Outflow-Driven Transients from the Birth of Binary Black Holes I: Tidally-Locked Secondary Supernovae
aa r X i v : . [ a s t r o - ph . H E ] N ov Draft version September 7, 2018
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OUTFLOW-DRIVEN TRANSIENTS FROM THE BIRTH OF BINARY BLACK HOLES I:TIDALLY-LOCKED SECONDARY SUPERNOVAE
Shigeo S. Kimura , Kohta Murase , and Peter M´esz´aros Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA Department of Astronomy & Astrophysics, Pennsylvania State UNiversity, University Park, Pennsylvania 16802, USA Center for Particle and Gravitational Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA Yukawa Institute for Theoretical Physics, Kyoto, Kyoto 606-8502, Japan
ABSTRACTWe propose a new type of electromagnetic transients associated with the birth of binary black holes(BBHs), which may lead to merger events accompanied by gravitational waves in ∼ . − ∼ − erg and an outflow velocity of ∼ cm s − , resulting in an optical transient with an absolute magnitude from ∼ −
14 to ∼ − ∼ − Keywords: supernovae: general — black hole physics — binaries: close — gravitational waves —accretion, accretion disks INTRODUCTIONThe advanced Laser Interferometer Gravitational-wave Observatory (LIGO) revealed the existence ofblack holes (BH) of ∼ ⊙ through the detectionof gravitational waves (GWs) from mergers of binaryblack holes (BBHs) (Abbott et al. 2016a,b,c). Theorigin of BBHs is under active debate, and severalscenarios have been proposed, such as primordial blackhole binaries (e.g., Nakamura et al. 1997; Sasaki et al.2016; Mandic et al. 2016), multi-body interactionsin star clusters (e.g., Sigurdsson & Hernquist 1993;Portegies Zwart & McMillan 2000; Rodriguez et al.2016), and evolution of field binaries (e.g.,Tutukov & Yungelson 1993; Kinugawa et al. 2014;Belczynski et al. 2016; Marchant et al. 2016;Mandel & de Mink 2016).Future GW observations may provide the mass, spin,and redshift distributions of merging BBHs, which areuseful to probe the environments where BBHs areformed (e.g., Kushnir et al. 2016; Hotokezaka & Piran 2017; Farr et al. 2017; Zaldarriaga et al. 2017). Search-ing for electromagnetic (EM) counterparts from merg-ing BBHs is another way to study them. However,there is a substantial time gap, typically ∼ . − not coincident with the GWemission at the BH-BH merger. Nevertheless, successfulobservations can provide important clues about the for-mation scenario of BBHs. We describe the basic binaryevolution process and the possible outcomes in Section2, where we consider two scenarios; one powered by thesecondary BH and the other powered by the primaryBH. In this paper I, we focus on the transient eventsdriven by the secondary BH. We analytically estimateobservable features of optical transients in Section 3,and the associated radio transients in Section 4. In Sec-tion 5, we summarize and discuss our results, includingthe observational prospects. The other type of tran-sients powered by the primary BH are discussed in Pa-per II (Kimura et al. 2017b). We use the notation of A = A x x throughout this work. CONSEQUENCES OF THE EVOLUTIONARYSCENARIOAccording to the isolated binary evolution models(e.g., Belczynski et al. 2016), the heavier primary col-lapses to a BH earlier than the secondary, which formsa BH and main-sequence star binary. When the sec-ondary evolves to a giant star, the binary separationdecreases considerably during a common envelope evo-lution (Paczynski 1976; Webbink 1984). After that,the secondary is expected to become a Wolf-Rayet star(WR), following the envelope ejection, and the BH-WRbinary becomes a BBH after the gravitational collapseof the WR (e.g. Dominik et al. 2012).At the end of the binary evolution, after the massivesecondary star has collapsed and the BBH has formed,its subsequent fate depends on the angular momentumof the secondary star. Although the angular momentumdistribution of the secondary is highly uncertain, thespin of the secondary star may be tidally locked in a closebinary system (Zahn 1977; Tassoul 1987). Kushnir et al.(2016) give the synchronization time as t TL ∼ . × (cid:18) t mer yr (cid:19) / yr , (1)where t mer = 5 c a / (512 G M ∗ ) ∼ . × a M − ∗ , . yris the GW inspiral time, M ∗ is the primary mass, and a isthe binary separation. We assume the mass ratio q = 1for simplicity and use M ∗ ∼ . M ⊙ and a ∼ cm for the purpose of an estimate, which indicates that t TL is shorter than the typical lifetime of massive stars, t life ∼ yr. However, for a low mass M ∗ ∼
10 M ⊙ orlarge separation a ∼ × cm, t TL > t life is pos-sible. We caution that this timescale has significantuncertainties caused by the strong dependence on thedetailed stellar structure, especially the size of the con- vective region (Kushnir et al. 2016). The size of the staralso affects this timescale.When t TL < t life , the spin period of the secondaryis synchronized to its orbital period. The spin an-gular momentum of the WR is high enough to pre-vent the WR from directly collapsing to a BH. Theouter region of the WR forms an accretion disk aroundthe newborn secondary BH. The accretion rate is highenough to produce radiation-driven powerful outflows(e.g. Ohsuga et al. 2005; Jiang et al. 2014), leading to atidally locked secondary supernova (TLSSN, see Figure1 for the schematic picture). The kinetic energy of thisoutflow is so large that we can expect a radio afterglow.In the opposite case when t TL > t life , the WR is likelyto spin slowly enough to collapse to a BH directly .When the WR collapses, the outer envelope of the WRis ejected due to energy losses by neutrinos (Nadezhin1980). The primary BH accretes the ejected material,and may produce powerful outflows owing to its high ac-cretion rate. This outflow energizes the ejecta and couldlead to a primary-induced accretion transient (PIATs),which is discussed in the accompanying paper (PaperII).A disk-driven outflow can produce a super-luminoussupernova (Dexter & Kasen 2013), a hypernova(MacFadyen & Woosley 1999), and an optical transientduring a single BH formation (Kashiyama & Quataert2015) and BH mergers (Murase et al. 2016). TLLSNeand PIATs provide different examples associated witha newborn BBH. OPTICAL EMISSION FROM TLSSNEWe consider a tidally-synchronized binary systemwhere the spin period of the secondary is synchronizedto the orbital period of the primary. As binary parame-ters, we choose the mass of the WR, M ∗ = 10 . M ⊙ , theradius of the WR, R ∗ = 10 cm, the binary separation, a = 10 cm, and the mass ratio, q = M ∗ /M BH = 1 .This parameter set satisfies t TL ∼ < t life , and is consistentwith stellar evolution models (Schaerer & Maeder 1992).The spin angular velocity is synchronized to the orbitalmotion, which is estimated to be ω s = p GM ∗ /a ≃ . × − M / ∗ , . a − / s − . This value is so high thatthe outer part of the stellar material cannot fall to- The centrifugal and Colioris forces do not affect a disk for-mation process when the WR star collapses even when the binaryseparation is considerably close. There is some uncertainty for radii of WR stars. A rela-tion R ∗ ∼ × ( M ∗ /
10 M ⊙ ) . cm is obtained by stellarevolution models (Schaerer & Maeder 1992; Kushnir et al. 2016),while R ∗ ∼ × cm are proposed from an atmospheric model(Crowther 2007). Besides, the radius is larger for lighter secon-daries, R ∗ ∼ cm for M ∗ ∼ ⊙ , according to a binaryevolution model (Yoon et al. 2010). Figure 1 . Schematic picture of tidally-locked secondary supernovae (TLSSNe); (i) A WR is synchronized via the tidal forcebefore its collapse. The inner part forms a secondary BH, while the outer material forms a disk around the BH. (ii) An ejectais launched by the disk-driven outflow. (iii) Thermal photons diffuse out from the ejecta. wards the BH directly. Thus, an accretion disk is formedaround the newborn BH. This produces a massive out-flow, which leads to a TLSSN.When the secondary collapses, the outer material ofthe secondary at a cylindrical radius ̟ is at the centrifu-gal radius, r cf ( R ) = ̟ ω s / ( GM R ) ≈ ̟ /a , where M R ∼ M ∗ is the mass enclosed inside the spherical ra-dius R = √ ̟ + z . Setting r cf = 6 GM ∗ /c , we obtainthe critical radius for disk formation: R cr ≈ (cid:18) GM ∗ a c (cid:19) / ≃ . × M / ∗ , . a / cm . (2)Since R ∗ > R cr for our parameter choice, the outer ma-terial can form a disk. The density profile of WRs canbe expressed as a polytropic sphere of index ∼ R ∼ > R ∗ /
2) ofa polytrope n can be fitted as ρ env ≈ ρ ∗ ( R ∗ /R − n (Matzner & McKee 1999), where ρ ∗ ≈ A ρ M ∗ / (4 πR ∗ )and A ρ ≃ . n = 3). This expression canreproduce the polytrope within errors of a few percents,except for the very outer edge which does not affect theresult. The disk mass is then estimated to be M d ≈ π Z R ∗ R cr d̟ Z √ R ∗ − ̟ dz̟ρ ∗ r R ∗ ̟ + z − ! n = A ρ I d M ∗ ≃ . M ∗ , . I − . M ⊙ , (3)where I d = R x cr dx R √ − x dyx (1 / p x + y − n ≃ . × − and x cr = R cr /R ∗ . Note that I d is a strong function of x cr that depends on M ∗ , so that the depen-dence of M d on M ∗ is not simple. The outer materialfalls to the disk in a free fall time, t ff ≈ p R ∗ / ( GM ∗ ) ≃ . × M − / ∗ , . R / ∗ , s. Then, the mass accretion rateis estimated to be˙ M env ≈ M d t ff ≃ . × − M / ∗ , . R − / ∗ , M d, − . M ⊙ s − . (4)This accretion rate is much higher than the Eddingtonrate, ˙ M Edd = L Edd /c ≃ . × − M ∗ , . M ⊙ s − ,while it is much lower than the critical mass ac-cretion rate for neutrino cooling, ˙ M ∼ ⊙ s − (Popham et al. 1999; Kohri & Mineshige 2002). Then,the physical state of the accretion flow is ex-pected to be the advection dominant regime, wherethe outflow is likely to be produced (Narayan & Yi1994; Blandford & Begelman 1999; Kohri et al. 2005).The wide-angle outflow production is also commonlyseen in numerical simulations for central engineof gamma-ray bursts (GRBs) (MacFadyen & Woosley1999; Fern´andez & Metzger 2013). The outflow lumi-nosity is estimated to be L w ≈ η w ˙ M env V w (5) ≃ . × M / ∗ , . R − / ∗ , M d, − . η − . V erg s − , where we assume that the η w ∼ / V w ∼ cm s − . Although these parameters relatedto the outflow are highly uncertain, these values of η w Figure 2 . Time evolution of physical quantities for a TLSSNwith the fiducial parameter set ( M ∗ = 30 M ⊙ , R ∗ = 10 cm, a = 10 cm, η w = 10 − . , V w = 10 cm s − ). The upperpanel indicates the bolometric luminosity of diffusing pho-tons L ph (blue-solid) and the effective temperature T eff (red-dashed). The lower panel shows absolute AB magnitudes for U (blue-solid), V (green-dashed), and R band (red-dotted). and V w are consistent with the recent simulation andobservation results (Hagino et al. 2015; Takahashi et al.2016; Narayan et al. 2017). The duration of the out-flow is comparable to the free-fall time, since the ac-cretion time after the disk formation is much shorterthan the free-fall time. The total mass of the outflowis M w = η w M d ≃ . M d, − . η − . M ⊙ and the totalenergy is E w ≈ η w M d V w ≃ . × M d, − . η − . V erg . (6)We assume that the outflow occurs at the escape ve-locity, and is launched at r lp ≈ GM ∗ /V w ≃ . × M ∗ , . V − cm. Assuming that the radiation energyis comparable to the kinetic energy at the launching Note that these simulations and observations are for the caseswith ˙ M ∼ − ˙ M Edd . The values of η w and V w for ˙ M ∼ ˙ M Edd should be investigated in the future.
Figure 3 . Same as Figure 2, but for η w = 10 − . and V w =10 . cm s − . point, the temperature at that point is T lp ≈ ˙ M w V w πa r r ! / (7) ≃ . × M − / ∗ , . R − / ∗ , M / d, − . η / − . V / K , where ˙ M w = η w ˙ M env . We assume a constant outflow ve-locity, which leads to R ∼ V w t . For t < t ff , the outflowis continuously produced. Considering adiabatic expan-sion, we obtain ρ w ∝ R − and T w ∝ R − / where ρ w and T w are the density and temperature in the outflow,respectively. At t ∼ t ff , the accretion rate decreases andthe powerful outflow stops. The radius of the outflowat t = t ff is R w, ≈ V w t ff . The total internal energy atthat time is E int , = 4 π Z R w, r pl a r T w r dr ≈ √ η w M d GM ∗ R ∗ . (8)The bulk of photons are trapped inside the outflow, buta small fraction of the photons can escape from the out-flow through a diffusion process. The luminosity of dif-fusing photons is estimated to be L ph , ≈ E int , t ph , ≃ . × M / ∗ , . R / ∗ , V erg s − , (9)where t ph , ≈ κη w M d / (4 π R w, c ) is the photon diffu-sion time at t = t ff . Since the optical depth is largeenough, the diffusing photons have a Planck spectrumwith an effective temperature of T eff , = L ph , πσR w, ≃ . × M / ∗ , . R − / ∗ , V / K , (10)where σ is the StefanBoltzmann constant.For t > t ff , the outflow decouples from the disk andexpands in a homologous manner. Then, the densityof the outflow evolves as ρ w ∝ t − . Considering adi-abatic expansion, T w ∝ ρ / w ∝ t − , which leads to E int ∝ R w T w ∝ t − . The diffusion time evolves as t ph ≈ η w M d / (4 π cR w ) ∝ t − . Thus, the luminosityof diffusing photons is constant, L ph ∝ t . The effectivetemperature then evolves T eff ∝ t − / .When the effective temperature drops to 10 K, theionized helium ions inside the outflow start to recombineand become neutral (e.g. Kleiser & Kasen 2014). Thetime at which the recombination surface deviates fromthe outflow surface is estimated to be (Popov 1993) t i ≈ (cid:18) L ph , πσT V w (cid:19) ≃ . × M / ∗ , . R / ∗ , V − / s , (11)The position of the recombination surface is given by(Popov 1993) R i ≈ V w (cid:20) tt i (cid:18) t i t a (cid:19) − t t a (cid:21) , (12)where t a = p t ph , R w, /V w is the photon breakout timewithout the recombination surface (Arnett 1980). Here,we assume t i ≪ t a when estimating t i . Since the opacityof the neutral gas is very small (e.g., Kleiser & Kasen2014), the photosphere is equal to the recombinationsurface. Thus, the effective temperature is T eff = T ion ,and the luminosity is estimated to be L ph = 4 πσT R i .Since t i ≪ t a is satisfied for the parameter range ofour interest, the luminosity has a maximum value of L pk ≈ πσT V w (cid:18) t i t a (cid:19) (13) ≃ . × M / ∗ , . R / ∗ , M / d, − . η / − . V / erg s − , and the time of the peak luminosity is t pk ≈ (cid:18) t i t a (cid:19) / (14) ≃ . × M / ∗ , . R / ∗ , M / d, − . η / − . V − / s . For t > t pk , R i rapidly decreases, and accordingly theluminosity decays quickly. The optical depth for the outflow becomes lower than unity in this phase. Theapproximate use of the Planck distribution would be-come inaccurate, especially at τ ∼ < −
10. To study thefeatures of the decay phase, a more careful treatment ofthermalization processes would be required.The evolution of T w and L ph are shown in the upperpanel of Figure 2, where we use the fiducial parame-ter set ( M ∗ = 30 M ⊙ , R ∗ = 10 cm, a = 10 cm, η w = 10 − . , V w = 10 cm s − ). The lower panel ofthe figure shows the evolution of the absolute AB mag-nitude in the U (365 nm), V (550.5 nm), and R (658.8nm) bands. Since the outflow parameter is uncertain,we show the results for the case with η w = 10 − . and V w = 10 . cm s − in Figure 3 for comparison. We cansee that the optical band light curves rapidly becomebright in several hours, remain bright and slowly varyingfor days, and then rapidly fade on a timescale of hours.The peak magnitude range is -14 to -17, which is similarto that of usual type II or type Ib/Ic SNe. However theirshorter durations are useful for distinguishing TLSSNefrom the usual SNe. Spectroscopic observations can alsodiscriminate TLSSNe from macronovae/kilonovae, sinceTLSSNe will show strong helium lines while macrono-vae/kilonovae are not expected to show such lines. Wenote that these TLSSNe are bright and short duration,compared to the PIAT events discussed in Paper II.Interestingly, t pk and L pk do not have a strong de-pendence on the parameters. However, the occurrenceof TLSSNe is sensitive to the value of x cr = R cr /R ∗ ≃ . M / ∗ , . R − ∗ , a / . For x cr >
1, an accretion disk isnot formed, which leads to a result similar to the PIATsthat we discuss in Paper II. For x cr ≪
1, a significantfraction of the stellar material falls onto the disk, andthe newborn BH has a large spin, probably resultingin a GRB. See Section 5 for discussion about possiblerelation between GRBs and TLSSNe. RADIO AFTERGLOWS OF TLSSNEOutflow-driven transients may lead to radio af-terglows (see Kashiyama et al. 2017 for details; seealso Murase et al. 2016). We briefly discuss this possi-bility here (cf. Chevalier 1998; Nakar & Piran 2011, forsupernovae and neutron star mergers). The decelerationradius and time is estimated to be R dec ≈ (cid:18) M w πn ext m p (cid:19) / (15) ≃ . × M / d, − . η / − . n − / − cm ,t dec ≈ R dec V w ≃ . × M / d, − . η / − . V − n − / − s , (16)where n ext = 0 . n − cm − is the number density of thecircum-binary medium. The deceleration time can beshorter for smaller η w and larger V w . After the decel-eration time, the evolution of the outflow is representedby the self-similar solution, R = R dec ( t/t dec ) / ( t ≥ t dec ) , (17) V = 0 . V w ( t/t dec ) − / ( t ≥ t dec ) . (18)We estimate the physical quantities around t ∼ t dec using V ∼ V w and R ∼ R dec . The magnetic field isestimated to be B = (9 πm p n ext ǫ B v ) ≃ . V n / − ǫ / − mG, where ǫ B is the energy fraction of the magneticfield. The minimum Lorentz factor of electrons is ap-proximately γ m ≈ ζ e (cid:18) m p m e (cid:19) (cid:18) Vc (cid:19) ≃ V ζ − . , (19)where ζ e ∼ ( p − ǫ e / (( p − f e ) ∼ . ǫ e is the en-ergy fraction of the non-thermal electrons, f e ∼ . p isthe spectral index of the non-thermal electrons. Thecooling Lorentz factor is γ c ≈ πm e c/ ( σ T B t dec ) ≃ . × M − / d, − . η − / − . V − n − / − ǫ − − , where σ T is theThomson cross section. Since γ m ≪ γ c , the synchrotronspectrum is in the slow cooling regime. The synchrotronfrequencies for the electrons of γ m and γ c are ν m ≈ γ m eB πm e c ≃ . × V n / − ǫ / − ζ − . Hz , (20) ν c ≃ . × M − / d, − . η − / − . V − n − / − ǫ − / − Hz . (21)If we ignore synchrotron self absorption (SSA), the syn-chrotron spectrum has a peak at ν m and its flux is F ν,m ≈ P m N e πν m d L (22) ≃ M d, − . η − . V n / − ǫ / − f − d − mJy , where P m ≈ γ m σ T cB / (6 π ) is the synchrotron radiationpower per electron, N e ≈ πR n ext f e / d L ≃ cm is the lu-minosity distance. Since F ν ∝ ν (1 − p ) / for ν m < ν < ν c without SSA, the observed flux at frequency ν obs is es-timated to be F ν, obs ≈ F ν,m (cid:18) ν obs ν m (cid:19) (1 − p ) / ≃ . ν − p M d, − . × η − . V p − n p +14 − ǫ p +14 − f − d − mJy , (23)where we use p = 3 to estimate the value. Since thesensitivity of current radio surveys is around 0.1 mJy, itis possible to detect this radio emission. If the opticaltransient discussed in Section 3 is observed, the deeperradio follow-up observation with a sensitivity of around µ Jy can be performed. In this case, we can expect de-tection of the radio signal even with much lower η w . The deceleration time is shorter for lower η w , which helps thecoincident detection. Using Equations (17) and (18), weobtain F ν, obs ∝ t for t < t dec and F ν, obs ∝ t (21 − p ) / for t > t dec . Note that F ν, obs has a strong dependence on V w , F ν, obs ∝ V w for p = 3. Thus, just a few times lower V w would make it difficult to detect the radio afterglow.The optical depth for SSA is estimated to be τ a ≈ A p ef e n ext R ( ν/ν m ) − ( p +4) / / ( Bγ m ), where A p is a func-tion of p ( A p = 26 .
31 for p = 3, see Murase et al. 2014).The SSA frequency at which τ a = 1 is estimated as ν a ≈ (cid:18) A p ef e n ext RBγ m (cid:19) / ( p +4) ν m ≃ . × M p +4 d, − . × η p +4 − . V p − p +4 n p +146 p +24 − ǫ p +22 p +8 − ξ p − p +4 − . f p +4 − Hz . (24)This frequency evolves as ν a ∝ t / ( p +4) for t < t dec and ν a ∝ t − (3 p +2) / ( p +4) for t > t dec (Nakar & Piran 2011).If we focus on ν obs > ν a , we can ignore the effect ofSSA. Since we typically expect ν a > ν m , the spectrumis modified by SSA as F ν ∝ ν / for ν m < ν < ν a and F ν ∝ ν for ν < ν m . SUMMARY & DISCUSSIONWe investigated outflow-driven transients from new-born binary black holes formed from BH-WR binaries,within the context of isolated binary evolution scenarios.When the binary separation is small or the binaries aremassive enough, the spin period of the WR is synchro-nized to the orbital period. When the WR collapses toa BH, the outer region of the WR has such a high angu-lar momentum that an accretion disk is formed arounda newborn secondary BH. This results in an energeticoutflow of kinetic energy of ∼ ergs for η w ∼ − . ,leading to a TLSSN whose bolometric luminosity can be ∼ − erg s − . Its optical band absolute mag-nitude reaches ∼ −
17, with a duration of around a day.Transient radio emission can also be expected, owing tothe large amount of kinetic energy involved.When the binary separation is larger or the stellarmass is lower, the tidal synchronization may not occurand the spin of the secondary is likely to slow down.Even in this case, a fraction of the outer material of thesecondary is ejected when the secondary collapses to aBH. This ejected material is expected to be accreted bythe primary BH, and a powerful outflow is produced,leading to a PIAT. We discuss this type of transient inthe accompanying paper (Paper II).The TLSSNe can be distinguished from usual SNe bytheir shorter duration, and from macronovae/kilonovaeby their strong helium lines. The light curves of TLSSNeare consistent with some of the rapid transients observed(Drout et al. 2014; Tanaka et al. 2016) on the basis oftheir timescale (around a day) and absolute magnitude( ∼ − ∼
21 mag, such as Pan-STARRS (Hodapp et al. 2004),PTF (Law et al. 2009), and KISS (Morokuma et al.2014), imply a detectability distance for TLSSNe of ∼
200 Mpc. Assuming that the event rate of TLSSNeis similar to the merger rate of BBHs, ∼ −
200 Gpc − yr − (Abbott et al. 2016a, 2017), the eventrate within the sensitivity range is 0.3–7 yr − . Thus,the current surveys could detect this type of tran-sients in the near future. However, we should notethat the event rate of TLSSNe has substantial uncer-tainties, related to the binary evolution and the out-flow from a super-Eddington accretion flow. Futureprojects, e.g., the Large Synoptic Survey Telescope(LSST, LSST Science Collaboration et al. 2009), wouldbe able to detect them or put a meaningful limit on theevent rate.The stellar wind, the ejected stellar envelopes dur-ing the common envelope phase, and/or the supernovaimpostors can significantly pollute the circum-binarymedium (e.g. Smith et al. 2011; Belczynski et al. 2016).This circum-binary matter can be more massive thanthe outflow of TLSSNe. Thus, they could affect boththe optical and radio light curves of TLSSNe.Since the core of the WR can be radiative, it is pos-sible that the core rotates faster than the envelope. Ifthe core rotates sufficiently fast, it forms a BH withan accretion disk ∼ ∼ s after the core accretion that is at-tributed to the GRB prompt emission. Note that a diskstate for a typical TLSSN discussed in this paper is dif-ferent from that of a collapsar disk discussed in the con-text of GRBs (MacFadyen & Woosley 1999). The diskin a TLSSN has much lower temperature than that ofa collapsar disk, so a TLSSN disk cannot produce a jetthrough the neutrino annihilation (Eichler et al. 1989;Popham et al. 1999). If the secondary BH has a highspin and global magnetic field, the magnetic jet can beproduced (Blandford & Znajek 1977; Komissarov 2004;Toma & Takahara 2016). Although the jet power seemstoo low to produce a typical long GRB, it may be ob-served as an ultra-long GRBs if the jet is directed tothe Earth (Quataert & Kasen 2012; Woosley & Heger2012). Since a wide-angle outflow can simultaneouslybe produced (MacFadyen & Woosley 1999), we may alsoobserve a TLSSN.An accretion disk around a BH in a BBH is left overafter the transients considered here. A few years later,this disk is expected to become a fossil disk, in which theangular momentum transport is inefficient, due to radia-tive cooling (e.g., Perna et al. 2014, 2016; Kimura et al.2017a). Since such fossil disks can remain for millionsof years, a possible outcome from them would be elec-tromagnetic counterparts of the GWs from the eventualBBH mergers (Murase et al. 2016; Kimura et al. 2017a;de Mink & King 2017).Besides the transients discussed here, which involvea WR companion, there are likely to be other forma-tion channels of BBHs through binary evolution, wherethe progenitor consists of a BH and a blue-super gi-ants (BSGs) or red-super giants (RSGs). Since BSGsand RSGs have larger radii than WRs, x cr <1 is easilysatisfied. In this sense, TLSSNe are likely in BH-BSGand BH-RSG binaries. However, whether the spin istidally synchronized or not depends strongly on the in-ternal structure of the secondary (Kushnir et al. 2016).Also, the tidal force from the primary distorts the WRstar to non-spherical shape, which could affect the stel-lar structure. A more accurate modeling will requiresolving the stellar evolution in detail. Due to these un-certainties related to the stellar structure as well as theoutflow properties resulting from the super-Eddingtonaccretion, it is currently difficult to derive a meaningfulluminosity distribution for such transients.The authors thank Kazumi Kashiyama, KunihitoIoka, and Tomoya Kinugawa for useful comments. Thiswork is partially supported by Alfred P. Sloan Foun-dation (K.M.), NSF Grant No. PHY-1620777 (K.M.),NASA NNX13AH50G (S.S.K. and P.M.), an IGC post- doctoral fellowship program (S.S.K).REFERENCES