Cosmic-Ray Spectra in Interstellar Space

At energies below ~300 MeV/nuc our knowledge of cosmic-ray spectra outside the heliosphere is obscured by the energy loss that cosmic rays experience during transport through the heliosphere into the inner solar system. This paper compares measurements of secondary electron-capture isotope abundances and cosmic-ray spectra from ACE with a simple model of interstellar propagation and solar modulation in order to place limits on the range of interstellar spectra that are compatible with both sets of data. INTRODUCTION Among the most important clues to the nature of Galactic cosmic-ray sources and accelerators are measurements of cosmic-ray energy spectra. There are now highresolution measurements of the spectra of almost all of the elements from H to Ni at 1 AU, but to relate these to the spectrum of cosmic rays accelerated in the cosmic-ray source(s) it is necessary to take into account significant changes that take place during cosmic-ray transport through the interstellar medium and the heliosphere. It is generally believed that most galactic cosmic rays are accelerated by supernova shock waves traveling through the interstellar medium (ISM) [1, 2], leading to “source spectra” of the form dJ/dT ∝ P, where T is kinetic energy/nuc, P is momentum/nuc and δ depends on the Mach number of the strongest shocks encountered. At energies above a few GeV/nuc, the spectra of “primary” species (e.g., H, He, C, O, Ne, Mg, Si, and Fe) all have observed slopes of dJ/dT ∝ T. In contrast, “secondary” species that are rare in the source material (e.g., Li, Be, B, and products of Fe fragmentation such as Sc, Ti, and V) all have softer spectra, and secondary/primary ratios such as B/C and (Sc+Ti+V)/Fe decrease with increasing energy due to rigidity-dependent escape from the Galaxy. The cosmic-ray transport/solar-modulation model used in this study assumes source spectra proportional to P for all primary species and a rigidity-dependent mean free path for escape from the Galaxy [3, 4] of a form suggested by Soutoul and Ptuskin [5]. At energies below a few hundred MeV/nuc our knowledge of interstellar cosmicray spectra is obscured by the heliosphere – low-energy cosmic rays are to a large extent prevented from entering the inner heliosphere by the interplanetary magnetic Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp field, and a considerable range of interstellar spectral shapes can be shown to be consistent with 1-AU observations with appropriate choices for the interplanetary diffusion coefficient. In addition, because cosmic rays lose at least several hundred MeV/nuc as they traverse the inner heliosphere [6], we have essentially no information on the interstellar spectra of cosmic rays below ~200 to ~300 MeV/nuc. It is hoped that the Voyagers, or an Interstellar Probe, will eventually escape the cosmic-ray modulation region and measure interstellar cosmic-ray spectra directly. However, it has recently become clear that a considerable fraction of “cosmic-ray modulation” occurs in the heliosheath, well beyond the present location of the Voyagers [7, 8, 9, 10]. A comparison of interstellar spectra used in several recent studies is shown in Figure 2, along with solar-minimum data from ACE and Voyager. For these interstellar spectra to be consistent with the observations, modulation in the heliosheath must be between ~1.5 and ~3 times that between 1 AU and 70 AU. FIGURE 1. Comparison of local interstellar carbon spectra used in several recent studies [11, 12, 13, 14]. Also shown are solar minimum carbon data from ACE at 1 AU and Voyager-1 at ~70 AU [13]. Recently, a new probe of this energy-loss process was demonstrated that is based on studies of the energy spectra of the secondary radioactive isotopes V and Cr, which decay only by electron capture (EC). In cosmic rays the abundances of EC isotopes is related to the probability of attaching an electron from the IS gas: at low energies attachment and decay is much more likely. In a recent paper Niebur et al. [15] used isotope observations from ACE to provide direct evidence that the amount of energy loss increases by 400 to 700 MV (~200 to 300 MeV/nuc) from solar minimum to solar maximum (1997-1998 to 2000-2001). In this paper we extend the work of Niebur et al. and investigate the range of interstellar spectra that is consistent with solar-cycle observations of both the V/Cr ratio and the Fe spectrum at 1 AU (note that V is the daughter of Cr decay, and that Fe fragmentation produces most of the Ti, V, and Cr observed in cosmic rays). Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp APPROACH Niebur et al. [15] used a cosmic-ray transport and solar-modulation model [4, 3], which we also adopt here. The model assumes that primary cosmic rays are accelerated to produce source spectra dJ/dT ∝ P. In addition, cosmic-ray sources are assumed to be uniformly distributed in space and time, with a rigidity-dependent mean free path for leakage from the Galaxy [3, 5] and a uniform interstellar density of 0.3 H atoms/cm, based on observations of four radioactive clocks [4]. Nuclear fragmentation, ionization energy loss, radioactive decay, and electron-attachment and stripping are taken into account. The first stage of the model results in interstellar spectra for species from Be to Ni, which then serve as input to a spherically-symmetric solar modulation model that includes diffusion, convection, and adiabatic energy loss. It is common to characterize the solar modulation level over the solar cycle by the “modulation parameter“, φ, [16], where φ ∝ ∫ (Vsw/κ)dr (in MV). Here Vsw is the solar wind speed, κ is the diffusion coefficient, and the integral extends from 1 AU to the boundary of the modulation region (Rb). In practice, many κ, Vsw and Rb combinations have the same effect. There is also a wide range of interstellar spectra that can produce the same intensity level at 1 AU with a judicious choice of κ, including the spectra in Figure 1. In this paper we will attempt to narrow the range of possible interstellar spectra by requiring agreement with EC isotope data. Calculations for the P source spectra considered by Niebur et al. [15] are compared with spectral and isotope data from ACE in Figure 2. Note that the Fe spectra at solar minimum require φ ≈ 400 MV, while solar-maximum Fe requires φ ≈ 800 to 1000 MV. The right hand panel shows that the solar minimum V/Cr ratio is consistent with φ ≈ 400 MV. Niebur et al. also used the Ti/V ratio in their study; in this paper we consider only the Cr to V decay. 0.2 0.3 0.4 0.5 0.6 0.7 100 200 300 400 500 51 V / 5 1 C r Kinetic Energy (MeV/nucleon) φ = 0 200