arXiv:astro-ph/0010225v1 11 Oct 2000 er rr20;Lrmr&Xlui 00;4 They lumi- with 4. emission 2000); X-ray Xilouris Eiken- of pulsed & persistent nosities soft Lorimer (e.g. infrared have 2000; identified optical, all Dror been No & see have berry reviews, counterparts 3. (for radio 1999); objects or Mereghetti young remnants, 1999; are supernova Hurley with they associated 1999); that are 1998, (clustered them indicating e.g. al. of periods et (see, Most Kouveliotou rotation rates 2. 1995; spin-down long Stella large have proper- & and Mereghetti following all seconds) the They 5-12 share within 1. They ties: sources. enigmatic groups two are of AXPs) (hereafter Pulsars X-ray Anomalous rpittpstuigL using typeset Preprint 2018 23, October version Draft ld:1 oto h usshv ue-digo lumi- in- super-Eddington bursts have SGR bursts the the (Hurley with of of remnants nosities Most characteristics supernova 1. main their clude: re- The of with cores positions velocities 1999). found the relative motion also their to is proper to soft spect It according larger occasional AXPs have show not. both than usually SGRs do between SGRs that AXPs difference that is while Thompson main bursts objects The gamma-ray (e.g. the sources of review). these types a of for energy 2000 down spin the [email protected] a oe,wihcnacutframs l h phenom- & the Thompson 1992; all Thompson almost & (Duncan for above account listed can ena soft which have model, bursts tar keV. Most 20-30 around 4. energy characteristic review); with a spectra (see for properties common August 2000 0526-66 some (the Thompson share 1900+14 SGR which SGR event), from and 1998 event) detected 27, 1979 3. been 5, March 2000); have in- (the 1999; flares time (G¨og¨us giant no the al. is bursts Two and et there the intensity and between burst power-law, tervals the a between is bursts correlation the of distribution otGmaryRpaes(eefe Gs and SGRs) (hereafter Repeaters Gamma-ray Soft h oua oe o GsadAP stemagne- the is AXPs and SGRs for model popular The 1 3 2 4 5 aoaoyo ihEeg srpyis AAGdadSpace Goddard NASA Astrophysics, Energy High of Laboratory rsn drs:Dprmn fAtooyadAstrophysics and Astronomy of Department address: Present Associate Research Council Research National A-K ejn srpyia etradAtooyDepart Astronomy and Center Astrophysical Beijing CAS-PKU CS WrdLbrtr)POBx83,Biig108,Chi 100080, Beijing 8730, P.O.Box Laboratory) (World CCAST h otgmarpaes(Gs.Acrigt hspcue ti e is it picture, this to headings: According Subject 2004-2005. th during for (SGRs). again c account active repeaters sph small-scale can become gamma the impacts some soft These through capture the kick will pass occasionally. large to they stars objects receive era, the strange comet-like also pre-supernova by these may the down When They during spun rapidly materials. velocities. fall-back be motion the could from stars formed these conditions, certain uigsproaepoin,srnesaswt lotbr quar bare almost with stars strange explosions, supernova During L x L ∼ b ∼ 10 AUEADNRUE OE O OTGMARYREPEATERS GAMMA-RAY SOFT FOR MODEL A NURTURE: AND NATURE A 1. T 35 10 E tl emulateapj style X INTRODUCTION 38 − − 10 crto,aceindisks accretion accretion, usr:gnrl—sas eto es atr—gamma-rays — matter dense — neutron stars: — general pulsars: 36 10 42 rss ergs r s erg − 1 − eli xesof excess in well , 1 igZhang Bing .Tefluence The 2. ; rf eso coe 3 2018 23, October version Draft 1 , 2 , ABSTRACT 3 .X Xu X. R. , et eigUiest,Biig107,China 100871, Beijing University, Peking ment, na lgtCne,Genet D20771 MD Greenbelt, Center, Flight 1 enyvnaSaeUiest,Uiest ak A16803 PA Park, University University, State Pennsylvania , n h oa ufc edstrength field surface polar the and rlojcso h Gsae“ae tag tr with stars strange “bare” cen- are (10 the SGRs fields that the magnetic propose in- normal of We without objects SGRs idea. tral the magnetar of the behavior troducing bursting the the derstand of behavior bursting the especially phenomenology SGRs. the was sources, to idea compared these “nurture” plausible as of the no connect magnetars) However, to pulsars. proposed (i.e. normal due the “nature” than with rather special due environment their be the may to from AXPs envi- “nurture” and that SGRs their denser argue the much to hence of a They behaviors peculiar in pulsars. the normal obser- located the the are the that than AXPs On ronment observed the (2000) interpret. and al. bursts to SGRs et the difficult Marsden ground, but are vational SGRs well, have can the phenomenology model scenario from The AXP a pulsar. such the Crab in the interpret & Alpar as stars fields Hernquist and neutron magnetic normal 2000) The (Chatterjee, Hernquist 2000). & (1999, al. independent Chatterjee et the 2000; from Narayan Chatterjee emerges by fossil-disk-accretion recently a studies AXPs hand, for other the model On addressed. erly ine pnonhsoya hthvn enproposed been having that as expe- have history they spindown and a progenitors, rienced massive explo- supernova some from from directly sions born are stars strange these oarmat,n la oiiedpnec between dependence super- positive associated clear the no of ages remnants, non-systematic the nova and the spindown dipolar assum- e.g., remains ing derived ages issues, also characteristic the It other between discrepancy some picture. how magnetar differ- the unclear intrinsically within not objects are straightforwardly ent objects not these are since AXPs interpreted and differ- SGRs the However, between ences 2000). Thompson 1996; 1995, Duncan nti etr eatmtt rps oe oun- to model a propose to attempt we Letter, this In 4 .J Qiao J. G. , eetn ussa bevdfrom observed as bursts repeating e mtcod n old ihsome with collide and clouds omet rcl“ot oe lu formed cloud comet “Oort” erical ufcsmyb omd Under formed. be may surfaces k 5 pce htSR10+4will 1900+14 SGR that xpected , qeeetdb h osldisks fossil the by exerted rque 4 n ec,hv ag proper large have hence, and s 12 − uss— bursts : 10 13 B ) easm that assume We G). p t. a eprop- be can etc., , L x , 2 for the AXPs within the fossil disk model (Chatterjee et star can naturally evade such a criticism, since the in- al. 2000; Alpar 2000). According to this model, some fall matter will be essentially converted into strange quark fallback materials from the supernova ejecta will form a matter within a very short period of time (∼ 10−7 s, Dai fossil disk around the strange star. The SGRs/AXPs are et al. 1995) when they penetrate into the star. A new- just such strange/neutron stars that have experienced the born bare strange star may have a very thin normal mat- “propeller” phase (rc ≪ rm < rl), and are now in the ter atmosphere (Xu et al. 2000), which is far less than “tracking” phase (rc ∼< rm < rl) when infall of the ma- the amount required to pollute the fireball. 3. Obser- terials onto the surface is possible and the star is X-ray vationally, SGRs tend to have larger proper motion ve- −1 bright. Here rl, rm and rc are the light cylinder, the mag- locities (∼ 1000km s ) than normal pulsars and AXPs. netospheric radius, and the corotating radius, respectively. Though we do not attempt to propose a detailed “kick” In our picture, AXPs may be still neutron stars. We will theory in the present Letter, we note that the formation attribute the SGR bursts to their occasionally collisions of a strange star rather than a neutron star may poten- with some comet-like objects in the dense environment of tially pose some possibilities to interpret the large proper the SGRs. We will show how various SGR properties as motion velocities of SGRs. Present kick theories invoke reviewed above could be accounted for within this picture. either hydrodynamically-driven or neutrino-driven mech- Our model differs from some other strange star SGR mod- anisms (Lai 2000). For the former, the kick arises from els (e.g. Alcock et al. 1986b; Cheng & Dai 1998; Dar & presupernova g-mode perturbations amplified during the de Rujula 2000). core collapse, leading to asymmetric explosion (Lai & Gol- dreich 2000). We note that the formation of a strange star 2. THE MODEL is a two-step process, i.e., the formation of a proto-neutron Strange stars (Haensel, Zdunik & Schaeffer 1986; Al- star and phase conversion. Neutrino emission in the sec- cock, Farhi & Olinto 1986a) are hypothetical objects based ond step could be significantly asymmetric since the phase upon the assumption that strange quark matter is more conversion may be off-centered due to the initial density stable than nuclear matter (Witten 1984; Farhi & Jaffe perturbation (Dong Lai, 2000, personal communication). 1984). Though the existence of such stars are still sub- An off-centered transition condition may be also realized ject to debate, some evidence in favor of strange stars in the presence of an electron-neutrino-degenerate gas in has recently been collected (e.g. Li et al. 1999a, 1999b; a proto-neutron star (Benvenuto & Lugones 1999). Thus Titarchuk & Osherovich 2000). Strange stars can be ei- the phase transition process may give an additional kick ther bare or have normal matter crusts (Alcock et al. to achieve a higher velocity. More detailed investigations 1986a). They can be formed directly during or shortly are desirable to verify these proposals. after some supernova explosions when the central density We now describe the model in more detail. We assume of the proto-neutron stars is high enough to induce phase that the progenitor of a strange star is surrounded by a conversion (e.g. Dai, Peng & Lu 1995; Xu, Zhang & Qiao huge spherical comet cloud which is similar to the Oort 2000). If a strange star is born directly from a supernova Cloud in the solar system. They may be formed during explosion, it is likely that the star might be almost bare the formation of the massive star, and have almost fin- (Xu et al. 2000). Some radio pulsars may be such strange ished gravitational relaxation. Since the progenitor of a stars with exposed bare quark surfaces (Xu, Qiao & Zhang strange star should have a mass larger than 10M⊙, we 1999). expect that the radius of the Oort Cloud in the progen- There are three main motivations for us to choose (bare) itor system may be one order of magnitude larger than strange stars rather than neutron stars to interpret the the solar value (∼ 2 × 1013 km Weissman 1990)., i.e., 14 SGRs. 1. A prominent feature of the SGR bursts is ro ∼ 2 × 10 km. Supernova explosion blast waves will their super-Eddington luminosities. This feature has been not destroy these comet clouds (Tremaine & Zytkow 1986). regarded as a strong support to the magnetar model, The luminous UV/optical emission from the progenitor is since superstrong magnetic fields may considerably sup- also unlikely to evaporate the comets. Although the radia- press the Thompson cross section and consequently raise tion flux received by the Oort Cloud comets of the massive the Eddington limit to several orders of magnitude higher star should be about a factor of 30 higher than that re- (Paczynski 1992; Thompson & Duncan 1995). However, ceived by the Solar Oort Cloud comets, the existence of the luminosities of the most luminous events, e.g., the ini- copious “Kuiper Belt” comets in the solar system (which tial spike of the March 5 event with L ∼ 1044ergs s−1, are is 4 orders of magnitude closer to the sun than the Oort still above the enhanced Eddington limit. An important Cloud) hints that comets can withstand shining with much merit of bare strange stars is that they are not subject higher luminosities. The influence of nearby stars may be to Eddington limit at all since the bulk of the star (in- also not prominent due to the same reason, even if SGRs cluding the surface) is bound via strong interaction rather are associated with luminous star clusters (e.g. Vrba et than gravity (Alcock et al. 1986a). This presents a clean al. 2000). Using the typical proper motion velocity of 3 −1 interpretation to the super-Eddington luminosities of the the SGRs, VSGR ∼ 10 km s , and the typical supernova 4 SGRs, as long as the impacts are not in the polar cap remnant age, tSGR ∼ 10 yr, the distance that a SGR has region where the accretion flow from the fossil accretion traveled since its birth is r ∼ 3 × 1014 km, remarkably disk is channeled. 2. As criticized by Thompson & Dun- consistent with the distance of the Oort Cloud ro. Thus can (1995), the impacting model for neutron stars suf- the age clustering of the SGRs near 104 yr is simply due fers the baryon contamination problem. The impact may to that this is the age when a lot of impacts are available. load too much baryonic matter to cause adiabatic dilu- The lack of bursts from the AXPs may be due to their tion of photons in an expanding fireball to energies well much smaller proper motion velocities, and probably also below the hard X-ray and γ-ray band. A bare strange their different nature, i.e., neutron stars. Although SGR 3

1806-20 has a smaller projected proper motion velocity (cf. Pineault & Poisson 1989). This is because the stars, −1 (V⊥ ∼ 100km s ), we assume that it has a similar veloc- which also belong to a gravitationally self-organized sys- ity as other SGRs, with a large velocity component along tem but in a larger scale, have a well-known Salpeter’s the direction of the line-of-sight. The capturing rate could power law mass distribution7. The bursting intervals de- ˙ ∼ 2 2 be estimated as N π(2GM∗/VSGR ) VSGR nc, where nc is pend on the spatial distribution of the comets within their the number density of the comets within the Oort Cloud. orbits, thus there should be no correlations between the −1 To produce a bursting rate of 1 yr , nc is required to be luminosity of a burst and the waiting time before or after ∼ (10−22 − 10−23)km−3. This is about 4 orders of mag- this burst. All these are in excellent agreement with the nitude higher than the inferred comet number density in statistics of the SGR bursts (G¨ug¨us et al. 1999, 2000). the solar Oort Cloud [∼ (10−26 − 10−27)km−3, Weissman Adopting the typical comet mass as the lowest value of 1990], but about 3-4 orders of magnitude lower than the the power-law distribution, the comet number density in- inferred number density in the Kuiper Belt of solar sys- ferred above gives a total comet mass of about 0.1M⊙, not tem [∼ (10−18 − 10−20)km−3, Weissman 1990]. Keeping unreasonable due to the same reasons discussed before. in mind that the mass density of the Oort Cloud and the When a comet falls into the strange star magnetosphere, number density of the comets may be enhanced due to it will endure tidal distortion and compression so that accretion from the dense environment in the supernova they are elongated dense solid objects when they reach the remnants (Marsden et al. 2000) and that the number den- strange star surface (Colgate & Petschek 1981). Because sity quoted for the solar system might be a lower limit they are globally neutral solid bodies, these comets will not (Weissman 1990), the required nc may be not unreason- be channeled to the polar cap regions where the asymp- able. Some SGRs have more frequent bursting rate. This totic accretion flow from the fossil-disk takes place. This may be due to that the strange star has captured a denser ensures the super-Eddington luminosity emission from a small-scale comet cloud. bare strange star. The large Coulomb barrier above the When the strange star passes through its Oort Cloud, it bare quark surface (Alcock et al. 1986a) will not prevent may capture some small-scale clouds and make them circu- the object from penetrating into the quark core. The ris- late around it within its rest frame6, and the comets within ing rate of the energy released from the falling object is the cloud will be occasionally accreted onto the strange similar to the rising rate of the density from vacuum to star surface. The different bursting luminosities (or more solid iron (Howard, Wilson & Barton 1981; Katz, Toole & precisely the different energies for different bursts) corre- Unrul 1994), so that the rising time of the bursts could be spond to different masses of the impacting objects. During of sub-millisecond to millisecond order, consistent with the each impact, the energy released is a sum of the gravita- observations of the giant flares (Hurley et al. 1999). The tion energy and the phase conversion energy. The former duration of the hard spike observed in the giant flares cor- 2 has an efficiency of ηgrav = GM/(Rc ), which is ∼ 20.6% responds to the continue infall time of the object, which is for typical strange star parameters, and the latter has an of the order of 0.1-1 s (e.g. Katz et al. 1994). The August efficiency of ηconv = ∆ǫ/(930MeV), where ∆ǫ is the en- 27 giant flare from SGR 1900+14 has slightly smaller to- ergy per baryon released during the phase conversion. The tal energy but both longer rising time and longer duration value of ∆ǫ is rather uncertain which depends on unknown of the initial spike than the March 5 event of SGR 0526- QCD parameters (e.g. MIT bag constant, strange quark 66. This may be understood by assuming that the falling mass and the coupling constant for strong interaction). object of the March 5 event is an asteroid while that of Some recent calculations (e.g. Bombaci & Datta 2000) the August 27 event is a comet, both with a similar mass. show that ∆ǫ ∼ 100 MeV may be reasonable, and we will During an impact, both gravitational energy and phase adopt this value for indicative purpose. The deviation of transition energy will be released in a sufficiently short this value from the exact value is not important since this period of time. Since there is no baryon contamination only reflects slightly different required comet masses. We for a bare strange star, the energy will be mainly released thus get ηconv ∼ 11%. Assuming that about one half of as photons and neutrinos. Soon an optically thick pair the energy will be brought away by neutrinos, the total fireball will form via the processes such as γ − γ (Thomp- − γ-ray emission efficiency is ηγ ∼ (ηgrav + ηconv)/2 ∼ 16%. son & Duncan 1995) and γ E (Usov 1998) processes 38 42 −1 Thus the repeating bursts with Lb ∼ 10 − 10 erg s near a bare quark surface. The magnetic field will con- and typical bursting time ∼ 0.1 s correspond to the comet fine this pair plasma, and the soft fading tail of the gi- masses within the range of 7 × (1016 − 1020) g. These are ant flares can be due to contraction of this pair bubble reasonable values for comet masses. The so-called giant (Thompson & Duncan 1995; Katz 1996). For the accre- flare requires an object (an asteroid or a comet) with a tion case discussed here, the energy deposited into the pair mass of several 1024 g. In view that the giant flares are bubble is continually supplied, which is different from the rather rare, it is reasonable to suppose that such large ob- abrupt-release case in the magnetar model. Thus the re- jects may exist in some dense clouds. Notice that all the quired magnetic field for confinement is less demanding, 2 1/2 10 1/2 −2 luminosities quoted above are derived under the assump- i.e. B > (2Lb/R c) =8 × 10 GL44 R6 (Katz 1996). tion of isotropic emission. For impacting events discussed The trapped pair plasma has a characteristic temperature here, during which the emission is anisotropic, the required of T ∼ 23keV, and the emergent spectrum is roughly a comet masses may be lowered by a factor of 10-100. There blackbody with absorption, which is almost independent is no mass distribution data available for the solar comets, on the size of the impacting object (Katz 1996). All these but we expect that the distribution should be a power law match the SGR phenomenology well.

6The fossil disk around the star may be a good perturber of the comets, which enhances the chances of captures. 7Observationally the giant flares belong to the high end of the power-law fluence distributions. 4

Sometimes the accreting matter is not solid, but is an In our model, a fossil-disk is assumed to interpret the ionized plasma. In such cases, the effect of the large spin-down behavior and the quiescent emission. It is ex- Coulomb barrier should be carefully investigated. The pected that emission (especially during the bursts) should kinetic energy of a proton when it is accreted onto the have some interactions with the disk with certain optimal strange star surface is Ek ∼ GmpM/2R ∼ 100 MeV. How- geometric configurations. The chance to see such inter- ever, when materials are accreted as fluid, it is possible actions should be small due to the small size of the disk. that the kinetic energy will be radiated away via heat be- The 6.4 keV emission line from the August 19 burst of fore hitting the surface. In the accretion column, the scale SGR 1900+14 (Strohmayer & Ibrahim 2000) may be due of the shock wave zone is dependent on the accretion rate. to the disk’s re-processing the bursting emission. It is found that when the accretion luminosity is less than ∼ 4 × 1036erg s−1, the deceleration of the accreting fluid 3. DISCUSSIONS can be neglected (Basko & Sunyaev 1976). This is true for In this Letter, we propose that the peculiar behaviors of SGRs and AXPs since the quiescent X-ray luminosities of 35 − 36 −1 the SGRs are due to both their Nature (bare strange stars) these objects are only 10 10 erg s . The Coulomb and their Nurture (the Oort Cloud in the dense environ- barrier of a bare strange star is EC = (3/4)Vq ∼ 15 MeV, 3 2 ∼ ment). Instead of invoking the magnetar hypothesis, we where Vq /3π 20 MeV is defined as the quark charge adopt the strange star hypothesis to interpret some inter- density inside the quark matter (Alcock et al. 1986a). esting features of the SGRs. It is worth pointing out that Thus the accreting fluid, including that from the fossil- the periodic activity does not depend on the nature of the disk, can also penetrate into the strange quark core. This central star. Although some authors argue that the burst- ensures the bare strange star picture conjectured in this ing phenomenology (e.g. super-Eddington luminosity) can paper. The accreted matter at the polar cap will un- be also interpreted by colliding comets with a neutron star dergo phase transition and release some extra energy. It (e.g. Katz 1996), we think that a bare strange star is a is unclear whether the slightly harder spectra of the qui- cleaner interpretation due to the reasons discussed above. escent emission of the SGRs with respect to the AXPs is An important criterion to differentiate our model from the caused by phase transition (we suppose AXPs to be neu- magnetar model is the activity period. If SGR 1900+14 tron stars). The enigmatic precursor of the August 29 will be turned on again in 2004, the magnetar model is event of SGR 1900+14 (Ibrahim et al. 2000) may be due then not favored, since it may be hard to find a mecha- to infall of an extended ionized cloud which is followed by nism to trigger the magnetic field decay instabilities peri- a solid object. odically. If it turns out that some problems (e.g. super- Depending on the impacting angles during the captures, Eddington luminosity, baryonic contamination, and large the small-scale comet clouds may have various orbital pe- proper motion velocity) are not solvable within the neu- riods and eccentricities, so that the precipitation onto the tron star impacting model, the bursts from SGR 1900+14 star surface is expected to be periodic, especially when the in time then present a support to the strange star hypoth- comets are clustered into a clump in the orbit rather than esis and will bring profound implications for fundamental being spread over the orbit. In fact, SGR 0526-66 has physics. been reported to have a 164-day period in bursts (Roth- According to this picture, there might be some other schild & Lingenfelter 1984). Its present quiescence may be bare strange stars which may also have super-Eddington because the previous comet cloud has been depleted due to bursts when they collide with comet-like objects. However, many cycles of precipitations. If it becomes active again, they must have passed through the Oort Cloud and/or in a different period is expected since it may have captured a much less dense environment, so that the chance to de- a different cloud. SGR 1900+14, on the other hand, has tect repeating bursts is rare. Single bursting events are experienced three active periods during 1979 (Mazets et possible and they may account for a small portion of the al. 1981), Jun. - Aug. 1992 (Kouveliotou et al. 1993), short, soft bursts in BASTE data. The association of SGR and May 1998 - Jan. 1999 (G¨og¨us et al. 1999). The ac- 1806-20 with a radio plerion may not be compatible with tive periods are short, and the interval between the first the present picture, but recent results indicate that the two is roughly twice of that between the last two (about 6 non-thermal radio core of the supernova remnant G10.0- year). This makes us to suspect a 6-year period for SGR 0.3 may be associated with another luminous blue variable 1900+14 activity. According to this picture, there should rather than with the SGR (Hurley 1999). be some bursts in 1986. But this is within the “detec- tion gap” of the SGR bursts when there is no gamma-ray mission in space before BATSE was launched. Thus we BZ acknowledges stimulated discussions with Matthew expect that SGR 1900+14 should become active again dur- Baring, Zigao Dai, Alice Harding, Dong Lai, David Mars- ing 2004-2005. This will give a definite test to our model. den and Vladimir Usov, and informative email contacts SGR 1806-20 activity does not have a clear periodicity. with Pinaki Chatterjee, Chryssa Kouveliotou, Tan Lu However, a plausible 733-day period is found from its tim- and Chris Thompson. RXX thanks supports from NNSF ing residual (Woods et al. 2000). This might be due to of China (19803001). GJQ acknowledges supports from that comets are almost spread over the whole orbit and the NNSF of China, the Climbing Project of China, and the spin-down of the strange star is perturbed by this comet Research Fund for the Doctoral Program Higher Educa- orbit. tion. 5

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