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Composition study of ultra-high-energy cosmic rays based on the Telescope Array surface detector data Yana Zhezher for the Telescope Array collaboration Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia July 17,

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Composition study of ultra-high-energy cosmic rays based on the Telescope Array surface detector data

Yana Zhezher for the Telescope Array collaboration Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia

July 17, 2017

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Abstract

◮ Overview ◮ Method: Multivariate analysis based on

Boosted decision trees

◮ Data set and results

  • Y. Zhezher

TA SD Composition

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SLIDE 3

UHECR 1018 eV composition measurements

Experiment detector Observable HiRes fluorescence stereo XMAX Pierre Auger fluorescence + SD XMAX (hybrid) Telescope Array stereo XMAX Telescope Array hybrid XMAX Yakutsk muon ρµ Pierre Auger SD X µ

MAX

Pierre Auger SD risetime asymmetry SD – surface detector XMAX – depth of the shower maximum X µ

MAX – muon production depth

risetime – time from 10% to 50% for the total integrated signal

  • Y. Zhezher

TA SD Composition

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SLIDE 4

Telescope Array Observatory

Largest UHECR statistics in the Northern Hemisphere

◮ Utah, 2 hrs drive

from Salt Lake City,

◮ 507 surface

detectors, S = 3m2, spacing 1.2 km

◮ 3 fluorescence

detectors

◮ 9 years of operation

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SLIDE 5

Method outline

  • 1. Reconstruct every event, get the values of

composition-sensitive observables.

  • 2. Multivariate analysis: (a, AoP, . . . ) → ξi. A set of
  • bservables is transformed into a single variable. The

latter is used for composition analysis.

  • 3. Compare distribution of ξ with Monte-Carlo modelling.
  • 4. Result: average atomic mass < log A > as a function of

energy.

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SLIDE 6

List of relevant observables

  • 1. Linsley front curvature parameter, a;
  • 2. Area-over-peak (AoP) of the signal at 1200 m;

Pierre Auger Collaboration, Phys.Rev.Lett. 100 (2008) 211101

  • 3. AoP slope parameter;
  • 4. Number of detectors hit;
  • 5. N. of detectors excluded from the fit of the shower front;
  • 6. χ2/d.o.f.;
  • 7. Sb = Si × r b parameter for b = 3 and b = 4.5;

Ros, Supanitsky, Medina-Tanco et al. Astropart.Phys. 47 (2013) 10

  • 8. The sum of signals of all detectors of the event;
  • 9. Asymmetry of signal at upper and lower layers of detectors;
  • 10. Total n. of peaks within all FADC traces;
  • 11. N. of peaks for the detector with the largest signal;
  • 12. N. of peaks present in the upper layer and not in lower;
  • 13. N. of peaks present in the lower layer and not in upper;
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SLIDE 7

Linsley front curvature parameter

Deeper shower maximum leads to more curved front. Shower front is fit using the following function: t0(r) = t0 + tplane+ + a × 0.67 (1 + r/RL)1.5LDF(r)−0.5 LDF(r) = f(r)/f(800 m) f(r) = r Rm −1.2 1 + r Rm −(η−1.2) 1 + r 2 R2

1

−0.6 Rm = 90.0 m, R1 = 1000 m, RL = 30 m η = 3.97 − 1.79(sec(θ) − 1) tplane – shower plane delay a – Linsley front curvature parameter LDF – lateral distribution function

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Area-over-peak (AoP) and area-over-peak slope

◮ Consider a surface station time-resolved signal ◮ Both peak and area are well-measured and not much

affected by fluctuations

◮ AoP(r) is fitted with a linear fit:

◮ AoP(r) = α − β(r/r0 − 1.0) ◮ r0 = 1200 m, α - value at 1200 m, β - slope

  • Y. Zhezher

TA SD Composition

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SLIDE 9

MVA BDT analysis

◮ The Boosted Decision Trees (BDT) technique is used to

build p-Fe classifier based on multiple observables.

Pierre Auger Collaboration, ApJ, 789, 160 (2014)

◮ BDT is trained with Monte-Carlo sets: Fe (Signal) and p

(Background)

◮ BDT classifier is used to convert the set of observables for

an event to a number ξ ∈ [−1 : 1]: 1 - pure signal (Fe), -1 - pure background (p).

◮ ξ is available for one-dimensional analysis.

  • Y. Zhezher

TA SD Composition

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Boosted decision trees

  • Y. Coadou, ESIPAP’16

◮ For each variable, find splitting value with best separation

between two branches: mostly signal in one branch, mostly background in another;

◮ Repeat algorithm recursively on each branch: take a new

variable or reuse the former;

◮ Iterate until stopping criterion is reached (e.g. number of

events in a branch). Terminal node = leaf;

◮ Boosting: create a good classifier using a number of weak

  • nes (building a forest).
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Data and Monte-Carlo sets

◮ 9-year data collected by the TA surface detector:

2008-05-11 — 2017-05-11

Cuts:

  • 1. Events with 7 or more triggered counters
  • 2. Events with zenith angle θ < 45◦.
  • 3. Events with reconstructed core position of at least 1200 m

away from the edge of the array.

  • 4. Events with χ2

G/d.o.f. < 4 and χ2 LDF/d.o.f. < 4.

  • 5. Events with geometry reconstructed with accuracy less

than 5◦.

  • 6. Events with the fractional uncertainty of the S800 less than

25 %.

  • 7. Events with E > 1018 eV.

18077 events after cuts

  • Y. Zhezher

TA SD Composition

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SLIDE 12

Data and Monte-Carlo sets

p and Fe Monte-Carlo sets with QGSJETII-03 Note: MC sets are split into 3 equal parts: (I) for training the classifier, (II) for MVA estimator calculation, (III) for determination of systematical uncertanties.

  • Y. Zhezher

TA SD Composition

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Distribution of MVA estimator ξ

h_pm Entries 1980 Mean 0.007598 RMS 0.03258 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 50 100 150 200 250 300 350 400 450 h_pm Entries 1980 Mean 0.007598 RMS 0.03258 Underflow Overflow h_fm Entries 3539 Mean 0.01908 RMS 0.03186 Underflow Overflow h_fm Entries 3539 Mean 0.01908 RMS 0.03186 Underflow Overflow

18.0<log(E)<18.2

h_dt Entries 741 Mean 0.01306 RMS 0.03416 Underflow Overflow h_pm Entries 11463 Mean 0.004902 RMS 0.03296 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 h_pm Entries 11463 Mean 0.004902 RMS 0.03296 Underflow Overflow h_fm Entries 16650 Mean 0.02295 RMS 0.03235 Underflow Overflow h_fm Entries 16650 Mean 0.02295 RMS 0.03235 Underflow Overflow

18.2<log(E)<18.4

h_dt Entries 3482 Mean 0.01412 RMS 0.03443 Underflow Overflow h_pm Entries 16362 Mean 0.001475 RMS 0.03762 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 500 1000 1500 2000 2500 h_pm Entries 16362 Mean 0.001475 RMS 0.03762 Underflow Overflow h_fm Entries 21888 Mean 0.02461 RMS 0.03629 Underflow Overflow h_fm Entries 21888 Mean 0.02461 RMS 0.03629 Underflow Overflow

18.4<log(E)<18.6

h_dt Entries 4707 Mean 0.0115 RMS 0.03832 Underflow Overflow h_pm

Entries 13720 Mean

  • 0.006592

RMS 0.03825 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 h_pm Entries 13720 Mean

  • 0.006592

RMS 0.03825 Underflow Overflow

h_fm Entries 16544 Mean 0.01769 RMS 0.03573 Underflow Overflow h_fm Entries 16544 Mean 0.01769 RMS 0.03573 Underflow Overflow

18.6<log(E)<18.8

h_dt Entries 3834 Mean 0.005332 RMS 0.03699 Underflow Overflow

/PRELIMINARY/ /PRELIMINARY/

proton, iron, data

  • Y. Zhezher

TA SD Composition

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Distribution of MVA estimator ξ

h_pm Entries 10050 Mean

  • 0.01024

RMS 0.03515 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 200 400 600 800 1000 1200 1400 1600 h_pm Entries 10050 Mean

  • 0.01024

RMS 0.03515 Underflow Overflow h_fm Entries 10757 Mean 0.01339 RMS 0.03306 Underflow Overflow h_fm Entries 10757 Mean 0.01339 RMS 0.03306 Underflow Overflow

18.8<log(E)<19.0

h_dt Entries 2762 Mean 0.000807 RMS 0.03439 Underflow Overflow h_pm Entries 4783 Mean

  • 0.01238

RMS 0.03627 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 100 200 300 400 500 600 700 800 h_pm Entries 4783 Mean

  • 0.01238

RMS 0.03627 Underflow Overflow h_fm Entries 4854 Mean 0.01036 RMS 0.03318 Underflow Overflow h_fm Entries 4854 Mean 0.01036 RMS 0.03318 Underflow Overflow

19.0<log(E)<19.2

h_dt

Entries 1393 Mean 0.0005126 RMS 0.03534 Underflow Overflow

h_pm Entries 2098 Mean

  • 0.01559

RMS 0.04427 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 50 100 150 200 250 300 350 h_pm Entries 2098 Mean

  • 0.01559

RMS 0.04427 Underflow Overflow h_fm Entries 2068 Mean 0.0121 RMS 0.04096 Underflow Overflow h_fm Entries 2068 Mean 0.0121 RMS 0.04096 Underflow Overflow

19.2<log(E)<19.4

h_dt Entries 691 Mean

  • 0.002341

RMS 0.04264 Underflow Overflow h_pm Entries 949 Mean

  • 0.01308

RMS 0.06157 Underflow Overflow ξ

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 20 40 60 80 100 h_pm Entries 949 Mean

  • 0.01308

RMS 0.06157 Underflow Overflow h_fm Entries 998 Mean 0.01716 RMS 0.05333 Underflow Overflow h_fm Entries 998 Mean 0.01716 RMS 0.05333 Underflow Overflow

19.4<log(E)<19.6

h_dt Entries 280 Mean 0.005376 RMS 0.05861 Underflow Overflow

/PRELIMINARY/ /PRELIMINARY/

proton, iron, data

  • Y. Zhezher

TA SD Composition

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SLIDE 15

Results: TA SD (MVA) composition

1 2 3 4 5 6 18 18.5 19 19.5 20

p He N Si Fe

/PRELIMINARY/

<ln A> log10 E, eV

TA SD, QGSJET II-03

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Results comparison: TA SD (MVA) vs TA hybrid

1 2 3 4 5 6 18 18.5 19 19.5 20

p He N Si Fe

/PRELIMINARY/

<ln A> log10 E, eV

TA SD, QGSJET II-03 TA hybrid, QGSJET II-03

[TA] W.Hanlon, UHECR’16, also the talk [646][CRI123]

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MVA result compared to other experiments

1 2 3 4 5 6 18 18.5 19 19.5 20 p He N Si Fe

/PRELIMINARY/

<ln A> log10 E, eV

TA SD, QGSJET II-03 HiRES stereo, QGSJET II-03

HiRes stereo, PRL, 2010

1 2 3 4 5 6 18 18.5 19 19.5 20 p He N Si Fe

/PRELIMINARY/

<ln A> log10 E, eV

TA SD, QGSJET II-03 Auger SD muon XMAX, QGSJET II-03 Auger SD risetime asymmetry, QGSJET II-03

1 2 3 4 5 6 18 18.5 19 19.5 20 p He N Si Fe

/PRELIMINARY/

<ln A> log10 E, eV

Yakutsk muon, QGSJET II-03 TA SD, QGSJET II-03

Pierre Auger Observatory Xµ

MAX and risetime asymmetry, ICRC’11

Yakutsk ρµ JPhysG, 2012

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Conclusion

◮ The composition is qualitatively consistent with the TA

hybrid results.

◮ It is also qualitatively consistent with the Auger SD results. ◮ The average atomic mass of primary particles corresponds

to ln A = 1.76 ± 0.08.

  • Y. Zhezher

TA SD Composition

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Backup slides

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ξ parameter conversion to ln A

  • 1. After applying the BDT method, ξ parameter distribution is

derived for proton and iron MC and for the data in each energy bin.

  • 2. The range between ln A = 0 (proton) and ln A = 4.02 (iron)

is divided into 40 equal parts. At every point a “mixture” of protons and iron (e.g. 5 % p and 95 % Fe) is produced.

  • 3. KS-distance between ξ parameter distribution of the each

“mixture” and data is performed, and the case with the smallest KS-distance is chosen.

  • 4. First approximation of average ln A is estimated as

ln A(1) = ǫp × ln (1) + (1 − ǫp) × ln (56), where ǫp is a fraction of protons in the mixture.

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Method verification

◮ The source of systematic uncertainties is the

two-component assumption.

◮ The method is tested with He and N Monte-Carlo sets. ◮ The biggest systematic uncertainty is in case of N

σsyst (ln A) = 0.17.

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Boosting (AdaBoost)

◮ Given a weak learner, run it multiple times on (reweighted)

training data.

◮ On each iteration t: weight each training example by how

incorrectly it was classified.

◮ New tree with reweighted events is built and optimized. ◮ Average over all trees to create a better classifier.

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Bias corrections

Since now proton and iron MC points don’t perfectly fit the straight lines ln A = 0 and ln A = 4.02, the data can be corrected assuming the MC points to be the endpoints of the segment ln A ∈ [0; 4.02] with the following linear function: ycor = y − yp (x) yFe (x) − yp (x) × ln (56) , where yp (x) and yFe (x) are linear approximations for the MC ln A distributions.

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The Sb parameter

Sb =

N

  • i=1
  • Si ×

ri r0 b Si – signal of i-th detector ri – distance from the shower core to this station in meters r0 = 1000 m – reference distance Best separation is for b = 3 & b = 4.5.

Ros, Supanitsky, Medina-Tanco et al. Astropart.Phys. 47 (2013) 10

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Why primary composition is important?

◮ understand the acceleration mechanisms ◮ predict the flux of cosmogenic photons and neutrino ◮ probe the interaction cross-section at the highest

energies

◮ precision tests of Lorentz-invariance