How to make a cosmic ray spectrum Hans

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

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

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

Stars and Cosmic Ray Energies Hottest stars ~ 30 000 K → Highest energies 100 e. V Cosmic rays 1 Ge. V … 100 Ee. V 1 Ge. V = 1 000 000 e. V 1 Ee. V = 1 000 000 Ge. V Ice. Top measures from ~ 0. 001 Ee. V to ~ 1 Ee. V Cosmic rays are obviously not made in stars. . . … but the energy spectrum still tells us a lot about how they are created.

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

Cosmic Rays and Air Showers ← This is a meteor. But if your eyes were really fast and could see ultra-violet light, then this is how an air shower would look. Velocities Car 100 km/h ~ 0. 03 km/s Meteor 40 km/s Air shower 300 000 km/s (speed of light)

Cosmic Rays and Air Showers 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.

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

Ice. Top: an Air Shower Detector South Pole Station Ice. Cube Counting Lab . . . where are the detectors?

Ice. Top: an Air Shower Detector Actually, they are under a layer of snow.

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

An Ice. Top Event Ice. Top 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. Air shower simulation Red Yellow Size of bubble … early arrival time … late arrival time … signal strength (particle density) Arrival times determine the shower direction. Signal strengths the shower energy.

Projections Reveal Patterns Intersection of shower front and ground plane s ax how is er shower core sh ow er f pl ron an t e r d shower core t 0 z=c t t, S t', S' t'0 Each Ice. Top 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 S 125. It is nearly proportional to the shower energy. To get S 125, 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.

Projections Reveal Patterns Lateral Density Function (LDF) sh ax ow is e r S 125 = S at 125 m sh ow er f pl ron an t e r d shower core t 0 z=c t t, S t', S' t'0 dt = t 0 – tshower core … zenith angle late side early side

S 125 and Shower Energy Computer, simulate one million air showers for me. I'm afraid, I can't do that, Dave. What? !

S 125 and Shower Energy Ha ha ha. Let's kill At least, not alone. all humans. Ha ha ha.

S 125 and Shower Energy That was a lot of work, Dave. Computers simulate air showers using all physics we know. They look just like the real events. The shower size S 125 is obtained in the same way. In simulations, the shower energy is known. The relationship between shower energy E and shower size S 125 is a line in a double-logarithmic plot. We use this line to compute the energy from S 125 values in real events.

Energy Spectrum Energy spectrum from one day of Ice. Top data After converting S 125 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.

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 Ice. Top. 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, Ice. Top counts 200 cosmic rays over the course of one day in the energy bin between 107. 00 e. V and 107. 05 e. V. Another detector, called Rock. Bottom, counts 100 cosmic rays in the same bin. How can that be if the arrival rates are the same? Ice. Top's evil doppelgänger: Rock. Bottom

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

Solid Angle Ice. Top 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. sh ow er ax is shower core angle = length of arc / radius Example: circumference of circle is 2 r → angle is 2 solid angle = surface area / radius 2 Example: surface area of sphere is 4 r 2 → solid angle is 4

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 Ice. Top data is 49. 12 x 109 km 2 sr s. The flux is the number of counted cosmic rays divided by the exposure: Flux = No. of cosmic rays 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 d. E = E 1 – E 0. This yields the differential flux, but people often just also call it flux. (Differential) Flux = Flux per bin Bin width

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

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 S 125 – – 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

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 log 10(energy) and log 10(S 125), respectively Make a graph of log 10(energy) versus log 10(S 125) Make a trend line, note the coefficients a and b down For real events: Compute log 10(energy) = a log 10(S 125) + b Part 2: Energy spectrum and flux – Copy over log 10(energy) and event weights – Compute Flux = Nevents / (d. E * exposure) • Every group has 1/6 of the data from one Ice. Top day, so they have 1/6 of the full exposure, the reduced number is given in the sheets

Media sources Meteor: http: //www. howardedin. com/photos/otsp 2008 -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 "HAL 9000" by Cryteria - Own work. Licensed under CC BY 3. 0 via Wikimedia Commons – http: //commons. wikimedia. org/wiki/File: HAL 9000. svg White Rabbit font – Copyright by Matthew Welch Particle collision – Copyright by Barcroft Media "South. Pole. Station. Destination. Alpha" by Daniel Leussler. Licensed under CC BY-SA 3. 0 via Wikimedia Commons http: //commons. wikimedia. org/wiki/File: South. Pole. Station. Destination. Alpha. jpg Animations of CORSIKA air showers – J. Oehlschlaeger, R. Engel, Forschungszentrum Karlsruhe, Germany