Optical Synchrotron Precursors of Radio Hypernovae
Daisuke Nakauchi, Kazumi Kashiyama, Hiroki Nagakura, Yudai Suwa, Takashi Nakamura
aa r X i v : . [ a s t r o - ph . H E ] J un Draft version October 27, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
OPTICAL SYNCHROTRON PRECURSORS OF RADIO HYPERNOVAE
Daisuke Nakauchi , Kazumi Kashiyama , Hiroki Nagakura , Yudai Suwa , and Takashi Nakamura Draft version October 27, 2018
ABSTRACTWe examine the bright radio synchrotron counterparts of low-luminosity gamma-ray bursts (llGRBs)and relativistic supernovae (SNe) and find that they can be powered by spherical hypernova (HN)explosions. Our results imply that radio-bright HNe are driven by relativistic jets that are choked deepinside the progenitor stars or quasi-spherical magnetized winds from fast-rotating magnetars. We alsoconsider the optical synchrotron counterparts of radio-bright HNe and show that they can be observedas precursors several days before the SN peak with an r -band absolute magnitude of M r ∼ −
14 mag.While previous studies suggested that additional trans-relativistic components are required to powerthe bright radio emission, we find that they overestimated the energy budget of the trans-relativisticcomponent by overlooking some factors related to the minimum energy of non-thermal electrons. If anadditional trans-relativistic component exists, then a much brighter optical precursor with M r ∼ − .
100 Mpc by current SN surveys like the Kiso SN Survey,Palomar Transient Factory, and Panoramic Survey Telescope & Rapid Response System.
Subject headings: supernovae: general, gamma rays: general INTRODUCTIONA good fraction of core-collapse supernovae (SNe) hasbright radio counterparts called radio SNe. The radioemission is due to the synchrotron emission from non-thermal electrons accelerated at the shock with a velocityof v ∼ . c (e.g., Chevalier 1982, 1998). Such fast-movingejecta are formed when SN shocks break out of the pro-genitor stars (Matzner & McKee 1999; Tan et al. 2001).Therefore, radio SNe are good probes of the dynamics ofthe SN ejecta, the progenitor structure, and the circum-stellar medium (CSM; e.g., Weiler et al. 2002).Intrinsically much brighter radio counterparts havebeen observed in several broad-lined Type Ibc SNe (SNeIbc) or hypernovae (HNe). Previous authors claimedthat these radio emissions are too bright to be pow-ered by the ejecta produced by SN/HN shock break-out so that additional trans-relativistic componentsare required (Soderberg et al. 2010; Chakraborti & Ray2011; Chakraborti et al. 2014; Margutti et al. 2014;Milisavljevic et al. 2015). They proposed that rela-tivistic jets which barely punch out the progenitorstars are the origins of the trans-relativistic compo-nents (Margutti et al. 2014). In fact, some of these radio-bright HNe are associated with low-luminosity gamma-ray bursts (llGRBs), while others, like SN 2009bb andSN 2012ap, did not show detectable high-energy emis-sion. The latter events are called relativistic SNe.To clarify the above arguments, in Figure 1, we showthe energy profile of SN/HN ejecta as a function of Γ β ,where β = v/c , and Γ = 1 / p − β is the Lorentz fac- Department of Physics, Kyoto University, Oiwake-cho, Ki-tashirakawa, Sakyo-ku,Kyoto 606-8502, Japan Einstein fellow—Department of Astronomy; Department ofPhysics; Theoretical Astrophysics Center; University of Califor-nia, Berkeley, Berkeley, CA 94720, USA Yukawa Institute for Theoretical Physics, Kyoto University,Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching, Germany tor. The solid lines correspond to the energy profiles ofa normal SN Ibc (black) and an HN (SN 2009bb; blue),which are theoretically predicted from spherical explo-sions (Matzner & McKee 1999; Tan et al. 2001). On theother hand, the yellow point on the dashed line was ob-tained by Soderberg et al. (2010) to explain the brightradio counterpart of SN 2009bb. As one can see, thereis a significant gap between the blue line and the yellowpoint on the dashed line. This is the reason why the pre-vious authors introduced an additional trans-relativisticcomponent driven by a relativistic jet (the dashed line).If this is the case, then radio-bright HNe may be a miss-ing link between ordinary SNe Ibc and HNe associatedwith GRBs.In this paper, however, we show that the previous stud-ies overestimated the energy and the speed of the trans-relativistic ejecta. In Section 2, we describe the refreshedshock model of a spherical SN/HN ejecta. This model isused to calculate the emission from a radio-bright HN inSection 3. In Section 3.1, we first estimate the energyprofile of HN ejecta, on the basis of the refreshed shockmodel. We find that the energy profile is consistent withthat predicted from the spherical HN explosion (the bluesolid line in Figure 1). Then, we point out that the previ-ous authors overlooked some factors related to the mini-mum energy of the non-thermal electrons. In Section 3.2,we consider the optical counterpart of a radio-bright HN,and show that it can be observed at 0 . MODEL optical precursorSN / HN S N ( ou r w o r k ) radio afterglows determined from !" $ % & ’ ( -1 E k i n ( > ! " ) [ e r g ] !" (spectroscopy) S N I b c S N ( S ode r be r g e t a l . ) Figure 1.
Energy profile of a SN/HN ejecta as a function of Γ β .The red points show the total energy of an SN/HN E in , and thesolid lines show the profiles theoretically predicted from spheri-cal SN/HN explosions (Equations (1)-(3)). The black line corre-sponds to the representative case of an SN Ibc with ( E in , M ej ) ∼ (10 erg , M ⊙ ), and the blue line to an HN with ( E in , M ej ) ∼ (10 erg , . M ⊙ ), which is consistent with SN 2009bb. The yellowpoint on the dashed line corresponds to the energy of the trans-relativistic ejecta which is estimated by Soderberg et al. (2010).The yellow and green regions on the blue line show the shells con-tributing to the radio (at 10-1000 days) and optical (at 0.01-1 days)synchrotron emissions, respectively. They are determined on thebasis of the refreshed shock model in this paper. Dynamics
First, we model the energy profile of the ejecta pro-duced by a spherical SN/HN explosion (Section 2.1.1),and then we model the deceleration of such ejecta in theCSM (Section 2.1.2).2.1.1.
Ejecta Profile
Let us consider an SN/HN explosion with a total en-ergy of E in and an ejecta mass of M ej . The SN/HNblast wave is accelerated as it propagates through theouter envelope of the progenitor where the density de-clines steeply (Sakurai 1960; Johnson & McKee 1971). Asmall fraction of the surface layer can be accelerated upto trans-relativistic velocities, Γ β ∼
1. After the break-out, the shocked ejecta are further accelerated by con-verting the internal energy into the kinetic energy. Theresultant cumulative kinetic-energy distribution can bedescribed as (Matzner & McKee 1999; Tan et al. 2001;the solid lines in Figure 1) E kin ( > Γ β ) = ˜ EF (Γ β ) , (1)where F (Γ β ) is a decreasing function of Γ β and is givenin Equation (38) of Tan et al. (2001) as F (Γ β ) ∼
20 [(Γ β ) − . / . + (Γ β ) − . / . ] . / , (2) ˜ E and F (Γ β ) also depend on the progenitor structure,for which we adopt the same stripped-envelope progenitor as inTan et al. (2001). Following their convention, we assume the fol-lowing set of parameters: q = 4 . γ p = 4 / C nr = 2 . f ρ = 0 . f sph = 0 .
85 and A = 0 . More precisely, the proportionality coefficient of Equation (2)is not a constant, but a complex function of Γ β (Tan et al. 2001).This evaluation is valid for Γ β . and the energy coefficient, ˜ E , is evaluated as˜ E ∼ . × (cid:18) E in erg (cid:19) . (cid:18) M ej M ⊙ (cid:19) − . erg . (3)In Figure 1, we show the representative case ofan SN Ibc (the black line) with ( E in , M ej ) =(10 erg , M ⊙ ), and an HN (the blue line) with( E in , M ej ) = (10 erg , . M ⊙ ), which is consistent withSN 2009bb (Pignata et al. 2011).2.1.2. Dynamics of the Decelerating Ejecta
We assume a power law for the CSM density pro-file, n w ( R ) = A R − , where R is the radius and A =˙ M / (4 πv w m p ) with ˙ M , v w , and m p being the mass lossrate, the wind velocity, and the proton mass, respectively.Here, we fix the wind velocity as v w = 1000 km s − ,which is a typical value for Wolf-Rayet (W-R) stars (e.g.,Crowther 2007).Since the outer shells have larger velocities and smallerenergies, they decelerate first by interacting with theCSM. The decelerated shells constitute a shocked re-gion. The inner, slower shells successively catch upwith the shocked region and energize it (refreshed shock;Rees & M´esz´aros 1998). The total energy in the shockedregion can be calculated as (Taylor 1950; Sedov 1959;Blandford & McKee 1976; De Colle et al. 2012) E sh (Γ β, R ) = R (Γ β ) n w ( R ) m p c × (cid:20) π β + 94 α (1 − β ) (cid:21) , (4)for a shock velocity βc and radius R . Here, α / =0 . As long as radiative cooling is negligible, E sh (Γ β, R ) is equal to the original kinetic energy E kin ( > Γ β ), so that the shock velocity can be esti-mated from (Sari & M´esz´aros 2000; Kyutoku et al. 2014;Barniol Duran et al. 2015) E kin ( > Γ β ) = E sh (Γ β, R ) . (5)By integrating dR/dt = β ( R ) c with respect to the lab-frame time t , the shock radius can be obtained as a func-tion of t as R = R ( t ). Moreover, the lab-frame timecan be related to the observer-frame time t obs through dt obs /dt = 1 − β ( R ).In the non-relativistic limit, Equation (5) can be ap-proximately represented as20 ˜ Eβ − s nr ∼ R β n w ( R ) m p c / α , (6)where s nr = 18 . /
3. From this, the time evolution of theblast wave radius can be calculated from R ( t obs ) ∼ [(4 α / c )(20 ˜ E/A m p c )] / ( s nr +2) × c ( t obs / ˜ s nr ) ˜ s nr , (7)where ˜ s nr = ( s nr + 1) / ( s nr + 2). After the shock velocitybecomes smaller than that of the slowest shell, the evolu-tion can be described by the Sedov-von Neumann-Taylorsolutions with an energy of E in . Equation (4) reproduces the numerical results of blast waveevolution within a maximum difference of 5%, both in the trans-relativistic and non-relativistic regimes (De Colle et al. 2012).
Synchrotron Emission
Next, we model the synchrotron emission from the de-celerating SN/HN ejecta based on the external shockmodel of non-relativistic fireballs (Waxman et al. 1998;Frail et al. 2000; Sironi & Giannios 2013). We note thatwhile the equations below explicitly contain the Lorentzfactor Γ of the shocked fluid, the non-relativistic regimecan be consistently calculated by approximating Γ ≈ − ≈ β / ǫ B and ǫ e , respectively. Second, all of the electronsthat are swept up by the blast wave are accelerated.Third, the injection spectrum of the non-thermalelectrons is a single power law with an index of p : n ( γ e ) dγ e = n γ − pe dγ e ( γ e ≥ γ m ), where γ e is the Lorentzfactor of the non-thermal electrons, γ m is the minimumvalue, n ( γ e ) is the number density of the acceleratedelectrons, and n is the normalization factor.The number density and the internal energydensity of the post-shock fluid are calculatedfrom (Blandford & McKee 1976) n ps = 4Γ n w , (8)and e int = 4Γ(Γ − n w m p c , (9)respectively. From the assumptions above, R ∞ γ m n γ − pe dγ e = 4Γ n w and R ∞ γ m n γ − pe m e c dγ e = ǫ e e int where m e is the electron mass. Then, n and γ m can becalculated from n = ( p − γ p − n w , (10)and γ m = 1 + m p m e p − p − ǫ e (Γ − . (11)The magnetic field strength is calculated from B / π = ǫ B e int as B = [8 πm p c ǫ B n w − / . (12)The electron energy spectrum becomes a broken powerlaw due to significant synchrotron cooling above a criticalLorentz factor γ c , where an electron loses almost all ofthe energy within the dynamical time: γ c = 6 πm e cσ T B Γ t . (13)The synchrotron frequencies corresponding to electronswith γ m and γ c are ν m , c = ν ( γ m , c ) = QB πm e c γ , c Γ , (14)where Q is the elemental charge. Synchrotron self-absorption (SSA) becomes important at radio fre-quencies. The optical depth for SSA can be cal-culated from τ ( ν ) ∼ α ( ν ) R/ Γ (Panaitescu & Kumar2000; Inoue 2004), where α ( ν ) is the absorption coeffi-cient (Rybicki & Lightman 1979). Note that the widthof the shocked region can be evaluated from ∆ R ∼ R/ Γ in the lab frame, and ∆ R ′ ∼ R/ Γ in the comovingframe. We determine the absorption frequency ν a from τ ( ν a ) = 1.We consider the emission only from the forward shockregion. In the observer frame, the total synchrotronpower emitted from a relativistic electron with γ e is givenby P ( γ e ) = (4 σ T c/ B / π ) γ e Γ (Rybicki & Lightman1979). Since the emitted photon energy concentratesaround the typical synchrotron frequency ν ( γ e ), the spec-tral peak power from a single electron P ν, max can be cal-culated from P ν, max ∼ P ( γ e ) ν ( γ e ) = m e c σ T Q B Γ . (15)If self-absorption is negligible, then the peak flux den-sity F ν, max from all of the non-thermal electrons can becalculated from F ν, max ∼ P ν, max πn w R πD , (16)where D is the distance to the source and R R πR ′ n w ( R ′ ) dR ′ = 4 πn w R is the total numberof the swept-up electrons.In the synchrotron emission model, the spectral en-ergy distribution (SED) has three break frequencies, ν a , ν m , and ν c (Sari et al. 1998; Panaitescu & Kumar 2000;Inoue 2004). In the radio-emitting phase, the follow-ing inequality holds among these frequencies: ν m <ν a < ν c . In this case, the SED can be approximatelycalculated from the broken power law (Sari et al. 1998;Granot & Sari 2002) F ν ∼ F ν, max (cid:16) ν a ν m (cid:17) − ( p − / (cid:16) νν a (cid:17) / , ν m < ν < ν a , (cid:16) νν m (cid:17) − ( p − / , ν a < ν < ν m , (cid:16) ν c ν m (cid:17) − ( p − / (cid:16) νν c (cid:17) − p/ , ν c < ν. (17)The SED peaks at the absorption frequency ν p = ν a , (18)where the peak flux density F p can be calculated from F p = F ν a ∼ F ν, max ( ν a /ν m ) − ( p − / . (19)Our model has five input parameters: ˜ E , ǫ e , ǫ B , p , and˙ M (or A ). On the other hand, the observed radio spec-trum is essentially characterized by three parameters, ν p , F p , and the spectral slope, which can be associated with ν a , F ν a , and p , through Equations (17)-(19). Thus, fromradio observations, one can determine ˜ E and ˙ M (or A )for a given set of ǫ e and ǫ B (see Equations 20 and 21 forthe explicit forms). RESULTFirst, in Section 3.1, we first estimate the energy pro-file of the ejecta of a radio-bright HN from the observedradio spectrum, on the basis of the refreshed shock modelin the previous section. We focus on SN 2009bb at D = 40 Mpc, since the observed data are available fromSoderberg et al. (2010). We find that the energy pro-file is consistent with that predicted from the spherical . G H z [ m Jy ] t obs [ day ]09bbM dot = 10 -5 -6 -7 . G H z [ m Jy ] . G H z [ m Jy ] Figure 2.
Radio light curve of SN 2009bb. The black data pointsare taken from Soderberg et al. (2010). The solid lines show ourtheoretical fit with ǫ e = ǫ B = 0 . p = 3, ˜ E = 6 × erg, and˙ M = 10 − M ⊙ yr − . Note that ˜ E = 6 × erg corresponds tothe blue solid line in Figure 1. The dashed and dotted lines showa higher ( ˙ M = 10 − M ⊙ yr − ) and a lower ( ˙ M = 10 − M ⊙ yr − )mass loss cases, respectively. HN explosion. Then, we discuss the origin of the dif-ference between our results and the previous studies. InSection 3.2, we focus on the synchrotron emission at op-tical frequencies and suggest that it can be an importantcounterpart for discriminating the origin of radio-brightHNe. Finally, in Section 3.3, we discuss the impact ofthe phenomenological parameters on our results.3.1.
Radio Afterglow
Here, to begin, we estimate the energy profile of a HNejecta from the observed radio spectrum on the basis ofthe refreshed shock model in the previous section. Bysubstituting Equations (7)-(16) into Equations (18) and(19), we can estimate ˜ E and ˙ M as functions of ǫ e and ǫ B as˜ E ∼ × (cid:20)(cid:16) ǫ B . (cid:17) ( s nr +10)(1 − p ) (cid:16) ǫ e . (cid:17) ( s nr − p +1) (cid:21) / (4 p +9) × (cid:18) ν p t fit
20 day (cid:19) ( − s nr (2 p +13)+24 p − / (4 p +9) × (cid:18) F p
20 mJy (cid:19) ( s nr ( p +6) − p − / (4 p +9) erg ∝ ǫ − . / B ǫ − . / e , (20) and˙ M ∼ − (cid:16) ǫ B . (cid:17) − (4 p +1) / (4 p +9) (cid:16) ǫ e . (cid:17) − p − / (4 p +9) × (cid:18) ν p t fit
20 day (cid:19) p − / (4 p +9) × (cid:18) F p
20 mJy (cid:19) − p − / (4 p +9) M ⊙ yr − ∝ ǫ − / B ǫ − / e , (21)where F p ∼
20 mJy and ν p ∼ t fit ∼
20 days in Soderberg et al. (2010).Note that s nr = 18 . / p ∼ ǫ e and ǫ B , are uncertain. Here, we adopt the equiparti-tion values, since the main aim is to compare our esti-mate of the energy profile with that of Soderberg et al.(2010). We discuss the impact of the phenomenologicalparameters on our results in Section 3.3. Note that theenergy profile with ˜ E = 6 × erg corresponds to theblue solid line in Figure 1. Therefore, our results implythat the energy profile of a radio-bright HN, SN 2009bb,is consistent with that predicted from the spherical HNexplosion, and it does not require the additional trans-relativistic component.In Figure 2, we compare the light curves of SN 2009bbin the radio band with those calculated by the refreshedshock model. The black points correspond to the ob-served data from Soderberg et al. (2010). The solid bluelines are the results of our theoretical calculation with˜ E = 6 × erg, ˙ M = 10 − M ⊙ yr − , ǫ e = ǫ B = 0 . p = 3. For comparison, we also show the casesof the higher ( ˙ M = 10 − M ⊙ yr − ) and lower ( ˙ M =10 − M ⊙ yr − ) mass loss rates with the dashed and dot-ted lines, respectively. The radio flux becomes larger andthe peak time comes later for the higher wind density.One can see that the radio counterpart of SN 2009bbcan be well explained by the refreshed shock model us-ing the estimated energy profile, CSM density, and theadopted equipartition parameters.Next, let us compare the obtained energy profile withthat of the previous studies. Using the yellow and greenregions on the blue solid line of Figure 1, we show theshells contributing to the radio and optical synchrotronemission, respectively. The radio-emitting shells haveΓ β ∼ . . E sh ∼ -10 erg for t obs ∼ days (the yellow regionon the solid line). On the other hand, Soderberg et al.(2010) estimated Γ β ∼ . E sh ∼ erg (the yellowpoint on the dashed line), and ˙ M = 2 × − M ⊙ yr − by fitting the radio spectrum of SN 2009bb at t obs ∼ E sh and Γ β by overlooking some factors related to the min-imum Lorentz factor ( γ m ) of the non-thermal electrons.Hereafter, we discuss the origin of the discrepancy intheir estimate following their arguments.By replacing E l (the minimum energy of the non-thermal electrons) in Equations (11) and (12) ofChevalier (1998) with γ m , fit m e c , we obtain the emissionradius R fit and the magnetic field strength B fit as R fit ∼ . × (cid:18) F p
20 mJy (cid:19) / (cid:16) ν p (cid:17) − × (cid:16) ǫ B . (cid:17) / (cid:16) ǫ e . (cid:17) − / γ − / , fit cm , (22)and B fit ∼ . (cid:18) F p
20 mJy (cid:19) − / (cid:16) ν p (cid:17) × (cid:16) ǫ B . (cid:17) / (cid:16) ǫ e . (cid:17) − / γ − / , fit G , (23)respectively. We can see that R fit and B fit at t fit weaklydepend on γ m , fit ≡ γ m ( t fit ). This is also pointed out inChevalier & Fransson (2006). From Equation (22), Γ β at t fit can be estimated as(Γ β ) fit ∼ R fit /ct fit ∼ . (cid:18) F p
20 mJy (cid:19) / (cid:18) ν p t fit
20 day (cid:19) − × (cid:16) ǫ B . (cid:17) / (cid:16) ǫ e . (cid:17) − / γ − / , fit . (24)The blast wave energy is given by E sh ∼ R B / ǫ B ,and substituting Equations (22) and (23), it is evaluatedas E sh ∼ . × (cid:18) F p
20 mJy (cid:19) / (cid:16) ν p (cid:17) − × (cid:16) ǫ B . (cid:17) − / (cid:16) ǫ e . (cid:17) − / γ − / , fit erg . (25)Finally, from the definition of the mass loss rate ˙ M =4 πR ρ w v w and Equation (12), one can obtain ˙ M =( v w / ǫ B c )( B R / Γ(Γ − ∼ ( v w / ǫ B ) t B , or˙ M ∼ . × − (cid:18) F p
20 mJy (cid:19) − / (cid:18) ν p t fit
20 day (cid:19) × (cid:16) ǫ B . (cid:17) − / (cid:16) ǫ e . (cid:17) − / γ − / , fit M ⊙ yr − , (26)where we use R ∼ βct obs in the non-relativistic limit.Equations (25) and (26) show that the blast wave en-ergy ( E sh ) and the CSM density ( ˙ M ) strongly dependon γ m , fit .If we set γ m , fit = 1, then we can reproduce the esti-mates of Soderberg et al. (2010) by a factor of less thana few from Equations (24)-(26). According to Equation(11), however, we should set γ m , fit ∼
100 for p = 3, ǫ e = ǫ B = 0 .
33, and Γ β = 0 .
85, which they adopted intheir study. If we substitute γ m , fit ∼
100 into Equations(24)-(26), then we obtain Γ β ∼ . E sh ∼ . × erg,and ˙ M = 2 . × − M ⊙ yr − . Thus, Soderberg et al.(2010) overestimated Γ β , E sh , and ˙ M by overlooking thelarge factor related to γ m , fit . If they correct this point,their results are consistent with ours.3.2. Optical Synchrotron Precursor -2 -1 -22-20-18-16-14-12-10 AB M agn i t ude a t r- band A b s . M agn i t ude a t r- band t obs [ day ] PTF / KISSPan-STARRSLSST09bb Figure 3.
Optical synchrotron precursor expected from the radioobservation of SN 2009bb (the blue solid line). The black pointscorrespond to the r -band light curve of SN 2009bb (Pignata et al.2011) and the dashed lines to the 5 σ sensitivity of PTF (60 s),KISS (180 s), Pan-STARRS (30 s), and LSST (30 s) from up to bot-tom, respectively, where the values in the parentheses correspondto the integration times. We see that an optical synchrotron pre-cursor is predicted against the canonical SN emission for t obs < t obs . . M = 10 − M ⊙ yr − ) and lower ( ˙ M = 10 − M ⊙ yr − )mass loss cases with the dashed and dotted lines, respectively. Theoptical synchrotron precursor will evolve as the orange dotted-dashed line if the estimates of Soderberg et al. (2010) were cor-rect. Note that in Section 3.1, we show that they overestimatedthe energy of the HN ejecta. Future observations of SN 2009bb-likeevents can confirm whether our predictions or theirs are correct. We can see from the blue line in Figure 1 that the trans-relativistic ejecta with Γ β ∼ ν opt is found to be larger than ν a , ν m , and ν c at all times, the light curve can be cal-culated from the equation given by the last column ofEquation (17), i.e., ν c < ν opt .In Figure 3, the solid blue line represents the opti-cal synchrotron flux calculated from the above param-eter values, and the black points represent the r -bandlight curve of SN 2009bb (Pignata et al. 2011). Here, weadopt the color excess of E B − V = 0 .
58 (Pignata et al.2011). The dashed lines show the 5 σ sensitivity ofthe Palomar Transient Factory (PTF, 60 s; Law et al.2009; Rau et al. 2009), Kiso Supernova Survey (KISS,180 s; Morokuma et al. 2014), Panoramic Survey Tele-scope & Rapid Response System (Pan-STARRS, 30 s;Kaiser et al. 2002), and Large Synoptic Survey Tele-scope (LSST, 30 s) from top to bottom, respectively,where the values in the parentheses correspond to theintegration times. We find that at ∼ t obs . . M = 10 − M ⊙ yr − )and lower ( ˙ M = 10 − M ⊙ yr − ) mass loss rates with thedashed and dotted lines, respectively. Brighter precur- sors can be expected for the denser wind envelopes, andso it can be a good probe of the circumstellar environ-ments. Note that the shells contributing to the opticalprecursor have velocities larger than those contributingto the radio afterglow: the former have Γ β ∼ . E sh ∼ -10 erg for t obs ∼ ∼ Dependence on Phenomenological Parameters
So far, we adopt the equipartition values for the phe-nomenological parameters, ǫ e = ǫ B = 0 .
33, since ourmain goal is to compare our estimate of the energy profilewith that of Soderberg et al. (2010). The plausible val-ues of these parameters are, however, rather uncertain.For example, from the combined analysis of the late-timeradio and X-ray emission of Type IIb SNe, lower values of ǫ e are obtained, ǫ e ∼ . , ǫ B ∼ . ǫ e ∼ . , ǫ B ∼ .
01 (Panaitescu & Kumar 2002; Yost et al. 2003).We can estimate the larger values of ˜ E and ˙ M for thesmaller values of ǫ e and ǫ B (see Equations 20 and 21).For example, for ǫ e ∼ . , ǫ B ∼ − , we can obtain˙ M ∼ . × − M ⊙ yr − and ˜ E ∼ × erg. Inthis case, the resultant energy profile passes through theyellow point in Figure 1, while the wind mass loss rate is abit larger than those of the Galactic W-R stars: ˙ M WR < − M ⊙ yr − (Crowther 2007; Smith 2014). If this isthe case, then we can suggest that a radio-bright HN mayrequire an additional trans-relativistic component.We also confirm that while the brightness of the op-tical precursor tends to become dimmer for the smallervalues of ǫ e and ǫ B , the difference is at most of 1 ABmagnitude, and that it is still be detectable even by thecurrent detectors at t obs & DISCUSSIONPrevious studies claimed that radio-bright HNe can-not be powered by the ejecta produced by a sphericalHN explosion, and that an additional trans-relativisticcomponent is required. They proposed that relativisticjets that barely punch out the progenitor stars can bethe origin of the trans-relativistic component. In thispaper, however, we focus on a radio-bright HN and findthat they overestimated the energy and the speed of thetrans-relativistic ejecta, since they overlooked some fac-tors related to γ m , fit . In addition to the radio afterglow,we also consider the optical counterpart of a radio-brightHN and find that it can be observed as the precursor of canonical SN emission by current and future SN sur-veys. An optical precursor can also be expected fromthe energy profile of the previous studies. We find that iftheir estimates were correct, then we would see an opti-cal precursor that is by ∼ ∼
100 Mpc. Since the fraction of 09bb-like HNe is ∼ .
7% of SNe Ibc (Soderberg et al. 2010), we may expect agood event rate of . . − for 09bb-like optical coun-terparts from PTF and KISS. In the LSST era, we canexpect the detection of optical precursors not only frommore distant events but also from ordinary HNe. Theywould provide deeper insight into the GRB-SN connec-tion. Note that they would not be hidden by the SNshock breakout emission since its duration and spectrumpeak are expected to be R WR /c ∼ & t obs . . ν a becomes larger than the cooling frequency ν c . Inthis case, self-absorption may become a heating sourcefor the accelerated electrons. Electrons are piled upat a Lorentz factor where self-absorption heating andsynchrotron cooling balance each other (McCray 1969;Ghisellini et al. 1988). Moreover, the radiation spectrumapproaches a quasi-thermal spectrum for ν < ν a . Wefind, however, that the absorption frequency may alwaysbe smaller than any frequency ν opt in the optical band: ν opt > ν a ∼ × ( t obs / . − . Hz for fiducialparameters ǫ e = ǫ B = 0 .
33, ˜ E = 6 × erg, and˙ M = 10 − M ⊙ yr − . Therefore, self-absorption heat-ing may not qualitatively change the optical precursor inFigure 3.We also check that inverse Compton (IC) emissiondoes not significantly vary our results as long as weadopt the fiducial parameters of equipartition. Here, weconsider the synchrotron-self-Compton (SSC) emissionand external-IC (EIC) emission. We find that SSC emis-sion is weak for all of the time, since the Compton Y parameter can be evaluated as Y SSC < .
62 (Sari & Esin2001). For EIC emission, since SN thermal photonsdominate the external radiation field, we should com-pare the energy density of SN thermal photons U rad ∼ . L bol / . erg s − )( t obs /
10 day) − . erg cm − with that of the magnetic filed U B ∼ .
034 ( t obs /
10 day) − erg cm − , where L bol is thebolometric peak luminosity. As we can see from Figure3, for t obs >
50 days, the SN becomes so dim that U rad ≪ U B , and EIC emission can be negligible, whilefor t obs .
50 days, the SN is still bright enough that U rad & U B , and EIC can be the dominant coolingprocess. Since the observed radio light curve can bereproduced quite well for t obs >
50 days with thesynchrotron emission model (Figure 2), EIC does notaffect for determining the model parameters.ACKNOWLEDGEMENTSWe thank the anonymous referee for giving us helpfulcomments and improving the quality of this paper. Wealso thank K. Kyutoku and K. Maeda for fruitful discus-sions and comments. This work is supported in part bythe Grant-in-aid from the Ministry of Education, Cul-ture, Sports, Science and Technology (MEXT) of Japan,Nos. 261051 (DN), 24740165, 24244036 (HN), 25103511(YS), 23540305, 24103006 (TN), HPCI Strategic Pro-gram of MEXT (HN), NASA through Einstein Post-doctoral Fellowship grant number PF4-150123 awardedby the Chandra X-ray Center, which is operated by theSmithsonian Astrophysical Observatory for NASA undercontract NAS8-03060 (KK), JSPS postdoctoral fellow-ships for research abroad, MEXT SPIRE, and JICFuS.50 days with thesynchrotron emission model (Figure 2), EIC does notaffect for determining the model parameters.ACKNOWLEDGEMENTSWe thank the anonymous referee for giving us helpfulcomments and improving the quality of this paper. Wealso thank K. Kyutoku and K. Maeda for fruitful discus-sions and comments. This work is supported in part bythe Grant-in-aid from the Ministry of Education, Cul-ture, Sports, Science and Technology (MEXT) of Japan,Nos. 261051 (DN), 24740165, 24244036 (HN), 25103511(YS), 23540305, 24103006 (TN), HPCI Strategic Pro-gram of MEXT (HN), NASA through Einstein Post-doctoral Fellowship grant number PF4-150123 awardedby the Chandra X-ray Center, which is operated by theSmithsonian Astrophysical Observatory for NASA undercontract NAS8-03060 (KK), JSPS postdoctoral fellow-ships for research abroad, MEXT SPIRE, and JICFuS.