The puzzling case of GRB 990123: prompt emission and broad-band afterglow modeling

Abstract

We report on BeppoSAX simultaneous X- and gamma-ray observations of the bright GRB 990123. We present the broad-band spectrum of the prompt emission, including optical, X- and gamma-rays, confirming the suggestion that the emission mechanisms at low and high frequencies must have different physical origins. In the framework of the standard fireball model, we discuss the X-ray afterglow observed by the NFIs and its hard X-ray emission up to 60 keV several hours after the burst, detected for about 20 ks by the PDS. Considering the 2-10 keV and optical light curves, the 0.1-60 keV spectrum during the 20 ks in which the PDS signal was present and the 8.46 GHz upper limits, we find that the multi-wavelength observations cannot be readily accommodated by basic afterglow models. While the temporal and spectral behavior of the optical afterglow is possibly explained by a synchrotron cooling frequency between the optical and the X-ray energy band during the NFIs observations, in X-rays this assumption only accounts for the slope of the 2-10 keV light curve, but not for the flatness of the 0.1-60 keV spectrum. Including the contribution of Inverse Compton (IC) scattering, we solve the problem of the flat X-ray spectrum and justify the hard X-ray emission; we suggest that the lack of a significant detection of 15-60 keV emission in the following 75 ks and last 70 ks spectra, should be related to poorer statistics rather than to an important suppression of IC contribution. However, considering also the radio band data, we find the 8.46 GHz upper limits violated. On the other hand, leaving unchanged the emission mechanism requires modifying the hydrodynamics by invoking an ambient medium whose density rises rapidly with radius and by having the shock losing energy. Thus we are left with an open puzzle which requires further inspection. Comment: Revised version, minor changes in Table 1 and Fig. 2; 21 pages including 6 figures, 4 tables. Accepted for publication in A&A. The Appendix will be available only on the electronic version of the journal

Full text

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arXiv:astro-ph/0504607v2 22 Jun 2005
Astronomy & Astrophysics manuscript no. 2532
(DOI: will be inserted by hand later)
February 2, 2008
The puzzling case of GRB 990123: prompt emission and
broad-band afterglow modeling
A. Corsi1,2, L. Piro1, E. Kuulkers3, L. Amati4, L.A. Antonelli5, E. Costa1, M. Feroci1, F. Frontera4,6, C. Guidorzi6,
J. Heise7, J. in ’t Zand7, E. Maiorano4,8, E. Montanari6, L. Nicastro9, E. Pian10, and P. Soffitta1.
1IASF-CNR, Via Fosso del Cavaliere 100, I-00133 Rome, Italy.
2University “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Rome, Italy.
3ESA-ESTEC,ScienceOperations &DataSystems Division, SCI-SDG,Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands.
4IASF-CNR, Via Gobetti 101, I-40129 Bologna, Italy.
5Rome Astronomical Observatory, Via di Frascati 33, I-00044 Rome, Italy.
6Physics Department, University of Ferrara, Via Paradiso 11, I-00044 Rome, Italy.
7Space Research Organization Netherlands, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands.
8Astronomy Department, University of Bologna, Via Ranzani1, I-40126 Bologna, Italy.
9IASF-CNR, Via Ugo la Malfa 153, I-90146 Palermo, Italy.
10INAF, Osservatorio Astronomico di Trieste, Via G.B. Tiepolo, 11 - I-34131 Trieste, Italy.
Abstract. We report on BeppoSAX simultaneous X- and γ-ray observations of the bright γ-ray burst (GRB) 990123. We
present the broad-band spectrum of the prompt emission, including optical, X- and γ-rays, confirming the suggestion that the
emission mechanisms at low and high frequencies must have different physical origins. In the framework of the standard fireball
model, we discuss the X-ray afterglow observed by the Narrow Field Instruments (NFIs) on board BeppoSAX and its hard X-
ray emission up to 60 keV several hours after the burst, detected for about 20 ks by the Phoswich Detection System (PDS).
Considering the 2 − 10 keV and optical light curves, the 0.1 − 60 keV spectrum during the 20 ks in which the PDS signal
was present and the 8.46 GHz upper limits, we find that the multi-wavelength observations cannot be readily accommodated by
basic afterglow models. Whilethe temporal and spectral behavior of the optical afterglow ispossibly explained by a synchrotron
cooling frequency between the optical and the X-ray energy band during the NFIs observations, in X-rays this assumption only
accounts for the slope of the 2 − 10 keV light curve, but not for the flatness of the 0.1 − 60 keV spectrum. Including the
contribution of Inverse Compton (IC) scattering, we solve the problem of the flat X-ray spectrum and justify the hard X-ray
emission; we also suggest that the lack of a significant detection of 15 − 60 keV emission in the following 75 ks and last 70 ks
spectra, should be related to poorer statistics rather than to an important suppression of IC contribution. However, considering
also the radio band data, we find the 8.46 GHz upper limits violated. On the other hand, leaving unchanged the emission
mechanism requires modifying the hydrodynamics by invoking an ambient medium whose density rises rapidly with radius and
by having the shock losing energy. Thus we are left with an open puzzle which requires further inspection.
Key words. gamma rays: bursts – X-rays: bursts – radiation mechanisms: non-thermal
1. Introduction
GRB 990123 was one of the brightest γ-ray bursts detected by the BeppoSAX satellite; it was also observed by the Burst and
Transient Source Experiment(BATSE) on-boardthe Compton Gamma-Ray Observatory(CGRO) as trigger # 7343 (Briggs et al.
1999). The Gamma-Ray Burst Monitor (GRBM) was triggered by GRB 990123 on 1999 January 23.40780 UT, approximately
18 s after the CGRO trigger. The burst was simultaneously detected near the center of the field of view in Wide Field Camera
(WFC) unit 1 (Feroci et al. 1999); the WFC “quick look” localized the burst within a radius of 2 arcmin (99% confidence level).
With a redshift of z = 1.6004 and a luminosity distance of 3.7 × 1028cm (Kulkarni et al. 1999a), a γ-ray (40 − 700 keV)
fluence of Fγ= (1.9 ± 0.2) × 10−4ergs cm−2implies an isotropic energy release in γ-rays alone of about 1.2 × 1054ergs (see
also Briggs et al. 1999; Kulkarni et al. 1999a). GRB 990123 would have been notable even just for this reason. Furthermore, it
was the first burst from which simultaneous γ-ray, X-ray and optical emission was detected. The prompt announcement of the
burst position resulted in intensive multi-wavelength follow-up observations that brought a wealth of new results: the discovery
of prompt optical emission (Akerlof et al. 1999), the detection of short lived radio emission (Kulkarni et al. 1999b), the first
Send offprint requests to: A. Corsi – Alessandra.Corsi@rm.iasf.cnr.it

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2A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
observation of a clear break in the optical afterglow light curve (Kulkarni et al. 1999a; Fruchter et al. 1999; Castro-Tirado et al.
1999; Holland et al. 2000), the first constraint on the polarization of a GRB afterglow (Hjorth et al. 1999).
We refer the reader to the paperof Maiorano et al. (2005) for the completeanalysis of the multi-wavelengthafterglowdata. In
this paper we present the BeppoSAX GRBM and WFC observations of the γ- and X-ray prompt event of GRB 990123 (section
2.1) and analyze the spectral properties of its X-ray afterglow (section 2.2). We discuss the observed prompt and afterglow emis-
sion comparing them with the predictions of the “forward plus reverse shock” standard model. While the broad-band spectrum
of the burst confirms a reverse shock origin of the optical flash (section 3.1), the multi-wavelength afterglow cannot be readily
explained by basic models (section 3.2). Errors on the parameters will be given at 90% confidence level (∆χ2= 2.7 for a one
parameter fit).
2. The observations
2.1. The prompt event
The burst was detected by the BeppoSAX GRBM and WFC. The GRBM (Amati et al. 1997; Feroci et al. 1997) consists of the
4 anti-coincidence shields of the Phoswich Detection System, PDS (Frontera et al. 1997; Costa et al. 1998) and it operates in the
40− 700 keV energy band. The normal directions of two GRBM shields are co-aligned with the viewing direction of the WFCs.
The WFCs (Jager et al. 1997) consist of two identical coded aperture cameras, each with a field of view of 40◦× 40◦full-width
to zero response and an angular resolution of about 5′. The bandpass is 2 keV to 28 keV. The spectral resolution is approximately
constant over the bandpass at 20% FWHM. In Fig. 1 the time profile of the burst is shown in various band-passes. The γ-ray
signal is detected for about 100 s with the GRBM (Fig. 1, bottom panel); it presents two major pulses, the brighter of which has
a peak intensity of (1.7 ± 0.5) × 10−5ergs cm−2s−1between 40 − 700 keV. The total fluence between 40 keV and 700 keV is
(1.9 ± 0.2) × 10−4ergs cm−2; this value improves the one given in Amati et al. (2002).
The burst profile at lower energies (2 − 10 keV and 10 − 25 keV) as measured by the WFC is shown in the top panels of
Fig. 1. Near the end of the measurement the WFC was pointingclose to the Earth horizon. Since the atmosphericabsorption then
plays an important role, the low-energyX-ray light curve was particularly affected: at 80 s after the trigger the Earth-atmospheric
absorption is about 30% at 5 keV and the subsequent decay in the X-ray curve is partially due to the atmosphere. The portion
of the light curve where more than 10% of the intensity is lost due to this effect is indicated by a dotted curve. The two X-ray
light curves end when GRB 990123 sets below the Earth horizon. Note that the GRBM light curve is not influenced by the Earth
atmosphere. The structure in the first 80 s of the X-ray light curves indicates a softening of each pulse, together with an increase
in duration with decreasing energy. As remarked by Briggs et al. (1999) and by Frontera (2004), during the first two pulses the
hardness of the GRB is correlated with the intensity. After the second pulse, a hard-to-soft evolution, typical of most GRBs, is
seen. In the 2−25 keV and 2−10 keV energy bands, the fluence is (7.8±0.4)×10−6ergs cm−2and (3.1±0.3)×10−6ergs cm−2,
respectively; these estimates must be considered as a lower limits due to the eclipse discussed above.
The model fitting of the data is done using the standard forward-folding technique (Briggs 1996): in each instrument we
assume a photon model and convolve it through a detector model to obtain a model count spectrum. The model count spectrum
is compared with the observed count spectrum and the photon model parameters are optimized so to minimize a χ2statistic. The
νfνdata points are then calculated by scaling the observed count rate in a given channel by the ratio of the photon to count model
rate for that channel; this ratio, and therefore the photon data points, are model dependent.
The spectrum of the burst can be modeled by using the smoothly broken power-law proposed by Band et al. (1993), whose
parameters are the low energy index η1, the break energy E0, the high energy index η2. If we express E and E0in keV, the Band
function has the following expression:
N(E) ∝
?
E
100 keV
?η1
× exp
?
−E
E0
?
(1)
for E ≤ (η1− η2) × E0, and:
N(E) ∝
?(η1− η2) × E0
100 keV
?η1−η2
× exp(η2− η1) ×
?
E
100 keV
?η2
(2)
for E ≥ (η1− η2) × E0. In the case of GRB 990123, the best fit values for the 2 − 700 keV integrated spectrum of the burst
are: η1 = −0.89 ± 0.08, η2 = −2.45 ± 0.97 and E0 = 1828 ± 84 keV (Amati et al. 2002), where E0is expressed in the GRB
cosmological rest-frame; at a redshift of z = 1.6, it corresponds to an observed value of E0= 703 ± 32 keV.
Using the Band function as the model spectrum, we performed a spectral fitting of the WFC and GRBM data at the epochs
of the detection of the prompt optical emission (Akerlof et al. 1999), indicated in the lower panel of Fig. 1. In Fig. 2 we plot the
time resolved X- to γ-ray spectra and the three ROTSE data points; in Table 1 we report the fluxes and the best fit spectral indices
in the WFC and GRBM.
Since the value of E0derived from the 2 − 700 keV integrated spectrum is consistent with being above the energy range
of the GRBM channels, we set the high energy spectral index η2equal to its best fit value for the mean spectrum, η2= −2.45

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A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 9901233
Fig.1. Prompt burst profile of GRB 990123 at X-ray (WFC: 2–10 keV and 10–25 keV) and at γ-ray (GRBM: 40–700 keV)
energies. Count rate (counts s−1) is given as a function of time after the GRBM trigger, i.e. 1999, Jan 23, 09:47:14 UT. Since
the X-ray burst was close to the Earth horizon, atmospheric absorption plays an important role. At 80 s after trigger the Earth-
atmospheric absorption is about 30% at 5 keV and the subsequent decay is partially due to the atmosphere. The dotted line refers
to the part where we loose more than 10% of the intensity due to this effect. The two X-ray light curves end when GRB 990123
sets below the Earth horizon. Note that the γ-ray light curve is not influenced by the Earth atmosphere. Typical error bars are
given in the left part of the panels. Indicated in the bottom panel are the time of the BATSE trigger and the prompt optical
measurements (ROTSE, Akerlof et al. 1999).
(Amati et al. 2002); the values we find for E0in the three time intervals are reported in Table 1. As can be seen in Fig. 2, the
spectrum of the burst shows a hard to soft evolution; the spectral photonindex for the first ROTSE exposureis η1= −0.57±0.06,
harder than the subsequent values of η1= −0.95 ± 0.09 and η1= −1.0 ± 0.1, for the second and last time intervals, respectively.
We find no evidencefor an X-ray excess duringthe first ROTSE observation,as suggestedby Briggs et al. (1999). In fact, our
value for the low-energy spectral index is consistent with η1= −0.63 ± 0.02, found by Briggs et al. (1999) analyzing the 10 keV
to 10 MeV spectrum (see Fig. 3 of Briggs et al. 1999): from the presence of an X-ray excess below 10 keV, we would expect
to find η1< −0.63 for ν < 10 keV, in contrast with our results. Moreover, performing a spectral fit by using a simple power-law
and considering only the WFC data at energies below 10 keV, yields a best fit photon index of −0.44 ± 0.28, consistent with the
spectral index we find for the overall spectrum.

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4A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
Fig.2. Simultaneous multi-wavelength spectra derived at three times during the burst (ROTSE V band, X-ray and γ-ray, see also
Table 1). The ROTSE data points have been connected with a line to the best fit model at 2 keV to guide the eye. The solid line
connects the points relative to the first ROTSE observation, the dashed line those relative to the second ROTSE observation and
the dashed-dotted line those relative to the third one. The correspondingtimes of the spectra are given in Table 1 in seconds after
the GRBM trigger. The data relative to the first (third) time interval have been shifted up (down) of a factor 1000.
Table 1. Fluxes and photon indices of GRB 990123 prompt emission measured during the first three ROTSE exposures
(Akerlof et al. 1999).
X-ray and γ-ray data simultaneously with ROTSE
Photon index
η1
11.70 ± 0.07
−0.57 ± 0.06
8.86 ± 0.02
−0.95 ± 0.09
9.97 ± 0.03
−1.0 ± 0.1
starta
s
4.38
29.58
54.87
endb
s
9.38
34.58
59.87
mv
E0
keV
2–10 keV flux
10−8ergs cm−2s−1
3.2
5.7
4.8
40–700 keV flux
10−6ergs cm−2s−1
7.3
1.3
1.2
530+1600
−230
180+90
250+160
−40
−70
aStart time since GRBM trigger.
bend time since GRBM trigger.
2.2. The X-ray afterglow.
The BeppoSAX follow-up observation lasted from 1999 January 23.65 UT until January 24.75 UT. A previously unknown,
bright X-ray source designated as 1SAX J1525.5+4446(Heise et al. 1999), was detected by the LECS and MECS units, at right
ascension α = 15 h 25 m 31 s and declination δ = +44◦46′.3 (equinox 2000), with an error-circle radius of 50′′. Within 22′′
of this position, Odewahn et al. (1999) detected a fading optical transient (OT) at magnitude R=18.2. During the first 10 min,

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A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 9901235
Table 2. Fit results for GRB 990123 X-ray afterglow. βXand βIC
component, respectively (see equation (5)); the galactic hydrogen column density NHis fixed to its value at the burst position,
NH = 2.1 × 1020cm−2; Nz
the degrees of freedom dof. Case [1] refers to a single power-law model spectrum with variable spectral index; case [2] refers
to the same model spectrum of case [1], but with a fixed spectral index βX = −1.23 (see Fig. 3); case [3] refers to a single
power-law model spectrum with the fit performed only on the LECS and MECS data points (PDS data excluded); case [4] is the
synchrotron plus IC model spectrum, with the spectral index of the synchrotron component fixed at βX= −1.23 and the one of
the IC componentat βIC
0
in [1], [2], [3] and at 2 keV, in units of µJy, in [4].
Xare the spectral energy indices for the synchrotron and the IC
His the hydrogen column density locally to the GRB site (in units of 1022cm−2); χ2is reduced for
X= −0.73(see Fig. 5 and Fig. 6). Fsyn
and FIC
0are givenat 1 keV, in units of 10−3photonscm−2s−1keV−1,
First 20 ks of the NFIs observation
Fsyn
0
βIC
X
2.3 ± 0.30
4.1 ± 0.20
2.6 ± 0.30
0.15+0.15
−0.15
−0.73
βX
FIC
0
0
0
0
Nz
H
χ2
1.3
2.1
1.2
1.3
dof
26
27
25
26
[1]
[2]
[3]
[4]
−0.82 ± 0.10
−1.23
−0.89 ± 0.10
−1.23
0.42+0.88
3.9+0.9
−0.6
1.0+0.7
−0.8
0.45+1.8
−0.24
0.72+0.43
−0.15
−0.35
the 2 − 10 keV photon rate of 1SAX J1525.5+4446 in the MECS is (0.16 ± 0.02) count s−1, corresponding to (1.38 ± 0.14) ×
10−11erg cm−2s−1.
The 2 − 10 keV flux steadily decreases with time following a power law decay FX(t) = FX(6 hr) × (t/6 hr)αXµJy, with
αX= −1.46±0.04(Maiorano et al. 2005). Here t is the time measured with respect to the γ-ray event.We refer to Maiorano et al.
(2005) for a complete description of the WFC, MECS and PDS data extraction and analysis relative to GRB 990123 light curves
in the 2 − 10 keV and 15 − 28 keV energy bands.
The observed fluence during the observations was 3.1× 10−7ergs cm−2(2− 10 keV) and 7.5× 10−7ergs cm−2(2− 60 keV).
Extrapolating to long times after the trigger (about 1000 s) this implies an X-ray afterglow energy fraction of at least ∼11% that
of the prompt X-ray emission (2 − 25 keV).
In the first 20 ks of the observation, between 1999 January 23.6498 UT and 1999 January 23.8813 UT, the total measured
photon rate in the PDS is (0.20 ± 0.05) count s−1, equivalent to (1.9 ± 0.5) × 10−11ergs cm−2s−1(15 − 60 keV). The possible
contamination by an X-ray source located in the MECS field has been analyzed by Maiorano et al. (2005). While its presence
affects the PDS data in the second and last part of the observation, it is comparatively negligible during the first 20 ks: for the
first time, an afterglow emission was detected at energies as high as 60 keV. In the following 75 ks and the last 70 ks of the
observation, the high energy tail of the afterglow emission (15 − 60 keV energy band) was not detected.
Since the first 20 ks of the observation are those in which we have the greater statistics and where the PDS signal is present,
we focus our attention on the spectrum of the burst relative to this first time interval. We fit the LECS (0.1 − 2 keV), MECS
(2−10 keV) and PDS (15−60 keV) data points during the first 20 ks of the observation, by using an absorbed power-law model
spectrum where we set NH= 2.1 × 1020cm−2, for the galactic hydrogen column density at the burst position, and account for
the effect of absorption locally to the GRB site by adding Nz
(1982) relative abundances.To providefor flux inter-calibrationwhen fitting simultaneouslythe LECS, MECS and PDS data, the
LECS/MECS andPDS/MECS normalizationratios have been variedin the range0.7−1 and 0.77−0.95,respectively(Fiore et al.
1999). The best fit value for the spectral index is βX= −0.82 ± 0.10 (see Table 2), consistent with the βX= −0.94 ± 0.12 found
by Maiorano et al. (2005) and obtained leaving unconstrained the range of values in which the normalizations ratio of the LECS
and PDS can vary, and considering the LECS data between 0.6 keV and 4 keV (see Fig. 3 of Maiorano et al. 2005).
Excluding the PDS data and fitting the only LECS and MECS points we get βX= −0.89 ± 0.10, which is not significantly
different from the previous result.
The best fit values for the spectral indices relative to the next 75 ks and to the last 70 ks of the LECS and MECS observation
are βX= −1.2 ± 0.2 and βX= −1.0 ± 0.2, respectively. These two values are consistent, within the errors, with the one obtained
during the first 20 ks, so they do not give any significant evidence of spectral evolution, in agreement with the results found by
Maiorano et al. (2005).
H(see Table 2). The NHwas modeled using the Anders & Ebihara
3. Discussion
3.1. The prompt event in the “forward plus reverse shock” standard model
The comparison of the optical, X-ray and γ-ray data presented in Fig. 2, shows that most of the energy is emitted in the γ-rays.
The extrapolation of the high energy time resolved spectra to optical frequencies falls at least 2 orders of magnitude below the
simultaneous optical measurements, indicating the presence of an unobserved break between the optical and X-ray bands. This
suggests different physical origins for the emission mechanism at low and high frequencies, confirming the idea of a reverse
shock origin for GRB 990123 optical flash (Sari & Piran 1999a; Galama et al. 1999; Briggs et al. 1999).

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6A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
Table 3. Closure relationships in the standard synchrotronfireball model and their correspondingvalues for βopt= −0.75±0.07,
βX= −0.82 ± 0.10, αopt= −1.1 ± 0.03 and αX= −1.46± 0.04.
νopt< νX< νc
[a] αopt− 3/2βopt= 0
0.02 ± 0.11
[b] αX− 3/2βX= 0
−0.23 ± 0.15
[c] αopt− αX= 0
0.360 ± 0.050a
[d] βopt− βX= 0
0.07 ± 0.12
νopt< νc< νX
[a] αopt− 3/2βopt= 0
0.02 ± 0.11
[b] αX− 3/2βX− 1/2 = 0
−0.73 ± 0.15b
[c] αopt− αX− 1/4 = 0
0.110 ± 0.050
[d] βopt− βX− 1/2 = 0
−0.43 ± 0.12c
aNot consistent with the expectations at the 7.2σ level.
bNot consistent with the expectations at the 4.9σ level.
cNot consistent with the expectations at the 3.6σ level.
The currentstandard modelfor γ-ray bursts and their afterglowsinvokesa “fireball” in relativistic expansion,probablywithin
a collimated structure (jet). The high energy burst is thought to be produced by internal shocks developing from collisions of
plasma shells with different velocities. When the outflow runs into the interstellar medium (ISM), it sweeps up the surrounding
gas and heats it. A reverse shock does the same to the ejecta. In these shocks, the accelerated electrons radiate via synchrotron
emission. The forward external shock, interacting with the ISM, produces the multi-wavelength afterglow.
Since the shocked region behind the reverse shock is denser and cooler than the region behind the forward shock, it can
radiate in the optical band (M´ esz´ aros & Rees 1997; Sari & Piran 1999b). Optical emission from the reverse shock is expected
to be detected during or soon after the high energy event (Sari & Piran 1999a), and was actually observed in GRB 990123
(Akerlof et al. 1999). Also the radio flare, observed at less than 3 d after the GRBM trigger, can be interpreted as radiation
from a reverse shock (Kulkarni et al. 1999b) rather than afterglow from a forward shock (Galama et al. 1999). The BeppoSAX
measurements of the prompt event agree with this scenario.
3.2. GRB 990123 afterglow
3.2.1. The optical to X-ray temporal and spectral indices in the standard fireball model
In the standard picture (Sari et al. 1998), for a spherical shock of energy E propagating into a surrounding medium of density n,
the afterglow emission Fν(t) scales as follows: for ν above the cooling frequency νc,
Fν(t) ∝ E(p+2)/4tανβ
(3)
with α = −3p/4 + 2/4 and β = −p/2 and, for ν < νc,
Fν(t) ∝ E(p+3)/4n1/2tανβ
(4)
with α = −3p/4 + 3/4 and β = −(p − 1)/2. Here p is the power-law index of the shocked electrons.
As we said in section 2.2, the afterglow light curve of GRB 990123 in the 2 − 10 keV energy band is well described by a
power law of index αX= −1.46 ± 0.04. During the first day, starting from 4.1hr after the burst, also the optical flux in the Gunn
r band decreases steadily, and can be described as Fr= 70× (t/6hr)αoptµJy with αopt= −1.10± 0.03, as found by Kulkarni et al.
(1999a); other authors give αopt = −1.12 ± 0.08 (Holland et al. 2000), αopt = −1.13 ± 0.02 (Castro-Tirado et al. 1999) and
αopt= −1.09 ± 0.05 (Fruchter et al. 1999), which are all consistent with the value of −1.10 ± 0.03 that we adopt here. Two days
after the burst, the optical flux declined more rapidly, with αopt= −1.65± 0.06 (Kulkarni et al. 1999a). This steepening has been
ascribed either to a transition of the fireball to a non-relativistic phase (Dai & Lu 1999) or to the signature of the detection of a
relativistic jet (Rhoads 1999; Sari et al. 1999; M´ esz´ aros & Rees 1999; Huang et al. 2000a,b,c; Wei & Lu 2000). Since both are
estimated to take place approximately 2 d after the GRB start time, i. e. after the end of the BeppoSAX follow-up observations,
they would not be relevant for the X-ray afterglow, that can therefore be studied assuming a spherically symmetric relativistic
expansion. Moreover, the faster decline at X-ray wavelengths is indicative of an evolution in a constant density environment and
it is opposite to the expectations of the wind model (Chevalier & Li 1999). Thus, in the standard synchrotron fireball model, the
optical and X-ray afterglow spectral and temporal indices of GRB 990123 should be compared with the closure relationships
indicated in Table 3, that have been derived from equations (3) and (4).
We have seen in section 2.2 that the best fit value for the X-ray spectral index during the first 20 ks of the NFIs observation
is βX= −0.82±0.10. The power-law which best fits the optical-to-IR spectrum during the first two days has an index −0.8±0.1
(Kulkarni et al. 1999a); this is consistent with the spectral index measured from the optical spectrum of the transient 19 hrs
after the burst: −0.69 ± 0.1 (Andersen et al. 1999). Reconstructing the radio to X-ray afterglow spectrum on January 24.65 UT,
Galama et al. (1999) found a spectral index of −0.75±0.23 in the optical range and a spectral slope of −0.67±0.02 between the
optical and the X-ray wavebands; moreover,recently Maiorano et al. (2005) have estimated a best fit optical-to-IR spectral index

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A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 9901237
Fig.3. GRB 990123 X-ray spectrum during the first 20 ks of the NFIs observation compared with the best fit power-law model
of fixed spectral index βX= −1.23. It is evident that the observed spectrum is too flat to be well reproduced by this model.
of −0.60 ± 0.04. In the following discussion, we set βoptequal to the mean optical-IR observed spectral index of −0.75 ± 0.07,
as derived by Holland et al. (2000), and address the differences with the case βopt= −0.60 ± 0.04 (Maiorano et al. 2005) where
necessary.
As shown in Table 3, if νopt< νX< νc, all the closure relationships are verified within 1−2 σ, except for the one relating the
temporal indices of the optical and X-ray afterglow, that is not consistent with the expectations (∼ 7σ level). If we consider that
GRB 990123 is one of the brightest γ-ray burst detected by the BeppoSAX satellite and that, consequently, the temporal indices
are measured with relative errors less than 5%, this result enables us to exclude the case of a cooling frequency above the X-ray
band.
On the other hand, if νopt< νc< νX, the temporal slopes of GRB 990123 optical and X-ray light curves are readily explained
within the standard synchrotron fireball model (Table 3). However, the closure relations involving βXare not consistent with the
expectations, giving evidence for a too flat X-ray spectral index. This last issue can also be addressed in the following way: the
observed value of αoptallows to estimate that of p and, according to (4), gives p = −4
αX= αopt− 1/4 = −1.35 ± 0.03, βopt=2
consistent with the observed ones within 2.2σ and 1σ respectively, the latter is consistent with βX= −0.82 ± 0.10 only at the
4σ level. A spectral fit of the X-ray data points with a power-law of index fixed to βX= −1.23 is shown in Fig. 3 and gives the
results reported in Table 2: a similar spectral index is clearly not consistent with the data.
It is then difficult to interpret GRB 990123afterglowwithin the basic synchrotronmodel: while for the optical afterglowboth
the temporaland spectralbehaviorare well explainedbysimplyassuming νcbetweenthe opticaland theX-rayenergybandat the
beginning of the BeppoSAX follow-up observation, in the X-rays this assumption only accounts for the slope of the 2 − 10 keV
light curve, but not for the flatness of the 0.1 − 60 keV spectrum.
Using the spectral indices found by Maiorano et al. (2005), βX= −0.94± 0.12 and βopt= −0.60± 0.04, the closure relations
[a], [b], [c], [d] for this case are verified within 2.8σ, 3σ, 2.2σ and 1.3σ, respectively; thus, since the difference between the
optical and the X-ray spectral index is enhanced, the observations are consistent with the relation [d], while [b] gives only
marginal evidence for the existence of an X-ray excess.
3αopt+ 1 = 2.47 ± 0.04; from this we get:
2= −1.23 ± 0.02. While the first two values are
3αopt= −0.73 ± 0.02, βX=2
3αopt−1

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8A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
Fig.4. The U, B, V, R, and I band data at t = 1999 Jan. 24.497,24.505,24.496,24.456,24.487UT (Galama et al. 1999), extrap-
olated at t ? 8.8 hr from the burst using a temporal decay index of αopt= −1.1 and extinction corrected (Galama et al. 1999),
are compared with the 0.1 − 60 keV spectrum corrected for galactic absorption (NH = 2.1 × 1020cm−2) and for absorption
locally to the GRB site (see the best fit results of case [1] in Table 2). The dash-dotted, dashed and dotted lines are the power-law
models of fixed spectral index βopt= −0.6 (Maiorano et al. 2005), βopt= −0.75 (Holland et al. 2000), βopt= −0.8 (Kulkarni et al.
1999a), respectively, for the optical extrapolated data points; the solid line is the power-law model of case [1] in Table 2, where
βX= −0.82.
Finally, we can look at the optical to X-ray normalization. As already noted by Kulkarni et al. (1999a), at the epoch of the
start of the NFIs observations the optical to X-ray spectral index appears to be rather flat, βX−opt= −0.54±0.02; this implies that
the observed2 keV flux is somewhathigher than one would expectedfrom the extrapolationof the optical spectrum. As shown in
Fig. 4, assuming a mean optical spectral index of βopt= −0.75 (Holland et al. 2000) the high energy extrapolation of the optical
data falls well below the X-ray points; similarly, the low energy extrapolation of the X-ray data falls well above the optical ones,
giving evidence for the presence of an X-ray excess. Assuming an optical spectral index of βopt= −0.6 (Maiorano et al. 2005),
the optical to X-ray normalizationproblem is solved by including a break at a frequencyν ? 1 keV at t ? 8.8 hr since the trigger.
On the other hand, if one assumes an optical spectral index of βopt = −0.8 (Kulkarni et al. 1999a), the normalization problem
is moreover strengthened, suggesting that the optical and X-ray emission could be related to different components. Different
cases have been found for GRB afterglows in which there is evidence for an X-ray excess of this kind, and a contribution
from IC scattering have been suggested as a possible explanation. In particular, Harrison et al. (1999) analyzed the case of
GRB 000926, finding that the broad-band light curves can be explained with reasonable physical parameters if the cooling is
dominated by IC scattering; for this model, an excess due to IC appears above the best-fit synchrotron spectrum in the X-ray
band. Castro-Tirado et al. (2003) analyzed the NIR/optical and X-ray spectra of GRB 030227, finding the two mismatching each
other’s extrapolationand suggesting that, in contrast to the NIR/optical band where synchrotronprocesses dominate,in the X-ray
spectrum there could be an important contributionof IC scattering. Finally, a mismatch in the optical to X-ray spectrum was also
found for the bright GRB 010222 (in’t Zand et al. 2001).

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A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 9901239
Considering that in the standard model the values of the temporal indices are determined by the hydrodynamical evolution
of the fireball, while the shape of the broad-band spectrum depends only on the assumption of synchrotron emission, from our
analysis we conclude that: (i) using the spectral indices βX= −0.82 ± 0.1 and βopt= −0.75 ± 0.07, the optical afterglow is well
explained by synchrotron emission and a standard hydrodynamical evolution (closure relation [a]), but the X-ray one seems to
require an additional flat spectrum emission component (closure relations [b] and [d]); (ii) on the other hand, using the spectral
indices found by Maiorano et al. (2005), the shape of the broad-band afterglow spectrum is consistent with a single spectral
componentand standard synchrotronemission (closure relation [d]), but the temporal slopes of the optical and X-ray light curves
are not consistent with the observations (closure relations [a] and [b]), suggesting the possibility of a different hydrodynamical
evolution. We discuss the issue (i) in the following section and (ii) in section 3.2.4.
3.2.2. A possible IC-scattering contribution: the synchrotron+IC model
In order to interpret the combined spectral and temporal properties of GRB 990123 afterglow, we consider the possibility of
relating the X-ray emission to an important contribution of IC scattering.
The X-ray spectral index, βX= −0.82 ± 0.10, similar to the optical one, βopt= −0.75 ± 0.07, and the difference between the
optical to X-ray temporal slopes αopt− αX? 0.36, suggest the presence of an additional hard component. This naturally leads to
a model in which the X-ray emission is dominated by IC-scattering of lower energy photons,while the optical one is synchrotron
dominated; furthermore, an IC contribution could also explain the unusual high-energy (15 − 60 keV) emission observed by the
PDS during the first 20 ks of the afterglow observations.
In a synchrotron+IC model, the afterglow spectrum at some time t0would be the sum of two power-laws:
Fν(t0) = exp?−σ(ν)NH− σ((1 + z)ν)Nz
with βXthe spectral index for the synchrotron component; βIC
spectrum, otherwise, βIC
2
If the fireball expands in a medium of constant number density, if the expansion is spherically symmetric and if we are in the
slow-coolingIC dominatedphase (Sari & Esin 2001), the contributionof IC scattering at a given frequencywill evolve with time
according to the following relations:
H
?×
?
Fsyn
0
?
ν
2keV
?βX
+ FIC
0
?
ν
2keV
?βIC
ν?
(5)
ν
=
1
3if ν < νIC
m(t0), where νIC
mis the peak frequency of the IC
ν=−(p−1)
.
FIC
ν ∝ t9/4;
ν < νIC
a
(6)
FIC
ν ∝ t;
νIC
a< ν < νIC
m
(7)
FIC
ν∝ t−(9p−11)/8;
νIC
m< ν < νIC
c
(8)
FIC
ν∝ t−(9p−10)/8+(p−2)/(4−p);
ν > νIC
c
(9)
assuming a power-law approximation for the IC spectrum (Sari & Esin 2001).
Observing the above spectral and temporal relations, and considering the analysis we have done in section 3.2.1, it is clear
that, if we want the synchrotron emission to be dominant in the optical band and the IC contribution to explain all the X-ray
emission, we should have: (i) a cooling frequency of the synchrotron component above the optical band, since this condition
explains well both the spectral and the temporal behavior of the optical afterglow (section 3.2.1); (ii) a peak frequency of the IC
component below the X-ray energy band, in order to account for the decreasing 2 − 10 keV light curve (if νIC
2 − 10 keV flux would increase with time, if dominated by IC emission).
We can also notice that in the slow-cooling IC-dominated phase, the IC contribution affects the temporal slope of the syn-
chrotron componentat frequencies above the cooling one, changing the temporal decay index from −3(p−1)
Sari & Esin 2001, equation (A.20) in the electronic version of this paper). This means that the difference between the temporal
decay index of the synchrotron flux at frequencies below and above the cooling one becomes1
of strong IC cooling makes the difference smaller than the case of pure synchrotronemission. Therefore,the case in which the IC
contributiondominates the 2−10keV emission seems to be favored with respect, for example, to one in which the IC component
becomes dominant only in the high energy tail of the X-ray spectrum (say, for ν ≥ 10 keV), with the 2 − 10 keV emission still
being dominated by synchrotron emission. In fact, if this was the case, we should have αopt = −3(p−1)
α2
only within 3.5σ.
For this reason, we analyze the hypothesis of the IC emission dominating the whole 2−60 keV spectrum. For νopt< νc< νX
and νX> νIC
relations should be those indicated in Table 4, that for GRB 990123 are all verified within 1σ.
m> 10 keV, the
4
−1
4to−3p2+12p−4
4(p−4)
(see
4−
p−2
8−2pinstead of1
4: the presence
4
, αX =
−3p2+12p−4
4(p−4)
and
opt−αXαopt+3
2αopt−9
4αX−15
16= 0. For GRB 990123, the latter has a value of 0.301± 0.085, consistent with the expected one
m, with the synchrotron component dominating the optical emission and the IC component the X-ray one, the closure

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10 A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
Table 4. Closure relationships between the temporal and spectral indices in the synchrotron+IC model and their corresponding
values for βopt= −0.75± 0.07, βX= −0.82± 0.10, αopt= −1.1 ± 0.03 and αX= −1.46 ± 0.04.
νopt< νc< νXand νX> νIC
αX− 9/4βX− 1/4 = 0
0.13 ± 0.23
m
αopt− 3/2βopt= 0
0.02 ± 0.11
αopt− 2/3αX+ 1/6 = 0
0.040 ± 0.040
βopt− βX= 0
0.07 ± 0.12
Fig.5. GRB 990123X-ray spectrum during the first 20 ks of the NFIs observation.The model spectrum is the sum of two power-
law components (see equation (5)): one represents the synchrotron contribution and has a fixed spectral index βX= −1.23, the
other accounts for IC scattering and has a fixed spectral index βIC
X= −0.73.
Using the relations αopt = −1.10 ± 0.03 = −3(p − 1)/4 and αX = −1.46 ± 0.04 = −(9p − 11)/8, we get for the index of
the electron energy distribution p = 2.47 ± 0.02 and 2.52 ± 0.03, respectively. Using the spectral indices βopt= −0.75 ± 0.07 =
−(p − 1)/2 and βX= −0.82 ± 0.10 = −(p − 1)/2 we obtain: p = 2.50 ± 0.14 and p = 2.64 ± 0.20, respectively. These values
are all consistent with each other within ∼ 1σ, as expected from the closure relations being verified at the 1σ level. We then
choose the one with the smaller error, that is p = 2.47 ± 0.02, derived from the optical temporal index αopt. In this way, we
estimate the expected spectral indices between 0.1 − 60 keV for both the synchrotron component and the IC one; these are:
βX= 2/3αopt− 1/2 = −1.23± 0.02, and βIC
In Fig. 5 and Fig. 6 we fit the 0.1 − 60 keV data during the first 20 ks of the NFIs observation with a model spectrum of the
form (5), where we set βX= −1.23 and βIC
are Fsyn
0
dominating on the synchrotron one in the X-ray band: Fsyn
flux at 2 keV we get only an upper limit.
Our following step is to relate νIC
fraction of the shock energy density that goes into the electrons and magnetic energy density, ǫeand ǫB, respectively; the energy
of the fireball E52in units of 1052ergs; the ambient medium number density n1, in units of particles/cm3.
X= 2/3αopt= −0.73± 0.02, respectively.
X= −0.73. The best fit values (see Table 2) for the synchrotron and IC flux at 2 keV
0= 0.72+0.43
0/FIC
= 0.15+0.15
−0.15µJy and FIC
−0.15µJy (χ2= 35.5/26),respectively,consistent with the hypothesis of an IC component
0≤ 0.15/0.72 ? 0.21, taking into account that for the synchrotron
m, νc, Fsyn
2keVand FIC
mat t = 0.37 d to the fundamental parameters of the fireball model: the

Page 11

A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 99012311
Fig.6. GRB 990123 FνX-ray spectrum: the data and the model are those of Fig. 5 corrected for LECS/MECS and PDS/MECS
flux inter-calibration normalization ratios and for absorption.
Using the formulas given by Granot et al. (1999), Sari et al. (1998), and by Sari & Esin (2001) in the slow-cooling IC domi-
nated regime (see the Appendix in the electronic version of this paper for details), for the synchrotron cooling frequency we can
write:
νc(Hz) = Aνc(ǫBE52)anb
1ǫc
e
(10)
where:
Aνc(Hz) = (2.7 × 1012)(1 + z)
p
2(p−4)(170)
p−2
p−4t
8−3p
2(p−4)
d
(11)
with tdthe time since the burst measured in the observer’s frame in units of days, and:
p
2(p − 4)
a =
(12)
b =
2
p − 4
(13)
c = 2
?p − 1
p − 4
?
(14)
For the peak frequency of the IC component:
νIC
m(Hz) = AνIC
mǫ1/2
Bǫ4
eE3/4
52n−1/4
1
(15)

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12A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
where:
AνIC
m(Hz) = 2(2.9 × 1015)(1.116× 104)2(1 + z)1/2
?p − 2
p − 1
?4
t−9/4
d
(16)
For the peak flux of the IC component:
FIC
m(µJy) = AFIC
m(E52n1)5/4ǫ1/2
B
(17)
where:
AFIC
m(µJy) = 0.39(2× 10−7)(1.7× 104)(1 + z)d−2
28t1/4
d
(18)
with d28the luminosity distance of the source in units of 1028cm. For the flux of the synchrotron component at a frequency
ν > νc:
Fν(µJy) = AFνǫd
Bne
1Ef
52ǫg
e
(19)
where:
AFν(µJy) = (1.7 × 104)(2.9 × 1015)
p−1
2(2.7 × 1012)1/2ν(Hz)−p/2d−2
28
?p − 2
p − 1
?p−1
(170)
p−2
2(p−4)(1 + z)
p2−12
4(p−4)t
−3p2+12p−4
4(p−4)
d
(20)
d =p2− 2p − 4
4(p − 4)
(21)
e =
p − 2
2(p − 4)
(22)
f =
p2− 12
4(p − 4)
(23)
g =p2− 4p + 3
p − 4
(24)
Setting p = 2.47, z = 1.6004, d28= 3.7 (Kulkarni et al. 1999a), td= 0.37 d, we have verified, by inverting the above relations
(see the calculations in the Appendix), if reasonable values of ǫB, ǫe, E52, and n1can be found when νc≥ 2 eV and νIC
2.0 keV.
In order to minimize the energy requirement (see equation (A.61)), it is convenient to set (i) νIC
(ii) νc ? 2 eV, that is to say to set these frequencies at the higher and lower edge of the range in which they can vary to
be consistent with the X-ray and optical data, respectively. These conditions are immediately evident taking into account that
FIC
observations; substituting into equation (A.61), yields E52 ∝ (νc)a13(νIC
minimizing νcand maximizing νIC
With the assumption (i) we have FIC
from the Gunn r data should be Fsyn
data best fit value of Fsyn
0
Fitting the 0.1−60keV spectrum with model (5) where βX= −1.23, βIC
FIC
0
= 10−2µJy, νIC
m(0.37 d) ≤
m(0.37 d) ? 2 keV and
2keV= FIC
m(2keV/νIC
m)−p−1
2 , so FIC
mcan be expressed as a function of νIC
mand FIC
m)a14−a15
2keV, the value of which is fixed from the
2 , and for p = 2.47: E52 ∝ νc(νIC
p−1
m)−0.36. Thus,
mgives the smallest value for E52.
m= FIC
2 keV? 70(8.8 hr/6 hr)−1.46(2 keV/2 eV)−1.23? 10−2µJy, which is consistent with the X-ray
= 0.15+0.15
X= −0.73 and Fsyn
m= 0.83 ± 0.04 µJy. We thus set νc= 2 eV, Fsyn
2keV; moreover, because of (ii), the synchrotron contribution at 2 keV extrapolated
−0.15µJy within the errors.
0
= 10−2µJy, yields FIC
0= FIC
2 keV=
m= 2 keV, FIC
m= 0.83 µJy, that give:
ǫB? 10−10ǫe? 10−1
(25)
E52? 7 × 104n1? 102
(26)
With those values for the intrinsic parameters of the fireball, the temporal and spectral propertiesof the optical to X-ray afterglow
are explained within the fireball model and the optical to X-ray normalization problem is solved.
A similar calculation can be done setting Fsyn
0
= 0.15 µJy and FIC
This choice yields a higher value for ǫBand a lower one for n1:
m= 0.72 µJy, that are the values we get from the X-ray data.
ǫB? 6 × 10−8ǫe? 5 × 10−2
(27)
E52? 6 × 104n1? 8(28)

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A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123 13
but has the problem that it predicts an optical extrapolated flux about 15 times above the observed one (0.15 µJy/10−2µJy ? 15).
The hypothesis of a “gray absorber” could explain an optical flux lower than expected from the X-ray data, without affecting the
optical spectral slope, and alternative scenarios to explain simultaneouslythe optical and X-ray data of some GRBs by invokinga
more gray extinction have recently been proposedby Stratta et al. (2004), for those GRBs for which some evidence of absorption
locally to the GRB site was found. In our case, we do not have a strong evidence for local absorption (see Table 2), but we can
neither exclude this hypothesis at all.
We can also notice that with the values (25), being ǫe/ǫB≥ 10, IC scattering dominates the total cooling over the whole rela-
tivistic stage of the afterglow evolution, as underlined by Sari & Esin (2001); thus, the transition to the slow-cooling synchrotron
dominated phase, in which the IC cooling rate is weaker than the synchrotronone and therefore has no effects on the synchrotron
spectrum, should not be observable. This implies that for the 0.1 − 60 keV spectra relative to next 75 ks and last 70 ks, we do
not expect changes in the spectral slope, in agreement with the results presented in section 2.2. However, we of course expect
the flux level of the following spectra becoming dimmer of a factor determined by the slope of the X-ray light curve. Since the
15 − 60 keV upper limits are in fact consistent with a decay slope of α = −1.46 ± 0.04 (see Fig. 1 in Maiorano et al. 2005), we
thus conclude that the lack of a significant detection by the PDS in the following 75 ks and last 70 ks spectra, has to be related to
poorer statistics rather than to a strong suppression of the IC contribution.
Since we are before 2 d from the burst, we have used the isotropic dynamical equations and E52is the fireball isotropic
equivalent energy at the beginning of the afterglow phase. Considering that the observed isotropic equivalent γ-ray energy,
Eiso(γ) = 4πFγd2
has to beEiso(γ)
E0
iso
To estimate the energy of the jet Ejat the beginning of the afterglow phase, we need the value of the jet opening angle θj.
According to Frail et al. (2001):
L(1+z)−1, is 1.2×1054ergs, the efficiency ηγof the fireball in convertingthe energyin the ejecta E0
= ηγ? 0.2%, a reasonable value according to Panaitescu et al. (1999) and Beloborodov (2000).
isointo γ-rays
θj= 0.057
?tj
1d
?3/8?1 + z
2
?−3/8
0.2 × E0
1053ergs
iso

−1/8?
n
0.1cm−3
?1/8
(29)
Since tj? 2 d, we obtain θj= 0.064 ? 3.7◦; this implies Ej? 1054ergs for the energy in the jet.
This estimate on the jet opening angle is based on the simple relation γ(tj) = θ−1
the structure of GRBs jets (M´ esz´ aros et al. 1998; Dai & Gou 2001; Rossi et al. 2002; Zhang & Me´ sz´ aros 2002). Conventionally,
the late time temporal index α2for the optical afterglow of jetted GRBs, is believed to be the same as p. However, there are
some caveats on this assumption (e.g. Wu et al. 2004), most importantly the fact that the ambiguity of the understanding on the
sideways expansionof the jet leads to a great uncertaintyon the value of α2. More specifically, as explained by M´ esz´ aros & Rees
(1999) for the case of GRB 990123, if one assumes that the steepening in GRB 990123 optical afterglow from t−1.1to t−1.65
is caused by sideways expansion of the decelerating jet (Rhoads 1997), one expects a large steepening from t−1.1to t−p(where
p = 2.47 in our case), more than one power of t. However, the edge of the jet begins to be seen when γ drops below the inverse
jet opening angle 1/θj. This occurs well before the sideways expansion starts (Panaitescu & M´ esz´ aros 1999) and the latter is
unimportant until the expansion is almost non-relativistic: GRB 990123, as well as other GRBs like GRB 010222, 020813,
021004, 000911 (Wu et al. 2004), are good candidates for non-lateral expansion jets, from which we expect a steepening by t3/4
in the late time optical light curve. The observed difference of α1− α2 = 0.55 ± 0.07, matches the expectations at the 2.8σ
level and is thus in agreement with the expected change in the decay slope from seeing the edge of the jet within a model of
typical electron index of p = 2.5 (M´ esz´ aros & Rees 1999). These arguments are sufficient to justify the hypothesis of a jet
structure within a synchrotron+IC model with p = 2.47, but there are of course several other plausible causes for steepening (e.
g. Dai & Lu 1999).
We can now compare our results with some previous analysis, bearing that those were not constrained by the 0.1 − 60 keV
afterglow spectrum, which is analyzed in this work. For what concerns the total energy in the fireball, a value of the order of 104
for E52has recently been proposed by Panaitescu & Kumar (2004) analyzing GRB 990123early optical emission in the frame of
the standard “reverse-forward shock” model.
In Panaitescu & Kumar (2001), fitting the light curves in the radio, optical and X-ray energy band, it was proposed p ?
2.2÷2.4,ǫe? 9×10−2÷2×10−1, ǫB? 10−4÷3×10−3, n1? 3×10−4÷2×10−3, θj? 1◦÷3◦and Ej? 1050÷5×1050ergs (values
taken from Fig. 2 in Panaitescu & Kumar 2001); in particular, for Ej= 5×1050ergs and θj= 3◦, the isotropic equivalent energy
is of about 4×1053ergs, 30 times less than the lower limit on the isotropic energy (E ≥ 1055ergs) found by Panaitescu & Kumar
(2004) and five times less than the observed isotropic energy emitted in γ-rays. A value of 4 × 1053ergs requires the existence
of a radiative evolution phase before the adiabatic one, causing the emission of more of the initial explosion energy and leaving
less for the adiabatic phase. The same considerations can also be done for the model proposed by Wang et al. (2000), who set
p = 2.44, ǫe? 0.57, ǫB? 3.1 × 10−3, n1? 0.01, E52? 5 and considered only synchrotron emission: in this case E52is about 30
times less than Eiso(γ).
Finally, about the power-law index of the electron energy distribution, values of p = 2.44 and p = 2.3 were found by
Wang et al. (2000) and Panaitescu & Kumar (2001) respectively, similar with the one of p = 2.47 we suggest in our analysis.
j, that itself cannot distinguish between

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14A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123
In this work, however, to fit the observed flat 0.1 − 60 keV spectrum and give an overall interpretation of the multi-wavelength
afterglow, we are adding a dominant contribution of IC up-scattering to the synchrotron emission process.
3.2.3. The radio observations: problems of the synchrotron+IC model
GRB 990123 has been largely discussed within the standard fireball theory and a reverse shock origin has been assigned to both
the optical flash and the radio flare (Sari & Piran 1999b; Galama et al. 1999; Briggs et al. 1999; Kulkarni et al. 1999b). The light
curvesin theradio,opticaland X-rayenergybandshave beenwell reproduced(Panaitescu & Kumar2001; Kulkarni et al. 1999b)
and different sets of values for the intrinsic parameters ǫe, ǫBE52and n1have been proposed (Panaitescu & Kumar 2001, 2004;
Wang et al. 2000).
In this paperwe are addinganotherpieceof informationto the puzzle:the spectrumofthe optical to X-rayafterglowextended
to the high energy tail of the 0.1 − 60 keV energy band. As we have underlined in the previous sections, GRB 990123 appears
anomalous and difficult to interpret within a standard synchrotron model when combining this spectral information with the
temporalpropertiesof the optical and X-ray light curves.This is what has broughtus to study the hypothesisof a synchrotron+IC
model with values for the intrinsic parameters (25) and (26).
We want now to verify if such a model is consistent with the 8.46 GHz data. The radio afterglow was observed from t > 1 d
after the burst (here we are not considering the data relative to the radio flare, to which we assign a reverse shock origin,
Kulkarni et al. 1999b). To estimate the value of the 8.46 GHz flux at about 1 d from the burst, we need to calculate the value of
the synchrotron self-absorption frequency. According to Granot et al. (2001), the self-absorption frequency νais:
νa(Hz) = 0.247 × 4.24 × 109(1 + z)−1
?p + 2
3p + 2
?3/5(p − 1)8/5
p − 2
ǫ−1
eǫ1/5
BE1/5
52n3/5
1
(30)
Using the values (25) and (26) we get νa? 15 GHz.
Further, substituting those values in equations (A.1) and (A.2) of the Appendix, we get νm(1 d) ? 13 GHz ? νaand fsyn
23 mJy. Thus we have:
m
?
F8.46GHz(1 d) ? 23 mJy
?8.46 GHZ
15 GHz
?2
? 7 mJy (31)
that is about a factor of 30 above the observations, that are lower than 260 µJy (Kulkarni et al. 1999b).
Another way to explain the problem is the following: over the first two days, the most abundant photons are between the
radio and the optical regimes; if these photons are up-scattered by the Compton process, then the required Thompson optical
depth is τ = fX/fm ? 0.83 µJy/Fsyn
(Kulkarni et al. 1999b), that imply τ ≥ 0.83/260 ? 3 × 10−3. On the other hand, the optical depth has the following dependence
on the parameters of the fireball model:
m . The observed radio/optical fluxes in the case of GRB 990123 are lower than ∼ 260 µJy
τ = σTnR ? 4 × 10−7(E/1054erg)1/4(n/1cm−3)3/4(t/6hr)1/4
(32)
which has a value of ∼ 10−4, for E52= 7 × 104, n1= 100 and t ? 8.8 hr. Thus, to reconcile this value of τ with the observations,
one should have Fsyn
ultimate result of our synchrotron+IC model.
m of the order of 3 × 10−3/10−4× 260 µJy, that is to say 30 times higher than the observed one, that is the
3.2.4. An alternative solution for the puzzle
In the previous sections we noticed that the observed temporal slopes of the optical and X-ray light curves of GRB 990123
afterglow cannot be reconciled with the observed value of the X-ray spectral index during the first 20 ks of the NFIs observation,
atleastintheframeofthebasicsynchrotronstandardmodel.ThuswetriedtoexplaintheX-rayspectrumbyinvokingasignificant
contribution of another emission mechanism in addition to the synchrotron one, that is IC scattering. However, we have some
problems when comparing our results with the 8.46 GHz upper limits.
A completely different approach could be to leave unchanged the emission mechanism, but change the hydrodynamics.
Assuming that synchrotron radiation from electrons with a power law energy distribution is the only efficient mechanism, the
shape of the afterglow spectrum is independent of the details of the hydrodynamics, thus the relation between p and β is fixed.
Fromthe opticalto X-rayspectral index,βX−opt= −0.54±0.02(Kulkarni et al. 1999a), we can infer p = 2.08±0.04if νc? 1keV;
this value of p predicts βopt= −0.54 ± 0.02 and βX= −1.04 ± 0.02, that agree at the ∼ 1σ level with the spectral indices found
by Maiorano et al. (2005). Assuming βopt= −0.75 ± 0.07 and βX= −0.82 ± 0.10, the agreement is at the 2σ level. However, in
this case, the closure relation βopt− βX− 1/2 = 0 is only verified at the 3.6σ level.
Further, in order to account for the temporal decay (a value of p = 2.08 predicts an X-ray temporal index of −1.06±0.03and
an optical temporal index of −0.81±0.03, that are not consistent with the observed ones), we need to change the hydrodynamics

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A. Corsi, L. Piro, E. Kuulkers et al.: The puzzling case of GRB 990123 15
and we do this by letting E ∝ tδEand n ∝ tδnwhere t is the time in the frame of the observer; we note that the standard model has
δE= δn= 0. Using (3) and (4), we find:
α(ν > νc) = (p + 2)δE/4 − 3p/4 + 2/4(33)
and
α(ν < νc) = (p + 3)δE/4 + δn/2 − 3p/4 + 3/4(34)
Substituting αX= −1.46 and αopt= −1.1 into (33) and (34) respectively, we obtain δE? −0.39, so the shock should lose energy,
and δn? 0.41. With those values for δEand δnwe obtain R(t) ∝ t0.05, where R is the radius of the shock. This result follows from
the fact that R(t) ∼ (Et/n)1/4. Thus, the density should increase rapidly with radius, as n ∝ R8.
An increase in the density could let one think to the termination shock radius of the wind model by Chevalier & Li (1999) or
totheGRB jet runningintoasharp-edgeddensecloud.Indeed,Vietri et al. (1999) suggestthatthe X-rayflareinGRB 970508and
GRB 970828 could arise from thermal bremsstrahlung emission of a shock-heated thick torus surrounding the central source.
However, the observed X-ray spectrum is too steep to be compatible with this model. Shi & Gyuk (1999) invoke a cloudlet
to explain the 2-day radio flare (Kulkarni et al. 1999b). The energy demands of this model are of the order of 1055ergs, but
Sari & Piran (1999b) have proposed a simpler model in which the radio flare arises in the same reverse shock which powers the
prompt optical emission. Moreover, in addition to the necessity of justifying such a density profile, we also need to consider
which observable effects could be expected from it e.g., the optical-near IR broad-band spectrum of the burst becoming redder
with time if the medium encountered by the fireball becomes very dense. Holland et al. (2000) have shown that there is no
evidence for βoptvaryingwith time between about 6 hr and 3 days since the burst, so that no observablereddeningeffect seems to
become important during the afterglow observations. Using the relations n1∝ t0.41and R ∝ t0.05, we can estimate that during the
afterglow phase, while expandingfor about R(3 d)−R(6 hr) =
?
fireball should encounter a medium whose density increases of a factor (3 d/6 hr)0.41? 3; this means that starting with a typical
value of n1 = 1, the afterglow phase will entirely develop while the fireball is expanding in a region where the ISM number
density is in the range of 1 − 3 particles/cm3. So, if we think the n ∝ R8profile only limited to the region of space where it is
required to explain the afterglow observations, no extreme values of the ISM number density would necessarily be implied by
this model, with no important reddening effects expected to be observed.
The simplest way to lose energyis to assume that the shock is radiative. However,from the optical to X-ray normalizationwe
know that νc? 1keV ≫ νmand thus the shock is not radiative. A possible mechanism of energy loss was recently suggested in
relation with the issue of accountingfor bumps observedin the light curvesof some GRBs (e.g. Schaefer et al. 2003; Klose et al.
2004); Schaefer et al. (2003) proposed that the bumps observed in the optical transient of GRB 021004 could be related to
inhomogeneities in the external gas in the form of clumps of denser material (Wang et al. 2000) which should increase the
afterglow brightness by enhancing the dissipation of the kinetic energy in the GRB remnant. This process could be of interest in
constructing a physical framework for this alternative scenario, since we find the energy loss being connected with an increase in
the density. Another possibility is energy loss via cosmic rays (e.g. Waxman 1995; Wick et al. 2004, and references therein). We
know little about the energy carried off in cosmic rays in such strong shocks and so this possibility requires further inspection.
(3 d/6 hr)0.05− 1
?
R(6 hr) ? 0.13 R(6 hr) ? 1016cm in radius, the
4. Conclusions
We have reported on BeppoSAX observations of GRB 990123 and discussed them in the frame of the standard fireball model.
We analyzed the broad-bandspectrum of the prompt emission, confirmingthe suggestion of a reverse shock origin for the optical
flash.
We have studied the properties of the 0.1−60 keV spectrum and compared the X-ray afterglow with the optical observations
and the 8.46 GHz upper limits. The temporal slopes of the 2 − 10 keV and optical light curves are readily explained assuming
νcbetween the optical and the X-ray energy band during the first 20 ks of the BeppoSAX follow-up observations, and setting
p = 2.47 for the index of the electron energy distribution; this implies βX = −1.23. Fitting the 0.1 − 60 keV spectrum with a
single power-law model, yields βX= −0.82 ± 0.10, which is flatter than the value of βX= −1.23 expected from the temporal
slopes.
We tried to relate the presence of this X-ray excess to the contribution of IC scattering and studied a model of synchrotron
plus IC emission. By constraining Fsyn
values of the intrinsic parameters of the fireball model: with ǫe ? 10−1, ǫB ? 10−10, E52 ? 7 × 104and n1 ? 102, this model
explains both the temporal and spectral behavior of the optical and X-ray afterglow, but violates the 8.46 GHz upper limits.
We have compared and discussed our choice for the values of the intrinsic parameters, underlining the importance of the
0.1−60 keV data as a new piece of information that should be taken into account when fitting the radio, optical and 2− 10 keV
light curves.
Finallywehaveproposedanalternativescenario,wheretheproblemofinterpretingtheobservedvalueofboththespectraland
temporalindices in the optical and X-ray energybandis solved by leaving unchangedthe emission mechanism(onlysynchrotron
2keV, FIC
m, νcand νIC
mat the time of the NFIs observations, we have found the corresponding