Determining the Spectrum of Cosmic Rays in Interstellar Space from the Diffuse Galactic Gamma-ray Emissivity C.D. DERMER (Code 7653, Naval Research Laboratory, 4555 Overlook Ave. SW, Washington, DC 20375 USA), A.W. STRONG, E. ORLANDO, L. TIBALDO on behalf of the Fermi Large Area Telescope Collaboration Goal: Determine the spectrum of cosmic rays (CRs) in interstellar space from Fermi-Large Area Telescope (LAT) measurements of the diffuse galactic gamma-ray emissivity. Why is this important? Knowledge of the 100 MeV/nuc – 1000 GeV/nuc interstellar CR spectrum tests theories of (1) cosmic-ray origin; (2) Galactic CR propagation; (3) Solar modulation; and (4) improves constraints on dark matter searches. Background: More than 90% of the Galactic gas-related gamma-ray emissivity above 1 GeV is attributed to the decay of neutral pions formed in collisions between CRs and interstellar matter. Leptonic processes, mainly electron bremsstrahlung, are increasingly important below 1 GeV. High-quality measurements of the gamma-ray emissivity of local interstellar gas between ∼ 50 MeV and ∼ 40 GeV obtained with the Fermi-LAT offer the best ever gamma-ray emissivity spectrum. Analysis technique: We (1) re-examine secondary nuclear physics, especially resonance production in p-p collisions, at energies below 10 GeV, and (2) use Bayesian methods to illustrate the technique used to derive the interstellar CR spectrum. Introduction: Recently, Casandjian [2] presented a new emissivity spectrum (emission rate per H atom) of local atomic hydrogen between Galactic latitudes 10°< |b|< 70° for energies ∼ 50 MeV to ∼ 40 GeV, with error bars ≤ 15% (cf. [1]) (see Jean-Marc Casandjian’s ICRC talk for details). Now is an optimal time to use the new emissivity measurements to deduce the interstellar cosmic-ray proton spectrum. Secondary Nuclear Production Physics: Models for p+p  p0  2γ rely on an incomplete 50-yr old data set to constrain models. Assembling the total inclusive and separate p0 and resonance production cross sections shows that isobaric channels are poorly characterized (Fig. 1). Determining the Interstellar CR Spectrum: We perform analysis by computing the matrices connecting model CR spectra to the observed gamma-ray emissivities, in energy bands, then making a Bayesian scan of the model parameter space, computing posterior probability distributions, mean values and error bars, while accounting for correlations among the parameters. Figure 1 (above): Cross section data for inclusive p0 and resonance production (red points) in p-p collisions [9, 4], and data for single p0 production, D(1238), and N∗ resonances, as labeled, from [8]. Component and total inclusive cross sections are shown by dashed and dotted curves for models of [3] and [6,7], respectively. Figure 2 Derived CR Proton Spectrum vs. CR proton data Solar modulation Solar modulation Derived CR Electron Spectrum vs. CR electron data Figure 2 (right): Spectra derived from model fitting for cross sections [3] (left column), and [7] below 20 GeV and [6] (QGSJET) above 20 GeV (right column), with a 0.1 interstellar He fraction by number. Yellow bands show model ranges with 1s uncertainty on fit. Top: Measured and derived cosmic-ray proton spectra. Data are AMS01 (asterisks) and PAMELA (diamonds). Middle: Measured and derived cosmic-ray electron spectra. Data are AMS01 (asterisks), PAMELA (diamonds), and Fermi-LAT (squares). Bottom: Fermi-LAT emissivity data (vertical bars), from [2], and model fit, with hadronic (red curves) and leptonic (green curves) contributions, with bremsstrahlung based on Fermi-LAT electron measurements above 10 GeV, with a break below 3 GeV as indicated by synchrotron [10]. Fermi-LAT emissivity and model Summary: The interstellar CR proton spectrum has been determined from g-rays and gas tracers alone, with no input from direct CR measurements except for the He/p ratio. The implied CR spectrum for cross sections [6, 7] has momentum index 2.4 (2.9) below (above) 6.5 GeV, with a scaling factor 1.3 relative to PAMELA at 100 GeV, similar to the results with cross sections [3]. Solar modulation is clearly seen in the deviation of the interstellar spectrum from direct measurements below 10 GeV. Bremsstrahlung gives an essential contribution below ≈ 1 GeV. The implied CR spectrum is close to that measured directly at high energies. Uncertainties in gas, instrumental response and cross sections on determining the interstellar CR spectrum is addressed in a forthcoming paper [11]. [1] Abdo, A. A., et al., 2009, Astrophys. J., 703, 1249 [2] Casandjian, J.-M., 2012, American Institute of Physics Conference Series, 1505, 37 [3] Dermer, C. D., 1986, Astronomy & Astrophysics, 157, 223 [4] Dermer, C. D., 1986, Astrophys. J., 307, 47 [5] Dermer, C. D., et al., 2013, Fermi Symposium 2012 Conf. Proc., eConf C121028, arXiv:1303.6428. [6] Kachelrieß, M., & Ostapchenko, S., 2012, Phys. Rev. D, 86, 043004. 2 [7] Kamae, T., Karlsson, N., Mizuno, T., Abe, T., & Koi, T., 2006, Astrophys. J., 647, 692 [8] Lock,W. O., Measday, D. F., “Intermediate energy nuclear physics,” 1970 (Methuen & Co., London) [9] Stecker, F. W., 1973, Astrophys. J., Vol. 185, 499 [10] Strong, A. W., Orlando, E., & Jaffe, T. R., 2011, Astronomy & Astrophysics, 534, A54 [11] Strong, A. W., Ackermann,M., Cohen-Tanugi, J., Dermer, C. D., Finke, J. D., Kachelriess, M., Kamae, T., Loparco, F., Mazziota, M. N., Mizuno, T., Murphy, R. J., Orlando, E., Ostapchenko, S., Stecker, F. W., Tibaldo, L., “Interstellar cosmic-ray spectra from gamma-ray emissivities,” 2013, in preparation see Luigi Tibaldo’s plenary talk on July 8