Early optical-IR emission from GRB 041219a: neutron-rich internal shocks and a mildly magnetized external reverse shock

Abstract

Very early optical and near infrared (IR) emission was discovered accompanying the long gamma-ray burst (GRB) 041219a. We show that the optical/IR flash tracking the gamma-ray lightcurve during the prompt emission could be understood as emission from neutron-rich internal shocks, as has been suggested by Fan & Wei. The early K_s-band afterglow lightcurve after the prompt phase could be well-modeled as the superposition of a reverse shock and a forward shock component. The radio data also support the reverse shock interpretation. Comment: 4 pages, including 2 figures, accepted for publication in ApJL (shortened to match the page limit)

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L25
The Astrophysical Journal, 628:L25–L28, 2005 July 20
? 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
EARLY OPTICAL-INFRARED EMISSION FROM GRB 041219a: NEUTRON-RICH INTERNAL SHOCKS
AND A MILDLY MAGNETIZED EXTERNAL REVERSE SHOCK
Y. Z. Fan,1,2,3Bing Zhang,3and D. M. Wei1,2
Received 2005 April 6; accepted 2005 June 9; published 2005 July 6
ABSTRACT
Very early optical and near-infrared emission was discovered to have accompanied the long gamma-ray burst
GRB 041219a. Here we show that the optical-IR flash tracking the gamma-ray light curve during the prompt
emission can be understood as emission from neutron-rich internal shocks, as has been suggested by Fan & Wei.
The early Ks-band afterglow light curve after the prompt phase can be well modeled as the superposition of a
reverse and a forward shock component. The radio data also support the reverse-shock interpretation.
Subject headings: gamma rays: bursts— ISM: jets and outflows—radiation mechanisms: nonthermal
1. INTRODUCTION
GRB 041219a was detected by both the IBIS detector on the
International Gamma-Ray Astrophysics Laboratory satellite
(Gotz et al. 2004) and the Swift Burst Alert Telescope (BAT)
(Barthelmy et al. 2004). This burst distinguishes itself from
other bursts in several respects: (1) It was very bright. The 15–
350 keV fluence measured by the Swift BAT wasapproximately
1.55#10?4ergs cm?2(Barthelmy et al. 2004), placing it in
the top few percent among the 1637 GRB events listed in the
comprehensive fourth Burst and Transient Source Experiment
catalog (Paciesas et al. 1999). (2) The duration of the prompt
g-ray emission (T90) was approximately 520 s, making it one
of the longest bursts ever detected. (3) Prompt optical and
infrared emission was found to accompany the prompt g-ray
emission (Vestrand et al. 2005; Blake et al. 2005). This is the
first such case since GRB 990123 (e.g., Akerlof et al. 1999).
(4) The location of this burst is near the Galactic plane and in
a direction with high optical extinction (Galactic coordinates
l p120?, b p ?0? .1), so the R-band extinction is very large
(∼4.9 mag or even larger). For this reason, no late optical after-
glow was detected. Fortunately, in the IR band the afterglow
(including that in the very early phase) has been well detected
(Blake et al. 2005). The redshift is unknown. In what follows,
we assume z p1.
The very early long-wavelength observation is very impor-
tant for diagnosing the composition of the outflow (Fan et al.
2004; Zhang & Kobayashi 2005; Fan et al. 2005),4since the
late afterglow, taking place hours after the burst trigger, is
powered by the forward shock, so that essentially all the initial
information about the ejecta is lost. In this Letter, we apply
our previous analyses to discuss the veryearlylong-wavelength
observation of GRB 041219a.
2. THE PROMPT OPTICAL AND NEAR-INFRARED FLASH
There was some interest in discussing and searching for
prompt long-wavelength radiation accompanying prompt g-ray
1Purple Mountain Observatory, Chinese Academy of Sciences, 2 West
Beijing Road, 210008 Nanjing, China.
2National Astronomical Observatories, Chinese Academy of Sciences,
20A Datun Road, 100012 Beijing, China.
3Department of Physics, University of Nevada, Las Vegas, 4505 Maryland
Parkway, Las Vegas, NV 89154-4002.
4In principle, the ejecta of GRBs may be Poynting flux–dominated (see
Lyutikov & Blandford 2003 and references therein), neutron-rich (e.g., Deri-
shev et al. 1999; Beloborodov 2003; Pruet et al. 2003), or both (e.g., Vlahakis
et al. 2003).
emission even in the pre-afterglow era (e.g., Katz 1994; Schae-
fer et al. 1994; Wei & Cheng 1997). In the afterglow era, more
theoretical attention has been paid to the topic. In the standard
internal-shock model, long-wavelength flashes are expected to
accompany the prompt g-ray emission (Me ´sza ´ros & Ress1997,
1999; Fan & Wei 2004a). If there is a large amount of neutrons
contained in the GRB outflow, the decayed-neutron shells will
provide more collisions at a larger distance from the central
engine. If a burst is long enough, the neutron-rich internal
shocks will give rise to detectable long-wavelength flashesdur-
ing the prompt g-ray emission phase (Fan & Wei 2004b).
In the standard internal-shock model, the synchrotron self-
absorption frequency can be estimated as na∼ 7#1016L2/7
#
RB
[2/(1? z)] Hz (e.g., Li & Song 2004), where
Gm,2.5 int,134
Lsynis the synchrotron radiation luminosity, Gmis the bulk
Lorentz factor of the two merged shells, Rint∼ 2
is the typical internal-shock radius with dt the observedvariable
timescale of the prompt g-ray light curve, B?is the comoving-
frame magnetic field strength in the internal-shock phase, and
the convention Qxp Q/10xhas been adopted in cgs units here
and throughout. For typical GRB parameters, one can see that
nais usually well above the optical band. This tends to suppress
the optical flux. Also, the Fnspectrum is expected to have a
power-law index 5/2, inconsistent with the prompt IR data on
GRB 041219a (see Fig. 2 of Blake et al. 2005). Although, with
the proper adjustment of parameters, the proton-dominated
internal shock models may be able to match the observation,
in this Letter we focus on an alternative interpretation, that is,
the neutron-rich internal shock model (Fan & Wei 2004b).
There are good reasons to assume that large amounts of
neutrons (comparable to the amount of protons) exist in GRB
ejecta (see, e.g., Derishev et al. 1999; Beloborodov et al. 2003;
Pruet et al. 2003). In the neutron-rich internal shock model,
the Lorentz factors (LFs) of the proton shells are variable, and
so are the LFs of the accompanying neutron shells. The slow
neutrons (with Gn,sp 50) coupled with slow proton shells do
not interact with other materials before decaying [the typical
b-decay radius is ∼(900 s)cGn,sp1.3#1015cm, where c is the
speed of light]. However, if the GRB lasts long enough, the
slow neutron shells ejected at earlier times will be swept
successively by the faster proton shells ejected at later times.
This happens over a distance range of ∼1013to several times
1015cm, in which the slow neutron shells decay continuously.
The proton shells interact with the b-decay products of the
slow neutron shells and power detectable long-wavelength
prompt emission, as shown in Fan & Wei (2004b).
syn,52
3/7
?4/7
?1/7
cdt/(1? z)
2
Gm

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L26FAN, ZHANG, & WEIVol. 628
Fig. 1.—Long-wavelength emission (the observer frequency has been
marked) powered by a proton shell interacting with the decay products of a
series of slow neutron shells as a function of time (similar to Fig. 2 of Fan
& Wei 2004b). The following parameters are adopted: Mpp 3.7#1026g,
M p1026g, Gmp 600, Gn, sp 50, dt p10?2(1? z) s, DLp 2.2#1028cm,
n
?ep 0.3, ?Bp 0.1, Lgp1052ergs s?1, and
should include the contributions from many proton shells.
0
p 250 keV. The real light curve
beg
A detailed treatment of the process has been presented in
§ 2 of Fan & Wei (2004b). A novel effect taken into account
here is the inverse Compton cooling of the electrons due to
the spacetime overlap between the proton shell–neutron shell
interaction region and the prompt MeV g-ray photon flow (see,
e.g., Beloborodov 2005; Fan et al. 2005). The inverse Compton
(IC) parameter is calculated as Y p PIC/Psyn, where PICis the
energy-loss rate of one electron by means of IC scattering with
the prompt g-ray emission and Psynp (4/3)jT(
energy-loss rate of one electron by means of synchrotron ra-
diation, with jTthe Thomson cross section, gethe random
Lorentz factor of the emitting electron, and UBthe magnetic
energy density generated during the interaction. Since the
Klein-Nishina correction is important for the IC process dis-
cussed here, we strictly use equations (2.47)–(2.51) and (2.56)
from Blumenthal & Gould (1970) to calculate PIC. The pho-
ton number distribution of the prompt g-rays is taken to be
n p n (eg/ )?3/2for/50 ! eg!
ee
eegg
gg
for
! eg! 50 , where
∼ 250 keV is the peak energy of
the observed spectrum5and n
eg
tion
n egdegp Ug, with Ug≈ Lg/4pR2g2c the initial g-ray
photon energy density, g the evolving bulk LF of the proton
shell during the sweeping process,6and Lgthe prompt g-ray
luminosity.
We calculated the synchrotron light curves for a proton shell
interacting with the decay products of a series of slow neutron
shells. The result is shown in Figure 1. The following param-
eters were adopted: Mpp 3.7#1026g is the rest mass of
one proton shell; M p1026g is the initial rest mass of one
n
neutron shell; Gmp 600; Gn,sp 50 (with these parameters, we
obtain g ? 300 at the end of the interaction; this will be re-
garded as the initial Lorentz factor in the afterglow phase, and
we rewrite it as h in § 3—this matches the value found in our
modeling of the early Ks-band afterglow [see § 3]); dt p10?2
#(1? z) seconds; DLp 2.2#1028cm is the luminosity dis-
tance; Lgp 1052ergs s?1; and ?ep 0.3 and ?Bp 0.1 are the
fraction of shock energy given to the shocked electrons and
the magnetic field, respectively. The light curves peak as the
observed frequency nobscrosses the synchrotron self-absorption
frequency na, and another break during the decay phase marks
the epoch when nobscrosses the typical synchrotron radiation
frequency. The nais much smaller than that in the standard
internal-shock model, for the following reasons: First, we have
R k Rint. Second, the forward-shock upstream proton number
density is much smaller than that in standard internal shocks
(see eq. [1] of Fan & Wei 2004b for details), which results in
a smaller B?and weaker synchrotron emission. Finally, with
the effect of IC cooling taken into account, and since syn-
chrotron emission is weaker, the Y-parameter is large, by some
tens to hundreds with the typical parameters. The synchrotron
radiation luminosity is further lowered by a factor 1/Y.
The detected flux should be the integrated emission powered
by a series of proton shells interacting with the decay trail
of slow neutron shells. For nobsp (1.4, 1.8, 2.2, 4.3, 10.0)#
1014Hz, the predicted fluxes are 18.8, 21.2, 23.3, 26.3, and
27.2 mJy, respectively. Such strong emission is detectable with
current telescopes and is consistent with the optical observation
of GRB 041219a when the extinction correction is taken into
account (Vestrand et al. 2005). The averaged spectrum is flat,
?1)UBc isthe
2
ge
and n p n (eg/ )?2.25
e
g
bbb
g
b
g
ee
bb
g
e
b
g
b
g
b
g
eee
is constrained by the condi-
b
∫
eg
0
5Given the same
photon spectral indices assumed.
6Note that we have adopted the same symbols as in Fan & Wei (2004b)
to maintain consistency between the two papers.
, the calculated results are not very sensitive to the
beg
which is roughly consistent with the earliest IR-band obser-
vation of GRB 041219a (Blake et al. 2005). As mentioned in
Fan & Wei (2004b), the predicted long-wavelength emission
is expected to be correlated with the prompt g-ray emission
but to have a ∼10(1? z)
with the tracking behavior of the prompt optical flashes (Ves-
trand et al. 2005). Note that it is not our intention to fit the
prompt opticalandnear-IRemissionlightcurvesclosely(which
requires additional complicated assumptions about the central
engine’s behavior). The main purpose of the current discussion
is to indicate that the neutron-rich internal shock model suffers
fewer constraints than the proton-dominated internal shock
model and can better account for the observed prompt optical-
IR spectrum.
s lag. This is also consistent
?1
Gn,s,1.7
3. THE VERY EARLY NEAR-INFRARED AFTERGLOW
After the internal-shock phase, as the fireball is decelerated
by the circumburst medium, a pair of shocks usually develops
(Me ´sza ´ros & Rees 1997; Sari & Piran 1999). The early optical
afterglow light curve is usually composed of the contributions
from both the forward and the reverse shock. Zhang et al.
(2003) pointed out that, depending on parameters, there are
two types of early optical-IR lightcurvefor afireballinteracting
with a constant-density interstellar medium (ISM), that is,
type I (rebrightening), in which distinct reverse-shock and
forward-shock peaks are detectable, and type II (flattening), in
which the forward-shock (FS) peak is buried beneath the
reverse-shock (RS) peak. The previous two strong cases of RS
emission (GRB 990123, Akerlof et al. 1999; GRB 021211, Fox
et al. 2003 and Li et al. 2003) all belong to type II. Visual
inspection of the early IR light curve of GRB 021219a (Blake
et al. 2005; see also Fig. 2) indicates that it is a clear type I
case. Below we will model the light curve in detail and show
that the data are indeed consistent with such an explanation.
Following the standard afterglow model for a fireball
interacting with a constant-density medium (e.g., Piran 1999),
we write the cooling frequency
frequency, and the maximum spectral flux F
nm
, the typical synchrotron
fnc
of the
ff
n,max

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No. 1, 2005NEUTRON-RICH INTERNAL SHOCKS IN GRB 041219aL27
Fig. 2.—Modeling the Ks-band afterglow data of GRB 041219a. The data
are taken from Blake et al. (2005). The earliest data are prompt emission,
which is not included in our fit. The dash-dotted line is the theoretical light
curve. Both the reverse-shock and the forward-shock emission components
are included. The best-fit parameters are listed.
FS emission:
p1.8#1013E
n
m
F
p 83Eiso,54
n,max
7(p ? 2)/[2(p ?1)], Eisois the isotropic energy of the outflow,
?eand ?Bare the fractions of the shock energy giventoelectrons
and to magnetic fields in the forward shock, respectively, n is
the number density of the external medium, and p ∼ 2.4 is the
power-law distribution index of the shocked electrons. Here-
after t p tobs/(1? z) denotes the observer’s time corrected for
the effect of cosmological time dilation and tdis in units of
days. The superscripts “f ” and “r” denote the FS and RS emis-
sion, respectively. We assume that ?eand the electron spectral
index p are essentially the same for both the FS and RS,7but
we will allow different ?B-values for both regions. One reason
for this assumption is that the magnetic field generated in the
internal-shock phase may have not been dissipated effectively
in a short time and would play a dominant role in the reverse-
shock region (Fan et al. 2004 and references therein). In this
Letter, we will write
p ?Band
?
B
ratio of the magnetic field in the RS emission region to that
in theFS emissionregion(Zhangetal.2003).Previousanalyses
have indicated that at least for some bursts (e.g., GRB 990123
and GRB 021211), the RS emission region is more magnetized
than the FS region (e.g., Fan et al. 2002; Zhang et al. 2003;
Kumar & Panaitescu 2003).
As shown in Figure 2 (data taken from Blake et al. 2005;
only the richest Ks-band data are plotted), the time when the
RS crosses the ejecta [(1? z)t#] is about 30 minutes after the
trigger, which is much longer than T90∼ 520 s. So, the RS is
nonrelativistic (see, e.g., Sari & Piran 1995; Kobayashi 2000;
Kobayashi & Zhang 2003). Further evidence for a nonrelativ-
istic RS is the rapid increase of the early afterglow light curve
(e.g., Kobayashi 2000; Kobayashi & Zhang 2003). The LF
of the decelerated outflow relative to the initial LF at t#,
g34,#≈ (h/G#? G#/h)/2, can be estimated by solving c dt/dD ≈
(1?
){1? h/[G3(4g34? 3)]}/(
b
G
3
Sari & Piran 1995; Fan et al. 2004). Here G3is the bulk LF of
the shocked ejecta, h is the initial bulk LF of the outflow, G#
is the LF of the decelerated ejecta at t#, and bAis the corre-
sponding velocity (in units of c) of the LF GA. For GRB
041219a, one has t#∼ 4T90/(1? z), so that g34,#?1 is much
smaller than 1, that is, the RS is nonrelativistic. In such a case,
t#can be approximated as
p1.4#1014E
1/2 1/2
?
iso,54
B,?2
n
?
x
B,?2
n t
0
[2/(1? z)] Hz,
Hz,
f
?1/2
iso,54
t
[(1? z)/2] mJy, where Cpp
L,28.34
?3/2
?
B,?2
C [2/(1? z)]
p
?1 ?1/2
d
n
c
and
f
2
e,?0.5 d
D
2
?3/2
?
f
?2
1/21/2
0
p
?B, where RBis the
fr
B
2
B
?
R
?
) numerically (e.g.,
bb
hG
3
1/3
iso,54
?1/3
0
?8/3
2.5
t ≈ 64En
h
s.(1)
#
The typical frequency of the RS emission is
r
2
f
2
n (t ) p R (g
?1) n (t )/(G ?1) ,
m
#
(2)
m
#
B
34,##
Following Zhang et al. (2003), we have
r
?3
B
frf
n ≈ R n ,
F
(t ) ≈ hR F
(t ).
#
(3)
cc
n,max
#
B
n,max
Generally, the Ks-band flux satisfies F
(t#)]?(p?1)/2.
Assuming z p1, p p 2.4, and Eiso,54p1 (consistent with
the g-ray fluence and our assumed redshift), ?e, n, and h can be
constrained by the following two conditions: (1) at td∼ 0.14,
≈ F
(t#)[/
r
n
nn,max
K
Ks
s
rnm
7If they are different, additional corrections are needed; see Zhang et al.
(2003) and Zhang & Kobayashi (2005) for details.
∼
, and F
∼ 0.6 mJy; (2) t#is about 30/(1? z)minutes.
ff
n
We then find
n
mK
n,max
s
?1/4
B,?2
?5 ?11/8
B,?2
? ∼ 0.2?
,
n ∼ 5#10 ?
,
h ∼ 380?
. (4)
eB,?2
It is interesting to see that since ?e! 1, we have ?B1 1.6#
10?5, n ! 3#10?2cm?3, and h 1 170. The parameter RBcan
be constrained by noting that F ((1? z)t#) ∼ 2.4 mJy and tak-
ing h ∼ 380, which yields
R ∼ 3[(g
hinting that the reverse-shock region is mildly magnetized.
Following Fan et al. (2005), the forward-reverse shockemis-
sion has been calculated numerically. Since the RS is non-
relativistic, the spreading of the ejecta (see, e.g., Piran 1999)
has been taken into account. The fits to the Ks-band data are
presented in Figure 2. We find that the data can bewellmodeled
with the following parameters: z p1, Eiso,54p1, ?ep 0.45,
?Bp 0.01, RBp 2.8, h p 300, and n p 10?4cm?3. These are
consistent with the analytical estimates above.
There are three radio datapointsavailable(Soderberg&Frail
2004; van der Horst et al. 2004a, 2004b). The 8.5 GHz flux
at 1.1 days is 0.45 mJy, and the 4.9 GHz flux at 1.6 and
2.6 days is 0.2 and 0.34 mJy, respectively. By taking our best-
fitting parameters, the corresponding FS fluxes are ∼0.04,
∼0.04, and ∼0.05 mJy, respectively, too low to interpret the
data. When we consider the RS contribution to the radio band
(see, e.g., Sari & Piran 1999; Kobayashi & Zhang 2003; Gou
et al. 2004), the overall corresponding fluxes become ∼0.60,
∼0.37, and ∼0.18 mJy, respectively, roughly matching the data.
Therefore, the radio data also support the reverse-forward
shock interpretation.
nKs
?14/17
?1)/0.2], (5)
B
34,#
4. SUMMARY AND DISCUSSION
The prompt optical-IR observations of GRB 041219a (Ves-
trand et al. 2005; Blake et al. 2005) offer a great opportunity
to diagnose the unknown composition of GRB ejecta. We have
shown that the prompt optical emission trackingtheg-rayemis-

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L28FAN, ZHANG, & WEIVol. 628
sion profile may be consistent with a picture in which the ejecta
is neutron-rich and the optical emission is powered by the
proton shells interacting with the neutron decay products at a
distance farther away from the central engine than the typical
internal-shock radius.
By modeling the Ks-band early afterglow light curve, we
identify a reverse-shock emission component, which is clearly
separated from the forward-shock emission component. Such
a rebrightening (type I) light curve was expected by Zhang et
al. (2003) to be more common if the RS is not strongly mag-
netized. Indeed, detailed modeling indicates that RBin GRB
041219a is, at most, mild, in contrast with GRB 990123 and
GRB 021211 (e.g., Fan et al. 2002; Zhang et al. 2003; Kumar
& Panaitescu 2003). This is also consistent with the neutron-
rich picture conjectured in interpreting the prompt opticalemis-
sion. The mild magnetization of the ejecta may be due to mag-
netic field generation during theinternal-shockphase.Theradio
data also support our reverse-forward shock interpretation.
It is interesting to note that for the three bursts with reverse-
shock identifications (GRB 990123, 021211, and 041219a), the
inferred number densities of the ISM are typically lower than
the standard value of n ∼ 1 cm?3(see also Kumar 2004): for
GRB 990123, n ∼ 10?3cm?3(e.g., Wang et al. 2000; Panaitescu
& Kumar 2002; Nakar & Piran 2004); for GRB 021211, n ∼
10?3to 10?2cm?3(e.g., Wei 2003; Kumar & Panaitescu 2003);
and for the current GRB 041219a, n ∼ 10?4cm?3. The reason
is unclear, but certain selection effects may play a role.
We thank L.-J. Gou and X.-F. Wu for helpful discussions,
and the referee for valuable comments. This work was sup-
ported by NASA grant NNG04GD51G and the NASA Swift
Guest Investigator (Cycle 1) program (B. Z.), the National
Natural Science Foundation of China (grants 10073022,
10225314 and 10233010), and the National 973 Project on fun-
damental research in China (NKBRSF G19990754) (D. M.W.).
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