Using recent polarimetric observations of the Crab Nebula in the hard X-ray
band by INTEGRAL, we show that the absence of vacuum birefringence effects
constrains O(E/M) Lorentz violation in QED to the level |\xi| < 9x10^{-10} at
three sigma CL, tightening by more than three orders of magnitude previous
constraints. We show that planned X-ray polarimeters have the potential the
potential to probe |\xi|~ 10^{-16} by detecting polarization in active galaxies
at red-shift ~1.Comment: 4 pages, 3 figure

A. J. Dean

Annalisa Celotti

C. Barcelo

D. Mattingly

G. Amelino-Camelia

John G. Kirk

L. Maccione

Luca Maccione

M. C. Weisskopf

Pietro Ubertini

Stefano Liberati

English

arXiv

We exploit recent polarimetric observations of the Crab Nebula in the hard X-ray band by IN- TEGRAL to show that the absence of vacuum birefringence effects constrains O(E/M) Lorentz violation in QED to the level |ξ | &lt; 9 × 10^{−10} (at 3σ CL). This tightens by more than three or- ders of magnitude previous constraints. We also show that planned X-ray polarimeters have the potential to probe |ξ | ∼ 10^{−16} by detecting polarization in active galaxies at red-shift ∼ 1

Maccione, L.

Liberati, S.

Celotti, A.

Kirk, J. G.

Ubertini, P.

SISSA Digital Library

Gamma-ray polarization constraints on Planck scale violations of special relativity

Using recent polarimetric observations of the Crab Nebula in the hard X-ray band by INTEGRAL, we show that the absence of vacuum birefringence effects constrains O(E/M) Lorentz violation in QED to the level |\xi| &lt; 9x10^{-10} at three sigma CL, tightening by more than three orders of magnitude previous constraints. We show that planned X-ray polarimeters have the potential the potential to probe |\xi|~ 10^{-16} by detecting polarization in active galaxies at red-shift ~1

MACCIONE L

Liberati, Stefano

Celotti, Anna Lisa

KIRK J. G

UBERTINI P.

Sissa Digital Library

PoS(CRAB2008)018Gamma-ray polarization constraints on Planck scaleviolations of special relativityLuca Maccione∗DESY, Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany)II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761Hamburg (Germany)E-mail: luca.maccione@desy.deStefano LiberatiSISSA, Via Beirut 2-4, I-34014 Trieste, ItalyINFN, Via Valerio 2, I-34127 Trieste, ItalyE-mail: liberati@sissa.itAnnalisa CelottiSISSA, Via Beirut 2-4, I-34014 Trieste, ItalyINFN, Via Valerio 2, I-34127 Trieste, ItalyE-mail: celotti@sissa.itJohn G. KirkMax-PIanck-Institute für KernPhysik, Saupfercheckweg 1, D-69117 Heidelberg, GermanyE-mail: john.kirk@mpi-hd.mpg.dePietro UbertiniIASF-INAF, via Fosso del Cavaliere 100, Roma, ItalyE-mail: pietro.ubertini@iasf-roma.inaf.itWe exploit recent polarimetric observations of the Crab Nebula in the hard X-ray band by IN-TEGRAL to show that the absence of vacuum birefringence effects constrains O(E/M) Lorentzviolation in QED to the level |ξ | < 9× 10−10 (at 3σ CL). This tightens by more than three or-ders of magnitude previous constraints. We also show that planned X-ray polarimeters have thepotential to probe |ξ | ∼ 10−16 by detecting polarization in active galaxies at red-shift ∼ 1.Polarimetry days in Rome: Crab status, theory and prospectsOctober 16-17, 2008Rome, Italy∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(CRAB2008)018Gamma-ray polarization constraints on Planck scale violations of special relativity Luca Maccione1. IntroductionRecent years have witnessed a growing interest in the possible high energy violations of localLorentz Invariance (LI) as well as a flourishing of observational tests. Indeed, specific hints ofLorentz invariance violations (LV) arose from various approaches to Quantum Gravity (QG, see[1, 2] for detailed references).In most of the above mentioned QG models, LV enters through dispersion relations which canbe cast in the general form (it is assumed, for simplicity, that rotational invariance is preserved andonly boost invariance is affected by Planck-scale corrections):E2 = p2 + m2 + f (E, p; µ ;M) , (1.1)where we set the low energy speed of light c = 1, E and p are the particle energy and momentum,µ is a particle-physics mass-scale (possibly associated with a symmetry breaking/emergence scale)and M denotes the relevant QG scale. Generally, it is assumed that M is of order the Planck mass:M∼MPl ≈ 1.22×1019 GeV, corresponding to a quantum (or emergent) gravity effect. The functionf (E, p; µ ;M) can be expanded in powers of the momentum (energy and momentum are basicallyindistinguishable at high energies, although they are both taken to be smaller than the Planck scale),and the lowest order LV terms (p, p2 and p3) have been mainly considered [1].At first sight, it appears hopeless to search for effects suppressed by the Planck scale. Eventhe most energetic particles ever detected (Ultra High Energy Cosmic Rays) have E . 1011 GeV∼10−8MPl. However, even tiny corrections can be magnified into a significant effect when dealingwith high energies (but still well below the Planck scale), long distances of signal propagation, orpeculiar reactions (see, e.g., [1]). A partial list of these windows on quantum gravity includes:• sidereal variation of LV couplings as the lab moves with respect to a preferred frame ordirection• cumulative effects: long baseline dispersion and vacuum birefringence (e.g. of signals fromgamma ray bursts, active galactic nuclei, pulsars)• anomalous (normally forbidden) threshold reactions allowed by LV terms (e.g. photon decay,vacuum ˇCerenkov effect)• shifting of existing threshold reactions (e.g. photon annihilation from blazars, GZK reaction)• LV induced decays not characterised by a threshold (e.g. decay of a particle from one helicityto the other or photon splitting)• maximum velocity (e.g. synchrotron peak from supernova remnants)• dynamical effects of LV background fields (e.g. gravitational coupling and additional wavemodes)However, most of these effects require a well established theoretical framework to calculatereaction rates and describe the particle dynamics. Although we study here a purely kinematiceffect, we prefer for definiteness to work within the framework of Effective Field Theory with2PoS(CRAB2008)018Gamma-ray polarization constraints on Planck scale violations of special relativity Luca Maccionenon-renormalizable, mass dimension 5 LV operators (see [1, 3] and references therein) restrictedto QED. In this framework the most general dispersion relations for photons and electrons areω2± = k2±ξ k3/MPl (1.2)E2± = p2 + m2 + η±p3/MPl , (1.3)where (1.2) refers to photons1 and (1.3) to fermions2. The constants ξ and η± indicate the strengthof the LV. The ± signs denote right and left circular polarization in (1.2), and positive and nega-tive helicity states of the fermion in (1.3). Equation (1.2) implies that the direction of polarizationrotates during propagation due to the different velocities of the right- and left-handed circular po-larizations, v± ≃ 1±ξ k/M. This effect is known as vacuum birefringence (VB).Recently η± have been constrained to have a magnitude less than 10−5 at 95% confidencelevel (CL) by a detailed analysis of the synchrotron component of the Crab Nebula (CN) broad-band spectrum [5], while the constraint |ξ | . 2× 10−7 has been obtained by [6] considering theabsence of VB effects during the propagation of optical/UV polarized light from Gamma-RayBursts (GRB). There are also preliminary indications, based on an analysis of the photon fractionin Ultra-High-Energy Cosmic Rays, that these coefficients might be less than 10−14 [7, 8, 9].In this contribution, we describe how the current constraints on O(E/MPl) suppressed LV canbe further tightened by about three orders of magnitude for photons [10], by considering the limitson VB effects implied by the recently detected [11] polarized hard X-rays from the CN. Firstly, weset such constraints following the arguments by [12, 13]. This approach is robust against systematicuncertainties related to astrophysical modeling. We then infer tighter limits that exploit and rely onmodeling of the Crab Nebula and pulsar.Note that this LV term violates CPT symmetry. Studies of higher order CPT conserving termswould be extremely important (see [2]). However, they cannot be constrained by the methods usedhere because they do not predict vacuum birefringence.Finally, we discuss the constraints which future X-ray polarization measurements of extra-galactic objects, e.g. Active Galactic Nuclei (AGN) will allow. This is of particular interest in thelight of current experimental efforts to build X-ray polarimeters [14, 15, 16, 17, 18, 19].2. BirefringenceDuring propagation over a distance d3, the polarization vector of a linearly polarized planewave with momentum k rotates through an angle [4, 12, 13, 2],θ(k,d) = ω+(k)−ω−(k)2d ≃ ξ k2d2MPl. (2.1)Depending on the available information on both the observational and the theoretical (i.e. sourcemodeling) side, observations of polarized light from a distant source can constrain |ξ | in two ways.1This kind of dispersion relation was also derived in some semi-classical limit of Loop quantum gravity [4].2For positrons we have ηpos± =−ηel∓ [2].3For an extragalactic object at redshift z, the (cosmological) distance is given by d(z) = 1H0∫ z01+z′√ΩΛ+Ωm(1+z′)3dz′ ,which includes a (1 + z′)2 factor in the integrand to take into account the red-shift acting on the photon energies. Asusual, H0 is the present value of the Hubble parameter, while ΩΛ and Ωm represent the density fractions of cosmologicalconstant and matter in the Universe, respectively.3PoS(CRAB2008)018Gamma-ray polarization constraints on Planck scale violations of special relativity Luca MaccioneDecrease in polarization degree Since detectors have a finite energy bandwidth, eq. (2.1) is neverprobed in real situations. Rather, if some net amount of polarization is measured in theband k1 < E < k2, an order-of-magnitude constraint arises from the fact that if the angleof polarization rotation (2.1) were to differ by more than pi/2 over this band, the detectedpolarization would fluctuate sufficiently for the net signal polarization to be suppressed [12,13]. From (2.1), this constraint isξ . pi MPl(k22 − k21)d(z). (2.2)This just requires that any intrinsic polarization (at source) is not completely washed outduring signal propagation. It thus relies on the mere detection of a polarized signal, withoutconsidering the observed polarization degree. A more refined limit can be obtained by calcu-lating the maximum observable polarization degree, given the maximum intrinsic value [20]:Π(ξ ) = Π(0)√〈cos(2θ)〉2P+ 〈sin(2θ)〉2P, (2.3)where Π(0) is the maximum intrinsic degree of polarization, θ is defined in eq. (2.1) andthe average is weighted over the source spectrum and instrumental efficiency, represented bythe normalized weight function P(k) [12]. Conservatively, one can set Π(0) = 100%, but alower value can sometimes be justified on the basis of source modeling. Using eq. (2.3), onecan then cast a constraint by requiring Π(ξ ) to exceed the observed value.Rotation of polarization angle Suppose that polarized light measured in a certain energy bandhas a position angle θobs with respect to a fixed direction. At fixed energy, the polarizationvector rotates by the angle (2.1)4; if the position angle is measured by averaging over a certainenergy range, the final net rotation 〈∆θ〉 is given by the superposition of the polarizationvectors of all the photons in that range:tan(2〈∆θ〉) = 〈sin(2θ)〉P〈cos(2θ)〉P, (2.4)where θ is given by (2.1). If the position angle at emission θi in the same energy band isknown from a model of the emitting source, a constraint can be set by imposingtan(2〈∆θ〉) < tan(2θobs −2θi) . (2.5)Although this limit is tighter than that obtained from the previous methods, it clearly hingeson assumptions about the nature of the source, which may introduce significant uncertainties.3. Constraints from the Crab nebulaIn the case of the CN, a (46±10)% degree of linear polarization in the 100 keV−1 MeV bandhas recently been measured by the INTEGRAL mission [21, 11] (see also [22]). This measurement4Faraday rotation is negligible at such energies.4PoS(CRAB2008)018Gamma-ray polarization constraints on Planck scale violations of special relativity Luca Maccioneuses all photons within the SPI instrument energy band. However the convolution of the instru-mental sensitivity to polarization with the detected number counts as a function of energy, P(k), ismaximized and approximately constant within a narrower energy band (150 to 300 keV) and fallssteeply outside this range [23]. Hence we shall, conservatively, assume that most polarized photonsare concentrated in this band. Given dCrab = 1.9 kpc, k2 = 300 keV and k1 = 150 keV, eq. (2.2)leads to the order-of-magnitude estimate |ξ |. 2×10−9. A more accurate limit follows from (2.3).In the case of the CN there is a robust understanding that photons in the range of interest are pro-duced via the synchrotron process, for which the maximum degree of intrinsic linear polarizationis about 70% (see e.g. [24]). The requirement Π(ξ ) > 16% (taking account of a 3σ offset from thebest fit value 46%) leads to the constraint (at 99% CL) |ξ |. 6×10−9 [10]. It is interesting to no-tice that X-ray polarization measurements of the CN already available in 1978 [25], set a constraint|ξ |. 5.4×10−6, only one order of magnitude less stringent than that reported in [6].This constraint can be tightened by exploiting the current astrophysical understanding of thesource. The CN is a cloud of relativistic particles and fields powered by a rapidly rotating, stronglymagnetized neutron star. Both the Hubble Space Telescope and the Chandra X-ray satellite haveimaged the system, revealing a jet and torus that clearly identify the neutron star rotation axis [26].The projection of this axis on the sky lies at a position angle of 124.0◦ ± 0.1◦ (measured fromNorth in anti-clockwise). The neutron star itself emits pulsed radiation at its rotation frequencyof 30 Hz. In the optical band these pulses are superimposed on a fainter steady component with alinear polarization degree of 30% and direction precisely aligned with that of the rotation axis [27].The direction of polarization measured by INTEGRAL-SPI in the γ-rays is θobs = 123◦±11◦ (1σerror) from the North, thus also closely aligned with the jet direction and remarkably consistentwith the optical observations. This compelling (theoretical and observational) evidence allows usto use eq. (2.5). Conservatively assuming θi−θobs = 33◦ (i.e. 3σ from θi, 99% CL), this translatesinto the limit |ξ |. 9×10−10 [10].4. DiscussionThe constraints presented in section 3 are remarkably strong. Although based on a cumulativeeffect, they are achieved using a local (Galactic) object. The reason lies, on the one hand, in thequadratic dependence of θ on the photon energy, in constrast with the linear gain given by distance(see e.g. eq. (2.1)). On the other hand, the robust theoretical understanding of the CN has enabledus to strengthen the constraints significantly.Further improvements on LV constraints via birefringenge are expected thanks to the forth-coming high-energy polarimeters, which will provide an unprecedented sensitivity, sufficient todetect polarized light at a few % levels also in extragalactic sources. The LV limits will be op-timized by balancing between source distance and observational energy range depending on thedetector sensitivity as shown in [10]. Remarkably, constraints of order |ξ | < O(10−16) could beplaced if some polarized distant sources (z ∼ 1) will be observed by such instruments at 1 MeV.AcknowledgmentsLM acknowledges support from SISSA where most part of this work was done.5PoS(CRAB2008)018Gamma-ray polarization constraints on Planck scale violations of special relativity Luca MaccioneReferences[1] D. Mattingly, Living Rev. Rel. 8 (2005) 5 [arXiv:gr-qc/0502097].[2] T. Jacobson, S. Liberati and D. Mattingly, Annals Phys. 321 (2006) 150 [arXiv:astro-ph/0505267].[3] R. C. Myers and M. Pospelov, Phys. Rev. Lett. 90 (2003) 211601 [arXiv:hep-ph/0301124].[4] R. Gambini and J. Pullin, Phys. Rev. D 59 (1999) 124021 [arXiv:gr-qc/9809038].[5] L. Maccione, S. Liberati, A. Celotti and J. G. Kirk, JCAP 0710 (2007) 013 [arXiv:0707.2673[astro-ph]].[6] Y. Z. Fan, D. M. Wei and D. Xu, Mon. Not. Roy. Astron. Soc. 376 (2006) 1857[arXiv:astro-ph/0702006].[7] M. Galaverni and G. Sigl, Phys. Rev. Lett. 100 (2008) 021102 [arXiv:0708.1737 [astro-ph]].[8] L. Maccione and S. Liberati, JCAP 0808 (2008) 027 [arXiv:0805.2548 [astro-ph]].[9] M. Galaverni and G. Sigl, Phys. Rev. D 78 (2008) 063003 [arXiv:0807.1210 [astro-ph]].[10] L. Maccione, S. Liberati, A. Celotti, J. G. Kirk and P. Ubertini, Phys. Rev. D 78 (2008) 103003[arXiv:0809.0220 [astro-ph]].[11] A. J. Dean et al., Science 321 (2008) 1183.[12] R. J. Gleiser and C. N. Kozameh, Phys. Rev. D 64 (2001) 083007 [arXiv:gr-qc/0102093].[13] T. A. Jacobson, S. Liberati, D. Mattingly and F. W. Stecker, Phys. Rev. Lett. 93 (2004) 021101[arXiv:astro-ph/0309681].[14] E. Costa et al., arXiv:astro-ph/0609576.[15] F. Muleri et al., arXiv:astro-ph/0609573.[16] Y. Kanai et al., Nucl. Instrum. Meth. A 570, 61 (2007).[17] E. Costa et al., arXiv:astro-ph/0207440.[18] J. Knodlseder, P. Von Ballmoos, F. Frontera, A. Bazzano, F. E. Christensen, M. Hernanz andC. Wunderer, arXiv:0707.4627 [astro-ph].[19] H. Krawczynski, Polarimetry with EXIST, same conference[20] McMaster, W. H. 1961, Reviews of Modern Physics, 33, 8[21] Parmar, A. N., Winkler, C., Barr, P., Hansson, L., Kuulkers, E., Much, R., & Orr, A. 2003,Proceedings of the SPIE, 4851, 1104[22] M. Forot, P. Laurent, I. A. Grenier, C. Gouiffes and F. Lebrun, arXiv:0809.1292 [astro-ph].[23] S. McGlynn et al., arXiv:astro-ph/0702738.[24] J. Petri and J. G. Kirk, Astrophys. J. 627 (2005) L37 [arXiv:astro-ph/0505427].[25] Weisskopf, M. C., Silver, E. H., Kestenbaum, H. L., Long, K. S., & Novick, R. 1978, Astrophys. J.Letters, 220, L117[26] C. Y. Ng and R. W. Romani, Astrophys. J. 601 (2004) 479 [arXiv:astro-ph/0310155].[27] G. Kanbach, A. Slowikowska, S. Kellner and H. Steinle, AIP Conf. Proc. 801, 306 (2005)[arXiv:astro-ph/0511636].6

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Maccione, Luca

Celotti, Annalisa

Kirk, John G.

Ubertini, Pietro

Max Planck Society eDoc Server

Kirk, J.

MPG.PuRe

Using recent polarimetric observations of the Crab Nebula in the hard X-ray band by INTEGRAL, we show that the absence of vacuum birefringence effects constrains O(E/M) Lorentz violation in QED to the level |\xi| < 9x10^{-10} at three sigma CL, tightening by more than three orders of magnitude previous constraints. We show that planned X-ray polarimeters have the potential the potential to probe |\xi|~ 10^{-16} by detecting polarization in active galaxies at red-shift ~1

Maccione, L

KIRK J., G

https://iris.sissa.it/bitstream/20.500.11767/15306/1/CRAB2008_018.pdf

Gamma-ray polarization constraints on Planck scale violations of special
  relativity

Gamma-ray polarization constraints on Planck scale violations of special relativity

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