We take a fresh look at high energy radioactive nuclei data reported in the 90's and at the positron data recently reported by PAMELA. Our aim is to study the model independent implications of these data for the propagation time scales of cosmic rays in the Galaxy. Considering radioactive nuclei, using decaying charge to decayed charge ratios -- the only directly relevant data available at relativistic energies -- we show that a rigidity independent residence time is consistent with observations. The data for all nuclei can be described by f_{s,i}=(t_i/100 Myr)^{0.7}, where f_{s,i} is the suppression of the flux due to decay and t_i is the observer frame lifetime for nucleus specie i. Considering positron measurements, we argue that the positron flux is consistent with a secondary origin. Comparing the positron data with radioactive nuclei at the same energy range, we derive an upper bound on the mean electromagnetic energy density traversed by the positrons, \bar U_T<1.25 eV/cm^3 at a rigidity of R=40 GV. Charge ratio measurements within easy reach of the AMS-02 experiment, most notably a determination of the Cl/Ar ratio extending up to R\sim100 GV, will constrain the energy dependence of the positron cooling time. Such constraints can be used to distinguish between different propagation scenarios, as well as to test the secondary origin hypothesis for the positrons in detail.
The sources of primary cosmic rays (CRs), the correct description of CR propagation and the mechanisms of CR trapping in and escape from the Galaxy are all essentially unknown [1,2,3]. Given the list of open questions, it is remarkable that very few detailed model independent analyses exist in the literature. In contrast, models of homogeneous diffusion have become a standard, where the general approach is to fit the parameters of the model to B/C and low energy 10 Be/ 9 Be data. It is difficult to extract generally applicable information from such studies.
In this work we present a model independent analysis of the propagation time scales of CR nuclei and positrons. These time scales are related to the CR residence time in the Galaxy, a key unknown of CR propagation. Motivated by the prospects for improved measurements in the near future [4,5,6,7,8], our analysis demonstrates that it is possible to extract significant quantitative information from CR measurements under general assumptions, without committing to any particular propagation model.
The main data we use are based on the decaying charge to decayed charge ratios Be/B, Al/Mg and Cl/Ar [9], measured to relativistic energies [10] and studied more than a decade ago by [11,12]. Earlier analyses of CR propagation time scales in the context of diffusion and leaky box models can be found e.g. in [13,14,15,16,17,18] and references therein. Being model dependent, the values deduced in these studies for the CR residence time differ by order of magnitude, as well as by their physical interpretation. In addition, these studies focused on low energy isotopic data, where various theoretical complications arise and where the limited dynamical range of the experiments precludes a direct inference of the energy dependence of the residence time. Apart from the work of [11,12], the high energy charge ratio measurements we analyze here were recently considered in [19,20] in the context of fits to the parameters of diffusion models.
Before proceeding to describe the plan of this paper we first emphasize the key concepts and approximations. A central tool in this work is the CR grammage, the mean traversed ISM column density experienced by CRs [1]. At high energy, where propagation energy gains/losses can be neglected, the local flux of any stable secondary nucleus can be calculated reliably as [21,22]
where X esc is the CR grammage and QS is the local net production (including spallation losses) per unit column density of ISM. Eq. ( 1) is an empirical relation; any acceptable model of CR propagation must reproduce it.
In our study we identify the effects due to decay in radioactive nuclei and due to radiative losses in positrons, by using Eq. ( 1) to compute the flux that would be expected had there been no decay and loss and relating it to the flux observed in practice. Doing so entails some approximation. For Eq. ( 1) to apply, the CR rigidity should remain unchanged during propagation, including fragmentation and decay events. In contrast, the decaying charge and decayed charge samples, reported at a given kinetic energy per nucleon, exhibit a spread in rigidity. This spread is more pronounced for lighter elements, the maximal change occurring in the decay 10 4 Be → 10 5 B in which the rigidity of the nucleus drops by 20%. Similar effects occur in certain spallation reactions and in the production of positrons and antiprotons, which do not inherit the rigidity of the primary CR. Due to these effects, typical calculations based on Eq. ( 1) are accurate only at the ten percent level or so [23,24].
In addition, various propagation effects cause energy change for CR rigidities R ∼ < 10 GV. Striking examples of such effects are the latitude dependent geomagnetic cutoff of the earth and the time dependent (charge dependent and independent) solar modulation [2,3]. Other mechanisms likely operate in interstellar space. Since the theoretical understanding of these effects is poor, we limit our analysis to CR rigidities R ∼ > 10 GV. The plan of this paper is as follows. In Section 2 we study the high energy radioactive nuclei data analyzed by [11]. We present the data in a new way, which makes the existence of an underlying time scale in the problem -the CR residence time -manifest. Our presentation of the data demonstrates that the charge ratio analysis of [11] does not suffer from gross systematics. We show how a combination of data from different nuclei species can be used to measure the functional form of the suppression due to decay. We show that a CR residence time which is mildly dependent or constant as a function of rigidity is consistent with the data.
In Section 3 we consider the PAMELA positron measurements [4,25]. We argue that the positron flux is consistent with a secondary origin [22]. Assuming secondary origin we compare the effects of cooling in positrons to the effects of decay in nuclei, extracting bounds on the cooling time of the positrons. Thes
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