Draft version April 2, 2018 A Preprint typeset using LTEX style emulateapj v. 5/2/11 MODEL-DEPENDENT ESTIMATE ON THE CONNECTION BETWEEN FAST RADIO BURSTS AND ULTRA-HIGH ENERGY COSMIC RAYS Xiang Li1,2, Bei Zhou1,2, Hao-Ning He1, Yi-Zhong Fan1, and Da-Ming Wei1 1 Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Science, Nanjing, 210008, China. and 2 Graduate University of Chinese Academy of Sciences, Yuquan Road 19, Beijing, 100049, China. Draft version April 2, 2018 ABSTRACT The existence of fast radio bursts (FRBs), a new type of extragalatic transients, has been established recently and quite a few models have been proposed. In this work we discuss the possible connection between the FRB sources and ultra-high energy (> 1018 eV) cosmic rays. We show that in the blitzar model and the model of merging binary neutron stars, the huge energy release of each FRB central engine together with the rather high rate of FRBs, the accelerated EeV cosmic rays may contribute significantly to the observed ones. In other FRB models including for example the merger of double white dwarfs and the energetic magnetar radio flares, no significant EeV cosmic ray is expected. We also suggest that the mergers of double neutron stars, even if they are irrelevant to FRBs, may play a non-ignorable role in producing EeV cosmic ray protons if supramassive neutron stars were formed in a good fraction of mergers and the merger rate is & 103 yr−1 Gpc−3. Such a possibility will be unambiguously tested in the era of gravitational wave astronomy. Subject headings: radio continuum: general— acceleration of particles—cosmic rays 1. INTRODUCTION 2. POSSIBLE HIGH-ENERGY COSMIC RAY ACCELERATION: MODEL-DEPENDENT ESTIMATE In a recent survey for pulsars and fast transients, Thornton et al. (2013) have confirmed Lorimer et al. In this section we focus on the cosmological models (2007) and Keane et al. (2012)’s discovery by uncov- and in particular the blitzar model, the merging dou- ering four millisecond-duration radio bursts (hereafter ble neutron star model, and model of merger of binary FRB) all more than 40 ◦ from the Galactic plane. Cur- white dwarfs. This is because the total energy released in 1 rent data favor celestial rather than terrestrial ori- the models of magnetar giant radio flares (Popov et al. gin, and the host galaxy and intergalactic medium 2007) and Galactic flaring stars (Loeb et al. 2014) are models suggest that they have cosmological redshifts too small to be sufficient to accelerate and then account (z) of 0.5 to 1 and distances of up to ∼ 3 Gpc. for a non-ignorable fraction of ultra-high energy cosmic The millisecond-duration suggests that central engine rays. is likely either a neutron star or a stellar-mass black 2.1. The blitzar model hole. Currently quite a few models have been pro- posed to interpret FRBs, including the mergers of binary In the blitzar model, the FRBs were triggered by the neutron stars (Hansen & Lyutikov 2001; Totani et al. collapse of the SMNSs to black holes. As a result of the 2013; Lipunov & Pruzhinskaya 2014), energetic magne- collapse of SMNS, the magnetic-field lines will snap vio- tar radio flares (Popov et al. 2007), delayed collapses of lently. Accelerated electrons from the traveling magnetic supramassive neutron stars (SMNS) to black holes (i.e., shock dissipate a significant fraction of the magneto- the so-called blitzar model (Falcke & Rezzolla 2014), a sphere and produce a massive radio burst that is observ- highly relevant hypothesis is the possible connection be- able out to cosmological distances (Falcke & Rezzolla arXiv:1312.5637v2 [astro-ph.HE] 23 Nov 2014 tween Gamma-ray Bursts and FRBs (Bannister et al. 2014). The difference between SMNS and normal NS is 2012; Zhang 2014; Ravi & Lasky 2014)), mergers of bi- that the former has to rotate very quickly to not collapse nary white dwarfs (Kashiyama et al. 2013), and flar- since the gravitational mass of SMNS is larger than that ing stars if FRBs are instead in the Galaxy (Loeb et al. allowed for a non-rotating NS (Friedman et al. 1986). 2014). The discussion of the advantages and disadvan- The rapid uniform rotation can enhance the maximum −2 tages of these models can be found in Kulkarni et al. gravitational mass by a factor of ∼ 0.05(P0/1 ms) and (2014) and is beyond the scope of this work. The rate of thus help make the SMNS stable (Friedman et al. 1986). FRBs is high up to ∼ 104 sky−1 day−1 (Thornton et al. In addition to the core-collapse supernovae (ccSNe) pro- 2013). If huge amount of energy was released into the cir- posed in Falcke & Rezzolla (2014), the merger of some cum interstellar medium by the central engine of FRBs, binary neutron stars can also produce SMNS or even ultra-high energy cosmic rays may be accelerated. The normal NS if the equation of state of the NS material is estimate of possible contribution of FRB central engines stiff enough (e.g., Davis et al. 1994; Dai & Lu 1998a; in producing ultra-high (> 1018 eV) energy cosmic rays 1 The newly-born magnetars with initial spin rates close to the is the main purpose of this work. centrifugal breakup limit had been suggested to be possible ∼ 1020 eV cosmic ray sources (Arons 2003). At present it is unclear whether the magnetars generating the giant fast radio bursts ini- [email protected] (YZF) tially rotated so quick or not. 2 Dai et al. 2006; Shibata et al. 2000; Baumgarte et al. of the massive star, Chevalier et al. (2004) assumed 2000; Gao & Fan 2006; Metzger et al. 2008; Zhang that the surrounding medium has a density typical of 2013). Usually the nascent NSs formed in both ccSNe the hot, low-density phase of a starburst galaxy (i.e., and merger of double NSs are differentially rotating and n ∼ 0.2 cm−3). If it is the case, the contribution to the differential rotation is suggested to be more efficient the DM by the surrounding medium can be ignored. to keep the SN stable. However, the differential rotation However, the ccSN may be born in molecular cloud 2 −3 is expected to be terminated by the magnetorotational with a typical number density ncloud ∼ 10 cm 2 1/3 instability as well as magnetic braking (Cook et al. 1992, and a size of Rcloud ∼ (3Mcloud/4πncloudmpc ) ∼ 1994; Hotokezaka et al. 2013) very quickly. That is why 4 1/3 2 −3 −1/3 10 pc (M /10 M⊙) (n /10 cm ) , we only consider the effect of uniform rotation in stabi- cloud cloud which can give rise to an observed DM ≈ 103 (1 + lizing the SMNS. Here we concentrate on ccSN-formed −1 4 1/3 2 −3 2/3 −3 SMNS and will discuss the merger-formed SMNS in some z) (Mcloud/10 M⊙) (ncloud/10 cm ) pc cm . Therefore the surrounding molecular cloud should not detail in section 2.2. 4 Before discussing the high-energy cosmic ray be very massive/dense (i.e., Mcloud < 10 M⊙ for 2 −3 acceleration, we examine whether the blitzar model ncloud ∼ 10 cm ) otherwise the central ccSNe could can account for the observed dispersion measures not be viable progenitors of the observed FRBs. Such or not. The SN outflow likely has a total mass a request is denoted as Request-III. All these three Msh ∼ a few M⊙, and the observed dispersion requests impose some challenges on the ccSN scenario in measures DM ∼ 1021 cm−2 (Thornton et al. 2013; the blitzar model. Nevertheless, the blitzar model can Lorimer et al. 2007) require that the SN outflow should explain some aspects of FRBs (e.g., Falcke & Rezzolla 1/2 2014) and is still widely adopted in the literature. reach a radius Rsh > (Msh/4πmp(1 + z)DM) ∼ 18 1/2 −1/2 Below we discuss the possible high energy cosmic ray 10 cm (Msh/10 M⊙) (1 + z) , where the term acceleration in such a scenario. (1 + z) is introduced to address the effects of both the In view of the sensitive dependence of stabilization cosmological time dilation and the frequency shift on the on P0, SMNS is unlikely to exist for P0 > 2 ms unless measured DM. Clearly, at such a huge radius the SN shell there is the fine tuning that the mass of SMNS is just is also transparent for the 1.3 GHz FRB. The velocity of 1/2 tiny above that allowed by the non-rotating NS. The the SN shell can be estimated as Vsh ∼ (Einj/Msh) ∼ rotational kinetic energy of SMNSs is quite large, i.e., 9 −1 −1/2 52 1/2 52 45 2 −2 10 cm s (Msh/10 M⊙) (Einj/10 erg) . The ESN,r ≈ 3 × 10 erg (I/1.5 × 10 g cm )(P0/1 ms) , life of the SMNS should satisfy tlife > Rsh/Vsh ∼ where I is the moment of inertia. Before collapsing 9 −1/2 52 −1/2 10 s (1 + z) (Msh/10 M⊙) (Einj/10 erg) , into a black hole, the SMNS should have lost its ro- suggesting a dipole magnetic field strength tational energy mainly via magnetic dipole radiation 12 1/4 B⊥ < 1.3 × 10 G (1 + z) (I/1.5 × and possibly also gravitational wave radiation (Usov 45 2 3/4 6 −3 1/2 −1/2 1992; Duncan & Thompson 1992; Fan et al. 2013a). 10 g cm ) (R /10 cm) (P /1 ms) (M /10 M⊙) , s 0 sh The amount of energy injected into the surrounding where B⊥ = Bs sin α, Bs is the surface magnetic field 52 strength at the pole, R is the radius of the NS and medium is Einj ∼ ESN,r/2 ∼ 1.5 × 10 erg (I/1.5 × s 45 2 −2 α is the angle between the rotational and dipole 10 g cm )(P0/1 ms) , if the gravitational wave radi- axes.