ABSTRACT
One prediction of particle acceleration in the supernova (SN) remnants in the magnetic wind of exploding Wolf–Rayet and red supergiant stars is that the final spectrum is a composition of a spectrum E−7/3 and a polar cap component of E−2 at the source. This polar cap component contributes to the total energy content with only a few percent, but dominates the spectrum at higher energy. The sum of both components gives spectra which curve upward. The upturn was predicted to occur always at the same rigidity. An additional component of cosmic rays from acceleration by SNe exploding into the interstellar medium adds another component for hydrogen and for helium. After transport, the predicted spectra J(E) for the wind-SN cosmic rays are E−8/3 and E−7/3; the sum leads to an upturn from the steeper spectrum. An upturn has now been seen by the CREAM mission. Here, we test the observations against the predictions and show that the observed properties are consistent with the predictions. Hydrogen can be shown to also have a noticeable wind-SN component. The observation of the upturn in the heavy element spectra being compatible with the same rigidity for all heavy elements supports the magneto-rotational mechanism for these SNe. This interpretation predicts the observed upturn to continue to curve upward and approach the E−7/3 spectrum. If confirmed, this would strengthen the case that SNe of very massive stars with magnetic winds are important sources of Galactic cosmic rays.
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1. INTRODUCTION
Since 2008 there has been increasing evidence for an extra component of cosmic-ray (CR) electrons and positrons, with a plateau of cosmic-ray electrons showing an E−3 spectrum, and the CR positron/electron ratio approaching E+1/3 (ATIC: Chang et al. 2008; Pamela: Adriani et al. 2009). These results confirm a quantitative model originally proposed in 1993 (Stanev et al. 1993), in which the supernova (SN) shock racing through a magnetic wind (Biermann 1951; Parker 1958) gives rise to a source spectrum of E−2 from the polar cap of the star, where the magnetic field is radial, and E−7/3 from most of 4π, where the magnetic field is nearly circular (Biermann 1993). Allowing for losses (Kardashev 1962a, 1962b), the polar cap component spectrum becomes E−3 for observers of CR electrons. Since acceleration is slower for a radial magnetic field (Jokipii 1987; Meli & Quenby 2003a, 2003b; Ellison & Double 2004; Meli & Biermann 2006) than for a tangential magnetic field, more secondaries are produced in the polar cap region, any resulting secondary spectrum is shifted down in energy and up in flux thus explaining the observations (Biermann et al. 2009a).
The prediction of the E−3 CR electron component was confirmed (HESS: Aharonian et al. 2009) with a spectrum of E−3.1±0.1(stat.)±0.4(syst.). This approach has also led to an understanding of the WMAP haze (Finkbeiner 2004; Hooper et al. 2007) with a predicted spectral behavior of ν−2/3, ν−1, and ν−3/2 (Biermann et al. 2010). This prediction is consistent with the detection of the inverse Compton component of the WMAP haze, the Fermi haze, and its spectrum (Dobler et al. 2010; Su et al., 2010). These spectral index predictions are derived from the assumption that a diffusive regime in a disk connects to a convective regime in a magnetic wind for CR transport. Thus, several independent observations support the quantitative model proposed in 1993 (Stanev et al. 1993) of massive star explosions. The original CR spectra are consistent with all these new observations.
There are a number of ideas that have suggested an upturn in the CR spectra, such as a nearby source or substructure in the accelerating shocks. Here, we focus on the upturn of the spectra predicted in 1993 (Biermann 1993; Stanev et al. 1993, parallel papers are summarized in Biermann 1994).
It had been proposed (see also Prantzos 1984, 1991, 2010; Völk & Biermann 1988) that the origin of CRs can be traced to three source components: (1) the CRs originating from SNe exploding into the interstellar medium (ISM); (2) the CRs from SNe exploding into red supergiant (RSG) winds; and (3) the CRs from SNe exploding into blue supergiant or Wolf–Rayet (W-R) star winds. Disregarding the possible binary character of the stars, this is essentially a mass sequence, and a key property of these stellar winds is that they are magnetic (Abbott et al. 1984; Barvainis et al. 1987; Drake et al. 1987; Churchwell et al. 1992). As Parker (1958) showed, the asymptotic magnetic field topology is radial in a polar cap, and tangential over most of 4π. Furthermore, observations of these stars and their interpretation (e.g., Woosley et al. 2002; Heger et al. 2003) show that the wind eats back down into the star, and so the abundances in the RSG star winds are enriched in helium (He), and those of W-R stars are concentrated in carbon (C) and oxygen. Therefore, it can be expected that in CRs at higher energy much of the He can be traced to these winds of RSG stars, and possibly all of the elements heavier than C to the W-R stars (Stanev et al. 1993; Biermann 1994).
We use here the concept that interstellar transport (e.g., Rickett 1977) is governed by a Kolmogorov spectrum (Kolmogorov 1941a, 1941b, 1941c), as discussed in Biermann (1993) and Biermann et al. (2001). We test this prediction with new data (CREAM; Seo et al. 2008; Ahn et al. 2009, 2010). The data are shown to be consistent with the prediction of 1993, and so we propose further tests.
2. THE UPTURN OBSERVED IN COSMIC-RAY SPECTRA
The general concept developed in 1993 is that, after transport is allowed for, the spectra are composed of a sum of a E−8/3 component, and an E−7/3 polar cap component, which is at a level of a few percent in integrated power. These components run up to the knee energy, with about Z 1015 eV, where the polar cap component cuts off completely, and the main component turns steeper, at about E−3.15 (Biermann 1994; Biermann et al. 2005). The spectrum finally cuts off completely at about Z 1017 eV. Here, Z is the charge of the CR nucleus.
It is not obvious a priori, whether RSG star winds should have the same properties in terms of their magnetic field as W-R star winds. It is not clear as to whether the energy fraction of the polar cap component is the same for both, and also whether the characteristic knee rigidity ratio is the same. However, for simplicity we will assume that the population energy fraction and the knee particle energy are the same for both kinds of stars until the data force us to accept otherwise.
We first deal with all elements from C through iron (Fe) and with the combined data as a function of energy/nucleon. Next we deal with He, and test whether the same numbers can describe its spectrum. Finally, we deal with hydrogen (H), which does have a major ISM-SN contribution. In our 1993 prediction, H had a crossover with He, when the spectra are plotted as a function of energy per particle, which is confirmed now. We also test whether He or any other elements also require an ISM component to understand its spectrum.
2.1. Carbon through Iron
The Ahn et al. (2010) data are plotted as E5/2n J(En), where En is the energy per nucleon. Since the prediction is that J(En) is the sum of one component with E−8/3n and the polar cap component with E−7/3n, we note that the product E5/2n(E−8/3n + E−7/3n) is a symmetric shallow near-parabola, with the break at the energy En,m, where the two contributions have equal flux. Fitting the shape of this function involves one parameter, that is the energy per nucleon at the break energy En,m.
First of all, the spectra before the break are determined by CREAM (Ahn et al. 2009) to be E−2.66±0.04, to be compared with the 1993 prediction of E−8/3−0.02±0.02, with an asymmetric predicted error distribution. The 2009 determination is reasonably close to the prediction, as the difference is only 0.007 plus the corresponding errors. So we stick with E−8/3n. The CR electron data suggest in turn that at source E−2 is a good fit for the polar cap component, and so we also stick with E−7/3n after transport.
Fitting this to the curves of the elements reveals that the break energy En,m is consistent with being the same for all these elements.
The fit curve E5/2n(E−8/3n + E−7/3n) to the plot demonstrates that a break energy of 10 TeV/N is consistent with the data. The present data are in fact also compatible with 3 or 30 TeV/N to within the errors, but 10 TeV/N is the best common fit. The 1993 arguments gave 12 TeV/N, derived from a fit to overall air shower data, at vertical and slanted zenith angles.
We show in Figure 1 the fits of all elements heavier than H compared to experimental data.
Figure 1. Fit for elements heavier than H with the spectral shape from Stanev et al. (1993). We use for the break energy 10 TeV/N and only fit the fluxes above 50 GeV/N because of solar modulation and low-energy spallation effects. No ISM-SN CR component is necessary to fit the spectra. Lower energy data imply a small ISM-SN CR component for He.
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Standard image High-resolution image2.2. Helium and Hydrogen
Measured in flux per energy/particle He crosses over H near about 10 TeV. The specific spectral index of the ISM contribution has to be determined best by the H component and that approaches E−2.78±0.009 for protons at low energy (AMS: Alcaraz et al. 2000). Since there is a slight flattening due to the wind component, we need to adopt a spectrum for the ISM component, originally predicted to be E−2.75±0.04, for which we write more generally 
.
Fitting then 
gives us an estimate of the ISM contribution. We show the fit for H in Figure 2, and for comparison repeat the fit for He.
Figure 2. Fit to proton and He data with the spectral shape given in Stanev et al. (1993). For He, we use for the break energy 10 TeV/N, and for H 20 TeV, since the rigidity E/Z is given. For H, the strongest component is from ISM-SN, a wind component is required to fit the data, but is weaker. Replotting these spectra in energy per particle would shift He up by a factor of 8 and to the right by a factor of 4, at 10 TeV/N, and so give the crossover near that energy with H.
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Standard image High-resolution image
Fitting the data (from AMS: Alcaraz et al. 2000) gives at higher energy a spectral index of 2.66 ± 0.02. This suggests that the ISM contribution has pISM ≃ 2.80 and then corresponds to bH ≃ 1 for H at the steeper spectral index 2.80, and about bH ≃ 4 for the slightly flatter index of 2.75. This corresponds to a wind contribution of the energetics for CR-H of 25% for the steeper index, and about 12% for the slightly flatter index. Using pISM = 2.70 does not give a satisfactory fit to the H data. The differences illustrate the uncertainties. For He, the ISM-CR component is very much smaller, and hard to define within the errors, using data from independent instruments.
The largest modification with respect to 1993 is the slightly larger contribution of the wind component to H.
2.3. Differential Spectra
Differential spectra are shown in Ahn et al. (2009). All of those show near constant ratios, with the exception of nitrogen: The nitrogen/oxygen ratio shows a weak dependence, consistent with E−5/9 suggesting interaction in an environment of a massive wind shell, where the spectrum of magnetic irregularities excited by CR particles themselves dominates over other spectra (Biermann 1998; Biermann et al. 2001, 2009a).
The iron/oxygen ratio shows a weak increase consistent with weak differential spallation; low-energy Fe has stronger spallation, so less iron is left. If this is the true interpretation, then at higher energy the ratio should approach a constant. The numbers suggest that up to about half of the low-energy iron is lost through spallation.
2.4. Supernova Mechanism
A rather remarkable observation that this break energy En,m, where the E−8/3 and the polar cap component E−7/3 have equal fluxes, is well defined, even if not precisely known, immediately shows that all participating SNe appear to approach asymptotically a commonality of correlated magnetic field strength and explosion energy (Biermann 1993). Stellar evolution of massive stars (see, e.g., Woosley et al. 2002) suggests that indeed a commonality of properties in their asymptotic state might well be quite plausible. Using the Parker limit (Parker 1958) for a tangential azimuthal magnetic field, this requires Bϕ(r) r U2SN to be the same for all such SNe, and since in this limit Bϕ(r) r is a constant, using the base of that regime rs requires Bϕ,s rs U2SN to be the same; here USN is the shock speed of the SN racing through the wind, and Bϕ ∼ 1/r is the azimuthal magnetic field. Assuming that the mass ejected is similar this connects the explosion energy directly to the magnetic field strength. The only mechanism that does this is the magneto-rotational mechanism (Kardashev 1964; Bisnovatyi-Kogan 1970; Bisnovatyi-Kogan & Moiseenko 2008; Moiseenko et al. 2010). One could speculate that the neutrinos couple to the exploded magnetized outflow through instabilities and irregularities, and so enhance the explosion just as photons can couple better to a wind in early-type stars since the wave speed in a magnetic wind is higher (Seemann & Biermann 1997); thus, it is conceivable that neutrinos play a concomitant role in the explosion mechanism (see, e.g., Woosley et al. 2002).
Since this mechanism employs rotation and magnetic field to their limits, this mechanism also gives rise to the axial symmetry seen in some SN explosions and required by gamma ray bursts (GRBs). So it is tempting to speculate that this is in fact the same mechanism that leads to SNe and GRBs.
2.5. Higher Cosmic-ray Energies
The sum of all these spectra should obey the observed total spectra of particles determined in other ways. This should be consistent with the overall spectra through all EeV energies. This test was used in 1993, and now, with increased H and He wind contributions, can be done again. Using the new data increased the H and He wind contribution, and so we may have to decrease the break energy by a small amount to compensate in the total from the knee and beyond.
We note that the particles near the knee, here with a notable contribution also from H and He, may constitute the seed particles for the next step up in energy, when a relativistic shock (Gallant & Achterberg 1999) may push the entire spectrum up by a considerable factor. Ultra-high-energy CRs could be drawn from a strongly enriched composition (Biermann et al. 2009b; Gopal-Krishna et al. 2010). With such a concept the results here suggest that in different parts of the sky, ultra-high-energy CRs might be dominated by low mass and very high mass elements (Abbasi et al. 2010; Abraham et al. 2010).
3. CONCLUSIONS
Here we demonstrate that the upturn recently observed in CR spectra matches the quantitative predictions from 1993. As now a number of independent observations (CR-positrons, CR-electrons, WMAP haze, Fermi haze, the 511 keV line emission from the Galactic Center region, and the CR-upturn observed by CREAM) have been shown to be consistent with the original quantitative proposal (Stanev et al. 1993), the implications originally suggested find support as well.
Since the upturn is consistent with being at the same energy/charge ratio for all heavy elements, and clearly very nearly the same for the very large number of participating SNe, this finding supports the magneto-rotational mechanism for massive star explosions (originally proposed by Bisnovatyi-Kogan 1970; see also Biermann 1993). Only if energy and magnetic field of the exploding star are strongly correlated can such a characteristic feature in the observed CR spectrum be the same for all such stars, whose explosions contribute to the CRs at high energy.
A clear prediction is that the upturn should continue to approach asymptotically a spectrum of E−7/3.
Much better data, extending to yet higher energy, will allow us to refine and test the concept at yet higher accuracy.
P.L.B. thanks G. Bisnovatyi-Kogan, L. Clavelli, T. K. Gaisser, B. Harms, A. Heger, P. Joshi, K. H. Kampert, Gopal-Krishna, N. Langer, S. Moiseenko, B. Nath, G. Păvălaş, B. Sadoulet, E. Salpeter, R. Sina, V. de Souza, P. Wiita, and many others for discussion of these topics, and O. Ofoha for help of the analysis. Support for work with P.L.B. has come from the AUGER membership and theory grant 05 CU 5PD 1/2 via DESY/BMBF and VIHKOS. J.K.B. and J.D. acknowledge the support from the Research Department of Plasmas with Complex Interactions (Bochum). Support for E.-S.S. comes from NASA grant NNX09AC14G and for T.S. comes from DOE grant UD-FG02-91ER40626.