PPPC 4 DM ID - A Poor Particle Physicist Cookbook for Dark Matter Indirect Detection

We provide ingredients and recipes for computing signals of TeV-scale Dark Matter annihilations and decays.

Data and Results from 1012.4515 [hep-ph] (and 1009.0224 [hep-ph]), from 1312.6408 [hep-ph], 1412.5696 [astro-ph.HE], from 1505.01049 [hep-ph] and from 1511.08787 [hep-ph].

If you use the data provided on this site, please cite:
    M.Cirelli, G.Corcella, A.Hektor, G.Hütsi, M.Kadastik, P.Panci, M.Raidal, F.Sala, A.Strumia,
    "PPPC 4 DM ID: A Poor Particle Physicist Cookbook for Dark Matter Indirect Detection'',

    arXiv
1012.4515, JCAP 1103 (2011) 051.
    Erratum: JCAP 1210 (2012) E01.

If you use the 'Fluxes at production', please also cite:
   P. Ciafaloni, D. Comelli, A. Riotto, F. Sala, A. Strumia, A. Urbano,
   "Weak corrections are relevant for dark matter indirect detection'',
    arXiv 1009
.0224, JCAP 1103 (2011) 019,
where the energy spectra have been computed including electroweak corrections.

If you use the '
DMν : Neutrinos from the Sun', please cite:
   P. Baratella, M. Cirelli, A. Hektor, J. Pata, M. Piibeleht, A. Strumia,
   "PPPC 4 DM
ν : A Poor Particle Physicist Cookbook for Neutrinos from DM annihilations in the Sun'',
    arXiv 1312
.6408, JCAP 1403 (2014) 053.

If you use the 'Fluxes of charged cosmic rays at the Earth, after propagation: antiprotons', please cite:
   M. Boudard, M. Cirelli, G. Giesen, P. Salati,
   "A fussy revisitation of antiprotons as a tool for Dark Matter searches
'',
    arXiv 1412
.5696, JCAP 1505 (2015) 05, 013.

If you use the 'Propagation functions...', the 'Fluxes of charged cosmic rays', the 'Fluxes of Inverse Compton gamma-rays', the 'Fluxes of bremsstrahlung gamma-rays' or the 'Fluxes of synchrotron radiation', please cite:
   J. Buch, M. Cirelli, G. Giesen, M. Taoso,
   "PPPC 4 DM secondary: A Poor Particle Physicist Cookbook for secondary radiation from Dark Matter
'',
    arXiv 1505.01049
, JCAP 1509 (2015) 09, 037.

If you use the 'Fluxes at production in models with cascade decays in the hidden sector', please cite:
   G. Elor, N. Rodd, T. Slatyer, W. Xue,
   "Model-Independent Indirect Detection Constraints on Hidden Sector Dark Matter'',
    arXiv 1511.08787.


This is Release 6.0 (Jan 2016). Log of changes here.


Fluxes at production:

Complete fluxes at production, including EW corrections as computed in 1009.0224:


Mathematica  functions: The file dlNdlxEW.m provides the spectra  Log10 [d N/d Log10 x ]. The notebook Sample.nb shows how to load and use it.
   
Numerical tables: Each table provides the spectra dN/d Log10x of stable SM particles (positrons, antiprotons...), normalized per one annihilation.
The columns are: [ mDM, Log10x , dN/d Log10x for 28 primary channels ].
The primary channels are:
DM DM -->
eL+eL-, eR+eR-, e+e-, μL+μL-, μR+μR-, μ+μ -, τL+τL-, τR+τR-,τ+τ -, qq, cc, bb, tt, WL+WL-, WT+WT-,W+W-, ZL+ZL-, ZT+ZT-, Z+Z-, gg, γγ, hh, νeνe, νμνμ, ντντ, VV → 4e, VV → 4μ, VV → 4τ.
The non-polarized fluxes are just obtained as the appropriate average of the Left and Right or Longitudinal and Transverse ones.
The channel into Higgs bosons assumes a Higgs mass of 125 GeV.
  Positrons
  Antiprotons
  Gamma rays
  Electron Neutrinos
  Muon Neutrinos
  Tau Neutrinos
  Antideuterons
  all of the above All the 7 tables, in a single zipped file.


Fluxes at production without EW corrections (for comparison with previous calculations):

Mathematica  functions: The file dlNdlxPythia.m provides the spectra  Log10 [d N/d Log10 x ].
The notebook Sample.nb shows how to load and use it. 
   
Numerical tables: Same as above, but here the primary channels are the following 12:
DM DM --> e+e-, μ+μ -, τ+τ -, qq, cc, bb, tt, W+W-, ZZ, gg, γγ, hh.
  Positrons
  Antiprotons
  Gamma rays
  Electron Neutrinos
  Muon Neutrinos
  Tau Neutrinos
  Antideuterons
  all of the above All the 7 tables, in a single zipped file.


Fluxes at production in models with cascade decays in the hidden sector:

Numerical tables, Mathematica and Python functions: Download here



Propagation functions for electrons and positrons everywhere in the Galaxy:

Energy loss coefficient function b[E, r, z] for electrons and positrons in the Galaxy: Mathematica function btot.m, refer to the notebook Sample.nb for usage.
Annihilation

Positrons: The file ElectronHaloFunctGalaxyAnn.m provides the halo functions I(x,Es,r,z) at a point (r,z) in the Galaxy. [Note: very large file, almost 4GB.]
The notebook Sample.nb shows how to load and use it.
Decay

Positrons: The file ElectronHaloFunctGalaxyDec.m provides the halo functions I(x,Es,r,z) at a point (r,z) in the Galaxy. [Note: very large file, almost 4GB.]
The notebook Sample.nb shows how to load and use it.


Propagation functions for charged cosmic rays at the location of the Earth:

Annihilation

Positrons: The file ElectronHaloFunctEarthAnn.m provides the halo functions I(x,Es,rEarth) at the location of the Earth.
The notebook Sample.nb shows how to load and use it.


  Table of fit coefficients for the reduced halo function I(λ)
(in the approximated formalism - see paper).


Antiprotons:
Table of fit coefficients for the propagation function R(T).


Antideuterons:
Table of fit coefficients for the propagation function R(T).
Decay

Positrons: The file ElectronHaloFunctEarthDec.m provides the halo functions I(x,Es,rEarth) at the location of the Earth.
The notebook Sample.nb shows how to load and use it.


  Table of fit coefficients for the reduced halo function I(λ)
(in the approximated formalism - see paper).


Antiprotons: Table of fit coefficients for the propagation function R(T).


Antideuterons: Table of fit coefficients for the propagation function R(T).


Fluxes of charged cosmic rays at the Earth, after propagation:

Annihilation

Positrons:
Mathematica function: the file ElectronFluxAnn.m provides the spectra Log10 [d Φ/d Log10 E ].
Refer to the notebook Sample.nb for usage.


  Numerical table: provides the spectra dΦ/d Log10E.
The columns are: [ mDM, halo, propagation, Log10E , dΦ/d Log10E for 28 primary channels ].
The spectra are computed at a benchmark annihilation cross of <σv> = 10-26 cm3/s and renormalized multiplying by (mDM/GeV)2.
Units are particles/(cm2 s sr).
   
Antiprotons:
Mathematica function: the file ProtonFluxELDRAnn.m provides the spectra Log10 [d Φ/d Log10 K ].
Refer to the notebook Sample.nb for usage.


 
Numerical table: provides the spectra dΦ/d Log10K.
The columns are: [ mDM, halo, propagation, Log10K , dΦ/d Log10K for 28 primary channels ].
The spectra are computed at a benchmark annihilation cross of <σv> = 10-26 cm3/s and renormalized multiplying by (mDM/GeV)2.
Units are particles/(m2 s sr).

  The file ProtonFluxAnn.m provides the spectra without ELDR (Energy Losses including tertiaries and Diffusive Reacceleration, see 1412.5696 for details): this is now superseded and provided here only for the purpose of comparison with previous calculations. 
 
Antideuterons:
Mathematica function: the file DeuteronFluxAnn.m provides the spectra Log10 [d Φ/d Log10 (Kd/n) ].
Refer to the notebook Sample.nb for usage.


 
Numerical table: provides the spectra dΦ/d Log10(Kd/n).
The columns are: [ mDM, halo, propagation, Log10(Kd/n) , dΦ/d Log10(Kd/n) for 28 primary channels ].
The spectra are computed at a benchmark annihilation cross of <σv> = 10-26 cm3/s and renormalized multiplying by (mDM/GeV)2.
Units are particles/(m2 s sr).
Decay

Positrons: Mathematica function: the file ElectronFluxDec.m provides the spectra Log10 [d Φ/d Log10 E ].
Refer to the notebook Sample.nb for usage.


  Numerical table: provides the spectra dΦ/d Log10E.
The columns are: [ mDM, halo, propagation, Log10E , dΦ/d Log10E for 28 primary channels ].
The spectra are computed at a benchmark decay life of τ = 1026 s and renormalized multiplying by (mDM/GeV).
Units are particles/(cm2 s sr). 
   
Antiprotons:
Mathematica function: the file ProtonFluxELDRDec.m provides the spectra Log10 [d Φ/d Log10 K ].
Refer to the notebook Sample.nb for usage.


 
Numerical table: provides the spectra dΦ/d Log10K.
The columns are: [ mDM, halo, propagation, Log10K , dΦ/d Log10K for 28 primary channels ].
The spectra are computed at a benchmark decay life of τ = 1026 s and renormalized multiplying by (mDM/GeV).
Units are particles/(m2 s sr).

  The file ProtonFluxDec.m provides the spectra without ELDR (Energy Losses including tertiaries and Diffusive Reacceleration, see 1412.5696 for details): this is now superseded and provided here only for the purpose of comparison with previous calculations. 

Antideuterons:
Mathematica function: the file DeuteronFluxDec.m provides the spectra Log10 [d Φ/d Log10 (Kd/n) ].
Refer to the notebook Sample.nb for usage.


 
Numerical table: provides the spectra dΦ/d Log10(Kd/n).
The columns are: [ mDM, halo, propagation, Log10(Kd/n) , dΦ/d Log10(Kd/n) for 28 primary channels ].
The spectra are computed at a benchmark decay life of τ = 1026 s and renormalized multiplying by (mDM/GeV).
Units are particles/(m2 s sr).


J factors for prompt gamma rays:
 
Annihilation
Mathematica function: the file JAnn.m provides Log10 [J(θ)].
Refer to the notebook Sample.nb for usage.
Decay
Mathematica function: the file JDec.m provides Log10 [J(θ)].
Refer to the notebook Sample.nb for usage.


Fluxes of Inverse Compton gamma rays:

Annihilation
Mathematica function: the file IICAnn.m provides the Inverse Compton halo functions  IIC(Es,Eγ,l,b).
Refer to the notebook Sample.nb for usage.

Such notebook contains also a Mathematica code bite to compute the resulting IC flux.
Decay
Mathematica function: the file IICDec.m provides the Inverse Compton halo functions  IIC(Es,Eγ,l,b).
Refer to the notebook Sample.nb for usage.

Such notebook contains also a Mathematica code bite to compute the resulting IC flux.


Fluxes of bremsstrahlung gamma rays:

Annihilation
Mathematica function: the file IBremAnn.m provides the bremsstrahlung halo functions  Ibrem(Es,Eγ,l,b).
Refer to the notebook Sample.nb for usage.
Decay
Mathematica function: the file IBremDec.m provides the bremsstrahlung halo functions  Ibrem(Es,Eγ,l,b).
Refer to the notebook Sample.nb for usage.


Fluxes of synchrotron radiation:

Annihilation
Mathematica function: the file ISynAnn.m provides the synchrotron halo functions  Isyn(Es,ν,l,b).
Refer to the notebook Sample.nb for usage.
Decay
Mathematica function: the file ISynDec.m provides the synchrotron halo functions  Ibrem(Es,ν,l,b).
Refer to the notebook Sample.nb for usage.


Fluxes of extragalactic gamma rays:

Cosmological Boost factor B: Mathematica function BoostF.m, refer to the notebook Sample.nb for usage.
Optical Depth of the Universe: transparency factor Exp[-τ ] for gamma rays: Mathematica function OpticalDepth.m, refer to the notebook Sample.nb for usage.
Annihilation
Mathematica function: the file EGgammaFluxAnn.m provides the spectra Log10 [d Φ/d Log10 E ].
Refer to the notebook Sample.nb for usage.
Decay
Mathematica function: the file EGgammaFluxDec.m provides the spectra Log10 [d Φ/d Log10 E ].
Refer to the notebook Sample.nb for usage.


DMν : Neutrinos from the Sun:

DM annihilation rate in the Sun: Mathematica function GammaAnn.m, refer to the notebook Sample.nb for usage.
Neutrino energy spectra at production: Mathematica function dlNnudlxEW.m, refer to the notebook Sample.nb for usage.   
                       [03 jun 2015] Warning: some bugs in these files have been brought to our attention, we are working to fix them. Sorry for the inconvenience.
Neutrino energy spectra at detection: Mathematica function dlNnudlxEarth.m, refer to the notebook Sample.nb for usage.
                       [03 jun 2015] Warning: some bugs in these files have been brought to our attention, we are working to fix them. Sorry for the inconvenience.


Log of changes and releases:

[30 oct 2011] Fixed typo in Sample.nb about the units of the spectra of positrons (the units are particles/(cm^2 sec sr), not particles/(m^2 sec sr)). No new Release.
[30 oct 2011] Fixed bug in the labelling of the files 'JAnn.m' and 'JDec.m' (which was causing runaway loops when evaluated for some profiles). No new Release.
[29 may 2012] Uploaded new version of extragalactic gamma rays. They are an anticipation of a new Release, which will appear soon.
[21 aug 2012] New Release: 2.0 . Main modifications:
  • Included higgs boson channel hh with mass mh =125 GeV. All previous channels hmhm removed.
  • Fixed normalization and interpolation problems in 'dlNdlxEW.m' and 'dlNdlxPythia.m' (and, as a consequence, in all derived ingredients), notably in the γγ channel.
  • New version of extragalactic gamma rays, fixing some mistakes in the redshift dependence, the energy dependences and the impact of absorption. Also improved interpolation.
  • New version of the 'Optical Depth of the Universe', employing updated models of EBL (Extragalactic Background Light), fixing the redshift dependence and with a better interpolation.
This Release corresponds to version 4 of 1012.4515 on arXiv and to the Erratum on JCAP.
[21 mar 2013] Fixed 2 broken links.
[23 dec 2013] Fixed some typos in Sample.nb file.
[23 dec 2013] New Release: 3.0 . Main modification: addition of the section 'DMν : Neutrinos from the Sun', based on 1312.6408.
[03 aug 2014] Note on Mathematica v10 compatibility: Mathematica v10, released in 2014, does not assure compatibility with the InterpolatingFunction feature of the previous versions. Wolfram Customer Support can only provide a manual solution (highly unpractical). We suggest that you keep using Mathematica v9.
[16 nov 2014] Note on Mathematica v10 compatibility: the issue above is now solved (Wolfram released a patch of Mathematica v10).
[17 nov 2014] Fixed an interpolation issue mainly affecting ProtonFluxAnn and ProtonFluxDec at DM masses larger than 50 TeV and 100 TeV respectively. No new Release.
[15 jan 2015] New Release: 4.0 . Main modification: addition of 'ELDR' (Energy Losses including tertiaries and Diffusive Reacceleration) in the computation of the antiproton fluxes, based on 1412.5696.
[06 may 2015] New Release: 5.0 based on the results in 1505.01049. Main additions and modifications:
  • New version of the 'Energy loss coefficient function' b[E,r,z].
  • New version of the 'Propagation functions for electrons and positrons everywhere in the Galaxy'.
  • New version of the 'Propagation functions for charged cosmic rays at the location of the Earth', for positrons.
  • New version of the 'Fluxes of charged cosmic rays at the Earth, after propagation', for positrons.
  • New version of the 'Fluxes of Inverse Compton gamma rays', functions IICAnn.m and IICDec.m.
  • Addition of the 'Fluxes of bremsstrahlung gamma rays'.
  • Addition of the 'Fluxes of synchrotron radiation'.
[03 and 14 nov 2015] Fixed some broken links.
[09 dec 2015] Fixed bug in the labels for magnetic fields in one of the numerical tables for positrons at the Earth, after propagation (affected file: AfterPropagation_Ann_positrons.dat).
[13 jan 2016] New Release: 6.0 based on the results in 1511.08787 on spectra at production in models with cascade decays in the hidden sector. These results are contributed by G. Elor, N. Rodd, T. Slatyer and W. Xue.
[23 may 2016] Improvements and bug fixing in the section 'Code bites to compute fluxes of ICS gamma rays' in the Sample.nb file. No new release.

Contact: marco.cirelli@gmail.com .
Last updated: 23 May 2016