Thermal and non-thermal emission from the cocoon of a gamma-ray burst jet

4.7 MB·

by  Fabio De Colle

MNRAS000,1–12(2017) Preprint20January2017 CompiledusingMNRASLATEXstylefilev3.0
Thermal and non-thermal emission from the cocoon of a
gamma-ray burst jet
Fabio De Colle,1(cid:63) Wenbin Lu,2 Pawan Kumar,2 Enrico Ramirez-Ruiz,3 George Smoot4,5,6
1Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, A. P. 70-543 04510 D. F. Mexico
2Department of Astronomy, University of Texas at Austin, Austin, TX 78712, USA
3Department of Astronomy and Astrophysics, University of California, Santa Cruz, California 95064
4Helmut and Ana Pao Sohmen Professor at Large, Institute for Advanced Study, Hong Kong University of Science and Technology,
Clear Water Bay, Kowloon, Hong Kong
7 5PCCP; APC, Universit´e Paris Diderot, Universit´e Sorbonne Paris Cit´e, 75013 France
1 6BCCP; LBNL & Physics Dept. University of California at Berkeley CA 94720, USA
0
2

n AcceptedXXX.ReceivedYYY;inoriginalformZZZ
a
J

8 ABSTRACT
1 We present hydrodynamic simulations of the hot cocoon produced when a relativistic
jet passes through the gamma-ray burst (GRB) progenitor star and its environment,
]
E and we compute the lightcurve and spectrum of the radiation emitted by the cocoon.
TheradiationfromthecocoonhasanearlythermalspectrumwithapeakintheX-ray
H
band, and it lasts for a few minutes in the observer frame; the cocoon radiation starts
.
h at roughly the same time as when γ-rays from a burst trigger detectors aboard GRB
p satellites. The isotropic cocoon luminosity (∼ 1047 erg s−1) is of the same order of
- magnitudeastheX-rayluminosityofatypicallong-GRBafterglowduringtheplateau
o
phase. This radiation should be identifiable in the Swift data because of its nearly
r
t thermalspectrumwhichisdistinctfromthesomewhatbrighterpower-lawcomponent.
s
Thedetectionofthisthermalcomponentwouldprovideinformationregardingthesize
a
[ anddensitystratificationoftheGRBprogenitorstar.Photonsfromthecocoonarealso

inverse-Compton (IC) scattered by electrons in the relativistic jet. We present the IC
1
lightcurve and spectrum, by post-processing the results of the numerical simulations.
v
TheICspectrumliesin10keV–MeVbandfortypicalGRBparameters.Thedetection
8
ofthisICcomponentwouldprovideanindependentmeasurementofGRBjetLorentz
9
factor and it would also help to determine the jet magnetisation parameter.
1
5
Key words: Hydrodynamics–radiationmechanisms:non-thermal–radiationmech-
0
anisms: thermal – relativistic processes – methods: numerical – gamma-ray burst:
.
1 general
0
7
1
:
v
1 INTRODUCTION bythisshockheatedplasma,whichcontributestothecolli-
i
X mation of the jet (Ramirez-Ruiz, Celotti, & Rees 2002).
Long duration gamma-ray bursts (GRBs) are produced
r when the core of a massive star collapses to a neutron star The total amount of energy deposited in the cocoon
a
or a black hole (for recent reviews on GRBs see, e.g., Pi- (which is equal to the work done by the jet on the medium
ran 2004; Woosley & Bloom 2006; Fox & M´esza´ros 2006; itpassesthrough)dependsonthesizeofthestarandthejet
Gehrels,Ramirez-Ruiz,&Fox2009;Kumar&Zhang2015). luminosity.Thetemperatureofthecocoonisdeterminedby
The newly formed compact object produces a pair of rel- thedensityofthestarwhichcontrolstheexpansionspeedof
ativistic jets that make their way out of the progenitor thecocoontransversetothejetaxisandhencethecocoon’s
star along the polar regions. Punching their way to the volume.Thetemperature,energy,andLorentzfactorofthe
stellar surface, these jets shock heat the material they en- cocoon are the main parameters that affect its luminosity.
counter pushing it both sideways and along the jet’s direc- Thus, the observation of radiation from the cocoon, once it
tion.Therefore,thejetissurroundedbyahotcocoonmade breaksoutofthestar,expandsandlaterdeceleratesintothe
stellarenvironment,shouldinprincipleprovideinformation
about the progenitor star.
The numerous GRB simulations performed to date
(cid:63) E-mail:[email protected] (e.g., Zhang, Kobayashi, & M´esza´ros 2003; Mizuta et al.
(cid:13)c 2017TheAuthors
2 Fabio De Colle et al.
2006; Morsony, Lazzati, & Begelman 2007; Bromberg et al.
1010
2011;Lazzatietal.2013;Lo´pez-Ca´maraetal.2013;Mizuta Mstar=5.45 M☉
M =9.23 M
& Ioka 2013; Bromberg & Tchekhovskoy 2016) have con- star ☉
sidered the hydrodynamic or magnetohydrodynamic inter-
105
actionsofthejetwiththeprogenitorstar,butnottheradi-
3]
ationescapingthecocoonortheinteractionofthisradiation -m
withtherelativisticjetHowever,itistheradiationfromthe c
g 1
cocoon that provides information on the GRB progenitor y [
star properties, and that is a big part of the motivation for sit
n
this work. e
D 10-5
The only paper we know presenting cocoon lightcurves
based on hydrodynamical simulation is by Suzuki &
Shigeyama (2013). However, this paper was mainly con-
10-10
cerned with the impact of the circumstellar medium on
the early thermal X-ray emission. Recently, Nakar & Pi- 107 108 109 1010 1011
ran (2017) provided an analytic calculation of the cocoon Radius [cm]
radiation which includes the mixing of the shocked jet and
Figure1.Densitystratificationofthestellarpre-supernovamod-
shockedstellarmaterial,butnottheICinteractionbetween
elsusedasinitialconditionsinthenumericalsimulations.Thetwo
the cocoon and the jet.
In this paper, we present lightcurves and spectra of ra- models are a 5.45 M(cid:12) and a 9.23 M(cid:12) pre-supernova stars (the
E25and12THmodelsfromHeger,Langer,&Woosley2000and
diation escaping the cocoon by post-processing special rel-
Woosley&Heger2006respectively).
ativistic hydrodynamic simulations which follow the evolu-
tion of the GRB jet and the associated cocoon from ∼ 108
cm to ∼ 3×1014 cm. The aforementioned mixing and its densityistakentobethatofthewindoftheprogenitorstar
effectontheemergentcocoonradiationisbuildintoourhy- which we assume had a mass loss rate of M˙ = 10−5 M
w (cid:12)
drodynamical simulations. We also compute the radiation yr−1 and a velocity of v =108 km s−1.
w
from the cocoon scattered by electrons in the relativistic Duringaperiodoftimet =20s,aconicaljetwithan
inj
jet, which produces higher energy photons. half-openingangleof0.2radisinjectedfromaspherical,in-
The paper is organised as follows: in Section 2 we pro- nerboundarylocatedatr=5×108 cm.Thejetluminosity
videinformationaboutthepre-collapseWolf-Rayetstar,the is L =2×1050 erg s−1 (corresponding to a total kinetic
jet
numericalmethodemployed,andthesimulationsetup.The energy of 4×1051 erg). Simulations are run with three dif-
jetdynamicsandthehydrodynamicpropertiesofthecocoon ferent values of the jet Lorentz factors: 10, 20, and 30. The
are discussed in Section 3. Details of the calculation of the jetinternalpressureisassumedtobeasmallfraction(10−5)
thermodynamicparametersandtheradiationaredescribed of the rest-mass energy density, giving a negligible amount
in Section 4, where we also present lightcurves and spectra ofthermalenergyinthejet.Thejetisswitchedoffafter20
for a number of selected jet and progenitor stellar models. seconds, and subsequently the spherical, inner region (from
Section5describestheinverse-Comptoninteractionbetween where the jet was injected until that time) becomes part of
therelativisticjetandthecocoonphotonsandthelightcurve the computational region.
oftheemergenthigh-energyphotons;themainresultsofthe A computational box with physical size (L /c,L /c)=
r z
paperarediscussedinSection6.Throughoutthispaper,we (104,104)s(alongther-andz-axisrespectively)isresolved
use the convention Gx =G/10x in cgs units. byusingagridwith40×40cellsand20levelsofrefinement,
corresponding to a maximum resolution of ∼1.4×107 cm.
Thejetattheinnerboundaryisresolvedby∼7cellsinthe
transverse direction. The propagation of the jet is followed
2 METHODS AND INITIAL CONDITIONS
for 104 seconds (time measured by a stationary observer at
Weruntwo-dimensionalaxisymmetricsimulationsusingthe the centre of explosion).
adaptive mesh refinement code Mezcal (De Colle & Raga As the jet expands, it would be impossible to keep the
2006; De Colle et al. 2012a,b,c), which solves the special sameresolutionduringtheentiredurationofthesimulation
relativistic, hydrodynamics equations on an adaptive grid. (as it would require employing ≈ 1015 cells!). For this rea-
The simulations span six orders of magnitude in space and son, we adapt dynamically the grid, refining (i.e., creating
time, and we consider the jet crossing the star and then four“sibling”cells from a parent cell) and derefining (i.e.,
moving in the wind of the progenitor star. replacing four sibling cells with one parent, larger cell) the
AsprogenitorsofGRBs,weemploytwopre-supernova, cells as a function of the evolutionary stage of the simula-
Wolf-Rayet stellar models (see Figure 1). The E25 stellar tion and the distance R from the origin of the coordinate
model (Heger, Langer, & Woosley 2000) is a star with an system. This is done by decreasing the maximum number
initialmassof25M reducedtoafinalmassof5.45M after of levels as N = 20 − 3.32 × log(t/20) for t > 20 s,
(cid:12) (cid:12) max
losingitshydrogenandheliumenvelopesbymassivewinds. in such a way that the cocoon (whose size increases with
The 12TH model (Woosley & Heger 2006) has an initial timeasR∼ct)isresolvedbyamaximumofapproximately
massof12M ,afinalmassof9.23M andamoreextended (N ,N )=(2000×2000) cells during its full evolution.
(cid:12) (cid:12) r z
stellar envelope. At a radius larger than the stellar radii of We also run simulations with 22 levels of refinement
these models (r > 3×1010 cm and r > 1011 cm for the (within a smaller computational box). Although the details
E25 and 12TH models respectively), the ambient medium of the jet propagation (i.e. the generation of instabilities at
MNRAS000,1–12(2017)
Emission from the cocoon of a GRB jet 3
the jet/cocoon interface) depend on resolution, the calcula- shockarrivestotheheadofthejet,thedoubleshockstruc-
tion of the flux and light curve shown in Section 4 do not ture gradually forms a thin shell which will move with con-
change by more than 10% when increasing the resolution stantspeeduptodistances10−100timeslargerthanthose
from 20 to 22 levels of refinement. simulated here before decelerating.
Resolvingthedensitystratificationofthewindmedium Figure 3 shows the time evolution of the shock aver-
outside the star requires setting initially a large number of age velocity R/ct, in the lab frame, as a function of the
cellswhichremainunuseduntiltheGRB/cocoonshocksar- shockpolarangle.Asdiscussedabove,thejetmovesatnon-
riveatthatradius.Tomakethesimulationfasterwederefine relativisticspeedswhileitcrossesthestar.Asitbreaksout
atthelowestlevelofrefinementallthecellsoutsideaspher- of the star, it accelerates during ∼ 10 seconds and achieves
ical region which is expanding at the speed of light. As this highly relativistic speeds along the jet axis (with a Lorentz
“virtual”sphereexpandsintheenvironment,themeshisre- factor equal to the Lorentz factor of the material injected
fined and the values of the density and the pressure are set from the inner boundary), and mildly relativistic speeds
using the initial conditions of the simulation. In this way, (with Lorentz factors of ≈ 2-5, see Figure 3) at large po-
wegetanimprovementbyafactorof∼2incomputational larangles.Thedecelerationphasestartsfirstatlargerpolar
time. angles. For instance, the cocoon shock velocity at polar an-
gles θ = 75◦-90◦ decreases from v ∼ 0.8 c at t = 100 s to
v∼0.7c after t=104 s.
3 DYNAMICS Figure 4 shows the energy distribution as a function of
polarangles.Theenergyincreasesduringthefirst20seconds
The different stages of the dynamical evolution of the (consistently with the duration of injection of the jet from
GRB/cocoon system1 are shown in Figure 2. The jet is in- theinnerboundary).Mostoftheenergyremainscollimated
jectedfromacircularboundary(top,leftpanelofFigure2). in a conical region of angular size θ (cid:46) 15◦ during the full
Due to the large stellar density the jet propagates at sub- duration of the numerical simulation. A smaller amount of
relativisticspeedinsidethestar,needingaboutfiveseconds energy(1049-1050erg)ispresentintheportionofthecocoon
to get to r/c∼ 0.45 (top, central panel of Figure 2), which movingatlargerangles.Whilealongthejetaxismostofthe
corresponds to an average velocity of v/c ∼ 0.1. A dou- energy is concentrated in a small region around the shock,
bleshockstructure(the“workingsurface”)iscreatedatthe at larger polar angles a significant fraction of the energy is
head of the jet, with a forward shock which accelerates the distributed through all the cocoon’s volume. Therefore, the
stellar material, and a reverse shock which decelerates the decelerationradiusobservedinthenumericalsimulationsis
fast-movingjetmaterial.Thehot,denseshockedplasmaex- smaller than one inferred by using the expression R/c ∼
pandslaterally(duetopressuregradients)formingadense, Ev /(M˙ Γ2c3)≈6×103E /Γ2 s.
w w 50 1
hotcocoonwhichhelpscollimatethejet.Inthecocoon,the
interface between the shocked jet and the shocked stellar
material (the“contact discontinuity”) is corrugated by the
presence of Kelvin-Helmholtz instabilities.
4 COCOON LUMINOSITY AND SPECTRUM
Thetop,rightpanelofFigure2showsthejetbreaking
out from the star. As the jet arrives at the stellar envelope, 4.1 Radiative diffusion
the lower entropy stellar material facilitates the lateral ex-
The average optical thickness of each cell in our simulation
pansion of the cocoon, which quickly encloses the star and
is
propagates into the wind medium. The amount of material
inthehotcocoonisthengivenbythestellarmaterialwhich δτ ∼ σ M /(2πm N R2) (1)
T c p cells
has crossed the forward shock when the jet was still inside
∼ 7(M /10−4M )R−2 (2)
thestarbutdidnothaveenoughtimetomovelaterallyand c (cid:12) 12
dissipate its thermal energy inside the star.
where N =2000 is the maximum number of cells in the
cells
The bottom panels of Figure 2 show the late evolution
simulations along the radial and transverse directions (the
(left to right) of the GRB jet/cocoon system. The cocoon cocoon terminal Lorentz factor for mass 10−4M and en-
(cid:12)
(bottomleftpanel)isstronglystratified,withamuchlarger ergyof1051 ergis∼5).However,thewholecocoonremains
density close to the jet axis and decreasing by 6-7 orders of opticallythickalongthepolaraxisfor∼103 swhentheco-
magnitude at large polar angles. The deceleration phase is coonreachesR∼3×1013 cm.Thecocoonisnearlyisobaric
clearly visible in the right, bottom panel where Rayleigh-
throughout the volume (except near the surface) and the
Taylor instabilities form at the interface between the GRB
pressureisdominatedbyradiation.Therefore,thefractional
cocoonandthe shockedambientmedium alongthe equato-
changetothethermalenergyofaninteriorcellinadynam-
rial plane. Along the direction of propagation of the GRB ical time is of order (N δτ)−1 (cid:28) 1. Therefore, for cells
cells
jet,thedynamicalevolutionismorecomplex.Att=20sthe
below the photosphere, diffusive radiation has a negligible
GRBjetisswitched-off,andararefactionwavemovesatthe
effect on the dynamics, and post-processing of the hydro-
speed of light towards the shock front (visible at z/c = 10
simulation output to calculate cocoon radiation is expected
and r/c = 0 in the left bottom panel). As the rarefaction
toyieldareasonablyaccurateresultatleastforsmallpolar
angles (cid:46) 45o. At large polar angles, the cocoon structure
1 We describe in this Section only the dynamical evolution of is affected by the loss of thermal energy at late evolution-
the GRB jet with Γjet = 10 propagating through the E25 pre- arytimes.Afullspecialrelativisticradiationhydrodynamics
supernova stellar model. The other models present a similar dy- calculationisnecessarytoproperlycomputethecocoonra-
namicalevolution. diation seen by an observer located off-axis. In this paper,
MNRAS000,1–12(2017)
4 Fabio De Colle et al.
Figure2.DensitymapatdifferentevolutionarytimesfromthesimulationwithΓj=10andE25progenitor.Theplotscorrespond(top,
left to right) to t = 0 s, t = 5 s, t = 6.4 s and (bottom, left to right) t = 28 s, t = 200 s, t = 6280 s. In the third frame (at t = 6.4
seconds)onecanseethatthecocoonhasburstoutoftheprogenitorstarandisevolvinginalessconstrainedmanner.
we only consider the case where the observer is on-axis at where ξ is a dimensionless quantity defined as
θ =0.
obs |∇e(cid:48) |
Althoughradiativediffusiondoesnotchangethehydro- ξ= rad . (5)
k ρ(cid:48)e(cid:48)
dynamical evolution of the system, it strongly modifies the es rad
temperature structure of the cocoon surface and the result-
Equation (3) gives the correct scaling in the optically thin
ing cocoon radiation. In our post-process procedure, radia-
and optical thick limits, although it represents only an ap-
tivediffusioniscoupledtothehydro-simulationsasfollows.
proximation of the intermediate case. In an optically thick
Given a snapshot of the numerical simulation, the flux dif-
medium ξ(cid:28)1 and λ=1/3, equation (3) reduces to
fusing across the boundaries of each cell is calculated by
c
employing the flux-limited diffusion approximation in the F(cid:126)(cid:48) =− ∇e(cid:48) , (6)
comoving frame of each cell 3kesρ(cid:48) rad
cλ whileintheopticallythinlimitR(cid:29)1andthefluxislimited
F(cid:126)(cid:48) =− ∇e(cid:48) , (3)
k ρ(cid:48) rad to
es
where e(cid:48)rad is the (comoving) radiation energy density of F(cid:126)(cid:48) =−c(cid:126)e(cid:48)rad , (7)
nearbycells,ρ(cid:48) isthematterdensity,andk =0.2cm2 g−1
es
istheelectronscatteringopacityforfullyionisedhelium(or Oncethefluxiscomputedusingequation(3),theeffect
heavierelements).Theparameterλisthefluxlimiter,given oftheradiationisincludedintheenergyequationbysolving
by (Levermore & Pomraning 1981): the following equation
2+ξ ∂e(cid:48)
λ= , (4) gas+rad =−∇·F(cid:48) , (8)
6+3ξ+ξ2 ∂t rad
MNRAS000,1–12(2017)
Emission from the cocoon of a GRB jet 5
1.2 being the total number of cells along the r and z directions
respectively). Finally, we notice that the stability condition
1 restricts the time step to ∆t≤(∆x)2/4νd.
0.8
4.2 Calculation of luminosity and spectrum
R/ct 0.6 For each simulation, we save a large number of snapshots
(typically103).Afterpost-processingeachsnapshotwiththe
0.4
radiative diffusion algorithm described above and assuming
θ = 0°-15°
θ = 15°-30° that the observer is located along the z-axis, we determine
0.2 θθ == 3405°°--4650°° the position of the photosphere for each snapshot, defined
θ = 60°-75° asthesurfacecorrespondingtoanopticaldepthτ =1,i.e.
θ = 75°-90°
0
1 10 100 1000 (cid:90) ∞
t [s] κesρ(cid:48)Γdz=1. (11)
z
Figure 3.Timeevolutionoftheshockaveragevelocity(R/ct= For each cell (j,k) located on the photosphere we compute
(cid:82)0tβ(t(cid:48))dt(cid:48)/t,inacertainrangeofpolarangles(measuredfromthe the specific intensity at the location of the observer and as-
jetaxis).Thejet/cocoonsystemacceleratestorelativisticspeed
sign it to the corresponding observing time, related to the
in t ∼ 10 s. For small values of θ the jet moves at relativistic
simulation time by
speeds during the duration of the simulation, while at θ (cid:38) 45◦
thecocoonbeginstodecelerateatt(cid:38)100s. t =t −z /c, (12)
obs k j
where z is the distance from the equatorial plane and t
j k
1052 is the simulation time in the lab frame. The duration of
the snapshot k can be defined as ∆t = (t −t )/2,
k k+1 k−1
and the flux in the observer’s frame lasts for ∆t =
1051 obs
(1−β cosα)∆t ,whereαistheanglebetweenthevelocity
j k
vectorandthez-axisandβ isthephotospherevelocity.As
j
1050 ourpurposeistocomputethespecificandtotalluminosity,
g]
er we neglect cosmological effects and take z=0.
E [ To compute the flux we add up the contributions from
1049
allcellsatthephotosphere(see,e.g.,DeColleetal.2012a)
θ= 0°-15° dS
1048 θ= 15°-30° dFobs =Iobscosθ dΩ ≈Iobs ⊥ , (13)
θ= 30°-45° νobs ν d d ν d2
θ= 45°-60°
θ= 60°-75°
θ= 75°-90° where d is the distance to the source, θd is the angle be-
1047
tween the line joining the observer to the centre of the star
1 10 100 1000
t [s] and the line from the observer to the volume element from
which radiation is being considered, and dΩ = dS /d2 is
d ⊥
Figure4.Jet/cocoonenergyindifferentintervalsofθasafunc- the differential solid angle of the cell as viewed by the ob-
tion of time. Most of the energy remains collimated in the jet server. As the angular size of the source according to the
half-opening angle θjet ≈ 10◦ and increases linearly with time observerisnegligiblysmall,itisjustifiedtotakecosθd ≈1.
over the duration of injection of relativistic material from the The specific intensity in the comoving frame is obtained by
centralengine(assumedheretobe20seconds).
assuming a blackbody spectrum
which in cylindrical coordinates takes the following form Iν(cid:48)(cid:48) ≈ Fπ(cid:48)(cid:82) BBνν(cid:48)(cid:48)((TT(cid:48)(cid:48)))dν(cid:48) =(cid:15)Bν(cid:48)(T(cid:48)), (14)
∂e(cid:48) 1∂(rF(cid:48)) ∂F(cid:48)
gas+rad =− r − z = where F(cid:48) is given by equation (3).
∂t r ∂r ∂r
1 ∂ (cid:18) cλ ∂e(cid:48) (cid:19) ∂ (cid:18) cλ ∂e(cid:48) (cid:19) The comoving-frame temperature T(cid:48) is computed from
=− r rad − rad , (9) the values of energy (obtained at each timestep by using
r∂r ρk ∂r ∂z ρk ∂z
es es equation 10) and density by inverting the equation
and is discretized as
3k ρ(cid:48)T(cid:48)
en+1 = en e(cid:48) =aT(cid:48)4+ B , (15)
gas+rad,i,j gas+rad,i,j 2 µm
p
∆tn (cid:18) ∆e ∆e (cid:19)
− r ∆r ri+νi+,j∆ri+ −ri−νi+,j∆ri− where µ = 4/3 is the mean molecular weight. The specific
i i,j i,j i,j
intensity in the observer’s frame is given by
− ∆∆ztin,j (cid:18)νi,j+∆∆ezji,+j −νi,j−∆∆ezji,−j(cid:19) , (10) Iobs =I(cid:48) (cid:16)νobs(cid:17)3, ν = ν(cid:48) . (16)
νobs ν(cid:48) ν(cid:48) obs Γ(1−βcosα)
where i± = i±1/2, ν = cλ , ∆e = e −e
d ρkes i+ rad,i+1,j rad,i,j
and the indexes i,j refer to the cell (i,j) of the computa- We employ the fact that the blackbody photon distri-
tional grid, with i = 1,...,N , j = 1,...,N (N and N bution function is invariant under Lorentz transformation,
r z r z
MNRAS000,1–12(2017)
6 Fabio De Colle et al.
1048 10-6
M =5.45M
star ☉
M =9.23 M
star ☉ 10-7
)
V
g/s] 1047 ke 10-8
er 0
osity [ 0.3-1 10-9
min x (
Lu 1046 T flu 10-10
R
X
10-11
1045
1048 10-12
Γjet= 10 10-3 10-2 10-1 100 101
Γjet= 20 tobs(days)
Γjet= 30
Figure 6. X-ray flux computed from the numerical simulations
1047
(Γjet = 10 and Mstar = 5.45 M(cid:12)) at redshifts z = 0.2,0.4,0.6
g/s] (black to grey curves), compared with a sample of GRBs with
er z < 0.8 (from Perley et al. 2014). The afterglow curve colours
sity [ correspond to isotropic energies Eiso < 1051 ergs (red), 1051−
no 1046 1052 ergs (orange), 1052 −1053 ergs (green), 1053 −1054 ergs
umi (cyan), >1054 ergs (blue). The figure shows that the cocoon X-
L
ray flux is of the same order as the X-ray flux of a typical GRB
duringtheplateauphase.
1045
10 100
t [s] 4.3 Results
obs
We present simulation results for cocoon luminosity and
Figure 5. Bolometric luminosity lightcurve (in the observer
spectra for two different GRB progenitor star models (E25
frame)computedbypost-processingtheresultsofthenumerical
and 12TH of Heger, Langer, & Woosley 2000; Woosley &
simulations. Top: This panel shows the effect of different stellar
structures on the lightcurve (see figure 1). Bottom: This panel Heger 2006). For the model E25, three different jet Lorentz
shows that the lightcurve is nearly independent on the Lorentz factors (10, 20 and 30) are considered.
factor of the GRB jet. Depending on the duration of the simu- Figure 5 shows the bolometric cocoon luminosity com-
lation and the jet Lorentz factor, some of the simulations have puted with the method described in the previous section.
luminositiesspanningashortertime. Theluminosityincreasesquicklyto∼1045−1046erg/sasthe
jet breaks out of the star and increases to values of ∼1047
erg/s after 100 s (in the observer’s frame) before dropping
as ∼t−3 for larger observing time. The X-ray lightcurve of
with the temperatures in the two frames related by the fol- obs
a sample of GRBs (Perley et al. 2014) is compared in fig-
lowing relation
ure 6 with the X-ray flux emitted by the cocoon, showing
T(cid:48) thatthecocoonX-rayfluxisofthesameorderastheX-ray
T = . (17)
obs Γ(1−βcosα) flux of a typical GRB. Thus, the cocoon radiation should
be detectable and can be identified by its distinct thermal
We compute the total flux in the observer frame (see, spectrum. Figure 5 also shows that the stellar structure is
e.g., De Colle et al. 2012a) by integrating over the entire the key parameter which determines the cocoon luminos-
photosphere ity. When a more extended stellar model is considered, the
lightcurve shows a peak luminosity slightly lower and is in
1 (cid:90) (cid:16) z(cid:17)
Fobs = dS (cid:15)B (T )δ t −t+ . (18) general dimmer at all observing times. As the jet break-out
νobs d2 ⊥ νobs obs obs c
happensatlatertimes,theluminosityincreasesonalonger
timescale. Finally, increasing the jet Lorentz factor (while
Integrated and averaged over the time interval ∆t , this
obs
keepingfixedthetotalenergyofthejet)doesnotproducea
equation reduces to
large change in luminosity (see the bottom panel of Figure
Fobs(t )= 1 (cid:88)(cid:15)B (T )dS dt , (19) 5).
νobs obs d2∆t νobs obs,j,k ⊥,j,k j Figure7showstheangularcontributiontothespectrum
obs
j,k
at t = 30 s for the E25, Γ = 10 model. The spectrum
obs jet
where the sum extends over all j-th snapshots (one at each peaks in the X-ray band were most of the energy is emit-
labframetimet )andk-thcellsrespectively.Theluminosity ted. Actually, a plot of the X-ray luminosity (in the 0.3–10
j
in the observer’s frame is keVband,whichcorrespondstoSwiftXRTenergycoverage)
would be indistinguishable from the bolometric luminosity
Lνobs(tobs)=4πd2Fνoobbss . (20) showninFigure5.Thespectrumisnearlythermal(ablack-
bodycurveisalsoshownintheFigureforcomparison),with
MNRAS000,1–12(2017)
Emission from the cocoon of a GRB jet 7
10-2
10-2
M =5.45 M
star ☉
10-4
10-4
10-6
y]
mJ 10-8 Jy]
[ m
Fν 10-10 F[ν 10-6
θ= 0°-15°
10-12 θ= 15°-30°
θ= 30°-45°
θ= 45°-60°
10-14 θθ== 7650°°--9705°° 10-8 totbosbs== 1 3000 ss
tobs= 300 s
0.01 0.1 1 10 100
10-2
E [keV]
M =9.23 M
star ☉
Figure 7.Spectra(Fν)asafunctionofthepolarangleθ (mea-
sured in the lab frame) at t = 30 s for an observer located
obs 10-4
on-axis.Mostoftheemissioncomesfromtheregionclosetothe
jetaxis.Theblack,fulllinerepresentsthetotalflux(computedin-
y]
tegratingoverthepolardirection).Forcomparison,ablackbody mJ
spectrumisalsoshown(pinkcurve). F[ν 10-6
alow-frequencyspectrumF ∝ν2andanexponentialdecay
ν
at large frequencies, and wider than a blackbody spectrum
10-8 tobs= 30 s
nearthepeak.Duetorelativisticbeaming,thefluxisdom- tobs= 100 s
inated by the emission at small angles (θ (cid:46) 30◦). Angles tobs= 300 s
largerthan45◦ produceanegligiblefluxwhenthejetisob- 10-2
M =5.45 M
served on-axis (they would dominate the cocoon’s emission star ☉
for off-axis GRBs).
Figures 8 and 9 show the time evolution of the spec-
10-4
t = 100 s
trumandenergypeakrespectivelyatt =30,100and300 obs
obs t = 30 s
obs
s. The cocoon spectrum for a more extended stellar model y]
J
(Figure 8, central panel) is less similar to a blackbody, and m
[
its evolution with time is more rapid. Also shown in the Fν 10-6
Figure8arespectraforthreedifferentvaluesofjetLorentz
factor;thespectrumbelow(cid:46)1keVisnearlyindependentof
Γ ,however,athigherenergiesthefluxislargerforcocoons Γjet= 10
jet 10-8 Γjet= 20
formed by jets with larger Γjet. Γjet= 30
0.01 0.1 1 10
4.4 Observations of thermal X-ray radiation E [keV]
Several groups searched for thermal X-ray emission after
the prompt γ-ray phase (e.g. Starling et al. 2012; Sparre & Figure8.Top,centrepanels:Spectra(Fν)attobs=30,100,300
sforthetwopre-supernovastellarmodelsconsidered(seeFigure
Starling2012,andreferencestherein).Starlingetal.(2012)
1). Bottom panel: Spectra at t = 30,100 s for different jet
obs
analysedspectrafor11GRBsandfoundthermalX-raysig- Lorentzfactors.
nal for three of these (GRBs 060218, 090618 and 100316D)
whichareknowntobeassociatedwithsupernovae.In4ad-
ditional cases the spectral fit is claimed to improve when a
an associated supernova. The thermal components in these
thermal component is included; these 4 cases are also pos-
6 cases were found during the steep decline or the plateau
sibly associated with supernovae. Sparre & Starling (2012)
phase of the X-ray lightcurve.
analysed Swift/XRT data for 190 GRBs and identified 6
Oneofthemodelssuggestedforthethermalcomponent
burstswithpossibleblackbodycomponents2(GRBs061021,
inGRBafterglowlightcurvesisthatitistheradiationasso-
061110A, 081109, 090814A, 100621A and 110715A). The
ciated with the supernova shock breaking through the sur-
threenewcandidatesidentifiedbySparre&Starling(2012,
face of the progenitor star. However, several papers (Ghis-
GRBs061021,061110Aand090814A)arenotknowntohave
ellini, Ghirlanda, & Tavecchio 2007; Li 2007; Chevalier &
Fransson 2008) point out a problem with this scenario, and
2 Theremighthavebeenmanymoreburstswithathermalafter- that is that the thermal luminosity is too large to be con-
glow component which the analysis of Sparre & Starling (2012) sistentwiththeshock-breakoutmodelforGRB060218;the
couldnotidentifyduetotheuncertaintyassociatedwithhydro- thermal luminosity for the other five cases are even larger
gencolumndensityandtheabsorptionofsoftX-rayradiation. than GRB 060218 (Sparre & Starling 2012).
MNRAS000,1–12(2017)
8 Fabio De Colle et al.
remainsopenandthebaryonsfromtheambientcocooncan
not enter the cavity. (ii) In the Late-IC case, a slower jet
10 Γjet= 10
ΓΓjjeett== 2300 wt ith L=or1e0n0tzsefca,ctoowrinΓgj t=o l5a0teistimlaeunccehnetrdalweinthginaedaecltaiyvitoyf
delay
causingX-rayflares.Thecocoonphysicalpropertiesaswell
V] 1 as the thermal radiation produced are only weakly depen-
e
[keak ≈5M☉ dcoemntpountetthheejeICt Leomreisnstizonfaicstoarls.oTnheuasr,lythiendaepppernodacehntuosnedthtoe
p
E ≈9M promptjetLorentzfactor,which,fornumericallimitations,
0.1 ☉
is smaller in our simulations than in typical GRBs.
In this section, all quantities in the comoving frame of
thefluidcellaredenotedwithaprimeandunprimedquanti-
0.01 tiesaremeasuredinthelabframe(restframeofthecentral
10 100
engine).
t [s]
obs
Figure 9.Timeevolution(intheobservingframe)oftheenergy 5.1 Method
peak of the quasi-thermal spectrum for the two progenitor stars
andjetLorentzfactorsconsideredinthenumericalsimulations. For each snapshot from the simulation, we first identify the
positionofthecocoonphotosphere(equation11).Eachpho-
tospheric cell has its own diffusive flux F(cid:48) (given by flux-
ph
The observed luminosity for the thermal component of limited diffusion in equation 3), temperature T(cid:48) , Lorentz
ph
theseGRBafterglowsisbetween1047 and1050 ergs−1,and factorΓ,andtheanglebetweenthefluidcell’svelocityvec-
the spectral peak is at ∼0.5 keV (Sparre & Starling 2012). tor and the jet axis is arctan(v /v ). The intensity in the
r z
Thesevaluesareconsistentwiththeexpectationsofcocoon comoving frame of each photospheric cell is assumed to be
radiation (see Figs. 5 and 9). Measurement of the evolu- isotropic (equation 14) and the lab-frame intensity in an
tion of the thermal component’s peak temperature and lu- arbitrary direction is given by the corresponding Lorentz
minosity in the future and its comparison with the cocoon transformation.
simulation would make it possible to draw a firm conclu- Then, for each scattering cell located in the hypothetic
sion regarding the origin of the radiation. If confirmed to jet at time t at the position R(cid:126)(r,z) = (r,0,z), we consider
be originated by the cocoon associated with the relativistic light rays coming from different directions denoted by the
jet,thenthatcouldbeusedtodeterminetheprogenitorstar unit vector (cid:126)e(θ,φ), where θ is the polar angle and φ is the
radius and density structure. azimuthangle.Atanearliertimet thepositionofthelight
0
ray is
R(cid:126) (t )=R(cid:126)(r,z)−c(t−t )(cid:126)e(θ,φ). (21)
0 0 0
5 INVERSE-COMPTON SCATTERING OF
For each of the previous snapshots at t <t, we do not ex-
COCOON RADIATION BY THE 0
pect R(cid:126) (t ) to be exactly on the photosphere surface (since
RELATIVISTIC JET 0 0
the snapshot times {t } are discrete), so the closest photo-
0
As thermal photons from the cocoon diffuse out from the sphericcellisconsideredaswherethelightraywasemitted.
photosphere and run into the relativistic jet, they can get Therefore,theintensityofthecocoon’sradiationfieldatany
inverse-Compton(IC)scatteredbyelectronstomuchhigher time t at the position of the scattering cell R(cid:126)(r,z) is given
energies. This will produce a flash of high energy photons by
when the faster jet surpasses the cocoon photosphere (Ku- I (θ,φ)=(cid:15)B (cid:0)T =D T(cid:48) (cid:1) (22)
mar & Smoot 2014). Because of the relativistic beaming ν0 ν0 ψ ph
alongthedirectionofcocoonlocalvelocityvector,onlypho- whereT(cid:48) isthetemperatureofthephotosphericcellfound
ph
tonsemittedwithinanangularpatchofsize∼Γ−1(Γ being bytheray-tracingmethodabove,(cid:15)=F(cid:48) /[σ (T(cid:48))4],D =
c c ph SB ψ
the cocoon Lorentz factor) surrounding the jet can interact [Γ (1−β cosψ)]−1 is the Doppler factor, and ψ is the an-
0 0
with electrons in the jet and contribute to IC luminosity. gle between (cid:126)e(θ,φ) and the velocity vector of the photo-
Sincetheanglebetweenthejetaxisandphotons’movingdi- spheric cell. Then, it is straightforward to integrate light
rection is of order Γ−1, IC scatterings boost cocoon photon rays of different directions and frequencies to calculate the
c
energy to ∼ kT (Γ/Γ )2 ∼ Γ2 /Γ2 MeV when electrons IC lightcurve and spectrum.
c j c j,2.5 c,1
are cold (γ ∼1) in the jet comoving frame. In the following, we describe the detailed integrating
e
We present in this section the IC lightcurves and spec- procedure presented in Lu, Kumar, & Smoot (2015). Expe-
tra computed by post-processing the results of the hydro- rienced readers may jump to the results in the next subsec-
dynamical simulations. To calculate the IC emission in real tion.
GRBs,weconsiderthefollowingtwocases.(i)IntheEarly- ConsiderascatteringcellattimetandpositionR(cid:126)(r,z)
IC case, a fast jet with Lorentz factor Γ =300 is launched withatotalnumberofelectronsdenotedbydN .Thecellis
j e
with a delay of t = 30 sec, owing to episodic central moving at an angle α from the z-axis with velocity(cid:126)v which
delay
engine activity (e.g., Ramirez-Ruiz, Merloni, & Rees 2001; corresponds to a Lorentz factor Γ = [1−(v/c)2]−1/2. We
Ramirez-Ruiz&Merloni2001).Weassumethatthedelayed define another set of Cartesian coordinates x˜y˜z˜ in which zˆ˜
jetdoesnotinteractwiththecocoonhydrodynamically.This is parallel to the cell’s velocity vector(cid:126)v, yˆ˜is parallel to the
isreasonableifthecavityinitiallyopenedbythepromptjet original y-axis yˆ, and xˆ˜ is in the original xz plane (which
MNRAS000,1–12(2017)
Emission from the cocoon of a GRB jet 9
goes through the scattering cell). The relation between the where we have used ∆Ω =4π for isotropic equivalent lu-
obs
twocoordinatesystemsisdescribedbyarotationalongthe minosity.Asintegratingequation(30)iscomputationallyex-
y-axis by an angle α according to the right-hand rule, and pensive,wemadethefollowingtwosimplifications.(i)When
the transformation matrix (in Cartesian coordinates) is electrons are cold (γ(cid:48) = 1), the differential cross section
e
is assumed to be isotropic and every electron has Thom-
 
cosα 0 sinα
son cross section. (ii) When electrons are hot (γ(cid:48) (cid:29) 1),
Λ(α)= 0 1 0 . (23) we use the full angle-dependent Klein-Nishina diffeerential
−sinα 0 cosα
cross section, but instead of the blackbody seed spectrum
Ilinghtthirsanye(cid:126)ew(θc,oφo)rdbiencaotmeesyss(cid:126)e˜t(eθm˜,,φ˜)th=e oΛri(cid:126)eg.inTahlidsirreeclattioionnogfitvhees Ihν(cid:48)ν0(cid:48)(cid:48)(θ˜=(cid:48),2φ˜.(cid:48)7)D=BkTν0(cid:48)(cid:48)(D/Dψ.Tp(cid:48)h/D),weuseaδ-functioncentredat
0 ψ ph
the mapping between (θ,φ) and (θ˜,φ˜) as follows At last, we add up the IC luminosity from all the scat-
(cid:40)cosθ =sinθ˜cosφ˜sinα+cosθ˜ teringcellsindifferentsnapshotsweightedbytheirindivid-
ual numerical timesteps.
(24)
tanφ = sinθ˜sinφ˜
sinθ˜cosφ˜cosα−cosθ˜sinα
Then, we convert the intensity of external radiation field 5.2 Results
I (θ˜,φ˜) to the comoving frame x˜(cid:48)y˜(cid:48)z˜(cid:48) of the scattering cell
ν0 Inthissubsection,wepresentthelightcurvesandspectrafor
by using the Lorentz transformations
the Early-IC and Late-IC cases. In the Early-IC case, the

 νco0s=θ˜Γ=(1(c+osβθ˜(cid:48)co+sβθ˜(cid:48)))/ν(0(cid:48)1=+Dβνco0(cid:48)sθ˜(cid:48)) ejeqtuiisvalaleunntchpeodwaetrlLabijs-ofra=me10t5i2meertgdelsa−y1=a3n0dsLwoirtehntizsotfaroctpoicr
 Iφ˜ν(cid:48)0=(cid:48)(θ˜φ˜(cid:48),(cid:48)φ˜(cid:48))=Iν0(θ˜,φ˜)/D3 (25) (ΓICcjo=lcdas3ee0l,e0ct.thrWeonejes)htaiavsnedlatuwγneoch=suedb1-0acat(shtedosetlcaeyolre=rcetsr1po0on0nsd)s.inwIgnitthtohLeγoeLrea=ntte1z-
factorΓ =50,andweconsidertwoluminositiesLiso =1051
where we have defined a new Doppler factor D in the first j j
and 1052 erg s−1. The duration of the delayed jets in all
expression. We are interested in the photons scattered to-
casesist =10s.Weignorethehydrodynamicalinteraction
wardstheobserver,whointheoriginalxyz frameislocated j
on the z-axis and in the direction (θ(cid:48) ,φ(cid:48) ) in the comov- betweenthejetandcocoonandonlyconsiderICscattering
obs obs
ing x˜(cid:48)y˜(cid:48)z˜(cid:48) frame given by after the jet emerges from below the photosphere.
The jet emerges from the cocoon surface at radius
(cid:40)
cosθ(cid:48) =(cosα−β)/(1−βcosα) R = 1013R and 1013.5R cm for the Early-IC
obs (26) em em,13 em,13.5
φ(cid:48) =π and Late-IC cases respectively, so the peak time is
obs
Thenumberofphotonsscatteredintothesolidangle∆Ω(cid:48) tpeak (cid:39)Rem/(Γ2jc)(cid:39)3.7×10−3Rem,13Γ−j,22.5 s
obs (31)
around the (θ(cid:48) ,φ(cid:48) ) direction in a duration dt(cid:48) and fre- (cid:39)0.4R Γ−2 s.
obs obs em,13.5 j,1.7
quency range dν(cid:48) can be obtained by integrating the radia-
The thickness of the transparent shell at the jet front that
tion incoming at different frequencies ν(cid:48) and from different
directions Ω˜(cid:48) =(θ˜(cid:48),φ˜(cid:48)), i.e. 0 external photons can penetrate through is
1 R2 Γ
dNγ = dNedν(cid:48)∆Ω(cid:48)obsdt(cid:48) ∆Rtr = n(cid:48)Γσ (cid:39)7.7×109 1L3isoj,2.5 cm
(cid:90) dΩ˜(cid:48)(cid:90) dν0(cid:48)Iν(cid:48)0(cid:48)(hθ˜ν(cid:48)(cid:48),φ˜(cid:48))∂ν(cid:48)∂∂2Ωσ(cid:48) e−τ, (27) e j T (cid:39)1.1×1011R123j,.552Γj,1.7 cm, (32)
0 obs Liso
j,51
where ∂ν∂(cid:48)2∂σΩ(cid:48) isthedifferentialcrosssectionandtheoptical whichneedstobecomparedtothesizeofthecausallycon-
depthτ describestheattenuationbythepartofthejetthat nected region given by
liesalongtheincidentphotons’trajectorybeforetheyenter
the scattering cell. These dNγ photons will arrive at the R/Γ2j (cid:39)1.1×108R13Γ−j,22.5 cm (33)
observer at time (cid:39)1.2×1010R Γ−2 cm.
13.5 j,1.7
tobs =t−z/c, (28) The duration of the peak IC luminosity is given by
and the lab-frame frequency is given by max(∆R ,R/Γ2)
∆t ∼ tr j . (34)
ν =[Γ(1−βcosα)]−1ν(cid:48) =D ν(cid:48) , (29) peak c
α
In the Early-IC case, we have ∆t (cid:39) 0.26 s. In the
peak
where we have defined another Doppler factor Dα. Differ- Late-IC cases with Liso = 1051 and 1052 erg s−1, we have
j
entiating equation (28) gives dtobs = (1 − βcosα)dt = ∆tpeak ∼3.7 and 0.4 s respectively. We plot the lightcurves
dt(cid:48)/Dα andtheLorentztransformationofsolidanglesgives and spectra in Figure 10-13 and the main results are sum-
∆Ω(cid:48)obs = Dα2∆Ωobs , so this scattering cell contributes a marized as follows (see the captions for details):
specific luminosity of (1) When electrons are cold, IC scattering generally
dLiso = dN 4πD2hν tapsafractionofafew×10−4 to10−3 ofthetotalenergyof
ν e α the delayed jet. This means the IC emission is likely over-
(cid:90) dΩ˜(cid:48)(cid:90) dν(cid:48)Iν(cid:48)0(cid:48)(θ˜(cid:48),φ˜(cid:48)) ∂2σ e−τ (30) whelmed by other radiation mechanisms. However, when
0 hν(cid:48) ∂ν(cid:48)∂Ω(cid:48) thereisamodestamountof jetdissipationsothatthe root
0 obs
MNRAS000,1–12(2017)
10 Fabio De Colle et al.
1051
.1 MeV 1053 4 MeV
.2 MeV 1e1 MeV
1050 .4 MeV 2e1 MeV
1052
.6 MeV 6e1 MeV
] ]
1−g s1049 12 MMeeVV 1−g s1051 12ee22 MMeeVV
er 6 MeV er 6e2 MeV
[Lν1048 [Lν1050
ν ν
1047 1049
104160-3 10-2 10-1 100 101 104180-3 10-2 10-1 100 101
t −30[s] t −30[s]
obs obs
1051 1051
.03 s .03 s
.1 s .1 s
1050 .3 s 1050 .3 s
.6 s ννννLLLLνννν∝∝∝∝νννν2222 .6 s ννννLLLLνννν∝∝∝∝νννν2222
] ]
1−g s1049 1−g s1049
er er
[Lν1048 [Lν1048
ν ν
1047 1047
1046 10-1 100 101 1046 10-1 100 101
E [MeV] E [MeV]
Figure 10. Lightcurves and spectra of the Early-IC case with Figure 11. Lightcurves and spectra of the Early-IC case with
cold electrons, corresponding to the hydro-simulation with pro- hot electrons, corresponding to the same hydro-simulation as in
genitormass5.45M(cid:12) andpromptjetLorentzfactor10.Thehy- Figure(10).ThejetparametersarethesameasinFigure(10),but
pothetical jet, launched with a delay of 30 s with respect to the electrons are assumed to be monoenergetic with Lorentz factor
prompt jet that produced the cocoon, has Lorentz factor 300 γe=10inthejetcomovingframe.TheICluminosityisafactor
and isotropic kinetic power 1052 erg s−1, duration 10 s (which of∼γ2 higherthaninthecoldelectroncase.TheICluminosity
e
does not really have an effect on the IC luminosity), and elec- exceeds the jet kinetic power for the first 0.3 sec, which means
trons in the jet are assumed to be cold (γe = 1). We find that thefrontofthejetmustbeComptondraggedtoalowerLorentz
the IC luminosity is initially ∼ 1050-1051 erg s−1 when the jet factor. The legend in the lower panel is t −30 s. The peak
obs
emerges from the cocoon surface, but it then drops quickly as of the IC spectra is at ∼ 300 MeV initially, so we may expect
the jet surpasses the cocoon. The legend in the lower panel is somepairproductionfromγγ interaction(whichisnotincluded
t −30 s. The IC emission peaks at ∼ 3 MeV initially and inourcalculation).Thespectraarebroaderthanblackbody(gray
obs
thenthepeakfrequencydropsquicklywithtimebecausecocoon dashedline),withthelow-frequencypower-lawbeingνLν ∝ν2.
photons are moving increasingly parallel with the jet. The spec- Therelativelysharpdropoff(comparedtothecold-electroncase
tra are broader than blackbody (grey dashed line), because the inFigure10)atthehigh-energyendiscausedbyourδ-function
low-frequencypower-lawischaracteristicICspectrumνLν ∝ν2 approximationoftheblackbodyspectrumfromeachofthecocoon
and the high-frequency part is broadened by multi-colour seed photosphericcellsandthetruespectrumshouldbebroader.
photons.
(3)Theeffectofprogenitorstar’smassanddensitypro-
mean squared Lorentz factor (cid:112)<γ2 > (cid:38) 10 at radii be- file has a much weaker effect on the IC emission than the
e
tween1013 and1014 cm,thepeakICluminosityexceedsthe Lorentz factor of the prompt jet. This is due to the strong
jet luminosity. This means that a fraction of a few to 10 dependenceofICemissiononthecocoonLorentzfactor(Ku-
percent of the jet is strongly dragged by the IC force to a mar&Smoot2014).Itmaybechallengingtoinferprogeni-
lower Lorentz factor. Further jet dissipation such as inter- torpropertiesfromtheICemission.SincetheICemissionis
nal shocks or magnetic reconnection could be triggered by very sensitive to the Lorentz factor of the delayed jet (peak
thisICdrag.Asignificantfractionofthe0.1-1GeVemission energy∝Γ2 andluminosity∝Γ4),ICfluxcouldprovidean
j j
duringthepromptphasemaybecontributedbyICemission independent measurement of the Γj.
off cocoon photons.
(2) The spectrum is always broader than blackbody,
evenwhenelectronsareinmonoenergeticdistribution(cold
6 CONCLUSIONS
or hot). A power-law electron distribution will lead to a
power-law spectrum in the high frequency part. Therefore, We have carried out numerical simulations of a long-GRB
the IC component off cocoon emission might have been jet propagating through the progenitor star and its wind,
missedinpreviousstudieslookingforathermalcomponent. the production of a cocoon that results from this interac-
MNRAS000,1–12(2017)