Mon. Not. R. Astron. Soc.
000
, 1–5 (2014)
Printed 11 September 2014
(MN L
A
T
E
X style file v2.2)
Early-time polarized optical light curve of GRB 131030A
O. G. King
1
?
, D. Blinov
2
,
7
, D. Giannios
9
, I. Papadakis
2
,
6
, E. Angelakis
4
,
M. Balokovi ́c
1
, L. Fuhrmann
4
, T. Hovatta
1
,
8
, P. Khodade
3
, S. Kiehlmann
4
,
N. Kylafis
2
,
6
, A. Kus
5
, I. Myserlis
4
, D. Modi
3
, G. Panopoulou
2
,
I. Papamastorakis
2
,
6
, V. Pavlidou
6
,
2
, B. Pazderska
5
, E. Pazderski
5
,
T. J. Pearson
1
, C. Rajarshi
3
, A. N. Ramaprakash
3
, A. C. S. Readhead
1
,
P. Reig
6
,
2
, K. Tassis
2
,
6
, J. A. Zensus
4
1
Cahill Center for Astronomy and Astrophysics, California Institute of Technology, 1200 E California Blvd, MC 249-17,
Pasadena CA, 91125, USA
2
Department of Physics and Institute of Theoretical & Computational Physics, University of Crete, PO Box 2208,
GR-710 03, Heraklion, Crete, Greece
3
Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune - 411 007, India
4
Max-Planck-Institut f ̈ur Radioastronomie, Auf dem H ̈ugel 69, 53121 Bonn, Germany
5
Toru ́n Centre for Astronomy, Nicolaus Copernicus University, Faculty of Physics, Astronomy and Informatics,
Grudziadzka 5, 87-100 Toru ́n, Poland
6
Foundation for Research and Technology - Hellas, IESL, Voutes, 7110 Heraklion, Greece
7
Astronomical Institute, St. Petersburg State University,Universitetsky pr. 28, Petrodvoretz, 198504 St. Petersburg, Russia
8
Aalto University Mets ̈ahovi Radio Observatory, Mets ̈ahovintie 114, 02540 Kylm ̈al ̈a, Finland
9
Department of Physics and Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We report the polarized optical light curve of a gamma-ray burst afterglow ob-
tained using the RoboPol instrument. Observations began 655 seconds after the
initial burst of gamma-rays from GRB 131030A, and continued uninterrupted for
2 hours. The afterglow displayed a low, constant fractional linear polarization
of
p
= (2
.
1
±
1
.
6) % throughout, which is similar to the interstellar polariza-
tion measured on nearby stars. The optical brightness decay is consistent with
a forward-shock propagating in a medium of constant density, and the low po-
larization fraction indicates a disordered magnetic field in the shock front. This
supports the idea that the magnetic field is amplified by plasma instabilities on
the shock front. These plasma instabilities produce strong magnetic fields with
random directions on scales much smaller than the total observable region of the
shock, and the resulting randomly-oriented polarization vectors sum to produce
a low net polarization over the total observable region of the shock.
Key words:
gamma-ray burst: individual: GRB 131030A – magnetic fields –
polarization – shock waves
1 INTRODUCTION
Gamma-ray burst (GRB) afterglows are usually at-
tributed to the synchrotron emission from a shock or
jet propagating through the circumburst medium. The
observed emission is thought to be the combination of
the forward shock and a reverse shock that propagates
backward into the flow (Piran 1999; Zhang, Kobayashi
& M ́esz ́aros 2003), with the reverse shock dominating at
early times. The light from the reverse shock might be
highly linearly polarized if ordered magnetic fields thread
the ejecta (Granot & K ̈onigl 2003; Lyutikov 2003; Lazzati
et al. 2004), while the polarization of the forward shock
?
E-mail:ogk@astro.caltech.edu
depends of the circumburst magnetic field (Uehara et al.
2012).
The early-time polarized optical GRB afterglow
emission has been measured five times. Mundell et al.
(2007) measured a 2
σ
upper limit of 8 % on the linear
polarization 203 s after the GRB event for GRB 060418.
They interpreted this relatively-low polarization level as
ruling out the presence of a large-scale ordered mag-
netic field. The next measurement of the early-time af-
terglow polarization was made by Steele et al. (2009) of
GRB 090102 160.8 s after the GRB. They, by contrast,
measured a level of (10
±
1) %, which they interpreted as
coming from the reverse shock. GRB 110205A was mea-
sured by Cucchiara et al. (2011) to have a 3
σ
upper limit
of 16 % 243 s after the BAT trigger time. A later mea-
c
©
2014 RAS
arXiv:1409.2417v2 [astro-ph.HE] 10 Sep 2014
2
O. G. King et al.
surement 56 min after the trigger time found a polariza-
tion level of 3
.
6
+2
.
6
−
3
.
6
% (2
σ
confidence levels). They ex-
cluded the zero-polarization hypothesis at a 92 % confi-
dence level, supporting a reverse plus forward-shock sce-
nario. Uehara et al. (2012) measured the optical polar-
ization afterglow of GRB 091208B from 149 to 706 s after
the burst trigger and found a linear polarization level of
(10
.
4
±
2
.
5) %. At the time of the measurement the op-
tical light curve exhibited a power-law decay (index of
−
0
.
75
±
0
.
02), which they interpreted as the signature of
the forward shock synchrotron emission.
Most recently, Mundell et al. (2013) obtained mul-
tiple measurements of the early-time optical polarization
light curve of GRB 120308A, making this the first mea-
surement of the temporal evolution of the early-time po-
larized optical afterglow emission. They began observing
the GRB afterglow 240 s after the GRB trigger and mon-
itored it for
∼
10 min, during which time the fractional
polarization dropped from 28
+4
−
4
% to 16
+5
−
4
%.
2 ROBOPOL OBSERVATIONS OF
GRB 131030A
The RoboPol project operates a four-channel imaging po-
larimeter on the 1.3 m telescope at the Skinakas Obser-
vatory in Crete, Greece
1
. The RoboPol instrument mea-
sures the Stokes parameters
I
,
q
=
Q/I
, and
u
=
U/I
,
simultaneously in a single exposure. It is used to monitor
the optical linear polarization of blazars (Pavlidou et al.
2014), and observations are performed by an automated
control system (King et al. 2014) that is capable of re-
sponding to target-of-opportunity (TOO) events such as
GRBs.
At 20:56:18 UT on 2013 October 30 the Swift Burst
Alert Telescope (BAT, Barthelmy 2004) triggered and
located GRB 131030A. The afterglow was located at
23
h
00’16.13”,
−
05
◦
22’05.1” (J2000) by the Swift Ultravi-
olet/Optical Telescope (UVOT, GCN#15402
2
). The du-
ration over which 90 % of the 15 – 350 keV GRB photons
were collected,
T
90
, was 41
.
1
±
4
.
0 s and it had a fluence
in the 15 – 150 keV band of 2
.
93
±
0
.
04
×
10
−
5
erg cm
−
2
(GCN#15456
3
). The GRB occurred at a redshift of 1.293
– 1.295 (GCN#15407
4
and GCN#15408
5
) and had an
isotropic energy release of
E
iso
= (3
.
0
±
0
.
2)
×
10
53
erg
(GCN#15413
6
).
The RoboPol control system automatically re-
sponded to the GRB notification by interrupting the reg-
ular observing schedule and slewing to the location of
the GRB afterglow. The telescope operator identified the
afterglow and began taking exposures in the Johnson-
Cousins
R
-band at 2013 October 10 21:07:13 UT, 655 s
after the GRB trigger. We continued monitoring the GRB
afterglow in a series of exposures until it set below our ob-
serving horizon about 2 h after the GRB, adjusting the ex-
posure time as the afterglow faded. A typical image from
the series of RoboPol exposures is shown in Figure 1.
The data were reduced using both the Aperture Pho-
tometry Tool (Laher et al. 2012) and the RoboPol pipeline
1
http://skinakas.physics.uoc.gr/
2
http://gcn.gsfc.nasa.gov/gcn3/15402.gcn3
3
http://gcn.gsfc.nasa.gov/gcn3/15456.gcn3
4
http://gcn.gsfc.nasa.gov/gcn3/15407.gcn3
5
http://gcn.gsfc.nasa.gov/gcn3/15408.gcn3
6
http://gcn.gsfc.nasa.gov/gcn3/15413.gcn3
N
E
Figure 1.
A raw frame showing the characteristic four-spot
pattern from the RoboPol instrument. The GRB is located
in the low-background central area (four spots against a dark
background arranged in a cross). The three reference stars used
to provide relative photometry are circled. The relative Stokes
parameters
q
and
u
are obtained by taking ratios of the flux in
pairs of spots.
(King et al. 2014), and were calibrated using the RoboPol
instrument model. Relative photometry was performed
using three field sources (circled in Figure 1), with
R
-band
magnitudes taken from the USNO-B1.0 photometric cat-
alog (Monet et al. 2003). The measurements from each
exposure are given in Table 1.
The linearly polarized light curve for the GRB af-
terglow is shown in Figure 2. The polarization measure-
ments have not been debiased, as most data points have
p/σ
p
>
√
2, the threshold at which debiasing is usu-
ally applied (Pavlidou et al. 2014). The linear polariza-
tion behavior of the afterglow appears to remain constant
throughout the 2 hour observing period. The mean polar-
ization percentage from our data is
p
= (2
.
1
±
1
.
6) %, and
the mean polarization angle is
χ
= 27
◦
±
22.
3 IS THE POLARIZATION INTRINSIC?
The measured polarization of the GRB might be due to
interstellar extinction in our Galaxy. We can estimate the
expected level of induced polarization in the direction of
the GRB from the level of Galactic extinction using the
standard empirical relation from Serkowski, Mathewson
& Ford (1975). According to the NASA Extragalactic
Database the extinction in the direction of the GRB is
A
B
= 0
.
208 and
A
V
= 0
.
157, which gives
E
(
B
−
V
) =
0
.
051 mag (Schlafly & Finkbeiner 2011). The resulting
level of stellar polarization is
P
max
6
9
.
0
E
(
B
−
V
), i.e.,
∼
0
.
5 %, though this method is approximate.
To obtain a more accurate estimate of the scale of
the interstellar scattering effect we measured the linear
polarization of four field stars around GRB 131030A in a
separate series of exposures. We show in Figure 3 a po-
larization vector map of the GRB and the field sources.
The mean polarization fraction for the field sources is
c
©
2014 RAS, MNRAS
000
, 1–5
Polarized light curve of GRB131030A
3
Table 1.
RoboPol data for GRB131030A.
t
m
is the middle
of the exposure time in the observer frame, in minutes since
2013 October 30 20:56:18 UT.
t
e
is the exposure duration. The
uncertainties in the
R
-band magnitude,
σ
R
, are dominated by
a systematic uncertainty from the relative photometry fit.
t
m
t
e
p σ
p
χ σ
χ
R σ
R
min
s
%
deg
mag
11.25
20
2.25
1.65
31.3
20.6
15.94
0.08
12.33
20
1.65
1.72
26.2
29.8
15.97
0.08
13.22
20
1.36
1.80
129.7
36.4
16.05
0.08
13.72
20
4.12
1.82
29.6
12.4
16.09
0.08
14.23
20
1.38
1.85
173.7
38.0
16.12
0.07
14.73
20
1.79
1.89
19.1
30.3
16.15
0.08
15.28
20
2.63
1.91
22.5
20.8
16.16
0.07
15.78
20
2.98
1.96
167.1
18.7
16.22
0.08
16.30
20
3.86
1.94
19.0
14.4
16.20
0.07
18.78
120
1.96
0.80
38.8
11.2
16.38
0.07
21.17
120
2.20
0.85
35.4
10.9
16.51
0.07
23.77
120
2.40
0.92
24.8
10.8
16.62
0.07
26.48
120
2.71
0.97
15.8
10.4
16.75
0.07
29.17
120
1.56
1.04
22.0
19.1
16.87
0.08
31.50
120
2.32
1.10
27.5
13.4
16.94
0.07
34.22
120
1.74
1.16
26.2
19.1
17.06
0.07
36.93
120
3.25
1.24
36.9
10.5
17.16
0.07
39.65
120
2.64
1.33
16.2
14.7
17.32
0.07
42.37
120
2.21
1.38
20.5
17.8
17.39
0.07
45.03
120
4.55
1.48
22.1
9.3
17.45
0.08
48.77
180
2.73
1.29
31.7
13.0
17.55
0.07
52.02
180
2.11
1.32
43.4
16.5
17.53
0.07
55.52
180
2.85
1.41
36.6
13.2
17.65
0.07
59.23
180
2.78
1.42
21.5
14.5
17.69
0.07
65.82
180
2.86
1.42
22.0
14.2
17.72
0.08
69.47
180
3.72
1.57
19.7
12.2
17.84
0.08
73.00
180
2.06
1.54
28.7
20.3
17.68
0.08
76.20
180
2.23
1.58
55.4
19.1
17.71
0.08
82.63
180
3.02
1.66
37.0
14.1
17.79
0.07
86.33
180
0.92
1.60
57.2
48.4
17.79
0.08
93.73
180
3.56
1.82
43.8
13.7
17.90
0.08
96.93
180
3.29
1.86
39.7
14.6
17.92
0.08
100.70
180
2.21
1.83
5.4
24.9
17.92
0.08
104.18
180
1.95
1.96
18.9
29.1
18.09
0.08
107.57
180
4.62
2.17
44.1
11.9
18.10
0.08
114.73
180
1.25
2.11
79.3
53.9
18.12
0.08
118.17
180
3.61
2.24
20.4
17.7
18.27
0.08
121.90
180
1.99
2.40
130.4
28.8
18.12
0.08
(1
.
66
±
0
.
43) %, and the polarization vectors are well-
aligned, indicating an ordered magnetic field in the ab-
sorbing interstellar medium (ISM).
The high level of polarization of the field sources
around GRB 131030A implies that the measured polar-
ization is dominated by interstellar extinction rather than
the intrinsic polarization of the GRB afterglow.
4 INTERPRETATION
The GRB occurred at a redshift of 1.294, so in the rest-
frame we started observing 655
/
(1 +
z
) = 285 s after the
GRB event, which corresponds to about 16
×
T
90
. This is
about 3–5 times longer than the time when the 5 early-
time optical polarimetric observations we mention in the
Introduction started; Table 2 summarizes these data.
The X-ray Telescope (XRT; Burrows et al. 2005)
started observing the GRB field 78.4 s
7
after the trig-
7
http://gcn.gsfc.nasa.gov/gcn3/15402.gcn3
0
1
2
3
4
5
6
p
[%]
0
500
1000
1500
2000
2500
3000
3500
Mid-time since GRB [seconds, rest frame]
−
90
−
60
−
30
0
30
60
90
120
χ
[degrees]
Figure 2.
The
R
-band linearly polarized light curve of
GRB 131030A as measured by the RoboPol instrument. The
fractional linear polarization
p
is listed as a percentage of the
total light, and the EVPA
χ
is given in degrees.
22:59:50.4
23:00:00.0
23:00:09.6
23:00:19.2
23:00:28.8
Right ascension (J2000)
-5:27:36.0
-5:25:12.0
-5:22:48.0
-5:20:24.0
-5:18:00.0
Declination (J2000)
2%
Figure 3.
A polarization vector map of the field around
GRB 131030A. Seperate observations were made of four field
stars around GRB 131030A, indicated by the grey wedges.
GRB 131030A is indicated by the light-red wedges. The diame-
ter of the wedge is proportional to the polarization percentage,
while the angle subtended indicates the 1
σ
polarization angle.
ger. The XRT light curve
8
is shown in Figure 4. At early
times, the X-ray light curve brightens until
∼
50 s (rest
frame) after the burst, and then the X-ray afterglow de-
cays steeply until
∼
150 s. At later times, coincident with
the RoboPol observations, the X-ray light curve declines
as a single power law
∝
t
−
1
.
01
±
0
.
02
. The RoboPol optical
light curve is also plotted in Figure 4. The optical flux
declines also as a single power law
∝
t
−
0
.
78
±
0
.
02
(we have
8
http://www.swift.ac.uk/xrt_curves/00576238/flux.qdp
c
©
2014 RAS, MNRAS
000
, 1–5
4
O. G. King et al.
Table 2.
Measurements of the optical polarization of the early GRB afterglow emission. The times are in the rest-frame, i.e.,
have been corrected for redshift. The interpretation column indicates whether the authors interpreted the optical emission as being
dominated by either the forward or reverse shock, or whether they contribute approximately equally.
Name
t
start
(s)
t
exp
(s)
Polarization
Interpretation
GRB 120308A (Mundell et al. 2013)
90
135
28
−
15 %
Reverse shock
GRB 090102 (Steele et al. 2009)
63
24
(10
±
1) %
Reverse shock
GRB 110205A (Cucchiara et al. 2011)
76
?
<
16 %
Reverse shock
GRB 060418 (Mundell et al. 2007)
82
12
<
8 % (2
σ
)
Both
GRB 091208B (Uehara et al. 2012)
72
551
(10
.
4
±
2
.
5) %
Forward shock
GRB 131030A (this work)
285
2894
<
2 %
Forward shock
10
2
10
3
10
4
Mid-time since GRB [seconds, rest frame]
10
−
13
10
−
12
10
−
11
10
−
10
10
−
9
10
−
8
10
−
7
Flux [erg cm
−
2
s
−
1
]
∝
t
−
0
.
78
±
0
.
02
∝
t
−
1
.
01
±
0
.
02
This work
GCN15418
GCN15423
Swift/XRT
Figure 4.
The optical and X-ray light curves GRB 131030A,
including measurements published in GCNs, with the best-fit
power-law curves.
included in the optical band light curve later
R
-band pho-
tometry from GCN circulars #15418
9
and #15423
10
).
Since we observe a single, power-law decline from
∼
5
up to
∼
55 min (rest-frame) after the burst, both in the
optical and X-rays, the simplest explanation is that a sin-
gle emitting component is responsible for the observed
emission in both bands. This is most probably the for-
ward shock propagating in the external medium, and we
observe the synchrotron emission from this shock. The X-
ray decline is consistent with the fast-cooling afterglow
from a shock that has a power-law distribution of elec-
tron energies with a spectral index of
p
E
= 2
.
01
±
0
.
03
(
F
X
∝
t
(2
−
3
p
E
)
/
4
, Granot & Sari 2002). If the GRB am-
bient density profile is similar to the ISM we would ex-
pect an optical light curve that evolves as
∝
t
−
3
/
4
while
in an environment with a stellar-wind density profile the
light curve would evolve as
∝
t
−
5
/
4
. The measured optical
power-law index of 0
.
78
±
0
.
02 implies that the medium
surrounding the GRB has a constant density with a pro-
file similar to the ISM. The blast decelerates in a constant
density medium and the cooling synchrotron break is be-
tween the optical and the X-ray bands
∼
5
−
55 min after
the burst. The observed flux in the X-ray and optical
bands is consistent with this model if a fraction
e
∼
0
.
1
of the dissipated energy goes into non-thermal electrons,
a fraction
B
∼
3
×
10
−
4
goes into amplifying the mag-
netic field while the ambient density of the circumburst
material is
n
∼
1 cm
−
3
. These values are similar to those
9
http://gcn.gsfc.nasa.gov/gcn3/15418.gcn3
10
http://gcn.gsfc.nasa.gov/gcn3/15423.gcn3
inferred in other bursts (e.g., Santana, Barniol Duran &
Kumar 2014).
In general, the GRB afterglow emission is believed to
consist mainly of the reverse and forward shock emission
and other possible components (such as radiation related
to jet reactivation). The reverse shock emission may dom-
inate at early times, i.e., comparable, or a few times longer
that the duration
T
90
of the burst (Kobayashi, Piran &
Sari 1999; Mimica, Giannios & Aloy 2009; Mimica, Gian-
nios & Aloy 2010) and may be strongly polarized, as in
Mundell et al. (2013); Steele et al. (2009). At later times,
the forward shock is the primary candidate for emission,
and its polarization may be much weaker as observed by
Mundell et al. (2007). Our results support this view, in-
dicating a disordered magnetic field in the shock front
as it propagates through the ambient medium around
GRB 131030A.
This result supports suggestions that the magnetic
field is amplified by plasma instabilities on the shock
front, which would produce strong magnetic fields with
random directions, on scales much smaller than the total
observable region of the shock (Medvedev & Loeb 1999).
On the other hand, Uehara et al. (2012) observed a strong
polarization signal of
∼
10 % from the early afterglow of
GRB 091208B, when the observed emission was also dom-
inated by the forward shock emission. Their observation
started
∼
72 s after the burst, and lasted for
∼
550 s (in
the source rest frame). They measured an
R
-band flux de-
caying as
t
−
0
.
75
, with the X-ray flux initially decaying as
t
−
0
.
18
and later steepening to
t
−
1
. The first
∼
200 s of our
observations overlap with the end of their observations in
rest-frame time, during which time both the optical and
X-ray light curve decay rates are very similar. Therefore,
if the same mechanism operates in all GRBs, then a very
fast decline in optical polarization must take place, indi-
cating a fast change in the mechanism that amplifies the
strong magnetic fields in the jet of these sources. On the
other hand, these mechanisms may not be the same in
all GRBs. More optical polarization data from different
GRBs, and on long time scales, are needed in order to
understand better the magnetic field structure in GRBs.
ACKNOWLEDGMENTS
The RoboPol project is a collaboration between Caltech
in the USA, MPIfR in Germany, Toru ́n Centre for As-
tronomy in Poland, the University of Crete/FORTH in
Greece, and IUCAA in India. The U. of Crete group ac-
knowledges support by the “RoboPol” project, which is
implemented under the “Aristeia” Action of the “Op-
erational Programme Education and Lifelong Learn-
ing” and is co-funded by the European Social Fund
c
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2014 RAS, MNRAS
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Polarized light curve of GRB131030A
5
(ESF) and Greek National Resources, and by the Euro-
pean Comission Seventh Framework Programme (FP7)
through grants PCIG10-GA-2011-304001 “JetPop” and
PIRSES-GA-2012-31578 “EuroCal”. This research was
supported in part by NASA grant NNX11A043G and NSF
grant AST-1109911, and by the Polish National Science
Centre, grant number 2011/01/B/ST9/04618. K. T. ac-
knowledges support by the European Commission Sev-
enth Framework Programme (FP7) through the Marie
Curie Career Integration Grant PCIG-GA-2011-293531
“SFOnset”. M. B. acknowledges support from the Interna-
tional Fulbright Science and Technology Award. I. M. and
S. K. are supported for this research through a stipend
from the International Max Planck Research School (IM-
PRS) for Astronomy and Astrophysics at the Universi-
ties of Bonn and Cologne. T. H. was supported by the
Academy of Finland project number 267324.
This research made use of Astropy,
http://www.
astropy.org
, a community-developed core Python pack-
age for Astronomy (Astropy Collaboration et al. 2013).
This research has made use of the NASA/IPAC Ex-
tragalactic Database (NED) which is operated by the Jet
Propulsion Laboratory, California Institute of Technol-
ogy, under contract with the National Aeronautics and
Space Administration.
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