THE ORIGIN OF INTERGALACTIC THERMONUCLEAR SUPERNOVAE A. G. Kuranov* and K. A. Postnov** SternbergAstronomicalInstitute,Universitetskiipr.13,Moscow,119992Russia Abstract—Thepopulationsynthesismethodisusedtostudythepossibilityofexplainingtheappreciable fractionof the intergalactic type-Ia supernovae (SN Ia), 20+12%, observedin galaxy clusters(Gal-Yam −15 4 etal.2003)whenclosewhitedwarfbinariesmergeinthecoresofglobularclusters.Inatypicalglobular 0 cluster,thenumberofmergingdoublewhitedwarfsdoesnotexceed∼10−13peryearperaveragecluster 0 starintheentireevolutiontimeofthecluster,whichisafactorof∼3higherthanthatinaMilky-Way-type 2 spiralgalaxy.From5to30%ofthemergingwhitedwarfsaredynamicallyexpelledfromtheclusterwith n barycentervelocities up to 150 km s−1. SN Ia explosionsduring the mergersof double white dwarfs in a densestarclustersmayaccountfor∼1%ofthetotalrateofthermonuclearsupernovaeinthecentralparts J ofgalaxyclustersifthebaryonmassfractioninsuchstarclustersis∼0.3%. 2 2 INTRODUCTION Atpresent,itisnotcompletelyclearwhichofthese 2 scenarios (or both) make the largest contribution 5 SNIa(thermonuclearsupernovae)areamongthe to the SN Ia rate, and a considerable observational 4 most important objects in modern astrophysics, be- effort is being made to find the Galactic population 1 0 causethemaximumoftheiropticallightcurveshasa of double WDs with a total mass close to or larger 4 smallspread.Therefore,theycanbeused1 asastan- than the Chandrasekhar limit (e.g., the SPY project 0 dard candle in modern cosmology, and fundamental by Napiwotzki et al. 2003). We will adhere to the h/ conclusions about the expansion kinematics of the scenarioofmergingdoubleWDsastheprogenitorsof p Universe can be reached (Riess et al. 1998; Perl- type-Iasupernovae.Therecentdiscoveryofhydrogen - mutter et al. 1999). The physical cause of an SN Ia emissionlinesinthespectrumofSN2002ic(Hamyu o explosion is the thermonuclear explosion of a white et al. 2003) cannot rule out this formation channel r of thermonuclear supernovae, because such SN Ia t dwarf(WD)withamassclosetotheChandrasekhar s areatypical;theiroriginisthesubjectofdebate(e.g., a limit(HoyleandFauler1960).Thisideaisfullycon- : firmed by detailed numerical calculations ofthe evo- LivioandRiess2003;ChugaiandYungelson2003). v lution of a white dwarf in a binary system (see, e.g., A purposeful search for supernovae in Abell i X Dunina-Barkovskataetal.2001).TheWDmasscan clusters of galaxies (the WOOTS project; Gal-Yam r increase during mass transfer between the compo- et al. 2003) has revealed that two of the seven a nents in a close binary, which determines the astro- SN Ia found (SN 1998fc in Abell 403 at z =0.1 physical sources of such supernovae—double WDs and SN 2001al in Abell 2122/4 at z =0.066)) have thatmerge throughgravitationalradiation(Ibenand no obvious host galaxies and can be associated Tutukov 1984; Webbink 1984) or accreting WDs in only with faint dwarf galaxies with M >−12m. R semidetached or symbiotic binaries with a second In reality, in both cases, the supernovae are pro- nondegenerate component (Whelan and Iben 1973; jected onto the halos of the central cD galaxies in Nomoto 1982). SN Ia are observed in galaxies of all the corresponding clusters. However, the authors morphologicaltypes(van denBergetal.2003),and rejected the possibility that they belong to these theirrate(inSNUunits)dependsweaklyonthetype galaxiesbecauseofthelargeradial-velocitydifference ofgalaxy(seeCapellaroetal.(1997)andmorerecent (750−2000kms−1)betweenthesupernovaeandthe papersofCapellaro’sgroup). correspondingcDgalaxies. Assuming a modified Schechter luminosityfunc- *E-mail:alex@xray.sai.msu.ru tion for the galaxies in the Virgo cluster (Trentham **E-mail:pk@sai.msu.ru and Tully 2002), the luminosity fraction of the dwarf 1However,withcertainreservations,upto40%ofSNIamay be peculiar (Lee et al. 2001), plus a significant spread of galaxiesintheclustersunderstudyshouldhavebeen theoreticallightcurves(Sorokinaetal.2000). less than 0.3%. If the supernova rate is proportional THE ORIGIN OF INTERGALACTIC SUPERNOVAE 141 to luminosity, and if the fraction of the supernovae then ∼1% of SN Ia in the cluster centers can be withoutobvioushostgalaxiesisontheorderof10%, naturallyexplainedwithoutadditionallyassumingthe thisleadstotheir∼30-foldexcessamongsuchdwarf presence of 10% of the intergalactic stellar popula- galaxiescomparedtohigh-massgalaxies.Therefore, tion. these supernovae are believed to have exploded out- sidegalaxies(intergalacticsupernovae)asaresultof theevolutionoftheintergalacticstellarpopulation.It isconcludedfromtheseobservationsthatthefraction THE MODEL of the intergalactic SN Ia is 20+12%, in accordance −15 with the theoretically expected fraction of the stars TheStructureandEvolutionofaGlobularCluster outsidegalaxiesduetotidalinteractionbetweenclus- ter galaxies. The authors themselves (Gal-Yam et al. 2003) point out a low statistical significance of Inourcalculations,weusedaMichie–Kingmodel theresultobtained,andsuchahighpercentageofthe (Michie1963)todescribethestructureoftheglobular extragalactic SN Ia should be confirmed by further cluster.Thestellarpopulationwasbrokendowninto observations. subsystems (depending on their mass); their space There is a potential channel for the formation of densityραwasfittedbyapowerlaw: intergalactic supernovae through the dynamical ex- pulsionofcloseWDpairsfromthesystemofgalactic ρcα, r ≤rcα, globularclusters (GCs).Thestellar mass fractionin ρα(r)=ρcα(r/rcα)−2, rcα Et, where E and J are the energy and the angular mo- energy E. Stars with E >E are assumed to have t mentum (per unit mass), respectively; and J (E) is c the value of J for a star in a circular orbit with escapedfromthecluster. 142 KURANOV, POSTNOV Detailedcalculationsoftheevolutionofthestan- of close systems. Note also that the above authors dard modelreveal acollapseoftheinner coreand an assumed up to 30% of the initially hard binaries in expansionoftheouterlayers.Asfollowsfromnumer- the GC. We choose an upper limit of 1000R for ⊙ icalcalculations(see,e.g.,Kimetal.1998),thecore theinitialbinarysemiaxes,whichcorresponds tothe contraction atlatestages asymptotically approaches criteria by Fregeau et al. (2003). Thus, the high (at apowerlaw: firstglance)percentageoftheinitiallybinarysystems thatweadoptedisnotoverestimatedandisconsistent ρ (t)∼ρ (0)(1−t/t )−1.2,v (t) (4) c c coll m with available observations. Unfortunately, we can- ∼v (0)(1−t/t )−0.12, notaccuratelyestimatethenumberofnewlyforming m coll binaries duetotidalcaptures. Inanycase, theirper- where t is the current time, and t is the collapse coll centageismuchlowerthanthefractionoftheinitially timeofthecluster. binarysystems. As the GC core contracts, the central number density of the stars rapidly increases, which causes the formation rate and the binding energy of bi- TheEvolutionofaBinaryinaGlobularCluster nary stars to increase. Once the initial collapse has TheScenario Machinepopulationsynthesis code stopped,onemightexpectanexpansionofthecluster (Lipunovetal.1996)wasusedtomodeltheevolution core due to the tidal formation of binary stars. For ofbinaryandsinglestars.Weusedtheinitialdistribu- some time, the newly forming binaries will be the tions energy source that maintains the expansion of the innerclusterregions.Theexpansioncanbedescribed f(lga)=const, (6) by the following asymptotic formulas (see Kim et 10R al.1998): max ⊙ v )×100∼100 (in this estimate, galaxies. Thus, this model predicts the existence of e faint ((cid:9)M (cid:10)∼−10m) host clusters for SN Ia. It is the fractionofthe binaries with barycenter velocities R hoped that the purposeful search for type-Ia super- higherthantheescapevelocityfromthecluster,v ∼ e novae being conducted at present as part of various 100kms−1,wastakentobef(>v )∼1/100),which is also insufficient to explain theetruly intergalactic projects(see,e.g.,Tonryetal.2003)willimprovethe existingstatisticsandwillrevealthefainthostgalax- supernovae. ies and astrophysical sources of intergalactic SN Ia. cD galaxies. Let us now turn to the central The absence of host clusters with M >−8m...− cD galaxy as the source of intergalactic supernovae. R 10m may serve as a critical argument for choosing AlthoughSN 1998fc in Abell403 and SN 2001al in the model of intergalactic type-Ia supernovae from Abell2122/4areprojectedontothehalosofthecen- intergalacticstars. tral сD galaxies (the projected distance is 160 kpc), we rule out the possibility that they belong to these galaxies because of the radial-velocity difference CONCLUSIONS (Gal-Yam et al. 2003). The giant elliptical galaxies in the cluster centers are known to have a huge We haveconsidered the possibleformation chan- system ofglobularclusters (upto10000). Usingthe nelofintergalacticSNIaduringthemergersofdou- results obtained in our calculations (∼300 mergers ble white dwarfs that evolve and are expelled from of double WDs in cluster cores and ∼100 merging dense star clusters (GCs, the nuclei of dwarf ellip- pairs escaped after the core collapse), we obtain an tical galaxies, etc.) when they dynamically interact average estimate of the maximum SN Ia rate due to with a third star (tripple collisions). The population the WD evolution in the GC in projection onto the synthesis method was used to model the formation halo of the cD galaxy, 400×104/(5×109)∼10−3 and evolutionofclose doublewhitedwarfs incluster peryear.OnlyafewpercentofsuchdoubleWDscan cores by taking into account the time evolution of havebarycentervelocitieshighenoughtoescapefrom their physical parameters and to calculate the rates thegalaxy;theycannotexplaintheobservations. ofescape ofsuchobjects fromclusters. Weobtained their distributions in escape velocities from clusters, inmergerrates,and indistances fromthehostclus- TheMergersofDoubleWDsinVirializedStar ter after escape. We showed that the mean merger ClustersattheCentersofGalaxyClusters rate of double WDs after the core collapse could Is there an alternative explanation for the obser- reach ∼10−13 per year per average GC star. In a vations by Gal-Yam et al. (2003) that does not ap- typical GC, the number of expelled WD pairs after peal to the evolution of 10−20% of the stars out- the GC core collapse is ∼100. For a galaxy cluster side galaxies? In our view, the most plausible expla- with several thousand members, this estimate yields nation for intergalactic supernovae is the merger of a formation rate of intergalactic thermonuclear su- WD pairs in a virialized system of star clusters in pernovae<0.005peryear,whichismuchlowerthan thecentral regionsofgalaxyclusters.Itfollowsfrom the observed highrate of intergalactic supernovae of observations of the central parts ofthe Virgo cluster this type. We hypothesize that the possible observed and from simulations (see the recent review article high percentage of intergalactic SN Ia without any by Lee (2002) and references therein) that a huge obvious host galaxies can be explained in part by system of blue GCs with a large velocity dispersion the evolution of double WDs in dense star clusters. mustbeformedduringtheformationofgiantelliptical A system of such clusters naturally arises near the galaxies. Recent observations of intergalactic (up to centerofgalaxyclustersduringtheformationofgiant 250 kpcfrom the center) GCs inthenearby Hydra I elliptical galaxies and, subsequently, during the tidal andCentaurusclusters(Hilker2002)leadtoasimilar interaction between the galaxies that pass near the conclusion. An enhanced density of star clusters in clustercenter.Thishypothesiscanbeverifiedthrough thecentralregionsofgalaxyclustersnaturallyarises observations of the faint host clusters of SN Ia in during the merger of the galaxies that form giant nearbygalaxyclusters. 146 KURANOV, POSTNOV ACKNOWLEDGMENTS The diffusion coefficients that contain E and J can be expressed in terms of (cid:9)∆v (cid:10),(cid:9)∆v2(cid:10) and WewishtothankA.S.RastorguevandO.K.Sil’chenko || || for helpful discussions and L.R Yungelson for valu- (cid:9)(∆v⊥)2(cid:10) are the locally calculated velocity diffusion able remarks. This work was supported by the Rus- coefficients: sianFoundationforBasicResearch(projectnos.03- 1 1 (cid:9)∆E(cid:10)=v(cid:9)∆v (cid:10)+ (cid:9)∆v2(cid:10)+ (cid:9)∆v2(cid:10), 02-16110аand03-02-06733mas). || 2 ⊥ 2 || (cid:9)∆E2(cid:10)=v2(cid:9)∆v2(cid:10), || APPENDIX J r2 (cid:9)∆J(cid:10)= (cid:9)∆v (cid:10)+ (cid:9)∆v2(cid:10), v || 4J ⊥ Thepositionofabinaryinaglobularcluster. J2 1 J2 The relative motions of stars in a GC produce (cid:9)∆J2(cid:10)= (cid:9)∆v2(cid:10)+ (r2− )(cid:9)∆v2(cid:10), continuous fluctuations of the gravitational field. In v2 || 2 v2 ⊥ turn,thesefluctuationscausethemagnitudeanddi- (cid:9)∆E∆J(cid:10)=J(cid:9)∆v2(cid:10) || rection of the velocity of each star to change. As a result, the energy E =v2/2+φ(r) and the angular For a Maxwellian velocity distribution of the field stars, the diffusion coefficients reduce to standard momentumJ =r×v ofthestarwillchange.When t form(Spitzer1987): calculating each evolutionary track, the changes in these parameters in a time interval ∆t due to the m (cid:9)∆v (cid:10)=−2 1+ n Γk2G(x), gravitational interaction with the surrounding stars || m f canbecalculatedbyusingtheformula (cid:17) f(cid:18) G(x) ∆E =nǫ1+n1/2y1ǫ22, (cid:9)(∆v||)2(cid:10)=2nfΓk x , ∆J =nj1+n1/2y2j22, (cid:9)(∆v )2(cid:10)=2n ΓkΦ(x)−G(x), ⊥ f x ∆t=nP(E,J), whereΦ(x)istheerrorfunction where y and y , the random numbers drawn from 1 2 x a normal distribution with a mean (cid:9)y (cid:10)=(cid:9)y (cid:10)=0 1 2 2 and a variance (cid:9)y2(cid:10)=(cid:9)y2(cid:10)=1, are chosen from the Φ(x)= exp−y2dy 1 2 π1/2 correlationconditioninsuchawaythat (cid:16) 0 (cid:9)y y (cid:10)=ξ2/ǫ j . and 1 2 2 2 Φ(x)−xΦ′(x) Weusedamethodwithaveragingovertheorbitsim- G(x)≡ . ilar to the method by Shapiro and Marchant (1978) 2x2 and Marchant and Shapiro (1979) to determine the Using E and J,we can determine the orbitalpa- coefficientsǫ andǫ : 1 2,1 rametersofthestarwithintheGC:theorbitalperiod ra ra ǫ1 =2 (cid:9)∆E(cid:10)dr/vr, P(E,J)=2 dr/vr, (cid:16)rp (cid:16)rp ra ǫ22 =2 (cid:9)∆E2(cid:10)dr/vr, the pericenter rp and the apocenter ra of the stellar (cid:16)rp orbitintheclusterfromthecondition ra v2 =2E−2φ(r)−J2/r2 =0. j =2 (cid:9)∆J(cid:10)dr/v , r 1 r (cid:16)rp The rate of interaction between a binary b and an j2 =2 ra(cid:9)∆J2(cid:10)dr/v , αsubsystemofstarsattimetisgivenbytheformula 2 r (cid:16)rp 2 ra R (t)=σ × n (r,t)v(r,t)/v dr. ξ2 =2 ra(cid:9)∆E∆J(cid:10)dr/vr. αb αb P(E,J) (cid:16)rp α r (cid:16)rp Here, rp and ra are the pericenter and apocenter of REFERENCES the stellar orbit in the cluster. These coefficients are 1. M.Bellazzinni,P.F.Fusi,P.Montegriffo,etal.,As- the mean rates of change in E and J due to several tron.J.123,2541(2002). approaches over the orbitalperiodand themean cu- 2. E.Capellaro,M.Turatto,D.Yu.Tsvetkov,etal.,As- mulativevaluesovertheorbitalperiod. tron.Astrophys.322,431(1997). THE ORIGIN OF INTERGALACTIC SUPERNOVAE 147 3. N. N. Chugai and L. R. Yungel’son, Pis’ma Astron. 24. R. W. Michie, Mon. Not. R. Astron. Soc. 125, 127 Zh.(2004,inpress);astro-ph/0308297(2003). (1063). 4. N. V. Dunina-Barkovskaya, V. S. Imshennik, 25. S. Mikkola, Mon. Not. R. Astron. Soc. 208, 75 S. I. Blinnikov, Pis’ma Astron. Zh. 27, 412 (2001) (1984). [Astron.Lett.27,353(2001)]. 26. R. Napiwotzki, N. Christlieb, H. Drechsel, et al., 5. M.B.Davis,W.Benz,andJ.G.Hills,Astrophys.J. Messenger112,25(2003). 424,870(1992). 27. G.Nelemans,L.R.Yungelson,S.F.PortegiesZwart, 6. J. M. Fregeau, M. A. Gurkan, K. J. Joshi, andF.Verbunt,Astron.Astrophys.365,491(2001). and F. A. Rasio, Astrophys. J. (in press); astro- 28. K.Nomoto,Astrophys.J.253,798(1982). ph/0301521(2003). 29. S.Perlmutter,G.Albering,G.Goldhaber,etal.,As- 7. M. Hamyu, M. M. Phillips, N. B. Suntzeff, et al., trophys.J.517,565(1999). Nature(inpress);astro-ph/0306270(2003). 30. D.Pooley,W.H.Lewin,S.F.Anderson,etal.,Astro- 8. W.E.Harris,Astrophys.J.112,1487(1996). phys.J.591,131(2003). 9. D. C. Heggei, C. Douglas, and P. Hut, Astrophys. J.Subbpl.Ser.85,347(1993). 31. A. G.Riess,A. V. Filippenko,P.Challis, et al., As- 10. D.C.Heggie,P.Hut,andS.L.W.McMillan,Astro- tron.J.116,1009(1998). phys.J.467,359(1996). 32. E.H.RubinsteinandC.D.Bailyn,Astrophys.J.474, 11. M.Hilker,astro-ph/0210566(2002). 701(1997). 12. F. Hoyle and W. A. Fauler, Astrophys. J. 132, 565 33. S.L.ShapiroandA.B.Marchant,Astrophys.J.225, (1960). 603(1978). 13. J.R.Hurley,C.A.Tout,andO.R.Pols,Mon.Not.R. 34. M.M.SharaandJ.R.Hurley,Astrophys.J.571,830 Astron.Soc.329,897(2002). (2002). 14. I. Iben, Jr. and A. V. Tutukov, Astrophys. J., Suppl. 35. E.I.Sorokina,S.I.Blinnikov,O.S.Bartunov,Pis’ma Ser.54,355(1984). Astron. Zh. 26, 90 (2000) [Astron. Lett. 26, 67 15. A. Gal-Yam, D. Maoz, P. Guhathakurta, and (2000)]. A.V.Filippenko,Astron.J.125,1087(2003). 36. L. Spitzer, Jr., Dynamical Evolution of Globular 16. S.S.KimandH.M.Lee,Astron.Astrophys.347,123 Clusters (Princeton Univ. Press, Princeton, 1987; (1999). Mir,Moscow,1990). 17. S.S.Kim,H.M.Lee,andJ.Goodman,Astrophys.J. 37. J.L.Tonry,B.P.Schmidt,B.Barris,etal.,Astrophys. 495,768(1998). 18. B. V. Kukarkin, Globular Star Clusters (Nauka, J.(inpress);astro-ph/0305008(2003). Moscow,1974)[inRussian]. 38. N. Trentham and R. B. Tully, Mon. Not. R. Astron. 19. M.G.Lee,J.KoreanAstron.Soc.35,1(2002). Soc.335,712(2002). 20. W.Lee,A.V.Filippenko,R.R.Treffers,etal.,Astro- 39. S. van den Berg, Li Weidong, and A. Fillippenko, phys.J.546,734(2001). Publ. Astr. Soc. Pac. (in press); astro-ph/0308195 21. V.M.Lipunov,K.A.Postnov,andM.E.Prokhorov, (2003). Astrophys.SpaceSci.Rev.9,1(1996). 40. R.F.Webbink,Astrophys.J.227,355(1984). 22. M.LivioandA.Riess,submittedtotheAstrophys.J.; 41. J. Whelan and I. Iben, Jr., Astrophys. J. 186, 1007 astro-ph/0308018. (1073). 23. A.B.MarchantandS.L.Shapiro,Astrophys.J.234, 317(1979). 4

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