EAS direction reconstruction with HiSPARC

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EAS direction reconstruction with HiSPARC

Arne de Laat, Bob van Eijk, David Fokkema, Hans Montanus, Jan-Willem van Holten, Jorian van Oostenbrugge, Jos Steijger, Niek Schultheiss, Norbert van Veen et al.

HiSPARC

HiSPARC is a research and outreach project already operating for more than 10 years. The HiSPARC network currently consists of over 100 detection stations. Stations are located at high

schools and research institutes in the Netherlands, United Kingdom and Denmark [1, 2].

HiSPARC network, each circle is one station [3].

Detection station

A single station consists of:

•

Two or four plastic scintillators (100 x 50 x 2 cm).

•

One photomultiplier tube per scintillator.

•

4-channel 12-bit ADC, 2.5 ns sampling.

•

GPS for station position and synchronised timing.

The station triggers when at least 2 scintillators simultaneously detect a minimum ionising particle (MIP). All events are sent to data storage at Nikhef and then publicly accessible through a web

interface [4] and API [5].

Station layout and event readout example.

Shower direction

Analytical formulae for azimuth and zenith for a thin and flat shower front define the shower direction

n

^:

The equations give two solutions; the one with shower direction under the horizon is discarded.

Due to the 2.5 ns ADC sampling the direction reconstruction results in a discrete distribution:

Discrete azimuth and zenith angles for the three outer scintillators of the station. The lines connect angles for fixed

timestamps in two scintillators while the third varies.

Netherlands United Kingdom

Denmark

Germany

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Easting [km]

Northing[km]

Netherlands United Kingdom

Denmark

Germany

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Easting [km]

Northing[km]

Netherlands United Kingdom

Denmark

Germany

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Easting [km]

Northing[km]

GPS 10m

5 m 60

Writing the normalvector of the shower front in spherical coordinates

n = 0

@ n_x n_y n_z

1 A =

0

@

sin^µcos^¡ sin^µsin^¡ cos^µ

1

A , (19)

we obtain for the azimuth angle tan^¡ ₌ n_y

n_x ⁼

(u£v)y±v_y^pv² _°u²

(u£v)x ±v_x^pv² _°u² . (20) Where the sign of the numerator and the sign of the denominator determine the quadrant of the azimuth angle. The zenith angle follows directly from the third component of n:

cosµ = (u£v)z ±v_z^pv² _°u²

v² . (21)

In case the two possible solutions are mirrored in a horizontal plane, the one corresponding to a negative sign for the zenith angle is discarded. This situation is of application when three detectors of a single station are hit, since the detectors of a single station are all on the same (horizontal) roof of a building. For this 2D-reconstruction it is advantageous to reduce the solution accordingly.

The detectors of a station are on the same roof of a building and therefore positioned in a horizontal plane. For three detectors of such a station the corresponding analytical expression is obtained by substituting ¢z_{1 =} ¢z_{2 =} 0 and u_{z =} v_{x =} v_{y =} 0 into Eqs. (20) and (21). The solutions for ^¡ and ^µ then reduce to

tan^¡ ₌ ^°u_xv_z

u_yv_z (22)

and

sin^µ ₌ vu

utu²_{x +}u²_y

v²_z (23)

respectively. In the latter expression we have taken a positive sign for the square root to ensure a positive ^µ. In expression (22) the sign of the numera- tor, _°u_xv_z, and the sign of the denominator, u_yv_z determine the quadrant of the azimuth angle.

If a shower hits more than three detection stations the direction is recon- structed with a fit procedure. Given the best plane with normal vector n, the dot product with the vectors s_i will not exactly cancel. That is, equation (5) becomes

s_i ·n = ±i . (24)

8

Writing the normalvector of the shower front in spherical coordinates

n = 0

@ n_x n_y n_z

1 A =

0

@

sin^µcos^¡ sin^µsin^¡ cos^µ

1

A , (19)

we obtain for the azimuth angle tan^¡ = n_y

n_x = (u£v)y ± vyp

v² ° u² (u£v)x ± vxp

v² ° u² . (20)

Where the sign of the numerator and the sign of the denominator determine the quadrant of the azimuth angle. The zenith angle follows directly from the third component of n:

cos^µ = nz = (u£v)z ± vzp

v² ° u²

v² . (21)

In case the two possible solutions are mirrored in a horizontal plane, the one corresponding to a negative sign for the zenith angle is discarded. This situation is of application when three detectors of a single station are hit, since the detectors of a single station are all on the same (horizontal) roof of a building. For this 2D-reconstruction it is advantageous to reduce the solution accordingly.

The detectors of a station are on the same roof of a building and therefore positioned in a horizontal plane. For three detectors of such a station the corresponding analytical expression is obtained by substituting ¢_{z1 =} ¢_{z2 = 0} and u_z = vx = vy = 0 into Eqs. (20) and (21). The solutions for ^¡ and ^µ then reduce to

tan^¡ = °uxv_z

u_yv_z (22)

and

sinµ = vu

ut u^2x + u²_y

v²_z (23)

respectively. In the latter expression we have taken a positive sign for the square root to ensure a positive ^µ. In expression (22) the sign of the numera- tor, °uxv_z, and the sign of the denominator, u_yv_z determine the quadrant of the azimuth angle.

If a shower hits more than three detection stations the direction is recon- structed with a fit procedure. Given the best plane with normal vector n, the dot product with the vectors s_i will not exactly cancel. That is, equation (5) becomes

s_i · n = ^±i . (24)

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Azimut

h ( )

Zenith ( )

KASCADE

A HiSPARC station was integrated in the

KASCADE experiment [6] for calibration. The

shower direction reconstructed by the HiSPARC station was compared with that of the KASCADE array and shows excellent agreement:

Azimuthal angle from KASCADE versus HiSPARC.

Science Park cluster

At the Amsterdam Science Park 9 HiSPARC stations are clustered:

HiSPARC – 4-scintillator – stations at Amsterdam Science Park.

The cluster detects showers with energy >10¹⁵ eV triggering three or more stations. This requires

calibration of each GPS. The GPS offset between stations is determined. The offset is defined as the mean of the time difference distribution:

Typical GPS time differences (Δt) between stations satisfies a normal distribution. The width of the distribution increases with station distance.

For more than three stations in coincidence formulae (1) generalise to:

This expression is minimised to derive the direction of the shower. Reconstruction was tested using full simulation of detection stations with air showers

generated by CORSIKA [7]. Various timing

uncertainties and detector response resolutions are taken into account.

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K ASC ADE ( )

HiSPARC()

Station o↵sets: 501 - 502

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dt (ns)

channel 1

channel 2

pre-trigger coincidence post-trigger GPS timestamp

Figure 5 – Here the readout and triggering of the electronics is shown. When two channels have a pulse crossing the thresholds (dotted lines) within the coincidence time window (dashed lines) a trigger will occur. The moment the trigger conditions are met the ^GPS timestamp is recorded. Later the arrival times in each channel relative to the

GPS timestamp can be determined.

The fit procedure, method of least squares, now consists in the minimization

of Xk

i

°¢_{xinx +}¢_{yiny +}¢_{zinz + c}¢_ti^¢2 , (25)

where k is the number of hitted stations. If the deviations in the arrival times are too large the fit procedure might fail. That is, large deviations can not be brought into correspondence with the velocity c of the showerfront resulting in complex values for the parameters [3]. The probability for such a fit failure is very small: there were no failures observed in the direction reconstruction of about 2900 showers, which hitted 7 stations (klopt dit wel ? navragen bij Jos) of the SPA site [4].

5 Timing

Plot of particle time distribution in showers of various energies at various core distances. Accurate timing and shower front understanding is important for accurate direction reconstruction...

Each ^HiSPARC electronic box samples the signal from each PMT with two ADCs. Each ADC polls the signal every 5 ns, which means that the signal

9

Reconstruction

The angular resolution for reconstructed events as a function of zenith is:

For a single station (black) with σt = 1.8 ns and the combination of three stations shown on the map (red) with σt = 5.5 ns for

NMIP ≥ 2. 66% of the events are within this error.

For the following reconstructions 4½ years of shower data from the Science Park cluster has

been used. Reconstructed angles for events which triggered any combination of 7 stations are shown:

Azimuth and zenith for showers that hit 7 or more Science Park cluster stations.

The reconstructed zenith distribution follows the expected distribution:

Histogram of zenith reconstructions for events that hit at least 3 stations. Expected zenith distribution as given by Rossi is in red.

Summary

HiSPARC is a sparse network of compact and

affordable stations allowing high school students to meet science. As all data and tools are publicly

available events can be analysed in the classroom.

With a single station we achieve reasonable

angular resolution on the cosmic shower direction, when we include more stations we observe a

significant improvement.

References

[1] Fokkema, D.B.R.A. The HiSPARC Cosmic Ray Experiment.

PhD thesis. Universiteit Twente (2012).

[2] de Laat, A.P.L.S. PhD thesis (work in progress).

[3] Map tiles by Stamen Design, under CC BY 3.0. Data by OpenStreetMap, under CC BY SA.

[4] HiSPARC Public Database, http://data.hisparc.nl .

[5] Fokkema, D.B.R.A. and de Laat, A.P.L.S. SAPPHiRE: A frame work for HiSPARC, http://docs.hisparc.nl/sapphire .

[6] Antoni, T. et al. The Cosmic-Ray Experiment KASCADE.

Nucl.Instr. and Meth. A513, 490-510 (2003).

[7] Heck, D. et al. CORSIKA: a Monte Carlo code to simulate extensive air showers. FZKA 6019 (1998).

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Angularresolution()

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18th International Symposium on Very High Energy Cosmic Ray Interactions

HiSPARC

AARHUS UNIVERSITY

AU

High-School Project on Astrophysics Research with Cosmics (HiSPARC)

100 m

(1)

(2)

Contact Arne de Laat adelaat@nikhef.nl +31205925015

Websites

www.hisparc.nl docs.hisparc.nl

github.com/hisparc

N

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N

<Δt> = -26.6 ns σ_Δt = 107.4 ns

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Time (ns)

Signal(ADCcounts)