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arXiv:1610.00416v1 [astro-ph.HE] 3 Oct 2016 in tiscne,teW olpe oanurnsa (NS) a to collapses WD reaching the WD center, (e.g., a re its If -capture at triggers (WDs). tions limit dwarfs mass white Chandrasekhar of the fate final dicted oee,ti lsia iwhsas enrcnl questio recently been also has (e.g., view classical cooling this However, the dense of becomes center because its O+Ne+Mg enough when the AIC cause limit, merger eventually mass the will Chandrasekhar WD by the formed WD than the heavier If is WD. O+Ne+Mg C+O an a into transforming center, WD WD the into propagates gradually 1985 Iben & (e.g., WDs on two depending WDs the massive 2015 of of ratio formation mass the the to lead can ers 2007 Bildsten ( rate 2007 burg the of site a 1991 Heuvel den (e.g., van way clusters a as globular argued 1990 been in lay has NSs AIC AIC. produce as referred to is NS a to WD e.g., egrlast h f-etrcro giin(e.g., ignition off-center the to leads merger is path other The sce- center. (DD) e.g., [double-degenerate nario, their WDs two at of merger r triggered the through electron-capture be the can and limit actions Chandrasekhar the to close non- from accretion [single-degenerate the WDs through O+Ne+Mg e.g., scenario, is onto (SD) path first degenerate The AIC. 2016 Kollmeier & Piro crto-nue olpe(I)i hoeial pre- theoretically a is (AIC) collapse Accretion-induced hr r w ao ugse vltoayptst cause to paths evolutionary suggested major two are There rpittpstuigL using typeset Preprint T HE ; ooo&Kno1991 Kondo & Nomoto M ooo&Kno1991 Kondo & Nomoto ˙ aoe l 2016 al. et Sato A acc STROPHYSICAL n oemlieodplas(e.g., millisecond some and ) a eue ocnr h I rgno bevdgravitationa observed of origin AIC the Keywords: confirm transie to used Array ma be AIC Kilometer can from Square waves gravitational the source, wave or detec gravitational Survey be Sky may Array ra systems Large fast single-degenerate emit the colla may from they and transients magnetized, instability strongly r-mode are star the stars neutron neutron by forms we energy AIC mergers, stars), rotational neutron dwarf If supramassive their white (i.e., satisfied. of themselves is result support to a condition as certain emi occurs a synchrotron AIC if produce if can coll Even shock star, AIC strong from companion cies. The ejecta a the shock. from strong Then, accretion a system. by progenitor triggered the is around AIC If accretion-ind cies. of properties observational investigate We ssfcetyhg ( high sufficiently is ) n lrhg-nrycsi a rdcin(e.g., production ray cosmic ultrahigh-energy and ) ebn 1984 Webbink r ; poesncesnhss(e.g., nucleosynthesis -process ,teON+gWscngo hi mass their grow can WDs O+Ne+Mg the ), ao&Nmt 1985 Nomoto & Saio iiino hoeia srnm,Ntoa Astronomical National Astronomy, Theoretical of Division AI RNINSFO CRTO-NUE OLPEO WHITE OF COLLAPSE ACCRETION-INDUCED FROM TRANSIENTS RADIO A T E 1. ooo&Kno1991 Kondo & Nomoto iais eea ai otnu:gnrl—wiedwarfs white — general continuum: radio — general binaries: tl mltajv 01/23/15 v. emulateapj style X eto uenve general supernovae: — neutron J .I a ogbe eivdta h WD the that believed been long has It ). ; OURNAL INTRODUCTION ). arse l 2013 al. et Tauris ; bn&Ttkv1984 Tutukov & Iben ; L .Ti rnfrainfo a from transformation This ). ETTERS oooe l 2007 al. et Nomoto eevd21 uut3;rvsd21 etme 3 accepte 23; September 2016 revised 31; August 2016 Received M ˙ acc ∼ .Tecro burning carbon The ). on&Lne 2005 Langer & Yoon a ta.2014 al. et Dan 10 .ACcnas be also can AIC ). − 7 .I h accretion the If ]. aln&Grind- & Bailyn − in&Wasser- & Qian -11Oaa iaa oy 8-58 Japan 181-8588, Tokyo Mitaka, Osawa, 2-21-1 htahra& Bhattacharya 10 .W merg- WD ]. − 5 ; M Nomoto hn& Shen [email protected] ⊙ T ; AKASHI Shen yr ABSTRACT ned ac- − e- 1 ). , .M J. bevtr fJpn ainlIsiuso aua Scienc Natural of Institues National Japan, of Observatory cdclas AC fwiedaf nrdofrequen- radio in dwarfs white of (AIC) collapse uced h urmsienurnsasmyimdaeylose immediately may stars neutron supramassive the idb I.Hwvr h usqetsuisby studies subsequent accompa- the be However, may AIC. transients by optical dur- nied luminous synthesized no much and not AIC is ing (SNe), supernovae of source ing ili dniyn hm al tde by studies Early them. identifying in tial efo h Dcanl(e.g., may channel they SD and the interaction from SN-CSM be the of signatures sug- possible (e.g., the them therefore of 2016 in favored al. most and is et out channel Chomiuk emission, DD rules the radio SNe and DD) models of Ia SD Type or gested lack many (SD The in channel CSM, has dense SNe. progenitor interaction Ia the CSM Type can the constrain of to radio to due emitting used emission waves to been Radio shock collide AIC strong formed. from and be ejecta CSM the Then, dense CSM. the dense oc- the AIC in and (CSM) curs media circumstellar dense makes outflow which disk supported rotationally a makes form may WDs rotating al. 2007 2010 (e.g., potenti (GWs) evo- a waves is gravitational the AIC of constrain Furthermore, source to AIC. Universe to leading the of- path how in lutionary know occurs to important actually also AIC is ten It AIC. c of to existence important the are firm surveys transient in them identifying and slkl oeita nTp aS rgntr rmS sys- SD from progenitors SN Ia Type in (e.g., as tems exist envelopes to common from outflow likely their large or is sys- a stars, accretion, SD companion large WDs, a in accreting to WDs due AIC O+Ne+Mg cause since tems Especially, frequencies. sever of timescale a in evolving days. transients optical faint by (e.g., s obakhls fteclasn supramassive collapsing the If holes. black to pse ORIYA eacmaidb ai-rgttaset which transients radio-bright by accompanied be y i ussa rvosysgetd h I radio AIC The suggested. previously as bursts dio nesadn lcrmgei E)sgaue fAIC of signatures (EM) electromagnetic Understanding nti ae,w netgt Mpoete fACi radio in AIC of properties EM investigate we paper, this In e nteftr ai rnin uvy ieVery like surveys transient radio future the in ted ( hc r omsieta oaini required is rotation that massive so are which s 2009 d otednecruselrmdu,making medium, circumstellar dense the to ide waves. l on htteradioactive the essen- that is found counterparts ) EM their of knowledge the and ) cwbe l 2016 al. et Schwab so hc a eosre nrdofrequen- radio in observed be can which ssion es icmtla eimcnb formed be can medium circumstellar dense a tsre.BcueACi ugse ob a be to suggested is AIC Because survey. nt 56 ru htACmycuefs ai bursts radio fast cause may AIC that argue ); irc uflw n htACcnb accompanied be can AIC that and outflows Ni-rich abae al. et Darbha hmu ta.2012 al. et Chomiuk 06Otbr3 October 2016 d rvttoa ae stars: — waves gravitational — , 2012 ( ; 2010 one l 2007 al. et Yoon ,atog oeTp aSeshow SNe Ia Type some although ), hwdta I rmrapidly from AIC that showed ) au ta.2003 al. et Hamuy 56 o umr) h large The summary). a for DWARFS i hc samjrheat- major a is which Ni, esr tal. et Dessart biaao tal. et Abdikamalov ). es, ; oe tal. et Foley eze et Metzger ( 2006 on- al al , 2 MORIYA

Table 1 3.1. AIC from SD systems Predicted AIC ejecta properties. AIC in SD systems occurs if the accretion rate onto a WD is large enough to keep the surface burning steady. model Mej Eej M56Ni reference − − − 51 ∼ 7 − 5 1 M⊙ 10 erg M⊙ The required accretion rate is 10 10 M⊙ yr (e.g., A ∼ 10−3 ∼ 0.01 ∼ 10−4 Dessart et al. (2006) Nomoto & Kondo 1991; Nomoto et al. 2007; Shen & Bildsten B ∼ 0.1 ∼ 1 ∼ 10−4 Dessart et al. (2007) 2007). There are several SD evolutionary channels for WDs C ∼ 0.01 ∼ 0.1 ∼ 0.01 Metzger et al. (2009) to achieve such a high accretion rate. The high accretion rates are often accompanied with high mass-loss rates, resulting in large CSM . Thus, the ejecta from AIC collide with 2012; Dilday et al. 2012). However, in the case of AIC, the the dense CSM and a strong shock emerges. can lack of the dense CSM in the DD channel does not prevent be accelerated at the shock and synchrotron emission can be the appearance of strong radio emission. There is a chance emerged from the accelerated relativistic electrons as found to cause fast radio bursts (FRBs, e.g., Lorimer et al. 2007; in SNe exploding within CSM (e.g., Fransson & Björnsson Thornton et al. 2013) from the collapse itself as we discuss in 1998). This synchrotron emission can be observed in radio this paper. frequencies. ˙ There are a few previous studies on radio transients from Let Mloss the mass-loss rate from a SD system leading to AIC. Piro & Kulkarni (2013) suggest that spin-down of newly AIC. Then, the CSM density ρCSM of the system is expressed born magnetarsby AIC makes a wind (PWN) in as ˙ Mloss −2 the AIC ejecta and the interaction between the AIC ejecta and ρCSM(r)= r , (1) the PWN can result in radio emission. In this paper, we study 4πvw radio emission due to the interaction between AIC ejecta and where r is the radius and vw is the wind velocity. We as- CSM created by their evolution towards AIC. Metzger et al. sume that the ejecta expand homologously with the density −n −δ (2015b) study the radio emission from AIC interacting with structure ρej ∝ r (outside) and ρej ∝ r (inside). Then, the interstellar media, but not with CSM. No previous studies forward shock radius (rsh) and velocity (vsh) can be obtained consider AIC as an FRB progenitor. analytically as a self-similar solution (Chevalier 1982). We We first overview the predicted ejecta properties of AIC in adopt this analytic solution with n = 7 and δ = 1. However, Section 2. Then, we discuss the radio emission expected from the analytic solution is no longer valid when the reverse shock AIC in Section 3. We discuss the rate and observations of starts to propagateinto the innerflat density region. This starts when the swept-up CSM mass becomes comparable to M , the radio transients from AIC in Section 4 and conclude this ˙ ej paper in Section 5. i.e., when Mej ∼ Mlossrsh/vw (e.g., Moriya et al. 2013). Af- ter this moment, we assume that the shock expands following ˙ 0.5 2. AIC EJECTA PROPERTIES vsh = [2Eej/(Mej + Mlossrsh/vw)] . Although we change the formulation of v abruptly when M = M˙ r v is satisfied We first summarize properties of ejecta from AIC. The sh ej loss sh/ w for simplicity, v is found to change smoothly. This transition ejecta properties affect the radio emission from AIC espe- sh only occurs in the highest CSM density models we show later cially when AIC occurs in the SD systems. in this section. Dessart et al. (2006) showed that AIC can result in explo- − Given the shock radius r and the shock velocity v , the sions with the ejecta mass (M ) of ∼ 10 3 M and the ex- sh sh ej ⊙ synchrotron luminosity at a frequency ν from the shock (L ) plosion energy (E ) of ∼ 1049 erg with the -driven ν ej can be estimated as (e.g., Björnsson & Fransson 2004; Frans- mechanism. Later, Dessart et al. (2007) found that the ejecta son & Björnsson 1998) mass and the explosion energy of AIC can be enhanced to 51 − Mej ∼ 0.1 M⊙ and Eej ∼ 10 erg if the AIC explosion is mag- 1 p −1 ≃ 2 γν 2 + tsync,ν netically driven. In both cases, they find that the production νLν πrshvshnrel,γν γν mec 1 , (2) 56 −4 of Ni is negligible (∼ 10 M⊙) and AIC is not optically γmin  h t i bright. where nrel,γ is the number density of the relativistic electrons However, subsequent studies by Metzger et al. (2009); 0.5 with the Lorentz factor γ, γν = (2πmecν/eB) is the Lorentz Darbha et al. (2010) proposed a different mechanism in AIC factor of the relativistic electrons with the characteristic fre- 56 ∼ to have Ni-rich ejecta with Mej 0.01 M⊙. When AIC oc- quency ν, γ ∼ 1 is the minimum Lorentz factor of the curs in rapidly rotating WDs, an accretion disk supported by min accelerated electrons, me is the electron mass, e is the elec- the centrifugal force can be formed. The disk initially be- tron charge, and B is a magnetic field strength. We assume comes neutron-rich because of its neutrino emission. How- that the number density distribution of the relativistic elec- ever, thanks to from the proto-NS, the -to- trons with the Lorentz factor γ follows dn /dγ ∝ γ−p with neutron ratio in the disk becomes ∼ 1 and the hot disk will rel,γ 56 p = 3. The synchrotron cooling timescale at ν is tsync,ν = be composed mostly of Ni. The disk can eventually start 6πm c/σ γ B2, where σ is the Thomson scattering cross to move outwards and become ejecta because of the viscous e T ν T 4 section. We also take the synchrotron self-absorption (SSA) stress and the energy provided by the He pro- at the shock into account (e.g., Chevalier 1998). The SSA op- ∼ − + duction. The typical ejecta velocity is estimated to be 0.1c, tical depth is =( ) (p 4)/2 with the SSA frequency ∼ 50 τSSA,ν ν/νSSA where c is the , and Eej is 10 erg. In this case, ν ≃ 3×105(r ǫ /ǫ )2/7B9/7 Hz in cgs units. Here, ǫ is the optical transients with the peak luminosity of ∼ 1041 erg s−1 SSA sh e B e − fraction of the post-shock energy used for the electron accel- and the rise time of 1 10 days can be accompanied by AIC. eration and ǫ is the fraction converted to the magnetic field Table 1 summarizes the three possible ejecta properties B energy. We assume ǫe = ǫB =0.1 in the rest of this paper. We from AIC currently predicted. neglect the free-free absorption in the unshocked CSM as the CSM density is not high enough for it to be effective. 3. RADIO TRANSIENTS FROM AIC The radio luminosity (Eq. 2) is proportional to the CSM RADIO TRANSIENTS FROM AIC 3

A = 10 A = 10 ejecta model A * ejecta model A * 29 1 29 1 10 1 GHz 0.1 10 10 GHz 0.1

) 0.01 ) 0.01

-1 0.001 -1 0.001 Hz Hz -1 -1 1028 1028

1027 1027 radio luminosity (erg s radio luminosity (erg s 1026 1026

1 10 100 1000 10000 0.1 1 10 100 1000 days after AIC days after AIC

A = 10 A = 10 ejecta model B * ejecta model B * 29 1 29 1 10 1 GHz 0.1 10 10 GHz 0.1

) 0.01 ) 0.01

-1 0.001 -1 0.001 Hz Hz -1 -1 1028 1028

1027 1027 radio luminosity (erg s radio luminosity (erg s 1026 1026

1 10 100 1000 10000 0.1 1 10 100 1000 days after AIC days after AIC

A = 10 A = 10 ejecta model C * ejecta model C * 29 1 29 1 10 1 GHz 0.1 10 10 GHz 0.1

) 0.01 ) 0.01

-1 0.001 -1 0.001 Hz Hz -1 -1 1028 1028

1027 1027 radio luminosity (erg s radio luminosity (erg s 1026 1026

1 10 100 1000 10000 0.1 1 10 100 1000 days after AIC days after AIC

Figure 1. Radio LCs of AIC from SD systems at 1 GHz and 10 GHz with the different ejecta properties (Table 1) and the different CSM (A∗ = 0.001 − 10). Note the difference in the x axis in the right and left panels. density. As the CSM density scales with M˙ /v (Eq. 1), the of the transferred mass is lost through the outer Lagrangian ˙ loss w radio luminosity scales with Mloss/vw. Following the conven- point (Chomiuk et al. 2012 and references therein), we ex- ˙ −5 −1 −1 ˙ −9 −7 −1 −1 tion, we define A∗ ≡ (Mloss/vw)/(10 M⊙ yr /1000km s ). pect Mloss ∼ 10 − 10 M⊙ yr with vw ∼ 100 km s , or The mass loss from the SD system determining A∗ depends on A∗ ∼ 0.001 − 0.1. However, the large accretion rate may re- SD channels. We consider several possible outflows from the sult in the optically thick wind when the accretion rate is −6 −1 ˙ SD systems as follows (see, e.g., Chomiuk et al. 2012 for a above ∼ 10 M⊙ yr (Hachisu et al. 1999). Then, Mloss ∼ −6 −5 −1 −1 summary). 10 − 10 M⊙ yr with vw ∼ 1000 km s can be achieved. One possible SD channel leading to a large accretion is the This outflow makes A∗ ∼ 0.1 − 1. Another possible SD chan- stable Roche-lobe overflow (RLOF) onto WDs. The RLOF nel is a symbiotic system in which the accreting mass is pro- can make nuclear burning stable at around the accretion rate vided by a red giant (e.g., Seaquist & Taylor 1990). The mass required for AIC. Assuming that a small fraction (∼ 1%) loss from the symbiotic system is dominatedby the wind from 4 MORIYA

˙ −8 −6 −1 the red giant. Assuming Mloss ∼ 10 − 10 M⊙ yr with sive WD up to around 4 M⊙ (e.g., Justham 2011 and refer- −1 vw ∼ 10 kms , we expect A∗ ∼ 0.1 − 10. To summarize, ences therein). Therefore, AIC of massive WDs can form A∗ ∼ 0.001 − 10 is expected in AIC from the SD model. supramassive NSs which are heavier than ∼ 2.2 M⊙ (e.g., The radio LCs expected from the abovementioned SD sys- Metzger et al. 2015a) and require rapid rotation to support tems are summarized in Figure 1. The three different AIC themselves. Such supramassive NSs can be a progenitor of ejecta in Table 1 are adopted. We show the radio LCs at FRBs if they are strongly magnetized (Falcke & Rezzolla two representative frequencies, 1 GHz and 10 GHz. The 2014). When their rotational energy goes below the minimum expected peak radio luminosity from AIC ranges ∼ 1026 − rotational energy required to support themselves, the strongly 29 −1 −1 10 erg s Hz . The peak luminosities of the A∗ ∼ 0.1 magnetized supramassive NSs collapse to BHs in a dynamical models are comparable to those of stripped-envelope SNe, al- timescale (e.g., Shibata et al. 2000). During the collapse, the though stripped-envelope SNe typically have A∗ ∼ 1. This is strong magnetic field may make a burst in radio which can be because of higher velocities in AIC ejecta. While stripped- observed as a FRB (so-called the “” model, Falcke & envelope SNe typically have Eej/Mej ∼ 1 /M⊙ where Rezzolla 2014). It is usually assumed that the rotational en- 1 foe ≡ 1051 erg (e.g., Lyman et al. 2016), the AIC ejecta ergy is lost through the dipole radiation in the blitzar model, have Eej/Mej ∼ 10 foe/M⊙ (Table 1). Therefore, their shock but strongly magnetized supramassive NSs created by AIC 0.5 velocities [∝ (Eej/Mej) ] are higher, making the radio lumi- can immediately lose their rotational energy by the r-mode nosities comparable to those of stripped-envelope SNe. The instability (Andersson et al. 1999). Therefore, supramassive higher shock velocities also makes radio luminosities of AIC NSs from AIC can collapse to BHs shortly after AIC and AIC higher than those of Type Ia SNe since Eej/Mej is ∼ 1 foe/M⊙ can be immediately accompanied by FRBs. in Type Ia SNe as well (e.g., Mazzali et al. 2007; Scalzo et al. The supramassive NS model for FRBs is argued to be less 2014). When A∗ & 1, the peak radio luminosities of AIC can favored because of the small number of observedin be comparable to, or even higher than, those of Type IIn SNe the Galaxy (Kulkarni et al. 2014). However, in our scenario, which are among the most radio luminous SNe (e.g., Perez- the spin down of supramassive NSs is presumed to occur im- Torres et al. 2015). mediately after the AIC due to the r-mode instability, not due The rise times trise,ν of the AIC radio LCs strongly de- to the electromagnetic dipole radiation. Therefore, the mag- pend on frequencies to observe, mainly because of the fre- netars resulting in FRBs can immediately collapse to BHs and quency dependence of SSA. The rise time follows trise,ν ∝ the observed population of magnetars are not necessarily re- −7(n−2)/(7n−12) (9n−22)/2(7n−12) ∝ −0.95 0.55 ν A∗ or trise,ν ν A⋆ in our case. lated to FRBs from supramassive NSs. Roughly speaking, the rise time is inversely proportional to FRBs need to occur in a relatively clean environment be- the frequency. Similarly, the peak radio luminosity is propor- cause the radio signals can be absorbed by the surrounding 19/(7n−12) 19(n−5)/2(7n−12) 0.51 0.51 tional to ν A∗ or ν A∗ . Shortly, the environment if it is too dense. In the canonical AIC model radio LCs at longer frequencies have shorter rise times. The leading to the NS formation, there are several suggested ways radio LCs at 1 GHz typically rise in 10 − 100 days, while they to make ejecta as discussed in the previous section. However, typically rise within 10 days at 10 GHz. when AIC forms supramassive NSs, it is not clear whether In the models with A⋆ = 10, the deviation from the self- there still remain ejecta as the BH formation can cease the similar solution for rsh and vsh makes the LC decline af- ejecta formation. Therefore, FRBs from the DD system can −2 ter the peak steeper (Lν ∝ t ). When the shock follows occurin a clean environmentand it is possible that they do not the self-similar solution, Lν after the peak is proportional to suffer from the strong absorption. Depending on the timescale t−(n+1)/(n−2) or t−8/5 in our case. of the BH transformation from the supramassive NSs, some Radio emission from AIC is also suggested to originate ejecta may exist and may explain FRBs from relatively dense from the interaction between AIC ejecta and PWN (Piro & environment (Masui et al. 2015; Kulkarni et al. 2015). Kulkarni 2013). It is important to distinguish the two differ- FRBs are also suggested to occur duringthe mergerof mag- ent origins of the AIC radio emission observationally. Piro netized WDs (Kashiyama et al. 2013). If FRBs from the NS & Kulkarni (2013) predict that the peak radio luminosity merger and the subsequent AIC can successfully emerged, from the AIC-PWN interaction is 1028 − 1029 erg s−1 Hz−1 at two FRBs may occur from the same progenitor system. Be- 1.4 GHz. The expected peak luminosity range for the AIC- cause the cooling timescale of the merged WD is ∼ 104 years, CSM interaction is 1026 − 1029 erg s−1 Hz−1 and the luminos- the second FRB during AIC may occur ∼ 104 years after the ity variation from the AIC-CSM interaction is larger. The ra- merger. dio LCs from the AIC-PWN interaction is likely to rise more Finally, the discovery of a repeating FRB (Spitler et al. quickly because the AIC ejecta are denser than the CSM and 2016; Scholz et al. 2016) revealed that FRB models with cat- the free-free absorption can be stronger in early phases in the aclysmic phenomena cannot account for all FRBs. Therefore, case of the AIC-PWN interaction. Finally, the radio lumi- ourFRB modelinvolvingAIC can only explaina part of FRBs nosity from the interaction between AIC ejecta and the in- at most. However, the repeating FRB has some different fea- terstellar medium is expected to be fainter than that from the tures compared to the other FRBs and it is still possible that interaction between AIC ejecta and the CSM (Metzger et al. FRBs come from several progenitors including those involv- 2015b). ing cataclysmic phenomena. 3.2. AIC from DD systems 4. EVENT RATES AND PROSPECTS FOR FUTURE Contrary to the case of AIC in SD systems, DD systems are RADIO TRANSIENT SURVEYS not expected to have dense CSM. Therefore, the strong radio The predicted event rates of AIC are quite uncertain. AIC emission from the shock as in SD systems is not expected. from SD systems is predicted to occur ∼ 10−4 − 10−6 yr−1 However, we argue that AIC from DD systems has a possibil- in our Galaxy (e.g., Yungelson & Livio 1998). AIC from ity to cause FRBs. DD systems can be as much as ∼ 10% of Type Ia SNe, or The mergerof two WDs can producea rapidlyrotating mas- ∼ 10−4 yr−1 in our Galaxy (Ruiter et al. 2009; Yoon et al. RADIO TRANSIENTS FROM AIC 5

2007). The AIC rate is also constrained by the amount of We have studied AIC as a progenitor of radio transients. neutron-rich elements produced by AIC, and the overall AIC When AIC occurs due to accretion onto an O+Ne+Mg WD rate should be less than ∼ 10−4 yr−1 in our Galaxy (e.g., Fryer from a companion star (the SD model), a dense CSM is likely et al. 1999). to exist around the progenitor because of the large accretion −4 −1 A Galactic AIC rate RAIC ≡ R−410 yr corresponds to rates required for AIC. Therefore, the ejecta from AIC col- 3 −3 −1 a volumetric AIC rate of 10 R−4 Gpc yr (Metzger et al. lide with the dense CSM and a strong shock emerges. The 2009) if we assume that the AIC rate is proportional to the shock can emit bright which is ob- blue stellar luminosity (Phinney 1991). As we discussed, it is servable in radio frequencies. We found that the peak ra- 26 likely that R−4 . 1. Because the volumetric rate of FRBs is dio luminosity from such progenitor systems can be ∼ 10 − estimated to be ∼ 104 Gpc−3 yr−1 (e.g., Kulkarni et al. 2014), 1029 erg s−1 Hz−1 at ∼ 1−10 GHz, depending on the SD chan- the AIC may not account for all FRBs, although the FRB rate nel, and the typical rise times are ∼ 10 − 1000 days in 1 GHz might be actually close to ∼ 103 Gpc−3 yr−1 (Totani 2013). and ∼ 1 − 100 days in 10 GHz. Because AIC is likely accom- However, the repeating FRB indicates that there can be sev- panied by faint optical transients whose peak luminosities are eral progenitors for FRBs (Spitler et al. 2016; Scholz et al. ∼ 1041 erg s−1, AIC is observed as radio-bright optically-faint 2016) and AIC may account for a fraction of FRBs. We also transients. Although we focused on radio transients in this note that AIC from DD systems is naturally expected to oc- Letter, the between dense CSM and AIC cur in evolved galaxies as may be found for a FRB (Keane et ejecta is also likely to result in strong X-ray emission. al. 2016, but see also, e.g., Williams & Berger 2016; Vedan- AIC can also occur after the merger of WDs if the merger tham et al. 2016; Akiyama & Johnson 2016 for the arguments results in the formation of a WD heavier than the Chan- against the host galaxy detection). Although it is argued that drasekahr mass limit (the DD model). Although there do the blitzar model involving young magnetars is disfavored if not exist dense CSM in AIC from the DD model, AIC of a FRB host galaxy is old (Keane et al. 2016), FRBs from the the massive WD may result in a FRB. If a strongly magne- blitzar model can appear in old galaxies because a collapsing tized supramassive NS is formed by AIC, the NS may quickly can be formed during the AIC after a WD merger as lose its rotational energy required to support itself because of we proposed in Section 3.2. the r-mode instability and it may immediately collapse into a Many radio transient surveys have been performed to in- BH. Then, the collapsing strongly magnetized NS may cause vestigate the radio transient sky (see, e.g., Mooley et al. 2016 a FRB through the “blitzar” mechanism (Falcke & Rezzolla for a summary). AIC is an excellent target for radio tran- 2014). Because the merger of strongly magnetized WDs is sient surveys as it is particularly bright in radio (see also also suggested to make a FRB (Kashiyama et al. 2013), two Metzger et al. 2015b for discussion on the detection of radio FRBs separated by ∼ 104 years may occur in the same pro- transients from AIC). Assuming that AIC becomes brighter genitor. than 1028 erg s−1 Hz−1 (Figure 1), we expect the AIC obser- The rates of AIC from both the SD and DD systems are −4 −2 −1 3 −3 −1 vational rate of ∼ 10 R−4 deg yr with the limiting bright- likely less than ∼ 10 Gyr yr . The observed FRB rates ness of 1 mJy at ∼ 1 − 10 GHz. Assuming a typical dura- (∼ 104 Gyr−3 yr−1, e.g., Kulkarni et al. 2014) are higher than tion of 100 days, this rate roughly corresponds to the all-sky the expected AIC rate and only a fraction of FRBs can be −1 snap-shot detection number of ∼ 1 R−4 sky . Given the low from AIC. The radio transient surveys with the limiting radio expected rates, it is likely that no previous radio transient sur- luminosity of 1 mJy are expected to detect AIC from the SD −4 −2 −1 −1 veys have detected AIC (e.g., Mooley et al. 2016). This limit model with the rate of ∼ 10 deg yr (∼ 1 R−4 sky ) or can be reached by a survey like Very Large Array Sky Survey less. Radio transient surveys like Very Large Array Sky Sur- with a proper cadence (Mooley et al. 2016). If we can reach vey have possibilities to detect radio transients with such a down to 1 µJy, the expected AIC observational rate becomes rate (e.g., Mooley et al. 2016). If radio transient surveys with −2 −1 4 −1 ∼ 3R−4 deg yr (or ∼ 3 × 10 R−4 sky ) and this can be the limiting luminosity of 1 µJy are performed as planned reached by planned radio transient surveys by Square Kilo- by Square Kilometer Array (e.g., Perez-Torres et al. 2015), meter Array (e.g., Perez-Torres et al. 2015). Radio transient we expect to detect AIC with the rate of ∼ 3 deg−2 yr−1 4 −1 surveys synchronized with optical transient surveys are im- (∼ 3 × 10 R−4 sky ) or less. These radio transient surveys portant to help identifying AIC, as AIC may be accompanied enable us to directly confirm the existence of AIC, to con- with faint or no optical transients. Such radio transient sur- strain the AIC rate, and to know the major progenitor path veys are important to directly confirm the existence of AIC, leading to AIC. to constrain the AIC rate, and to unveil the major evolution- AIC is also suggested to be GW sources (e.g., Abdikamalov ary path to AIC. et al. 2010). It is essential to understand the EM counterparts It is also important for radio transient surveys to perform of GWs to identify their origins. We have shown that GWs coordinated observations with GW observatories to look for from AIC can be accompanied by radio-bright optically-faint possible radio counterparts of GW sources, as AIC is a pos- (possibly X-ray-bright) transients. Because the rise times of sible GW emitter (e.g., Abdikamalov et al. 2010). Because the AIC radio LCs are much shorter in the longer frequen- the rise times of the accompanied radio transients are shorter cies, the follow-up radio observations in longer frequencies in higher frequencies (Figure 1), the radio follow-up observa- can be more beneficial to identify the EM counterparts of GW tions in higher frequencies are easier to associate the detected sources in radio frequencies. transients to the GW sources. Although the poor source lo- calization ability of the current GW observatories makes it hard to perform follow-up EM observations (e.g., Abbott et al. 2016), the localization will be improved with the upcom- I would like to thank the referee for the constructive ing additional GW observatories. comments that improved this work significantly. This re- search is supported by the Grant-in-Aid for Research Activity 5. CONCLUSIONS Start-up of the Japan Society for the Promotion of Science 6 MORIYA

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