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

Transcription

1 First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Leyre Nogués, 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 19,17 1 / 19

2 Outline 1 Introduction Lorentz Invariance Violation LIV experimental study 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 / 19

3 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. Hôrawa s gravity. Experiment - prove Quantum effects in Space-time structure. Example: Time-Of-Flight Studies. E p c [ 1 n=1 ( ) ] E n ±, E QG 3 / 19

4 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. 4 / 19

5 Introduction LIV current limits Mrk 41 (Whipple) 4 16 Mrk 51 and Crab Pulsar (MAGIC and VERITAS) 3 17 Crab Pulsar and PG 1553 (MAGIC and H.E.S.S.) 4 17 GRB 8916C (Fermi) 1 18 PKS 155 (H.E.S.S.) 18 E Planck GRB 95 (Fermi) 19 GRB AGN Pulsar E QG1 /GeV Crab Pulsar (VERITAS) 7 9 GRB 8916C (Fermi) 8 19 PG 1553 (H.E.S.S.).6 Mrk 51 (MAGIC).6 Crab Pulsar (MAGIC) 4 4 PKS 155 (HESS) 6.4 GRB 95 (Fermi) E QG /GeV 11 5 / 19

6 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(E s )C(E s, t)g(e E s, σ E (E s ))F s (t D(E s, E QGn, z))de s. 6 / 19

7 Methodology ML Combined Analysis ML Combined Analysis Every source has a Likelihood function - the combination of several of them is straightforward. 1 They must share a common estimator parameter. The estimator has to be redshift independent. L Comb (λ) = Nsource i=1 L i (λ) Nsource log(l Comb (λ)) = log(l i (λ)), Typically each likelihood function has a parabolic shape in logarithmic scale. i=1 Look for the minimum in negative logarithmic scale. Easy CLs computation. 7 / 19

8 Simulations Simulation procedure Simulation procedure Simulated sources for the study. Mrk 51 5 flare detected by MAGIC. PG flare detected by H.E.S.S. PKS flare detected by H.E.S.S. VHE Crab Pulsar radiation detected by VERITAS. Simulation steps 99 simulation sets of each source. E true and t true /φ true from parametrized published data. Injection of LIV effect ( t E n ) Application of IRFs to obtained measured values. 8 / 19

9 Simulations Simulated distributions ON-OFF events 7 6 PKS155 (time) Entries 535 Mean 193 RMS 1 Underflow ON-OFF events Mrk51 (time) Entries 73 Mean 89.3 RMS 6.6 Underflow 5 Overflow 4 Overflow Time (s) Time (s) ON-OFF events Crab (phase) Entries Mean.51 RMS.4569 ON-OFF events 4 18 PG1553 (time) Entries 15 Mean 46 RMS 4 14 Underflow 16 Underflow 1 Overflow 14 Overflow Phase Time (s) 9 / 19

10 Results on LIV and QG limits Stack of results The analysis, applied over the 99 sets of simulations, uses λ as a fit parameter,that is related to the QG energy scale E QG, t n E n h E n l n z (1 + z ) n s ± H EQG n dz n = s ± Ωm (1 + z ) 3 + Ω Λ H EQG n κ(z), λ = t n E n κ(z) = 1, E QG H 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 E QG. / 19

11 Results on LIV and QG limits Stack of results counts 1 Linear χ / ndf.1 / 19 counts 16 Quadratic χ / ndf 4.3 / 18 Constant 8.6 ± 4. Mean.41 ±.9 14 Constant ± 5.6 Mean.484 ±.864 Sigma ± Sigma 6.68 ± λ (s/tev) λ (s/tev ) 11 / 19

12 Results on LIV and QG limits Stack of results Log(κ l (z)) PG PKS Mrk 51 Log(κ q (z)) PG PKS Mrk Combination 6 Combination 8 8 Crab Pulsar Crab Pulsar λ (s/tev) λ (s/tev ) 1 / 19

13 Results on LIV and QG limits Stack of results Parameter PKS 155 Mrk 51 PG 1553 Crab Combination λ best (s/tev ) -4.5±.6 4.9± ± ± ±. 1σ CL (s/tev ) 84.6± ± ± ± ±1.6 λ LL (s/tev ) RMS LL (s/tev ) λ UL (s/tev ) RMS UL (s/tev ) Parameter PKS 155 Mrk 51 PG 1553 Crab Combination λ best (s/tev ) 1.3± ±1.1 1.± ± ±.9 1σ CL (s/tev ) 59.8± ± ± ± ±.7 λ LL (s/tev ) RMS LL (s/tev ) λ UL (s/tev ) RMS UL (s/tev ) / 19

14 Results on LIV and QG limits Energy limits E QG /E Planck 1 Planck Scale E QG /E Planck 6 Combination 7 1 PKS Crab Pulsar Mrk 51 8 Combination PG Crab Pulsar Mrk 51 PKS PG κ l (z) κ q(z) Source E QG linear ( 18 GeV ) E QG Quadratic ( GeV ) Redshift PKS Mrk PG Crab kpc Combination / 19

15 Conclusions and prospects Conclusions and prospects Combination - Improvement visible at λ parameter level. Energy limits. Linear Dominated by the PKS limit. Combination - 4% improvement respect to best individual case. Quadratic Dominated by Mrk 51 limit. Combination - % 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). 15 / 19

16 Backup slides Case λ for AGN combination. 16 / 19

17 Backup slides Systematic effects Limits and CLs in presence of Nuisance Parameters. Procedure in construction will follow. Rolke, Lopez & Conrad (9) arxiv:4359 Systematic uncertainties Typical range per source (%) Selection cuts 5 - Background contribution 1-5 Acceptance factors - 5 Energy resolution - 5 Energy calibration Spectral index 5 Calibration systematics (constant, shift) Time template parametrization 5-3 Due to limited statistics for certain sources: Time template uncertainties dominate systematic effects 17 / 19

18 First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Backup slides Combination plots - Linear case counts 1 λ LL Comb χ / ndf.38 / 1 counts 16 λ Comb χ / ndf 9.45 / 15 counts 1 λ UL Comb χ / ndf.9 / Constant 4.4 ± 4.1 Constant ± 5.5 Constant 6.7 ± 4. Mean 118. ±. 14 Mean.373 ±.193 Mean ±. Sigma ± Sigma 67.6 ± 1.57 Sigma ± λ (s/tev) 3 3 λ (s/tev) λ (s/tev) 18 / 19

19 First combined studies on Lorentz Invariance Violation from observations of astrophysical sources Backup slides Combination plots - Quadratic case counts 1 λ LL Comb χ / ndf 3. / counts 14 λ Comb χ / ndf / 1 counts 1 λ UL Comb χ / ndf 19.4 / 19 Constant 9. ± Constant ± 4.9 Constant 1.9 ± 4.6 Mean ±.94 Sigma 8.11 ±.69 Mean.554 ±.8599 Sigma 6.7 ±.7 Mean 48.1 ±.93 Sigma 8.11 ± λ (s/tev ) λ (s/tev ) λ (s/tev ) 19 / 19