Limits on Neutrino Lorentz Violation from Multimessenger Observations of TXS 0506+056

The observation by the IceCube Collaboration of a high-energy ($E \gtrsim 200$ TeV) neutrino from the direction of the blazar TXS 0506+056 and the coincident observations of enhanced $\gamma$-ray emissions from the same object by MAGIC and other experiments can be used to set stringent constraints on Lorentz violation in the propagation of neutrinos that is linear in the neutrino energy: $\Delta v = - E/M_1$, where $\Delta v$ is the deviation from the velocity of light, and $M_1$ is an unknown high energy scale to be constrained by experiment. Allowing for a difference in neutrino and photon propagation times of $\sim 10$ days, we find that $M_1 \gtrsim 3 \times 10^{16}$ GeV. This improves on previous limits on linear Lorentz violation in neutrino propagation by many orders of magnitude, and the same is true for quadratic Lorentz violation.

It is desirable to probe fundamental physical principles as sensitively as possible, and Lorentz invariance is no exception. Specifically, one may ask how accurately we know that different species of massless particles travel at the speed of light, and how accurately we know that massive particles travel at the same speed in the high-energy limit. Over the past two decades, since the publication of [1], considerable effort has been put into constraining different forms of Lorentz violation, and specifically a linear coefficient M 1 in the velocity v of energetic photons: ∆v = −E/M 1 , using distant time-dependent astrophysical sources of energetic photons such as pulsars, gamma-ray bursts (GRBs) and active galactic nuclei (AGNs). However, analyses of possible Lorentz violation in photon propagation have been beset by difficulties in disentangling intrinsic time delays in the sources from time delays accumulated during propagation, and we consider that the strongest robust limit on M 1 for photons is between 10 17 and 10 18 GeV [2]. There have also been analyses of possible Lorentz violation in neutrino propagation from Supernova 1987A and in a terrestrial neutrino beam, but these are sensitive only to M 1 ∼ 2 × 10 11 GeV and potentially ∼ 4 × 10 8 GeV, respectively [3]. More recently, data on the first observed black-hole binary merger [4] were used to to set the much weaker limit M 1 100 keV for graviton propagation [5], and the near-coincidence of gravitational waves and γ-rays from a neutron-star binary merger has been used to establish that their velocities are the same to within ∼ 10 −17 [6]. Very recently, the IceCube Collaboration has reported the observation of an ultrahigh-energy neutrino from the direction of the blazar TXS 0506+056, and together with a number of other groups, most notably the MAGIC Collaboration, have reported [7] an enhanced level of activity in γ-ray and photon emission from this source, which is located at a distance ∼ 4 × 10 9 ly. As we discuss in this paper, the great distance of TXS 0506+056 and the high energy 200 TeV of the observed high-energy neutrino, in conjunction with the γ-ray observations, provides unique sensitivity to Lorentz violation in neutrino propagation, which almost rivals that to linear Lorentz violation in photon propagation. The sensitivity to linear Lorentz violation in neutrino propagation is to M 1 3 × 10 16 GeV, approaching the Planck energy scale that might be characteristic of the possible quantum-gravity effects that were the original motivation for [1].
We first review the observations of TXS 0506+056 reported by the IceCube Collaboration and the teams studying its electromagnetic emissions [7]. The primary observation by IceCube was that of a single neutrino with energy ∼ 290 TeV (90% CL lower limit 183 TeV) on 22 September 2017, dubbed IceCube-170922A, coming from a direction within 0.1 o of the catalogued γ-ray source TXS 0506+056, whose redshift z = 0.3365 ± 0.0010. Several γ-ray experiments, notably MAGIC, VERITAS, HESS, Fermi-LAT, AGILE and Swift made observations showing that TXS 0506+056 was in a flaring state over a period within about 10 days of IceCube-170922A [7]. The IceCube Collaboration has also reported an excess of neutrinos observed earlier from the direction of TXS 0506+056, confirming this as the source of IceCube-170922A [8], and analyses have supported the hypothesis that a single astrophysical mechanism is responsible for emitting both the neutrino and the γ-rays [9].
The similarity in arrival times of IceCube-170922A and the electromagnetic emissions can be used immediately to estimate the corresponding sensitivity to a difference ∆v νγ in the propagation speeds in vacuo of the neutrino and photons, assuming that both speeds are independent of energy. We assume a distance of 4 × 10 9 ly and an illustrative time difference of 10 days 1 , so that ∆v νγ /c ∼ 10 days/4 × 10 9 years ∼ 10 −11 2 . This is six orders of magnitude worse than the corresponding constraint on the difference in propagation speeds of gravitational waves and photons derived from the near-simultaneous observations of the binary neutron-star merger: ∆v GW γ 10 −17 [6]. However, it is much better than the corresponding sensitivity to an energy-independent ∆v νγ from the observations of neutrinos emitted during the collapse of supernova 1987A: ∆v νγ 4 hours/1.5 × 10 5 years ∼ 3 × 10 −9 .
An energy-independent difference between the velocities of neutrinos (or gravitational waves) and photons would require the extremely radical step of abandoning the framework of special relativity. A less radical hypothesis would be that Lorentz invariance is an emergent symmetry in the low-energy limit, but is subject to modification that increases with energy. This is indeed the suggestion that has been made in a number of different theoretical frameworks, including the 'space-time foam' expected in models of quantum gravity [10], phenomenological models suggested by features of cosmic-ray physics [11] and other considerations [12], the suggestion that Lorentz invariance may be broken spontaneously [13,14], models of loop quantum gravity [15], doubly-special relativity theories [16] and quantum field theories of the Lifshitz type [17]. In such frameworks, Lorentz invariance is a good symmetry in the low-energy limit, but is violated increasingly at high energies.
The first such possibility that we consider is that ∆v νγ increases linearly with energy: In such a case, one's first guess could be that M 1 would be comparable to the Planck mass: M 1 ∼ M P 10 19 GeV. However, the value of M 1 would depend in a stringinspired model on unknown quantities such as the string coupling, the density of defects in space-time, and the strength of particle interactions with such defects, which may not be universal between different particle species [19], so we maintain phenomenological open minds about the possible magnitude of M 1 . The model of space-time foam proposed in [18] would suggest that the velocities of neutrinos would deviate from the low-energy velocity of light less than photons, so that (in an obvious notation) (1 + z) which is over 6 orders of magnitude stronger than the limit obtained previously [3] from an analysis of the neutrino signal from supernova 1987A 4 . The sensitivity (1) is, nevertheless, an order of magnitude weaker than the robust limit on photon Lorentz violation [2], so refers directly to the neutrino. It is instructive also to compare the sensitivity (1) to the possible improvement in the supernova limit, should another core-collapse supernova be observed in our galaxy.
Multi-dimensional simulations of such events suggest that their neutrino emissions might 4 In calculating (1) we used the standard cosmological ΛCDM model with dark energy and dark matter contributions Ω Λ = 0.7 and Ω M = 0.3, respectively, and Hubble expansion rate H 0 = 68 km/s/Mpc. See [2] for detailed derivation of (1). exhibit time variations in the millisecond range, in which case measurements might attain a sensitivity to M 1 ∼ 2 × 10 13 GeV [20], still 3 orders of magnitude less than the IceCube-170922A/MAGIC sensitivity (1). This sensitivity is also far beyond that we can envisage using a terrestrial neutrino beam. It was estimated using the timing capabilities of the OPERA detector and assuming that timing information could be available for neutrino events upstream in rock that a sensitivity to M 1 ∼ 4 × 10 8 GeV could be attained [3] 5 . Thus the IceCube-170922A/MAGIC sensitivity seems to outclass the capabilities of terrestrial experiments as well as possible future supernova observations. One can also consider a possible quadratic violation of Lorentz invariance: ∆v = −E 2 /M 2 2 , which would be an option in some of the alternative models of Lorentz violation mentioned above [11][12][13][14][15]17]. In this case, the IceCube-170922A/MAGIC sensitivity would be to which is over 5 orders of magnitude stronger than the corresponding limit from supernova 1987A [3]. In the case of quadratic Lorentz violation, the supernova 1987A limit was estimated to be to M 2 ∼ 4×10 4 GeV, the possible sensitivity of a future galactic supernova event was estimated to be to M 2 ∼ 10 6 , and the potential sensitivity of a terrestrial experiment was estimated to be to M 2 ∼ 7 × 10 5 GeV. Again, the large distance of TXS 0506+056 and the high energy of the IceCube-170922A event enable it to outclass the competition.
We conclude that the advent of multimessenger neutrino/photon astronomy [7,8] has not only launched a new era in the study of the origins of high-energy cosmic rays, but also made possible a breakthrough in the exploration of Lorentz symmetry using neutrinos. We may anticipate that more coincidences between high-energy neutrino events and electromagnetic emissions will be observed, enabling the rough estimates made here to be refined and improved. Such coincidences would contribute to fundamental physics as well as resolving important issues in astrophysics.