7.3.2. Edit source, transport…¶
As discussed in Section 6.2.3, all models have mandatory parameters (even if many of the are unused) related to (i) Geometry , (ii) ISM, (iii) Sources, (iv) Transport parameters. Let us detail below how it works.
7.3.2.1. Geometry¶
It is illustrated below for Model2DKisoVc (Maurin et al., 2001).
Model parameters: radial extension
R
, halo half-heightL
, thin disc half-height (h
), and a possible local-underdensityrhole
(Putze et al., 2010). All these parameters can later be used as fit parameters (e.g.,L
), see also Table 6.9:Model2DKisoVc @ Geometry @ ParNames @ M=0 @ L,h,R,rhole Model2DKisoVc @ Geometry @ ParUnits @ M=0 @ kpc,kpc,kpc,kpc Model2DKisoVc @ Geometry @ ParVals @ M=0 @ 4.,0.1,20.,0.122D cylindrical model: 1st axis is radial coordinate (
r
, 10 linear bins[0,R]
), 2nd axis is vertical coordinate (z
, 10 linear bins[0,L]
). In these coordinates the sun position is set tor=8.5
(same unit as XAxis) andz=0
(same unit as Yaxis):Model2DKisoVc @ Geometry @ XAxis @ M=0 @ r:[0,R],10,LIN Model2DKisoVc @ Geometry @ YAxis @ M=0 @ z:[0,L],10,LIN Model2DKisoVc @ Geometry @ XSun @ M=0 @ 8.5 Model2DKisoVc @ Geometry @ YSun @ M=0 @ 0.Warning
The only values the user may change are Geometry@ParVals values and the position of the sun Geometry@XSun. See syntax in Section 6.2.3.1.
7.3.2.2. ISM¶
All the model currently implemented have a constant distribution. The syntax below means that the ISM is described by a formula which is just a constant value (that the user can modify) for H (atomic, ionised, and molecular) and He densities (in \({\rm cm}^{-3}\)), and plasma temperature (in K):
Model2DKisoVc @ ISM @ ParNames @ M=0 @ - Model2DKisoVc @ ISM @ ParUnits @ M=0 @ - Model2DKisoVc @ ISM @ ParVals @ M=0 @ - Model1DKisoVc @ ISM @ Density @ M=1 @ HI:FORMULA|0.867 Model1DKisoVc @ ISM @ Density @ M=1 @ HII:FORMULA|0.033 Model1DKisoVc @ ISM @ Density @ M=1 @ H2:FORMULA|0. Model1DKisoVc @ ISM @ Density @ M=1 @ He:FORMULA|0.1 Model1DKisoVc @ ISM @ Te @ M=0 @ FORMULA|1.e4Warning
The only values the user may change are those in FORMULA|. See syntax in Section 6.2.3.2.
7.3.2.3. Sources¶
Implemented models do not handle point-like sources and only correspond to steady-state sources. The parameters below correspond to:
a generic type of sources
ASTRO_STD
(any other name would have been fine too), which accelerates all CRs selected for propagation (ASTRO_STD|ALL
), except those declared as pure secondaries in the list of CRs to propagate - see Section 7.3.1.this source is based on the spectrum template
POWERLAW
\(= q\times \beta^{\rm eta\_s}\times {\rm Rig}^{\rm -alpha}\), which has three parameters (q, alpha, and eta_s), and where the normalisation parameter is q (ASTRO_STD|POWERLAW|q
). This template is one of the available templates defined in the same parameter file (see Section 6.2.5):
the source abundance initialisation
kSSISOTFRAC,kSSISOTABUND,kFIPBIAS
assumes Solar system isotopic abundances biased by the first ionization potential (we recommend at least to havekSSISOTFRAC
to fix isotopic fractions). If data to normalise is not an empty list, q values are rescaled (unless q_X set as a fitted parameters):Base @ CRData @ NormList @ M=0 @ H,He:PAMELA|20.|kEkn;C,N,O,F,Ne,Na,Mg,Al,Si,P,S,Cl,Ar,K,Ca,Sc,Ti,V,Cr,Mn,Fe,Ni:HEAO|10.6|kEkn UsineRun @ Calculation @ IsUseNormList @ M=0 @ truein the example below, eta_s is taken to be a universal parameter (same for all CR species), whereas q and alpha are taken per CR (internally, usine creates q_X and alpha_X parameters, with X any CR in source).
any of the source parameters could be left as a free parameter!
the spatial distribution of the source is taken to be
SNRMODIFIED
, with universal values for all CRs (SHARED
).The fact that all parameters are M=1 means than in principle we could declare several types of sources (different name possibly form different templates and/or species accelerated):
Model2DKisoVc @ SrcSteadyState @ Species @ M=1 @ ASTRO_STD|ALL Model2DKisoVc @ SrcSteadyState @ SpectAbundInit @ M=1 @ ASTRO_STD|kSSISOTFRAC,kSSISOTABUND,kFIPBIAS Model2DKisoVc @ SrcSteadyState @ SpectTempl @ M=1 @ ASTRO_STD|POWERLAW|q Model2DKisoVc @ SrcSteadyState @ SpectValsPerCR @ M=1 @ ASTRO_STD|q[PERCR:DEFAULT=1.e-5];alpha[PERZ:DEFAULT=2.1,H=2.1,He=2.2];eta_s[LIST:DEFAULT=-1.,1H_HE=-1.5,C_N_O=-2] Model2DKisoVc @ SrcSteadyState @ SpatialTempl @ M=1 @ ASTRO_STD|SNRMODIFIED Model2DKisoVc @ SrcSteadyState @ SpatialValsPerCR @ M=1 @ ASTRO_STD||rsol[SHARED:8.5];a[SHARED:1.];b[SHARED:1.];dex[SHARED:1.]Warning
The values the user may change are (i) the name of the source
ASTRO_STD
(can be anything), (ii) the template spectrum (POWERLAW
) and/or spatial distribution (SNRMODIFIED
) used for the source, (iii) the types of parameters in the source (universalSHARED
, by CRPERCR
, by elementPERZ
, or a listLIST
) and their default values. See syntax in Section 6.2.3.4 for more details.
7.3.2.4. Transport¶
It can be as generic as it needs to be (see Section 6.2.3.5)! However, semi-analytical models implemented and solved in USINE cannot be as flexible as the user would wish them to be. First, only isotropic diffusion models are implemented (so we only need
K00
coefficient below). Second the 1D and 2D models can only have a galactic wind perpendicular to the disc (wind componentW0
only). For illustration purpose, we provide two examples below, one with a standard diffusion coefficient, and a second one with a break (as used in Génolini et al., 2018). The diffusion coefficient can be any function of the USINE-interpreted energy variables beta (lorentz factor), gamma, p (momentum in GV), Rig (rigidity in GV), Ekn (kinetic energy per nucleon in GeV/n), Etot (total energy in GeV), and Ek (kinetic energy in GeV)→ No break:
Model1DKisoVc @ Transport @ ParNames @ M=0 @ Va,Vc,K0,delta,eta_t Model1DKisoVc @ Transport @ ParUnits @ M=0 @ km/s,km/s,kpc^2/Myr,-,- Model1DKisoVc @ Transport @ ParVals @ M=0 @ 55.,18.7,0.008,0.86,0. Model1DKisoVc @ Transport @ K @ M=1 @ K00:FORMULA|beta^eta_t*K0*Rig^delta→ With break:
Model1DKisoVc @ Transport @ ParNames @ M=0 @ Va,Vc,K0,delta,eta_t,Rbreak,Deltabreak,sbreak Model1DKisoVc @ Transport @ ParUnits @ M=0 @ km/s,km/s,kpc^2/Myr,-,-,GV,-,- Model1DKisoVc @ Transport @ ParVals @ M=0 @ 85.4,19.5,0.0358,0.61,-0.059,125.,0.023,0.01 Model1DKisoVc @ Transport @ K @ M=1 @ K00:FORMULA|beta^eta_t*K0*Rig^delta*(1+(Rig/Rbreak)^(Deltabreak/sbreak))^(-sbreak)With or without a break, the remaining parameters are:
Model1DKisoVc @ Transport @ Wind @ M=1 @ W0:FORMULA|Vc Model1DKisoVc @ Transport @ VA @ M=0 @ FORMULA|Va Model1DKisoVc @ Transport @ Kpp @ M=0 @ FORMULA|(4./3.)*(Va*1.022712e-3*beta*Etot)^2/(delta*(4-delta^2)*(4-delta)*K00)Warning
The values the user may change are the names/number of parameters and associated formulae for
K00
andKpp
. The other parameters are fixed by the model (Va
andVc
) and only their default value can be changed.