The peculiar light curve of GRB100814A:
an interplay of forward and reverse
shocks?
Massimiliano De Pasquale (MSSL-UCL)
N. P. Kuin, S. Oates, S. Schulze, Z. Cano, C. Guidorzi, A.
Beardmore, P. Evans, Z. Uhm, B. Zhang, M. Page, S.
Kobayashi, A. Castro-Tirado, J. Gorosabel, T. Sakamoto, T.
Fatkhullin, S. Pandey, M. Im, P. Chandra, D. Frail, H. Gao, D.
Kopac, Y. Jeon, C. Akerlof, L. Huang, S. Pak, S. Zane, C.
Mundell, A. Melandri, A. Gomboc, C. J. Saxton, S. Holland, F.
Virgili, Y. Urata, I. Steele , D. Bersier, N. Tanvir

Properties of the γ-ray prompt emission are
unremarkable
14

Optical source; redshift z=1.44
Energy emitted 1-10000 keV: 7 x 1052 erg.

[Counts/s][Counts/s/det]Fluence 0.02-2 MeV: 1.2 ± 0.2 10-5 erg cm-2

[Counts/s/det]

Typical powerlaw * exponetial cut-off spectrum:
Photon Index 0.4; E peak = 128 keV (Konus-Wind)

BAT: 15-25 keV

BAT: 25-50 keV[Counts/s/det]

T90 = 174.5 ± 9.5 s in Swift
Peak count rate: 2.5±0.2 ph cm−2 s−1 in the 15−150
keV band.

XRT: 0.3-10 keV

BAT: 50-100 keV[Counts/s/det]

Detected by Swift, Konus-Wind, Suzaku, FermiGBM

BAT: 100-200 keVTime since BAT trigger time [s]Very rich data set for the afterglow•

Bright X-ray afterglow detected by Swift/XRT•An optical source was detected by Swift/UVOT, ROTSE, Faulkes Telescope,
Lulin Telescope, Nordic Optical Telescope, CQUEAN at McDonald
Observatory, Gran Telescopio Canarias, Calar Alto and BTA 6-m•

Radio emission detected by Expanded VLA•

X-ray and optical follow up from 100 till 106 second, and radio follow up till
60 x106 seconds

The optical afterglow shows a rebrightening withno counterpart in the X-ray band.
Swift, ground-based,
observations of GRB100814A
days afterradio
burst

10−3

10−2

10−1

100

101

15

102

2

log Fν [mJy]

0
−2

−6
−8

white×10

−10

0.75

r’ ×102.25

0.4

uvw2×10−2.25 uvm2×10−2.0

uvw1×10−1.75 u×10−1.5−0.25

log (Fν, obs /Fν, fit)

However, at ~15 ks
the optical LCs
show a flux rise,peaking at~1 day followed by plateau−4

Filters:
10 keV×100.0

z’ ×10b×10−1.25

There is no analogous
beheaviour in the
X-ray: decay as before

v ×100.5

0.0

g’ ×101.25

1.75

i’ ×10

Rc ×10

2.0

7.9 GHz×10

4.7 GHz×102.75

0.2
0.0
-0.2
-0.4

102

103

104

Initially, both X-ray
and optical LCs
show similar slow
decay slope

105

106

107

t(seconds after burst in the observer frame)

But both the X-ray andopticalbreak to a steep decay
at ~150 ks

Then, while the X-ray and optical decay rapidly, we have a broad radio peak as welligure 2. The afterglow GRB 110814A from 10−5 eV to 1.73 keV. Individual light curves were shifted according to the text in theAnalysis of the afterglow and rebrightening
F ~ t -α ν-βOptical early decay slope is α1 = 0.55c0.03

X-ray LC early decay slope is αx,1 = 0.52±0.03, break time t x, b2 = 133±2.4 ks, latedecay slope is α X,2 = 2.11±0.14

F

α1

α3

α2

α4

We fit of the light curves built up
in several filters during therebrightening with a double
broken power law model.
Fixed α3 , α4 , tb2 for all filters:
α 3 = 0.48 ± 0.03 ; α 4 = 1.97 ±0.02 ; t b2 = 217±2.4 ks

αx,1
αx,2

tb1

tb2

Peak flux, α2, tb1 free to vary foreach filter…

t... and we find correlations between the fit
parameters.

The optical rebrightening itself is chromatic!
•

The redder bands peak later that the bluer;•

The peak flux is higher as time goes by, that is,
the redder bands have larger peak fluxes.

For example:
i’ band peaks at 90 ks, while u band peaks at 56 ks.
The peak flux in r’ band is ~180 µJy, while the peak flux in uw1 band (300 nm) is
100 µJyAnalysis of spectral energy distributions (SEDs)

Swift, ground-based, radio observations of GRB100814A

101

102

105

106

107

log Fν [mJy]

0
−2
−4
−6
−8

log (Fν, obs /Fν, fit)

−10
0.4

Filters:
10 keV×100.0

uvw2×10−2.25 uvm2×10−2.0

uvw1×10−1.75 u×10−1.5

b×10−1.25

white×10−0.25 g’ ×100.0v ×100.5

1.25

r’ ×100.75

Rc ×10z’ ×10

7.9 GHz×10

2.25

2.0

i’ ×101.75

4.7 GHz×102.75

0.2
0.0
-0.2
-0.4

102

103

104

t(seconds after burst in the observer frame)

10−3

100

2

10−4

10−1

10−5

10−2

Flux Density (keV / cm^2 s keV)days after burst
10−3

0.01

0.1

1

GRB100814A SEDs

10−3

0.01

0.1
Energy (keV)

1

Figure 6. SEDs at 4500s (black), 22000s (red), 50000s (blue) and 400000s (green).

10Analysis of SEDs: spectral break in the optical
24

The SEDs have been fitted with:--

Simple power law;
Broken power law;
Broken power law with Δβ = 0.5 (asexpected in the External Shock Afterglow
model);For the 50 ks SED only: Sum of two
broken power law: first with low energy
index β1 = -0.33 (this value is expected
in a synchrotron spectrum below theinjection frequency νM ), second with Δβ= 0.5

Results:
50 ks SED is best-fitted by the sum of two
broken power law model;
The break of the first component is at ~4.1
eV, in the near UV;Consistent with the peak of therebrightening reached at ~50 ks in the UV.

500 s

4.5 ks

22 ks

50 ks

Simple power law
βχ20.96 ± 0.01
53.1/44

Broken power law
β1
Ebreak eVβ2
χ2 /dof0.07+0.31−0.26
90.4+910−47.4
0.89+0.04
−0.06
5.8/4

0.52+0.07−2.30
641+313−640
1.02−0.08
11.8/14

Broken power law
with ∆β = 1/2
β1
Ebreak eVβ2
χ2 /dof0.34+0.06
540+580−138
0.84+0.06
5.95/50.52−0.06
655+305−390
1.02−0.06
11.8/15

Sum of two power laws
β1,I
Ebreak,I eV
β2,I
β1,II
Ebreak,II eVβ2,IIχ2 /dof400 ks

0.16+0.05−0.13
482+600−282
0.84+0.09
58.3/34

0.10 ± 0.22
9.9+1.5−3.8
1.02−0.05
119.3/113

0.50+0.02−0.04
46.36+41.22−21.551.00+0.02−0.04
123.4/114−0.33
4.10+0.5−0.3

8.5+unconstrained−6.3
0.52−0.04
92.5+43.5−20.1
1.02−0.04
111.6/111

Off-Axis double jet model
Fluxθ NARROW	θ wide	θ OBS	

ΓNarrow-1 ~θOBS - θNAR

For an observer angle θobs ≈ 1.5 θwide and θnarrow = 0.5 θwide, the temporalslopes of the observed light curves can be explained (Granot, Panaitescu et al.
2005).

timeNow,
defininga ≡ (1/θ+ Γ 2θ 1)](θ
) , we /θ
have−(GP2002)
Tpeak
= [5
+ 2 ln(θ1) tj sNow,defininga ≡obs(1 + Γj2−θ )−1 , weobs
havej(GP2002)(2) obsjmponent scenario, because one should
not see
be at
3
ν(θ
)
=
aν(θ
=
0)
F
(ν,
θ
,
t)
=
a
F
(ν/a,
0,
at)
(3)
obs
obs
decrease
of
the
X-ray
and
opticalflux
before
it.
3
for
the
weθobshave" 25
× tj . (3)Since
Tpeak "
ν(θobs) =valuesaν(θ = above,0) F (ν,, t) =Tapeak
F (ν/a,0, at)
T
peak = [5 + 2 ln(θobs /θj − 1)](θobs /θj −where Γ is the Lorentz factor. At the peak time we have

Parametersin the double jet model
90−1ks, tj " 3.6ks.
Γ−= 2θonassuming
is−1θobstime− θjwe, ashave
P2002
erved
flux
blast
wave
parameters
j . Bywhere∼
Γθobs
isdepends
theθj Lorentz
factor.
Atthepeak
for the values above, we have Tpeak " 2
2 θ2
Now,
defining
a
≡
(1
+
Γ
θ
)
,
we
have
(GP2002)
Weuse−1
suggest,wesucha2θ=
0.5fractionsin the equations
parameters
theof blastabove.
waveΓ ∼ θobs−haveθj =asj . By assuming θ is θobs − θj , as P2002 90 ks, tj " 3.6 ks.
The peak electrons
frequency forθobs= 0 is givenbytoradiatingandmagnetic
field
defining a ≡ (1 + Γ2 θ2 )−1 , w
suggest,
we
have
a
=
0.5
in
the
equationsabove.
ν(θobs ) = aν(θ = 0)
F (ν, θobs , t) = a3 F"e(ν/a, 0, at)Now,(3)wherecircumburst medium density n, and the index! 0 is given"2 by
The peak frequency for θobs =ν(θobs ) = aν(θ = 0)
F (ν, θobs , t) = a
p
−
2
-law
energydistributionofradiating−3/2 time we have14
1/2 1/2factor. Atelectron
2 1/2
where
Γ
is
the
Lorentz
the
peak
νM =
3.3 × 10 (z peak+ 1) frequency"B,−2"e EpeakHz(4)Thesynchrotron
νM andF(νM) are given by
52 td flux−1p−1
al Γevolutionofsuchparameters
might
explainΓ is the Lorentz factor. At the∼ θobs − θj = 2θj . By!assuming
j , as P2002"2 θ is θobs − θwhere−1
behaviour.
Anexampleis a pThechangeden− 2 maximum−3/2∼ θobs − θj = 2θj . By assuming θ i
14
1/2
2of1/2
where
td indicates
time
in1/2
days.
flux
is Γ
suggest,
we
have
a
=
0.5
in
the
equationsabove.
ν
=
3.3
×
10
(z
+
1)
"
"
E
t
Hz(4)
M
e
52
B,−2
d
vironment n. For frequencies below
the coolingsuggest, we have a = 0.5 in the equatio
p−
1
The
peak
frequency
for
θ
=
0
is
given
by
obs
x is proportional to n,−2
while
in bands
1/2 the flux
The peak frequency for θobs = 0 is
1/2
−3/4
F
(ν
)
=
1600(z
+
1)D
"
E
n
(t/t
)
µJy
(5)
M
52
j
28
B,−2
indicates
timeoninit.days.
maximum
flux isakwheredoestdnot
dependIt isThe
thereforepossi!energy "id(Yostincreasen causes
opticalrebrightening!
et al.in2003).
E52 anis thekineticof2the ejecta,
p
−
2
1/2
1/2
−3/2
14
1/2
2
p−2
14
1/2 1/2
while
"e3.3
and
"B,−2
the
fractionsofshockwave
energyeouslyleaves
X-ray
flux
decay
unperturbed,
νConditions:
×the
10
(zare
+
1)
"
"
E
t
Hz(4)
M =
ν
=
3.3
×
10
(z
+
1)
"
e
1/2
−2
52 M
B,−2
d
B,−2
−
1 µJy
FDoes
(νM )to=this1600(z+ 1)DE52
n1/2the(t/tpjspectral
)−3/4
(5)
p−1
radiatingelectrons
andmagnetic
field
respectively.
28 "B,−2e.givenexplanation
predict- Peak flux of rebrightening (narrow jet) is ~ 200 µJy at 90 ks after trigger.

theluminosity
distanceof the burst,
while p is28
weD
seeisinthe
GRB100814
rebrightening?
Since
where
where
t
indicates
time
in
days.
The
maximum
flux istd indicates time in days. The m
(Yost
et
al.
2003).
Eisthekinetic
energyoftheejecta,
d
52
the
index
of
the
power-lawenergydistributionofradiatingne- maythink
thatndecline
could increase
so
much
−3
Flux
at
the
slow
(wide
jet)
is
µJy
at 4.5 ks after trigger
while
"
and
"
are
the
fractionsofshockwave
e n theB,−2electrons,density in particles cm ~100of theenergy
circumrs the optical band and changes the shape of−2 1/2
1/2
burst
medium.
Substituting
theknown fieldparameters,
takinggiven
toradiatingelectrons
andmagnetic
respectively.
F(ν)=
1600(z
+
1)D
"
E
n
M
52
1/2
−2
1/2
−3/4
28
B,−2
wever,
severalsimulations
have
shown
that (t/tthe j )
F(ν
1600(z
+
1)D
"
E
µJy
(5)
M) =
52 n and
p
=
2.02
to
explain
the
flat
X-ray
spectrum,remember28
B,−2Solutions:
D28 show
is the luminosity rebrightening
distance of the burst,if thewhile p is
o ing
not
(Yost et al. 2003). E52 is the kinetic ethat forprominent
θobs = 3θj the observed νevenwillbe
1/2 of the
M
the
index
of
the
power-lawenergydistributionofradiatingcountersenhancement
ofis density(Nakar&etanal.
2003). we
E52havethe kinetic
energyofwhilethe ejecta,"B,−2 areν(Yoston-axisM−3 observed fluxes
For
n=10,(seeε eq.3),= ε =1/3,
p=2.02, thecan"ebeand
explained
if: the fractions o

Belectrons,
nand
thee "densityin particles
cm of thecircum- given energy
while
"
are
of54 shockwave
radiatingandrad.	

magne
54
e
B,−2
1.27Ethe0.77 fractions
1.02
1/2
E
=
2
x
10
erg,
=
5.6
x
10
erg; θ Narrow=to0.023
rad; θelectrons= 0.046
Narrow
Wide
wide
F
(ν
,
θ
,
t
)
=
0.17E
"
"
n
(6)
i
obs
peak
52
B,−2
e
concludea single component
FS model takingD28 is the luminosity distance of th
burst medium.
Substituting
the known
parameters,
given
to thatradiatingelectrons
and magnetic
field respectively.
"curve. In the 14
inwherethe
GRB100814A
light
next
p = 2.02νi tois explain
spectrum,the fluxtheinflat
theX-rayi band
(3.9 × and10 rememberHz). At thethe index of the power-law energy distdensityThis modeling, however, does not yet take into account the
take into
presence of a spectral break during the rebrightening, whichdV theseems
to cross thebehaviour:
optical band fromhigher to lower
Chromatic
problemthefrequendouble jet(Uhm 2cies. Such crossing may also explain the chromatic behaviour
should b
modelof
the optical afterglow at the rebrightening. Taking into acnario; w
count equations (3) and (4), which give the value of νM as
Howeverobserved
on-axis
and
how
its
value
is
modifiedbyobservingIf νM does cross the optical band at ~90 ks, we must haveclosurethe outflow off-axis, we find the condition
the para
1/2 1/2of the s
E52 "B,−2 "2e " 4.2 × 103(9)
νM,RS <The high value for the right-hand is needed to have νM in the
bands) s
This high value is needed
5 to keep νM inthe optical range ∼ 90 ks after the trigger,
optical∼off-axis
10 s observer.
after the trigger, even from a largely
also
from range
a largely
ble indeoff-axis observer.
produce61
Evenassuming
largest possible
valuesε enow= ε B assuming, E ~ 10 erg!!
Eq (7)
has to thebe modified,becauseweforarethat
X-ray bat the rebrightening we are observing the peak flux FνM . It
sion, i.e.
becomes
observed
Therefore,
1/2 the1/2model cannot be considered viable if, during the rebrightening,
ward an
E
"
n
" 28
(10)
52 B,−2
there
is chromatic
evolution due to the transit of νM
would leTo satisfy these equations together, one would need
These v
the isotropic energy E52 ∼ 109 and a value of density oftained w−14n ∼ 10, both unphysical. As a further consequence of

head at early times tobs ! 10 s and proceeds to the tail. Equation (2) becomes valid in the tail.
The emission produced by the FS with usual parameters
ee p 0.1, eB p 0.01, and p p 2.3 is shown by the thin curves
in Figure 2e. Both X-ray and optical light curves are inconsistent with observations and illustrate the problems of the FS

Following point C, the X-ray light curve has a sl
1 until the last break at point D. This break correspon
2

It deviates from the power law because of energy injection ifrom the tail. The growth of blast-wave energy (by a factor of 3)
deviation from the standard deceleration law G2r1r3 p const.

Reverse Shock and Forward Shock interplay

Piran et al. 2003

& Beloberodov 2007
Fig. 2.—(a–d) Blast-wave evolution in the mechanical model. (a) Density of the preshock ejecta nUhm
ej(RS) p rej/mp as a function of radius r of theblast wave; the assumed external density n1 p r1/mp p 1 cm!3 is shown for comparison. (b) Lorentz factors of the preshock ejecta, Gej(RS), and th(c) Pressures at the FS and RS, pf and pr. (d) Relative Lorentz factor of the RS, g43 (see BU06). (e, f) Observed emission from the blast wave as a f
observer time. The emission parameters are eB p 0.01, ee p 0.1, and p p 2.3. (e) Observed spectral ﬂux, assuming the burst is at a cosmological re1. Thin curves show the FS emission—X-ray (dashed line) and optical (dotted line). Thick curves show the RS emission—X-ray (solid line) and opt
dotted line). (f) Evolution of spectral indices bX (X-ray) and bO (optical) for the RS emission. The transition from the slow cooling spectrum b p (p0.65 (nc 1 n) to the fast cooling spectrum b p p/2 p 1.15 (nc ! n) occurs early in the X-ray band and later in the optical band. The peaks in bX anddiscussed elsewhere (Z. L. Uhm & A. M. Beloborodov 2007, in preparation). The correspondence between the marked points in dynamical panels a–d anpanels e–f is approximate: radiation received at a given tobs is emitted by the blast as it propagates a range of radii r ∼ 2G2tobsc . [See the electronic edi
Journal for a color version of this ﬁgure.]

If the central engine produces a long-lived relativistic outflow, emission from Reverse
Shock may be significant and extend for long time.

Depending on physical parameters, the RS can give different contributions in Opt and
X-ray
Can a superposition of Reverse Shock and Forward Shock emissions reproduce
the complex behaviour of GRB 100814A ?

Modeling of RS and FS emission•

Light curve slopes

No. 1, 2000

SARI & MÉSZÁROS

L35

We use the predictions of Sari & Meszaros 2000 (SM00):

TABLE 1
Temporal Exponents of the Peak Frequency nm, the Maximum FluxFnm, the Cooling Frequency nc, and the Flux in a Given Bandwidth Fn
Fn
nm

Fnm

nc

!

24 ! 7g " sg2(7 " s ! 2g)

6s ! 6 " g ! 3sg
2(7 " s ! 2g)

4 " 4s ! 3g ! 3sg!
2(7 " s ! 2g)!

12 ! 3g " sg 6s ! 12 " 3g ! 3sg
2(7 " s ! 2g)2(7 " s ! 2g)

Shock

F ......
R ......

!

n 1 max (nc, nm)

nm ! n ! nc
6 ! 6s ! g " 3sg " b(24 ! 7g " sg)2(7 " s ! 2g)!

!4 ! 4s " g " sg " b(24 ! 7g " sg)2(7 " s ! 2g)

12 ! 6s ! 3g " 3sg " b(12 ! 3g " sg)
4 " 4s ! 3g ! 3sg!
2(7 " s ! 2g)2(7 " s ! 2g)!

8 ! 4s ! 3g " sg " b(12 ! 3g " sg)2(7 " s ! 2g)!

Note.—F is forward, R is reverse. Calculated both in the adiabatic regime nm ! n ! nc [Fn ∝ Fnm(nm /n)b ∝ t!an!b , where b = (p ! 1)/2 ] and in the cooling regime
nc ! nm ! n [Fn ∝ (nc /nm)1/2(nm /n)b ∝ t!an!b, where b = p/2].

(whichuses the forward
shock only).theA goodsamplingof theFor withslow cooling,nc 1 nm 1 E(>
na, nmaxΓ)= n~
selfm, andParameters describes
energyassociatedthe shells:
E0synchrotron(Γ/Γ0)–s+1
spectrum, especially at low frequencies, can therefore show theabsorption occurs at
It
is
also
tells
us
the
rate
of
energyinjection
into the front shell.
existence or nonexistence of such a feature. The forward shock
always dominates above n 1 max (nmf , nc ) by a small factor of
t 3/5(s!1)/(7"s)
-g
f
!1
!1
1/5
1/5
3/5
describes
theexternal
p!2
na = 3.6
GHz (1 "medium:z) ee, 0.5eB, !2 Eρ52 ~
n0 r
, (9)
gParameter. Since p ! 2g, theforward shock
doesdensity
not radiateprofile
much of thet0
more than the reverse at high frequencies.
In the case of fast cooling, we have ignored the effect of()The early optical is RS emission; the Xray emission and optical rebrightening isfrom FS
Late steep decay is jet break.

Flux

RS + FS interplay: Scenario I
α1

α2

α3

Optical
α4

α1, X
RS
FS

X-ray

α2, X

time

No solutions for g=0, (interstellar medium, ISM), nor for g=2, the density profile of stellar
wind expected around a massive star progenitor.
Instead, g=1.15, s =2.75, p=2.02, can reproduce the decay slopes within 3 sigma:
α1 = α1,X = 0.58; α 3= 0.51. Note g=1.15 is intermediate between ISM and wind.
α2 = -0.57 is not consistent with observation, and α2,X = 1.3 is way off. However, themodel is approximate and numerical simulations indicate that jet break decay slope
might be steeper (Granot et al. 2006, Van Eerten et al. 2010, etc.)

The peak frequency for θobs = 0 is given by! explain"2
But ModelI
cannotchromaticp−2
14
1/2 1/2
2 1/2 −3/2
νM = 3.3 × 10 (z + 1) "B,−2"e E52 td Hz(4)p−1
behaviour due to transit of νM at rebrightening.
where td indicates time in days. The maximum flux is
For wind-like media, the synchrotron peak frequency νM is given by
"2
!
p
−
2
1/2
1/2 −3/2"2e E52 td Hz(5)νM = 4×1014 (z+1)1/2 (p−0.69)"B,−2p−1−2 1/2
1/2 GRB100814A
d-based,radio
observations
9
F (νMet)=1)D(t/tj )−3/4µJy Forward
(6)
(Yost
al.1600(z2003).+At
rebrightening,allof
emissionis from
Shock.
28 "B,−2 E52 n(Yost et al. 2003). E52 is the kinetic energy of the ejecta,
The
50 ks SED
indicateofFSν electrons
have top=2.02.
temporalevolutionaccording
SM00 forg = 1.15
while "e and "B,−2 are theMfractions of shockwave
energy
−1.28
and
s
=
2.75.
We
find
that
ν
∝
t
. Thus, at 90 ks,
M,FS
given
to
radiatingelectrons
andmagnetic
field
respectively.
To
have
νM at
optical band at rebrightening, the equation above* requires
we
would
have
D
is
the
luminosity
distance of the burst, while p is28
1/2index
1/2the power-law energy distribution of radiating
the
#B,−2
#2e Eof(11)
52 ! 760
electrons, n the density in particles cm−3 of the circum58 erg.
burstmedium.
theknownparameters,
takingEvenassuming
assuming
large
valuesforToo#B,−2and, 33GRBand model.
Even
εSubstituting= εBvery= 1/3,
E ~ 10much
for#eanye thep1/3= 2.02
to explain theflat X-ray
spectrum, andrememberrespectively
at theequipartition,
we would
still need58 θobs = 3θj the observed νM will be 1/2 of the
ing
that
E ∼
10for
erg. Such large energy is not predicted by any
GRB100814A
mediumprofileintermediate between ISM and Wind. We therefore calculate
ν*models
on-axiseq.3), has
wehave engine.
Mof (seethe GRB
centralνM at deceleration time ~860 s as in wind medium and then we follow its evolution with s=2.75,
1.27
1.02themore
plausible
variantofasSM00.
Fg=1.15,(νi ,Aθobs, tinpeak) = 0.17E52"0.77
n1/2previous model,(7) whichB,−2 "ealso keeps all the advantages described above, predicts that

Numerical simulations for Scenario I
Detailed simulations, which takes into account:
Stratification in the Lorentz factors of ejecta;
Mechanical work (pdV) done by the gas.
Parameters of the simulation:
Kinetic Energy E = 1054 erg;	ε e,FS = 0.1, ε B,FS = 0.01;
ε e,RS = 0.1, ε B,FS = 0.05;
p = 2.1 ; θ jet = 0.07 rad
RS energizes 100% of electrons of ejecta; but FS
energizes only 1.5% of medium.
Agreement of light curves with observations;
Harder spectrum around peak time predicted;
It can produce many curves changing Γ(t).
Problem: how FS energizes only ~1.5% of electrons?

FS+RS (solid)
FS (dotted)
RS (dashed)

10 keV (red)The early optical and X-ray are RS
emission;
The optical rebrightening is FS emission;
Late steep decay is jet break.

Flux

RS + FS interplay: Scenario II
α1

α2

α3

Optical
α4

α1, X
RS
FS

X-ray

α2, X

time

We can now model the FS assuming a very steep spectrum. This eases the energy
requirements. We take pFS=2.85. We take pRS = 2.02 to explain the hard X-ray
spectrum.
Parameters s=2.65, g=1.25 can reproduce the decay slopes within 3 sigma:
α1 = 0.57; α 1, X = 0.58; α 4= 2.07; α 2,X ~ α4α2 = -0.52 is not consistent with observation, and α 3 = 1.1 is way off. However, themodel is approximate; and observed α 3 < 1.1 can be explained because ν M ~ ν opt

opticalbandof
and
the
model
is approximated,thus
wewithin 2.8σ
theobserved
values,except
the
rise,
which
within2.8σoftheobserved
values,except
the
rise,
which
ay
within2.8σ
the observed
values,exceptis slightly
steeperthan ofpredicted,
and decay
slope after
the the rise, which
considerthissolution
satisfactory.
The
spectralslopesis slightly steeper than predicted, and decay slope after theis for,slightly
predicted,
and decay
rebrightening,which
is slower than
than predicted.
However,the slope after theaccounted
too. steeper
rebrightening,which
is slower than predicted. However, thedecay slope
maybecomes
be shallower
νM,FS thanis stillpredicted.
closetoModeling
ofbecauseFS
andin
Scenario
II theenrebrightening,which
is slower
Equation(11)
decay slope
may be shallower
becauseνM,FSRSis stillclose
to However,

the optical band and the model is approximated, thus we
06)
slope
be shallower
because
νM,FS
the
band
and may
the satisfactory.
model
is approximated,thus
we is still close to2
1/2 decay
2 optical
canconsiderthissolutionThe
spectralslopes
#
E
&
0.58
(12)
e modeling
52
FS
−2can
considerthis
The spectral
slopesinare
the opticaland the model
is approximated,thus weaccounted
for, solution
too.bandsatisfactory.
accounted
for, didtoo.forcanwe, anothercondition.
The spectral slopes
M,FS
Equation
becomesaare
canasconsider
solution
satisfactory.
The
Thederive,
condition
ν(11)~ν optthisat νtherebrigtening
time
becomesM
Equation(11)
becomes
ximum
flux
F (ν
) has
to too.
be equal to the peak flux
M,FS
1/2
1/2 accounted
2 are
RS
for,
#1/2
E52
(12)
B,−2
ched
at#e2&
90 &ks,0.58
which is & 200 µJy. We find
1/2
0.58
(12)
of#B,−2 #e E52 &Equation(11) becomescan derive, as we −3
did for νM,FS , another condition. The
2 We1/2
E
A
&
1.6
×
10
(13)
∗
52can derive,−2We
didfor νtoM,FSanother
condition.
The
1/2
1/2
maximum
flux F) has
be ,equal
to thepeak flux
2as(νwe
M,FSThe conditionF(ν) ~ 200µJy at the rebrigtening time is
#
#
E
&
0.58
(12)
M52
e
B,−2
ay
maximum
flux
F
(ν
)
has
to
be
equal
to
the
peak
flux
reached
at
&
90
ks,
which
is
&
200
µJy.
We
find
M,FS
ese equations have to be solved jointly. Assuming the typ1/2
1/2
at &we90findks,
which&µJy.&Wefind
1/2= 1/3,
1/2
−3 is
lso
If, anotherwe (13)take condition. The#reached
that
#B,−2
E
derive,
as
we200
did
ν5.3.
#eB,−2
E52We
A∗ can
& 1.6
× 10
M,FS
52 for
1/2
1/2
−3
as
well
(thesevaluesof the# parametersareart−2# = 33
E
A
&
1.6
×
10
(13)
maximumflux(νM,FS) has
to be theequal
to the peak flux∗
52
B,−2 equations
These
have to be F
solvedjointly.
Assuming
typchedatequipartition)
then
E#1/2
&
0.86
the
onset
of
the
1/2 atAssuming
toTheseThese
equationsmustbesolvedtogether.
ε=ε= 1/3,
reachedatfind
&to
90
ks,
which
is
&
200
µJy.
We
findwe obtain
&
5.3.
If
we
take
ical
#e equations=
1/3, we
that
E
e
B
52
have
be
solvedjointly.
Assuming
thetypB,−2ernal
andenergyinjection.
is thin,
1/2 of The
1/2 #medium
jet#B,−2#shock
=
33
as
well
(thesevaluestheparameters
&
5.3.
If
we are
take
ical
=
1/3,
we
find
that
#
E
1/2 −4 1/2
e
−3
52
B,−2
h reachedA∗ & 3#at
×
10
.
E52 A
1.6
×&100.86
(13)
E52
0.86
∗ &thenEat theonset of theare
he#B,−2 = B,−233equipartition)
as well(thesevaluesof the# parameters
ceexternal
we haveobtained
the valuesof TheE andcircumburst
shock
and energy
injection.
mediumis thin,reachedatequipartition)
then
E
&
0.86
at
the
onset
ofAssuming
the
he
−4
These
equations
have
to
be
solvedjointly.
the typnsity,
we
can
also
derivethevaluesofthemicrophysiwith A∗ & 3 × 10 .
external shock and energy injection. The medium
is thin,
1/2
1/2
ore
Since
we
have
obtainedthevaluesofE
andcircumburst#e10=
thatX-ray#B,−2
E52 &is 5.3. If we takeparameterstheks, theemission−4 RS.
with A∗ ical
& 3for×.1/3,Atwe50find
density, we by
can =also
derivethevaluesofthefitmicrophysiare
l dominated
RS
and,
from
the
best
model,
33
as
well(thesevaluesof the we# parameters are
Since we#B,−2
have theobtainedthevaluesofE
andcircumburst+43.5
16X-ray emission iscalparameters
for
the
RS.
At
50
ks,
the
ve
a breakreached92.5also
eV &the2.2values
× 10
break
nddensity,−20.1
weatcanderiveofHz.
theatequipartition)then
E Such&microphysi0.86
at the onset of theill dominated by the RS
and, from the best fit model, we
−20.1
+43.5
16
got to at
be 92.5
the synchrotron
cooling
frequency
νC,RS
. For
avehasa break
eV
&
2.2
×
10
Hz. Such
break
−20.1
the tochosenvaluesof s andcoolingg, its value
decaysas .t−0.06
as gotbe thesynchrotron
frequency
νC,RS
For .
can compute its
atand
the deceleration
time
Modeling
FSvalue
RSasint−0.06
Scenario
II - 2he Thus,chosenwevaluesof s andofg,valueits
decays.
860 s as function of the relevant parameters, multiply it byhus, we can−0.06
compute its value at the deceleration time
(50/0.86)& 0.76 and force the result to be equal to the
60 sbreakas functionof therelevant
parameters, multiply it byenergy
we
find
at
50
ks.
Modeling
of
RS
−0.06
50/0.86)For
0.76 ofandforceatthe
result to time,
be equal
to thethe&value
νC,RSdeceleration
we takethe
Atenergy
50 ks, wetheoffind
X-ray
RS.
50 ks (2003),
SED tells
us thereis a cooling break at ~0.1 keV
reakatis50ks.Theformulation
Kobayashi& Zhang
theireq.9. We
(notthewellvalue
constrained).
calculate νC time,at deceleration
time, ~860 s:
Forof νC,RS We
at deceleration
we take thehave! & Zhang"−3/2 (2003), their eq.9. We
rmulation of Kobayashi
1+z
−3/2
1/2
11
#B,RS,−2 E52 A−2
aveνC,RS = 2.12 × 10
∗ tdec (14)
2
!
"−3/2
1
+
z
−3/2
1/2
11
−2 above wevaluesof density andenergychosen= For
2.12the× 10
A#
E
C,RS(Kobayashi∗ tdec (14)52
B,RS,−2& Zhang19
2003).
From
SM00,
we
calculate
how much it becomes at 50 ks.
find νC,RS = 4.7 × 10 2 #B,RS,−2 Hz at the deceleration time.
We findThus
Eq.14
impliesthat #B,RS,−2 must be very high; taking
For thevaluesof
16 density and energy chosen above weν	

 C,RS & 2.2 × 10 19Hz-3/2
would imply #B,RS,−2 ≈ 1. Such valuend ν	

 C,RS = 4.7 × 10 #B,RS,−2 Hz at the deceleration time.
hus Eq.14 implies that #B,RS,−2 must be very high; taking
εB,RS must be16very large; but it can’t be too large, otherwise the RS would not produce
C,RS & 2.2 × 10 Hz would imply #B,RS,−2 ≈ 1. Such valueemission. Since the cooling break has a large error, we take ε B,RS = 0.60.

the slopes of RS emission after a jet break. It is reasonable

3
Where
ν
peak = max(νM,RS , νSA,RS ) . Now, we know thatto assume that these post-jet slopes are similar to that of! X-ray"2decay! slope"1/2
the FS. Thus, the latecan be explained
"
"
e,RS
B,RS
−2
νby
Γ νwe
Rp2
(16)
the =
model
are discussing.
M,RS
M,FS
"
"
e,FS
B,FS
We can now determine ". The optical flux at 860 s

andt
for brightening
higher valuesbecomesof "e ofmore
the RS,
outflow,
one could
movespectrum
νM,RScomponent
hasnota blueat 4500
s. For thatto happen,onea
the observed
SED,
which isbly becomeshigh valuesof andE orlessa muchhighe
lesssteep.
however constrained to be pRS < 2.0
now investigate thindex, inWe
ourshallmodel.

Modeling of RS and FS in Scenario II - 3e,RSis RS emission,
fluxg =
density
is F −! 1).
300µJy.
Thefindwhere
Rp = gRSand/gFSthewith(p − 2)/(pWe first
the context of the scen
opticalis obviously
At Γdeceleration
time ~860
flux is ~ 300 µJy. It is givencurves
byour inout
atemission
the deceleration
time,s,Γthedec , using eq. 2 of MolinariIn
scenario,
more reasonab
radio flux is stillarising
after th−452
et al. (2007), A∗ = 3 × 10νOpt and−βE = 0.86 × 10 erg. We the spectral
evolution
between
1 and
6
)
(15)
F (νOpt ) = F (νpeak,RS ) (at 10 s and decaying afterwar
νpeak,RSfind that Γdec ! 125, weakly
depending on density and E. as time goes by, the second compo
can be ascribed to a few possib
For the values of the RS parameters
already defined, and brightening becomes more and more
3
Where
νpeak
= max(ν) hand,. Now, self-absorption
we know thatcomponentiscausingthM,RS , νSA,RSat
For thevaluesof parameters
frequency
ν has whichν M,RS;a >blue
spectrum(βeven assuming a very high value for "e,RS = 0.4, we have componentSA,RS
!
"2 !
"1/2
radio
band.
However,
wea findt
ν peak,RS= ν
theobserved
SED,
which
is
sum
νthus
ν−2
deceleration
time.
Thus,
the
peak
flux
SA,RS
"
M,RS <
SA,RS at "
e,RS
B,RS
in thelesscontext
of steep.
the model a
νM,RS = Γ νM,FS
Rp2(16)
becomesand lessof the RS will be reached
and
in
Eq.15
ν
is
peak
"e,FS at ν"SA,RS
B,FS
optical peak at 105 s is causedthefrequency. We know that
We shall now investigate the beh
Weself-absorption
know
the same peak frequency to cros
where
Rp =thatgRS /gFS with g = (p − 2)/(p − 1). We first findcurves in6the context of the scenario
! Γ "
1/2
out Γ at the deceleration time,
,
using
eq.
2
of
Molinari
at 10 s, would require that νM
dec
"B,RS
radio flux is still rising after the put
−4
52
F
(ν
)
=
ΓF
(ν
)
(17)
peak,RSet al.
(2007), A∗ = 3M,FS× 10
E = 0.86 × 10 erg. We
is6notpossibleevenin the con
"and
at 10
s and
decaying
afterwards.
T
B,FSfind that Γdec ! 125, weakly depending on density and E.
radio pcanpossibility
be ascribedistothata fewthepossibilitie
4
For
the
valuesoftheRSparameters
alreadydefined,andwhereΓdecelerationis the Lorentztime
factorat sany
given
time
. For
valSuch Sincea transit
expected-4, thewhich
isiscausing
the to
optio
From
860
and
A
=
3
x10
we
find Γcomponent= 125.
εB,RS
=
4
*
even
assuming
a
very
high
value
for
"
=
0.4,
we
have
e,RS
ues already found, we have F (νpeak,RS)4= 2.2 × 10 µJy at radio
hours
from
the trigger
for this
a typ
band.
However,
we find
sc
0.60,
we
find
F(
ν
)
=
2.2
x
10
µJy.
peak,RSν<ν
atdeceleration
time.
Thus,
the
peak
flux
M,RS
SA,RS
the onset of the deceleration. We can obtain the value of the in theνM,RSevolution
GRB10081
contextof the inmodel
adopte
of
the
RS
will
be
reachedatν
SA,RS and in Eq.15 νpeak isfrequency νSA,RS must be, in order to produce the observed optical
the peakusualatbecause
the cont
105 s is ofcausedby t
the self-absorption frequency. We know that10
10frequency
opticalflux,equationfrom eq.15.
We findνSA,RS× 10= νHz.
profile
the
same
peak
cross them
From first
above,
we thus
find!ν9.8= density
9.8 x10
Hz.of thetoshocked
peak,RSSA,RS!
"
6
1/2other parameters, from
Knowing this value and thatof theat 10s, would requireνM,FSshdeceleration
time, that
νM,RS
! 8.
"B,RS
F
(ν
)
=
ΓF
(ν
)
(17)
−0.8
M,FS
peak,RSnotpossibleinit.thecontext
Eq.9
of SM00canalsoon"e,RS ,parameterswhich is theand
onlyε re- , iswetcan
for
theevenchosenvalues
of s
"find
Since
ν SA,RSwedepends
known
determine
B,FS
e,RS
8
possibilityis 1.5
that×thepeakit i
maining unknown. We find that "e,RS ! 0.19.
νM,RS !
10 radioHz, and
4
We
find
ε
~
0.21
where Γ is theLorentz factor at any given time . For the vale,RS
Sucha transit
is expected
thispoint. Thus,νM,RStoisoccur
not4
ues already found, we have F (ν) = 2.2 × 10 µJy atModeling of the radio afterglow - 1
1000

What causes the late radio peak?

7.9 GHz
4.5 GHz

Flux density (uJy)ν M,FS (optical rebrightening). It must
evolve fro 1014 Hz at ~105 s to 109 Hz
at t ~106 s. Can’t be.
ν M,–RS
5 ~– 9 x109 Hz at deceleration-0.8time.
According to SM00, evolves as t.
It will be ν M, RS ~ 1.5 x108 Hz at 1 day
after trigger, then decays faster (jetbreak). Can’t be.

For the Wind-like CBM:
100
10
Days since GRB

100

−0.5
Fνmax =
7.7 (p + 0.12) (z + 1)1.5 D28−2 !0.5
E
A
t
mJy
52
∗
B,−2
d
−0.4 1.2 −0.6
= 3.3 × 109 (z + 1)−0.4 fW (p) !¯e−1 !0.2
E
Hz
νSA, FS . We have νaB,−2 52 A∗ td
146 Hz at deceleration
0.5 0.5
0.5 −1.5(Yost et al. 2003). ννSA, FS =will be 4.0
below
10
time.!¯2 Can’t
be.
×
10
(p
−
0.69)
(z
+
1)
!
E
Hz
m
B,−2 e 52 td
13
0.5 -0.65−2 0.5
νcat deceleration= 4.4 × 10time.
(3.45− p)e0.45pSM00,(z + 1)it−1.5
!−1.5
E
A
Hz
νSA,RS ~ 9.8 1010 Hz
Following
evolvesast
B,−2 52 ∗ t.d Thus

νSA,RS ~ 3.5 109 Hz at jet break time. Then, νSA,RS ~ Γ 8/5 νSA,FS ; Γ ~ t -1/2 , νSA,FS ~ t-1/5 ;thus νSA,RS ~ t-1 after jet break. At 10 days,
0.6 νSA,RS ~ 0.5 GHz. However, energy
where
f
(p)
=
(
(p
−
1)/(3p+2)). The Could
units are:
D28 = luminosity distance inW push ν
injection will likely
into
~
GHz
range.
be.
SA,RS!B,−2 = !B in %, n = density in cm−3 , A∗ = density scaling for the Wind-like profile

Modeling the radio afterglow - 2•

νSA,RS can be the peak frequency crossing the observing radio band. Is
the observed flux right?

We found that F(νSA,RS ) ~ 2.2 x 104 µJy at deceleration time 860 s.
For the chosen values of s and g, the flux at peak frequency evolves as t -0.16
up to t jet = 1.3 x 105 s.
F (peak,RS) ~ Γ F (peak,FS). In jet break regime, Γ ∼ t -½ while F (peak,FS) ~ t-1.
But the late shells produce energy injection and E ~ t 0.4 and F (peak,FS) ~ E½.
All together, we expect F (peak,RS) ~ t -1.3. We have F (peak,RS) ~ 700 µJy at
10, as observed.

Some comments on Scenario II•

Physical parameters are not uniquely determined: other values of s and g canreproduce similar light curves.

•

A kinetic energy E52 ~ 0.86 implies an efficiency η = Eγ / (Eγ + Ekin) ~ 0.9, rather
high for any model to produce the gamma-ray emission.

•

However, E52 is only the energy at deceleration time, when energy injection
begins. It is possible that the energy injection is due to trailing shells that haveproduced Eγ as well. If we use E at the end of observation, we have η = Eγ /(Eγ + Ekin) ~ 0.2, more reasonable.

•

The beaming-corrected energetics is much smaller. A jet break occurs whenΓ ∼ θ-1 . Γ=125 at deceleration time, then evolves as t-0.21 . Then, at 133 ks
Γ ∼ 44 and θ = 0.023 rad. Correcting for beaming, Eγ = 1.9 x 1049 erg.
The circumburst medium is very thin, with A* = 3 10-4, which implies n ~ 3 x 10-4 at~ 1 light year from the burst. This is not unusual (observed for other bursts, e.g.
130427A, Perley et al. 2013). Some GRB progenitor emit a very thin wind at
the end of their lives.

0

Is GRB100814A unique? No.

J. Greiner et al.: The unusual afterglow oNardini Marco et al.: On the nature of the extremely fast optical rebrightening of the afterglow of
GRB 081029

0.001

Time since GRB trigger [d]
0.01
0.1
1

ca
da
SD
fo
±
of
in

10

10000

Flux [counts/s]

Nardini et al. 2011,

1000
100
10
1

2.

0.1
0.01
XRT
K
H
J
z
i
r
g

Fν [µJy]

1000

14
15
16
17
18

100

19
20

Brightness [magAB]

0.001
10000

21

10

22
100

1000
10000
100000Time since GRB trigger [s]

1e+06

Sw
vi
to
th
co
0.
ta
ar

2.

N
A
ks
21
to
of
da
bl
w
tu
th

Fig. 2. Afterglow light curve of GRB 100621A as observed with2.
Swift in X-rays (top) and GROND in its seven filter bands (bottom). The J-band data points at 14 ks are from SOFI imaging,Si
the HK s -band data at 20 ks from a GROND-observation instFig. 5. andTemporalevolutionoftheAB
magnitudes
differences
bemorning twilight at which the J-band was already saturated byaf!
!
tween the
GROND
g and
z verticalbands.lines
Verticaldashedrepresent
rising Sun.
The 7
mark thetimes lines
at which
specsetral energy
distributions
been extracted(seedescribedtext and Fig.
the transition
time
between havethe different
phasesin3).
§3. Patu

GRB081029A(Nardini et al. 2011, Holland, DP
Fig. 4. r! band νFν light-curve (empty circles) superposed on theunabsorbed(black crosses) of the
et al.
2012)0.3–10 keV XRT light-curve!

GRB100621A (Greiner et al 2013)

afterglow of GRB 081029. The r band data were corrected for
the Galactic foreground extinction. Vertical dashed lines represent the transition time between the different phases described inra(Milvang-Jensen
et al., 2010),
and to
also
faint
UVOT
detections
Can a complex ejecta structure explain
fast
variability?
w
any this
temporalextrapolation.
Thanks
the
very
small
errorsin§3.
were recovered (Ukwatta et al., 2010b).
ab
the GROND
photometry
to the good skyobservations
conditionsand
duringHere,
we describe due
our multi-wavelength
reforof
GRB
100621A, andof the data
the firstsults
nightobservations
andpresent
thanksantoanalyses
the brightness
ofinthe daOther scenarios•

Internal dissipation: the optical emission occurs when shells interact with eachothers and Γ is very high. Some GRBs shows optical flares and fast and variablerebrightening. Internal dissipation can explain these features, but the emission
mechanism itself is not clear and we lack predictions;•

Change of microphysical parameters. If εe and εB of the shocks evolve incertain ways, one could have an optical rebrightening without X-ray counterpart.
But the required evolution is un-explained and contrived;•

End of energy injection. When the energy emission process ceases, bright FS
and RS reverberates throughout the ejecta, causing the rebrightening. Before andafter the rebrightening, the emission is from FS only. The rebrightening is
prominent only if the ejecta are narrowly collimated. However, this model
predicts a radio flare at the time of the rebrightening, while in GRB100814A
the radio peak is ~10 times later than the optical peak. Some peculiar valuesof parameters might allow for an extended radio rebrightening.

Conclusions- We have gathered a rich set of X-ray, UV/Opt/IR and radio data of the Swift
GRB100814A. The afterglow shows a prominent optical rebrightening peaking at ~1 day,which has no counterpart in the X-ray. The rebrightening is chromatic. Shortly after the
optical rebrightening, both X-ray and optical fluxes start to decay fast. A radio transient
peaks ~ 10 days after the trigger.
- A double component jet observed off-axis can explain the observed light curves.
However, it cannot explain the rebrightening chromatic behaviour if this is due to transitof synchrotron peak frequency νM;- In a second scenario, the early optical afterglow is due to Reverse Shock emission,caused by energy injection in form of late shells, while the X-ray and the opticalrebrightening and Forward Shock emission. This model can reproduce the observed
light curves. However, the transit of νM in the optical as late as 1 day requires
implausibly high Energy. Numerical modeling constrains how the Lorentz factor of ejecta
evolves in time to produce the light curves. But it still requires that the FS imparts all its
energy only to 1% of electrons.
- A third scenario assumes that early optical and all X-ray emission is from RS, while FS
with a steep spectrum produces the rebrightening. The required E is ~ 1052 erg. The light
curves features can be recovered, and the late radio peak can be qualitatively explained.
There are other GRBs like 100814A!

What are Gamma-Ray Bursts?

• Cosmological sources of gamma-ray occurring
randomly in the sky, associated with an explosion of a
massive star (long GRBs) or the merge of two
compact objects such two Neutron Stars or NeutronStar and Black Hole• Last from ~10e-3 to 1000 s• Followed by a long-lived