The energy spectrum of ultra-high-energy cosmic rays measured by the Telescope Array FADC fluorescence detectors in monocular mode
Introduction
Ultra-high-energy cosmic rays (UHECRs) are charged subatomic particles of extraterrestrial origin with kinetic energies above eV, making them the most energetic particles in the known universe. A clear understanding of their origins and chemical composition has not yet been experimentally established, largely due to the scarcity of UHECRs: collecting enough data to suppress uncertainty from small-number statistics requires a detector that can observe a large area for a long time. The Telescope Array (TA) experiment in western Utah is the largest UHECR detector currently operating in the northern hemisphere1 [2], [3]. Centered at approximately 112.9° W, 39.3° N near the city of Delta in Millard County, TA is a “hybrid” detector consisting of three atmospheric fluorescence detector (FD) stations and a ground array of 507 surface detectors (SDs) on a square grid with 1200-meter spacing (see Fig. 1).
Each of the FDs and the SD array operate independently, collecting data for UHECR measurements. The SDs, which directly detect secondary particles in the extensive air shower produced by a primary UHECR, collect data night and day in all weather and thus have a duty cycle of nearly 100%. The FDs use telescopes to measure ultraviolet light produced when an air shower excites atmospheric N2. For best sensitivity, FDs operate only on moonless nights, so their duty cycles are each approximately 10%.
Although the SD array alone boasts the strongest statistical power within the experiment, combining and comparing data from different components of TA allows distinct, corroborating measurements of physical quantities of interest. Using the simultaneous observation of a single cosmic-ray air shower by one FD and either the SD array (“hybrid”) or a second FD (“stereo”), we tightly constrain certain geometric properties of the air shower, but the majority of UHECRs do not satisfy this observation criterion. The “monocular” observation of UHECRs, reconstructing events using measurements from a single FD station, accumulates data at a rate second only to the SD array, and has several additional advantages over hybrid or stereo analysis: it encompasses a broader range of UHECR energies, its aperture calculation is less sensitive to atmospheric variation than the corresponding stereo calculation,2 and its systematic uncertainties are independent of those used in the SD analysis. A monocular measurement of the energy spectrum is therefore an important complement to the same spectrum as measured by the SD array.
Two different designs of FD station are in use at TA: the northern station, Middle Drum (MD), uses refurbished hardware from the High Resolution Fly’s Eye (“HiRes”) cosmic-ray experiment, which collected data at Utah’s Dugway Proving Ground from 1997 to 2006 [4]. MD’s data acquisition (DAQ) system is based on sample-and-hold electronics, in which each pixel of a telescope’s image reports a single value for signal intensity and a time reference. The southeastern and southwestern FD stations, respectively dubbed Black Rock Mesa (BRM) and Long Ridge (LR), consist of new telescopes designed for TA that use flash analog-to-digital converter (FADC)-based electronics to record the evolution of each pixel’s signal intensity.
In this paper, we report the UHECR energy spectrum above eV as measured by the two FADC-based FDs operating in monocular mode. The corresponding measurement by the MD FD has been reported elsewhere [5], as has the energy spectrum measured by the SD array [6]. In Section 2, we elaborate on the construction and operation of the BRM and LR FDs, whose data we analyze as described in Section 3. Section 4 describes the Monte Carlo simulation process by which we calculate the detectors’ sensitivity. We present the energy-spectrum measurement in Section 5, followed by a combination of our measurement with that from the MD FD (Section 6). We conclude with a discussion of our results in Section 7. Our results are corroborated by a separate monocular analysis not described in detail here, using computer programs and processing techniques developed independently from ours [7], [8].
Section snippets
FADC-based fluorescence detectors
The TA experiment’s FADC-based FDs occupy two sites at the southern end of the array. The BRM FD site contains twelve telescopes with a contiguous field of view ranging from 3° to 33° in elevation in directions to the west and northwest (as shown in Fig. 1). The LR FD site is identical to BRM in its construction, but with an eastward orientation. Each telescope consists of a segmented spherical mirror 3.3 m in diameter, which focuses light from a 15-degree (elevation) by 18-degree (azimuth)
FD data analysis
Analyzing the data collected by the FDs is a process of several steps, beginning with the raw data and ending with a set of cosmic-ray events whose trajectories and air-shower longitudinal profiles satisfy quality cuts carefully chosen via Monte Carlo simulation. Steps of data reduction alternate with steps of further processing.
Our first step in data analysis is preprocessing to remove unwanted PMTs: those telescopes that are not neighbor to a triggered telescope are discarded, and those PMTs
Aperture calculation
The UHECR energy spectrum is related to each FD’s data (Fig. 3) by that detector’s exposure, the subset of a multidimensional phase space in which cosmic rays of a given energy are detected and pass all quality cuts. In practice, this is the product of the detector’s live time and its energy-dependent aperture. The former is a straightforward calculation that subtracts dead time from the gross on-time of each detector as described in Section 2. The latter is calculated by Monte Carlo simulation.
Monocular FADC FD energy spectrum
The energy spectrum of the UHECR flux is the ratio of the number of data events to the exposure. In the ith energy interval of width and where is the geometric mean of the interval limits, there are events, and
For clarity’s sake, we have multiplied the spectrum by in Fig. 9. For comparison, we also present the published results from the MD FD and the SD ground array. Using a binned maximum-likelihood fit, we determine parameters for the twice-broken power law
Combined FD monocular spectrum
To obtain a unified Telescope Array measurement of the UHECR spectrum in monocular mode, we combine our FADC-based FD result with the independent measurement performed using the MD FD [5]. To combine these measurements properly, we merge their observed UHECR data sets (an event observed by more than one detector enters the merged data set with the geometric mean of its two or three measured energies) and their respective exposures. Combining the exposures requires that we account for their
Discussion and conclusions
The UHECR energy spectrum, as measured by TA’s FADC-based FDs in monocular mode using 3.5 years of data, is shown in Fig. 9. The shape of the spectrum plot is dominated by a power-law dependence of flux on energy, punctuated by two abrupt changes in the spectral index. These breaks, a hardening of the spectrum near eV and a softening near eV, are respectively recognizable as the “ankle” and a high-energy suppression consistent with the Greisen-Zatsepin-Kuzmin (GZK) mechanism [27],
Acknowledgments
The Telescope Array experiment is supported by the Japan Society for the Promotion of Science through Grants-in-Aid for Scientific Research on Specially Promoted Research (21000002) “Extreme Phenomena in the Universe Explored by Highest Energy Cosmic Rays,” and the Inter-University Research Program of the Institute for Cosmic Ray Research; by the US National Science Foundation awards PHY-0307098, PHY-0601915, PHY-0703893, PHY-0758342, PHY-0848320, PHY-1069280, and PHY-1069286 (Utah) and
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