An external-shock model for GRB afterglow 130427A
aa r X i v : . [ a s t r o - ph . H E ] N ov submitted to MNRAS on 27 June 2013, now in press An external-shock model for GRB afterglow 130427A
A. Panaitescu, W.T. Vestrand, P. Wo´zniak
Space & Remote Sensing, MS B244, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
ABSTRACT
The complex multiwavelength emission of GRB afterglow 130427A (monitored in theradio up to 10 days, in the optical and X-ray until 50 days, and at GeV energies until1 day) can be accounted for by a hybrid reverse-forward shock synchrotron model,with inverse-Compton emerging only above a few GeV. The high ratio of the earlyoptical to late radio flux requires that the ambient medium is a wind and that theforward-shock synchrotron spectrum peaks in the optical at about 10 ks. The latterhas two consequences: the wind must be very tenuous and the optical emission before10 ks must arise from the reverse-shock, as suggested also by the bright optical flashthat Raptor has monitored during the prompt emission phase ( <
100 s). The VLAradio emission is from the reverse-shock, the Swift X-ray emission is mostly from theforward-shock, but the both shocks give comparable contributions to the Fermi GeVemission. The weak wind implies a large blast-wave radius (8 t / day pc), which requiresa very tenuous circumstellar medium, suggesting that the massive stellar progenitorof GRB 130427A resided in a super-bubble. Key words: radiation mechanisms: non-thermal – relativistic processes – shock waves
Gamma-Ray Burst (GRB) 130427A may well be the burstwith the most comprehensive afterglow follow-up, its mul-tiwavelength monitoring covering radio, optical, X-ray, and γ -ray frequencies, and extending from seconds to tens ofdays after trigger. The X-ray prompt emission (up to 100s) was accompanied by the second brightest optical flash,monitored by Raptor (Vestrand et al 2013), with the opticalafterglow light-curve displaying a steepening at 300 s anda flattening at 10 ks. The Swift X-ray light-curve (X-raylight-curve repository – Evans et al 2009) is consistent witha single power-law from 500 s to 5 Ms. The Fermi-LAT γ -ray light-curve (Tam et al 2013) displays a peak at 10–20 s,simultaneous with the optical flash peak, and a steepeningat 550–800 s (Zhu et al 2013). The VLA radio light-curves(Laskar et al 2013) display a slow decay at 1-10 day.With such a rich dataset, GRB afterglow 130427A de-mands a theoretical interpretation, done here in the frame-work of the external-shock model (M´esz´aros & Rees 1997)where some relativistic ejecta, produced by the black-holeresulting from the core-collapse of a massive star, drive a forward-shock into the ambient medium while the ejecta areenergized by the reverse-shock . The synchrotron and inverse-Compton emissions from both shocks are calculated assum-ing that electrons and magnetic field acquire a certain frac-tion of the post-shock energy. The shock-accelerated elec-trons are assumed to have a power-law distribution with energy (hence the synchrotron and inverse-Compton spec-tra are also power-laws), with a break at the cooling energy(where the radiative-loss timescale equals the shock age).Analytical treatments for the forward-shock emissionhave been provided by M´esz´aros & Rees (1997), Sari, Pi-ran & Narayan (1998), Waxman, Kulkarni & Frail (1998),Granot, Piran & Sari (1999), Wijers & Galama (1999),Chevalier & Li (2000), Panaitescu & Kumar (2000), andfor the reverse-shock by Kobayashi (2000). Both shockshave been studied with 1-dimensional hydrodynamical codesby Panaitescu & M´esz´aros (1998) and Kobayashi & Sari(2000), the former focusing on the two-shock synchrotronand inverse-Compton emission, the latter on the dynamicsof the shocks.To model the multiwavelength emission of GRB after-glow 130427A, we employ a 1-dimensional code that fol-lows the ejecta–medium interaction, with the dynamics ofeach shock calculated from conservation of energy and us-ing the shock jump-conditions (Blandford & McKee 1976).After the onset of deceleration, the dynamics of the forward-shock is determined by the ejecta initial energy, injected en-ergy (Rees & M´esz´aros 1998), and ambient medium density.The dynamics of the reverse-shock is determined by that ofthe shocked fluid and two properties of the incoming ejecta:their energy and Lorentz factor. Here, we consider that theejecta add energy to the blast-wave as a power-law in ob-server time and that they have a single Lorentz factor. The Panaitescu, Vestrand & Wo´zniak self-absorption and cooling frequencies of the synchrotronspectrum and the inverse-Compton parameter are calculatedself-consistently from the electron distribution and the mag-netic field strength (Panaitescu & M´esz´aros 2000). Radiativelosses are also calculated from the electron distribution, butthey are negligible for the following best-fit models. Theemissions from both shocks are integrated over their motionand over the angle at which the fluid moves relative to the di-rection toward the observer. More details about this numer-ical model and its application to the multiwavelength emis-sion of ten GRB afterglows are given in Panaitescu (2005).
The choice of the model features that may accommodate thetemporal decay of the broadband emission of GRB afterglow130427A starts with the X-ray light-curve because its tem-poral decay index ( F ∝ t − α ) and spectral slope ( F ν ∝ t − β )are the best determined: α x = 1 . ± .
01 at 20 ks – 5 Ms(Fig 1) and β x = 0 . ± .
16 at mean time 24 ks (Kenneaet al 2013). These lead to α x − . β x = 0 . ± .
24, whichis compatible with the value expected (zero) for the syn-chrotron emission from the forward-shock interacting witha homogeneous medium and for the X-ray being below thecooling frequency ν c of the synchrotron spectrum.As the optical flux also decays at that time, the opti-cal must be above the peak energy ν p of the synchrotronspectrum, hence optical and X-ray are in the same spectralregime: ν p < ν o (2 eV) < ν x (10 keV) < ν c . Consequently, theintrinsic afterglow optical flux can be calculated from theX-ray flux: F o = F x ( ν o /ν x ) β x . For instance, the observed F keV (54 ks) = 1 . µ Jy implies that F eV (54 ks) = 1 . F eV (53 ks) =0 .
47 mJy, requiring A R = 1 mag of dust extinction in thehost galaxy.The 10 keV – 100 MeV spectral slope β xg (43 ks) ≃ . ± . > ∼ β x indicates that ν c is well above 10 keV.That the LAT flux decays slower than in the X-ray ( α g =1 . ± .
09 at 500 s – 50 ks) indicates that ν c is belowthe LAT range (otherwise, for ν c >
100 MeV, the modelexpectation is α x = α g ) and that the electron radiativecooling is dominated by inverse-Compton scatterings (other-wise, for synchrotron-dominated electron cooling, ν c ∝ t − / and α g − α x = − . d log ν c /d log t ) = 1 /
4, incompatiblewith the observed α g < ∼ α x ). More exactly, for a Compton-dominated electron cooling, the decay index of the syn-chrotron flux above ν c is α = 3 p/ − / (4 − p ) = 1 .
27, whichmatches well the observed α g , with p = (4 α x + 3) / . dN/dǫ ∝ ǫ − p ) that is required by theforward-shock model, given the measured flux decay index α x below the cooling frequency.In summary, the optical, X-ray, and γ -ray fluxes of GRBafterglow 130427A, their decay indices, and the X-ray spec-tral slope, require that ν p < ν o < ν x < ν c < ν g , if theafterglow emission is synchrotron from the forward-shock. Under the assumption that the two microphysical parame-ters of the forward-shock ( ǫ B and ǫ i ) that quantify the post-shock fractional energy in the magnetic field and in electronsare constant, the forward-shock synchrotron light-curve atany frequency below the optical can be easily calculatedfrom the optical light-curve, using the expected evolutionof the synchrotron peak flux ( F p = const ) and peak energy( ν p ∝ t − / ) for a homogeneous medium. If ν p crosses theoptical at some time t o , yielding an optical flux F o , then theradio flux at frequency ν r < ν p is F r ( t ) = F p ( ν r /ν p ) / = F o ( t o )( t/t o ) / ( ν r /ν o ) / ∝ t / (1)Here, F o ( t o ) ≃ t o /
10 ks) − α o mJy is the intrinsic opticallight-curve after 10 ks (corrected for the above-inferred hostextinction of A R = 1 mag) and α o = 1 .
36 (the forward-shock model requires that α o = α x ). The largest t o requiredby equation (1) arises from the radio measurement with thehighest ν / r t / /F r ; taking the F
36 GHz (9 . .
43 mJymeasurement as an upper limit for the forward-shock radioflux, implies t o > ∼
23 ks.This means that, for the forward-shock emission (thataccommodates the observed optical flux) not to exceed themeasured radio fluxes, the synchrotron peak should crossthe optical at 23 ks. Conversely, if the synchrotron peakcrossed the optical before 23 ks, then the synchrotron fluxfrom the forward-shock would violate VLA measurements.That may be avoided if the magnetic field parameter ǫ B decreases (roughly as t − ), and if energy injection in theforward-shock is allowed (to match the optical and X-rayflux decays at 1–10 day, which are faster when ǫ B decreases),but this scenario requires fine-tuning and we do not pursueit. Fig 1 illustrates the failure of the forward-shock syn-chrotron model with a homogeneous medium to accom-modate simultaneously the radio, optical, X-ray, and γ -rayfluxes of GRB afterglow 130427A: while it can explain theoptical afterglow emission after 10 ks and the X-ray flux at50 s – 5 Ms (excluding the second GRB pulse, which is afeature that cannot be accounted for by any type of exter-nal shock), this model over-predicts either the lowest or thehighest frequency data. The closure relation α x − . β x = 0 . ± .
24 is also compat-ible with the forward-shock model expectation for a wind-like medium (with an n ∝ r − particle density distributionwith radius) and for X-ray below the cooling frequency, pro-vided that there is an energy injection in the forward-shockthat slows its deceleration and the decay of the afterglow X-ray flux. If that energy injection is parametrized as E ∝ t e in observer time (a power-law flux decay requires that thedynamics of the forward-shock is a power-law in observertime), then α x − . β x = [1 + ( β x + 1) e ] /
2, from where e = 3 − α x + 1) / ( β x + 1) = 0 . ± . RB afterglow 130427A time since GBM trigger (s) -6 -4 -2 GH z , e V , k e V , M e V f l ux ( m J y ) RAPTOR/2eV 2eV
BAT/10 keVLAT/100 MeV
XRT/10 keV
VLA/14 GHz
Figure 1.
Multiwavelength light-curves for GRB afterglow130427A and the synchrotron forward-shock/homogeneous-medium model best-fit to the radio, optical after 10 ks, X-rayafter 50 s, and γ -ray measurements (the second X-ray pulse at100–400 s is not included in the fit). Numbers adjacent to light-curves give the local power-law flux decay index (and its 1 σ un-certainty). Solid lines are for a model excluding radio measurements; thepeak of the synchrotron spectrum crosses the R-band (2 eV) at10 ks and the model over-predicts some of the VLA radio mea-surements at 1–10 day and 1–90 GHz (as expected from eq 1).The parameters of this model are: ejecta initial kinetic energy E = 3 . erg/sr, ejecta initial Lorentz factor Γ = 850 (to yielda 20 s peak for the 100 MeV flux, when the ejecta decelerationbegins), ambient medium density n = 2 . − cm − , magnetic-field parameter ǫ B = 10 − , electron minimum-energy parameter ǫ i = 0 .
11, index of electron power-law distribution with energy p = 2 .
5, host dust-extinction A V = 1 . Dashed lines are for a model including the radio measurements,which forces the peak of the synchrotron spectrum to be higher(crossing the optical at 20 ks). This model still over-predicts someradio measurements as well as the γ -ray flux measured by LATduring the prompt phase. Its parameters are similar to the solidlines model, the most notable difference being ǫ i = 0 . after 10 ks) has e = 0 .
30 and that forward-shock energyshould increase by a factor E i /E = 3 until t e ≃ t i = t e ( E /E i ) /e = 20 ks.It is important to note that the forward-shock interact-ing with a wind-like medium does not produce more radioemission than measured because the synchrotron peak fluxdecreases as F p ∝ t − / (instead of being constant, as for a homogeneous medium). The evolution of the synchrotronpeak energy is the same as for a homogeneous medium( ν p ∝ t − / ), hence the radio flux expected from the op-tical emission is F r ( t ) = F p ( ν r /ν p ) / = F o ( t o )( ν r /ν o ) / ∝ t (2)Then, F o ( t o ) ≃ t o /
10 ks) − . mJy and F
36 GHz (9 . .
43 mJy require that the time when the synchrotron peakcrosses the optical is t o > ∼ ν p crossingthe optical and is compatible with t o > ∼ χ ν = 5 . χ ν = 7 . χ ν = 6 . χ arising from the X-raydata, ∆ χ = 392 for 79 points. The model light-curves fol-low well all flux trends and relative intensities except thebrightness of the prompt emission until 50 s, but cannot de-scribe well the early GeV light-curve and cannot capture thefluctuations in the X-ray and optical measurements (after 10ks, optical data are from different instruments). Compared to the parameters inferred for other afterglowsby modelling their multiwavelength emission, the wind den-sity of the best-fit shown in Fig 2 is very small, but notunprecedented (Chevalier, Li & Fransson 2004). Its param-eter, A = 0 . M /v ) that is 300 smallerthan for a typical Wolf-Rayet (WR) star (as the progeni-tor of long bursts with an associated Type Ic supernovae),for which ˙ M = 10 − ˙ M − M ⊙ / yr and v = 10 v cm/s. Thereason for that low density is the requirement that the syn-chrotron peak crosses the optical after 3 ks and matches theoptical flux detected at that time. For z = 0 .
34 and for thefluid moving directly toward the observer, the forward-shocksynchrotron peak energy and peak flux are hν p (10 ks) = 0 . E / ǫ / B, − ǫ i, − eV (3) F p (10 ks) = 240 E / ǫ / B, − A mJy (4)Imposing that ν p (10 ks) = ν o = 2 eV and F p (10 ks) = F o (10 ks) = 2 mJy, yields E / ǫ / B, − ǫ i, − = 0 . , E / ǫ / B, − A = 2 . × − (5)Taking the ratio of these two equations leads to A =2 . × − ǫ i, − . The ǫ i parameter that quantifies the typicalelectron energy corresponds to a total electron energy thatis a fraction ǫ e = ( p − / ( p − ǫ i of the post-shock energy.Equipartition with protons sets an upper limit, ǫ e ≤ / ǫ i ≤ .
12 for p = 2 .
32, from where
A < ∼ . Panaitescu, Vestrand & Wo´zniak time since GBM trigger (s) -6 -4 -2 GH z , e V , k e V , M e V f l ux ( m J y ) RSRSFSFSRS FS
FSRS
14 GHz10 keV100 MeV 2 eV
FS w/o KN
Figure 2.
Best-fit with a hybrid reverse(RS)/forward(FS) shockmodel for the broadband emission of GRB afterglow 130427A andfor a wind-like medium. Solid lines are for the reverse-shock light-curves, dashed lines for the forward-shock; the dotted line showsthe 100 MeV forward-shock flux when the Klein-Nishina effect isignored. RS parameters: at 10s–3ks : leading ejecta energy E = 10 erg/sr, incoming ejecta energy E (1) i = 4 . erg/sr ( E (1) i < E ,hence the dynamics of the forward-shock is not affected by thisfirst energy injection episode), incoming ejecta Lorentz factorΓ i = 1800, wind-density parameter A = 0 .
004 (see text for whysuch a low density is required), ǫ B = 10 − , ǫ i = 0 . p = 2 . at 3ks–1Ms : same E and A as above, E (2) i = 4 . erg/sr( E (2) i > E + E (1) i , thus this second energy injection mitigatesthe blast-wave deceleration), Γ i = 3000, ǫ B = 2 . − , ǫ i = 0 . p = 2 . FS parameters: same E , E (2) i and A as above, ǫ B = 2 . − , ǫ i = 0 . p = 2 . ǫ e and p , but an ǫ B closeto equipartition and an ejecta kinetic energy that is 1000 timessmaller). high wind velocity. Provided that can happen at the endof a WR’s life, it has a strong consequence on the mediumin which that star resides, as following. Owing to low winddensity and high ejecta kinetic energy, the forward-shockthat fits the late time broadband emission of GRB afterglow130427A is highly relativistic, having Γ ≃ t/ − / ,hence the shock radius is R a = 2Γ ct = 8( t/ / pc. Re-quiring that R a at the latest observation epoch (50 day) isless than the size of the bubble blown by a WR star during its 10 yr lifetime, R s = 36 ( ˙ M − v /n ) / pc (cf. Castor,McCray & Weaver 1975), with n the medium density aroundthe star, we find that n < ∼ . − v ( t s /
50 d) − / cm − for awind with ˙ M − /v = 0 . t s is the observer-frameepoch when the afterglow shock encounters the wind termi-nation shock. Such a low ambient density suggests that theprogenitor of GRB 130427A occurred in a supper-bubble(Scalo & Wheeler 2001) blown by many preceding super-novae. There are two interesting facts related to the LAT emissionproduced by the forward-shock synchrotron model shownin Figs 1 – 3. First is that the scattering of the synchrotronemission (at the peak of the spectrum) by the forward-shockelectrons (of typical energy) occurs near the Klein-Nishina(KN) regime. When the electron cooling is dominated byinverse-Compton scatterings (i.e. Compton parameter
Y > ν c ∝ Y − . Inclusion of theKN effect reduces the Compton Y parameter, thus, takinginto account the KN effect, increases ν c and the synchrotronflux at ν > ν c : F ν ∝ ν / c ∝ Y − . In other words, thesynchrotron emission from fast-cooling electrons increaseswhen a competing radiative process (inverse-Compton) isreduced (by inclusion of the KN effect).For the forward-shock best-fit to GRB afterglow130427A, the LAT range is above ν c and Y >
1; inclusionof the KN effect reduces Y by about 10 and increases the100 MeV flux by an order of magnitude (see Fig 2). Fur-thermore, as the electrons at the peak of their distributionwith energy enter and exit the KN regime, the synchrotronlight-curve at 100 MeV displays more structure than whenthe KN effect is ignored.The second is that radiative cooling during one gyrationtime limits the energy that electrons acquire through first-order Fermi acceleration to a corresponding synchrotroncharacteristic energy hν ∗ ≃ z + 1) − Γ / ( Y + 1) MeV,independent of the magnetic field B . For the best-fit param-eters given in Fig 2, the forward-shock has Γ(1 ks) = 240 and Y (1 ks)18, so the maximal synchrotron energy is hν ∗ (1 ks) ≃
600 MeV (see synchrotron spectrum cut-off in Fig 3). Atearlier times, that cut-off is higher, but the inverse-Comptonemission from the forward-shock takes over above 2 GeV (asshown by the t = 75 s spectrum) and can account for thehigher-energy LAT emission until about 10 ks, after whichthe inverse-Compton flux is too low.Interestingly, a hardening of the LAT spectrum aboveseveral GeV was identified by Tam et al (2013), from β ( low ) g = 1 . ± . β ( high ) g = 0 . ± . β ( high ) g = − /
3, corresponding to theGeV range being below the peak of the upscattered spec-trum.
RB afterglow 130427A photon frequency (Hz) -9 -7 -5 -3 -1 ene r g y f l u x den s i t y ( m Jy ) RS FSFSRS
ICSYN ν p ν c ν * ν c ν p ~ ν a ν p ν c ν * SYN ν p Figure 3.
Sequence of spectra for the reverse-forward shock model of Fig 2, at the epochs indicated in the legend. Data at same epoch andthe corresponding model spectrum have the same colour, solid lines are for the reverse-shock, dashed for the forward-shock. The spectralbreaks indicated are: ν a (self-absorption frequency), ν p (peak frequency, for electrons of typical post-shock energy, parametrized by ǫ i ), ν c (cooling frequency, corresponding to electrons whose radiative cooling timescale equals the shock’s age), and ν ∗ (cut-off frequency,corresponding to electrons that lose their energy during one gyration). The dotted line shows the fit to the 50 ks γ -ray spectrum obtainedwith the synchrotron FS emission if the electron acceleration timescale were much shorter than the gyration time. The forward-shockinverse-Compton emission emerges above the synchrotron cut-off, yielding a harder spectrum above a few GeV and accounting for thehigher-energy LAT emission until several ks. The estimation of the expected radio emission given in equa-tion (2) led to the conclusion that the forward-shock can-not account for the optical afterglow emission prior to ∼ γ -ray) afterglow emission accom-modated by the forward-shock, thus, for the calculation ofthe reverse-shock emission, the dynamical parameters E , E (2) i , e , and A are fixed at the values determined from theforward-shock best-fit. The free parameters of the reverse-shock are the Lorentz factor Γ i of the incoming ejecta (whichsets the post-shock energy density) and the three micro-physical parameters ( ǫ B , ǫ i , and p ) that determine the syn-chrotron spectrum. The best-fit obtained with the reverse-shock emission to the 1–10 day radio data is shown in Figs2 and 3. Unfortunately, it has a large χ ν = 25 for 25 dof, because it underestimates the radio flux above 50 GHz. Asshown in Fig 3, those radio data cannot be explained bythe forward-shock either, if its microphysical parameters areconstant. Requiring the same microphysical parameters forboth the reverse and forward shocks yields a much worseradio data fit, with χ ν = 47.The best-fit to the early optical emission with a reverse-shock includes also the earlier X-ray data and all GeV data,to ensure that the reverse-shock emission does not exceedwhat was observed. Again, the dynamical parameters E and A are fixed to the values obtained for the forward-shock,but the energy E (1) i carried by the incoming ejecta arrivingat the blast-wave prior to 10 ks is only weakly constrainedby the forward-shock fit to the optical and X-ray data af-ter 10 ks, which sets an upper limit E (1) i < E . With freemicro-parameters, the best-fit with the reverse-shock to theearly afterglow has χ ν = 5 . ǫ B prior to 10 ks (from fitting the early optical afterglow)is 100 times larger than after 10 ks (from modelling for theradio emission). If the reverse-shock microphysical parame-ters were held constant across 10 ks, then the fit to the radioemission would have a χ ν twice larger, thus a decrease in ǫ B Panaitescu, Vestrand & Wo´zniak at 10 ks is required. That may mean that the ejecta arrivingat the blast-wave later are less magnetized.
As discussed in § § M − /v = 0 . R a (3 ks) = 1 . R s = 12 ( v /n ) / pc. Thus, if the circumstellar medium is sufficiently dense, itpossible that R a (3 ks) = R s . Alternatively, if the stellar windhad the average density, the wind termination shock couldbe encountered by the forward-shock at 3 ks, provided thatthe burst is embedded in a hot, highly pressurized environ-ment (Chevalier et al 2004). At frequencies below the coolingbreak, the afterglow light-curve should display a flatteningwhen the forward-shock crosses the wind termination shock,transiting from the r − free wind to the quasi-homogeneousshocked wind.To be self-consistent, the interpretation of the 3 ks opti-cal light-curve flattening as the blast-wave encountering thewind termination shock should attribute the entire after-glow emission to the same shock. Then, the peak of the syn-chrotron spectrum must be below optical at all times whena decaying optical flux is measured, a model which overpro-duces radio emission, if the optical afterglow originates inthe forward-shock (as shown in § δα = 1 / δβ = 1 / r − wind, which is theearlier WR wind or the wind of the nearby star, producing a light-curve steepening, with the flux decay index α return-ing to the value it had during the interaction with the freeWR wind. Only the dense cluster scenario provides a naturalexplanation for the very weak wind inferred here from mod-elling the afterglow 130427A: the wind of a B star locatedwithin 1 pc of the GRB progenitor. However, this scenariocannot explain why that weak wind extends over tens of pcs(as required by the duration of the afterglow, § The closure relations expected between the forward-shocksynchrotron flux decay index and spectral slope suggest ahomogeneous ambient medium for GRB afterglow 130427A.Although long GRBs arise from massive stars that drivepowerful winds, a homogeneous medium is possible if theafterglow emission is produced in the shocked wind. How-ever, this afterglow’s (10 ks) optical flux to (1–10 day) radioflux ratio and its slowly decaying radio light-curves disfavourthat type of mbient medium. Instead, for an unevolving con-stant magnetic field parameter, the synchrotron spectrumpeak flux is constant and the radio emission should havebeen brighter and slowly rising. With some fine-tuning of theevolutions of those micro-parameters, it may be possible toreduce the forward-shock model radio flux below measure-ments, while still accounting for the observed optical andX-ray light-curves.A wind-like medium ( n ∝ r − ) is the more natural ex-pectation for a massive star as the GRB progenitor. Theforward-shock emission still cannot account for the radiodata because the expected radio light-curve is flat, however,a wind-like medium yields a decreasing synchrotron spec- RB afterglow 130427A trum peak flux, making it easier to keep the forward-shockradio emission below radio measurements. To explain the op-tical and X-ray flux decay after 10 ks with the forward-shocksynchrotron emission, a moderate energy injection into theforward-shock is required, increasing the shock energy by afactor 4 from 10 ks to 1 Ms. The agent of that energy injec-tion should be some ejecta that arrive at the forward-shockat that time, which provides a natural explanation for theafterglow radio emission: the reverse-shock that crosses theincoming ejecta.The reverse-shock must have been operating at evenearlier times because the high early-optical to late-radio fluxratio precludes a forward-shock origin of the optical after-glow emission prior to 10 ks. Such a reverse-to-forward shockswitch for the origin of the optical emission, occurring at fewks, is supported by the optical afterglow becoming bluer ⋆ atthat time (Vestrand et al 2013), when the forward-shockemission, with a spectrum F ν ∝ ν / in the optical, be-gins to dominate the softer reverse-shock emission, with aspectrum F ν ∝ ν − / . As the peak of the forward-shocksynchrotron spectrum falls below optical at about 10 ks, theoptical afterglow should become redder after 10 ks, as wasobserved by Perley et al (2013).However, for the reverse-shock to explain the 100 s –few ks optical afterglow and the 1–10 day radio afterglowemission, the properties of the reverse-shock (microphysicalparameters, kinetic energy and Lorentz factor of the incom-ing ejecta) must change around 10 ks. Furthermore, Ves-trand et al (2013) have shown that the reverse-shock canalso account for the optical flash (up to 100 s) and the GeVlight-curve peak, but for microphysical different than afterthat peak.For this hybrid reverse-forward shock model, we findthat the X-ray flux of GRB afterglow 130427A is accountedmostly by the forward-shock emission, from the tail of thefirst GRB pulse (50–100 s) up to 5 Ms, excluding the secondGRB pulse at 100-500 s. The reverse-shock may have had asignificant contribution to the early X-ray emission, at 500s – 2 ks. Both shocks give comparable GeV emissions. Asshown in Fig 2, the radio emission from the forward-shockis expected to overshine that from the reverse-shock at 30day (or somewhat later, if energy injection continues after 1Ms), yielding a flat flux < ∼ . ∼
200 day, when thepeak of the synchrotron spectrum falls below 10 GHz. If thatflat radio flux is not seen, then the magnetic field parameter ǫ B of the forward-shock must be decreasing, so that thepeak flux of the forward-shock synchrotron spectrum falls-off faster than the F p ∝ t − / expected for ǫ B =const.The relative dimness of the radio afterglow suggeststhat the peak of the synchrotron spectrum has crossed theoptical range at 10 ks. An immediate consequence is thatthe wind-like ambient medium is a factor 20 less dense thanthe most tenuous wind measured for Galactic WR stars. Wecannot provide a good argument for why GRB 130427A’sprogenitor had such a low mass-loss rate –to– wind-speedratio ( ˙ M/v = 4 × − (M ⊙ / yr) / (km / s)), but note that, ⋆ This feature, accompanied by a flattening of the optical flux de-cay, was previously observed in two other GRB afterglows: 061126(Perley et al 2008) and 080319B (Wo´zniak et al 2009) owing to the weak wind, the afterglow remains highly rela-tivistic and travels ∼
100 pc until the last observation epoch(50 day). For such a large afterglow radius to remain insidethe free WR wind (i.e. within the wind termination shock),the GRB progenitor must have been embedded in a verytenuous medium, suggesting a supper-bubble blown by pre-ceding supernovae and stellar winds.Owing to tenuous ambient medium, the afterglow trans-verse size, 2 R ⊥ = 2Γ ct ≃ . t/ / pc, is unusu-ally large, and implies a source apparent diameter of θ =0 .
63 ( t/
100 d) / mas, which may be resolved with radio in-terferometry.If the GeV emission of GRB afterglow 130427A arisesfrom the forward-shock, then the up-scattering of the syn-chrotron emission occurred at the onset of the KN regime,where the reduction of the electron scattering cross-sectionlowers the Compton parameter, increases the synchrotroncooling-break frequency, and increases the synchrotron fluxabove that break (i.e. in the LAT range). Furthermore, LATmust have measured the forward-shock inverse-Comptonemission at photon energies above a few GeV. ACKNOWLEDGMENTS
This work was supported by an award from the LaboratoryDirected Research and Development programme at the LosAlamos National Laboratory and made use of data suppliedby the UK Swift Science Data Centre at the University ofLeicester.