Full calculation of clumpiness boost factors for antimatter cosmic rays in the light of Lambda-CDM N-body simulation results

Anti-proton and positron Galactic cosmic ray spectra are among the key targets for indirect detection of dark matter. The boost factors, corresponding to an enhancement of the signal and linked to the clumpiness properties of the dark matter distribution, have been taken as high as thousands in the past. The dramatic impact of these boost factors for indirect detection of antiparticles, for instance with the PAMELA satellite or the coming AMS-02 experiment, asks for their detailed calculation. We take into account the results of high resolution N-body dark matter simulations to calculate the most likely energy dependent boost factors linked to the cosmic ray propagation properties, for anti-protons and positrons. Starting from the mass and space distributions of sub-halos, the anti-proton and positron propagators are used to calculate the mean value and the variance of the boost factor for the primary fluxes. We take advantage of the statistical method introduced in Lavalle et al. (2007) and cross-check the results with Monte Carlo computations. By spanning some extreme configurations of sub-halo and propagation properties, we find that the average contribution of the clumps is negligible compared to that of the smooth dark matter component. Sub-halos do not lead to enhancement of the signals, unless they are taken with some extreme (unexpected) properties. This result is independent of the nature of the self-annihilating dark matter candidate considered, and provides precise estimates of the theoretical and the statistical uncertainties of the antimatter flux from dark matter substructures. Spectral distortions can still be expected in antimatter flux measurements, but scenarios invoking large and even mild clumpiness boost factors are strongly disfavoured by our analysis.

[1]  Dark matter detection in the light of recent experimental results , 2003, hep-ph/0309346.

[2]  The shape of the gravitational potential in cold dark matter haloes , 2006, astro-ph/0612327.

[3]  O. University,et al.  The survival and disruption of cold dark matter microhaloes: implications for direct and indirect detection experiments , 2006, astro-ph/0608495.

[4]  David Merritt.  Evolution of the dark matter distribution at the galactic center. , 2004, Physical review letters.

[5]  L. Bergstrom,et al.  Observability of γ rays from dark matter neutralino annihilations in the Milky Way halo , 1998 .

[6]  Michael Kuhlen,et al.  Dark Matter Substructure and Gamma-Ray Annihilation in the Milky Way Halo , 2006, astro-ph/0611370.

[7]  A. Helmi,et al.  The radial velocity dispersion profile of the Galactic halo : constraining the density profile of the dark halo of the Milky Way , 2005, astro-ph/0506102.

[8]  Production and propagation of cosmic ray positrons and electrons , 1997, astro-ph/9710124.

[9]  A. Kravtsov,et al.  The Robustness of Dark Matter Density Profiles in Dissipationless Mergers , 2005, astro-ph/0510583.

[10]  C. Carollo,et al.  The evolution of dark matter halo properties in clusters, filaments, sheets and voids , 2007, 0704.2595.

[11]  Bars and Cold Dark Matter Halos , 2005, astro-ph/0506627.

[12]  Kathryn V. Johnston,et al.  A TWO MICRON ALL SKY SURVEY VIEW OF THE SAGITTARIUS DWARF GALAXY. III. CONSTRAINTS ON THE FLATTENING OF THE GALACTIC HALO , 2004 .

[13]  R. Somerville,et al.  Profiles of dark haloes: evolution, scatter and environment , 1999, astro-ph/9908159.

[14]  Gaelle Boudoul,et al.  Antiprotons from Spallations of Cosmic Rays on Interstellar Matter , 2001 .

[15]  Department of Physics,et al.  The spin and shape of dark matter haloes in the Millennium simulation of a Λ cold dark matter universe , 2006 .

[16]  Michael S. Warren,et al.  The cosmic code comparison project , 2007, 0706.1270.

[17]  D. Nagai,et al.  The Astrophysical Journal, submitted Preprint typeset using L ATEX style emulateapj v. 11/12/01 THE RADIAL DISTRIBUTION OF GALAXIES IN ΛCDM CLUSTERS , 2004 .

[18]  Earth-mass dark-matter haloes as the first structures in the early Universe , 2005, Nature.

[19]  Oleg Y Gnedin,et al.  Dark matter profile in the galactic center. , 2004, Physical review letters.

[20]  The observed concentration–mass relation for galaxy clusters , 2007, astro-ph/0703126.

[21]  J. Stadel,et al.  Convergence and scatter of cluster density profiles , 2004, astro-ph/0402267.

[22]  J. Stadel,et al.  Radial distribution and strong lensing statistics of satellite galaxies and substructure using high‐resolution ΛCDM hydrodynamical simulations , 2005, astro-ph/0506125.

[23]  Stefan Hofmann,et al.  The power spectrum of SUSY-CDM on subgalactic scales , 2003, astro-ph/0309621.

[24]  Cosmic ray positron excess and neutralino dark matter , 2001, astro-ph/0109318.

[25]  G. Bertone,et al.  Antiproton and positron signal enhancement in dark matter minispikes scenarios , 2007, 0704.2543.

[26]  P. Kroupa,et al.  The spatial distribution of the Milky Way and Andromeda satellite galaxies , 2006 .

[27]  Aleksandr V. Gurevich,et al.  Distribution of dark matter in the galaxy and the lower limits for the masses of supersymmetric particles , 1992 .

[28]  Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry , 2006, astro-ph/0606216.

[29]  Supersymmetry and the Cosmic Ray Positron Excess , 2002, hep-ph/0202156.

[30]  Model independent approach to focus point supersymmetry: From dark matter to collider searches , 2005, hep-ph/0507282.

[31]  D. Nagai,et al.  Submitted to the Astrophysical Journal Preprint typeset using L ATEX style emulateapj v. 11/12/01 RESPONSE OF DARK MATTER HALOS TO CONDENSATION OF BARYONS: COSMOLOGICAL SIMULATIONS AND IMPROVED ADIABATIC CONTRACTION MODEL , 2004 .

[32]  P. Ullio,et al.  Clumpy Neutralino Dark Matter , 1998, astro-ph/9806072.

[33]  G. Lake,et al.  Density Profiles and Substructure of Dark Matter Halos: Converging Results at Ultra-High Numerical Resolution , 1999, astro-ph/9910166.

[34]  Thermal decoupling of WIMPs from first principles , 2007 .

[35]  Circular velocity profiles of dark matter haloes , 2004, astro-ph/0403077.

[36]  Is the dark halo of our Galaxy spherical , 2003, astro-ph/0309579.

[37]  Walter Dehnen,et al.  Mass models of the Milky Way , 1996 .

[38]  Cosmic-ray positrons: are there primary sources? , 1999, astro-ph/9902162.

[39]  Supersymmetry and the positron excess in cosmic rays , 2001, hep-ph/0108138.

[40]  R. Bouwens,et al.  Discovery of a Ringlike Dark Matter Structure in the Core of the Galaxy Cluster Cl 0024+17 , 2007, 0705.2171.

[41]  J. Bullock,et al.  Dark energy and dark matter haloes , 2005 .

[42]  M. Elmi.  VELOCITY TRENDS IN THE DEBRIS OF SAGITTARIUS AND THE SHAPE OF THE DARK-MATTER HALO OF THE GALAXY , 2008 .

[43]  Damping scales of neutralino cold dark matter , 2001, astro-ph/0104173.

[44]  Influence of Orbital Behaviour and Chaos on the Shape of Dark Matter Halos , 2007, 0704.3078.

[45]  Francisco Prada,et al.  Where Are the Missing Galactic Satellites? , 1999, astro-ph/9901240.

[46]  J. Carr,et al.  Indirect detection of dark matter , 2006 .

[47]  V.Berezinsky,et al.  Small - scale clumps in the galactic halo and dark matter annihilation , 2003 .

[48]  F. Boudjema,et al.  Relic density of neutralino dark matter in the MSSM with CP violation , 2006 .

[49]  The origin and tidal evolution of cuspy triaxial haloes , 2003, astro-ph/0310660.

[50]  U. Washington,et al.  The inner structure of ΛCDM haloes – III. Universality and asymptotic slopes , 2003, astro-ph/0311231.

[51]  The distribution of satellite galaxies: the great pancake , 2005, astro-ph/0503400.

[52]  A. Morselli,et al.  Measurements of the absolute energy spectra of cosmic-ray positrons and electrons above 7 GeV , 2002 .

[53]  U. Florida,et al.  Weak-Lensing Mass Reconstruction of the Interacting Cluster 1E 0657–558: Direct Evidence for the Existence of Dark Matter , 2003, astro-ph/0312273.

[54]  Brian Fields,et al.  Big-Bang nucleosynthesis (2006 Particle Data Group mini-review) , 2006, astro-ph/0601514.

[55]  C. Muñoz,et al.  GLAST versus PAMELA: a comparison between the detection of gamma rays and positrons from neutralino annihilation , 2006, hep-ph/0607266.

[56]  S McKee,et al.  New measurement of the cosmic-ray positron fraction from 5 to 15 GeV. , 2004, Physical review letters.

[57]  Is the dark matter halo of the Milky Way flattened , 2006, astro-ph/0608175.

[58]  R. Taillet,et al.  Clumpiness of dark matter and the positron annihilation signal , 2007 .

[59]  Stuart P. D. Gill,et al.  The evolution of substructure - I. A new identification method , 2004, astro-ph/0404258.

[60]  J. Wadsley,et al.  The removal of cusps from galaxy centres by stellar feedback in the early Universe , 2006, Nature.

[61]  Heavy wino-like neutralino dark matter annihilation into antiparticles , 2005, hep-ph/0511118.

[62]  Dark matter subhaloes in numerical simulations , 2004, astro-ph/0406034.

[63]  E. Branchini,et al.  Dark matter annihilation in substructures revised , 2007, 0706.2101.

[64]  Observability of gamma rays from neutralino annihilations in the Milky Way substructure , 2003, astro-ph/0309464.

[65]  J. Read,et al.  The Causes of Halo Shape Changes Induced by Cooling Baryons: Disks versus Substructures , 2007, 0707.0737.

[66]  HongSheng Zhao.  Analytical models for galactic nuclei , 1996 .

[67]  M. Carollo,et al.  Cusps in CDM halos , 2005, astro-ph/0504215.

[68]  A. Klypin,et al.  The Anisotropic Distribution of Galactic Satellites , 2005, astro-ph/0502496.

[69]  Tucson,et al.  Strong and Weak Lensing United. III. Measuring the Mass Distribution of the Merging Galaxy Cluster 1ES 0657–558 , 2006, astro-ph/0608408.

[70]  STScI,et al.  The Tumultuous Lives of Galactic Dwarfs and the Missing Satellites Problem , 2004 .

[71]  S. White,et al.  A Universal Density Profile from Hierarchical Clustering , 1996, astro-ph/9611107.

[72]  M. Zaldarriaga,et al.  Small-scale power spectrum of cold dark matter , 2005, astro-ph/0504112.

[73]  Detecting the dark matter annihilation at the ground EAS detectors , 2006, hep-ph/0610387.

[74]  Major mergers of galaxy haloes: cuspy or cored inner density profile? , 2003, astro-ph/0309243.

[75]  M. Valluri,et al.  On Relaxation Processes in Collisionless Mergers , 2006, astro-ph/0609612.

[76]  Tucson,et al.  A Direct Empirical Proof of the Existence of Dark Matter , 2006, astro-ph/0608407.

[77]  What mass are the smallest protohalos? , 2006, Physical review letters.

[78]  George Lake,et al.  Dark Matter Substructure within Galactic Halos , 1999, astro-ph/9907411.

[79]  Effects of cold dark matter decoupling and pair annihilation on cosmological perturbations , 2006, astro-ph/0607319.

[80]  The galactic positron flux and dark matter substructures , 2006, astro-ph/0611872.

[81]  Michael Kuhlen,et al.  Formation and Evolution of Galaxy Dark Matter Halos and Their Substructure , 2007, astro-ph/0703337.

[82]  Cosmic positron signature from dark matter in the littlest Higgs model with T parity , 2006, hep-ph/0602157.

[83]  Y. Hoffman,et al.  Evolution of Characteristic Quantities for Dark Matter Halo Density Profiles , 2006, astro-ph/0610090.

[84]  Daisuke Nagai,et al.  The Effect of Gas Cooling on the Shapes of Dark Matter Halos , 2004, astro-ph/0405189.

[85]  G. Bertone,et al.  Particle dark matter: Evidence, candidates and constraints , 2004, hep-ph/0404175.

[86]  A. Noutsos,et al.  HESS observations of the galactic center region and their possible dark matter interpretation. , 2006, Physical review letters.

[87]  S. Jogee,et al.  Stellar Bar Evolution in Cuspy and Flat-cored Triaxial CDM Halos , 2005, astro-ph/0501352.

[88]  Preservation of Cuspy Profiles in Disk Galaxy Mergers , 2005, astro-ph/0506290.

[89]  J. Silk,et al.  Local dark matter clumps and the positron excess , 2006, astro-ph/0602320.

[90]  Y. Suto,et al.  The Dependence of Dark Halo Clustering on Formation Epoch and Concentration Parameter , 2006, astro-ph/0610099.

[91]  Michael Kuhlen,et al.  Early Supersymmetric Cold Dark Matter Substructure , 2006 .

[92]  Garching,et al.  Substructures in cold dark matter haloes , 2003, astro-ph/0306205.

[93]  B. Moore,et al.  Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models , 2005, astro-ph/0509417.

[94]  Astronomy,et al.  The statistics of lambda CDM Halo Concentrations , 2007, 0706.2919.

[95]  Kaluza-Klein dark matter and Galactic antiprotons , 2005, astro-ph/0506389.

[96]  D. Maurin,et al.  Cosmic Rays below Z = 30 in a Diffusion Model: New Constraints on Propagation Parameters , 2001 .

[97]  P. Ullio,et al.  Cosmological dark matter annihilations into γ rays: A closer look , 2002, astro-ph/0207125.

[98]  The dependence of the mass assembly history of cold dark matter halos on environment , 2006, astro-ph/0606360.

[99]  S. McGaugh,et al.  The collision velocity of the bullet cluster in conventional and modified dynamics , 2007, 0704.0381.

[100]  G. Lake,et al.  Resolving the Structure of Cold Dark Matter Halos , 1997, astro-ph/9709051.

[101]  Dark matter dynamics and indirect detection , 2005, astro-ph/0504422.

[102]  Asymmetries in the inner regions of ΛCDM haloes , 2006, astro-ph/0605687.

[103]  J. Silk,et al.  Clumpy cold dark matter , 1993 .

[104]  B. Moore,et al.  Empirical models for Dark Matter Halos , 2005 .

[105]  Amina Helmi,et al.  Velocity Trends in the Debris of Sagittarius and the Shape of the Dark Matter Halo of Our Galaxy , 2004, astro-ph/0406396.

[106]  Numerical study of halo concentrations in dark-energy cosmologies , 2003, astro-ph/0309771.

[107]  Joachim Stadel,et al.  Velocity and spatial biases in cold dark matter subhalo distributions , 2004, astro-ph/0402160.

[108]  A. Green,et al.  The first WIMPy halos , 2005, astro-ph/0503387.

[109]  The mass function and average mass-loss rate of dark matter subhaloes , 2005 .

[111]  Ben Moore,et al.  Concentration, spin and shape of dark matter haloes: Scatter and the dependence on mass and environment , 2007 .

[112]  J. Weller,et al.  The Bound Mass of Substructures in Dark Matter Halos , 2006, astro-ph/0603150.

[113]  H. Shan,et al.  THE WEDDING OF MODIFIED DYNAMICS AND NON-EXOTIC DARK MATTER IN GALAXY CLUSTERS , 2007, 0706.1279.

[114]  G. Tarlé,et al.  Cosmic-Ray Electrons and Positrons from 1 to 100 GeV: Measurements with HEAT and Their Interpretation , 2001 .

[115]  Oliver Hahn,et al.  Properties of dark matter haloes in clusters, filaments, sheets and voids , 2006, astro-ph/0610280.

[116]  New signature of dark matter annihilations : Gamma rays from intermediate-mass black holes , 2005, astro-ph/0509565.

[117]  Destruction of small-scale dark matter clumps in the hierarchical structures and galaxies , 2005, astro-ph/0511494.

[118]  James S. Bullock,et al.  Halo Substructure and the Power Spectrum , 2003 .

[119]  D. Syer,et al.  Survival of substructure within dark matter haloes , 1997, astro-ph/9712222.

[120]  Supersymmetric dark matter in light of WMAP , 2003, hep-ph/0303043.

[121]  Baryonic pinching of galactic dark matter halos , 2006, astro-ph/0608634.

[122]  W. Dehnen,et al.  The velocity dispersion and mass profile of the Milky Way , 2006, astro-ph/0603825.

[123]  A. Helmi,et al.  Erratum: The radial velocity dispersion profile of the Galactic halo: constraining the density profile of the dark halo of the Milky Way (Monthly Notices of the Royal Astronomical Society (2005) 364 (433-442)) , 2006 .

[124]  Positron propagation and fluxes from neutralino annihilation in the halo , 1998, astro-ph/9808243.

[125]  Padova,et al.  On the environmental dependence of halo formation , 2004 .

[126]  Quantification of discreteness effects in cosmological N -body simulations: Initial conditions , 2004, astro-ph/0410451.

[127]  On the proof of dark matter, the law of gravity, and the mass of neutrinos , 2006, astro-ph/0609125.

[128]  Joachim Stadel,et al.  Cusps in cold dark matter haloes , 2005 .

[129]  Fabrizio Brighenti,et al.  The X-Ray Concentration-Virial Mass Relation , 2006, astro-ph/0610135.

[130]  U. Chicago,et al.  The Astrophysical Journal, in press Preprint typeset using L ATEX style emulateapj v. 6/22/04 THE DEPENDENCE OF HALO CLUSTERING ON HALO FORMATION HISTORY, CONCENTRATION, AND OCCUPATION , 2005 .

[131]  K. Griest,et al.  Supersymmetric dark matter , 1992 .

[132]  M. Steinmetz,et al.  The Power Spectrum Dependence of Dark Matter Halo Concentrations , 2000, astro-ph/0012337.

[133]  J. Stadel,et al.  Density Profiles of Cold Dark Matter Substructure: Implications for the Missing-Satellites Problem , 2003, astro-ph/0312194.

[134]  Spatial Origin of Galactic Cosmic Rays in Diffusion Models: I- Standard sources in the Galactic disk , 2002, astro-ph/0212112.

[135]  M. Meneghetti,et al.  Effects of the halo concentration distribution on strong-lensing optical depth and X-ray emission , 2007, 0705.3169.

[136]  P. Madau,et al.  The Shapes, Orientation, and Alignment of Galactic Dark Matter Subhalos , 2007, 0705.2037.

[137]  V. A. Dogiel,et al.  Astrophysics of cosmic rays , 1990 .

[138]  I. Shlosman,et al.  Growing Live Disks within Cosmologically Assembling Asymmetric Halos: Washing Out the Halo Prolateness , 2006, astro-ph/0603487.

[139]  Empirical models for dark matter halos II: inner profile slopes, dynamical profiles, and ρ/σ<3 , 2006, astro-ph/0608613.

[140]  Joseph Silk,et al.  Can supersymmetry naturally explain the positron excess , 2004 .

[141]  Reconstructing the Triaxial Shapes of Dark Matter Halos from the Anisotropic Spatial Distributions of their Substructures in the Concordance Cosmology , 2005, astro-ph/0505179.

[142]  X. Bi.  Gamma rays from the neutralino dark matter annihilations in the Milky Way substructures , 2005, astro-ph/0510714.

[143]  Padova,et al.  Populating a cluster of galaxies - I. Results at z=0 , 2000, astro-ph/0012055.

[144]  Risa H. Wechsler,et al.  The shape of dark matter haloes : dependence on mass, redshift, radius and formation , 2005, astro-ph/0508497.

[145]  R. Taillet,et al.  New results on source and diffusion spectral features of Galactic cosmic rays: I- B/C ratio , 2002, astro-ph/0206286.

[146]  Environmental influences on the morphology and dynamics of group-sized haloes , 2007, astro-ph/0703440.

[147]  Formation and Evolution of the Self-Interacting Dark Matter Halos , 2003, astro-ph/0412169.

[148]  On mini-halo encounters with stars , 2006, astro-ph/0604142.

[149]  A. Dekel,et al.  Shapes of Stellar Systems and Dark Halos from Simulations of Galaxy Major Mergers , 2006, astro-ph/0604121.

[150]  S. White,et al.  The subhalo populations of ΛCDM dark haloes , 2004, astro-ph/0404589.

[151]  Lars Bergström,et al.  Non-baryonic dark matter: observational evidence and detection methods , 2000 .

[152]  Uncertainties of cosmic ray spectra and detectability of antiproton mSUGRA contributions with PAMELA , 2005, astro-ph/0502406.

[153]  S. Colafrancesco,et al.  Multi-frequency analysis of neutralino dark matter annihilations in the Coma cluster , 2005 .

[154]  D. Maurin,et al.  Antiprotons in cosmic rays from neutralino annihilation , 2004 .

[155]  P. J. McMillan,et al.  The haloes of merger remnants , 2007, astro-ph/0701541.

[156]  Antiprotons from primordial black holes , 2001, astro-ph/0112486.

[157]  Halo evolution in the presence of a disc bar , 2005, astro-ph/0508647.

[158]  Joachim Stadel,et al.  The Structural evolution of substructure , 2003 .

[159]  Review of Big Bang Nucleosynthesis and Primordial Abundances , 2000, astro-ph/0001318.

[160]  M. Viel,et al.  Is the Concentration of Dark Matter Halos at Virialization Universal? , 2007, 0706.0856.

[161]  Assembly bias in the clustering of dark matter haloes , 2006, astro-ph/0611921.

[162]  Concentrations of Dark Halos from Their Assembly Histories , 2001, astro-ph/0108151.

[163]  G. Angus,et al.  Cold dark matter microhalo survival in the Milky Way , 2007 .