1. How to make a cosmic ray spectrum Hans Dembinski, University of Delaware March 2015

2. Outline Energy spectrum = abundance of cosmic rays arriving at Earth as a function of their energy How do we measure it? What do we learn from counting cosmic rays? 1 EeV 1 PeV abundance

3. Energy Spectra are Cosmic Fingerprints Energies of particles (even light particles!) in hot bodies follow a Boltzmann distribution. 6000 K 10 000 K 100 000 K If cosmic rays were generated by stars, their energy spectrum would tell us the temperature of the star. Can you tell the temperature of a flame without touching it?

4. Stars and Cosmic Ray Energies Hottest stars ~ 30 000 K → Highest energies 100 eV Cosmic rays 1 GeV … 100 EeV 1 GeV = 1 000 000 000 eV 1 EeV = 1 000 000 000 GeV IceTop measures from ~ 0.001 EeV to ~ 1 EeV Cosmic rays are obviously not made in stars... … but the energy spectrum still tells us a lot about how they are created.

5. Recipe for an Energy Spectrum You need  Some cosmic rays (duh!)  A big detector to catch them, like IceTop  A mighty computer to crunch some math and physics for you What can I do for you, Dave? Why do you keep calling me “Dave”? South pole station IceTop

6. ← This is a meteor. But if your eyes were really really fast and could see ultra-violet light, then this is how an air shower would look. Velocities Car100 km/h ~ 0.03 km/s Meteor40 km/s Air shower300 000 km/s (speed of light) Cosmic Rays and Air Showers

7. Meteors are slowed down by pushing air molecules out of their way. Cosmic rays are slowed down by converting energy to matter, after Einstein: E = mc 2. Cosmic rays are so fast, that they smash into air molecules. New particles are created out of pure kinetic energy in these collisions. The new particles are still so fast that they collide again and create more particles. This leads to a cascade of generated particles, called an air shower. Most meteors disintegrate before they reach ground, but nearly all air showers hit the surface. Cosmic Rays and Air Showers

8. Simulated Air Shower The lateral density profile is very regular. Measuring the density in a few places is enough to characterize the shower.

9. IceTop: an Air Shower Detector...where are the detectors? IceCube Counting Lab South Pole Station

10. IceTop: an Air Shower Detector Actually, they are under a layer of snow.

11. IceTop: an Air Shower Detector IceTop is basically a camera. It has low resolution and gaps between pixels, but it is extremely fast. Frames per second Cinema movie~ 25 IceTop~ 3 000 000 000 Light moves 1 meter per frame in IceTop. IceTop tank: a pixel of the camera.

12. An IceTop Event IceTop pixel measure a signal S proportional to the local particle density and its arrival time t. The smallest signals come from single particles. The largest signals from thousands. Red…early arrival time Yellow…late arrival time Size of bubble…signal strength (particle density) Air shower simulation Arrival times determine the shower direction. Signal strengths the shower energy.

13. Projections Reveal Patterns Each IceTop event is a short movie. A lot of numbers are needed to fully describe it, but it shows regular patterns that always repeat. For our analysis, we use the patterns to reduce the data to just one number, the shower size S125. It is nearly proportional to the shower energy. To get S125, we draw the signals S over their radial distance r to the shower axis. To find the shower axis, we guess one and compute the projected time t 0 from the measured time t. If the guess is correct, all t 0 's tightly align around the same value. shower core Intersection of shower front and ground plane r z = c  t t, S shower front plane t0t0 t', S' t' 0  d  shower axis shower core

14. Projections Reveal Patterns r z = c  t t, S shower front plane t0t0 t', S' t' 0  d  shower axis Lateral Density Function (LDF) S125 = S at 125 m dt = t 0 – t shower core shower core  … zenith angle early sidelate side

15. S125 and Shower Energy I'm afraid, I can't do that, Dave. Computer, simulate one million air showers for me. What?!

16. Ha ha ha. Let's kill Ha ha ha. S125 and Shower Energy all humans. At least, not alone.

17. S125 and Shower Energy Computers simulate air showers using all physics we know. They look just like the real events. The shower size S125 is obtained in the same way. In simulations, the shower energy is known. The relationship between shower energy E and shower size S125 is a line in a double-logarithmic plot. We use this line to compute the energy from S125 values in real events. That was a lot of work, Dave.

18. Energy Spectrum After converting S125 to energy, we sort the energies into narrow bins and count them. This yields a histogram, which has a very simple pattern in double-logarithmic scale. This is the energy spectrum. We could almost stop here. But for comparisons with other experiments and theories, it is better to convert our counts into a flux. Energy spectrum from one day of IceTop data

19. Flux The flux measures the rate of cosmic rays arriving at Earth, which is the same everywhere on Earth in the energy range covered by IceTop. The flux is designed to show this directly, independent of the detector. To find the definition for the flux, let's think about two detectors which count cosmic rays. Let's say, IceTop counts 200 cosmic rays over the course of one day in the energy bin between 10 7.00 eV and 10 7.05 eV. Another detector, called RockBottom, counts 100 cosmic rays in the same bin. How can that be if the arrival rates are the same? IceTop's evil doppelgänger: RockBottom

20. How Can the Counts Differ? Measured over different time interval T Detectors have different area A Counted within different solid angle  1/2 day 1 day IceTopRockBottom 580 000 m 2 290 000 m 2 Solid what?!

21. Solid Angle IceTop only uses showers with inclinations up to about 30°, because they are the easiest to simulate. If another detector accepts larger inclinations, they will count more cosmic rays. angle = length of arc / radius solid angle = surface area / radius 2  shower axis shower core Example: surface area of sphere is 4  r 2 → solid angle is 4   Example: circumference of circle is 2  r → angle is 2 

22. Exposure and Flux The time interval T, area A, and solid angle  of an experiment can be easily computed and are combined into the exposure. The exposure for one day of IceTop data is 49.12 x 10 9 km 2 sr s. The flux is the number of counted cosmic rays divided by the exposure: There is one more thing that two groups could do differently. They could bin the histogram differently. If a bin is wider, more cosmic rays fall into it. To be perfectly comparable, we need to divide by the bin width dE = E 1 – E 0. This yields the differential flux, but people often just also call it flux. Flux = No. of cosmic rays (Differential) Flux = Bin width Exposure Flux per bin

23. The Final Result Now you know everything to make your own energy spectrum from IceTop data. We wish you luck!

24. Hints for the exercise: Fitting General hints – Use the Movie button to see how the event evolves in time – Small signals scatter more than larger signals → larger signals are better guides for the LDF – You can go back and forth between the events, if you realized a mistake A: Fit shower direction – Guess azimuth from the time flow of signals – Adjust zenith angle until the shower front is flat – Iterate steps as needed B: Fit S125 – Place the shower core in midst of the tanks with the largest signals – Move the LDF so that it touches most of the signals – Try to move the core to align signals more tightly with the LDF – Iterate steps as needed

25. Hints for the exercise: Spectrum Open the Google Spreadsheet for the exercise http://tinyurl.com/latdtsk Select the sheet that corresponds to your group (Red, Yellow,...) Import the CSV file into the spreadsheet Part 1: Energy calibration – Sort data by column “energy” to separate simulations and real events – For simulations: Compute log10(energy) and log10(S125), respectively – Make a graph of log10(energy) versus log10(S125) – Make a trend line, note the coefficients a and b down – For real events: Compute log10(energy) = a log10(S125) + b Part 2: Energy spectrum and flux – Copy over log10(energy) and event weights – Compute Flux = Nevents / (dE * exposure) Every group has 1/6 of the data from one IceTop day, so they have 1/6 of the full exposure, the reduced number is given in the sheets

26. Media sources Meteor: http://www.howardedin.com/photos/otsp2008-bolideb.html, http://creativecommons.org/licenses/by-nd-nc/1.0/ Candle: https://www.flickr.com/photos/tortipede/3223692730, https://creativecommons.org/licenses/by-nc-sa/2.0/ "HRDiagram" by Richard Powell - The Hertzsprung Russell Diagram. Licensed under CC BY-SA 2.5 via Wikimedia Commons – http://commons.wikimedia.org/wiki/File:HRDiagram.png "HAL9000" by Cryteria - Own work. Licensed under CC BY 3.0 via Wikimedia Commons – http://commons.wikimedia.org/wiki/File:HAL9000.svg White Rabbit font – Copyright by Matthew Welch Particle collision – Copy right by Barcroft Media "SouthPoleStationDestinationAlpha" by Daniel Leussler. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:SouthPoleStationDestinationAlpha.jpg Animations of CORSIKA air showers – J. Oehlschlaeger, R. Engel, Forschungszentrum Karlsruhe, Germany