GeV-TeV Galactic cosmic rays

This short review aims at presenting the way we currently understand, model, and constrain the transport of cosmic rays in the GeV-TeV energy domain. This is a research field per se, but is also an important tool e.g. to improve our understanding of the cosmic-ray sources, of the diffuse non-thermal Galactic emissions (from radio wavelengths to gamma-rays), or in searches for dark matter annihilation signals. This review is mostly dedicated to particle physicists or more generally to non-experts. Introduction: The theoretical grounds of cosmic-ray (CR) physics have been developed for almost 5 decades [1], but it is only since very recently that observations with sufficient precision have become available to test the main features of the models. The sources of GeV-TeV CRs are mostly byproducts of supernova explosions. Supernova remnants (SNRs) and pulsar wind nebulae (PWNe) are the main Galactic CR (GCR) accelerators. The former accelerate hadrons and electrons at non-relativistic shocks, whereas the latter mostly accelerate electron-positron pairs produced from the annihilation of curvature photons with the strong magnetic fields around pulsars. Though the details of the acceleration mechanisms are not completely established, direct observations of these sources in radio, X-rays or gamma-rays prove that they do accelerate CRs up to 10-100 TeV. The transport of Galactic cosmic rays: For reviews and/or books, see [1–3] and references therein. In this section, I will introduce basic ingredients to help the non-experts understand CR transport and some degeneracies that currently plague even the most evolved models. GCRs are charged particles that diffuse off magnetic inhomogeneities δB in the Galaxy, with typical amplitudes δB/B ∼ 1 (with B ≈ O(1μG). Even though the Galactic magnetic field exhibits clear patterns in the spiral arms, these magnetic fluctuations still “isotropize” GCRs over scales of the order of a few times the Larmor radius rl ≃ 10 pc× {1/|Z| (pc/1TeV) (B/1μG)−1}, much shorter than the coherence length of the regular magnetic component. Let’s first forget about the specific geometry of the Milky Way (MW) and the details of CR transport. Let’s focus on stable CR nuclei, and consider only two different timescales: the confinement (or escape) time τesc (magnetic confinement in the MW), and the spallation time τs (inelastic interactions with the ISM gas) — for nuclei, energy losses mostly play a role at sub-GeV energies. The former must be a decreasing function of rigidity (R ≡ p/|Z|) because when E-mail: [email protected] A PWN must be paired with an SNR (not necessarily observable), though the contrary is not true, as for type 1A SNe rl reaches the size of the MW, CRs are no longer confined. The latter is a much weaker function of momentum as far as nuclear cross sections are considered. We can write a simple evolution equation for the differential CR density N = dn/dp: dN dt = Q − N τesc − N τs , where Q is a source term. We can assume that the latter is constant in time (related to the SN explosion rate) and take the steady-state limit of the above equation to link the source features to the local CR density from τesc and τs (much smaller than the age of the Galaxy). This is the so-called leaky-box (LB) model, which allows to estimate the confinement time. Nevertheless, this requires to know the source term accurately, which we don’t. This can be circumvented by considering two different kinds of CRs together: the primaries produced at sources (denoted A), and the secondaries produced only from inelastic scatterings of primaries with the ISM gas (denoted B, and assumed unique for simplicity). The source term for B is then merely NA/τs,A, and using the steady state regime of the previous equation, we get: NB NA = τescτs,B (τesc+τs,B)τs,A Rրր ≈ τesc(R) τs,A , where the last approximation is obtained from the different rigidity dependences of τesc and τs,B, for large R (this can be checked a posteriori, taking 1/τs,B = σB v n̄ism, where σB is the B+ISM → X cross section and n̄ism < nism is the average ISM gas density encountered by a CR while it is confined). Therefore the secondary-to-primary (II/I) ratio, as derived in the LB model, allows to determine the energy dependence of τesc. For its amplitude, one needs to refine the description of the spallation timescales by considering more elaborated distribution functions for the grammage (the column-density equivalent for CRs propagating in the ISM). The most widely used II/I ratio is the boron-to-carbon (B/C) because it is best measured. One typically finds a good fit to the data by taking τesc = τ 0 esc(R/1GV), with τ esc ≈ 100 Myr and δ ≈ 0.3-0.5 (for kinetic energies above 1 GeV/nucleon). We can now improve the physical picture by considering diffusion. It is a much involved theoretical field to try to infer the diffusion properties from those of magnetic turbulences, but we can first assume that the magnetic scatterers are distributed homogeneously in an extended slab that encompasses the Galactic disk, and that the diffusion coefficient is a scalar function of the rigidity K(R). The former is motivated by e.g. radio observations of the MW and of external disk galaxies. This slab has a half-height L, unknown a priori, but expected to be much larger than that of the disk, h ≃ 100 pc. Assuming that the ISM gas is confined to an infinitely thin disk (h ≪ L), we may write for a stable CR species: ∂tN − ~ ∇(K(R)~ ∇N ) + 2 hnism δ(z)σ vN = Q , where σ is the spallation cross section. For simplicity, we assume the slab radially extends to infinity. This reduces the above equation to one spatial coordinate z, perpendicular to the disk. We take the steady-state limit, and, to account for the escape, demand that N (|z| = L) = 0. For primary as well as secondary astrophysical CRs, the source term is confined to the disk, such that we may assume that Q = 2 h δ(z)Q0(R). For z 6= 0, a solution satisfying the boundary conditions is given by N (z 6= 0) = N (0)(1 − |z|/L). By integrating the previous equation in the range [−ǫ,+ǫ] in the limit ǫ → 0 (ǫ > 0), we get: K hL N (0) + nism σ vN (0) = Q0 . By analogy with the LB equation, one can readily conclude that the II/I ratios allow us to constrain K/L ∝ 1/τesc ∝ Rδ. This suggests that K(R) = K0 (R/1GV)δ provides a good description of the data — typical values are K0 ∼ 0.01 kpc/Myr and δ ∼ 0.3-0.5. Such a powerlaw shape for the diffusion coefficient is actually supported independently by theoretical results, in case diffusion originates from magnetic turbulence with a power-law spectrum (which is widely encountered in hydrodynamic systems) — an idealized example is the Kolmogorov turbulence spectrum, for which δ is close to 1/3. Note that a full theory connecting any turbulence properties to diffusion is yet to be derived, but models exist and can be tested [4]. An important consequence of the above result is that the normalization of the diffusion coefficient K0 and the slab size L, both unknown a priori, are found degenerate in the II/I ratio (K/L ∝ 1/τesc). Since we have seen from the LB model that the primary source term cancels out in the ratio, it is not surprising that any prediction made for other astrophysical secondary species from a primary spectrum should not be affected by uncertainties in K0 and L, provided the K0/L is fixed. This remains roughly valid in any diffusion model, because the source terms for primary as well as secondary CRs originate in the Galactic disk. This is no longer the case for CRs that would be produced in the whole magnetic halo; a constant source term would then give N (0) ∼ ∝ L/K: any prediction made for such a case is therefore very sensitive to L. This is typical of what happens for antimatter flux predictions made for dark matter signals, while the so-called secondary background prediction is under control (except for positrons, see below). Indeed, from the II/I ratios only, L can typically range from 1 to 15 kpc [5]. This K0 − L degeneracy is rather endemic of all CR diffusion models, but, fortunately, there are ways to break it, based on two different approaches: (i) probe physical observables which are not sensitive to the spatial boundary L; (ii) probe physical observables that exhibit non-linear dependences on K0 and L. For case (i), on may use unstable (radioactive) secondary CRs with decay timescales τ0 such that the associated diffusion scalelength is λd ∼ √ K γ τ0 ≪ L, beyond which contributions are suppressed. One can therefore only observe those unstable CRs which have been produced within a distance ∼ λd. The most used CR “clocks” range from τ0 = 0.301 Myr ( Cl) to 1.36 Myr (Be), for which, assuming a kinetic energy of 1 GeV/nucleon one finds λd ranging from 100 to 240 pc. Using such constraints, the available data strongly favor large-halo models, with L > 5 kpc [3]. Nevertheless, there are two important drawbacks. First, measuring fluxes of radioactive species is very challenging, and current data have large error bars (AMS02 should improve). Second, the fact that λd ∼ 200 pc implies that this method is very sensitive to the details of the local ISM, and there are hints that the local ISM is underdense over a scale of ∼ 100 pc (known as the local bubble). Therefore, this procedure could be affected by large systematic errors [6, 7]. As for case (ii), different observables can be used. Studies based on predictions of the diffuse Galactic gamma-ray emission [8] (see I. Moskalenko’s contribution in these proceedings), and of the diffuse Galactic radio emission [9], strongly favor values of L > 5 kpc. In both cases, this comes from the contribution of CR electrons (gamma-rays from inverse Compton on CMB outside the disk, radio from synchrotron losses). Nevertheless, these are indirect constraints which also strongly depend on the descriptions of the radiation fields in the disk and of the magnetic field. More direct constraints come from the local secondary positron flux at low energy, for which small values of K0 lead to predictions in excess with respect to the data (the correlation with L induced by the II/I ratios implies strong constraints on small values of L). This is clear from the predictions made in [10,11], and was pointed out in the context of dark matter searches [12]. State-of-the-Art: Evolved CR transport models include more ingredients than those discussed above. They generally rely on the following general CR transport equation (and then may differ in the assumptions used to solve it):