C [ ] -4 Evidence of Stochastic Acceleration of Secondary 2.2 1.0 2.0 1.8 1.6 1.4 1.2 C k p p Φ /Φ ratio fit Antiprotons by Supernova Remnants! 0.8 0.6 0.4 0.2 0.0-6 - 1 k [ GV ] -1 AMS-02 PAMELA Fermi 1.0 2 Rigidity [GV] IC, D. Hooper, T. Linden, Phys. Rev. D 95, 123007 (2017)! IC, D. Hooper, T. Linden Phys. Rev. D 93, 043016 (2016)! IC, D. Hooper, Phys. Rev. D 89, 043013 (2014) 1 2 Ilias Cholis, 08/09/2017
Acceleration in SNR p e Producing hard CR Secondary component from Diffusive Shock Acceleration Stochastic Acceleration inside SNRs Blasi, PRL 2009, Mertsch & Sarkar PRL 2009 pp Propagation in Galaxy pp accelerated secondary e ± secondary e ± (ν, γ ) primary protons secondary e ± primary e new component conventional component Pic from: Ahlers, Mertsch, Sarkar PRD 2009 Interplay of three typical timescales for CRs: Spallation, Escape and Acceleration inside the Sources. If: spall A!B < A esc, then we have secondaries produced inside the acceleration region If: acc < spall, then secondaries are efficiently accelerated So:Acc A! Spall A!B! Acc B! Escape! P ropagation! Obesrvation Blasi, PRL 2009
Some details on the accelerated secondary CRs: Source term inside the SNR: Q i (E kin )=Σ j N j (E kin ) [ ] j i β cn ( ) 1 gas + E kin τj i dec ( σ sp Propagation inside the SNR (diffusion, advection, source, decay/spallation and adiabatic E losses): v f i x = D 2 f i i x 2 + 1 3 Bohm diffusion: dv dx p f i p Γ if i + q i, D ± i (E) =K B r L (E) c 3 =3.3 22 K B B 1 EZ 1 i cm 2 s 1 (9) Here the factor that defines the amplitude of the enhancement is: allowing for faster diffusion around the shock front. ge and energy of t K B ' (B/ B) 2 CRs around the s Thus the source term of SNR CR changes: f + i (x, p) =f i(0,p)+ q+ i (0,p) Γ+ i (p)f i(0,p) v + x,
Accounting for all galactic SNRs and in-! cluding propagation effects, one can! expect a rise in other secondary/primary! CR ratios should be observed with AMS-02. B C ratio This results in Limits from B/C! (including background uncertainties),! on the acceleration of secondary! CRs in supernova remnants: 0.50 0.30 0.20 0.15 0. Background K B 4.3 K B 8.0 K B 12.6 K B 40 HEAO 3 PAMELA AMS 02 q i Di B C ratio The impact of this additional! secondary component is more! evident for high E, light nuclei: Integrating the transport equation over infinitesimal 1 5 50 0 500 00 1 5 50 0 500 00 distance one gets [26]: E kin GeV n E kin GeV n 0.50 0.50 p f i(x, p) = γfi (0,p) γ(1 + r 2 ) Γ i (p)d i (p) f i (0,p) 1 r 2 v 2 f i 4 0 1 0.01 4 B 12 C 16 O 28 Si IC and Dan Hooper PRD 2014 20 50 0 200 500 00 p GeV c nucleon 0.50 FIG. 1: The ratio of the secondary cosmic rayheao acceleration 3 term to the primary cosmic ray acceleration term PAMELA in Eqs. 7 and0.30 8, as a function of momentum per nucleon. AMS 02 The impact of including the acceleration of secondary cosmic rays produced 0.20inside and around the supernova shock front is most important 0.15 at high energies and for lighter species. For B the ratio is significantly Background higher since f is suppressed. As B in Ref. [26], we K B have 9.9 adopted optimistic values for K B, B, n 0. gas, v and r K(see B 12.6 text for more details). K B 15.9 K B 40 2 f w d m a l c b a f f C i c W ( c f f t v W
Implications on the Positron fraction e e e 0.50 0.20 0. 0.05 Background K B 4.3 K B 8.0 K B 15.9 K B 40 PAMELA AMS 02 e e e 0.50 0.20 0. 0.05 Background E max 3 TeV E max TeV E max 0 TeV PAMELA AMS 02 0.02 20 50 0 200 500 E GeV 20 50 0 200 500 Secondary CRs produced in SNRs can NOT explain the full positron fraction excess even for optimistic cases of energy losses inside the SNRs. 0.02 IC and Dan Hooper PRD 2014 E GeV What about the Antiproton to Proton Ratio? Antiprotons background uncertainties are very large. They are associated with:! i) the antiproton production cross-section from CR protons and heavier nuclei collisions with the ISM gas! ii) the propagation of CRs through the ISM! iii) Solar Modulation
I) Antiproton production cross-section uncertainties The are significant uncertainties on the antiproton production cross-section directly from p-p collisions. Most parametrizations have only used data from the 70s. Di Mauro et al. PRD 2014 Di Mauro et al. PRD 2014 Also one has to include the production of antiprotons from collisions with heavier nuclei (mainly He), which can contribute ~40% more antiprotons than the p-p collisions alone. Also contribution from antineutrons produced first at p-p. FIG. 8. Estimate of the uncertainties in the antiproton source term from inelastic pp scattering. The blue band indicates the 3 uncertainty band due to the global fit with Eq.(13), while the red band corresponds to the convolution of the uncertainties brought by fits to the data with Eq.(13), Eq.(12) and with the spline interpolation (see Fig.6.). The orange band takes into account the contribution from decays of antineutrons produced in the same reactions. Vertical bands as in Fig.6. See text for details. See also results from Kappl & Winkler JCAP 2014
II) Accounting for ISM galactic propagation uncertainties for Cosmic Rays diffusion Voyager 1 sources @ (r, p, t) ~ (Dxx r ~ ) = q(r, p, t) + r @t h i h i @ 2 @ @ p ~ ~ + p Dpp ( 2 ) + (r V ) @p @p p @p 3 re-acceleration convection Voyager 1 (ISM) proton flux: Regime where Outter HS or BW! may matter True ISM I.C., D.Hooper, T.Linden PRD 2016 We use a numerical! solver, GALPROP, and build several models that are in agreements with CR measurements
B/C from PAMELA and AMS-02; Sets the time scale for CRs to! diffuse away from the galactic disk. Also sets constraints on the! combination of convection and re-acceleration.
Figure 6. Same as Figure 5, but for the A < 0 polarity cycle. III) Dealing with Solar Modulation Uncertainties Strauss et. al ApJ 2011 There is Charge Dependence Figure 7. Three-dimensional spatial representation of the particle trajectories shown in Figure 1. Two representative particle trajectories (black and gray lines) are shown for the A > 0 (left panel) and A < 0 (right panel) HMF polarity cycles. In the A < 0 cycle, the pseudo-particles (galactic electrons) are transported mainly toward higher latitudes, while in the A > 0 cycle, the particles remain confined to low latitudes and drift outward mainly along the HCS. This illustration is consistent with the results of galactic electrons shown in the previous figure. Drifts Can NOT be ignored7 PAMELA, Adriani et al. 2013 0 Differential intensity [part. (m2 s sr MeV) 1] 40 z (AU) 20 0 20 Diffusion is not isotropic 1 qa < 0 qa > 0 40 20 0 20 40 x (AU) 60 80 0 Jul08 Jan08 IC, DH, TL, PRD 2016 Jan09 CR proton flux 4-week intervals 2 3 40 Jul09 = 15 Jan There is Time Dependence! AND Energy Dependence 1 0 1 Kinetic Energy [GeV] Jul07 Jan07 Jul06
Let the CR archival Data tell us how the CR fluxes have been modulated: Constraining the qa>0 era: Constraining the qa<0 era: IC, DH, TL, PRD 2016 Assuming we know the! ISM proton spectrum
II) & III) Cross-checking every time with all the PROTON data;! monthly AND total (i.e ISM & Solar Modulation): True ISM p! spectrum Modulated p spectrum! at Earth Constraining the form of the Modulation potential and the ISM p spectrum! The boron-to-carbon ratio predicted for the various Galactic cosmic-ray models given in Tab incr a recursive manner. between the cosmic-ray proton spectrum for the same set of models and the PAMELA data. In e
Combining all uncertainties together and! marginalizing over them: IC, Hooper, Linden PRD 2017
(kpc/myr) (µg 1 ) (kyr/cm 3 )... (kpc/myr) (µg 1 ) (kyr/cm 3 ). We do get Positive Potential Signal of Stoch. Accel. of Secondaries from antiproton/proton ratio at energies above 0 GeV: 0.0165 ± 0.0003 0.0 ± 5.8 24.0 ± 2.0 14/38 0.0165 ± 0.0011 9.8 ± 2.9 46.5 ± 8.1 11 0.0176 ± 0.0003 0.01 ± 0.13 45.6 ± 1.6 21/38 0.0152 ± 0.0001 6.45 ± 2.46 59.0 ± 5.0 12 0.0159 ± 0.0002 0.0 ± 0.3 27.1 ± 1.6 22/50 0.0134 ± 0.0006 4.3 ± 2.4 67.4 ± 4.9 25 0.0155 ± 0.0002 0.01 ± 0.06 52.6 ± 1.2 77/50 0.0111 ± 0.0003 0.5 ± 32 76.5 ± 1.6 36 0.0156 ± 0.0002 0.01 ± 0.18 29.1 ± 1.4 31/59 0.0129 ± 0.0005 3.19 ± 2.26 70.9 ± 4.2 27 0.0148 ± 0.0002 0.01 ± 0.04 55.9 ± 1.1 122/59 0.05 ± 0.0003 0.2 ± 0.86 78.8 ± 1.4 46 gorov [ best-fit ] p / p ratio -3 (b) p/p ratio - Kolmogorov [ best-fit ] ) 3 ( kyr / cm 60 (c) Kolmogorov [ best-fit ] -4 IC, Hooper, Linden PRD 2017 n- τ snr 40 p/p -A TOT -B AMS 2 etic energy (GeV/n) 3-5 -6 1 ISM SNR-A TOT SNR SNR-B AMS 2 kinetic energy (GeV) 20 B/C 0.015 0.02 K 0 /L ( kpc / Myr ) p/p ratio (b) measured by AMS (Aguilar et al. 2016,b) incomparisonwiththebest-fitmodels(lightblu V/n of kinetic energy. Contributing components fromif standard nearby SNRs secondary are production efficient accelerators (orange, long-dashe the component from secondary production in SNRs (green of secondaries, short-dashedbut lines). have Thelow shaded abundances and of p/p-driven intermediate (b) fits mass performed nuclei, atthen E> bands represen imensional contour plots (c) are shown for the parameters snr n and K 0 /L at 68 % (shaded blue area) an fidence levels. The plots correspond to B/C-driven (a) GeV. the B/C ratio (Aguilar et al. tio (Aguilar et al. 2016) have See also Di Mauro et al. JCAP 2014 Tomassetti & Oliva 2017 Variations between SNRs. For example the connection between the B/C ratio the description pbar/p ofcould the AMS be weakened. data because, at high-energy the expected decrease of the ISM-induced B/C ratio i
Conclusions Production and stochastic acceleration of secondaries in SNRs is a likely source of high energy hard secondary CR spectra The amplitude of that additional component is not well understood Using the CR secondary/primary spectra we can probe it From B/C we have been able to place some upper bound on the contribution of the stoch. accel. secondaries On the antiproton/proton ratio we find an increase/hardening of the spectrum compared to theoretical expectations above 0 GeV To study the pbar/p ratio we have taken into account all basic uncertainties (injection and propagation through the ISM, antiprotons production cross-sections). May possibly be an indication of a lower bound on the contribution of the stoch. accel. secondaries and tell us something about variations between SNRs (in distance from us and/or in their metallicity environments)
Thank you
Why the *Rise* of the positron fraction is interesting: For all *primary *CRs: q(e) inj E at injection into the ISM For CR protons: with Diff E n(e) p = q(e) Diff Thus: n(e) p E For CR electrons: n(e) e q(e) loss p D(E) loss with: loss E 1 Thus: n(e) e E For CR positrons (secondary CRs): pp! K ± ±! e ± Thus: Expect: n(e) e+ E n(e) e+ sec n(e) e prim E 1+1/2 /2 Φ e Φ e Φ e 0.1 1+1/2 /2 Additional Source of Positrons? 1 0 1 0 Energy GeV 0.1 Near-by Pulsars? Dark Matter signal?!