Strict constrains on cosmic ray propagation and abundances Aaron Vincent IPPP Durham MultiDark - IFT Madrid - Nov. 23 25
U. Reykjavík Gulli Johannesson Stanford/SLAC Igor Moskalenko Troy Porter Elena Orlando NASA Goddard Phil Graff Cambridge Mike Hobson Farhan Feroz Imperial Roberto Trotta IFIC (Valencia) Roberto Ruiz de Austri IPPP Durham Aaron Vincent MPE Garching Andrew Strong The Galbayes collaboration
Galbayes in a nutshell Most sophisticated ever Bayesian determination of the cosmic ray injection abundances and propagation parameters in the Galaxy using the GALPROP numerical package. Follow-up to Trotta et al 2 We use MultiNest nested sampling algorithm and SkyNet neural network machine learning tools. Fantastic four issue
Cosmic rays and dark matter Local p, p, e +,e,... direct observation Galactic centre p, p, e +,e,... Inverse compton scattering of CRs with Starlight, IR and CMB Bremsstralung secondary gammas
For DM hunters, cosmic ray propagation tells us: What the backgrounds look like What the DM signal looks like
(Standard, intragalactic) cosmic ray production Primaries Secondaries Particles interact with the Interstellar Medium (ISM) or decay, producing new particles along the way Supernovae, SNRs, pulsars, stellar winds accelerate particles to relativistic energies
Charged particles in the turbulent ISM Big whirls have little whirls, which feed on their velocity, and little whirls have lesser whirls, and so on to viscosity Lewis Fry Richardson Energy is injected into plasma on large scales Diffuses to smaller scales Energy in plasma Energy in B field fluctuations
Particle-plasma interaction ~B ~B ~ B ~B ~ B ~B ~ B CR diffusion in the turbulent ISM is a resonant process. Particles will scatter predominantly on B irregularities with a projected scale equal to the gyroradius: k r g = pc ZeB R B Looks like a random walk (diffusion) with coefficient 2 B vr g R /3 D xx ' B If E(k)dk k 5/3 dk Example: GeV proton in microgauss field: r g 6 pc ( Kolmogorov turbulence )
Diffusion Theory tells us D(R) ~ power law of the rigidity, but given all the unknowns about the ISM, we can t get the normalization or power from first principles @ (~x, t) @t D xx = D R R = rd xx (R)r (~x, t)+q(r, ~x, t) R = pc Ze free parameter
Other effects Diffusive reacceleration: scattering on bulk plasma (transverse B) waves, governed by Alfvén speed valf. Spallation/fragmentation: heavier elements probe a smaller (closer) region of the ISM. Nuclear decay: radioactive elements must have been produced nearby. Energy loss: Inverse-Compton, Bremsstrahlung, synchrotron Convection
Model: the galaxy as a cylinder Axially-symmetric, 2D galactic propagation zone R =8.5kpc gas 2z h diffusion zone R @ ' 2kpc Solve for steady state @t = source diffusion reacceleration @ @t = q(~r, p, t)+r(d @ @ xxr V ~ )+ @p p2 D pp @p energy loss fragmentation decay + @ h i p ṗ @p 3 r ~V ) f r p 2
Secondary/Primary ratios Ratio of secondary (e.g. B) to primary (e.g. C) is a measure of the column density of ISM stuff traversed by the cosmic ray on its way from a source to the earth. This is given by Long distance few bounces Dxx (diffusion coeff ~ /diffusion time) zh (height of the diffusion zone) Degeneracy: To break this degeneracy, one looks at radioactive secondaries, e.g. Be, 26 Al, which limits the distance from which we observe particles (i.e. sensitive only to Dxx, not zh) Short distance many bounces
GALPROP: http://galprop.stanford.edu R =8.5kpc gas 2z h diffusion zone R ' 2kpc We use an updated version of the publicly available code Fully Numerical 3d grid in r, z and p Position-dependent source, gas and radiation distributions based on observations Can simultaneously compute CRs, gammas and synchrotron
Free parameters Propagation Abundances: H, He, C, N, O, Ne, Na, Mg, Al, Si 2 Free parameters!
Nuisance parameters Modulation by solar magnetic field account for possible inconsistencies between data sets 2 Free parameters + nuisance parameters
Bayesian Inference Since small Z probes a different distance scale, it makes sense to separate out Z =,2 from heavier (Z > 4) Slow Few elements: fast Linear: very fast
Nested Sampling: MultiNest L 2 L L 3 L 2 L L 3 L Parameter space X X X 3 2 Technique for construction of isocontours in the parameter volume These allow the transformation of the likelihood volume integral to a onedimensional one Allows for a ~ order of magnitude speedup with respect to standard MCMC
Neural Networks Machine learning tool to train a set of hidden nodes to replace the likelihood evaluation (in this case GALPROP) with a set of simpler nonlinear operations SkyNet: NN training tool BAMBI: implementation for acceleration of bayesian searches 2-5% speedup Galprop only BAMBI: low tol. BAMBI: med tol. Posterior probability.8.6.4 Posterior probability.8.6.4 Posterior probability.8.6.4.2.2.2 2 4 6 8 2 4 6 8 D ( 28 cm 2 s! ).2.4.6.8 2 2.2 2.4 2.6 2.8 8.2.3.4.5.6.7.8.9 /
Data Data Experiment Energy Range PAMELA.44 GeV/n p CREAM 3 2 TeV/n p PAMELA.28 28 GeV/n He B/C Be/ 9 Be PAMELA.3 54 GeV/n CREAM.8 5 TeV/n ACE-CRIS ( 97-98) 72 7 MeV/n HEAO-3.62 35 GeV/n CREAM.4 45 GeV/n ACE-CRIS ( 97-99) 8 32 MeV/n ISOMAX.5.5 GeV/n B HEAO-3.62 35 GeV/n HEAO-3.62 35 GeV/n C CREAM 86 745 GeV/n N HEAO-3.62 35 GeV/n CREAM 95 826 GeV/n O HEAO-3.62 35 GeV/n CREAM 64 7287 GeV/n + abundance scans: Data Experiment Energy Range ACE-CRIS 85 24 MeV/n Ne HEAO-3.62 35 GeV/n CREAM 47 45 GeV/n Na ACE-CRIS 285 MeV/n HEAO-3.8 35 GeV/n ACE-CRIS 285 MeV/n Mg HEAO-3.8 35 GeV/n CREAM 27 425 GeV/n Al ACE-CRIS 285 MeV/n HEAO-3.8 35 GeV/n ACE-CRIS 2 285 MeV/n Si HEAO-3.8 35 GeV/n CREAM 27-248 GeV/n TRACER 38 288 GeV/n
Results.9 million likelihood evaluations (~2% by neural nets) 35 CPU years A few days (no big deal) 2. million likelihood evaluations (~2% by neural nets) 5.5 CPU years
Results: abundances 4 C N O Ne Na Mg Al Si this work (to appear) Abundance Xi=XSi 3 2 2 4 6 8 2 22 24 26 28 3 Atomic number A previous (ACE-only results) Solar (photosphere) Meteoritic Volatiles (C,N,O) depleted with respect to stellar abundances since CRs are preferentially accelerated from refractory-rich dust grains
Results: propagation parameters Posterior probability Posterior mean: 6.2 Best fit: 6.332.2 Posterior mean: 9.296 Best fit: 8.762.8.6.4.2 Posterior probability Posterior mean:.4665 Best fit:.46588.2 Posterior mean:.3832 Best fit:.49.8.6.4.2 Posterior probability Posterior mean: 8.9699 Best fit: 8.9223.2 Posterior mean: 3.65 Best fit: 3.4466.8.6.4.2 5 5 D ( 28 cm 2 s ).2.3.4.5.6.7.8.9 δ 2 3 4 v Alf (km/s) Light (B Si) elements p, p, He Trotta et al 2 Consistent; more free parameters = wider posteriors
Posterior bands 9 C 8 O 8 7 C 7 6 O E 2:3 #[GeV m 2 s sr]! 6 5 4 3 2 E 2:3 #[GeV m 2 s sr]! 5 4 3 2 primaries - 2 3 E/nuc (GeV) - 2 3 E/nuc (GeV).4.35.3 B/C Be/ 9 Be.25 B/C.2.5 Be/ 9 Be - secondaries..5-2 3 E/nuc (GeV) -2 - E/nuc (GeV)
Hydrogen and Helium 4 2 p p 5 4.5 4 p 7p E 2:7 #[GeV m 2 s sr]! 8 6 4 E 2:7 #[GeV m 2 s sr]! 3.5 3 2.5 2.5 2.5-2 3 E kin /nuc (GeV) - 2 3 E kin /nuc (GeV) 5 He # -4 2.5 7p=p He 2 p/p E 2:7 #[GeV m 2 s sr]! 5 7p=p.5.5-2 3 E kin /nuc (GeV) - 2 3 E kin /nuc (GeV)
2D posteriors Light (B Si) elements p, p, He v Alf Z ~ are probing larger scales in the ISM (don t disintegrate) Propagation properties are significantly different from the local ones responsible for B/C + heavier elements!! z h D,xx v Alf
Antiproton ratio 2.5 # -4 2.5 # -4 7p=p 2 2 7p=p.5.5 Simultaneously fitting everything.5 leads to significant tension between datasets, 7p=p bad fit.5-2 3 E/nuc (GeV) Fit to B, C, N, O, Ne Na, Al, Mg, Si - 2 3 E kin /nuc (GeV) Fit to H, He PAMELA AMS-2 (unpublished)
Summary Largest ever scan over the propagation parameters in a fully numeric implementation of the cosmic ray diffusion equation. Sensitivity of small vs large Z to propagation distance is very important. If you re looking for an excess, make sure you re consistently using the CR propagation parameters. Paper out very soon Also: GALDEF files with best parameters for GALPROP Future: extension to more models, nuclear cross sections, heavier elements
Extras
AMS-2 PAMELA AMS-2 2.5 # -4 4 p 2 2 7p=p.5.5 2.5 2 # -4 7p=p E 2:7 #[GeV m 2 s sr]! 8 6 4 2.5-2 3 E/nuc (GeV) 7p=p - 2 3 E kin /nuc (GeV).5-2 3 E kin /nuc (GeV)
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Modulation Parameters
Rescaling parameters
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