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PoS(HEPRO VII)048 . ∗ B https://pos.sissa.it/ sica, Universitat de Barcelona, Spain ∗ G are favoured as FRB progenitors. [email protected] [email protected] 11 Speaker. 10 The origin of Fast Radio Bursts (FRBs)brightness is still temperatures, mysterious. requiring All FRBs a to coherentfrom date show the emission extremely high physics mechanism. of Using onewe constraints of show that these derived accretion mechanisms, induced the explosions of synchrotron neutron maser, as with surface well magnetic as fields observations, of ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). High Energy Phenomena in Relativistic Outflows9-12 VII July - 2019 HEPRO VII Facultat de FÃ Asaf Pe’er Bar Ilan University, Israel E-mail: Killian Long University College Cork, Ireland E-mail: Synchrotron Maser From Weakly Magnetised Neutron Stars As The Emission MechanismRadio Of Bursts Fast PoS(HEPRO VII)048 , an 3 − to 2596pc cm 3 − 1Jy and are distinguished ∼ 972Mpc (4; 5; 6). This, as well as further = L d 1 . They have typical fluxes of 1 K (17). As we show here, this requirement holds the key to under- 37 10 ∼ b T G are similar to those required for a coherent emission mechanism, the syn- 11 10 . 10%, and the FRB rate is comparable to this fraction of the neutron formation rate. ∗ B ∼ 193, equivalent to a luminosity distance of . http://www.frbcat.org/ Fast Radio Bursts (FRBs) are bright radio transients of millisecond duration. A total of 98 Of the 98 FRBs to date, 11 have been observed to repeat. The localisation of the first repeater, The of FRB progenitors is still unknown. The small scale and large energies involved Despite the large degree of uncertainty regarding the nature of the progenitor, there is a consen- We find that the conditions found in the environments of neutron stars with surface magnetic Several mechanisms have been proposed to explain the coherent emission required to produce Here we examine the synchrotron maser as the mechanism responsible for FRBs. The maser 0 1 = FRBs have been published to date (1) FRB 121102 (3) allowed az persistent counterpart and host galaxy to be identified at a of has led most modelsthe to production consider of compact FRBs. objectsnon-cataclysmic. such The Cataclysmic as numerous models neutron proposed include models starsmergers binary fall playing neutron (11) into star crucial and mergers two roles neutron (e.g. classes,pulses in star-black 10), from cataclysmic white extragalactic hole and dwarf mergers and young (12).repeaters neutron (SGRs) stars (e.g. (e.g. Non-cataclysmic 15; 13; models 16). 14) and include flares giant from soft gamma sus on the need fortemperatures a of coherent up emission to process. This follows from the extremely high brightness fields of the extreme brightness temperatures of19), FRBs. the cyclotron/synchrotron Models maser include (15; coherent 16; turbulence (22). curvature 20; emission 21) and (18; collisionless Bremsstrahlung in strong has the advantage of being a viable emissiondensities, mechanism over as a range well of magnetic as fieldscoherent and not number emission requiring (21). particles Previous16; to works 20) be or invoking the the bunched mechanism maser itself in (21), haveconstraints but small examined on have not the specific volumes used progenitor. the models in mechanism’s (15; properties order to derive to general obtain Synchrotron Maser From Weakly MagnetisedKillian Neutron Long Stars As The Emission Mechanism Of Fast Radio Bursts 1. Introduction by their large measures (DM).order These of are magnitude in greater the than rangeextragalactic values origin 176pc expected for cm FRBs. from electrons (1; 2), suggesting an localisations (7; 8; 9) provide a strong case for the extragalactic origin of FRBs. standing the nature of thecoherent progenitor. emission Analysing allows the us to conditions place required strong to constraints produce on the possible necessary FRB progenitors. chrotron maser, to produce a FRB. Furthermore,fields the proportion is of neutron stars with theseThese magnetic results allow us to propose weakly magnetised neutron stars as FRB progenitors. 2. The Basic Physics of the Synchrotron Maser PoS(HEPRO VII)048 ) is Γ c η / d . of the particle is the number η n . Γ is the average energy of ≈ . Here i e γ , and their number density, e ) m 1), relativistic, nonthermal E i h e > πγ E / h B 2 erg for the repeater (4; 30)), ν η ( / ne 40 p / ν p E 10 = = − e . Maser emission in these conditions has p ) 38 N ν c e . The minimum thickness of the shell depends m Γ / πγ 2 R 2 ( ∼ / d eB = B ν from the central object. The maser will be activated by the R is the Lorentz factor of the electrons. The gyration frequency of is the Lorentz factor of the blast wave. This typical width provides the γ and is not important in strongly magnetised plasmas, as in this scenario Γ

B , is given by ν B / ν p ν is the plasma frequency, given by p p , ν γ (29), where  is the energy of the bursts (in the range 10 , located a distance Γ / d E min R p ν ∼ Constraint (ii) originates from the efficiency of the maser. For the maser to be a viable emission The data enable us to obtain constraints linking the size and number density of the masing We consider a cataclysmic FRB progenitor where masing takes place in a spherical shell of The physical conditions in the region where the masing takes place can be constrained using Maser emission is produced due to interaction between electromagnetic waves and energetic Here we consider the maser in a weakly magnetised ( that enables the production of FRBs ∗ ≈ . Here, R e the masing electrons. These shocked electrons have a thermal energy of mechanism, the growth rate of the signal must be large enough to extract a fraction required suggest this object isthe a duration neutron of star, the though maser thewidth itself timescale (21). for maser Assuming emission a is relativisticfirst given blast constraint, by on wave the the thickness shocked of plasma the shell: has a n the fraction of the electrons’ energy that contributes to the maser and formation of a population inversion in the shell. The magnetic fields and short timescale ( on the number of particles that contribute to the masing, region to the magnetic fieldgetics of of the the . burst and Thesethe size constraints dispersion of are measure the obtained of masing the from: burst region, (i) and (ii) the (iv) the ener- the efficiency frequency of of thethickness the signal. maser mechanism, (iii) the physics of themagnetic maser fields and and number constraints densities frommechanism where for observations, the FRBs. synchrotron allowing maser us can to plausibly be place the limits emission on the the emission peaks at a frequency below the plasma frequency. 3. Physical and observational constraints of the allowed parameter space region plasma, where density of the plasma and been proposed as thescenario source the of masing radio emission emissionrelativistic is plasma from with due respect gamma to to ray the thea vacuum burst Razin case, population which afterglows effect, can inversion (26). a result is in modificationchange either present, In suppression of in amplification or, this the the when of beaming emission the angle fromunity emitted of (25). a the signal For radiation (27; this when case, 28). theand a refractive so relativistic This would index plasma not of is is effect required, the due cyclotron asν plasma emission. to the is The Razin a less emission effect than is is strongest a near relativistic the effect Razin frequency of the plasma particles, particles in a plasma, which can resultconditions in (23; negative absorption 24). and stimulated The emissionbution under behaviour certain and of the the maser environment is whereelectron determined distribution it is by occurs. required the (23; form For 25). of masing the to particle occur, distri- a population inversion in the Synchrotron Maser From Weakly MagnetisedKillian Neutron Long Stars As The Emission Mechanism Of Fast Radio Bursts PoS(HEPRO VII)048 for d in the c n η G. This , derived 5 = 15 − 10 10 the Razin fre- shell 2 < denote the cold . γ ∗ e DM η B n > B < ν and / G (e.g. 31; 32). In the case p (22; 34). c 7 1 ν B n , where − T 10 4GHz. The maser frequency . shell gives the magnetic field in the 1 . For . B Γ ∼ ν η , (3.2) DM / . (3.1) = p 10 = . obs 3 ν γ 3 ν γ 10 − 3 e p γ n p × ν source (23). The exact value, however, depends on 4 q . 3 = 2 13 − DM ∗ − < R . The contribution to this from the galaxy rather 10 10 ν 3 e 225pc cm and noting 3 n − − × Γ . 1 / < − 32 . obs 10 10 shell 1 as ν ∼ 10 = 3 for a relativistic plasma. Here, DM γ 3.1 η × 225pc cm M , where the growth rate is at a maximum. Equating the Razin γ 4 ∗ 2 B . . R / 2 ν d e host n = DM in this work. (33) give upper limits to the efficiency of . shell delimits the range where 1 2 − γ . While masing emission is still possible in this regime, the allowed parameter DM p 10 < γν . p B ν ν = η ∗ < . R 3 ν − We investigate neutron star surface magnetic fields in the range 10 The growth rate, and therefore the efficiency, depends on the distribution function of the elec- The third constraint comes from the dispersion measure. Assuming the DM from the source Constraint (iv) is derived from equating the masing frequency to the emission frequency of the quency is space is restricted to a smallsize region and with observed low emission magnetic frequency. fields Including the duestatistics neutron to for stars constraints our in from model this the region discussed DM, will below.of shell not The the change range number the of density interest using can equation therefore be expressed in terms The range 1 This provides upper and lower limitsthe on electrons. the number density which depend on the Lorentz factor of 4. Results Synchrotron Maser From Weakly MagnetisedKillian Neutron Long Stars As The Emission Mechanism Of Fast Radio Bursts energy. The maser will be quenched whenmechanism the in maser simulations reaches of saturation. relativistic The shocks efficiency was of shown the to maser be of AKR, the efficiency is in the range trons. There is ainversion. wide range We do of not possible specify distributionsvided an which the exact can growth form provide rate for the is thecavity. requisite large distribution enough population as to our extract results the are required unchanged energy pro- over the widthis of solely the due masing to the particles in the shell, one has range 10 from limits on theexperiments brightness suggest temperature that this from saturation induced effect is Compton not scattering. observed for high However, plasma masing region as the form of the particle distribution, which is uncertain. We therefore examine values of than the source region depends onguidelines, the the location DM of due the FRB to within the the shell galaxy. is Using these values as bursts, which have observed frequencies of approximately and relativistic electrons in theuncertain. shell The (35). total The DM value contributionthe also to intergalactic contains the medium contributions DM (IGM) from from and theto the the the Milky source host Way, host Milky region galaxy. galaxy Way is as For halo, 55 FRB 121102, (4) estimate the DM due is given by the Razin frequency, frequency to the emission frequency of a cold plasma and -3 -3 ) Γ R 2 (d= <γ >1 B B /ν /ν p p

PoS(HEPRO VII)048ν ν cm cm cm 13 15 17 , 40 ≈ 10, Lower limit from DM=100 pc cm Lower limit from DM=200 pc cm Limit from Limit from R=10 R=10 R=10 Upper limit from cavity 3.2 10 V were = . The = 6 2 γ E . Increasing 10, 3 and10 3 − = γ G is required for 10 cm 10 , 8 1, 11 10 10 > 10 100 , B − ∼ G only in the extremely ν inside the light cylinder, 10 / n , 10 12 p 3 5 r ν , 10 10 / . Thus, the allowed surface 2 1 3 . / . = 1 ∝ ∗ ∗ γ 9 γ B B B ∝ is the radius at which the co-rotating 10 . As the volume of the shell is π R 2 max , / ∗ ) B cP -3 = L as an example. In this case, the results indicate r 4 1 8 n(cm (38; 39). The allowed parameter space for 10 . Lorentz factors of is the period of the . We also investigate the full 6 P cm are preferred. For larger DM values the lower limit will 3.2 , the surface magnetic field can therefore be expressed 10 13 ∼ 3.1 10 ∼ R results in less restrictive DM constraints, lower allowed number densities 7 γ and is shown in Figure 10 3 3 − − 8 are attainable. 10 cm 10 14 12 ∗ 8 10 B is given by equation

=

10 10 10

. Using equation

10

e

* - 6 , η 3

3 *

n   B G R

/ P ∼ . Solid lines show limits while the dashed lines show lines of constant radius. Values - 3 . Taking into account the maximum allowed number density from equation 2 1 3 2 n  / − e 3 n , the maximum surface magnetic field is γ G, 10 outside (37). The light cylinder radius 2 1 6 r / 10 − Parameter space (shaded region) for the synchrotron maser with mc E erg and = e 7 / γ n 1 10 η πη 40 , the distance to the masing region and the number density are related by the expression 4 ∝ ∝ ∝ . d  10 We find that a neutron star with a surface magnetic field of http://www.atnf.csiro.au/research/pulsar/psrcat The allowed surface magnetic field values depend on the Lorentz factor, number density in The range of ∗ 2 B ∗ 2 B R B max = ≈ , only low values of π e emission at the appropriate frequency and energy, increasing to erg and decrease. Increasing the value of of and higher allowed neutron star surface magnetic field values. the masing region and the distance to the masing region, the allowed values of the DM results in the lower limit decreasing. magnetic field depends only weakly onγ the Lorentz factor. Therefore, even for very large values of Figure 1: that the allowed parameter space is restricted to low magnetic fields and 4 R as Synchrotron Maser From Weakly MagnetisedKillian Neutron Long Stars As The Emission Mechanism Of Fast Radio Bursts encompasses the full range ofmagnetic surface field magnetic outside field the surface valuesand was for taken all to published be pulsars of (36) the form n speed is equal to the speedrange of of light. number densities Here in the masing region. examined. The larger valueswhich were have chosen Lorentz to examine factors conditions of similar up to to pulsar nebulae, E PoS(HEPRO VII)048 and 3 − in which cm at radii of 6 Γ depends on 3 − / e − R G have typical n 10 cm 11 G leaves approx- ∼ ∼ 15 10 11 (40), while the rate n 1 10 < . − 6 ∗ − yr B 10 are thus very strong con- 3 13 − ∗ G. Less than 10% of pulsars cm. As, at constant velocity, = B 5 γ . 13 9 Gpc 10 5 10 (2). The ratio of the two rates is ∼ 10 1 ∼ − R × 2. The lower limit on yr ) 3 3 = . − 0 Γ ± Gpc 4 was achieved for 42 . 3 1 5 10 ( − × ∼ 15 89 . . 1cm 1 0 SN + − ∼ R also constrain our results significantly. They have a partic- 98 09 of the total population (36), comparable to the ratio of the G are expected (15; 39; 38; 43). Neither of these values lie . . 1 0 0 − shell ∼ ∼ 10 − DM 1. . FRB 15% of the known pulsar population that meet the criteria are there- 2 0 − R ∼ ∼ 10 ∼ M cm (45). While these density values are too high for the maser, our scenario case. Ruling out pulsars with magnetic fields greater than 10 B 10 6 07. This value is similar to the fraction of pulsars with surface magnetic fields of . 10 0 G, which is few ms and make up = ∼ 10 5% of the total population (36). For FRBs with lower energy and greater efficiency, the γ . ∼ SN , the particles from the accretion induced explosion could plausibly provide suitable number R 2 / − Emission from the synchrotron maser can be circularly, elliptically or approximately linearly The density constraints obtained from the maser can be compared to the densities found in The limits obtained from In order to account for the larger density values required by our constraints, we are lead to r FRB ∝ straints as they rule out thethe majority of context pulsars of as FRBs. being possible The hosts for the synchrotron maser in the case under consideration. Burstsnumber with densities. higher The energies lowest and density Lorentz of factors have lower allowed fore candidates to be FRB progenitors.neutron Therefore, star the formation FRB rate. rate The shouldsupernova be neutron rate a star which similar formation is fraction rate approximately of is the approximated by the core-collapse ularly marked effect in thehigher cases energy bursts with the larger DM numbers limitsfor of severely the constrain particles lower the in energy cases the bursts with masing they lower region. Lorentz are factors, only For while relevant the for polarised, depending on the electronilarly, distribution both function circular and (e.g. plasma 41)vations. parameters and (24; However, linear the 26). polarisation heterogeneous Sim- difficult (e.g. nature to of 42) draw FRB useful has constraints polarisation been from measurements measured the to data. in date FRB makes obser- it the vicinity of neutron stars. In the case of pulsar wind nebulae, densities of Synchrotron Maser From Weakly MagnetisedKillian Neutron Long Stars As The Emission Mechanism Of Fast Radio Bursts relativistic imately 14 have magnetic fields lower than this value. These upper limits on of FRBs is approximately R 5. Discussion magnetic fields of suggest a scenario where weakly magnetised(44). neutron stars undergo The an accretion material induced expelled explosion by this explosion can then form a shell of width upper limit on the magnetic field can be significantly lower at less than 10 within the allowed parameter space for the synchrotron maser, ruling out this scenario. a population inversion is formed,low and mass as X-Ray a binaries result (LMXBs) masing have takes typical place. wind Accreting densities neutron of stars 10 in periods of FRB and neutron star formation rates.of As a low result, magnetic this scenario field would neutron require a stars significant fraction in binaries to undergo such an event due to the similarities approximately 10 n densities for the maser at these distances. Pulsars in binary systems with considers the masing emission to occur at larger distances of PoS(HEPRO VII)048 . A , , The 365 (2017) A . 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