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Galactic cosmic RAy Propagation: an Extensive Study

Periodic Reporting for period 1 - GRAPES (Galactic cosmic RAy Propagation: an Extensive Study)

Reporting period: 2017-10-01 to 2019-09-30

The problem of the origin of Cosmic Rays (CRs) is a central one in high energy astrophysics. While it is firmly established that the bulk of CRs originates within the Galaxy, the way in which these particles are accelerated at their sources, as well as the way in which they are confined in the magnetized and turbulent interstellar medium (ISM) are still a matter of debate.
The last few years have seen improvements in our knowledge of CR energy spectra. In particular, the orthodox picture of a universal injection spectrum of Galactic sources and a power law scaling of the CR diffusion coefficient with energy has been undermined by more precise measurements of individual chemical spectra by a number of experiments: ATIC, AMS, BESS, CREAM, DAMPE and PAMELA.

The GRAPES goal was to face this wealth of data to achieve a better understanding of the physics of CR transport.

I developed a model where the turbulence responsible for the scattering of CRs is described by two components: the external turbulence with a Kolmogorov spectrum, and the waves generated by CR themselves through streaming instability.
A simple estimate shows that the nonlinear damping rate of turbulent waves equals the growth rate CR streaming instability at a rigidity of 300 GV tantalisingly close to the rigidity where a break is observed. CRs above the break diffuse on external turbulence, while self-generated turbulence dominates at lower energies.
By taking additionally into account the advection of turbulence from the Galactic disk where the sources of CRs and turbulence are assumed to be located, I obtained that the diffusive halo naturally arises, with a size of a few kiloparsecs, compatible with the value that typically best fits observations in parametric approaches to CR transport. Within this model local observables, as the proton spectrum, are consistently reproduced (figure).
Self-generated turbulence can also play a role around sources. For the first time, I showed that the steep cosmic-ray lepton density produced by the pulsar source excites turbulence, which significantly inhibits the propagation of these same CRs. This model fits some observational characteristics of the gamma-ray emission observed around these sources (known as TeV halos), as the increasing size of these TeV halos as a function of the pulsar age.
An effective approach aiming at describing primary and stable secondary CR nuclei was developed afterwards. This model is based on the weighted slab approach which allows one to solve the advection-diffusion equation including the whole chain of spallation reactions from heavier nuclei to lighter nuclei. By comparing the results of my calculations with observations I obtained solid estimates of the grammage transversed by CRs in the Galaxy and their characteristics confinement time (figure).
Scientific activities

- I implemented a novel numerical model to solve the two coupled nonlinear differential equations, one describing the transport of CRs and the other describing the excitation, advection, and cascading of waves.
- I derived for the first time the streaming instability growth rates from electron/positron pairs emitted by pulsars and I implemented these rates in a time-depedent model of lepton production by galactic pulsars.
- I developed a comprehensive library (released as a public code) of cross sections of interest for CR studies, including inelastic, fragmentation, anti-matter production.
- I developed a phenomenological approach for CR galactic transport with up-to-date models for secondary production.
- I contributed to write a review aiming at providing a critical assessment of the standard paradigm for the origin of galactic CRs.

Training activities

- I gave a course on ``Numerical Methods'' to graduated students of GSSI and L'Aquila University and I was involved in the supervision of a student individual research project.
- I was involved in writing a national grant application, I contributed to some extent to formulate the research topics and to plan the budget of the group. The project has been granted for 2 years.
- I attended a specialised course on parallel programming and optimisation of scientific applications arranged by the Italian research center for computation (CINECA).
- I coordinated the Organisation of Colloquia at GSSI for the Astroparticle Physics division.
- My network skills have been improved through the organisation of two workshops, successfully attended by about 50 international experts.

Dissemination activities

- Dissemination of scientific results was ensured by presenting in a total of 12 occasions (mainly as invited lecturer) in 7 countries.
- I joined numerous outreach activities. In particular, I organised dedicated events aiming at introducing the MSCA actions and at encouraging researchers at the Institute to prepare and submit their application
- I contributed to organise the 2018 and 2019 International Cosmic Day aimed at high-school students.
- I gave 5 public talks to diverse audiences.
- I participated in the 2019 European Researchers’ Night.
Galactic CR diffusion is often described in the literature by means of a phenomenological diffusion coefficient that is a power law in energy whose normalisation and slope is fit to data. This simple picture has been threatened by the observational finding of a change of slope at rigidity around 300 GV in the spectrum of all CR species.

In GRAPES, I performed numerical investigations of a novel model which implements the well known fact that CRs may generate their own scattering centres through the excitation of streaming instability. In these scenarios, a crucial role for the determination of the saturation of streaming instability is played by the processes governing the damping of excited waves. However, a critical assessment of the role of this mechanism is still missing. Magnetic fluctuations are also produced by other phenomena, for instance supernova explosions and stellar winds also stir the interstellar plasma on large scales. Such perturbations cascade to smaller spatial scales as it is usually the case for turbulence. By cascading toward smaller scales, magnetic perturbations become anisotropic, which makes the problem of particle scattering rather tricky. These effects are often neglected in current approaches to describe CR diffusion by scattering on magnetic perturbations. Further investigations of this non-linear interplay between CRs and ISM, following the methodology exploited for the first time in GRAPES, will allow us to achieve a consistent global picture of CR transport.

In the second part of the project, I developed a model in which the diffusion coefficient entering the transport equation was modeled as to reproduce the features typical of the non-linear model. New unexpected results were found, as that the protons, Helium and heavier elements need to be injected into the ISM with different spectra, contrary to what expected in the common wisdom. This result leads inevitably to the conclusion that the acceleration process and/or the process of escape of CRs from the sources are more complex than usually modelled.

I also pointed out that the unprecedented quality of available CR data requires an equally accurate knowledge of the cross-sections describing CR interactions. Their availability is mandatory in order to interpret correct data, and an experimental work in this direction has to be considered as a priority.
The ratio between Beryllium and Boron as a function of the galactic halo size
The local proton spectrum compared with a model aiming at describing cosmic ray self-confinement