ENERGY SPECTRA OF COSMIC-RAY NUCLEI AT HIGH ENERGIES

Experimental studies of charged cosmic rays (CRs) are focused on the understanding of the acceleration mechanism of high-energy CRs, identification of their sources, and clarification of their interactions with the interstellar medium (ISM). The origin of CRs is still under debate, although direct measurements with instruments on stratospheric balloons or in space have provided information on their elemental composition and energy spectra, and indirect detection by ground-based experiments has extended the measurements up to the end of the observed all-particle spectrum.

It is generally accepted that CRs are accelerated in blast waves of supernova remnants (SNRs), which are the only galactic candidates known with sufficient energy output to sustain the CR flux (Bell 1978; Hillas 2005). Recent observation of emission of TeV gamma rays from SNR RX J1713.7-3946 by the HESS Cherenkov telescope array proved that high-energy charged particles are accelerated in SNR shocks up to energies beyond 100 TeV (Aharonian et al. 2004). This result is consistent with expectations of the class of theoretical models that predict the existence of a rigidity dependent limit, above which the diffusive shock acceleration becomes inefficient. The maximum energy attainable by a nucleus of charge Z may range from Z × 10¹⁴ eV to ∼Z × 10¹⁷ eV depending on the model and types of supernovae considered (Lagage & Cesarsky 1983; Berezhko 1996; Parizot et al. 2004). In this scenario, the energy spectra of elements exhibit a Z-dependent cutoff. As a consequence, the CR elemental composition is expected to change as a function of energy, marked by a depletion of low-Z nuclei in the several hundred TeV region. This mechanism has been proposed as a possible explanation of the steepening ("knee") in the CR energy spectrum (described by a power law: dN/dE ∝ E^−γ) with a change of the spectral index from γ ≈  2.7 to γ ≈  3.1, observed at energies around 4 PeV. An alternative approach is adopted by models that relate the knee to leakage of CRs from the Galaxy. In this case, the knee is expected to occur at lower energies for light elements as compared to heavy nuclei, due to the rigidity dependence of the Larmor radius of CR particles propagating in the galactic magnetic field (Hörandel 2004).

A detailed understanding of the propagation of CRs during their wanderings inside the Galaxy and their interactions with the ISM is needed to infer the injection spectra of individual elements at the source from the observed spectra at Earth. CR nuclei can be divided into primaries (i.e., H, He, C, O, Fe, etc.) that come from CR sources, and secondaries (such as Li, Be, B, Sc, Ti, V, etc.), which are products of the interactions of primary nuclei with the ISM. The amount of material traversed by CRs between injection and observation can be derived from the measured ratio of secondary-to-primary nuclei, such as the boron-to-carbon ratio (B/C) or the ratio of sub-iron elements to iron. Likewise, their confinement time in the Galaxy can be determined through measurements of long-lived radioactive secondary nuclei (Longair 1994; Yanasak et al. 2001). Observations from space-based experiments like cosmic ray nuclei (CRN) on the Spacelab2 mission of the Space Shuttle (Swordy et al. 1990) and C2 (Engelman et al. 1990) and Heavy Nuclei Experiment (HNE; Binns et al. 1988) onboard the HEAO 3 satellite have shown that the energy spectra of the secondary nuclei are steeper than those of the primaries. The escape path length of CRs from the Galaxy depends on the magnetic rigidity as R^−δ, with the parameter δ ≈  0.6. This implies that the spectra observed at Earth are steeper than the injection spectra, i.e., the spectral index at the source is smaller by the value δ.

Those pioneering measurements were statistically limited at energies of order ∼10¹¹ eV. Accurate direct measurements of the energy spectra of individual elements into the knee region are needed to discriminate between different astrophysical models proposed to explain the acceleration and propagation mechanisms. Recently, a new generation of balloon-borne experiments has performed accurate measurements of CRs in the previously experimentally unexplored TeV region (Panov et al. 2006; Ave et al. 2008). Among these, the Cosmic Ray Energetics And Mass (CREAM) experiment was designed to measure directly the elemental composition and the energy spectra of CRs from hydrogen to iron over the energy range 10¹¹–10¹⁵ eV in a series of flights (Seo et al. 2004). Since 2004, four instruments were successfully flown on long-duration balloons in Antarctica. The instrument configurations varied slightly in each mission due to various detector upgrades. The first flight produced important results extending the measurement of the relative abundances of CR secondary nuclei B and N close to the highest energies (∼1.5 TeV/n) allowed by the irreducible background generated by the residual atmospheric overburden at balloon altitudes. The data clearly indicate that the escape path length of CRs from the Galaxy has a power-law rigidity-dependence, with the parameter δ in the range 0.5–0.6 (Ahn et al. 2008).

In this work, we present new measurements of the energy spectra of the major primary CR nuclei from carbon to iron, up to a few TeV/n made with the second CREAM flight (CREAM-II). A new measurement of the nitrogen intensity with unprecedented statistics is also presented up to 800 GeV/n. The measured N/O ratio confirms the results of CREAM-I. The procedure used to analyze the data and reconstruct the CR energy spectra is described in detail together with an assessment of the systematic uncertainties.

The instrument for the second flight included: a redundant system for particle identification, consisting (from top to bottom) of a timing-charge detector (TCD), a Cherenkov detector (CD), a pixelated silicon charge detector (SCD), and a sampling imaging calorimeter (CAL) designed to provide a measurement of the energy of CR nuclei in the multi-TeV region. Figure 1 depicts the detector arrangement.

Zoom In Zoom Out Reset image size

The TCD is made of two orthogonal layers of four 5 mm thick plastic scintillator paddles each, covering an area of 120 × 120 cm². The paddles are read out by fast photomultiplier tubes (PMTs) via twisted-strip adiabatic light guides. A custom design of the electronics combines fast peak detection with a threshold timing measurement of the PMTs signals in order to determine each element's charge with a resolution ≲0.35 e (in units of the electron charge) and to discriminate against albedo particles. A hodoscope (S3) of 2 × 2 mm² square scintillating fibers read out by two PMTs is located just above the calorimeter, and provides a reference time for TCD timing readout. Further details about the TCD design and performance can be found in Ahn et al. (2009). The CD is a 1 cm thick plastic radiator with 1 m² surface area, instrumented with eight PMTs viewing wavelength shifting bars placed along the radiator edges. It is used to flag relativistic particles and to provide a charge determination complementary to that of the TCD.

The SCD is comprised of two layers of 156 silicon sensors each. Each 380 μm thick sensor is segmented into an array of 4 × 4 pixels, each of which has an active area of 2.12 cm² (Park et al. 2007). The sensors are slightly tilted and overlap each other in both lateral directions, providing a full coverage in a single layer, with a 77.9 × 79.5 cm² area. The dual layers, about 4 cm apart, cover an effective inner area of 0.52 m² with no insensitive regions. The overall SCD vertical dimension, including the ladders, the mechanical support structure and the electromagnetic shielding cover, is 97.5 mm (Nam et al. 2007). The readout electronics of the 4992 pixels is based on a 16-channel ASIC chip followed by 16-bit analog-to-digital converters (ADCs), providing a fine charge resolution over a wide dynamic range from hydrogen to nickel.

The CAL is a stack of 20 tungsten plates, each 1 radiation length (X₀) thick and with surface area 50 × 50 cm², interleaved with active layers of 1 cm wide and 50 cm long scintillating-fiber ribbons. Each ribbon is built by gluing together 19 scintillating fibers of 0.5 mm diameter each. The light signal from each ribbon is collected by means of an acrylic light mixer coupled to a bundle of 48 clear fibers. This is split into three sub-bundles (with 42, 5 and 1 fibers, respectively), each feeding a pixel of a hybrid photodiode (HPD). This optical division is used to match the wide dynamic range of the calorimeter to that of the front-end electronics, providing three readout scales (low, medium, and high) with different sensitivity. A total of 2560 channels are readout from 40 HPDs powered in groups of 5 units.

The longitudinal and lateral segmentations of the CAL correspond to 1 X₀ and 1 Moliere radius, respectively. The ribbon planes are alternately oriented along orthogonal directions to image in three dimensions, the development of showers produced by the incoming nuclei which interact inelastically in the ∼0.46 λ_int thick carbon target preceding the CAL (Marrocchesi et al. 2004). The finely grained sampling calorimeter can track, by reconstructing the shower axis, the incident particle trajectory with enough accuracy to determine which segment of each charge detector it traversed, and thereby allowing discrimination against segments hit by the backscattered particles produced in the shower. This feature is essential for a reliable and unambiguous charge identification.

The second CREAM instrument was launched from McMurdo station in Antarctica on 2005 December 16th. The balloon circled the South Pole twice at a float altitude between 35 and 40 km. The flight was terminated on 2006 January 13th, 28 days after the launch. During the whole flight, the instrument housekeeping system monitored online temperatures, currents, voltages of the front-end electronics boards, and the high-voltage supply values of the HPDs and PMTs. The performance of all sub-detectors met the design technical specifications. The CAL and TCD high-voltage systems worked successfully at low atmospheric pressure. The thermal behavior of the various detectors was found to be in good agreement with expectations from thermal models. The temperature of the instrument crates stayed within the required operational range with daily variation of a few °C, depending on the inclination of the Sun during each 24 hr cycle. Front-end electronics channels showed stable gains over the whole flight. Pedestal values of the 2560 CAL and 4992 SCD channels were collected automatically every 5 minutes in order to monitor their drift as a function of the detector temperature and to perform accurate pedestal subtraction. 1.7% of the SCD and 0.7% of the CAL channels were noisy or inefficient and were masked off.

During the flight, the data acquisition was enabled whenever a shower developing in at least six planes was detected in the CAL (CAL trigger) and/or a relativistic CR with Z ⩾ 2 was identified by the TCD and CD (TCD trigger). The high-energy data, i.e., the CAL triggered events, were transmitted via Tracking and Data Relay Satellite System (TRDSS), while the low-energy data, i.e., events triggered only by the TCD and not by the CAL, were recorded on an onboard disk. A total of 57 GB of data were collected. In order not to saturate the disk space too early in the flight, the highly abundant low-energy particles triggered only by the TCD were pre-scaled, so that only a fraction of these events were recorded. This fraction of recorded TCD triggers (pre-scale factor) could be set by the data acquisition program and changed during the flight depending on the trigger rate. On average, only one every six TCD triggered events was retained. A detailed description of the instrument performance during the second flight may be found in Marrocchesi et al. (2008).

The present analysis uses a subset of data collected from December 19th to January 12th, under stable instrument conditions, representing a total of 24 days' worth of data taking (e.g., removing periods early in the flight and at the very end, when the instrument was either being adjusted and optimized, or prepared for flight termination). The first step in the analysis is to correct the raw data for the gain variations among the channels and the drift of the pedestals with temperature. Then, the trajectory of each CR through the instrument is reconstructed and each event assigned a charge and an energy. At this point, the events of each charge species are sorted into energy intervals and the number of counts in each bin is corrected for several effects in order to compute the differential intensity. The various steps of the analysis procedure are described in detail in the following subsections.

4.1. Trajectory Reconstruction

4.2. Charge Assignment

The identification of the charge Z of a CR relies on two independent samples of its specific ionization dE/dx provided by the SCD layers. Since dE/dx depends on Z² and for solid absorbers it is nearly constant in the relativistic regime, the particle charge Z can be determined by measuring the amount of ionization charge a CR produces when traversing the silicon sensors. In order to avoid charge misidentification of the incident nucleus, caused by the backscattered shower particles reaching the SCD, and to obtain high-purity samples of CR elements, the signals, S_top and S_bottom, of the two pixels selected by the tracking algorithm are compared and required to be consistent within 20%. If this coherence cut is satisfied, they are corrected for the path length (estimated from the track parameters) traversed by the particle in the silicon sensors, which is proportional to 1/cos(θ), θ being the angle between the particle trajectory and the axis of the instrument. A reconstructed charge Z_rec is assigned to the particle by combining the ionization signals matched with the track on both layers, according to the formula

$$\begin{equation} Z_{\rm rec} = \sqrt{\frac{S_{\rm top} + S_{\rm bottom}}{2} \times \frac{\cos {\left(\theta \right)}}{s_0}, } \end{equation} \tag{ 1 }$$

where s₀ is a calibration constant, inferred from the flight data, to convert the pulse heights into an absolute charge scale. The reconstructed charge distribution is shown in Figure 2. The elemental range from boron to silicon is fitted with a multi-Gaussian function (Figure 2(a)). From the fit, a charge resolution σ is estimated as: 0.2e for C, N, O and ∼ 0.23e for Ne, Mg, Si. Though a multi-Gaussian fit in the elemental region from sulfur to nickel cannot be done due the limited statistics, the charge resolution for iron is estimated to be ∼0.5e from the width of the Fe peak. A 2σ cut around the mean charge value is applied to select samples of C, O, Ne, Mg, and Si. A cut of Z_rec ± 1σ is imposed for Fe due to the corresponding lower SCD resolution, while for N a cut of Z_rec ± 1.5σ and 10% coherence level between the selected pixels signals, are used to avoid contamination from more abundant adjacent charges.

Zoom In Zoom Out Reset image size

4.3. Energy Measurement

4.4. Energy Deconvolution

Once each CR is assigned a charge and energy, the reconstructed particles of each nuclear species are sorted into energy intervals commensurate with the rms resolution of the calorimeter. Due to the finite energy resolution of the detector, the measured number of events in each energy bin must be corrected for overlap with the neighboring bins. This unfolding procedure requires solving a set of linear equations

$$\begin{equation} M_i = \sum _{j = 1}^{n} A_{ij} N_j \;\;\;\;\;\;\;\; i=1,..., m \end{equation} \tag{ 2 }$$

relating the "true" counts N_j in one of n incident energy bins to the measured counts M_i in one of m deposited energy bins. A generic element of the mixing matrix A_ij represents the probability that a CR particle, carrying an energy corresponding to a given energy bin j, produces an energy deposit in the calorimeter falling into bin i instead. A detailed MC simulation of the instrument, based on the FLUKA 2006.3b package (Fassò et al. 2005), was developed to estimate the unfolding matrix. Sets of nuclei, generated isotropically and with energies chosen according to a power-law spectrum, are analyzed with the same procedure used for the flight data. Each matrix element A_ij is calculated by correlating the generated spectrum with the distribution of the deposited energy in the calorimeter (Zei et al. 2008). In order to get a reliable set of values of the unfolding matrix for each nucleus, the MC simulation is finely tuned to reproduce both flight data and the calibration data collected with accelerated particle beams. The agreement of the MC description with the real instrument behavior was carefully checked. As an example, in Figure 3 the response of the calorimeter to carbon nuclei from the flight data is compared with an equivalent set of simulated events.

Zoom In Zoom Out Reset image size

The elements of the unfolding matrix depend on the spectral index assumed for the generation of MC events. For each nucleus, we used the spectral index value reported by Hörandel (2003), obtained by combining direct and indirect CR observations. In order to check the stability of our final results, the unfolding procedure was repeated by scanning several values of the spectral index in the range ± 0.2 around the reference value. No significant bias of the final results was observed.

4.5. Corrections for Interactions in the Atmosphere and the Detector

CRs may undergo spallation reactions when traveling through the atmosphere above the balloon or crossing the instrument material of CREAM above the SCD. This results in the generation of secondary nuclei with lower charge than the parent's, and of about the same energy per nucleon. Then, for each nuclear species, inelastic interactions lead to a loss of primary particles but also a gain of secondaries produced by heavier nuclei. For a correct determination of the CR fluxes, the data must be corrected for this effect. A two-step procedure is used which takes into account separately the CR path length in air (correction to the top of the atmosphere (TOA)) and the amount of instrument material encountered by the particle before reaching the SCD. The latter leads to a correction to the TOI. For each step, the corrections are calculated by solving the matrix equation

$$\begin{eqnarray} &&\left(\begin{array}{@{}c@{}} N_{\rm{C}} \\ N_{\rm{N}} \\ N_{\rm{O}} \\ N_{\rm{Ne}} \\ N_{\rm{Mg}} \\ N_{\rm{Si}} \\ N_{\rm{Fe}}\end{array}\right)_{\mathcal {F}}= \nonumber\\ &&\left(\begin{array}{@{}c@{\ \ } c@{\ \ } c@{\ \ } c@{\ \ } c@{\ \ } c@{\ \ } c@{}} S_{\rm{C}} & F_{{{\rm N}} \rightarrow {\rm C}} & F_{\rm{O} \rightarrow {\rm C}} & F_{\rm{Ne} \rightarrow {\rm C}} & F_{\rm{Mg} \rightarrow {\rm C}} & F_{\rm{Si} \rightarrow {\rm C}} & F_{\rm{Fe} \rightarrow {\rm C}} \\ 0 & S_{\rm N} & F_{\rm{O} \rightarrow {\rm N}} & F_{\rm{Ne} \rightarrow {\rm N}} & F_{\rm{Mg} \rightarrow {\rm N}} & F_{\rm{Si} \rightarrow {\rm N}} & F_{\rm{Fe} \rightarrow {\rm N}} \\ 0 & 0 & S_{\rm O} & F_{\rm{Ne} \rightarrow {\rm O}} & F_{\rm{Mg} \rightarrow {\rm O}} & F_{\rm{Si} \rightarrow {\rm O}} & F_{\rm{Fe} \rightarrow {\rm O}} \\ 0 & 0 & 0 & S_{\rm{Ne}} & F_{\rm{Mg} \rightarrow {\rm Ne}} & F_{\rm{Si} \rightarrow {\rm Ne}} & F_{\rm{Fe} \rightarrow {\rm Ne}} \\ 0 & 0 & 0 & 0 & S_{\rm{Mg}} & F_{\rm{Si} \rightarrow {\rm Mg}} & F_{\rm{Fe} \rightarrow {\rm Mg}} \\ 0 & 0 & 0 & 0 & 0 & S_{\rm{Si}} & F_{\rm{Fe} \rightarrow {\rm Si}} \\ 0 & 0 & 0 & 0 & 0 & 0 & S_{\rm{Fe}} \end{array}\right)\nonumber\\ &&\quad\times \left(\begin{array}{@{}c@{}} N_{\rm{C}} \\ N_{\rm{N}} \\ N_{\rm{O}} \\ N_{\rm{Ne}} \\ N_{\rm{Mg}} \\ N_{\rm{Si}} \\ N_{\rm{Fe}} \end{array}\right)_{\mathcal {I}}, \end{eqnarray} \tag{ 3 }$$

which describes the transport process of the nuclei from an incident level $\mathcal {I}$ (e.g., TOI) to a final level $\mathcal {F}$ (e.g., the SCD). The vector $\mathbf {N}_{\mathcal {I}}$ represents the number of nuclei of each species counted in a given energy interval, while the vector $\mathbf {N}_{\mathcal {F}}$ is the number of counts corrected for the charge-changing interactions in the materials between the levels $\mathcal {I}$ and $\mathcal {F}$. The diagonal elements of the transport matrix represent the survival probabilities of each species Z in the passage from $\mathcal {I}$ to $\mathcal {F}$, while a generic off-diagonal element $F_{Z_2 \rightarrow Z_1}$ gives the fraction of nuclei Z₂ which spallate to produce nuclei of charge Z₁ (<Z₂).

The TOI transport matrix is obtained from the MC simulation of the instrument. The mass thickness of the CREAM-II materials above the SCD is estimated to be ∼4.8 g cm⁻². The fraction of surviving nuclei, i.e., the diagonal matrix elements, ranges from 81.3% for C to 61.9% for Fe. These MC values are compared with the ones calculated using the semiempirical total cross section formulae for nucleus–nucleus reactions given in Sivher et al. (1993). Good agreement, within 1%, is found as shown in Figure 4.

Zoom In Zoom Out Reset image size

The TOA matrix elements are calculated by simulating with FLUKA the atmospheric overburden during the flight (3.9 g cm⁻² on average). Since the probability of interaction depends on the nucleus path length in air, the simulated events are generated according to the measured zenith angle distribution of the reconstructed nuclei, which is peaked around 20°. Survival probabilities ranging from 84.2% for C to 71.6% for Fe are found (Figure 5). They turn out to be in good agreement with the values calculated from two different empirical parameterizations (Sivher et al. 1993; Kox et al. 1987) of the total fragmentation cross sections of heavy relativistic nuclei in targets of different mass.

Zoom In Zoom Out Reset image size

The off-diagonal elements $F_{Z_2 \rightarrow Z_1}$ of both the TOI and TOA transport matrices are of order 1%–2%. The comparison between values obtained from different models is discussed in Section 5.1.

4.6. Absolute Differential Intensity Calculation

The absolute differential intensity dN/dE at an energy $\hat{E}$ is calculated for each elemental species according to the formula

$$\begin{equation} \frac{\mbox{\mbox{\it d}}N}{\mbox{\mbox{\it d}}E}(\hat{E}_i) = \frac{\tilde{N_i}}{\Delta E_i}\times \frac{1}{\epsilon \times S\Omega \times \mbox{\mbox{\it T}} }, \end{equation} \tag{ 4 }$$

where $\tilde{N_i}$ is the number of events obtained from the unfolding algorithm and corrected to the TOA, ΔE_i is the energy bin width, T is the exposure time, SΩ the geometric factor of the instrument, and the efficiency of the analysis selection. Since a significant fraction of the reconstructed events at energies, <3 TeV did not satisfy the CAL trigger condition and were triggered only by the TCD, the number of these events in the first energy intervals must be further divided by the pre-scale factor (1/6 on average during the flight) of the TCD-based trigger system.

Median energy. According to the work of Lafferty & Wyatt (1995), each data point, i.e., each differential intensity value, is centered at a median energy $\hat{E}$, defined as the energy at which the measured spectrum is equal to the expectation value of the "true" spectrum. For a power-law spectrum (E^−γ) with spectral index γ, the median energy is calculated as

$$\begin{equation} \hat{E} = \left[ \frac{E_{2}^{1 - \gamma } - E_{1}^{1 - \gamma }}{\left(E_{2} - E_{1} \right) \left(1 - \gamma \right)} \right]^{-\frac{1}{\gamma }}, \end{equation} \tag{ 5 }$$

where E₁ and E₂ are the lower and upper limits of a given energy bin. If the highest energy interval is not limited, i.e., E₂ → ∞, the median energy is $\hat{E} = 2^{\frac{1}{\gamma - 1}}\, E_1$. In this case, the energy interval is an integral bin and its width (to be used in Equation (4)) is calculated as

$$\begin{equation} \Delta E = \frac{E_1}{2^{\frac{\gamma }{1 - \gamma }}\, (\gamma - 1)}. \end{equation} \tag{ 6 }$$

Since γ is not known a priori, an iterative procedure is performed to compute the median energy of each bin. For each element, the spectral index reported by Hörandel (2003) is used as the initial value of γ. We found that $\hat{E}$ depends weakly on γ for a variation of ± 0.1 around the initial value.

Geometric factor. The geometric factor SΩ is estimated from MC simulations by counting the fraction of generated particles entering the trigger-sensitive part of instrument. Two groups of events are distinguished as shown in Figure 1: CRs crossing both the TCD and the SCD before impinging onto the CAL (named "golden" events), and particles entering the instrument through the side (i.e., crossing neither the TCD nor the CD) and traversing only the SCD and the CAL. The estimated acceptance is (0.19 ± 0.01) m² sr in the first case, while including both event types yields a value of (0.46 ± 0.01) m² sr. Both values are charge and energy independent. For the second group of events, the corrections to the TOI are not necessary.

Live Time. During the flight, the total time and the live time T (i.e., the time during which the data acquisition was available for triggers) were measured by means of a pair of 48 bit counters incorporated in the housekeeping system onboard, and providing better than 4 microseconds resolution. The selected data set amounts to a live time of 1,454,802 seconds, close to 75% of the total time of data taking.

Reconstruction efficiency. The overall efficiency , including the trajectory reconstruction and the charge selection efficiencies, is estimated from MC simulations as a function of the particle energy. This efficiency curve is characterized by a steep rise below 2 TeV and reaches a constant value at energies >3 TeV for all nuclei. The rise is caused by the high sparsification threshold (∼10 MeV) of the CAL cells, which limits the CAL tracking accuracy at low energy and consequently the charge identification capability of the instrument. For C, O, Ne, Mg, and Si, the plateau value in the efficiency curve is about 80% when considering only the "golden" events, and decreases to 65% when including also events at large angle within the SCD–CAL acceptance. Instead, the more conservative charge cuts applied to select N and Fe samples (see Section 4.2) yield a reduced plateau efficiency of about 65% and 35% (for "golden" events), respectively.

The differential intensities at the TOA as measured by CREAM-II for the elements C, N, O, Ne, Mg, Si, and Fe are given as a function of the kinetic energy per nucleon in Table 1, together with the corresponding number of raw observed particles. The quoted error bars are due to the counting statistics only: the upper and lower limits are computed as 84% confidence limits for Poisson distributions as described by Gehrels (1986).

Table 1. Differential Intensities Measured with CREAM-II

Element	Energy Range (GeV/n)	Kinetic Energy $\hat{E}$ (GeV/n)	No. of Events	Intensity (m2 sr s GeV/n)−1
C	66–117	86.2	171	(1.67 ± 0.13) × 10−4
Z = 6	117–175	141.6	139	(3.37 ± 0.29) × 10−5
	175–304	228.2	215	(9.42 ± 0.64) × 10−6
	304–529	397.2	134	(2.28 ± 0.20) × 10−6
	529–919	691.0	66	(5.17 ± 0.63) × 10−7
	919–1597	1201.5	29	(1.31 ± 0.24) × 10−7
	1597–2776	2088.7	13	(3.6 +1.3−1.0) × 10−8
	2776–4824	3630.5	7	(1.04 +0.58−0.40) × 10−8
	4284–	7415.1	5	(1.49 +0.98−0.63) × 10−9
N	56–175	95.7	86	(7.28 ± 0.79) × 10−6
Z = 7	175–529	295.3	63	(5.39 ± 0.68) × 10−7
	529–	826.3	19	(3.8 +1.1−0.9) × 10−8
O	49–87	64.0	224	(3.48 ± 0.23) × 10−4
Z = 8	87–175	120.8	371	(4.82 ± 0.25) × 10−5
	175–304	228.0	241	(7.33 ± 0.47) × 10−6
	304–529	396.9	127	(1.90 ± 0.17) × 10−6
	529–919	690.5	57	(4.51 ± 0.60) × 10−7
	919–1597	1200.5	25	(1.25 ± 0.25) × 10−7
	1597–2776	2087.0	10	(2.9 +1.2−0.9) × 10−8
	2776–4824	3627.4	6	(8.3 +4.9−3.3) × 10−9
	4284–	7287.1	3	(8.4 +9.7−5.4) × 10−10
Ne	40–58	47.0	37	(1.20 ± 0.20) × 10−4
Z = 10	58–101	74.8	65	(2.59 ± 0.32) × 10−5
	101–175	130.7	67	(5.53 ± 0.68) × 10−6
	175–304	227.9	36	(1.06 ± 0.18) × 10−6
	304–529	396.7	19	(2.86 +0.84−0.66) × 10−7
	529–919	690.0	8	(6.5 +3.1−2.2) × 10−8
	919–1597	1199.8	4	(1.8 +1.4−0.9) × 10−8
	1597–2776	2085.6	2	(3.7 +5.6−2.0) × 10−9
	2776–	4150.9	3	(2.2 +2.1−1.2) × 10−9
Mg	20–40	27.0	48	(4.68 ± 0.67) × 10−4
Z = 12	40–58	47.0	45	(1.07 ± 0.16) × 10−4
	58–101	74.9	103	(2.91 ± 0.29) × 10−5
	101–175	130.8	94	(5.41 ± 0.56) × 10−6
	175–304	228.0	51	(1.42 ± 0.20) × 10−6
	304–529	397.0	26	(3.72 ± 0.73) × 10−7
	529–919	690.6	12	(8.5 +3.3−2.4) × 10−8
	919–1597	1200.8	4	(1.9 +1.6−1.0) × 10−8
	1597–2776	2087.5	3	(6.7 +7.1−4.0) × 10−9
	2776–	4215.9	1	(6.0 +16.0−5.8) × 10−10
Si	20–40	27.0	66	(4.54 ± 0.56) × 10−4
Z = 14	40–58	47.0	64	(1.35 ± 0.17) × 10−4
	58–101	74.9	116	(3.03 ± 0.28) × 10−5
	101–175	130.8	89	(5.04 ± 0.53) × 10−6
	175–304	228.0	54	(1.50 ± 0.20) × 10−6
	304–529	397.0	24	(3.88 ± 0.79) × 10−7
	529–919	690.6	10	(1.15 +0.48−0.35) × 10−7
	919–1597	1200.7	3	(1.9 +1.7−0.9) × 10−8
	1597–	2418.3	2	(3.2 +3.6−1.8) × 10−9
Fe	18–40	25.4	108	(5.19 ± 0.56) × 10−4
Z = 26	40–58	47.0	88	(8.38 ± 0.89) × 10−5
	58–101	74.9	70	(2.06 ± 0.25) × 10−5
	101–175	131.0	27	(4.46 ± 0.85) × 10−6
	175–304	228.2	15	(1.36 +0.46−0.36) × 10−6
	304–529	397.2	9	(4.0 +1.8−1.3) × 10−7
	529–919	690.9	4	(1.09 +0.79−0.48) × 10−7
	919–	1406.9	4	(1.6 +1.4−0.8) × 10−8

Download table as:  ASCIITypeset image

The energy spectra of the major primary CR nuclei from carbon to iron are plotted as a function of the kinetic energy per particle in Figure 6. To emphasize the spectral differences, the differential intensities are multiplied by $\hat{E}^{2.5}$ and plotted as a function of the kinetic energy per nucleon in Figure 7. The error bars shown in the figures represent the sum in quadrature of the statistical and systematic uncertainties. The assessment of systematics is discussed in detail in the following section. The particle energy range covered by CREAM-II extends from around 800 GeV up to 100 TeV. The absolute intensities are presented without any arbitrary normalization to previous data and cover a range of six decades.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The energy spectrum of nitrogen is shown in Figure 8. The statistical and systematic errors in the differential intensity are shown separately to point out that the systematic uncertainties from the corrections for secondary particle production in the atmosphere and the instrument, are particularly relevant for this measurement. In practice, they impose a limit on the maximum energy at which measurements of nitrogen in CRs might be pursued on a balloon flight.

Zoom In Zoom Out Reset image size

The elemental abundances with respect to oxygen are calculated from the differential intensities at the TOA and are shown as a function of energy in Figure 9. Energy bins at high energy are merged together in order to reduce the statistical error in the ratio to an acceptable level.

Zoom In Zoom Out Reset image size

5.1. Estimate of the Systematic Errors

The CREAM-II results for primary nuclei are found to be in good agreement with previous measurements of space-based (HEAO 3–C2 (Engelman et al. 1990), CRN (Müller et al. 1991)) and balloon-borne (ATIC-2 (Panov et al. 2006), TRACER (Ave et al. 2008)) experiments (see Figures 6 and 7). All the elements appear to have the same spectral shape, which can be described by a single power law in energy E^−γ. The spectral indices fitted to our data (Table 2) are very similar, indicating that the intensities of the more abundant (evenly) charged heavy elements have nearly the same energy dependence. Our observations, based on a calorimetric measurement of the CR energy, confirm the results recently reported by the TRACER collaboration (Figure 10), using completely different techniques (Cherenkov, specific ionization in gases and transition radiation) to determine the particle energy. The weighted average of our fitted spectral indices is $\bar{\gamma } = 2.66 \pm 0.04$, consistent, within error, with the value of 2.65 ± 0.05 obtained from a fit to the combined CRN and TRACER data (Ave et al. 2008). The great similarity of the spectral indices suggests that the same mechanism is responsible for the source acceleration of these primary heavy nuclei.

Zoom In Zoom Out Reset image size

Although all the elemental spectra can be fitted to a single power law in energy, hardening (flattening) of the spectra above ∼200 GeV/n is apparent from the overall trend of the data (Figure 7). A detailed analysis to investigate possible features in the spectra is in progress to evaluate the significance of a change in the spectral index.

CREAM-II data extend the energy range spanned by the previous elemental abundance measurements up to ∼1 TeV/n (Figure 9). The C/O ratio measured by CREAM-II is consistent with the one reported by CREAM-I (Ahn et al. 2008) within the overlapping energy region covered by the two flights and slightly higher than the CRN result. The Ne/O and Mg/O ratios confirm, up to 800 GeV/n, the nearly flat trend of HEAO 3–C2 low-energy data, while the fractions of Si and Fe with respect to O seem to increase with energy. This could represent the clue of a possible change in composition of CRs at high energies with an enhancement of heavier elements, as expected from SNR shock diffusive acceleration theories. Nevertheless, the statistics of the data are too limited for a definitive conclusion at this time.

Unlike the primary heavy nuclei, nitrogen is mostly produced by spallation in the interstellar medium, but it also has a primary contribution of order 10%, as recently measured by CREAM-I (Ahn et al. 2008). The measurement of nitrogen intensity at high energy is challenging because it requires an excellent charge separation between N nuclei and the much more abundant C and O neighbors, as well as a complete understanding of the corrections for secondary N particle production in the atmosphere and the instrument. The nitrogen data collected by CREAM-II are more statistically significant at high energy than any previous observation. We notice that, above 100 GeV/n, the N spectrum flattens out from the steep decline which characterizes the energy range 10–100 GeV/n (Figure 8). The combined CRN and CREAM-II data at energies higher than 200 GeV/n, are well fitted to a power-law in energy with spectral index 2.61 ± 0.10, consistent within the error with the average value $\bar{\gamma }$ of the primary nuclei. This supports the hypothesis of the presence of two components in the cosmic nitrogen flux. In fact, since the escape path length decreases rapidly with energy, the secondary nitrogen component is expected to become negligible at high energy, where only the primary component should survive. This might result in a change of the spectral slope, as observed.

As a cross-check to the measurement reported here, we calculate the relative abundance ratio of N/O and compare it with the CREAM-I observation (Figure 9), in which the energy of CRs was measured with a transition radiation detector. A N/O ratio (at the TOA) equal to 0.080 ± 0.025 (stat.)±0.025 (sys.) is measured at an energy of ∼800 GeV/n, in good agreement with recent results from CREAM-I (Ahn et al. 2008).

CREAM-II carried out measurements of high-Z CR nuclei with an excellent charge resolution and a reliable energy determination. The use of a dual layer of silicon sensors allowed us to unambiguously identify each individual element up to iron and to reduce the background of misidentified nuclei. We demonstrated the feasibility of measuring the particle energy up to hundreds of TeV by using a thin ionization sampling calorimeter, with sufficient resolution to reconstruct accurately the CR spectra.

The energy spectra of the major primary heavy nuclei from C to Fe were measured up to ∼10¹⁴ eV and found to agree well with earlier direct measurements. All the spectra follow a power law in energy with a remarkably similar spectral index $\bar{\gamma } = -2.66 \pm 0.04$, as is plausible if they have the same origin and share the same acceleration and propagation processes.

A new measurement of the nitrogen intensity in an energy region so far experimentally unexplored indicates a harder spectrum than at lower energies, supporting the idea that nitrogen has secondary as well as primary contributions. These results provide new clues for understanding the CR acceleration and propagation mechanisms, but further accurate observations with high statistics beyond 10¹⁴ eV are needed to finally unravel the mystery of CR origin.

This work is supported by NASA research grants to the University of Maryland, Penn State University, and Ohio State University, by the Creative Research Initiatives program (RCMST) of MEST/NRF in Korea, and INFN and PNRA in Italy. The authors greatly appreciated the support of NASA/WFF and NASA/GSFC, Columbia Scientific Balloon Facility, National Science Foundation's Office of Polar Programs and Raytheon Polar Services Company for the successful balloon launch, flight operation and payload recovery in Antarctica.