Collisions of Neutron Stars with Primordial Black Holes As Fast Radio Bursts Engines

Draft version October 5, 2018 Typeset using LATEX twocolumn style in AASTeX61

COLLISIONS OF NEUTRON STARS WITH PRIMORDIAL BLACK HOLES AS FAST RADIO BURSTS ENGINES

Marek A. Abramowicz,1, 2, 3 Micha lBejger,4, 2 and Maciek Wielgus5

1Physics Department, University of Gothenburg, 412-96 Göteborg, Sweden 2Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland 3Physics Department, Silesian University of Opava, Czech Republic 4APC, AstroParticule et Cosmologie, UniversitéParis Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cité, F-75205 Paris Cedex 13, France 5Black Hole Initiative, Harvard University, 20 Garden Street, Cambridge, MA 02138, USA

ABSTRACT 25 17 If primordial black holes with masses of 10 g & m & 10 g constitute a non-negligible fraction of the galactic dark- matter haloes, their existence should have observable consequences: they necessarily collide with galactic neutron stars, nest in their centers and accrete the dense matter, eventually converting them to neutron-star mass black holes while releasing the neutron-star magnetic ﬁeld energy. Such processes may explain the fast radio bursts phenomenology, 43 in particular their millisecond durations, large luminosities ∼10 erg/s, high rate of occurrence & 1000/day, as well as high brightness temperatures, polarized emission and Faraday rotation. Longer than the dynamical timescale of the Bondi-like accretion for light primordial black holes allows for the repeating fast radio bursts. This explanation follows naturally from (assumed) existence of the dark matter primordial black holes and requires no additional unusual phenomena, in particular no unacceptably large magnetic ﬁelds of neutron stars. In our model, the observed rate of fast radio bursts throughout the Universe follows from the presently known number of neutron stars in the Galaxy.

Keywords: fast radio bursts — black holes, primordial — neutron stars arXiv:1704.05931v3 [astro-ph.HE] 3 Oct 2018

Corresponding author: Micha lBejger [email protected] [email protected] [email protected] 2 Abramowicz, Bejger and Wielgus

1. INTRODUCTION cretes its material. This causes a NS to turn into a light, Fast Radio Bursts (FRB) are one of the most am- ∼1.5M BH, in accretion timescales depending on the biguous astronomical phenomena. The first FRB was initial PBH mass. Magnetic energy released during this discovered in archived data taken in 2001 by the Parkes process powers the FBR event. radio telescope as a 30 Jy, heavily dispersed burst of 5 2. FRB OCCURRENCE RATE ms duration with no clear connection to a host galaxy In the following we will discuss the rate of the FRB (Lorimer et al. 2007). To date, a few tens of FRB were events, using simple order-of-magnitude estimations, detected (for the up-to-date reference, see the Swin- and the numerical simulations of the PBH halo inter- burne Pulsar Group FRB catalogue, Petroff et al. 2016). acting with a typical spiral galaxy. So far a multitude of models was proposed to explain the FRB, ranging from the cataclysmic events involving 2.1. Analytic estimate mergers of neutron stars (NS) with other NS or black We argue that collisions of hypothetical PBH in the holes (BH), magnetized NS collapses, NS-quakes, active mass range galactic nuclei, accretion processes in the vicinity of BH, 1017 g < m < 1025 g (1) to soft gamma repeaters and processes occurring in pul- with NS may explain the FRB phenomenology. This sars’ magnetospheres (see Katz 2018 for a recent review mass range is currently weakly explored by the astro- regarding the proposed FRB models and caveats). nomical observations (Carr et al. 2016), in principle al- From an observational point of view, FRB are char- lowing for the PBH to constitute a fraction of the galac- acterized by millisecond durations, large radio luminosi- tic dark matter. We will adopt the values of m from this ties, high occurrence rates, and large dispersion mea- mass range and to show that they are consistent with sures suggesting their extragalactic origin, with dis- the results obtained. In the description of our model tances of the order of a Gpc. Their extremely high below, we will adopt a “reference” PBH mass from the brightness temperatures suggest the presence of plasma unconstrained range of masses, and/or magnetic fields (Katz 2014). In at least one 23 FRB source the event is (non-periodically) repeated m0 = 10 g, (2) (FRB 121102, Spitler et al. 2016), and another one in order to be numerically specific. (FRB 121002, Champion et al. 2016) shows a clear two- Abramowicz et al.(2009) calculated the number of component peak profile. For FRB121102, recent obser- the PBH-NS collisions that occur in one day in a single vations show that pulse of radio waves passes through galaxy (see their Table 3) and found that the number a veil of magnetized plasma (Michilli et al. 2018), re- scales inversely with the PBH mass: sulting in detectable Faraday rotation. Currently, the −1 main difficulty in selecting the ‘true’ FRB model lies in m n˙ ∼ 10−8 1/day. (3) the ambiguity of the available scant data, and in the m0 problem of reconciliation the singular nature of the vast The repeating FRB 121102 (Spitler et al. 2016) observed majority of the FRB with the repeating FRB121102. by the Arecibo telescope has been identified with the To us, the above feature list suggest a NS origin of the host galaxy at z = 0.193 (' 1 Gpc distance). According FRB engine. In the three following Sections, we show to the FRB catalogue (Petroff et al. 2016), a number of that the most puzzling FRB features, namely FRB detected by the Parkes telescope have the disper- 3 sion measure several times higher than the FRB 121102, • FRB occurrence rate,n ˙ obs∼10 1/day (Sect.2), which suggests they are located at at least a few Gpc • FRB luminosities, L ∼1043 erg/s (Sect.3) obs distances. Here we assume the FRB are detected from −3 • FRB duration times, δtobs∼10 s (Sect.4), a large fraction of all the galaxies in the observable Uni- 11 • FRB repeaters (Sect.3 and5), verse N ' 10 . One should multiply the Eq.3 by N to get an estimate of the rate of the FRB detections, may be naturally explained by adopting one single as- −1 3 m sumption: that the FRB phenomenon is due to collisions n˙ model ∼ 10 1/day. (4) of NS with primordial black holes (PBH) that are one m0 of the constituents of the galactic dark matter haloes. This value agrees with that estimated from observations Specifically, we show that during a PBH-NS collision, (Champion et al. 2016; Caleb et al. 2017). In the next the PBH kinetic energy is dissipated via the gravita- section we show that the occurrence rate ∼103 1/day tional drag. This energy loss bounds the PBH to NS. is consistent with the observed number of NS in the Eventually, the PBH settles at the NS center and ac- Galaxy. Collisions of NS with PBH as FRB engines 3

distribution. Light BH result from the NS-PBH colli- R b sions and stellar BH are the outcome of the standard

Hd stellar evolution. Evolution of the number densities ni of the four species result from interactions between them which is described by collision and creation coeﬃcients, Cij [pc3/y] and Ki [pc−3 y−1], respectively. If mass of i-th R d element dominates over mass of j-th element, we assume a rate of collisions between species i and j to be: Figure 1. The galaxy model: galactic disk thickness Hd = 1.0 kpc, galactic disk radius Rd = 30 kpc, radius of the 2 ij Vi 2 spherical galactic bulge Rb = 5.0 kpc. C n n = n n R , (8) i j i j V (r) i

2.2. Numerical simulations V (r) is the rotational velocity given by Eq.5, Vi is the The approximated shape of a galaxy is parametrized escape velocity characteristic to the i-th species, with 3 numbers, for which we assume following values: r 2GMi For the rotation of the galaxy we adopt a simplified ro- Vi ≡ v∗ = , (9) R tational curve: i  which in case of BH species leads to VP = V0 = V1 = v = 220 km/s, for r > R , c. Creation operators aim at capturing the rate of NS V (r) = d b (5) vd and BH creation in standard stellar evolution processes.  r km/s, for r ≤ Rb, Rb Therefore, we assume a total creation rate for the whole i which allows to calculate the total mass density from galaxy, Ktot, and weight it with a total local density GM(r)/r2 = V 2(r)/r, where M(r) is the mass within ρ(r), the radius r. The density ρ(r) within the radius r is Ki Ki(r) = tot ρ(r), (10) Mtot  2 vd  2 , for r > Rb, where M is a total mass of the galaxy, Eq.7. As- ρ(r) = 4πGr (6) tot 3v2 N 1 −1 d sumed total creation rates are Ktot = Ktot = 0.01 y ,  4πGR2 , for r ≤ Rb. b reflecting the average supernova rate in typical galaxy. Total density remains unchanged during the simulation From this considerations it follows that the evolution of and mass of the galaxy is found by integration, the four species number densities are given by a following set of differential equations: 2 vd Hd Rd 10 Mtot = Rb + ln ∼ 7 × 10 M . (7) ∂n G 2 Rb N = − CNP n n − CNN n n − CN0n n (11) ∂t N P N N N 0 In the model we consider evolution of four classes of N1 N − C nN n1 + K , astrophysical species, listed in the Table1. ∂n P = − CNP n n − CP 0n n − CP 1n n (12) ∂t N P P 0 P 0 (Index) Name Mass Ri/RG,i Number − CPP n n , Mi ratio density ni P P ∂n0 (N) NS MN = 1.5M 2.5 nN = CNP n n − C00n n − C01n n , (13) ∂t N P 0 0 0 1 (P) PBH hMP i = m 1 nP ∂n1 NN 1 = C nN nN + K . (14) (0) Light BH M0 = 1.5M 1 n0 ∂t

(1) Stellar BH M1 = 10M 1 n1

Table 1. Main parameters of the astrophysical species Both collision and creation coeﬃcients depend on the adopted in the analysis: their masses M , radii R and num- i i location within a galaxy. Hence, we solve the Eqs. 12- ber densities ni. The gravitational radius for each species is 14 separately in multiple zones, characterized by their denoted by RG,i. speciﬁc rotational velocity V (r) and density ρ(r). For the computational reasons we divide galactic disk into 2 Here RG,i = 2GMi/c is the gravitational radius of 50 cylindrical zones, in which ρ and V were assumed to a species with the index i and the mass Mi. The pa- be constant. Similarly, bulge region was divided into 50 rameter m represents the mean value of the PBH mass spherical zones. 4 Abramowicz, Bejger and Wielgus

In the simulation we fix the PBH mass MP = m. 4 N Nevertheless, for the presented system of equations, as 10 Ktot long as MP MN , this is tantamount to having a distribution of PBH masses, with expected value m. The 10 6 equations are independent of the higher moments of the PBH mass distribution. The simulations were initial- 10 8 ized with nN (0) = n0(0) = n1(0) = 0. Initial number density of PBH is zone-dependent, 10 10 = 0.01 ρ(r) = 0.10 nP (t = 0, r) = ξ , (15) galaxy FRB frequency [1/d] m = 1.00 10 12 where ξ represents the ratio between PBH mass density 1017 1018 1019 1020 1021 1022 1023 1024 1025 and total gravitating density in the galaxy. Equations mean mass of PBH [g] 10 are then integrated for Ttot = 1.3 × 10 y in parallel for all zones. Finally, a current total rate of FRB events in Figure 2. Galactic rates of FRB (NS-PBH interactions) as function of mean PBH mass for three values of the ratio a galaxy can be calculated by multiplying expressions between PBH mass density and total gravitating density in NP C nN (Ttot)nP (Ttot) times the respective zone volume the galaxy ξ = 1.0, 0.1, 0.01. Obtained with the numerical and summing it up over all zones. Results are shown in simulation (continuous lines) and with Eq.3 (dashed line). Fig.2 as function of m. We have evaluated models with Gray horizontal line denotes the frequency of 10−8 1/day, three values of ξ: 1.0, 0.1, 0.01. Note that the value of necessary to explain the FRB occurrence rate. ξ = 1.0 is used here for comparison. We do not a priori assume that PBHs are the dominant ingredient of DM, 10 4 but that PBHs may constitute a small fraction of DM. bulge, m = 1e23 g 5 For larger ξ results are consistent with a simple estima- 10 disk, m = 1e23 g bulge, m = 1e18 g tion given by Eq.3 for m > 1020 g. Models with lower ξ 10 6 disk, m = 1e18 g predicts lower FRB frequency for the same mean PBH 10 7 mass. For m < 1020 g numerical models qualitatively 10 8 deviate from Eq.3. In this regime a large number density of light PBH is limiting the total number of NS. In 10 9 the low m limit rate of FRB asymptotically reaches the 10 10 N NS creation rate Ktot, indicating equilibrium between 10 11 number of NS created and destroyed in a unit time. NS-PBH colision events per day 10 12 Parameters such as geometry of a model galaxy were 10 2 10 1 100 101 found to have a limited influence on the results and may time [Gy] modify the galactic FRB frequency only by a factor of order of unity. Figure 3. Number of NS-PBH collisions in a galactic bulge and disk for different mean PBH masses and ξ = 0.1, as Pani & Loeb(2014) discusses constraints on the PBH function of the age of a galaxy. fraction in dark matter in the relevant mass range, suggesting that ξ of at most few percent should be adopted (see also Carr et al. 2016 for similar conclusions). In our the age of a galaxy. Our simulation shows that the num- model this corresponds to a shift in mean PBH mass, ber of NS in the bulge saturates with time because NS necessary to explain the FRB occurrence rate, from are destroyed by numerous PBH. Indeed, in Eq. 14 the about 1023 g for ξ = 1.00 to about 1021 g for ξ = 0.01, dominant terms are the first one (local rate of NS-PBH still within the acceptable mass range. Figure3 shows collisions) and the last one (local NS creation rate). As the number of NS-PBH collisions in a galactic bulge and first one grows with NS local number density nN , and disk for different mean PBH masses and selected value the latter is modeled as time-independent, Eq. 10, the of ξ = 0.1, as function of the age of a galaxy. In general, saturation of NS number may be reached on a relevant N N there is far more PBH-NS collisions in the bulge than in timescale with nN ∝ K /np ∝ K m. This also means the disk. However, for small values of m the number of that if m is small, then with increasing cosmological collisions in the bulge saturates after ∼10 Gy. Therefore, time, the total number of NS in the disk surpasses the this general trend reverses for small m. Figure4 shows NS number in the bulge. the total number of NS in a galactic bulge and disk for different mean PBH masses and ξ = 0.1, as function of 3. FRB LUMINOSITIES Collisions of NS with PBH as FRB engines 5

1e13 bulge, m = 1e23 g 108 m = 1e23 g disk, m = 1e23 g 3 m = 2e23 g bulge, m = 1e18 g disk, m = 1e18 g 2 107

1 106 0 distance [cm]

total number of NS 105 1

2 104 2 1 0 1 10 10 10 10 0 200 400 600 800 time [Gy] time [days]

Figure 4. Total number of NS in a galactic bulge and disk Figure 5. Examples of PBH trajectories in NS gravitational for diﬀerent mean PBH masses and ξ = 0.1, as function of ﬁeld after the initial interaction. Each pass through NS re- the age of a galaxy. duces PBH’s kinetic energy by E∗, Eq. 16.

In our model, the energetics of an individual FRB is After loosing energy E∗ a PBH will have, typically, in- quite universal, in the sense that the energy output and sufficient kinetic energy to escape to infinity after pass- the duration of the event follow from the typical param- ing through the NS: it will turn at the “escape radius” eters of the NS. r0 and collide with the NS again. From the equation of energy conservation, 3.1. Energetics of the PBH passage through a NS GMm − + E∗ = 0, (17) Close gravitational encounters of PBH and NS, their r0 capturing and orbital energy loss via e.g., the tidal inter- and, from Eqs. 16-17, we derive for the escape radius, action were extensively studied by Capela et al.(2013); 13 m0 Defillon et al.(2014); Kouvaris & Tinyakov(2014); Pani r0 ≈ 10 cm. (18) & Loeb(2014). To make our case here, we provide sim- m pler arguments to show that once a PBH interacts suf- The gradual loss of PBH’s kinetic energy as it nests in- ficiently closely with the NS, fate of the latter is de- side a NS is illustrated in Fig.5. termined. Let us assume that a PBH directly collides “Magnetic drag” extorted on a PBH during its passage with the NS (Abramowicz et al. 2009). The PBH-NS through NS is irrelevant even in the case of B ∼1015 G. collisions occur with velocity which at the NS surface is Motion of a BH in an external magnetic field was stud- equal, or (slightly) higher than the NS escape velocity ied by many authors, including Wald(1974), and more (Eq.9). recently Morozova et al.(2014). From this recent study During the passage through the NS, a PBH does not we adopt their Eqs. (74–76) relevant to our model. It interact directly with the NS matter, in particular it describes the PBH kinetic energy losses due to its inter- does not accrete. The strongest interaction is only in- action with the NS magnetic field, direct – via gravitational drag. When the PBH passes m 2 B 2 through the dense matter gas, gravity transfers momen- L ≈ 1030 erg/s, (19) tum to nuclei nearby. This focuses matter behind the m0 B0 PBH and creates a wake that gives rise to a force acting 15 with B0 = 10 G. This is far too small to be relevant for on the PBH and causes a decrease in its kinetic energy, the FRB energetics for realistic internal magnetic fields Ekin. A relevant case (i.e. when the PBH velocity is of NS. highly supersonic) was studied by Ruderman & Spiegel If the PBH is spinning (a = dimensionless spin) and (1971), Ostriker(1999) and more recently by Capela et the NS possesses a substantial magnetic field in its inte- al.(2013). Abramowicz et al.(2009) employed these sort rior, then one expects that the Blandford-Znajek mech- of studies to calculate the kinetic energy losses when the anism (Blandford & Znajek 1977) will give the following PBH moves through an NS (see their Table 3), power:

2 2 2 35 m BZ 29 2 m B E∗ = 3 × 10 erg. (16) L ∼ 10 a erg/s, (20) m0 m0 B0 6 Abramowicz, Bejger and Wielgus see e.g., Lee et al.(2000) (their Eq. D.29). This is again energy for multiple 1040 erg bursts (1043 erg/s and a far too small to be relevant for the FRB energetics. millisecond duration): 2 3.2. Energy reservoir for the burst B 4 3 41 EB = πR ' 10 erg. (23) From Eq. 18 it follows that lighter PBH with masses 8π 3 m < 1018 g have a chance to fly away for more than Note again that our model does not necessarily require about 1 pc, i.e., a typical distance between stars in extremely large (i.e. magnetar size, B ∼1015 G) mag- a galaxy. All other PBH return, collide again, subse- netic fields. Magnetic fields play a role only in the emis- quently settle at the NS center and start to accrete the sion of radio waves. dense NS matter. The timescale of Bondi-like accretion onto a PBH and creation of a NS-mass BH was 3.4. Repeating nature of FRB121102 estimated in several works, e.g., Giddings & Mangano From the timescales estimated above, it is likely that (2008) and Fuller et al.(2017): for large enough MP most of the FRB are observed pro- ducing one, final burst. However, for a small-mass PBH, dMP (t) 2 2 ∼ AG MP (t)ρc, (21) the accretion may take much longer time (of the order dt 20 of years or more, for MP < 10 g). A long-lasting where A is a constant of the order of 10, depending on accretion scenario creates a tantalizing opportunity to the details of the equation of state of dense matter. For explain the repeating FRB - as the gradual accretion 15 3 a central density of the order of ρc = 10 g/cm , cor- takes place in the superfluid, magnetized interior of the responding to NS of mass MN = 1.5 M , the NS→BH NS (see e.g., Glampedakis et al. 2011), occasional re- conversion time is connection of the magnetic field line bundles confined in the superfluid may be responsible for irregular bursts of −3 m0 T = 10 y, (22) FRB121102 (Oppermann et al. 2018). MP which for MP = m0 is of the order of a few hours. In 3.5. Gravitational waves emission the works quoted above it was convincingly argued that The conversion of an NS into a light BH is also re- the accretion of the NS matter onto a PBH is a Bondi- lated to spinning up the object, and possibly also mass- like one. For our model the Bondi-likeness would be shedding of some outermost NS layers (see Fuller et al. a convenient feature (as it allows a simple theoretical 2017 in the context of the r-process elements produc- description), but it is by no means necessary. Instead, tion). it is quite sufficient that the timescale in Eq. 22 is, in The NS→BH conversion and related NS spin-up al- a range of PBH masses, much longer than a free-fall ters the quadrupole moment of the object from a spin- collapse timescale. dominated quadrupole moment of a NS, The accretion ends with a newly-born, light BH is 43 2 formed, while the FRB results from a reconnecting NS QNS ≈ 10 g cm , (24) magnetosphere. From this point of view of the FRB, (for a typical NS of mass M = MN rotating at 500 Hz), a scenario presented here is a version of the “blitzar” to a well-defined quadrupole moment of a Kerr BH (see, model proposed by Falcke & Rezzolla(2014), in which e.g. Misner et al. 1973), the magnetosphere of a collapsing NS reconnects and 2 22 3 2 provides a source of energy for the FRB (see also Fuller QKerr = Ma = G/c M χ & Ott 2015, where the collapse is triggered by accumu- 44 3 2 2 ≈ 10 × (M/MN ) χ g cm , (25) lation of the dark-matter particles). where a = J/(Mc) denotes the BH spin, χ = ac2/(GM) 3.3. The energetics of the final burst the dimensionless spin, and J the total angular momen- According to our model, the FRBs do not originate tum. Quadrupole moments QNS and QKerr for the during the passage of a PBH through NS, but during same M = MN are plotted in Fig.6 as functions of the final collapse of NS to a light BH. Due to the no χ. hair conjecture (Israel 1968; Carter 1971), the final BH In the following we will assume that the difference of cannot have magnetic field. From this general principle, ∆Q in the NS→BH transition is of the order of 1043 g one gets an estimate of the energy available for an FRB cm2. Depending on the initial PBH mass and hence on in the NS magnetic field. the timescale of conversion, the process will be accom- A typical NS of radius R and the surface dipole mag- panied by the emission of gravitational waves with fre- netic field of the order of B = 1012 G contains enough quencies in the planned spaceborne laser interferometer Collisions of NS with PBH as FRB engines 7

1e44 1.6 GW170817 merger consisted of two NS, or a NS and a ] 2 Kerr BH light (NS mass) BH (Abbott et al. 2017, 2018; Yang et

m 1.4

c Sly4 EOS NS al. 2018). g [

1.2

Q The PBH-NS collisions provide a natural creation

n 1.0 channel for light BH. To estimate a fraction of NS-mass e

m 0.8 binary system mergers containing a light BH we will use o m a simple rate estimate from Sect. 2.1. For the reference

e 0.6 l

o PBH mass m we get from Eq.3, for a typical galaxy p 0

u 0.4 r n˙ ∼ 3 × 10−6 y−1. If the GW170817 merger rate cor- d a 0.2 −2 N −4 −1 u responds ton ˙ GW ∼ 10 × Ktot ∼ 10 y , then the Q 0.0 fraction of merging binaries containing a light BH should 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless spin be of the order ofn/ ˙ n˙ GW ∼ 3%.

Figure 6. Quadrupole moment Q of a realistic EOS NS 4. FRB DURATION (Sly4 EOS of Douchin & Haensel 2001), and the Kerr BH The duration of an FRB event naturally stems from with the same mass M (equal to MN along the curves), as a the characteristic NS mass and size timescale, which in- function of the dimensionless spin parameter χ = ac2/(GM). fluences the reconnection processes in the NS magneto- 3 sphere. NS dynamical time is ∆t ≈ rG/c ≈ 2GMN/c . 1 −4 −1 LISA band, between 10 Hz and 10 Hz (see Cornish Thus, 24 & Robson 2018 for a sensitivity curve) for MP > 10 −3 δtmodel ≈ 10 s. (28) g. In general, gravitational-wave energy emission due to This universal value does not depend on the PBH mass. the change of the quadrupole moment Qij in time T can be approximated from the quadrupole formula (Einstein 5. DISCUSSION 1918) as We present the analysis of a FRB creation scenario 2 dE G D...... ijE G ∆Q in which the dark-matter halo PBH from a mass range = Qij Q ≈ 25 17 dt 5c5 5c5 T 3 of 10 g & m & 10 g collide with galactic NS, nest ∆Q 2 1 s6 at their centers and accrete the dense matter converting ≈ 5 × 1025 erg/s. (26) the NS into a NS-mass BH. 1043 g cm2 T The FRB event itself is powered by the reconnecting The instantaneous gravitational-wave amplitude h0 may NS magnetic field. Typical NS magnetic field (surface be approximated in the similar way as field of the order of 1012 G) stores enough energy to 2G 2G ∆Q provide for several FRB. h0 = Qïj ≈ Depending on the timescale of Bondi-like accretion of c4r c4r T 2 dense matter onto the PBH, which for initially small- 2 1 Gpc ∆Q 1 s 20 ≈ 5 × 10−34 . (27) mass PBH (MP < 10 g) may take years, gradual ac- r 1043 g cm2 T cretion of magnetic field confined in the superfluid dense The above considerations suggest that even if the matter provides a source of repeating non-periodic FRB, timescales of the conversion are of the order of the NS explaining the FRB121102 observations. The ratio of dynamical timescale, 10−3 s, the resulting strain ampli- the number of repeating FRB to non-repeating ones may tude is too small to be detectable at the cosmological indicate that the mass function of PBH is dominated by distances. heavier masses. The Advanced LIGO and Advanced Virgo observa- Some FRB show a double peak structure: two bursts tions of the GW170817 event (Abbott et al. 2017) re- separated by a millisecond-length interval. In the port a NS-mass binary system merger accompanied by a NS→BH conversion model, the duration of the interval short gamma-ray burst and a subsequent kilonova. The is naturally associated with the rotation period of the +3200 −3 −1 NS being spun-up in the process of BH formation in its estimated rate or such events is 1540−1220 Gpc y (Abbott et al. 2017) which roughly correspond to 1% center. N Numerical simulations of the evolution of galactic of the core-collapse supernova event rate Ktot. The ob- servation does not provide a conclusive answer whether PBH and NS populations were performed. For the PBH fraction of 0.01, allowed by current observational constraints, we find that the mean PBH mass of order of 1 https://www.elisascience.org 1021 g yields a rate of FRB throughout the Universe 8 Abramowicz, Bejger and Wielgus and the number of NS in the Galaxy consistent with ob- analysis suggests that the frequency of gravitational servations. Simulations indicate qualitative differences waves for a wide range of PBH masses lies within the between galactic disk and bulge populations of NS, de- planned spaceborne LISA detector sensitivity range, but pending on the mean PBH mass. Presented numerical the characteristic gravitational-wave amplitude is too model is rudimentary and can only be trusted to pro- small to be detected from cosmological distances. vide the order of magnitude results accuracy. Employing Detailed analysis of the gravitational-wave back- more sophisticated model for relevant parameters, such ground from this type of sources and its detectability by as NS creation rate, will allow for more specific predic- the current and planned detectors is beyond the scope tions in the future. of this paper, and will be addressed in a future work. Presented model predicts a population of light, NS- mass BH. From the micro-lensing observations point of view, this population is indistinguishable from galactic NS. However, NS-mass BH may also be present in the This research was partially supported by the National relativistic binary systems. Recent LIGO-Virgo obser- Science Foundation under grant NSF PHY-1125915 vations of the binary NS-mass merger GW170817 does and by the Polish NCN grants 2014/14/M/ST9/00707, not exclude the possibility of one component being a 2015/19/B/ST9/01099 and 2016/22/E/ST9/00037. light BH. Using the merger rate obtained by the LIGO MAA acknowledges the Czech Science Foundation grant and Virgo collaborations, based on these recent obser- No. 17-16287S which supported one of his visits to the vations, we estimate the fraction of events containing a Paris Observatory. We benefited from discussions with light BH to be of the order of a few per cent of the whole Ramesh Narayan, Pawe lHaensel, Avi Loeb, Axel Bran- binary NS merger population. denburg and Krzysztof Belczyński. Some of this work We also estimate the change of the quadrupole mo- was conducted at the Black Hole Initiative at Harvard ment of the object and related gravitational-wave emis- University, which is funded through a grant from the sion during the NS→BH conversion. Our approximate John Templeton Foundation.

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