1. 35th International Cosmic Ray Conference
What Shapes the Energy Spectra of Galactic Cosmic Rays in the Local Interstellar Medium? A. C. Cummings and E. C. Stone, Caltech N. Lal and B. Heikkila, Goddard Space Flight Center W. R. Webber, New Mexico State University
35th International Cosmic Ray Conference
Busan, South Korea
17 July 2017

2. From Cummings et al., 2016
V1 H, He energy spectra for 2012/ /181. Also shown are 1 AU modulated spectra and four models of interstellar spectra. V1 spectra flatten below ~1 GeV/nuc – so not close to a source of GCRs. GCR H, He spectra in the LISM peak at ~10-50 MeV/nuc with H/He ratio = 12.2±0.9 at ~3-346 MeV/nuc (see green line).
Why do LISM energy spectra roll over at low energies?

3. Will address question of spectral flattening by using WebRun ver
Will address question of spectral flattening by using WebRun ver. 54 of GALPROP, which is publicly available at by changing parameters. WebRun ver. 54 is capable of handling at most one break in power-law specification of injection spectrum. GALPROP models used in Cummings et al., 2016, used two breaks for He, but injection spectrum for GALPROP PD1 model for He can be approximated well-enough for this investigation with one break. The observed GCR He spectrum in LISM rolls over from a power law at high energies with index -2.8 to one with index +0.2 at low –energies (~3 MeV/nuc).

4. Rigidity spectrum Energy/nuc spectrum
Part of the observed roll-over is due simply to the conversion of an injection spectrum, which is a (broken) power law in rigidity, to an energy/nuc spectrum. If dJ/dR ~Rγ, then at high energies, dJ/dE ~Eγ, and at low energies, dJ/dE ~E(γ-1)/2 So, a pure power law R-2.24 would be E-2.24 at high energies and E-1.62 at low energies.
Rigidity spectrum
Energy/nuc
spectrum

5. In addition to the rigidity-to-MeV/nuc roll-over effect, we will consider 1) effect of turning on and off ionization energy loss 2) effect of spectral break in injection spectrum 3) effect of rigidity dependence of diffusion coefficient

6. PD1 diffusion coefficient for He. Solid line was used in Cummings et al., 2016 (except note error in that normalization rigidity is actually 40 GV, not the 10 GV stated in that paper). Dotted line will be used in parameter effect study.

7. Summary Plot: First run is green line: pure power law for injection spectrum, no break in the diffusion coefficient, and ionization energy losses turned off. Index at low energies is -1.9, expected from rigidity-to-MeV/nuc effect: (-2.8-1)/2 = Deficit from ~ MeV/nuc thought to be due to nuclear interactions.

8. Total nuclear interaction cross-section for protons on various isotopes from Wellisch and Axen, Peaks in the MeV energy range.

9. Summary Plot: Model 2 (cyan line) turns on ionization energy losses
Summary Plot: Model 2 (cyan line) turns on ionization energy losses. Index at low energies is ~0, so has big effect, as expected (see, e.g., Ip and Axford, 1985.) Model 3 adds break in injection spectrum. Model 4 adds break in rigidity dependence of diffusion coefficient. Models 3 and 4 serve to fine tune the slope and bring the intensity down by a factor of ~3 to match the observations.

10. Summary
Total change in power-law index of observed GCR He energy spectrum from high energies to low energies is by 3 units (-2.8 to 0.2)
Within the confines of the GALPROP PD1 model, due to combination of:
Conversion from rigidity spectrum to MeV/nuc spectrum (~0.9 units).
Ionization energy losses (~1.9 units).
Rigidity dependence of source injection spectrum, and rigidity dependence of diffusion coefficient (~0.2 units).
So, mostly (~2/3) due to ionization energy losses.
Not investigated here include effects from a possible galactic wind (see Schlickeiser et al., 2014) or other energy-changing effects, such as diffusive reacceleration.
Acknowledgement: We appreciate discussions with Marty Israel, Igor Moskalenko, and Guðlaugur Jόhannesson.

11. Gradient of GCRs in LISM (time permitting)
Gradient of GCRs in LISM (time permitting). V1 has been in LISM since late 2012, about 17 AU in distance traveled.

12. (Mostly >70 MeV protons)
Black vertical dotted lines mark period for radial gradient results.

13. GCR H intensities in units of (cm2 s sr MeV)-1 in 4 energy bands
Radial Gradients
GCR H intensities in units of (cm2 s sr MeV)-1 in 4 energy bands
vs radial distance in the LISM
with fits that yield radial gradients.
Some periods removed – known transient events and spacecraft maneuvers.

14. Average of four is -0.002 ± 0.025 %/AU;
consistent with no radial gradient

15. Gradient Summary
No significant gradients of GCRs over 1st ~17 AU of LISM
1-σ upper limit is %/AU for protons over MeV

16. The End