GALPROP tutorial Igor Moskalenko (Stanford U.). Igor V. Moskalenko 2 November 17, 2005GALPROP manual/Rome2, Italy Obtaining GALPROP The link: aws/dlp/zxc/kty/v42.3p

GALPROP tutorial

Igor Moskalenko (Stanford U.)

Igor V. Moskalenko 2 November 17, 2005 GALPROP manual/Rome2, Italy

Obtaining GALPROP

The link:http://www.mpe.mpg.de/~aws/dlp/zxc/kty/v42.3p/

Contains c++, fortran routines & input files (dat-files, compass gas maps, and isrf)

Dedicated GALPROP Web-site will go online soon!

– Controlled changes in GALPROP: tests + documentation +…

– New version(s) + archive versions– Post relevant information: best models, gas maps, ISRF,

nuclear cross sections…– Allow for communication with users – Ability to run GALPROP on-line…


I/O

galdef-filegas: COR, HIR, IAQ-filesRFComposite –(fits) file

dat-files (xsec, nuc.network)

GALPROP(c++ & fortran)

nuclei –(fits) file (R=Rsun)nuclei_full –(fits) file (whole galaxy)

γ-ray emissivities –(fits) files (brems, IC, π0)γ-ray skymaps –(fits) files (rings; brems, IC, π0)

FITS

GALDEF

v42.3

v42.3

FITS

sameleveldirs

Heliospheric modulation: on-the-fly in a plotting routine


Example Makefile

#CXX = g++-2.95#FC = g77-2.95CFITSIO = ${GLAST_EXT}/cfitsio/v2470CPPFLAGS = -O3 -Wno-deprecated -I${CFITSIO}/includeFFLAGS =LIBS = -lm -lg2cFITSLIB = -L$(CFITSIO)/lib -lcfitsio -Wl, rpath,$(CFITSIO)/libLDFLAGS = $(FITSLIB) $(LIBS)FOBJS := $(patsubst %.f,%.o,$(wildcard *.f))CCOBJS := $(patsubst %.cc,%.o,$(wildcard *.cc))galprop: ${FOBJS} ${CCOBJS} $(CXX) *.o -o $@ ${LDFLAGS}


Some Editing

Tested for g++ v2.9x compiler.New g++ compiler v3.x is more strict –routines require

some editing:

using namespace std;

#include<iostream>#include<cstdlib>#include<string>#include<cctype>#include<fstream>#include<cmath>


GALPROP Input: galdef-files

GALPROP is parameter-driven (user can specify everything!)

Grids• 2D/3D –options; symmetry options (full 3D, 1/8 -quadrants)• Spatial, energy/momentum, latitude & longitude grids• Ranges: energy, R, x, y, z, latitude & longitude • Time steps

Propagation parameters

• Dxx, VA, VC & injection spectra (p,e)

• X-factors (including R-dependence)

Sources• Parameterized distributions• Known SNRs• Random SNRs (with given/random spectra), time dependent eq.Other• Source isotopic abundances, secondary particles (pbar , e±, γ,

synchro), anisotropic IC, energy losses, nuclear production cross sections…


Algorithm

primary source functions (p, He, C .... Ni)source abundances, spectraprimary propagation -starting from maxA=64

source functions (Be, B...., e+,e-, pbars)using primaries and gas distributions secondary propagation

tertiary source functionstertiary propagation

-rays (IC, bremsstrahlung, πo-decay) radio: synchrotron

(i) CR –fixing propagation

(ii) γ-rays


GALPROP Output/FITS files

Provides literally everything:• All nuclei and particle spectra in every grid point

(x,y,R,z,E) -FITS files

Separately for π0-decay, IC, bremsstrahlung:• Emissivities in every grid point

(x,y,R,z,E,process)• Skymaps with a given resolution (l,b,E,process)

• Output of maps separated into HI, H2, and rings to allow fitting X, metallicity gradient etc.


Spatial Grids

Z

R,x,y0 1 2 3 4 5 6 7

1

-1

Typical grid steps (can be arbitrary!)Δz = 0.1 kpc, ΔΔz = 0.01 kpc (gas

averaging)ΔR = 1 kpcΔE = x1.2 (log-grid)


GALPROP Calculations

Constraints• Bin size (x,y,z) depends on the computer speed, RAM; final run can be

done on a very fine grid ! • No other constraints ! –any required process/formalism can be

implemented

Calculations (γ -ray related)

Vectorization options Now 64 bit to allow unlimited arrays Heliospheric modulation: routinely force-field, more sophisticated

model ?1.For a given propagation parameters: propagate p, e, nuclei, secondaries

(currently in 2D)2.The propagated distributions are stored3.With propagated spectra: calculate the emissivities (π0-decay, IC,

bremss) in every grid point4.Integrate the emissivities over the line of sight: • GALPROP has a full 3D grid, but currently only 2D gas maps (H2, H I, H II)• Using actual annular maps (column density) at the final step• High latitudes above b=40˚ -using integrated H I distribution


Dark Matter in GALPROP

DM annihilation products:χ0χ0−> p, pbar, e+, e−, γ

A set of routines (gen_DM_source.cc) to assign• The DM density profile (NFW, isothermal etc.)• Source functions for p, pbar, e+, e−

• Source function for γ’s• A set of user-defined parameters (10 int, 10

double precision) in galdef-file

DM annihilation products particles are propagated in the same model as CR particles.

Calculation of skymaps for DM γ-rays


galdef_44_599278 -I


galdef_44_599278 -II


galdef_44_599278 -III


galdef_44_599278 -IV


Nuclear Reaction Network+Cross Sections

p,EC,p,EC,ββ++

ββ--, , nn

Be7 Be10

Al26

Cl36

Mn54

Plus some dozens of more complicated reactions.But many cross sections are not well known…

V49

Ca41

Cr51

Fe55Co57

Ar37

SecondarySecondary,,radioactive ~1 Myrradioactive ~1 Myr

& & K-captureK-capture isotopesisotopes


Nuclear Reaction Network

III

I

II

IV

V

nuc_package.cc


nuc_package.cc: Stable & Long-lived Isotopes


nuc_package.cc: Long-Lived Isotopes


nuc_package.cc: “Boundary” Nuclei


isotope_cs_eval.dat


Transport Equations ~90 (no. of CR Transport Equations ~90 (no. of CR species)species)

ψψ((rr,p,t),p,t) – – density per total momentum

df

Vpdt

dp

p

ppppDp

p

Vxx

D

prqt

tpr

3

1

22

][

),(),,(

sources (SNR, nuclear reactions…)sources (SNR, nuclear reactions…)

convectionconvectiondiffusiondiffusion

diffusive reaccelerationdiffusive reacceleration

E-lossE-loss convectionconvection

fragmentationfragmentation radioactive decayradioactive decay


Finite Differencing


Finite Differencing: Example


Tri-Diagonal Matrix


Coefficients for the Crank-Nicholson Method


Near Future Developments

Full 3D Galactic structure:• 3D gas maps (from S.Digel, S.Hunter and/or smbd else)• 3D interstellar radiation & magnetic fields (A.Strong & T.Porter)Cross sections:• Blattnig et al. formalism for π0-production • Diffractive dissociation with scaling violation (T.Kamae –param.)• Isotopic cross sections (with S.Mashnik, LANL; try to motivate BNL,

JENDL-Japan, other Nuc. Data Centers)Modeling the local structure:• Local SNRs with known positions and ages• Local Bubble, local clouds –may be done at the final calculation

step (grid bin size ??)Energy range:• Extend toward sub-MeV range to compare with INTEGRAL diffuse

emission (continuum; 511 keV line)Heliospheric modulation:• Implementing a modern formalism (Potgieter, Zank etc.)Visualization tool (started) using the classes of CERN ROOT package:

images, profiles, and spectra from GALPROP to be directly compared with data

Improving the GALPROP module structure (for DM studies)


More developments

Point sources: develop algorithm(s) for modeling the background and interface to the rest of GLAST software

Instrumental response: how to implement Diffuse emission analysis has to include point source catalog! At least, two diffuse models: with/without the “excess” Develop test case(s) to test the accuracy of the numerical

model (simple gas distribution, no energy losses, uniform ISRF etc.)

Complete C++ package: rewrite several fortran routines in C++

Develop a fitting procedure to make automatic fitting to B/C ratio, CR spectra and abundances

Develop a dedicated Web-site:– Controlled changes in GALPROP: tests +documentation +…– Allow for communication with users– Post relevant information: best models, gas maps, ISRF, nuclear

cross sections…– Ability to run GALPROP on-line…


Fixing Propagation Parameters: Standard Way

Using secondary/primary nuclei ratio:•Diffusion coefficient and its index•Propagation mode and its

parameters (e.g., reacceleration VA,

convection Vz)

Radioactive isotopes:

Galactic halo size Zh Zh increase

B/C

Be10/Be9

Inte

rste

llar

Ek, MeV/nucleon

Ek, MeV/nucleon


Peak in the Secondary/Primary Ratio

• Leaky-box model: fitting path-length distribution -> free function

B/C

• Diffusion models: Diffusive reacceleration Convection Damping of interstellar

turbulence Etc.

Accurate measurements in a wide energy range may help to distinguish between the models

EEkk, MeV/nucleon, MeV/nucleon

too sharp max?


Distributed Stochastic Reacceleration

Fermi 2-nd order mechanism

BB

Scattering on magnetic turbulences Dpp~ p2Va

2/D

D ~ vR1/3 - Kolmogorov spectrum

Icr

E

strongreaccelerati

onweakreacceleration

ΔE

Simon et al. 1986Seo & Ptuskin

1994

1/3

Dxx = 5.2x1028 (R/3 GV)1/3cm-2 s-1

Va = 36 km s-1

γ ~ R-δ, δ=1.8/2.4 below/above 4 GV


Convection

Galactic wind

Escape length

Xe

E

vR-0.6

wind orturbulentdiffusion

resonantdiffusion

Jones 1979

problem: too broad sec/prim peak

D~R0.

6

Dxx = 2.5x1028 (R/4 GV)0.6cm-2 s-1

dV/dz = 10 km s-1 kpc-1

γ ~ R-δ, δ=2.46/2.16 below/above 20 GV


Damping of Interstellar Turbulence

p

l(p)

Iroshnikov-Kraichnan cascade:

Kolmogorov cascade:

W(k)

k

dissipation

1/1012cm1/1020cm

Simplified case:

• 1-D diffusion• No energy losses

Mean free path

nonlinearcascade

Ptuskin et al. 2003, 2005


Dxx – Diffusion Coefficient

Plain diffusion

Diffusivereacceleration

Reaccelerationwith damping

~R0.6

~β-3


• Positrons/electrons p+p->π,K->e± (MS 1998)– Dermer 1986 method: LE –Stecker Δ-isobar model (isotropic

decay), HE –scaling (inv. x-section: Stephens & Badhwar 1981), plus interpolation in between

– Pion decay “includes” polarization of muons– Kaon decay – scaling (Stephens & Badhwar 1981)

• Antiprotons (M et al. 2002)– pp Inclusive production x-section (Tan & Ng 1983)– pA, AA-> pbar –scaling using Gaisser & Schaeffer 1992 or

Simon et al. 1998 –results similar– Total inelastic x-section (p: TN’83, A: Moiseev & Ormes 1997)

– p+pbar annihilation x-section = (p+pbar)tot – (p+p)tot (LE: TN’83, HE: PDG’00 –Regge parameterization)

How It Is Really Done: Secondary Particles


Elemental Abundances: CR vs. Solar System

CR abundances: ACE

Solar system abundances

LiBeB

CNO

F

Fe

ScTiV

CrMn

Si

Cl

Al

O

Na

S

“input”

“output”


Fitting to Measured CR Abundances (ACE vs HEAO-3)

Fitting to measured CR abundances in the wide energy range (~0.1 – 30 GeV) is problematic: May indicate systematic or cross-calibration errors


Total Nuclear Cross Sections

Ekin, MeV/nucleonWellisch & Axen 1996


Isotopic Production Cross Sections of LiBeB

Semi-empirical systematics are not always correct.

Results obtained by different groups are often inconsistent and hard to test.

Very limited number of nuclear measurements:

Evaluating the cross section is very laborious and can’t be done without modern nuclear codes.

Use LANL nuclear database and modern computer codes.


LiBeB: Major Production Channels

Propagated Abundance * Cross-sectionPropagated Abundance * Cross-section

Be B

C

Li

N

OLi6

79 10

1113

1514

•Well defined (65%):C12, O16 ->LiBeBN14 -> Be7

(see Moskalenko & Mashnik 28 ICRC, 2003)

•Few measurements:C13,N -> LiBeBB -> BeB

•Unknown:LiBeB,C13,N -> LiBeB

“Tertiary” reactions also important! -35%

12 16

A=


Effect of Cross Sections: Radioactive Effect of Cross Sections: Radioactive SecondariesSecondaries

Different Different size from different ratios…size from different ratios…

Zhalo,kpc

STST

WW

2727Al+pAl+p2626AlAl

•ErrorsErrors in CR measurements (HE & LE) in CR measurements (HE & LE)•ErrorsErrors in production cross sections in production cross sections•ErrorsErrors in the lifetime estimates in the lifetime estimates•DifferentDifferent origin of elements (Local origin of elements (Local Bubble ?)Bubble ?)

natnatSi+pSi+p2626AlAl

WW

STST

TT1/21/2==??

Ek, MeV/nucleon


How It Is Really Done: Nucleons

• Calculated for p+A reactions and scaled for α+A (Ferrando et al. 1988)

• Calculation of total nuclear cross sections– Letaw et al. 1983– Wellisch & Axen 1996 (corrected), Z>5– Barashenkov & Polanski 2001

• Calculation of isotopic production cross sections– Webber et al. 1993 (non-renormalized, renormalized); E>200

MeV/nucleon, essentially flat– Silberberg & Tsao 2000 (non-renormalized, renormalized); claim that

it works at all energies, but is problematic sometimes– Fits to the available data (LANL, Webber et al., etc.) in the form of a

function or a table (see .dat files), but data may not be always available

– Use the best of all three, but very time consuming work

• Nuclear reaction network– Nuclear Data Tables (includes several decay channels + branching)– Standard β± -decay, emission of p, n– K-capture isotopes can be treated separately


Interstellar Gas

► Extend CO surveys to high latitudes– newly-found small molecular clouds will otherwise be interpreted as

unidentified sources, and clearly limit dark matter studies

► C18O observations (optically thin tracer) of special directions (e.g. Galactic center, arm tangents)

– assess whether velocity crowding is affecting calculations of molecular column density, and for carefully pinning down the diffuse emission

20

0

-20

-40

Gal

acti

c L

atit

ud

e

220 200 180 160 140 120 100 80 60 40 20 0

CfA 1.2mGalactic Longitude

Dam

e, H

artman

n, & T

haddeus (200

1)D

ame

& T

haddeus (20

04)


Distribution of Interstellar Gas

• Neutral interstellar medium– 21-cm H I & 2.6-mm CO (stand in for H2)

• Near-far distance ambiguity, rotation curve, optical depth effects, …

Dame et al.(1987)

Hartmann &Burton (1997)

(25°, 0°)

W. Keel

CO

H IG.C.

25°

Seth Digel


Seth Digel’05


Gas Distribution

Sun

Molecular hydrogen H2 is traced using J=1-0 transition of 12CO, concentrated mostly in the plane (z~70 pc, R<10 kpc)

Atomic hydrogen H I (radio 21 cm) has a wider distribution (z~1 kpc, R~30 kpc)

Ionized hydrogen H II (visible, UV, X) small proportion, but exists even in halo (z~1 kpc)

Z=0,0.1,0.2 kpc


Gas Rings: HI (Inner & Outer Galaxy)

Seth Digel’05


Seth Digel’05

Gas Rings: HI (Our Neighborhood)


• Bremsstrahlung (Koch & Motz 1959, SMR2000) –many different regimes:– LE: 0.01 < Ekin < 0.07 MeV –nonrelativistic non-screened brems– Intermediate: 0.07 < Ekin <2 MeV– HE: Ekin > 2 MeV arbitrary screening: unshielded charge, 1-, 2-

electron atoms (form factors, Hylleraas, Hertree-Fock wave functions)

– Fano-Sauter limit: k->Ekin • “Anisotropic” IC (MS2000)

– Takes into account the anisotropic angular distribution of background photons

• Neutral pion decay (see “secondary positrons/electrons”)• Synchrotron radiation (Ginzburg 1979, Ghisellini et al. 1988)

– Averaging over pitch angle– Uses total magnetic field (regular + random)

• Emissivities: uses “real” H2, H I gas column densities (“rings”)• Skymap calculations: integration over the line of sight

How It Is Really Done: Gammas


Uncertainties in the Propagation Models

• Production cross sections of isotopes and pbarsTypical errors ~50%

Fitting to B/C ratio may introduce errors in Dxx

• Propagation models and parameters Gas distribution in the Galaxy

Ambient spectrum of CR (solar modulation, GeV excess in γ’s !) Current knowledge of CR diffusion

• Heliospheric modulation Depends on rigidity Similar for all nuclei A/Z~ +2

Different for protons A/Z=+1 and pbars A/Z=-1

• Systematic errors of measurementsDifficult to account for

Simultaneous measurements of Li, Be, B, C, secondary e+, p in a wide energy range ~100 MeV/nucleon – 100 GeV/nucleon are needed to understand CR propagation and distinguish between the models: looking forward to Pamela launch!

_

GALPROP tutorial Igor Moskalenko (Stanford U.). Igor V. Moskalenko 2 November 17, 2005GALPROP manual/Rome2, Italy Obtaining GALPROP The link: aws/dlp/zxc/kty/v42.3p

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