arXiv:0910.4184v2 [astro-ph.HE] 3 Apr 2010
Indications of Proton-Dominated Cosmic Ray Composition above
R.U. Abbasi,1T. Abu-Zayyad,1M. Al-Seady,1M. Allen,1J.F. Amman,2R.J. Anderson,1
G. Archbold,1K. Belov,1J.W. Belz,1, ∗D.R. Bergman,1,3S.A. Blake,1O.A. Brusova,1
G.W. Burt,1C. Cannon,1Z. Cao,1W. Deng,1Y. Fedorova,1C.B. Finley,4R.C. Gray,1
W.F. Hanlon,1C.M. Hoffman,2M.H. Holzscheiter,2G. Hughes,3P. H¨ untemeyer,1
B.F Jones,1C.C.H. Jui,1K. Kim,1M.A. Kirn,5E.C. Loh,1J. Liu,6J.P. Lundquist,1
M.M. Maestas,1N. Manago,7L.J. Marek,2K. Martens,1J.A.J. Matthews,8
J.N. Matthews,1S.A. Moore,1A. O’Neill,4C.A. Painter,2L. Perera,3K. Reil,1R. Riehle,1
M. Roberts,8D. Rodriguez,1N. Sasaki,7S.R. Schnetzer,3L.M. Scott,3G. Sinnis,2
J.D. Smith,1P. Sokolsky,1C. Song,4R.W. Springer,1B.T. Stokes,1S. Stratton,3
S.B. Thomas,1J.R. Thomas,1G.B. Thomson,1, 3D. Tupa,2A. Zech,3and X. Zhang4
(The High Resolution Fly’s Eye Collaboration)
1University of Utah, Department of Physics, Salt Lake City, UT, USA
2Los Alamos National Laboratory, Los Alamos, NM, USA
3Rutgers University — The State University of New Jersey,
Department of Physics and Astronomy, Piscataway, NJ, USA
4Columbia University, Department of Physics and
Nevis Laboratory, New York, New York, USA
5Montana State University, Department of Physics, Bozeman, MT , USA
6Institute of High Energy Physics, Beijing, China
7University of Tokyo, Institute for Cosmic Ray Research, Kashiwa, Japan
8University of New Mexico, Department of Physics and Astronomy, Albuquerque, NM, USA
We report studies of ultra-high energy cosmic ray composition via analysis of depth of airshower
maximum (Xmax), for airshower events collected by the High Resolution Fly’s Eye (HiRes) ob-
servatory. The HiRes data are consistent with a constant elongation rate d <Xmax> /d(log(E))
of 47.9 ± 6.0(stat.) ± 3.2(syst.) g/cm2/decade for energies between 1.6 EeV and 63 EeV, and are
consistent with a predominantly protonic composition of cosmic rays when interpreted via the
QGSJET01 and QGSJET-II high-energy hadronic interaction models. These measurements con-
strain models in which the galactic-to-extragalactic transition is the cause of the energy spectrum
“ankle” at 4 × 1018eV.
PACS numbers: 98.70.Sa, 95.85.Ry, 96.50.sb, 96.50.sd
∗Corresponding author: email@example.com
The observation of a break in the cosmic ray energy spectrum at approximately 6 ×
1019eV [1–3] provides evidence that the highest energy cosmic rays are both extragalactic
and protonic [4, 5]. Direct evidence for a proton-dominated composition from airshower
data would lend further support to this model, as would the observation of a transition from
(heavy) galactic to (light) extragalactic cosmic rays at lower energies. A second feature, the
“ankle” of the energy spectrum at 4 × 1018eV may be indicative of this transition or it
may further strengthen the model in which the end of the cosmic ray spectrum is shaped
by interactions with the cosmic microwave background . Composition studies can provide
decisive evidence in the choice between interpretations.
An important clue to chemical composition which is accessible to air fluorescence obser-
vatories is the depth of shower maximum Xmaxof cosmic ray induced extensive airshowers.
Simple arguments [7, 8] show that the average value of airshower maximum <Xmax> will
depend logarithmically on the primary energy and atomic mass, and that the elongation rate
d <Xmax> /dlogE will be constant for unchanging primary compositions. Further, to first
order, a nucleus-induced shower may be thought of as a superposition of showers induced
by single nucleons. Therefore due to averaging effects we also expect the width of the Xmax
distribution at a given energy to be sensitive to the atomic mass of the primary.
The two fluorescence observatories of the High-Resolution Fly’s Eye collected data in
stereoscopic mode between December 1999 and April 2006. Located on the U.S. Army
Dugway Proving Ground in Utah, at a mean elevation of 1,575 m MSL, a mean latitude of
40.16◦N, and separated by 12.6 km, the observatories operated on clear moonless nights.
Each detector consisted of an array of telescope modules, each module included a mirror of
3.7 m2effective area which focused UV light from airshowers on a 16 × 16 photomultiplier
tube (PMT) camera. The field of view of each PMT subtended a one degree diameter cone
of the sky. The HiRes-I detector covered nearly 360◦in azimuth, 3◦–17◦in elevation and
was read out by means of sample-and-hold electronics, while the HiRes-II detector covered
3◦–31◦in elevation and was read out by a custom FADC system .
The calibration of the HiRes telescope modules has been described previously . A
portable Xenon flash lamp (∼ 0.5% stability) was used to illuminate each mirror monthly.
Between Xenon runs, nightly calibrations were performed using YAG laser light delivered
to the cameras via optical fiber . A pulsed nitrogen laser was fired into the atmosphere
from various locations within 3.5 km of the two detector sites. An overall accuracy of ∼ 10%
RMS is achieved in the HiRes photometric scale.
Steerable lasers fired patterns of shots which covered the aperture of the HiRes fluores-
cence detectors, in order to monitor UV attenuation in the atmosphere. The vertical aerosol
optical depth (VAOD) was measured to be 0.04(mean)±0.02(RMS) [12, 13], corresponding
to a mean correction of ∼15% upward in energy for an event 25 km distant from the obser-
vatory. In the present analysis, the steerable laser measurements were used to compile an
hourly database of the atmospheric parameters.
A mirror trigger was initiated if a sufficient number of PMTs were in temporal and spatial
coincidence, then a stereo data set was obtained by the time-matching of HiRes-I and HiRes-
II triggers. Geometrical reconstruction of stereo events proceeded by determination of the
shower-detector plane from each HiRes site, the intersection of these two planes was taken
to be the shower core trajectory. The resolution in the shower zenith angle is 0.6◦, and the
resolution in Rp(distance of closest approach to the detector) is 1.2%.
Hit information from multiple tubes in the HiRes-II data only are sorted into discrete
time bins. In each bin, FADC signals are converted to a number of photoelectrons Npe,
then adjusted for the effective area of each bin as determined by ray tracing. The geometry
of the shower and the atmospheric databases are used to determine the atmospheric slant
depth X for each shower bin. Shower segments that have emission angles within 5◦of a
bin’s pointing direction are flagged and not used for fitting due to excessive Cherenkov light
contamination. The Npe profile is then converted to a profile of the fluorescence light at
the shower by a routine that simulates the light production and propagation through the
atmosphere, and subtracts the Cherenkov contribution.
The intensity of fluorescence light emitted from an airshower is proportional to the total
ionization energy deposited by the charged particles in the shower . We use the average
fluorescence yield of several groups [15–17] and the spectral distribution given by Ref. ,
along with the average dE/dX determined from CORSIKA simulations  to determine
the number of charged particles in the shower as a function of slant depth.
The shower profile is then fit to a Gaussian function of the age parameter s(X) = 3X/(X+
2Xmax) in order to determine the airshower energy and Xmax. (Alternatively fitting by the
Gaisser-Hillas parametrization  had little overall effect on the analyses and conclusions
presented here.) Further details of the reconstruction used in this analysis are contained in
Ultra-high energy cosmic ray composition studies require a detailed comparison of data
with the predictions of airshower models and are hence model dependent. In practice, these
models are airshower Monte Carlo simulations. In order to completely understand the effects
of the geometrical aperture of the detector, HiRes applies a full detector simulation to the
Monte Carlo events.
HiRes uses libraries of simulated proton- and iron-induced airshowers generated by the
CORSIKA 6.003 (6.501)  package, using the QGSJET01 , QGSJET-II , and
SIBYLL [25, 26] hadronic interaction models and the EGS4  electromagnetic interaction
driver. The number of particles versus slant depth is recorded at 205 points along each
Detector simulation proceeds by drawing an event from the shower library, assigning it
a random core location, zenith and azimuthal angle and determining if it can trigger the
detector. The number of charged particles at many discrete points along the shower is de-
termined, and fluorescence light is then propagated from the shower to the detector. Light
attenuation by the atmosphere is realistically simulated by using an hourly database de-
scribing the measured aerosol content, temperature, and pressure. Ray tracing is performed
to determine which phototubes see the light, allowing for photocathode response and in-
active space between PMTs. An electronics simulation then determines the pulse height
and time for each tube for HiRes-I and forms a FADC waveform for HiRes-II. For all tubes
the channel gains, DAC settings, thresholds and channel variances are simulated by using
hourly database information. The same trigger algorithms used in hardware are simulated,
and if either detector would have been triggered the simulated data is written to disk in the
identical format as real data, allowing the study of Monte Carlo events by the same analysis
chain. The Monte Carlo set for each hadronic interaction model contains approximately
20 times the number of reconstructed stereo events as the data.
The major challenge in studying cosmic ray composition by the <Xmax> technique lies in
understanding the systematic biases that occur during reconstruction and event selection.
Low-energy showers which are nearby the detector may reach Xmaxabove the field of view of
the mirrors, thus biasing a data set towards deeper showers. High-energy showers with small
zenith angles are likely to reach maximum below the field of view of the mirrors, resulting
in a bias towards shallow showers.
It is useful to divide the types of biases which can occur into two types, called “accep-
FIG. 1: Difference between HiRes-II (XII) and HiRes-I (XI) Xmaxfor HiRes stereo data (points)
overlaid with QGSJET-II proton Monte Carlo. Xmaxbracketing by HiRes-I is required.
tance biases” and “reconstruction biases”. Acceptance biases are due to events which fail
reconstruction altogether, including detector triggering and event selection effects. Recon-
struction biases are due to events which are successfully reconstructed, but with the wrong
Xmax. The strategy in the following analysis is to choose event selection cuts which minimize
the reconstruction bias, and make the acceptance bias as independent of energy as possible.
After geometrical reconstruction and fitting of the shower profiles to obtain energy and
Xmax, a set of cuts are applied in order to select an appropriate event sample. The chance
probability that the event is due to noise must be less than 1%, and the χ2/DOF of the
fit must be less than 4. Data must have been taken in good weather conditions. Fit
uncertainty in the zenith angle must be less than 2◦, the fit uncertainty in Xmaxmust be
less than 40 g/cm2, and the angular RMS with respect to the event plane of hit PMTs must
be greater than 0.15◦. The zenith angle of the event itself must be less than 70◦, and the
Rp with respect to HiRes-II must be at least 10 km. Events are required to have Xmax
bracketed by the HiRes-II field of view, and have a shower-detector plane angle between
40◦and 130◦. Finally, events with energies 18.2 < log(E(eV)) < 19.8 are selected for this
analysis. A total of 815 events pass all cuts.
In Fig. 1 the resolution in Xmaxof data and Monte Carlo events are compared by plotting
the difference between Xmaxas measured by HiRes-I and HiRes-II. The agreement is excel-
lent, including the asymmetry caused by HiRes-I covering only half the range in elevation
angle. This supports the use of Monte Carlo to determine Xmaxresolution, which is found
to be better than 25 g/cm2over most of the HiRes energy range.
FIG. 2: Top: Xmaxoverlay of HiRes data (points) with QGSJET-II proton Monte Carlo airshowers
after full detector simulation. Bottom: Xmaxoverlay of HiRes data (points) with QGSJET-II iron
Monte Carlo airshowers.
After application of the cuts above, we compare the distribution in Xmax to the pre-
dictions obtained from simulated proton and iron showers.Fig. 2 shows the excellent
overall agreement between the HiRes stereo data and the predictions of the QGSJET-II
proton Monte Carlo. In Fig. 3, we compare the development with energy of the mean
Xmax in HiRes data with the predictions (after full detector simulation) for QGSJET01,
QGSJET-II and SIBYLL proton and iron. The data agrees best with the QGSJET-II pro-
ton prediction, with a χ2= 6.9/8 df. In a linear fit with χ2= 5.2/(6 df) we measure
47.9 ± 6.0(stat.) g/cm2/decade for the elongation rate. Systematic effects are considered
FIG. 3: HiRes stereo <Xmax> compared with the predictions for QGSJET01, QGSJET-II and
SIBYLL protons and iron after full detector simulation. The number of events in each energy bin
is displayed below the data point.
Due to detector, reconstruction, and event selection acceptance effects, the proton and
iron “rails” in Fig 3 are shifted relative to the raw CORSIKA predictions. However, we find
that the shift in mean Xmaxfor QGSJET01 and QGSJET-II protons is independent of energy
to approximately 1.8 g/cm2/decade. We assign a systematic uncertainty of 2.7 g/cm2/decade
to the elongation rate based on small variations of event selection cuts. Uncertainties in
the energy do not have a large effect on elongation rate results due to the logarithmic
energy scale. The choice of VAOD was the main systematic in a previous elongation rate
analysis , however the use of an hourly atmospheric database in the present analysis
renders this source of systematics negligible.
The phototube pointing directions have been confirmed by studies using stars  to
within 0.3◦, corresponding to a shift in Xmaxof approximately 15 g/cm2. Averaging over
mirrors, this contributes a net uncertainty of 3.3 g/cm2to the value of <Xmax>. The
subtraction of the Cherenkov light from the phototube signal can introduce an uncertainty
in Xmaxdue to uncertainties in electron multiple scattering. Previous studies  in which
the width of the Cherenkov beam was varied by 2◦(1 σ) indicated negligible effect on the
elongation rate or absolute value of <Xmax>. Finally, a systematic uncertainty of 0.7 g/cm2
is assigned to the absolute value of <Xmax> in the predictions due to Monte Carlo statistics.
The fluctuations of Xmaxas a function of energy are also a probe of primary particle com-
position. Because the distributions tend to be both asymmetric and possess non-Gaussian
tails, care must be taken to use a suitable definition of the Xmaxwidth. The uncorrected
RMS and sample standard deviations are biased estimators of the width  and tend to be
subject to large fluctuations in distributions with broad tails.
In order to focus attention on the center of the Xmaxdistribution and reduce sensitivity
to fluctuations in the tails, the width is quantified as the width σXof a unbinned likelihood
fit to a Gaussian of a distribution truncated at 2 × RMS. The results of this analysis
applied to both the HiRes data and to QGSJET-II proton and iron Monte Carlo are shown
in Fig. 4. The HiRes Xmaxwidth data are consistent with the predictions of QGSJET-II
protons. The width of the Xmaxdistribution of protons within the QGSJET01 model tends
to be about 5 g/cm2broader than that of QGSJET-II, while SIBYLL protons are 2-3 g/cm2
narrower than those of QGSJET-II. Both of these shifts are small compared with statistical
uncertainties, particularly at the highest energies.
In summary, the HiRes data are consistent with a constant elongation rate of 47.9 ±
6.0(stat.)±3.2(syst.) g/cm2/decade above 1.6 EeV, and thus with an unchanging composition
across the ankle. This places strong constraints on models in which the ankle is the result
of a transition from heavy galactic to light extragalactic cosmic rays.
Of the hadronic interaction models tested, the best agreement is with the QGSJET-II
pure proton model. Within current uncertainties the data are completely consistent with
this model, and close to QGSJET01 pure protons. Comparison with SIBYLL suggests a
mixture dominated by light elements. The observed constant elongation rate would imply
that this mixture is unchanging, or at most steadily changing over nearly two orders of
magnitude spanning the energy spectrum ankle.
The present analysis, taken together with the HiRes spectral results [1, 3] on the shape
and location of the high-energy cutoff and ankle, suggests the simple picture in which cosmic
rays above 1 EeV are protons of extragalactic origin and the end of the energy spectrum is
shaped by interactions with the cosmic microwave background.
PHY-9904048, PHY-9974537, PHY-0098826, PHY-0140688, PHY-0245428, PHY-
0305516, PHY-0307098, and by the DOE grant FG03-92ER40732.We gratefully acknowl-
FIG. 4: Results of fitting HiRes stereo data Xmaxdistribution to Gaussian truncated at 2 × RMS
(black points). Superimposed are expectations based on QGSJET-II proton (squares) and iron
(triangles) Monte Carlo. Monte Carlo points are shown with small offsets in energy to provide
edge the contributions from the technical staffs of our home institutions. The cooperation
of Colonels E. Fischer, G. Harter and G. Olsen, the US Army, and the Dugway Proving
Ground staff is greatly appreciated.
Note added. — In a recent paper , the Pierre Auger collaboration draws different
conclusions as to the composition of the highest energy cosmic rays.
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