Using Muon Rings for the Optical Throughput Calibration of the Cherenkov Telescope Array

Experimental Astronomy manuscript No. (will be inserted by the editor) Using Muon Rings for the Optical Throughput Calibration of the Cherenkov Telescope Array M. Gaug · K. Bernlöhr · M.C. Maccarone · P. Majumdar · T. Mineo · A. Mitchell Received: date / Accepted: date Abstract The analysis of images produced by muon rings in an Imaging At- mospheric Cherenkov Telescope (IACT) provides a powerful and precise method to calibrate the optical throughput and optical point-spread-function of such a telescope. Being first proposed by Vacanti and collabotors in the early 90's, this method has been refined in different aspects by the collaborations forming the so- called second generation of IACTs: H.E.S.S., MAGIC and VERITAS. We present here a compilation of the progress that has been made by these instruments and investigate their applicability for the different telescope types forming the future Cherenkov Telescope Array (CTA). We find that several smaller modifications in hardware and analysis need to be made to ensure that such a muon calibration works as precisely as expected from previous telescopes and derive estimates for the statistical and systematic precision of the method. 1 Introduction The muon ring calibration, first advocated by Rowell et al. (1991) and further elabored in detail by Vacanti et al. (1994), has been used as a method to calibrate the optical throughput, first of the Whipple telescope (Rose, 1995; Rovero et al., 1996) and later practically all currently operating Imaging Atmospheric M. Gaug UAB, Barcelona, Spain E-mail: [email protected] K. Bernlöhr MPIK, Heidelberg, Germany M.C. Maccarone INAF IASF-Palermo, Italy T. Mineo INAF IASF-Palermo, Italy A. Mitchell MPIK, Heidelberg, Germany 2 M. Gaug et al. Cherenkov Telescopes (IACTs) (Guy, 2003; Leroy et al., 2003; Humensky, 2005; Shayduk et al., 2003; Meyer et al., 2005; Goebel et al., 2005), plus the optical point-spread-function of the MAGIC telescopes (Meyer et al., 2005; Goebel et al., 2005). In-depth studies of the muon method were furthermore carried out in several PhD theses, dedicated to the optical throughput calibration of the H.E.S.S. telescopes (Bolz, 2004; Leroy, 2004; Mitchell, 2016). The next generation gamma-ray observatory, the Cherenkov Telescope Array (CTA) (Actis et al., 2011; Acharya et al., 2013) is based on the IACT technique, but will largely outperform current installations (?) in terms of sensisivity (im- proved by at least a factor ten at 1 TeV, but considerably more at higher energies or off-axis), energy coverage (ranging from several tens of GeV to more than 300 TeV), angular resolution (0.05◦ at 1 TeV), energy resolution (∼7% at 1 TeV) and systematic uncertainties (<10% on the overall energy scale required)1. The CTA is built to boost the number of known Very High Energy (VHE, E > 10 GeV) sources from currently a few more than hundred to over a thousand, and hence move from the discovery mission of its predecessors to perform pop- ulation studies and precision measurements, resolving spectral features and the morphology of gamma-ray sources with unprecedented precision (?). A thorough calibration strategy must hence be included in its design (?). Recently, the CTA site selection has been completed, with as outcome, for its Southern observatory (CTA-S), a plateau of the Cerro Armazones in Northern Chile, close to Paranal, while the \Roque de los Muchachos" Observatory (ORM) on the island of La Palma, Canary Islands, has been selected for its Northern part (CTA-N). Both observatories are located around 2200 m a.s.l. The CTA counts with a large variety of telescope types and sizes (Actis et al., 2011; Acharya et al., 2013), which are listed in Table ??. It is therefore not imme- diately clear whether the muon calibration method will work for each case, and at which precision and accuracy. To address these issues is the scope of this article. The following points were given special importance: 1. Resume in a comprehensive way the different muon analysis algorithms em- ployed by H.E.S.S., MAGIC and VERITAS 2. Determine whether all telescope designs are able to provide sufficient muon triggers per night 3. Determine the expected statistical and systematic precision of muon calibration for the CTA telescopes 4. Formulate additional requirements needed to make muon calibration successful for the CTA We will first introduce the main concepts for muon calibration in Sections 2 and 3. The selection and reconstruction of muon rings is explained in Sections 4, 5 and 6. Systematic effects are investigated in Section 7 and simulations carried out in Section 8. Muon flagging in the camera servers and fast algorithms to achieve this, are treated in Section 9. Expected muon image rates are summarized in Sec- tion 10, and the results are discussed and recommendations given in Section 11. Assumptions and remaining caveats are treated in Section 12. The main conclu- sions are drawn in Section 13. 1 see also https://www.cta-observatory.org/science/cta-performance/ Title Suppressed Due to Excessive Length 3 primary camera optics mirror FOV reference (m2) (deg ) LST parabolic 387 5 Teshima et al. (2013) MST Davies-Cotton 104 8 Acharya et al. (2013) MST-SC Schwarzschild-Couder 50 8 Vasiliev et al. (2013) SST (ASTRI ) Schwarzschild-Couder 6:0 10 Pareschi et al. (2013) SST (GCT) Schwarzschild-Couder 8:2 10 Zech et al. (2013) SST-1M Davies-Cotton 7:6 10 Moderski et al. (2013) Table 1 List of the proposed telescopes of the CTA. The following common abbreviations are used: LST: Large-Size-Telescope, MST: Medium-Size-Telescope, SST: Small-Size-Telescope, SC: Schwarzschild-Couder, 1M: single mirror. 4 M. Gaug et al. 2 Muon spectra and expected event rates The muon spectrum on ground has been measured for momenta from 100 GeV/c to about 1.5 TeV/c with statistical and systematic uncertainties better than 10% per momentum bin for the central 141 to 1122 GeV/c range and better than 15% from 100 to 1500 GeV/c (Schmelling et al., 2013). The data fit very nicely a parameterization for the vertical muon flux from Hebbeker and Timmermans (2002), based on theoretical calculations from (Bugaev et al., 1998): F (y) = 10H(y)m−2 sr−1 s−1 GeV−1 with: (1) y = log10(p=GeV) H(y) = 0:133 · (y3=2 − 5y2=2 + 3y) −2:521 · (−2y3=3 + 3y2 − 10y=3 + 1) −5:78 · (y3=6 − y2=2 + y=3) −2:11 · (y3=3 − 2y2 + 11y=3 − 2) : The spectral index at 100 GeV is then approximately −3:11. The muon flux dependence with altitude has been measured by balloon ex- periments (e.g. Haino et al., 2004) and can be parameterized for muon momenta above 10 GeV and altitudes less than 1000 m as: F (h) = F (0) · exp(h=L) (2) with: L = 4900 + 750 · (p=GeV) m ; where h is the altitude in meter. The flux ratio between a location at 2770 m a.s.l. and 1270 m at 10 GeV muon energy results to be ∼13%. The dependency of the 2 muon flux on zenith angle can be described as / cos (θ) at Eµ ≈ 3 GeV, while it steepens with higher energy to reach approximately 3 −2:7 n 1 0:054 o F (cos θ) = 1:4 · 10 · Eµ × + 1:1·Eµ·cos θ 1:1·Eµ·cos θ 1 + 115 GeV 1 + 850 GeV m−2 sr−1 s−1 GeV−1 (3) for energies Eµ 115 GeV (Behringer et al., 2012; Sanuki et al., 2002). Monte- Carlo simulations may perfectly simulate a simple power-law for the muon spectra and the events weighted correctly later on in an analysis. The correspondence between Cherenkov angle and muon energy can be estab- lished following the Cherenkov equation: 1 cos θc = ; (4) p 2 n · 1 − (E0=Eµ) where E0 ∼ 0:105 GeV is the muon rest mass, and n the refractive index of air, e.g. n ∼ 1:00023 at 2200 m a.s.l. Figure 1 shows the dependency of θc on Eµ, using Eq. 4, for various altitudes. One can see that above ∼30 GeV, the Cherenkov angle approaches its high energy limit, which lies between 1.2◦ and 1.24◦ at our altitudes of interest. Title Suppressed Due to Excessive Length 5 ) ° 1.3 ( c θ 1.2 1.1 1 0.9 0.8 1500 m a.s.l. 0.7 2000 m a.s.l. 0.6 2500 m a.s.l. 0.5 0.4 6 7 8 9 10 20 30 40 50 60 70 80 102 Eµ (GeV) Fig. 1 Dependency of Cherenkov angle on muon energy, for different observatory altitudes. Using the assumptions n = 1 + , 1 and Eµ E0, the Cherenkov angle can be approximated as: p 2 θc ' θ1 · 1 − (Et=Eµ) (5) with : p θ1 = 2 ; (6) E0 Et(h) = ; (7) p1 − 1=n(h)2 where the threshold energy for Cherenkov emission yields Et ≈ 4:9 GeV for a reference altitude of 2200 m a.s.l. 6 M. Gaug et al. Fig. 2 Sketch of the introduced parameters to describe the geometry of a local muon µ and its image in an IACT camera: The muon emits Cherenkov light under the Cherenkov angle θc along its trajectory, which is inclined by the angle i with respect to the optical axis of the telescope. It finally hits the telescope mirror, of radius R, at an impact distance ρ from its center (figure from Bolz, 2004). 3 Review of the muon-calibration method for IACTs Single muons, which form naturally part of hadronic air showers, emit Cherenkov light in a same way as secondary electrons in a gamma-ray shower do.

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