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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Leyre Nogu es, Tony T.Y. Lin, Cedric Perennes,

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources

First combined studies on Lorentz Invariance Violation from observations of astrophysical sources

Leyre Nogu´ es, Tony T.Y. Lin, Cedric Perennes, Alasdair E. Gent, Julien Bolmont, Markus Gaug, Agnieszka Jacholkowska, Manel Martinez, A.Nepomuk Otte, Robert M. Wagner, John E. Ward, Benjamin Zitzer for the LIV Consortium July 19,2017

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources

Outline

1 Introduction

Lorentz Invariance Violation LIV experimental study

2 Methodology

Maximum Likelihood Analysis ML Combined Analysis

3 Simulations

Simulation procedure Simulated distributions

4 Results on LIV and QG limits

Stack of results Energy limits

5 Conclusions and prospects

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Introduction Lorentz Invariance Violation

Lorentz Invariance Violation

Theory - Aim to build a common theory covering General Relativity and Quantum Mechanics. Different approaches, leading to modified dispersion relations inducing LIV.

Loop Quantum Gravity. SM extension. Hˆ

  • rawa’s gravity.

Experiment - prove Quantum effects in Space-time structure. Example: Time-Of-Flight Studies. E 2 ≃ p2c2 ×

  • 1 −

∞

  • n=1

± E EQG n ,

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Introduction LIV experimental study

LIV experimental study

The ToF studies - opportunity to the experimental gamma-ray sector. Proportional to E n and redshift. Fast, variable, very energetic, distant sources → Gamma-rays source options.

Pulsars, AGNs, GRBs.

Associated challenges to the study.

Low statistic data sets. Few adequate sources for the study. EBL absorption of very energetic photons.

Solution - Combination between experiments.

Increase of the statistics. Intrinsic effects and redshift dependence study. LIV multi-type source combination.

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Introduction LIV current limits EQG1/GeV EQG2/GeV 1020 1019 1018 1017 1016 1011 1010

GRB AGN Pulsar

M r k 4 2 1 ( W h i p p l e ) 4 ⋅ 1 016 Mrk 501 and Crab Pulsar (MAGIC and VERITAS) 3⋅1017 Crab Pulsar and PG 1553 (MAGIC and H.E.S.S.) 4⋅1017 PKS 2155 (H.E.S.S.) 2⋅1018 GRB 080916C (Fermi) 1⋅1018

EPlanck

GRB 090510 (Fermi) 2⋅1019 Crab Pulsar (VERITAS) 7⋅10

9

GRB 080916C (Fermi) 8⋅1019 Mrk 501 (MAGIC) 2.6⋅10

1

Crab Pulsar (MAGIC) 4⋅410 P K S 2 1 5 5 ( H E S S ) 6 . 4 ⋅ 1 010 GRB 090510 (Fermi) 1.3⋅1011 PG 1553 (H.E.S.S.) 2.6⋅10

1

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Methodology Maximum Likelihood Analysis

Methodology

Maximum Likelihood analysis (ML) is very adequate Supports very low photon statistics. Any complex temporal distribution is allowed. Unbinned method: maximum use of information. Can be adapted in different ways. Maximization of Likelihood source function. Likelihood is created from the event PDFs of the source emission. One estimator parameter and some optional nuisance parameters.

dP dEdt = N ∞ Γ(Es)C(Es, t)G(E −Es, σE(Es))Fs(t−D(Es, EQGn, z))dEs.

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Methodology ML Combined Analysis

ML Combined Analysis

Every source has a Likelihood function - the combination of several

  • f them is straightforward.

1 They must share a common estimator parameter. 2 The estimator has to be redshift independent.

LComb(λ) =

Nsource

  • i=1

Li(λ) − → −2log(LComb(λ)) = −2

Nsource

  • i=1

log(Li(λ)),

Typically each likelihood function has a parabolic shape in logarithmic scale. Look for the minimum in negative logarithmic scale. Easy CLs computation.

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Simulations Simulation procedure

Simulation procedure

Simulated sources for the study. Mrk 501 2005 flare detected by MAGIC. PG 1553+113 2012 flare detected by H.E.S.S. PKS 2155-304 2006 flare detected by H.E.S.S. VHE Crab Pulsar radiation detected by VERITAS. Simulation steps 990 simulation sets of each source. Etrue and ttrue/φtrue from parametrized published data. Injection of LIV effect (∆t ∝ E n) Application of IRFs to obtained measured values.

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Simulations Simulated distributions

Time (s) 500 1000 1500 2000 2500 3000 3500 4000 ON-OFF events 20 30 40 50 60 70

PKS2155 (time)

Entries 2535 Mean 1930 RMS 1100 Underflow Overflow

Phase 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ON-OFF events 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Crab (phase)

Entries 127639 Mean 0.2501 RMS 0.04569 Underflow Overflow

Time (s) 200 400 600 800 1000 1200 1400 ON-OFF events 10 20 30 40 50 60 70

Mrk501 (time)

Entries 703 Mean 809.3 RMS 226.6 Underflow Overflow

Time (s) 1000 2000 3000 4000 5000 6000 7000 8000 ON-OFF events 2 4 6 8 10 12 14 16 18 20 22 24

PG1553 (time)

Entries 152 Mean 4260 RMS 2040 Underflow 0 Overflow

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Results on LIV and QG limits Stack of results

The analysis, applied over the 990 sets of simulations, uses λ as a fit parameter,that is related to the QG energy scale EQG,

∆tn E n

h − E n l

≃ s± n + 1 2 H0 1 E n

QG

z (1 + z′)n

  • Ωm (1 + z′)3 + ΩΛ

dz′ = s± n + 1 2 H0 1 E n

QG

κ(z), λ = ∆tn ∆E nκ(z) = 1 EQGH0 ,

From every analysis, for individual and combined cases and for linear and quadratic case, we get: Distribution of best fit value of the parameter λ. Distribution of 1-sided 95% CLs. Upper limits on EQG.

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Results on LIV and QG limits Stack of results

Linear

/ ndf

2

χ 20.12 / 19 Constant 4.2 ± 108.6 Mean 2.109 ± 2.041 − Sigma 1.39 ± 64.63

(s/TeV) λ 200 − 150 − 100 − 50 − 50 100 150 200 counts 20 40 60 80 100 120

Linear

/ ndf

2

χ 20.12 / 19 Constant 4.2 ± 108.6 Mean 2.109 ± 2.041 − Sigma 1.39 ± 64.63

Quadratic

/ ndf

2

χ 24.32 / 18 Constant 5.6 ± 131.3 Mean 0.8642 ± 0.4084 − Sigma 0.74 ± 26.68

)

2

(s/TeV λ 100 − 80 − 60 − 40 − 20 − 0 20 40 60 80 100 counts 20 40 60 80 100 120 140 160

Quadratic

/ ndf

2

χ 24.32 / 18 Constant 5.6 ± 131.3 Mean 0.8642 ± 0.4084 − Sigma 0.74 ± 26.68

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Results on LIV and QG limits Stack of results

(s/TeV) λ

1000 − 800 − 600 − 400 − 200 − 200 400 600 800 1000

(z))

l

κ Log10(

10 − 8 − 6 − 4 − 2 −

PG 1553+113 Mrk 501 PKS 2155-304 Crab Pulsar

Combination )

2

(s/TeV λ

1000 − 800 − 600 − 400 − 200 − 200 400 600 800 1000

(z))

q

κ Log10(

10 − 8 − 6 − 4 − 2 −

PG 1553+113 Mrk 501 PKS 2155-304 Crab Pulsar

Combination

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Results on LIV and QG limits Stack of results

Parameter PKS 2155 Mrk 501 PG 1553 Crab Combination λbest (s/TeV )

  • 4.5±2.6

4.9±5.6

  • 11.3±13.4
  • 5.4±4.7
  • 2.37±2.2

1σ CL (s/TeV ) 84.6±2.1 168.6±4.4 412.0±9.7 146.0±3.8 67.6±1.6 λLL (s/TeV )

  • 154.9
  • 296.6
  • 687.7
  • 254.2
  • 118.2

RMSLL (s/TeV ) 88.8 169.9 414.5 150.4 67.52 λUL (s/TeV ) 142.5 299.5 658.6 244.7 117.8 RMSUL (s/TeV ) 83.72 171.6 421.4 151.3 66.1 Parameter PKS 2155 Mrk 501 PG 1553 Crab Combination λbest (s/TeV 2) 1.3±1.9

  • 0.8±1.1

1.0±17.5 3.8±6.4

  • 0.6±0.9

1σ CL (s/TeV 2) 59.8±1.7 31.85±1.0 533.7±13.2 189.5±5.6 26.7±0.7 λLL (s/TeV 2)

  • 104.4
  • 59.2
  • 912.1
  • 326.6
  • 49.5

RMSLL (s/TeV 2) 69.2 33.2 542.1 351.0 28.9 λUL (s/TeV 2) 100.0 56.8 921.1 354.2 48.1 RMSUL (s/TeV 2) 67.9 34.1 554.2 355.0 28.0

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Results on LIV and QG limits Energy limits

(z)

l

κ

5 −

10

4 −

10

3 −

10

2 −

10

1 −

10 1 10

2

10 Planck

/E

QG

E

3 −

10

2 −

10

1 −

10 1

Mrk 501 PKS 2155-304 PG 1553+113 Crab Pulsar Planck Scale Combination

(z)

q

κ

5 −

10

4 −

10

3 −

10

2 −

10

1 −

10 1 Planck

/E

QG

E

10 −

10

9 −

10

8 −

10

7 −

10

6 −

10

Mrk 501 PKS 2155-304 PG 1553+113 Crab Pulsar Combination

Source EQG linear(1018GeV ) EQG Quadratic(1010GeV ) Redshift PKS 2155 1.86 6.20 0.116 Mrk 501 0.91 8.57 0.034 PG 1553 0.38 2.08 0.5 Crab 1.07 4.14 2kpc Combination 2.31 9.34

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Conclusions and prospects

Conclusions and prospects

Combination - Improvement visible at λ parameter level. Energy limits.

Linear

Dominated by the PKS 2155-304 limit. Combination - 24% improvement respect to best individual case.

Quadratic

Dominated by Mrk 501 limit. Combination - 10% improvement respect to best individual case.

PG 1553 contributes with redshift and Crab Pulsar with statistics. The list of used sources - constantly increasing with publications. Predictions and preparation for Cherenkov Telescope Array (CTA).

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Backup slides

Case λ = 0 for AGN combination.

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Backup slides

Systematic effects

Limits and CLs in presence of Nuisance Parameters. Procedure in construction will follow.

Rolke, Lopez & Conrad (2009) arXiv:0304059

Systematic uncertainties Typical range per source (%) Selection cuts 5 - 10 Background contribution 1 - 5 Acceptance factors 2 - 5 Energy resolution 2 - 5 Energy resolution 2 - 5 Energy calibration 10 Spectral index 5 Calibration systematics (constant, shift) 10 Time template parametrization 5 - 30

Due to limited statistics for certain sources: Time template uncertainties → dominate systematic effects

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Backup slides

Combination plots - Linear case

Comb

LL

λ

/ ndf

2

χ 20.38 / 21 Constant 4.1 ± 104.4 Mean 2.2 ± 118.2 − Sigma 1.50 ± 66.71

(s/TeV) λ 350 − 300 − 250 − 200 − 150 − 100 − 50 − 50 100

counts

20 40 60 80 100 120

Comb

LL

λ

/ ndf

2

χ 20.38 / 21 Constant 4.1 ± 104.4 Mean 2.2 ± 118.2 − Sigma 1.50 ± 66.71

Comb λ

/ ndf

2

χ 9.045 / 15 Constant 5.5 ± 139.1 Mean 2.193 ± 2.373 − Sigma 1.57 ± 67.62

(s/TeV) λ 300 − 200 − 100 − 100 200 300

counts

20 40 60 80 100 120 140 160

Comb λ

/ ndf

2

χ 9.045 / 15 Constant 5.5 ± 139.1 Mean 2.193 ± 2.373 − Sigma 1.57 ± 67.62

Comb

UL

λ

/ ndf

2

χ 22.09 / 20 Constant 4.2 ± 106.7 Mean 2.2 ± 117.8 Sigma 1.52 ± 65.43

(s/TeV) λ 100 − 50 − 50 100150200250300 350

counts

20 40 60 80 100 120

Comb

UL

λ

/ ndf

2

χ 22.09 / 20 Constant 4.2 ± 106.7 Mean 2.2 ± 117.8 Sigma 1.52 ± 65.43

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First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Backup slides

Combination plots - Quadratic case

Comb

LL

λ

/ ndf

2

χ 30.02 / 20 Constant 4.4 ± 109.2 Mean 0.94 ± 49.47 − Sigma 0.69 ± 28.11

)

2

(s/TeV λ 160 − 140 − 120 − 100 − 80 − 60 − 40 − 20 − 0 20 40

counts

20 40 60 80 100 120

Comb

LL

λ

/ ndf

2

χ 30.02 / 20 Constant 4.4 ± 109.2 Mean 0.94 ± 49.47 − Sigma 0.69 ± 28.11

Comb λ

/ ndf

2

χ 18.68 / 21 Constant 4.9 ± 116.1 Mean 0.8599 ± 0.5504 − Sigma 0.7 ± 26.7

)

2

(s/TeV λ 100 − 80 − 60 − 40 − 20 − 0 20 40 60 80 100

counts

20 40 60 80 100 120 140

Comb λ

/ ndf

2

χ 18.68 / 21 Constant 4.9 ± 116.1 Mean 0.8599 ± 0.5504 − Sigma 0.7 ± 26.7

Comb

UL

λ

/ ndf

2

χ 19.24 / 19 Constant 4.6 ± 110.9 Mean 0.93 ± 48.12 Sigma 0.78 ± 28.11

)

2

(s/TeV λ 40 − 20 − 0 20 40 60 80 100120140

counts

20 40 60 80 100 120 Comb

UL

λ

/ ndf

2

χ 19.24 / 19 Constant 4.6 ± 110.9 Mean 0.93 ± 48.12 Sigma 0.78 ± 28.11

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