Probes of Lorentz Invariance Violation (with gamma-rays) Ulisses Barres de Almeida CTA Science Meeting - Leicester

Transcription

1 Probes of Lorentz Invariance Violation (with gamma-rays) Ulisses Barres de Almeida CTA Science Meeting - Leicester

2 Talk Outline Lorentz Invariance Violation Time-of-Flight Experiments Search Methodologies: GRB Unbinned Methods Kolmogorov Distance CTA Discussion Ulisses Barres de Almeida 2

3 Quantum Space-Time Planck Scale: Natural scale derived from dimmensional analysis of the fundamental constants G, c, h. Extreme scale at which quantum, relativistic and gravitational effects are relevant to the description of phenomena. Wheeler, 1953 quantum foam Ulisses Barres de Almeida 3

4 Quantum Space-Time Uncertainty principle: λ/2 p = h/λ Wheeler, 1953 quantum foam Ulisses Barres de Almeida 4

5 Quantum Space-Time Quantum gravity: E = pc L Geometry tensor: G μν ~ δg μν /L 2 Field tensor: T μν ~ E/L 3 = pc/l 3,for Δp ~ p ~ E P /c = (hc 3 /G) 1/2 Δx ~ L Planck Ulisses Barres de Almeida 5

6 Ulisses Barres de Almeida 6 Propagation through discrete space-time L = 23 λ L = 16 λ

7 Time-of-Flight Experiments Magnitude of the energy-dependent correction to c is very small. For 1 TeV photon: δc ~ E/E P ~ λ/l P c But propagation over cosmological distances will magnify the effect to a measurable difference on the arrival time of photons E 1 and E 2 :» (Amelino-Camelia+98) Where ξ=e QG /E P is the energy-scale for LIV, to be tested by experiments (E << E QG ) Ulisses Barres de Almeida 7

8 Time-of-Flight Experiments The form of the dispersion relation modified by QG is not known exactly, but for E << E P the low energy approximation to order (n) can be used: to which corresponds c' ~ c(1-ξ(e/e P )) for n = 1. The cosmological expression for the propagation delay (corrected for the proper distances) is (Jacob+Piran 08): 4s, (ξ,n =1) for Mpc dist. Ulisses Barres de Almeida 8

9 Time-of-Flight Experiments BF1 BF2 BF3 BF4 BF5 Ulisses Barres de Almeida 9

10 Time-of-Flight Experiments Net observational effect is that the light-curve will look skewed/deformed with the lagging of the HE photons MRL = l- < l(p,q) > s l (p,q) Ulisses Barres de Almeida 10

11 Census of ToF searches Ulisses Barres de Almeida 11

12 The sub-planckian Fermi limit: GRB Nature, 09 This was a distant, short GRB (z ~ 0.9; d L 5 Gpc) observed by Fermi with a maximum photon energy of ~ 31 GeV. - Intrinsic lags for short bursts at kev-mev energies are very small (~ 10 ms), which is of the order of the spike widths. Ulisses Barres de Almeida 12

13 GRB : critique of methodology Nature, GeV LIV tested using two methods: 1. limits from one photon arrival times: Conservative assumption: 31 GeV photon has not been emitted before the onset of the low energy emission. Δt ~ 859 ms, and ξ > 1.19 Lack of knowledge about the intrinsic GRB emission structure (e.g., detection of an earlier precursor to the emission by Troja et al. 2010) is a problem to onephoton approaches and the revised conservative limit with this new information is of ξ > 0.09

14 GRB : critique of methodology Nature, GeV LIV tested using two methods: 2. testing for an energy-dependent dispersion in the high-energy light curves: Δt/ΔE < 30 ms/gev, and ξ > 1.22 Ulisses Barres de Almeida 14

15 Robust LIV Limits from GRBS: population sampling A propagation-dispersion model make specific predictions on the dependence between the magnitude of the lags and the distance to the source This fact can be used to separate extrinsic from intrinsic effects and account for spurious non-systematic contributions to a single measurement that the observer could be unaware of or could fall out of his control. Ellis+ '06 A combination of different types of sources, such as AGNs and GRBs is also an important addition to the tests, and the use of AGNs is particularly advantageous because they are not one-off as GRBs. Ulisses Barres de Almeida 15

16 Robust LIV Limits Ellis+ '06 Derived QG scale cannot be unambiguously disentagled from intrinsice source delays: Mavromatos, astro-ph of today. Ulisses Barres de Almeida 15

17 Additional notes on methodology The detection of an energy-dependent dispersion is limited mainly by the 'sensitivity factor', defined by Amelino-Camelia+98» η Δt/δt = delay burst width Since usually is the case that delay << burst width (by over an order of magnitude) one wants to probe the maximum temporal resolution of the light-curve by using unbinned methods. Usually, the emission mechanisms at the source are poorly known, and even observational parameters such as emission spectrum can contain many systematics and model dependencies and we prefer to concentrate on non-parametric tests.» Ulisses Barres de Almeida 16

18 VHE Astronomy: The situation with AGNS HESS '08 (PKS ): Ulisses Barres de Almeida 15

19 The how-to of non-parametric approaches The delay is always an assymetric effect in time, whose result will be to disperse the light-curve. This assymetry will have another systematic effect which is to change the shape of the profile, skewing it. Unbinned representation Scargle+08 Dispersion Cancellation algorithm developed by Scargle+08 and Ellis+08 Ulisses Barres de Almeida 18

20 Choice of Cost function The cost-function is a choice of measure to describe the undispersed state of the light-curve Typical cost functions try to maximise a sharpness-related quantity, such as: 1. The total photon-energy inside a window around the peak of the transient feature: 2. The total entropy of the distribution, which decreases for sharper distributions (Scargle+08) Ulisses Barres de Almeida 19

21 Testing Lorentz Invariance with VHE Gamma-rays Kolmogorov Metric: A new approach to a choice of cost function, which looks into the discrepancy between the high and low-energy burst profiles. Barres de Almeida, 2010 Ph.D. thesis Ulisses Barres de Almeida 20

22 Testing Lorentz Invariance with VHE Gamma-rays Kolmogorov Metric: A new approach to a choice of cost function, which looks into the discrepancy between the high and low-energy burst profiles. Barres de Almeida, 2010 Ph.D. thesis Ulisses Barres de Almeida 17

23 Census of ToF searches PRELIMINARY CTA LIMITS Ulisses Barres de Almeida 22

24 Extra Slides

25 Kolmogorov Metric The advantages of a metric-minimisation approach are three-fold: illustration of iii. the minimisation of the CDF discrepancy is i. a fit to the entire profile with a natural weight towards the most transient part of the profile; ii. because it averages over the data set twice min(sup(x-y)) it suffers less from statistical fluctuations and works with very small number of events; iii. It turned out to be very little sensitive to the limitations on the energy resolution. illustration of ii.

26 Relation to other cost functions

27 Application to HESS data: Analysis of PKS large flare Over 10,000 events registered in ~ 90 min, and time-resolved transient features down to a s width: η ~ 0.1

28 Application to HESS data: Analysis of PKS large flare To assess the significance of our tests we parameterised the five individual bursts BF1-5 following the original fits by HESS original paper, for consistency BF2

29 Performance of the Method: number of events For CTA: an increase in the sensitivity by an order of magnitude around 1 TeV is likely to improve significantly the RMS for otherwise not very well sampled features (likely to be the shortest ones) and has also the potential to viabilise the test on broader features.

30 Performance of the Method: energy cuts For CTA: by increasing the low energy boundary by lowering the energy threshold, and accumulating more statistics towards highest energies, we will decrease the overall rms level of the curves, maybe extending the low plateau to higher energies.

31 Dispersion Recovery Same test, for fixed dispersion, for each flare BF1-5, showing that despite the lack of sensitivity (large RMS) the method re-constructs very well the true dispersion parameter Accuracy on the recovery of true dispersion parameter as function of its value for each BF1-5

32 Analysis Results E GeV