Fat Cosmic Ray Tracks in CCDs

Cosmic rays create difficulties for astronomers since it is impossible to protect telescopes from them. Highly energetic particles incident on Earth’s atmosphere create secondary particles which leave tracks in CCD images, the most common particles being muons [1]. These tracks appear practically in each image with long enough exposure, and they must be removed before useful analysis can occur.

While CCDs detect incident photons through the photoelectric effect, with generated electrons drifting through the silicon until they are collected at the gates, charged particles such as cosmic rays deposit energy in the detectors through ionization and excitation of electron-hole pairs in the silicon. The energy deposition depends on the characteristics of the incident particle, so the images they create can reveal information about the particle which generated them [2].

Typically, due to the high momentum of incident muons, the tracks appear straight and narrow [3]. If multiple exposures of a target are obtained, the tracks can be removed simply by observing the difference between exposures. If only one exposure is available, though, it is necessary to identify cosmic rays through their morphology; in particular, the muon tracks can be identified by their sharper edges. These tracks are smeared only due to the processes internal to silicon, such as diffusion, without contribution from the telescope optics nor the atmosphere, and, therefore, are sharper than typical star images [4]. The sharpness of star images is defined by the point spread function (PSF) with contributions from the telescope optics and atmosphere.

However, one type of track which was noticed in dark exposures from the Prime Focus Spectrograph (PFS), referred to here as a “fat” cosmic ray, is much brighter and wider than typical muon tracks, as seen in Figure 1. These fat tracks may be difficult to identify and remove using morphology-based cosmic ray detection. In this study, we investigate the properties of fat tracks in order to identify their cause. We compare these measurements to simulations of cosmic rays in CCDs, as well as to expected abundances of different particles. Understanding the origins of these fat tracks could enable astronomers to devise the best ways to ensure they do not interfere with on-sky data.

Our analysis suggests that protons are the most likely source of these tracks. For slow particles, energy deposition into CCDs follows $\beta^{-2}$ (the Bethe-Bloch equation [1]), so fat tracks must necessarily be caused by particles significantly slower than typical cosmic rays. At sea level, this is true of protons, which have nine times the mass of muons but lower mean kinetic energy, i.e., significantly lower mean velocity. In addition, strongly interacting cosmic ray protons become less common at lower altitudes as they interact with the atmosphere and create secondary cosmic rays, such as muons [1]. This agrees with our observations of lower rates of fat tracks at lower altitudes.

Large energy deposition in silicon sensors has been studied before. One example is a phenomenon known as the “plasma effect,” which has been researched in the context of interactions of $\alpha$-particles in semiconductor detectors. The $\alpha$-particles have been seen to leave large, round spots of ionization due to the deposition of charge dense enough to satisfy the plasma condition [6, 7, 8, 9]. One consequence of this effect is that the high charge density repels charge carriers away from the initial path of the particle, which is the mechanism by which we believe fat tracks are produced. However, typical $\alpha$-particle energies (a few MeV) result in the production of ${\sim}10^{6}$ electron/hole pairs in a compact volume of few pixels. We note that in our case of fat tracks the ionization density is equal to about $10^{4}$ electrons per pixel, which is at least an order of magnitude lower than the ionization from alphas described above.

Other studies report the appearance of protons in a silicon pixel detector for radiation imaging [10, 11]. The authors find tracks that look very similar to our own tracks when the protons are incident to the detector at large angles, supporting our proton origin theory for fat tracks.

In Section 2, we describe how we measure observed cosmic rays and compare them to simulations of cosmic rays in CCDs, and we discuss the method by which high energy deposition results in wider than usual cosmic ray tracks. Section 3 examines the particles which cause fat tracks, and Section 4 states our conclusions on the origin of fat tracks.

In addition to identifying the mechanism by which cosmic ray tracks are broadened, we also wish to identify the particles which cause fat tracks. Since $dE/dx$ of cosmic rays in CCDs scales as $\beta^{-2}$, fat tracks must have relatively low velocities to obtain their brightness. One particle which fits this requirement is cosmic ray protons. Muon cosmic rays (mass 106 MeV) have a mean energy of 4 GeV at sea level, with $\beta<<1$ muons rare [1]. Meanwhile, cosmic ray protons (mass 938 MeV) have a mean energy of 1 GeV at sea level, and so typically have much lower $\beta$ than muons [20].

Fat tracks were not observed in images from Rubin Observatory CCDs while being developed at Brookhaven National Laboratory (although a systematic search has not been performed); they were only first noticed once images had been taken at higher altitudes. Protons match this observation as well, as their interactions with the atmosphere result in the creation of secondary particles such as pions, which then decay to muons. At lower altitudes, protons become less common as they produce more secondary particles. On the other hand, muons do not interact strongly with the atmosphere, and therefore many of them reach the surface [1]. The fluxes of muons and protons in the atmosphere as a function of altitude can be approximated using methods described by Refs. 21, 22. The calculated fluxes of cosmic ray nucleons, muons and pions at different altitudes using these methods is shown in Figure 7.

To compare expectations of proton and muon abundances to observations, we analyze dark images from three different cameras: Prime Focus Spectrograph at the Mauna Kea Observatory; ComCam at Rubin Observatory; and the LSST Camera, located at SLAC National Accelerator Laboratory during data collection. Cosmic rays were extracted from images and fat tracks were identified using the same methods described above. The number of tracks identified in each camera, along with the cameras’ altitudes, are listed in Table 1. Note that in the case of PFS at Mauna Kea, the statistics are limited and, therefore, the uncertainty is large.

The observed amount of fat tracks at each altitude matches the amount estimated by Figure 7, though further study is necessary to obtain more precise predictions and observations. The predictions are only an estimate based on Refs. 21, 22, and the observed amounts are limited by the manner in which tracks are selected, which is highly dependent on the angle of particles incident on the detector. Streaks originate from particles incident at grazing angles, while particles which strike the detector too obliquely appear as spots instead, and thus are excluded from the analysis by the linear correlation coefficient filter. This means that the orientation of the CCDs during data collection could also affect the results. Since vertical cosmic rays are more common, following a distribution $\propto\cos^{2}\theta$ for muons and approximately $\propto\exp{(-1/\cos{\theta})}$ for nucleons [1], CCDs perpendicular to the ground should be struck by more grazing particles and have a higher occurrence of streaks over spots than CCDs parallel to the ground. While the ComCam and PFS CCDs were perpendicular to the ground during observations, the LSST Camera CCDs were parallel to the ground, meaning they likely had proportionally fewer total cosmic rays which were included in our analysis. This study would benefit from both more careful data collection and more detailed calculations of atmospheric cosmic ray fluxes.

The distinction between muon and proton tracks in CCDs could be confirmed with a measurement of the masses of observed cosmic ray tracks. In principle, an estimate of the mass of a cosmic ray could be found by measuring the change in its energy deposition rate. However, due to high amounts of variation in $dE/dx$ in single tracks, we were unable to produce reliable mass estimates of any of our tracks, either fat or non-fat. Despite this, we believe that the increasing abundance of fat tracks with altitude does suggest protons as a strong candidate for the origin of fat tracks.

Muons and protons could additionally be distinguished with the use of simulation tools such as Geant4 [23], which allows customized modelling of the passage of particles through matter. Such a study could be useful in determining the expected distributions of dE/dx for muons and protons, which could be directly compared to the distribution observed in Figure 3.

An alternate proposal for the method by which fat tracks occur is $\delta$ ray electrons, which are electrons which have been given enough energy by the primary cosmic ray to leave their own ionization trails. A large number of $\delta$ rays produced by the primary cosmic ray could have the effect of carrying energy away from the center of the track, producing a broadened image.

Ref. 24 calculates the continuous slowing down approximation (CSDA) range of a 10 keV electron in silicon to be about 1 $\upmu$m. The maximum transferable kinetic energy to an electron from a proton with a velocity $\beta=0.5$ (the average velocity of our measured fat tracks) is about 500 keV [1]. Thus the number of $\delta$ rays we expect to travel a non-negligible distance (i.e., greater than 1 $\upmu$m) are those with energies between 10 and 500 keV.

Ref. 1 gives the distribution of $\delta$ rays per energy and distance. After integrating with respect to kinetic energy, we have

for $\beta=0.5$, or about one $\delta$ ray every 140 $\upmu$m in silicon. As this is the rate at which all $\delta$ rays with ranges greater than 1 $\upmu$m occur, we conclude that $\delta$ rays are incapable of producing the uniform broadening seen in fat tracks.

Although fairly uncommon, fat cosmic ray tracks have the potential to disrupt on-sky astronomical images, and we thus want to understand their causes in order to minimize their impact. We believe that fat tracks are most likely caused by proton cosmic rays, whose high energy deposition in CCDs results in significant electrostatic repulsion between electrons, broadening the resulting tracks in the image. Other mechanisms may contribute, but most of the measured widths of fat tracks can be explained by this phenomenon.

Because fat tracks come from grazing incident particles, we note that they are most likely to appear in detectors which are oriented perpendicular to the ground. Detectors at small angles relative to the ground should still see proton cosmic rays, but they should appear more like the round spots studied in the context of the plasma effect [6, 7, 8]. While cosmic ray removal algorithms based on difference images are likely minimally impacted by fat tracks, those which rely on morphological identification of cosmic rays may need to consider how to remove tracks such as these, which do not match the typical narrow muon cosmic ray signature.

The data utilized in this study were obtained from Vera C. Rubin Observatory and the Subaru Telescope. Data are available from the authors upon reasonable request, and with permission from their respective sources. The code used to generate results and figures is available at https://doi.org/10.5281/zenodo.8015806.

This paper has undergone internal review in the LSST Dark Energy Science Collaboration. We thank the reviewers Pierre Astier, Zhiyuan Guo, and Craig Lage for their helpful comments. Additional thanks go to Merlin Fisher-Levine and Robert Lupton for their discussions.

This project was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internships Program (SULI), and by the Brookhaven National Laboratory (BNL) Physics Department under the BNL Supplemental Undergraduate Research Program (SURP).

The DESC acknowledges ongoing support from the Institut National de Physique Nucléaire et de Physique des Particules in France; the Science & Technology Facilities Council in the United Kingdom; and the Department of Energy, the National Science Foundation, and the LSST Corporation in the United States. DESC uses resources of the IN2P3 Computing Center (CC-IN2P3–Lyon/Villeurbanne - France) funded by the Centre National de la Recherche Scientifique; the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231; STFC DiRAC HPC Facilities, funded by UK BEIS National E-infrastructure capital grants; and the UK particle physics grid, supported by the GridPP Collaboration. This work was performed in part under DOE Contract DE-AC02-76SF00515.

Author contributions: TAG wrote and carried out the analysis code and wrote the paper. AN conceived the analysis idea, and contributed to the analysis and paper.