2,3,4,5,6,7,8,9, 10]. Among several plausible scenarios for particle physics candidates for dark matter, the case for weakly interacting massive particles (WIMPs) is particularly appealing (for a review on dark matter candidates see, e.g. [11]). WIMPs are generated as thermal relics from the early Universe. A massive stable state with sizable coupling to Standard Model particles would be in thermal equilibrium at high temperatures and tend to decouple from the thermal bath when it becomes non-relativistic. It is easy to show that the relic abundance ap- proximately scales with the inverse of its pair annihilation rate into lighter Standard Model particles [12] and matches the cosmological dark matter abundance for a coupling of weak-interaction strength. The phenomenology of WIMPs is very rich. They can be produced at colliders and detected as missing energy. They can also be directly detected through measuring the recoil energy in their elastic scattering off nuclei of underground detectors, or indirectly via searching for the products of the WIMPs pair annihilations which happen today in dark matter halos. The traces of WIMPs annihilation might be seen in the spectra of cosmic rays (such as positrons, antiprotons and anti-deuterons), in the spectra of photons in a broad wave- length range (ranging from the radio frequencies, in connection to synchrotron emission from electron/positron WIMPs yields, to the X-ray and γ-ray bands) as well as in WIMP- induced neutrino fluxes. In most of these cases and for most viable observational targets, the WIMPs contribution is in general rather small compared the component induced by more standard astrophysical sources. Therefore, to constrain the WIMPs annihilation properties a deep understanding of astrophysical backgrounds is crucial. 7 8 CHAPTER 1. INTRODUCTION Among the mentioned detection channels, γ-rays are exceptionally important to study for two reasons. Firstly, γ-rays, unlike the charged particles propagate on straight lines through the Universe almost without losing energy and thus directly point back toward their sources. Secondly and especially timely, the Fermi γ-ray telescope [13] has been providing extremely detailed γ-ray sky maps in the last few years. The Fermi telescope has opened a new era in γ-ray astronomy; its high angular resolution, wide energy coverage with excellent energy resolution together with large effective area and field of view has made it possible to measure the γ-ray radiation with unprecedented quality. Thereby, it gives unique insights into the most energetic processes in our Universe [14]. At energies above few tens of MeV more than 80% of the observed photons are con- nected to diffuse emission. The bulk of these photons is from the decay of neutral pions which themselves are produced by inelastic collisions of cosmic ray protons and helium nuclei with the interstellar gas. Moreover, cosmic ray electrons and positrons yield γ-rays via bremsstrahlung emission in the interstellar gas or by inverse Compton scattering off the interstellar radiation field. In order to constrain the contribution of astrophysical backgrounds to diffuse γ-rays a thorough understanding of the properties of cosmic rays propagation within the Galaxy is highly demanded. Cosmic rays with energies up to 1015 eV, which are accelerated in our own Galaxy, do not freely propagate in the interstellar medium but rather get deflected by magnetic fields. There are irregularities in magnetic fields which are caused either by fluctuations in the field or the growth of instabilities due to the flow of cosmic rays. The random scattering of cosmic rays by these irregularities give rise to their diffusion through the interstellar medium. The correlation between diffusion and magnetic fields manifests itself as the weaker magnetic field, the larger diffusion length. The energy dependence of diffusion is also correlated to the mechanism that builds up the turbulence in magnetic fields. Furthermore, the stochastic re-acceleration of cosmic rays by scattering on the magnetohydrodynamic waves leads to diffusion in momentum space which is inversely proportional to the diffusion in physical space. In addition, the drift of cosmic rays by the Galactic winds affects the diffusion timescale. Little is known about the absolute value of diffusion and its spatial and spectral properties. In this thesis, a systematic study has been performed on a variety of propagation models in which the spatial and spectral properties of diffusion vary in a fairly large range. The propagation parameters are fitted to the local fluxes of cosmic rays. The local measurements of the spectrum of cosmic ray primaries, the ratio of secondary to primary cosmic ray nuclei and the flux of electrons and positrons are used. To discriminate between the models the evaluated spectra of antiprotons and diffuse γ-rays are compared against the data from PAMELA [15] and 9 Fermi [16]. Another important aspect in estimating the diffuse γ-ray background is the distribu- tion of the gas in the interstellar medium. The diffuse γ-ray components produced by decays of neutral pions and bremsstrahlung of electrons and positrons are strongly cor- related to the gas distribution in the Galaxy. Small scale features of the gas distribution along the line of sights manifest themselves in the sky maps of these components. These structures can be traced in high angular resolution maps of the Fermi γ-ray telescope. One of the major constituents of the interstellar gas is atomic hydrogen HI . It can be traced by 21cm emission line which is due to the transition between the atomic hydrogen 2S ground state levels split by the hyperfine