Galaxy Structure - Study of cosmic nuclei fluxes with AMS-02: implication for dark matter searc

In GALPROP è possibile specificare tutto attraverso il galdeffile

In primo luogo bisogna impostare la griglia su cui lavora GALPROP

1234567890123456789012 ======================value Title = SS/Kcap. 1 iter/Dxx=3.30e28 @3.e3 Dg=0.47 Va=23 inj=2.28 beta_rig/exp n_spatial_dimensions = 2 r_min =00.0 min r r_max =30.0 max r dr = 1.0 delta r z_min =-4.0 min z z_max =+4.0 max z dz = 0.1 delta z x_min = 0.0 min x x_max =+20.0 max x dx = 0.2 delta x y_min = 0.0 min y y_max =+20.0 max y dy = 0.2 delta y

Più la griglia è fine più la simulazione è lunga

bisogna trovare un buon compromesso tra

precisione e tempo richiesto

(una griglia troppo fine può non aggiungere significativi cambiamenti)

Uno dei parametri più importanti è l’altezza

dell’alone z

40Kpc sun 8,5Kpc 100 pc 60 Kpc (4-12) Kpc halo

UTILIZZO DI GALPROP : DIMENSIONI GALATTICHE

Emanuele

Emanuele OraziOrazi Figure 5.1:7 lu7 luSchematical view of the Galaxy structure in the GALPROP model[189].glio, 2006 glio, 2006 UnivUniv. . PerugiaPerugia, Italia, Italia

The fundamentals of any cosmic ray model reside in the assumptions that we make on the properties of the Galaxy. To have a complete description we use information taken from different fields of astronomy and astrophysics. In this section we will try to give an exhaustive description of the galactic frame as used in GALPROP model, focusing on the parameters tuned in our work to obtain good agreement with the experimental data. Each parameter can be specified using a galdef file, so the first

thing to do to get a GALPROP simulation is to built up a grid on which GALPROP works, paying attention to the fact that the more the grid is accurate the more will last the computation process: a compromise is thus necessary between this two factors. GALPROP is designed to treat both two and three spatial dimensional models, the corrisponding galdef parameter is n_spatial_dimensions.

In our work we tested both the options, obtaining comparable results despite very

In GALPROP è possibile specificare tutto attraverso il galdef

file

In primo luogo bisogna impostare la griglia su cui lavora GALPROP

Più la griglia è fine più la simulazione è lunga

bisogna trovare un buon compromesso tra

precisione e tempo richiesto

(una griglia troppo fine può non aggiungere significativi cambiamenti)

Uno dei parametri più importanti è l’altezza

dell’alone z

40Kpc sun 8,5Kpc 100 pc 60 Kpc (4-12) Kpc halo

UTILIZZO DI GALPROP : DIMENSIONI GALATTICHE

Emanuele

Emanuele OraziOrazi 7 lu7 luglio, 2006 glio, 2006 UnivUniv. . PerugiaPerugia, Italia, Italia

Figure 5.2: Section of a geldef grid containing Galaxy structure parameters. Here dr and dz represent respectively the cell size in galactocentric radius and in z direction, avaible in both the 2D and 3D case, and expressed in kpc[189].

different computational times (∆t2D ' 3min whereas ∆t3D' 8h); for the two dimen-

sional case we assumed a cylindrical symmetry (R,z) with isotropy in momentum space, whereas for the 3D a (x,y,z) system that may be fully asymmetric or not (as specified by the parameter use_symmetry). In this framework the Galaxy is considered as a dense central disk of thickness 2h, where h is assumed to be 100 pc, surrounded by a cylindrical halo (centered on the disk) where cosmic rays are trapped by the galactic magnetic field (see Fig. 5.1). In the disk the CR sources are located and this is the only place where interactions with matter take place. The half height of the halo (z_min and z_max in galdef file) is one of the most important parameter defined by the user, usually running in an interval from 1 kpc to 15 kpc as suggested by previous studies on radioactive nuclei [127] and distribution of synchrotron radiation [122]. The radial

extension of the halo usually runs from 10 kpc to 30 kpc and corresponds to the galdef parameter r_max. Beyond the halo cylindrical box, cosmic rays are free to escape, while inside it diffusion and reacceleration are supposed to work. The Solar System is located at about 8.3 ÷ 8.5 kpc from the center of the Galaxy [125,126].

All the galdef parameters described above are shown in Fig. 5.2

5.2.1 Galactic Source Distribution

In the previous section we argued that supernovae may be a reasonable source of cosmic rays. Therefore in GALPROP particular attention is dedicated to the supernovae distribution inside the disk. The source parameterization used in the model turns out to be

qi(r, z, R) = fi(r, z)· β−1R−γiδ(r− rmax) (5.1)

where R is the rigidity, γiare the spectral index γi ≡ γe(R), γp(R), γnuclei(R), rmaxis the

galdef parameter source_prameter_3 and fi(r, z) is the spatial sources distribution

and can be parameterized as

fi ∝ rαe−βre

|z|

zscale (5.2)

where α corresponds to the galdef parameter source_parameter_1 and its value runs from 0.4 to 2, β corresponds to source_parameter_2 and its value runs from 1 to 5. Finally zscale is a modulation factor that takes into account the confinement of

sources into the disk and corresponds to source_parameter_0 : all these parameters are expressed in kpc.

In GALPROP there is the possibility to introduce point-like supernovae but we did not consider this option for our purpose.

5.2.2 Interstellar Gas Distribution

The most important component of the interstellar medium gas is Hydrogen, followed by Helium. The Hydrogen is present in the medium in three possible forms: atomic Hydrogen (HI), molecular Hydrogen (H2) and ionized Hydrogen (HII). A good fit

to the atomic Hydrogen distribution is parameterized as an exponentially decreasing function of the halo height and can be written as

nHI(r, z) = nHI(r)e−(ln2)(

where nHI(r) is taken from [48] and represented in Fig. 5.3, while z0(r) has the form proposed in [129], namely z0(r) =    0.25kpc r≤ 10kpc 0.083_{· e}0.11r_{kpc r 10kpc}

with a breaking at the galactocentric radius, approximately equal to the one of the Solar System. Concerning the molecular Hydrogen we can parameterize its density as

3.1 The Galaxy

57 remnants cosmic ray acceleration is assumed to work for 10

yr. This means that

we have at least one cosmic ray acceleration site every cubic kpc at any time. Let

us mention that in [51] has been suggested that considerable amount of C and O is

accelerated in C- and O- enriched pre-supernovae Wolf-Rayet wind material but this

do not affect our source model since the origine sites still coincide with supernovae

remnants.

3.1.3 Gas Distribution in the Galaxy

The most important component of the interstellar medium gas is hydrogen followed

by helium. The hydrogen is present in the medium in three possible forms: atomic

hydrogen HI, molecular hydrogen H

and ionized hydrogen HII. A good fit to the

Figure 3.1: A schematic profile of the radial dependence of the three components of

hydrogen as a function of the radius at z = 0 from [55].

atomic hydrogen distribution is parameterized as an exponentially decreasing function

of the halo height and can be represented by

n

(r, z) = n

(r)e

−(ln 2)(z/z0(r))

,

(3.2)

Figure 5.3: A schematic profile of the radial dependence of the three components of hydrogen

from[51].

nH2(r, z) = nH2e

−ln2·(70pcz )2cm−2kpc−1 (5.4)

Finally for the last component we consider a first term which represents extensive warm ionized gas added to a second component that takes into account the concentration around r = 4 kpc. Thus we have the following parameterization, taken from [136]

nHII(r, z) = 0.025e−

|z|

1Kpc−(20Kpcr )2 + 0.2e−0.15Kpc|z| −(2Kpcr −2)2

The Helium distribution in interstellar medium has been determined exploiting the photospheric methods explained in[131]. It turns out that the Helium follows the Hy- drogen distribution with a factor He/H = 0.10 ± 0.08, that corresponds to the galdef parameter H _He_ratio and its value runs from 0.08 to 0.11.

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