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J. Astrophys. Astr. (2018) 39:14 © Indian Academy of Sciences https://doi.org/10.1007/s12036-017-9499-9

Review

Collapsing supra-massive : FRBs, the repeating FRB121102 and GRBs

PATRICK DAS GUPTA∗ and NIDHI SAINI

Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India. ∗Corresponding author. E-mail: [email protected], [email protected]

MS received 30 August 2017; accepted 3 October 2017; published online 10 February 2018

Abstract. Fast Radio Bursts (FRBs) last for ∼ few milli-seconds and, hence, are likely to arise from the of supra-massive, spinning after they lose the centrifugal support (Falcke & Rezzolla 2014). In this paper, we provide arguments to show that the repeating burst, FRB 121102, can also be modeled in the collapse framework provided the supra-massive object implodes either into a Kerr surrounded by highly magnetized plasma or into a strange . Since the estimated rates of FRBs and SN Ib/c are comparable, we put forward a common progenitor scenario for FRBs and long GRBs in which only those compact remnants entail prompt γ -emission whose kick velocities are almost aligned or anti-aligned with the stellar spin axes. In such a scenario, emission of detectable gravitational radiation and, possibly, of neutrinos are expected to occur during the SN Ib/c explosion as well as, later, at the time of implosion.

Keywords. FRBs—FRB 121102—Kerr black holes—Blandford–Znajek process—strange stars—GRBs— pre-natal kicks.

1. Introduction 43% linear polarization and 3% circular polarization (Petroff et al. 2015; Ravi & Lasky 2016; Petroff et al. Ever since the serendipitous discovery of FRB 010724, 2017). the very first (FRB) gleaned from Have FRB counterparts been seen in other wave- archival survey data by Lorimer and his team bands? FRB 131104, the first one to be detected in members (Lorimer et al. 2007), about 24 FRBs have a targeted search using Parkes radio telescope, lies in been detected so far whose physical nature still con- the direction of Carina dwarf spheroidal (Ravi tinue to confound astrophysicists (Katz 2016; Zhang et al. 2015). According to DeLaunay et al. (2016), the 2017). FRBs are bright radio transients with very gamma ray transient Swift J0644.55111 is a counterpart high brightness temperatures, lasting for ∼ few mil- of FRB 131104 at 3.2σ confidence level. The estimated liseconds with peak flux densities ranging from ∼0.1 DM for this FRB is about 779 pc cm−3 implying a Jy to ∼10 Jy at frequencies of about ∼700 MHz–2 redshift of z =∼ 0.55 while Swift J0644.55111 has a GHz. fluence and duration of about 4 × 10−6 erg cm−2 and The associated large dispersion measure (DM) 377 s, respectively (Ravi et al. 2015; DeLaunay et al. ∼500–1200 pc cm−3 and high galactic latitudes stron- 2016; Murase et al. 2017). However, Shannon and Ravi gly suggest that FRBs are extragalactic events with (2017) reported that the absence of radio afterglow in redshifts z in the range ∼0.3to∼1, implying that they the direction of Swift J0644.55111 strongly constrains lie at distances 1 Gpc, if DM is largely due to elec- the energetics indicating that this gamma ray transient trons in the IGM. As of now, polarization data exist is unlikely to be a standard long-duration Gamma Ray only for few FRBs like FRB 110523 (z < 0.5),FRB Burst (GRB). 140514 (z  0.5) and FRB 150215 ( dis- If FRBs result from such catastrophic events then tance <3.3 Gpc), with the first showing 44% linear a natural model that can account for their millisecond polarization, second less than 10% linear polarization duration radio emission at ∼1 GHz is that of initially but ∼20% circular polarization and the third, about rapidly rotating supra-massive neutron stars collapsing 14 Page 2 of 9 J. Astrophys. Astr. (2018) 39:14 into black holes (BHs) due to loss of centrifugal support It is plausible that if the core of a rotating, mas- as they spin down due to magnetic braking (Falcke & sive (M∗  35M) Wolf–Rayet-like star collapses Rezzolla 2014; Zhang 2013). eventually to form a rapidly spinning (P ∼ 1ms), However, a catastrophic event like a collapsing neu- supra-massive magnetar (M0  3M), then as this rem- tron star is unlikely to produce a FRB candidate nant spins down due to magnetic braking, it can further that exhibit recurring outbursts. There certainly is one collapse after it loses its centrifugal support (CS). In par- such source from which sporadic radio transients are ticular, since the observed radio transients from FRBs observed – FRB 121102 (Spitler et al. 2016; Scholz have millisecond duration, the model posited by Falcke et al. 2016). About 200 such intermittent outbursts in and Rezzolla (2014) attains a special status, in which radio have already been detected from it so far. This FRBs result from gravitational collapse of spun down repeater is unlikely to be an active magnetar since recent supra-massive NSs on dynamical time scales, simultaneous observations of FRB 121102 with the help  of Chandra Observatory and XMM-Newton place strin- R3  −11 −2 −3 gent upper limits, 3 × 10 erg cm on X-ray fluence τcoll ∼ ∼ 1 Gρnuc ∼ 10 s, (1) GM during the episodic radio-bursts and 3 × 1041 erg s−1 on a possible persistent X-ray luminosity (Scholz et al. where M and R are the mass and radius, respectively, 2017). ∼ of the NS at the onset of the collapse, while ρnuc = Several models for such repeating FRBs have been 1012−1014 gm cm−3 is the nuclear density inside the posited ranging from intense plasma wind sweeping NS. across the magnetosphere of an extragalactic pulsar ± If the NS collapses to a final radius Rf , energy that (Zhang 2017), episodic relativistic e wind from an can be released is given by (AGN) impinging on a plasma   cloud nearby (Vieyro et al. 2017), active young remnant ∼ 2 1 1 of a or a magnetar (Kashiyama & Murase E = GM − . (2) Rf R 2017; Metzger et al. 2017), intense flares from young magnetars leading to shock-induced maser emission According to the above expression, in case the NS col- (Kulkarni et al. 2014; Lyubarsky 2014; Beloborodov lapses to form a black hole (BH), energy generated and 2017) to asteroids falling randomly on a neutron star shared among high energy particles like photons and (Dai et al. 2016; Bagchi 2017). neutrinos created during the implosion is of In the present study, we explore two distinct scenar- explosion energy scale ios to show that a repeating FRB can also be brought within the ambit of a collapsing supra-massive mag- E ≈ 8 × 1053 erg. (3) netar framework. In the penultimate section, we also delve into the possibility of linking FRBs with long (One has substituted M = 1.4M, R = 12 km and 2 GRBs. Rf = 2GM/c = 4.2 km in equation (2), to obtain equation (3). It will be an order of higher if M ∼ 2.5M.) 2. Magnetar collapse and FRB 121102 However, several factors like short time scale of col- lapse, small mean free path due to density being >ρnuc Magnetars are highly magnetized neutron stars (NSs) and ever increasing space-time curvature prohibit the with surface |B|  1014 Gauss. However, they spin rela- hot, relativistic particles to escape out of the collaps- tively at slower rates (period P ≈ 2−12 s) compared to ing object. Under such conditions, only the radiation . They display episodic intense X-ray outbursts caused by physical processes that take place in the that are powered by internal magnetic field instead of ephemeral magnetosphere left behind outside is likely rotational kinetic energy (Thompson & Duncan 1993; to be detected, entailing an event akin to a FRB (Falcke Usov 1993). Magnetars could have originated initially & Rezzolla 2014). Since the deduced FRB brightness with high spin rates (P ≈ few milliseconds) so that temperatures are 1030 K, one needs to invoke coherent small seed magnetic fields could have been amplified to emission mechanisms to explain these observed bright, very high B by α − dynamo action, and then, because short duration radio transients. of magnetic dipole radiation depleting the rotational For many FRBs, flux density Sν shows power law α kinetic energy, their period increased steadily (Thomp- behavior, i.e. Sν ∝ ν . The isotropic luminosity L for son & Duncan 1993). FRBs can then be readily obtained from the expression J. Astrophys. Astr. (2018) 39:14 Page 3 of 9 14     1+α ν Sν sensitivity of Arecibo radio telescope that could pick up L = 6.76 × 1043 1.4 GHz 2Jy the intermittent radio transients from FRB 121102 (Lu   2 & Kumar 2016; Spitler et al. 2016). D − × L erg s 1, (4) On the other hand, for the currently available FRB 10 Gpc sample, Palaniswamy and Zhang (2017) studied the dis- where DL is the luminosity distance corresponding to tribution of ratios of adjacent peak flux densities and the the cosmological parameters m = 0.27,  = 0.73 time intervals between corresponding successive bursts and H0 = 68 km/s/Mpc. Given millisecond duration, and concluded that either the repeater belongs to a dis- equation (4) implies that FRBs radiate energy ∼1038 − tinct class or that all FRBs physically originate from a 1041 erg in radio, about 12 orders of magnitude less common progenitor system with FRB 121102, however, compared to the total energy released in most stellar being extra-active. Espousing their latter conclusion, we core collapse events. attempt here to reconcile the catastrophic model involv- Falcke and Rezzolla (2014) have shown that it is ing magnetar collapse with the observed repeater. For possible to obtain the required radio luminosity (equa- this purpose, we explore two distinct scenarios – one tion (4)) from curvature radiation in the magnetosphere that involves Blandford–Zjanek process and the other, wherein bunched charge particles, ∼Nbunch in number, related to compact stars made of . flow out coherently with a net velocity along smoothly bent (radius of curvature RB) magnetic field lines emit- ting energy at a rate given by 2.1 Collapse to a Kerr BH and Blandford–Zjanek process γ 4 2 2 2 Nbunche c Lcurv = (5) 3R2 Suppose, apart from a co-rotating magnetosphere within B  2 the light-cylinder, the magnetar that imploded to give Nbunch ≈ 2 × 1043 rise to the repeating FRB is surrounded by magnetized 2 × 1028     plasma. After losing the CS, this spun down magnetar 4 −2 γ RB − collapsed into a Kerr BH. Since FRB 121102 lies close × erg s 1 (6) 102 30 km to a weak AGN in a dwarf galaxy (Chatterjee et al. 2017; Marcote et al. 2017; Tendulkar et al. 2017), one at a characteristic radio frequency, may argue that the episodic AGN wind triggers spo-    − 3γ 3c γ 3 R 1 radic of the magnetized matter present outside ν = ≈ 2.4 B GHz, (7) curv 4π R 102 30 km its EH. Because of the Blandford–Znajek mechanism B (BZM) this leads to an unsteady bipolar jet emanating where γ is the Lorentz factor of the charge particles. from FRB 121102 (Blandford & Znajek 1977). The magnetic field lines that were originally anchored As the jet drills through the ambient plasma, it can to the NS matter are expected to last only for ∼ few cause shocked shells to develop and, as discussed by milliseconds, the time scale over which the magnetar Waxman (2017) recently (in the context of AGN itself collapses to acquire a newly formed (EH). driving the shocked shells in the dwarf galaxy), it can But this scenario, as it stands, obviously cannot explain entail emission of coherent radiation at GHz frequency recurring radio transients detected from FRB 121102. by virtue of a synchrotron maser action, provided that It has been discovered recently that FRB 121102 is the number density of electrons in the shocked plasma, =∼ . located in a dwarf galaxy at z 0 193 that also con- as a function of the Lorentz factor γe, increases faster γ 3 tains a compact radio-source (Chatterjee et al. 2017; than e . Tendulkar et al. 2017). This persistent radio-source is In what follows, we make quick estimates of jet relatively weaker with Sν ∼ 200 μJy while the flux energy resulting from the BZM. The rotating EH of densities at 1.7 GHz from FRB 121102, on different a Kerr BH embedded in a plasma threaded with B is, occasions, vary from ∼ 0.1Jyto∼ 4 Jy. The compact in many ways, analogous to a rotating conducting shell radio-source and the FRB are separated by a projected in an external magnetic field (Hartle 2003). Hence, the distance less than ∼40 pc (Marcote et al. 2017). potential difference generated due to changing magnetic The question whether the only known repeating radio flux is given by burst belongs to an altogether different class of FRBs has also been addressed in the literature. Some advo- 1   V ∼ ( /2π) B · π R2 , (8) cate that all FRBs are repeaters and it is just the higher el c H BH 14 Page 4 of 9 J. Astrophys. Astr. (2018) 39:14 where  = J is the angular speed of the EH. 2.2 Formation of a from the magnetar H MRs RBH The EH radius of the Kerr BH is collapse      R R 2 J 2 R = s + s − , (9) It is evident from equation (9) that the angular momen- BH 2 2 2 Mc tum of the BH cannot exceed cMRs/2 = GM /c. In that case, what happens if the core of the magne- where R ≡ 2GM, J and M is mass of the BH remnant. s c2 tar which collapses has angular momentum too large to The ensuing jet power due to mining of BH rotational form a BH? energy via BZM is given by (Hartle 2003) Suppose, the initial angular momentum of the supra- 2 2 ∼ 2 Vel cVel massive magnetar is J0 M0 R0 0, with an initial L B−Z ≈ current × Vel ∼ ∼ . (10) R 4  < ≡ GM0 angular speed 0 Break−up 3 so that the R0 For extremal BHs, J = cMRs/2 ⇒ RBH = Rs/2and c magnetar does not get torn apart due to centrifugal force. H = ⇒ Vel ∼ Rs B/8, so that Rs As the magnetar spins down due to magnetic braking, 2 2 cB Rs it starts contracting so that at any instant of time t, L − ≈ (11) 2 B Z M0 R (t)(t) ∼ β J0, assuming that there is no mass 256     2 2 loss during the process. (The factor β  1 has been B M − = 5.45 × 1043 erg s 1. included because a small fraction of the initial angular 12 . 10 G 2 3M momentum gets carried away by the magnetic dipole (12) radiation.) From the above equation, it is evident that if the syn- As the magnetic braking proceeds, the equatorial chrotron maser, driven by the jet-induced shocked shells region separates from the rest of the contracting mag- (Waxman 2017), radiates at a rate that is ∼0.1 frac- netar, forming a disc-like structure because of the tion of the jet luminosity, one can explain the recurring centrifugal force being larger there, while the central = − radio-transients. core of mass Mc M0 Mdisc and angular momentum = β − However, few caveats are in order: Jc J0 Jdisc collapses gravitationally. Taking the disc to be sufficiently√ thin so that angular momentum (a) Equation (12) requires B ∼ 1012 G to be present per unit mass is GMcr (assuming local orbital speed near the EH of the BH remnant. When a magnetar with to be Keplerian), one obtains field B ∼1014–1015 G collapses to form a BH, can an ambient plasma threaded with magnetic field rD  12 ∼10 G be maintained near the EH? (In the context of Jdisc = GMcr (r) 2πrdr (14) GRB modeling, Contopoulos et al. (2017) found that Rc r  B ∼ 104 G can hover near the horizon.) D ≈ 4πρdisch GMcrrdr, (15) (b) Accretion of plasma by itself cannot generate such Rc high B since the Eddington limit for the magnetic field is where we have assumed that the disc density ρdisc(r)  and the disc thickness h(r) do not vary appreciably 8πc4m between the size Rc of the core and the outer disc radius = p ∼ × 8 ( / . )−1/2 . BEdd = 2 10 M 2 3M G rD. σTGM One can estimate the outer radius rD of the disc by (13) assuming that it is the equatorial radius of the contract- The required high B could also arise from a magne- ing magnetar when the equatorial centrifugal force just tized nebula around the magnetar that collapsed to form crossed the gravitational force so that  = GM0 . r3 the Kerr BH. For instance, a wind nebula has been dis- D covered near the magnetar Swift J 1834.9-0846 (Younes Therefore, et al. 2016; Granot et al. 2016). We now move on to another scenario that is relevant  β2 J 2 when the magnetar is much more massive and, there- = β = 2  = ⇒ = 0 . J J0 M0rD M0 GM0rD rD 3 fore, has to rotate faster in order to garner the required GM0 CS. (16) J. Astrophys. Astr. (2018) 39:14 Page 5 of 9 14

≈ π ρ( 2 − 2) Since Mdisc h rD Rc , it can be easily shown Equation (21) has been used to obtain the value for Rc, from equation (15)that and rD = 15 km has been assumed (this is the radius of a . 8  NS of mass 2 3M). One may note that this lower limit Jdisc = M0(1 − Mc/M0) GMcrD on the initial angular speed does not violate the initial 5   = . − ( / )5/2 stability criteria since for M0 2 3M, one can still × 1 Rc rD . (17) × 3 −1 < < ∼ GM0 = 1 − (R /r )2 have 5 10 rad s 0 Break-up 3 c D rD From the extremal BH criteria that follows from equa- 9.5 × 103 rad s−1. So, in this alternate scenario, for 2 = β − > GMc FRB 121102, a supra-massive magnetar spinning very tion (9), no BH is formed if Jc J0 Jdisc c . Then, making use of equations (16)and(17), the con- rapidly could have collapsed into a rotating SS. dition for no BH formation can be expressed as Since the inside the SS are held together by strong forces, the electrons due to their mutual elec- GM2 8  β J > c + M (1 − M /M ) GM r trostatic repulsion (and no strong interactions) migrate 0 c 5 0 c 0 c D  /  radially outwards, distributing themselves above the 1 − (R /r )5 2 ∼ × c D (18) quark matter surface within a height of few 100 fm. − ( / )2 1 Rc rD  This results in a strong radially outwards electric field | |≈ × 17− 18 2 E 5 10 10 V/cm that keeps this thin layer GMc 8 Mc = + β J0(1 − Mc/M0) of electrons bound to the SS (Alcock et al. 1986). c 5 M0   One can readily estimate the number of electrons Ne − ( / )5/2 in the layer above the SS using Gauss law: × 1 Rc rD 2 (19) 1 − (Rc/rD)    π | | 2/3 4  2 ∼ 36 E M so that one arrives at Ne = |E|R = 7 × 10 . e 1018 V/cm M GM2 J > c 0 −( / )5/2 (23) β − 8 ( − / )( / )1/2 1 Rc rD c 1 1 Mc M0 Mc M0 2 5 1−(Rc/rD) (20) Equation (21) has been made use of in the above equa- tion. as a condition for no BH formation. As FRB 121102 lies close to a persistent radio- What is the fate of such a spinning and collapsing source, sporadic flaring up of the AGN can drive a core? As it contracts, its density rises and when the den- e± wind that triggers various oscillatory modes of the ∼( − )× 14 −3 sity overshoots 5 7 10 gm cm ,itturnsintoa electron layer of the SS. We make simple estimates to strange star (SS), composed roughly of equal number of arrive at the power radiated due to dipole oscillation. u, d, s quarks and a small fraction of electrons, to main- If Ndp denotes the effective number of electrons that tain charge neutrality (Itoh 1970; Witten 1984; Alcock participate in dipole oscillation stimulated by the AGN et al. 1986). During the collapse, a burst of thermal pho- wind, the induced electric dipole moment is de(t) ∼ tons and neutrinos with average energy of ∼ few MeV is eNdp(R + δZ(t)) (for simplicity, one has assumed a emitted from the SS. As long as the total baryon number z-direction deformation of the electron layer). Then is 100, this is more stable compared to ˙ ˙ ¨ ¨ the standard hadronic matter. de ∼ eNdpδZ ⇒ de ∼ eNdpδZ ∝ 3   The mass–radius relation for SSs goes as M R so  2  e|E| e Ndp|E| that (Xu 2005) = eNdp = (24)   / me me M 1 3 R =∼ 10 km. (21) | ¨ |2 M so that the luminosity 2 de due to dipole radiation is 3c3 This may be contrasted with that of the NS case (Lat- given by timer & Schutz 2005),   4 2  2 1/4 2e N |E| ∼ M L ≈ dp R = 15 km. (22) dip 3m2c3 2.3 M e     N 2 | | 2 As an illustration, if one substitutes in equation (20), = × 43 dp E −1. 4 10 14 18 erg s β = 0.8, M0 = 2.3M and Mc = 1.4M, one finds 10 10 V/cm 3 −1 0 > 5 × 10 rad s in order that no BH is formed. (25) 14 Page 6 of 9 J. Astrophys. Astr. (2018) 39:14

Hence, only a minuscule fraction of the total number of electrons Ne (equation (23)) needs to participate in the dipole oscillation to generate the required power. Using detailed calculations, Mannarelli et al. (2014)showed that torsional oscillation of the thin electron layer rel- ative to the positively charged SS can cause emission of GHz radio waves with luminosity as high as ∼1045 erg/s. If FRB 121102 is indeed associated with a rapidly spinning SS, then due to r-mode instability one would expect the repeater to also be a persistent source of grav- itational waves (Andersson et al. 2002).

3. GRBs and FRBs: Common progenitor systems? Figure 1. Plot of fluence F against number of FRBs with fluence greater than equal to F for 24 FRBs. Flattening of It is well established that long duration GRBs (T90 > 2 the counts at fainter fluence is clearly observed. A linear fit s) are associated with type Ib/c supernovae and thus, to the plot has also been shown. are likely to be the byproduct of collapsing Wolf– Rayet stars (for recent reviews, see Granot et al. 2015; Kumar & Zhang 2015). Prompt γ -emission ensues from 3.5 internal shocks in colliding shells ejected from a cen- 3 tral engine along narrow jets with opening solid angle  ∼ θ ∼ . 0.01 str (i.e. jet 0 1 radian). The observed ] 2.5 afterglows reveal interesting interplay of relativistic 1.5 shocks and radiative processes (Resmi & Bhattacharya 2 2008). The hard X-ray polarimetry of AstroSat has recently succeeded in detecting prompt emission polar- log[N(>F)F 1.5 ization in the case of GRB 151006A, even though it is 1 a faint burst lasting for ∼20 s (Rao et al. 2016). The short GRBs (T90 < 2 s), on the other hand, con- 0.5 stitute only ∼30% of the total GRB population and are -0.5 0 0.5 1 1.5 2 2.5 log(F) plausibly the aftermath of a final merger of the binary NSs. However, a common progenitor model for short Figure 2. FRB number counts illustrating the marked and long GRBs based on jet opening solid angles in the departure from a hypothetical non-evolving distribution in ratio ∼3 : 7 was speculated upon (Das Gupta 2004). an Euclidean universe. The sub-pulses of short GRBs show distinct statistical correlations with other observed parameters (Bhat et al. 2000; Das Gupta 2000; Gupta et al. 2000a,b). is clearly discernible (Figures 1 and 2). It is to be noted It is interesting to note the similarity between the that N(>F) − F for GRBs too show similar features SN Ib/c rate ∼6 × 104 Gpc−3yr−1 (Frail et al. 2001) (e.g. Petrosian and Lee 1996). The extent of evolution and the FRB rate ∼104−105 Gpc−3yr−1 which follows exhibited by the FRB population can be determined later from the all-sky rate ∼2100 day−1 for FRBs brighter when many more FRBs are detected in the future. than ∼2Jy(Champion et al. 2016). While SN Ib/c rate Motivated by the remarkable similarity in the FRB and FRB rate are of comparable magnitude, long GRB and SN Ib/c rates, we briefly explore a scenario in rate has been estimated to be ∼ 102−103 Gpc−3yr−1 which all FRBs and a majority of long GRBs are asso- (i.e. ∼10−3−10−2 times the FRB rate). ciated with the collapse of the central iron core of WR In an Euclidean universe, the number of FRBs with stars. FRB 121102 too lies inside a low- fluence exceeding F is expected to be ∝ F−3/2 if the dwarf galaxy and such tend to host hydrogen- FRBs are distributed uniformly in space. For 24 FRBs deficient, high luminosity supernovae and long GRBs belonging to the Swinburne pulsar group catalog (Petrof (Lunnan et al. 2014; Scholz et al. 2017). On the other et al. 2016), if one performs a simple N(>F) − F hand, in the context of FRB–GRB connection, Zhang test, then flattening of FRB counts at the fainter end (2013) proposed that a large fraction of GRBs would J. Astrophys. Astr. (2018) 39:14 Page 7 of 9 14 lead to FRBs after 102−104 s, and as a consequence, velocities have been observed. For instance, the kick some FRBs would be physically associated with GRBs. velocity component perpendicular to the line-of-sight Swift/XRT observations have revealed X-ray plateau of the magnetar Swift J 1834.9-0846 is ∼580 km/s pro- followed by a steep decay in many long GRBs that could vided it is at a distance of ∼15 kpc (Younes et al. 2016; naturally be explained by magnetic braking of a rapidly Granot et al. 2016). spinning magnetar (Metzger et al. 2011; Granot et al. In other words, the SPNS could lead to a GRB with a −3 2015). Adopting this basic picture for long GRBs, we probability of ∼10 , assuming that θF ∼ 0.1 rad (equa- posit that FRBs and long GRBs result from the collapse tion (26)), if its kick velocity is more or less aligned of massive (35M), rotating WR stars. The unstable or anti-aligned with the rotation axis of the progenitor Fe core of such a rotating He star, having mass ∼2 − star. In all other situations, the compact remnant will 3M and initial size of ∼108 cm, would undergo free be hindered by the stellar matter before the emergence fall on a time scale of ∼1 s, giving rise to a rapidly of the ν −¯ν wind. The spinning magnetar would con- spinning supra-massive proto-neutron star (SPNS) that tinue to accrete matter as it crosses the He envelope moves with a velocity vkick ranging from 0 to ∼1000 until the supernova explosion occurs. Eventually, the km/s with respect to the progenitor star because of a supra-massive magnetar would collapse after it loses the pre-natal kick. The SPNS would then cool and contract CS, giving rise to a burst of radio emission due to the to form a spinning supra-massive NS/magnetar in ∼5− physical processes taking place in the temporary mag- 10 s. netosphere outside the EH. In this scenario, one would Due to rapid rotation and the sudden collapse of the expect emission of gravitational waves with frequency core, two narrow funnel-shaped regions oriented along in the ∼kHz band and, possibly of neutrinos with energy the stellar spin axis, pointing away from each other ∼ few MeV, twice – first, during the SN Ib/c event and and straddling across a near spherical cocoon of size second time, when the magnetar thereafter collapses to ∼108 cm surrounding the SPNS, are created (Meszaros form a BH. A detailed study on this subject is under & Rees 2001). These regions are essentially devoid of progress. stellar (baryonic) matter. If the direction of vkick lies within the funnel-shaped regions, the impellent gamma ray jet ensuing later from the magnetar would not face 4. Conclusion any baryon loading problem, thereby could break out of the He envelope and giving rise to a long GRB. It is to Implosion of spun down supra-massive NSs can natu- be noted that WR stars are relatively small helium stars rally lead to FRBs. In this paper, we have shown that it is with size ∼ few × 1010 cm, as they have already blown possible to explain recurring bursts from FRB 121102 their upper H layer away. by invoking either sporadic Blandford–Znajek process If the opening angle θF of the funnel-shaped regions occurring near a Kerr black hole or torsional oscillations of the WR star is also ∼0.1 rad corresponding to a solid of electrons close to the surface of a strange star, both angle F ∼ 0.01 str, then the probability that the triggered by AGN wind from the weak radio-source prompt gamma rays are not quenched due to baryon co-located in the dwarf galaxy. If the observed radio loading is transients are attributed to electronic oscillations of the  rotating strange star, one would expect to detect persis- ≈ F ≈ × −3 tent gravitational waves from the compact remnant due 2 π 5 10 (26) 4 to its r-mode instability. which is consistent with the long GRB rate being Since the FRB and the SN Ib/c rates are almost equal, ∼10−3–10−2 times the FRB rate. it is plausible that the collapsing iron core of a WR If the SPNS moves in any other direction it would star gives rise to a moving supra-massive magnetar (due encounter stellar material after traversing the cocoon, to an imparted pre-natal kick) whose implosion shows and due to baryon loading the γ -rays resulting from up as a FRB in most cases and, in those rare situa- electron–positron pairs generated by the neutrino wind tions, when its kick velocity is nearly either aligned would get degraded to softer photons and so, there or anti-aligned with the rotation axis of the star, the wouldbenopromptγ -emission. Even with a low kick spinning down magnetar launches prompt emission of velocity, vkick ∼ 100 km/s, the SPNS would cross the γ -ray bursts before it implodes. If this picture is right, baryon evacuated cocoon of size ∼1000 km in ∼10 one would expect to see emission of observable gravi- s, well before the compact remnant becomes transpar- tational waves and of neutrinos, first during the SN Ib/c ent to the neutrinos. In fact, magnetars with high kick event and also later, during the radio burst. 14 Page 8 of 9 J. Astrophys. Astr. (2018) 39:14

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