Magnetars, Gamma-ray Bursts, and Very Close Binaries
aa r X i v : . [ a s t r o - ph . H E ] M a y Magnetars, Gamma-ray Bursts, and Very CloseBinaries
A. I. Bogomazov ∗ , S. B. Popov † Sternberg Astronomical Institute, Moscow State University,Universitetski pr. 13, Moscow, 119992, Russia
Astronomy Reports, volume 53, no. 4, pp. 325-333 (2009)We consider the possible existence of a common channel of evolution of binary systems,which results in a gamma-ray burst during the formation of a black hole or the birth of amagnetar during the formation of a neutron star. We assume that the rapid rotation of thecore of a collapsing star can be explained by tidal synchronization in a very close binary. Thecalculated rate of formation of rapidly rotating neutron stars is qualitatively consistent withestimates of the formation rate of magnetars. However, our analysis of the binarity of newly-born compact objects with short rotational periods indicates that the fraction of binariesamong them substantially exceeds the observational estimates. To bring this fraction intoagreement with the statistics for magnetars, the additional velocity acquired by a magnetarduring its formation must be primarily perpendicular to the orbital plane before the supernovaexplosion, and be large.
The nature of magnetars and gamma-ray bursts (GRBs) is a hotly debated topic in as-trophysics. Some standard models for these objects and their origin exist, but alternativemodels are still discussed, and a number of problems remain in the standard models.Magnetars [1, 2] are neutron stars whose activity is related to the dissipation of mag-netic energy, which distinguishes them from other neutron stars. The observational man-ifestations of neutron stars may be connected with the release of potential energy ofinfalling matter (accreting sources), rotational energy (radio pulsars), or thermal energy(cooling neutron stars, such as compact objects in supernovae remnants and the so-called“Magnificent Seven” — nearby, single, radio-quiet cooling neutron stars). Presumed mag-netars (soft gamma repeaters, SGRs, and anomalous X-ray pulsars, AXPs) display energyreleases that exceed the rate of dissipation of rotational energy or stored heat, and ac-cretion is not a possible source of their activity. Magnetars display large magnetic fieldsof ∼ G. Their periods of rotation are roughly 2-12 s. There exist ordinary radiopulsars with comparable fields and periods; i.e., magnetars are not specified only by theirstrong magnetic fields. It is important that the energy of the field is being dissipated, ∗ [email protected] † [email protected] ≈
15 objects of this type known are single. Since no explicit strong selection favoringthe detection of single magnetars is known, this restriction must be additionally takeninto consideration (it was first discussed in [20]).
Since the principles of the “Scenario Machine” have been described many times be-fore, here, we will only note the parameters of the evolutionary scenario adopted as freeparameters in solution of our problem. A detailed description of the code can be foundin [21]-[23]. The population-synthesis technique is also described in [24].For each set of parameters of the evolutionary scenario, we carried out a population2ynthesis for 10 binaries. The rates of events and the numbers of objects in the Galaxy aregiven assuming that all stars are binaries. As free parameters of the scenario, we adoptedthe kick velocity acquired during the formation of neutron stars and the mass-loss ratefor non-degenerate stars. In our calculations we supposed that a neutron star may acquire some additionalvelocity v during the supernova explosion in which it is formed (see, for example, [25]and references therein). Here, we use two versions for the distribution of the speed anddirection associated with this kick velocity.In the first, the kick velocity is random and distributed according to a Maxwellianfunction: f ( v ) ∼ v v e − v v , (1)where v is a free parameter.In the second case, the distribution of the kick velocity is a δ function; i.e., all neutronstars acquire the same kick velocity v .The kick velocity was considered to be either uniformly directed, or to be directedalong the rotational axis of the neutron star. The latter case is associated with the factthat the direction of the rotational axis essentially provides a preferred direction. First,in the course of a prolonged kick, averaging about this axis will occur, and the resultingvelocity will be directed along it [26]. Second, the magnetic field generated by a dynamomechanism will also be oriented primarily along the rotational axis, while, in some models,the appearance of the kick is due to asymmetrical neutrino radiation in strong magneticfields [26]. Third, in the magneto-rotational model of a supernova explosion, the kickvelocity is primarily directed along the rotational axis [27]. Finally, in a number of modelsin which the kick is associated with the development of instabilities at the supernovastage, the rotational axis also represents a preferred direction, and calculations reveal acorrelation between the direction of the kick velocity and this axis [28]. Observations ofradio pulsars present some very strong arguments suggesting that the directions of thekick velocity and rotational axis coincide [29]-[31], while the rotational axis in binariesmay be expected to be perpendicular to the orbital plane.Note that the kick may not only disrupt, but also bind some systems, which wouldhave decayed without the kick due to the large mass loss in the supernova explosion.However, in most cases, increasing the kick velocity acquired by the neutron star duringits formation decreases the probability that a binary will be preserved. Here, we use two evolutionary scenarios (A and C) that differ in the mass-loss rate fornon-degenerate stars. The stellar wind is an important evolutionary parameter, since itspecifies the masses of the remnants of the stellar evolution and the semi-major axes ofbinary systems. 3volutionary scenario A features a classical weak stellar wind (see [22], as well asevolutionary scenario A in [23]). On the main sequence and in the supergiant stage, astar loses no more than 10% of its mass in each of these stages, and in the Wolf-Rayetstage it loses 30% of its initial mass.Evolutionary scenario C [23] features a higher mass-loss rate. In each stage of itsevolution, a star fully loses its envelope, which may mean the loss of more than half itsinitial mass by the end of its evolution.
The main basis for the model considered here is the acceleration of the rotation of apre-supernova core in a close binary due to tidal synchronization of the rotation of itscompanion. In this case, we can formally assume that the synchronization occurs justbefore the collapse. The period of axial rotation of the newborn neutron star should thenbe approximately 10 − of the orbital period of the binary at the time of the supernovaexplosion, since the radius of the core, whose mass before the collapse is approximately1 . M ⊙ , is ∼ cm [32], while the characteristic size of the neutron star is ∼ cm.We assume that the rotational angular momentum of this core is conserved during thecollapse.However, the lifetime of the core of a star in the carbon-burning stage is ∼ years[32], while, as a rule, the time for the tidal synchronization of components is no less than ∼ yrs, even in very close systems [33]. Thus, we can take the synchronization ofthe axial rotation of the core with the orbital rotation of the companion to occur at thecarbonburning stage, or at the end of the helium-burning stage [13]. During the stage ofthe burning of carbon and subsequent elements, the period of axial rotation of the coreis shorter than the orbital period of the system. In this case, the rotational period ofthe newborn neutron star will be approximately 10 − of the orbital period of the binarywhen the components’ rotation becomes synchronized: the radius of a CO core with anapproximate mass of 1 . M ⊙ is ∼ cm [32], while the characteristic size of the neutronstar is ∼ cm. It is assumed that the rotational angular momentumis conserved thecore has possessed at the onset of the carbon-burning stage.We decided to call a magnetar a neutron star that has originated in a close binary,with an initial period of axial rotation that does not exceed 5 ms. Such rapid rotationshould make it possible to increase the magnetic field substantially due to the dynamomechanism. Consequently, if we suppose that the synchronization of the rotation occursbefore the collapse, then the maximum orbital period at the epoch when the orbitalrotation of the components becomes synchronized with the rotation of the core of thefuture collapsar should not exceed ∼
10 days.If the formally defined rotational period of the newborn neutron star is shorter than0.001 s (the limiting minimum rotational period for neutron stars), we consider the periodof the neutron star to be equal to this value. It seems to us that the excess angularmomentum may lead to additional peculiarities of supernova explosions in such closebinaries. 4 .4 Other Parameters of the Evolutionary Scenario
In this section, we present some parameters of the evolutionary scenario that are notyet known accurately, and so can be adopted as free parameters in the population synthesiscarried out using the “Scenario Machine”. The maximum mass of the neutron star (theOppenheimer-Volkov limit) that can be attained via accretion is taken to be M OV =2 . M ⊙ , and the initial masses of the young neutron stars to be distributed randomly inthe interval 1 . − . M ⊙ .We assume that main-sequence stars with initial masses in the range 10 – 25 completetheir evolution as neutron stars. There is some evidence that the progenitors of magnetarsare the most massive stars among those forming neutron stars [34]; however, this is nota firm fact for all magnetars, and we do not take this possibility into account. It wouldbe important to distinguish supernovae in which magnetars are formed (see, for example,[35]), but this question is likewise unclear.Main-sequence components of close binaries that increase their masses as a result ofmass exchange until their values appear in the above interval were also added to theprogenitors of neutron stars. More massive stars evolve into black holes, and less massivestars to white dwarfs. In our present calculations, we assumed a uniform (flat) distributionof component-mass ratios for the initial binaries [32] and zero initial eccentricity for theirorbits. We also adopted a flat distribution of the initial semi-major axes of the binaries, d (lg a ) = const in the interval 10 − R ⊙ . The efficiency of the mass loss at the common-envelope stage is described by the parameter α CE = ∆ E b / ∆ E orb = 0 .
5, where ∆ E b = E grav − E thermal is the binding energy of the ejected matter of the envelope and ∆ E orb thedecrease in the orbital energy of the system as its components approach [32, 36]. We note first that the synchronization of the core just before the collapse is essentiallyincompatible with the available observational data. The rate of formation of magnetarsunder this assumption would be ∼ − per year, which is more than two orders ofmagnitude below the lowest observational estimates (one per several hundred years). Thebinarity of magnetars if the synchronization of the core rotation occurs just before thecollapse begins to differ substantially from unity only for very high kick velocities ( ∼ km/s), which do not seem likely. Therefore, we consider further only the possibility thatthe core maintains the rotational angular momentum it possesses at the onset of thecarbon-burning stage.According to our computations, the rate of formation of rapidly rotating neutronstars (supposed to be magnetars) is approximately one per 400-500 yrs. This agrees withempirical estimates for the rate of formation of these objects (see the analysis and detaileddiscussion in [15]). Figures 1-4 present the results of our computations. All the curves inFigs. 1-3 assume that the angular momentum due to the axial rotation of the CO coreis maintained, and, just before the collapse, the pre-supernova core rotates with a periodshorter than the orbital period of the system at the time of the supernova. The maximum The period of axial rotation of a newborn neutron star is 10 − of the orbital period before the collapse.We consider a magnetar to be a neutron star whose rotational period does not exceed 5 ms. v ( >
700 km/s). Thecurves in Fig. 2 assume that the kick velocity has some specific value v (it is a δ function).This makes it possible to reduce the predicted binarity of magnetars. The presence ofa strong stellar wind (evolutionary scenario C) decreases the binarity (curves 2 and 4in Figs. 1 and 2, and curve 2 in Fig. 3) compared to scenarios with a weak wind. Ifthe kick is uniformly directed and the stellar wind is weak (evolutionary scenario A),consistency with observations can be reached for v ≈
700 km/s (curve 1 in Fig. 2), evenif the additional kick is represented by a δ function. With curves 3 and 4 in Fig. 2 andmoderately large kick velocities (350-450 km/s), it is possible to reach a level of binarityfor magnetars that corresponds to the current observational data (the fraction of binariesis < / δ function, but also de-pends on the orbital period at the time of the supernova as v = v · . /P NS , where0 .
001 s ≤ P NS ≤ .
005 s is the period of the forming neutron star. The orbital periodis restricted to approximately 10 days. The need for this computation stems from thefollowing consideration. Our model assumes that the very strong magnetic field of themagnetar is generated as a result of the collapse of a very rapidly rotating core. In ourpresent study, the maximum and minimum periods of magnetars differ by a factor of five.The kick velocity at the time of the collapse may depend on the magnetic field, whilethe predicted binarity of magnetars may depend on the orbital period at the time of thesupernova. Figure 3, shows that curve 3 corresponds to observational data starting from v = 1700 km/s. For systems whose orbital periods at the time of tidal synchronizationare, for example, 5 days, the kick velocity will not exceed 400 km/s, while the largest kickwill be obtained by neutron stars forming in binaries with orbital periods . Discussion
We were not able to obtain a sufficient number of single magnetars in our evolutionaryscenario for binaries without making additional assumptions, for example, about the kick(recoil) velocity at the time of the supernova. This could be considered indirect argumentagainst the generation of the magnetar magnetic field in rapidly rotating newborn neutronstars. In this connection, we will recall and briefly discuss alternatives to the consideredscenario.
One currently popular hypothesis suggests that the fields of magnetars are formed inthe collapses of stellar cores with magnetic-flux conservation, when the progenitor star hasa sufficiently strong magnetic field (see [16] and references therein). Some observationssuggest that magnetars are related to the most massive stars among those giving riseto neutron stars [37]. According to some observational data, about a quarter of thesemassive stars display sufficiently strong magnetic fields (see [38] and references therein).In addition, studies of supernova remnants related to magnetars have not revealed anydirect signs of intense energy release that could have been connected with the presence inthem in the past of rapidly rotating neutron stars with magnetic fields [39]. These studiescan be considered indirect arguments against the hypothesis that the magnetar fieldswere generated in the course of a collapse. Simple population estimates [16] indicatethat current estimates for the rate of formation of magnetars can be explained in thishypothesis.However, there are serious objections against this hypothesis, some of them recentlysummarized by Spruit [40]. The simplest is that, even if there exists a strongly magnetizedmassive star, only 2% of its cross section (which is important when calculating the fieldduring a collapse with flux conservation) will be included in the compact object.The rate of formation of magnetars remains very uncertain. Recent detections oftransient anomalous X-ray pulsars [41]-[43] and the detection of a new source of repeatingGRBs [44, 45] suggest that the number of magnetars may exceed previous estimates. Iftrue, this may raise the problem of the lack of sufficiently strongly magnetized massivestellar progenitors able to provide the high formation rate of magnetars. Finally, studiesof stellar magnetic fields are able to probe only the surface fields. A compact objectemerges from the stellar core, whose field is unknown.Thus, to explain the origin of the fields of magnetars, it is difficult to get away withoutsome mechanism for its generation. All the possible mechanisms [40] use the rotationalenergy of a newborn neutron star or collapsing core in some way; i.e., the question ofwhat makes 10% to several tens of per cent of cores of massive stars rotate rapidly justbefore their collapse remains open.
A more optimistic scenario than ours is considered in [20]. While here we consideronly stars that rotate rapidly just before the collapse, several possible means for spinning7p stars in binaries are suggested in [20], neglecting the possible subsequent decelerationof the rotation. It is not surprising that this led, first, to a substantially higher rate offormation of rapidly rotating neutron stars, and second, to a fraction of preserved binariesthat was much lower. Unlike the channels considered in [20], in the scenario consideredabove, rapidly rotating neutron stars originate only in very compact systems, and, inaddition, the exploding star is often less massive than its companion.There are a number of objections against the optimistic suggestion that a normal starspun up by accretion in an early stage of its evolution, or an object formed as a result ofa merger, can maintain the high angular momentum of its core until its collapse. For ex-ample, three processes that can transfer the rotational angular momentum from one layerto another are considered in [13] convection, diffusion (shear diffusion), and meridionalcirculation. Convection tends to make the angular velocity constant, thereby transferringangular momentum from inner to outer layers of the convective zone. Diffusion weakensdifferential rotation and also transfers angular momentum outwards. Meridianal circu-lation can transfer angularmomentumboth outward and inward in the star. Mass lossaffects the angular momentum of the core in part indirectly, since it influences the rota-tional angular velocity of the star and the angularvelocity gradient inside the star. Themost important conclusions related to the evolution of the rotation listed in [13] are asfollows (see also references therein): • The angular momentum of the star decreases during the star’s evolution up to thesupernova explosion. • The largest loss of angular momentum occurs on the main sequence. • After helium burning has finished, convection transfers angular momentum frominner parts of the convective zone to its outer layers, without involving the core;therefore, the rotational angular momentum of the core at the end of the helium-burning stage can be taken as a fairly reliable estimate of the rotational angularmomentum of the collapsing core.
In our scenario, with an isotropic kick, an appreciable fraction of magnetars remainin bound binaries. In this connection, we should discuss possible manifestations of closebinaries with magnetars.Since the magnetic fields of magnetars apparently rapidly decrease to values typicalfor common radio pulsars (see, for example, [46] and references therein), the consideredstage will be short. The secondary component does not have sufficient time to undergosubstantial evolution (the characteristic time of the decay for the magnetar field lies inthe interval from several thousand years to several tens of thousand years). Possibleconfigurations can be identified in which some feature of a magnetar, such as its strongmagnetic field, will be manifest in a critical way.One example of a close binary system with a magnetar may be provided by the centralobject in the supernova remnant RCW 103 [47]. This object displays variability with a8eriod of 6.7 h. One possible interpretation of the observations is that the secondary issituated within the magnetosphere of the magnetar [47, 48]. In this case, 6.7 h is theorbital period of the system. The binary is similar to polars, in which the compact objectis a white dwarf whose magnetic moment ia approximately equal to that of the magnetar.In the classification suggested by Shvartsman and Lipunov [49], such systems are called magnetors . We are planning to estimate the number of such objects in the Galaxy.
We have considered the hypothesis that GRBs and magnetars originate during theevolution of massive stars in close binary systems, which spins up the core of the pre-supernova. The statistics for the expected rate of formation of magnetars are in satis-factory agreement with observational estimates. However, this scenario predicts a largefraction of binary magnetars, whereas all known magnetars or magnetar candidates aresingle. This problem may be solved by introducing an additional component of the kickvelocity acquired during the formation of the neutron star, perpendicular to the orbitalplane (i.e., along the direction of the magnetic-dipole axis of the newborn compact ob-ject), and requiring that the magnitude of the kick not be small ( .
400 km/s). Thepresence of a moderately strong stellar wind (evolutionary scenario C) also promotes adecrease in the predicted binarity of potential magnetars; the requirement that the kickvelocity be high ismandatory, but it should be preeminently directed perpendicular to theorbital plane of a system.
Acknowledgments
In our study, the population synthesis of close binaries was carried out using the “Sce-nario Machine” code developed by V.M. Lipunov, K.A. Postnov, and M.E. Prokhorov[22] in the Department of Relativistic Astrophysics of the Sternberg State Astronomi-cal Institute, Lomonosov State University, Moscow. This work was supported by theProgram of Support for Leading Scientific Schools of the Russian Federation (grant no.NSh-1685.2008.2), the Analytical Departmental Targetted Program “The Developmentof the Science Potential of Higher Education” (grant no. RNP 2.1.1.5940), the INTASFoundation (grant no. 06-1000014-5706), and the Russian Foundation for Basic Research(grant no. 07-02-00961). The authors thank Professor A.V. Tutukov for discussions anduseful remarks.
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00 200 300 400 500 600 700 800 900 1000 v -1 N b /(N b +N s ) Figure 1: The fraction of binary neutron stars formed in very close binaries as a functionof the characteristic kick velocity v acquired during the formation of a neutron star.The kick velocity is distributed according to (1). The vertical axis plots N b / ( N b + N s ),where N s is the number of singular neutron stars and N b the number of neutron stars inbinaries that originated in the course of the computations. The numbers on the graphdenote the curves calculated for the following scenarios: ( ) equiprobable directions forthe kick, type A evolutionary scenario; ( ) equiprobable directions for the kick, typeC evolutionary scenario; ( ) kick always perpendicular to the plane of axial rotation ofthe star, type A evolutionary scenario; ( ) kick always perpendicular to the plane ofaxial rotation of the star, type C type evolutionary scenario; ( ) upper limit for binarityaccording to observations ( ≈ /
00 200 300 400 500 600 700 800 900 1000 v -2 -1 N b /(N b +N s ) Figure 2: Same as Fig. 1 for a δ -function distribution for the kick velocity. The numberson the graph denote the curves calculated for the following scenarios: ( ) equiprobablekick-velocity direction, type A evolutionary scenario; ( ) equiprobable kick-velocity direc-tion, type C evolutionary scenario; ( ) kick velocity directed along the rotational axis ofthe star, type A evolutionary scenario; ( ) kick directed along the rotational axis of thestar, type C evolutionary scenario; ( ) upper limit for binarity according to observations( ≈ /
00 300 500 700 900 1100 1300 1500 1700 1900 2100 v -2 -1 N b /(N b +N s ) Figure 3: Same as Fig. 1 for a δ -function kick-velocity distribution with the kick directedalong the rotational axis of the star; the absolute value of the kick also depends onthe initial rotational period of the young neutron star (see text for the details). Thenumbers on the graph denote the curves calculated for the following scenarios: ( ) typeA evolutionary scenario, ( ) type C evolutionary scenario, ( ) upper limit for binarityaccording to observations ( ≈ //