Magnetically Accreting Isolated Old Neutron Stars Robert E

MAGNETICALLY ACCRETING ISOLATED OLD NEUTRON STARS ROBERT E. RUTLEDGE Space Radiation Laboratory, MS 220-47, California Institute of Technology, Pasadena, CA 91125; rutledge=srl.caltech.edu; and Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106 Received 2000 December 13; accepted 2001 February 2

ABSTRACT Previous work on the emission from isolated old neutron stars (IONSs) accreting from the interstellar medium (ISM) has focused on gravitational captureÈi.e., Bondi accretion. We propose a new class of sources that accrete via magnetic interaction with the ISM. While for the Bondi mechanism the accretion rateM0 decreases with increasing neutron star velocity, in magnetic accretors (MAGACs) Bondi P ~3 P 1@3 M0 MAGAC increases with increasing neutron star velocity(M0 Bondi v vs.M0 MAGAC v ). MAGACs will be produced among high-velocity(Z100 km s~1), high magnetic Ðeld (B [ 1014 G) radio pulsarsÈthe ““ magnetars ÏÏÈafter they have evolved Ðrst through magnetic dipole spin-down, followed by a ““ propeller ÏÏ phase (during which the object sheds angular momentum on a timescale[1010 yr). The properties of MAGACs may be summarized thus: dipole magnetic Ðelds ofB Z 1014 G; minimum velocities relative to the ISM of 25È100 km s~1 or higher, depending on B, well below the median in the observed radio pulsar population; spin periods of greater than days to years; accretion luminosities of 28 31 ~1 \ 10 È10 ergs s ; and e†ective temperatureskTeff 0.3È2.5 keV if they accrete onto the magnetic polar cap. We Ðnd no examples of MAGACs among previously observed source classes (anomalous X-ray pulsars, soft gamma-ray repeaters, or known IONs). However, MAGACs may be more prevalent in Ñux-limited X-ray catalogs than their gravitationally accreting counterparts. Subject headings: pulsars: general È stars: magnetic Ðelds È stars: neutron È X-rays: stars

1. INTRODUCTION Bondi accretion rate decreases with the NS velocity, while in MAGACs, the accretion rate increases with increasing Accretion onto isolated old neutron stars (IONSs) velocity: through the spherical Bondi accretion mode (Bondi & \ 2 Hoyle 1944; Bondi 1952) has been investigated as a means M0 MAGAC nRM vo , (2) to produce a population of neutron stars detectable in the \ 2 2 1@6 ROSAT All-Sky Survey (RASS; Treves & Colpi 1991; Blaes whereRM [k /(4nov )] is the size scale for the magne- & Madau 1993; Madau & Blaes 1994; Zane et al. 1995; tosphere of a nonrotating NS with the magnetic energy density from the NSÏs magnetic moment k, equal to the ram Popov et al. 2000). The estimated number of these sources P 1@3 in the RASS was initially high (D103È104). However, as pressure of the WIM. This yieldsM0 MAGAC v . So, for a observations of higher mean velocities in the radio pulsar given magnetic Ðeld strength, Bondi accretion dominates at population (Lorimer, Bailes, & Harrison 1997; Hansen & low velocities, while magnetic accretion dominates at high Phinney 1997; Cordes & Cherno† 1998 and references velocities. therein) were considered, the predicted number of detect- The evolutionary scenario of magnetically accreting NSs able IONSs accreting from the interstellar medium (ISM) has been outlined by Harding & Leventhal (Harding & decreased dramatically (D102È103). This is because the Leventhal 1992, hereafter HL92). HL92 found that magne- Bondi accretion rate is a strong function of the neutron star tized NSs Ðrst spin down via dipole radiation, followed by a (NS) velocity through the ISM:1 longer spin-down period via the propeller e†ect. They restricted their attention to sources with surface magnetic \ 2 ~3 M0 Bondi 4n(GMNS) ov , (1) Ðelds[1013 G and found that they are unable to accrete where o is the local mass density of the ISM. Bondi- onto the compact object, as the propeller spin-down time is accreting IONSs are expected to have X-ray luminosities longer than the age of the universe. A similar line of argu- D1031 ergs s~1 and e†ective temperatureskT [ 200 eV, ment is followed in the review by Treves et al. (2000) in the eff context of Bondi-accreting IONSs. This limitation does not both dependent upon the accretion rate. 14 There will be a di†erent accretion mode, however, when apply to NSs with magnetic ÐeldsZ10 G: an NS with magnetic Ðeld B \ 1015 G and velocity v \ 300 km s~1 the NS magnetic Ðeld dominates over the gravitational Ðeld ] 9 in attracting accretion from the ISM. In this mode, the spins down in D4 10 yr. warm ionized medium (WIM) attaches to the NS magnetic On the other hand, this same evolutionary scenario has been used to argue for magnetic Ðeld decay in the IONSs Ðeld at the magnetosphere, accreting directly onto the NS [ surface. These magnetically accreting isolated old neutron RX J0720.4 3125 (Wang 1997; Konenkov & Popov 1997) stars (MAGACs, pronounceable ““ magics ÏÏ) contrast with and in NSs in general (see Livio, Xu, & Frank 1998; Colpi IONSs, which accrete through the Bondi mode, in that the et al. 1998). We suggest, instead, that high magnetic Ðeld IONSs have not been discovered because strong magnetic 1 \ 2] 2 1@2 Ðeld sources accreting from the ISM are spectrally harder Herev (V Cs ) , the geometric sum of the spatial velocity of the NS and the sound speed in the accreted medium. The sound speed of (as we Ðnd below) than Bondi accretors and have been the ISM is low (D10 km s~1) compared with spatial velocities relevant to selected against by observers, or confused with background ~1 the present work(v Z 100 km s ), so we assumev ? Cs throughout. active galactic nuclei. 796 MAGACs 797 45 2 Moreover, since HL92Ïs work, observations have whereI45 is the moment of inertia in units of 10 gcm. revealed NSs with considerably stronger magnetic Ðelds This is a short timescale, compared with the life of the NS. 15 than considered by HL92, in the range of 10 GÈthe After reaching this period, the light cylinder is at RM ; magnetars. Pulse timing of soft gamma-ray repeaters however, the NS still cannot accrete (or accretes in- (Kouveliotou et al. 1998, 1999) conÐrms their existence as efficiently) as a result of the ““ propeller e†ect ÏÏ (Illarionov & proposed in earlier theoretical work (Thompson & Duncan Sunyaev 1975), in which matter is spun away by the magne- 1993; Duncan & Thompson 1992). Circumstantial evidence tosphere, which is outside the Keplerian orbit in corotation suggests that anomalous X-ray pulsars have similarly with the neutron star (the corotation radius). This matter is strong B-Ðelds (Thompson & Duncan 1996; Vasisht & Got- ejected from the system, carrying angular momentum with thelf 1997; Heyl & Hernquist 1997), and precision pulsar- it and spinning down the NS until the corotation radius timing evidence also implies magnetic Ðelds in excess of reachesRM, at which point the NS will have a spin period of 14 10 G (Kaspi, Chakrabarty, & Steinberger 1999), conÐrm- \ ] 6 1@2 ~1@2 ~1@4 ~1@2 ing less precise, multiepoch timing solutions that nonethe- PP 3.9 10 k33 v7 n~1 MNS s . (6) less led to a magnetar interpretation (Gotthelf, Vasisht, & This spin period is substantially longer (by 3 orders of Dotani 1999). Static solutions for NSs have been proposed magnitude) than any spin period yet observed from an NS. for surface Ðelds up to D1018 G (Bocquet et al. 1995; The propeller spin-down timescale, when the accretion rate Cardall, Prakash, & Lattimer 2001), although no objects is dominated by magnetospheric accretion, is with magnetic Ðelds as high as this have yet been observed. \ ] 10 ~4@3 ~5@3 ~1@3 Thus, with theoretical and observational motivation, we qP 2.3 10 I45 k33 v7 n~1 yr (7) reconsider the scenario of HL92, but with particular atten- (Illarionov & Sunyaev 1975; Davies, Fabian, & Pringle tion paid to NSs with magnetic Ðelds above 1013 G. 1979). TheqP timescale dominates the evolutionary time In ° 2, we describe the model for this population, follow- between NS birth and emergence of the NS as a magnetic ing the scenario of HL92. In 3, we summarize the proper- ° accretor. It is comparable to the age of the Galaxy ([1010 ties of MAGACs, discuss observational ramiÐcations, and yr) for velocities already observed among the NS popu- conclude. lation, but only for high magnetic Ðeld sources(Z1015 G). MODEL This makes magnetic accretors with the right combination 2. of magnetic Ðeld and velocity observable. 2.1. Evolutionary Model Following spin-down via the propeller, matter is accreted We assume that the neutron star is born with a velocity onto the polar cap of the NS. The maximum accretion rate v \ v 107 cm s~1 relative to the ISM and a magnetic onto the compact object is 7 \ 33 3 momentk k33 10 G cm , which corresponds to a dipole M0 \ nR2 vo \ 9.6 ] 107k2@3 v1@3 n2@3 gs~1 . (8) Ðeld strength at the NS surface (10 km) of 1015 G MAGAC M 33 7 ~1 (appropriate for magnetars; Thompson & Duncan 1993; (HL92). This is an upper limit to the mass accretion rate Duncan & Thompson 1992). The spin period is initially onto the NS surface and could be potentially much lower short (P > 10 s). We assume that the magnetic Ðeld does not (see ° 2.2). Moreover, the Bondi and MAGAC accretion decay. We assume a compact object mass M \ M 1.4 M rates are simply related to the magnetospheric and Bondi \ 6 NS _ and radiusR RNS 10 cm. We assume the NS travels radius: through a spatially uniform proton density n \ 0.1n ~3 p ~1 M0 R 2 cm in the WIM (Boulares & Cox 1990; Ferriere 1998a, MAGAC \ A M B . (9) 1998b). A more detailed examination of the properties of M0 Bondi RBondi this population, which would include a distribution of NS If we assume free-fall accretion onto the NS surface, this kick velocities, orbits about a realistic Galactic potential, provides an accretion luminosity of and the Galactic gas density and ionization stateÈsuch as that performed for Bondi accretors and cooling NSs (Popov \ ] 28 2@3 1@3 2@3 ~1 ~1 L MAGAC 1.8 10 k33 v7 n~1 MNS RNS ergs s . et al. 2000; Popov 2001)Èwill be the subject of forthcoming work. (10) First, HL92 argue that magnetic accretion dominates To estimate the e†ective temperature, we take the size of the over Bondi accretion when the magnetospheric radius \ 1@2 \ ] 12 1@3 ~1@3 ~1@6 polar cap to beRcap RNS(RNS/RM) . This might seem RM 4.2 10 k33 v7 n~1 cm is larger than the Bondi unusually smallÈapproximately 50 m for B \ 1015 G. accretion radiusR \ 2GM /v2. This inequality results Bondi NS Nonetheless, the e†ective temperatureTeff of this emission in a velocity limitation for a MAGAC of is v [ 94k~1@5 n1@10 M3@5 km s~1 . (3) \ 1@4 1@8 1@4 ~1 lim 33 ~1 NS kTeff 0.39k33 n~1 MNS RNS keV . (11) Electromagnetic dipole radiation pressure inhibits accre- Note thatkTeff is independent of the NS velocity. The accretion from the ISM until the light cylinder is external to the tion luminosity will remain below the local Eddington lumi- magnetospheric radius(RLC [ RM), which occurs at a spin nosity if period of p L R 2 GM P \ 1@3 v~1@3 n~1@6 es MAGAC A NSB NS LC 880k33 7 ~1 s . (4) 2 \ 2 , (12) mH cnRcap r r The timescale to reach this period through dipole radiation is wheremH is the proton mass. The electron scattering cross section in a strong magnetic Ðeld,pes, is suppressed from \ ] 7 ~4@3 ~2@3 ~1@3 \ ] ~6 qLC 2.3 10 I45 k33 v7 n~1 yr , (5) the Thomson ratepT by pes/pT 4 10 [E/ 798 RUTLEDGE Vol. 553 2 2 \ ] 14 (1keV)] (BQED/B) , withBQED 4.4 10 G and photon justiÐes our assumption that MAGACs must accrete from energy E (Herold 1979). This result yields the constraint the WIM, and not from the neutral ISM. ~1 1@2 ] 9 k33 n~1 \ 3 10 . This will not be violated for NSs with B [ 1013 G unless the ISM is unphysically overdense 2.3. L imits on the Observability of MAGACs 6 (n~1 Z 10 ). Thus, the accretion rate will be locally sub- Here we list those e†ects that will limit the observability Eddington. of MAGACs and which determine the luminosity, spectral Finally, the ratio ofM0 MAGAC toM0 Bondi is hardness, velocity, magnetic Ðeld, and pulse-period parameter space in which they may be observable. In Figure 1, we M0 MAGAC \ 2@3 10@3 ~1@3 ~2 divide the NS B-Ðeld dipole strength and velocity param- 1.8k33 v7 n~1 MNS . (13) M0 Bondi eter space on the basis of the following limits: Thus, for the same velocity distribution, MAGACs will be 1. M0 MAGAC [ M0 Bondi.ÈAs we Ðnd above, this results in a more luminous than Bondi accretors. We discuss the obser- velocity limit (eq. [3]) above which the NS is a MAGAC, vational ramiÐcations of this in ° 3. and below which the NS is a Bondi accretor (dashed line). 2. T he propeller phase must be shorter than the age of the 2.2. Comments on the Accretion L uminosity Galaxy.ÈWe use as a limit (eq. [7]) thatq \ 1 ] 1010 yr p ] 9 We have two comments on the accretion luminosity. The (dotted line), and also include the line forqp \ 1 10 yr. Ðrst regards the accretion at magnetopause, and the second This age limit also e†ectively sets a magnetic Ðeld strength limit: NSs with B \ 1014 G will not spin down in a Hubble regards the need for the ISM to be ionized in order to be 14 accreted. time. Thus, if magnetic Ðelds in NSs decay to below 10 G Arons & Lea (1976) have performed a detailed analytic in less than a Hubble time, they will not be observed as description of mass transfer across magnetopause in a 1012 MAGACs. ~1 3. T he pulsar must not escape the Galaxy.ÈWe adopt an G neutron star system fed by a B600 km s wind from its ~1 companion, but with a substantially higher accretion rate at escape speed limit of 700 km s (cf. Miyamoto & Nagai magnetopause (6 ] 1019 gs~1) than we consider here. Even 1975;Paczyn ski 1990), although the exact value depends on where in the Galaxy the NS is formed. This limit is indi- at this lower magnetic Ðeld strength and higher mass accre- ~1 tion rate, they found that a cusp forms with a stando† cated by the hatched area at v [ 700 km s . 4. T he NS magnetic Ðeld should not exceed the stability shock, causing an interchange instability that mediates acc- 18 retion onto the compact object. While inÑow at the cusp limit.ÈWe assume a surface dipole Ðeld of B \ 10 G increases with increasing density, the interchange instability (Bocquet et al. 1995; Cardall et al. 2001; dash-dotted line). operates more efficiently and prevents very high densities from arising at magnetopause. Three-dimensional MHD simulations Ðnd similar results (Toropin et al. 1999). If the interchange instability of Arons & Lea (1976) permits accretion across the entire NS surface (rather than just at the magnetic poles), then the luminosity will remain the same, while dramatically decreasing the e†ective temperature to \ 1@3 1@12 1@6 1@4 ~3@4 kTeff 0.0076k33 v7 n~1 MNS RNS keV . (14) Further analysis of accretion onto a magnetic dipole with strength 1013È1018 G is necessary to estimate the magnitude of the e†ect on the luminosity and spectrum. For now, we adoptM0 MAGAC as an upper limit. Second, to accrete material via magnetic interaction, the material must be ionized. Throughout, we have therefore assumed that MAGACs accrete from the (ionized) WIM, and not from the neutral ISM. However, one might wonder whether a MAGACÏs luminosity would be sufficient to ionize the ISM by the time it reached the magnetosphere (assuming that accretion was already taking place). Ioniza- tion of the ISM by an accreting IONS has been examined FIG. 1.ÈMagnetic Ðeld strength (B) vs. velocity for pulsars, showing previously (Shvartsman 1971; Blaes, Warren, & Madau regions where MAGAC IONSs can be observed and their accretion lumi- 1995). These investigations found that a Bondi accretion nosities. The observability of MAGACs are limited at low velocities (left; luminosity was capable of ionizing the ISM well beyond the dashed line) by a large magnetosphere (these then accrete always via Bondi accretion radius. However, we have applied a similar Bondi); at high velocities (right; hashed area) by the likelihood they will approach to MAGACs accreting onto the magnetic polar escape the GalaxyÏs gravitational Ðeld; at low B (below; dotted line) from the fact that the NSs will not spin down via the propeller mechanism in less cap and Ðnd the fraction of a neutral ISM that would be \ than 10 Gyr (we also include a line forqP 1 Gyr); and at high B (above; ionized by the MAGAC atR to be >1, for a broad range dash-dotted line) by the instability of high-B neutron stars. Note also that a M 12 of velocities(0.1 \ v7 \ 10) and densities (0.1 \ n~1 \ 100) moderate, magnetic-Ðeld NS (10 G) with an average velocity of 500 km for the magnetic Ðeld strengths considered here. Therefore, s~1 will not accrete gravitationally due to the propeller mechanism. We include lines of the maximum-accretion luminosity for the MAGACs after MAGACs must accrete from the WIM, which has a typical being spun down via the propeller. The right axis shows the e†ective density of D0.13 cm~3 for a Ðlling factor of 20% in the temperature for accretion onto the magnetic cap, which is independent of plane and a scale height of 1 kpc (Ferriere 1998b). This velocity and only weakly dependent on density (Pn1@8). No. 2, 2001 MAGACs 799

We see in Figure 1 that acceptable magnetic Ðelds are limit; its velocity is unmeasured. At a velocity of D300 km 14 ~1 11 above 10 G, and acceptable velocities range from D25 s , this NS will spin down on a timescale ofqP B 210 yr, km s~1 to the escape speed from the Galaxy. We include much longer than the age of the Galaxy. Thus, there are no \ ~3 lines of constantL MAGAC (for density 0.1 protons cm ; observed radio pulsars in which the magnetic Ðeld is clearly eq. [10]); the luminosities of MAGACs are between 1028 strong enough to evolve into a MAGAC. This is possibly and 1031 ergs s~1 (again, assuming free-fall accretion from due to the relatively short timescale during which such 6 the magnetosphere onto the NS). On the right axis of the objects are dipole emitters(qLC [ 10 yr). Ðgure, we markkTeff, which is independent of velocity and The observed spin periods of magnetars are P D 1È15 s, only weakly dependent upon the density of the ISM which, for the magnetic Ðelds implied (1015 G), is still within P 1@8 \ ( n ). MAGACs havekTeff 0.3È2.5 keV. These are the range where electromagnetic dipole radiation will harder than observed from any of the identiÐed IONSs to inhibit accretion. In addition, their X-ray luminosities are a date (Treves et al. 2000), perhaps as a result of an obser- factor ofZ1000 larger than those we expect for MAGACs. vational bias. These objects therefore are not presently MAGACs; Finally, we note that for values of B \ 1012 G and however, depending on their spatial velocities, they may v \ 400 km s~1, which are not unusual in pulsars, such an evolve into MAGACs. object will not accrete via the Bondi mode from the ISM, as The (model dependent) age of the isolated NS RX the magnetic Ðeld is in the propeller range. In addition, the J185635[3754 (D1 Myr; Walter, Wolk, & Neuhauser 10 source will not spin down in a \10 yr timescale; so it will 1996; Walter 2001) is shorter thanqP, unless the NS has wander the Galaxy as a dipole, spun-down, propelling NS. close to B D 2 ] 1018 G. With such a high magnetic Ðeld, ~1 DISCUSSION AND CONCLUSIONS along with the implied velocity (B200 km s ), the source 3. would be within the MAGAC parameter space. Its X-ray Strong magnetic Ðeld (B [ 1014 G) NSs go through three luminosity is B2 ]1031 ergs s~1, which is within a factor of stages of evolution: (1) dipole emission, (2) propeller slow- a few of the expected luminosity for a MAGAC with this B \ down, and Ðnally, the MAGAC stage, (3) magnetic accre- and v. However, the e†ective temperature (kTeff 0.057 tion onto the NS surface. MAGACs have the following keV) is substantially below that expected from a MAGAC properties: surface magnetic Ðelds between 1014 Gup with B ] 1018 G (2.6 keV; eq. [11]). The spectral hardness through the NS stability limit (D1018 G); spin periods seems to rule out this object as a MAGAC for the polar-cap between 106 and 108 s; X-ray luminosities 1028È1031 ergs accreting scenario. Since all previously observed INSs have s~1 for a WIM density of 0.1 protons cm~3; and e†ective e†ective temperatures below 200 eV (Treves et al. 2000), it \ temperatureskTeff 0.3È2.5 keV. The low X-ray lumi- seems similarly unlikely that any known INS is a MAGAC. nosities of these sources make it unlikely that the very long It is possible, however, that an interchange instability at the spin periods will be detected as pulsations with present magnetosphere permits accretion over a larger fraction of X-ray instrumentation, as prohibitively long integrations the NS, which results in a softer spectrum, such as that with frequent monitoring would be required. observed here (eq. 14). At the median velocity for radio pulsars, MAGACs will Discovering these objects in the RASS/BSC requires a be D130 times more luminous than Bondi accretors (for similar approach taken in previous work to identify \ v7 3, a typical median velocity for pulsars; Lorimer et al. IONSsÈi.e., identifying an X-ray source with no apparent 1997; Hansen & Phinney 1997; Cordes & Cherno† 1998). optical counterpart, down to an X-ray to optical Ñux ratio Although the birthrate of magnetars has been estimated to offX/fopt Z 1000, with conÐrmation coming from an optical be D10% of isolated pulsars (Kouveliotou et al. 1994; Kou- detection at an appropriate value. However, MAGACs can veliotou et al. 1998), they can be observed to B10 times the be spectrally harder than their Bondi-accreting counter- distance and B130 times the volume of the Galactic disk of parts(kTeff D 1È3 keV; cf. Popov 2001), and searches for Bondi accretors at the radio pulsar median velocity. Mag- these objects must take this into account. Also, given their netic accretors, therefore, may be more prevalent in Ñux- strong magnetic Ðelds, these objects may have a cyclotron limited X-ray catalogs, such as the ROSAT All-Sky emission line, which may aid identiÐcation through X-ray Survey/Bright Source Catalog (RASS/BSC; Voges et al. spectroscopy (Nelson et al. 1995). Moreover, because we 1999), than the lower-magnetic Ðeld Bondi accretors. Note, have assumed no magnetic Ðeld decay, the absence of however, that Popov et al. (2000) found that the detected MAGACs in the Galaxy, in combination with a population RASS/BSC isolated neutron stars are more naturally inter- synthesis with high magnetic Ðeld soft gamma-ray repeaters preted as soft, young, nearby cooling neutron stars, rather and anomalous X-ray pulsars, would support Ðeld decay than Bondi accretors; in this interpretation, no NSs accret- models. ing from the ISM have yet been discovered. The relative We conclude that MAGACs may present a population number of detectable MAGACs versus Bondi accretors will that is equally prevalent in Ñux-limited X-ray catalogs as ultimately depend upon the particulars of the distribution Bondi-accreting sources. However, no observed examples of of magnetic Ðelds at birth in NSs, the kick velocities (and this class are yet known. their possible dependence on B), as well as magnetic Ðeld decay, which we have neglected herein. I thank Lars Bildsten, Omer Blaes, David Cherno†, and A brief comparison between observations and the pre- Chris Thompson for useful discussions. I thank Lars Bild- dicted properties of this population reveals no strong candi- sten and Omer Blaes for comments on the draft of this dates for MAGACs among known source classes. paper, which improved the manuscript. I am grateful to the Among radio pulsars, there are no known objects with participants in the ITP Workshop, ““ Spin and Magnetism implied B and v that would place them in the MAGAC B, v in Young Neutron Stars,ÏÏ for stimulating discussions which parameter space. The strongest B-Ðeld radio pulsar is brought about this work. This research was supported in 5.5 ] 1013 G (Camilo et al. 2000), just below the low-B part by National Science Foundation grant PHY 99-07949. 800 RUTLEDGE

REFERENCES Arons, J., & Lea, S. M. 1976, ApJ, 207, 914 Kouveliotou, C., et al. 1998, Nature, 393, 235 Blaes, O., & Madau, P. 1993, ApJ, 403, 690 Kouveliotou, C., et al. 1999, ApJ, 510, L115 Blaes, O., Warren, O., & Madau, P. 1995, ApJ, 454, 370 Livio, M., Xu, C., & Frank, J. 1998, ApJ, 492, 298 Bocquet, M., Bonazzola, S., Gourgoulhon, E., & Novak, J. 1995, A&A, Lorimer, D. R., Bailes, M., & Harrison, P. A. 1997, MNRAS, 289, 592 301, 757 Madau, P., & Blaes, O. 1994, ApJ, 423, 748 Bondi, H. 1952, MNRAS, 112, 195 Miyamoto, M., & Nagai, R. 1975, PASJ, 27, 533 Bondi, H., & Hoyle, F. 1944, MNRAS, 104, 421 Nelson, R. W., Wang, J. C. L., Salpeter, E. E., & Wasserman, I. 1995, ApJ, Boulares, A., & Cox, D. P. 1990, ApJ, 365, 544 438, L99 Camilo, F., Kaspi, V. M., Lyne, A. G., Manchester, R. N., Bell, J. F., Paczynski, B. 1990, ApJ, 348, 485 DÏAmico, N., McKay, N. P. F., & Crawford, F. 2000, ApJ, 541, 367 Popov, S. B. 2001, Astrophysical Sources of High Energy Particles and Cardall, C., Prakash, M., & Lattimer, J. 2001, ApJ, in press Radiation, preprint (astro-ph/0101031) Colpi, M., Turolla, R., Zane, S., & Treves, A. 1998, ApJ, 501, 252 Popov, S. B., Colpi, M., Treves, A., Turolla, R., Lipunov, V. M., & Cordes, J. M., & Cherno†, D. F. 1998, ApJ, 505, 315 Prokhorov, M. E. 2000, ApJ, 530, 896 Davies, R. E., Fabian, A. C., & Pringle, J. E. 1979, MNRAS, 186, 779 Shvartsman, V. F. 1971, Soviet. Astron., 14 Duncan, R. C., & Thompson, C. 1992, ApJ, 392, L9 Thompson, C., & Duncan, R. C. 1993, ApJ, 408, 194 Ferriere, K. 1998a, ApJ, 497, 759 ÈÈÈ. 1996, ApJ, 473, 322 ÈÈÈ. 1998b, ApJ, 503, 700 Toropin, Y. M., Toropina, O. D., Savelyev, V. V., Romanova, M. M., Gotthelf, E. V., Vasisht, G., & Dotani, T. 1999, ApJ, 522, L49 Chechetkin, V. M., & Lovelace, R. V. E. 1999, ApJ, 517, 906 Hansen, B. M. S., & Phinney, E. S. 1997, MNRAS, 291, 569 Treves, A., & Colpi, M. 1991, A&A, 241, 107 Harding, A. K., & Leventhal, M. 1992, Nature, 357, 388 (HL92) Treves, A., Turolla, R., Zane, S., & Colpi, M. 2000, PASP, 112, 297 Herold, H. 1979, Phys. Rev. D, 19, 2868 Vasisht, G., & Gotthelf, E. V. 1997, ApJ, 486, L129 Heyl, J. S., & Hernquist, L. 1997, ApJ, 489, L67 Voges, W., et al. 1999, A&A, 349, 389 Illarionov, A. F., & Sunyaev, R. A. 1975, A&A, 39, 185 Walter, F. M. 2001, ApJ, 549, 433 Kaspi, V. M., Chakrabarty, D., & Steinberger, J. 1999, ApJ, 525, L33 Walter, F. M., Wolk, S. J., & Neuhauser, R. 1996, Nature, 379, 233 Konenkov, D. Y., & Popov, S. B. 1997, AZh PisÏma, 23, 569 (English transl. Wang, J. C. L. 1997, ApJ, 486, L119 Astron. Lett., 23, 498) Zane, S., Turolla, R., Zampieri, L., Colpi, M., & Treves, A. 1995, ApJ, 451, Kouveliotou, C., et al. 1994, in AIP Conf. Proc. 307, Second Huntsville 739 Gamma-Ray Burst Workshop, ed. G. Fishman, J. Brainerd, & K. Hurley (New York: AIP), 167