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Repeating Fast Radio Bursts Caused by Small Bodies Orbiting a Pulsar Or a Magnetar Fabrice Mottez1, Philippe Zarka2, and Guillaume Voisin3,1

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Repeating Fast Radio Bursts Caused by Small Bodies Orbiting a Pulsar Or a Magnetar Fabrice Mottez1, Philippe Zarka2, and Guillaume Voisin3,1 A&A 644, A145 (2020) Astronomy https://doi.org/10.1051/0004-6361/202037751 & c F. Mottez et al. 2020 Astrophysics Repeating fast radio bursts caused by small bodies orbiting a pulsar or a magnetar Fabrice Mottez1, Philippe Zarka2, and Guillaume Voisin3,1 1 LUTH, Observatoire de Paris, PSL Research University, CNRS, Université de Paris, 5 Place Jules Janssen, 92190 Meudon, France e-mail: [email protected] 2 LESIA, Observatoire de Paris, PSL Research University, CNRS, Université de Paris, Sorbonne Université, 5 Place Jules Janssen, 92190 Meudon, France 3 Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M19 9PL, UK Received 16 February 2020 / Accepted 1 October 2020 ABSTRACT Context. Asteroids orbiting into the highly magnetized and highly relativistic wind of a pulsar offer a favorable configuration for repeating fast radio bursts (FRB). The body in direct contact with the wind develops a trail formed of a stationary Alfvén wave, called an Alfvén wing. When an element of wind crosses the Alfvén wing, it sees a rotation of the ambient magnetic field that can cause radio-wave instabilities. In the observer’s reference frame, the waves are collimated in a very narrow range of directions, and they have an extremely high intensity. A previous work, published in 2014, showed that planets orbiting a pulsar can cause FRBs when they pass in our line of sight. We predicted periodic FRBs. Since then, random FRB repeaters have been discovered. Aims. We present an upgrade of this theory with which repeaters can be explained by the interaction of smaller bodies with a pulsar wind. Methods. Considering the properties of relativistic Alfvén wings attached to a body in the pulsar wind, and taking thermal consider- ation into account, we conducted a parametric study. Results. We find that FRBs, including the Lorimer burst (30 Jy), can be explained by small-size pulsar companions (1 to 10 km) between 0.03 and 1 AU from a highly magnetized millisecond pulsar. Some parameter sets are also compatible with a magnetar. Our model is compatible with the high rotation measure of FRB 121102. The bunched timing of the FRBs is the consequence of a moderate wind turbulence. An asteroid belt composed of fewer than 200 bodies would suffice for the FRB occurrence rate measured with FRB 121102. Conclusions. After this upgrade, this model is compatible with the properties discovered since its first publication in 2014, when repeating FRBs were still unknown. It is based on standard physics and on common astrophysical objects that can be found in any type of galaxy. It requires 1010 times less power than (common) isotropic-emission FRB models. Key words. radio continuum: general – pulsars: general – stars: magnetars – minor planets, asteroids: general – plasmas – magnetic fields 1. Introduction characteristics correspond to young neutron stars. This paper is an upgrade of this revised model, in the light of the discov- Mottez & Zarka(2014, hereafter MZ14) proposed a model of ery of repeating radio bursts made since the date of publica- FRBs that involves common celestial bodies, neutron stars (NS), tion of MZ14 (Spitler et al. 2016; CHIME/FRB Collaboration and planets orbiting them, well-proven laws of physics (elec- 2019). The main purpose of this upgrade is modeling the ran- tromagnetism), and a moderate energy demand that allows for dom repeating bursts, and explaining the strong linear polariza- a narrowly beamed continuous radio-emission from the source tion that might be associated with huge magnetic rotation mea- that sporadically illuminates the observer. When these ingredi- sures (Michilli et al. 2018; Gajjar et al. 2018). ents are put together, the model is compatible with the localiza- The MZ14 model consists of a planet that orbits a pulsar tion of FRB sources at cosmological distances (Chatterjee et al. and is embedded in its ultra-relativistic and highly magnetized 2017), it can explain the millisecond burst duration, the flux den- wind. The model requires that wind and planet are in direct con- sities above 1 Jy, and the range of observed frequencies. tact. Then, the disturbed plasma flow reacts by creating a strong MZ14 is based on the relativistic Alfvén wings theory potential difference at the companion. This is the source of an of Mottez & Heyvaerts(2011), and the authors concluded electromagnetic wake, called Alfvén wing, because it is formed that planetary companions of standard or millisecond pulsars of one or two stationary Alfvén waves. Alfvén wings support could be the source of FRBs. In an erratum that reevaluated an electric current and an associated change in magnetic field the magnetic flux and thus the magnetic field in the pulsar direction. According to MZ14, when the wind crosses an Alfvén wind, Mottez & Heyvaerts(2020, hereafter MH20) revised the wing, it sees a temporary rotation of the magnetic field. This emitted radio frequency and flux density and concluded that perturbation can be the cause of a plasma instability that gener- observed FRB characteristics are rather compatible with com- ates coherent radio waves. Because the pulsar companion and panions of millisecond highly magnetized pulsars. These pulsar the pulsar wind are permanent structures, this radio-emission A145, page 1 of 14 Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A&A 644, A145 (2020) process is most probably permanent as well. Because the source frequencies much lower than the gyrofrequency, as is the case of these radio waves is the pulsar wind when it crosses the in the highly magnetized inner regions of pulsar environments. Alfvén wings, and because the wind is highly relativistic with Removing the constraint that the observed frequencies are above Lorentz factors up to an expected value γ ∼ 106, the radio source the gyrofrequency allows for FRB radiation sources, that is, pul- has a highly relativistic motion relative to the radio-astronomers sar companions, much closer to the neutron star. Then, it is pos- who observe it. Because of the relativistic aberration that results, sible to explore the possibility of FRB sources such as asteroid all the energy in the radio waves is concentrated into a narrow belts or streams at a close distance to the neutron star. The ability beam of aperture angle ∼1/γ rad (the green cone attached to of these small companions to resist evaporation must be verified. source S in Fig.1). We only observe the waves when we cross the We therefore include a detailed study of the thermal balance of beam. The motion of the beam (its change of direction) results the companion. primarily from the orbital motion of the pulsar companion. The The model in MZ14 with a single planet leads to the con- radio-wave energy was evaluated in MZ14 and MH20, as well clusion that FRBs must be periodic, with a period equal to the as its focusing, and it was shown that it is compatible with a companion orbital period, provided that propagation effects do brief emission that can be observed at cosmological distances not perturb the observation conditions too strongly. The possi- (∼1 Gpc) with flux densities higher than 1 Jy. bility of asteroid clusters or belts might explain the existence In the nonrelativistic regime, the Alfvén wings of planet- of nonperiodic FRB repeaters such as those that have been satellite systems and their radio emissions have been well discovered. studied because this electromagnetic structure characterizes the We also include a more elaborate reflection than in MZ14 of interaction of Jupiter and its rotating magnetosphere with its the duration of the observed bursts and of their nonperiodic repe- inner satellites Io, Europa, and Ganymede (Saur et al. 2004; tition rates. The MZ14 model proposed a generation mechanism Hess et al. 2007; Pryor et al. 2011; Louis et al. 2017; Zarka et al. for FRB that led to predict isolated or periodic FRBs. We adapted 2018). It is also observed in the Saturn-Enceladus system this here to irregularly repeating FRBs. Nevertheless, we can (Gurnett et al. 2011). already note that it contains a few elements that have been dis- The central question is how the pulsar wind can be in direct cussed separately in more recent papers. For instance, the energy contact with the obstacle. The solution proposed in MZ14 was involved in this model is lower by orders of magnitudes than the to assume that the pulsar wind is sub-Alfvénic. energy required by quasi-isotropic emission models because this Although the wind velocity is almost the speed of light c, the model involves a very narrow beam of radio emission. This con- MZ14 model assumed that the wind is slower than Alfvén and cept alone was discussed by Katz(2017), who concluded, as did fast magnetosonic waves. The planet was then supposed to orbit MZ14, that a relativistic motion in the source, or of the source, inside this sub-Alfvénic region of the wind. The Alfvénic mach can explain the narrowness of the radio beam. This point is key number is to the observability of a neutron star-companion system at cos- 2 mological distances. 2 vr γ vr MA = 1 + ; (1) The MZ14 proposed the basic mechanism. We broaden the c σ c range of companions. Using the main results of MZ14 and the where vr is the radial wind velocity, and σ is the magnetiza- thermal analysis summarized in Sect.2, we perform a para- tion parameter, defined as the ratio of magnetic to kinetic energy metric study and select relevant solutions (Sect.3).
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