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Modeling the broadband emission of Fermi/LAT GRB 090902B

GRB 090902B, detected by Fermi Large Array Telescope (Fermi/LAT), shows extend high-energy emission (>100 MeV) up to 10^3 s after the burst, which decays with time in a power-law as t^{-1.5}. It has been also observed by several follow-up low-energy instruments, including an early optical detection around 5000 s after the burst. The optical emission at early time decays faster than t^{-1.6}, which has been suspected to originate from the reverse shock. We here explore the models that can possibly explain the the broadband afterglow emission of GRB 090902B. We find that the reverse shock model for the early optical emission would overpredict the radio afterglow flux that is inconsistent with observations. A partially radiative blast wave model, which though is able to produce a sufficiently steep decay slope, can not explain the broadband data of GRB 090902B. The two-component jet model, which consists of a narrow and bright jet component in the core and a surrounding wider and less energetic jet component, is shown to be able to explain the broadband afterglow data, including the LAT high-energy data after ~50 s and low-energy (radio, optical and X-ray) afterglow data. The early-time high-energy emission detected by LAT before ~50 s is likely due to internal origin as that of the sub-MeV emission. The highest energy (33 GeV) photon of GRB090902B detected at 80 s can be marginally accommodated within the forward shock emission under the optimistic condition that electrons are accelerated by the Bohm diffusive shock.


INTRODUCTION
GRB 090902B, triggered the Fermi Gamma-ray Burst Monitor (GBM), is a long, intense burst with a redshift of z = 1.822 (Cucchiara et al. 2009) and a fluence of (4.36 ± 0.06) × 10 −4 ergcm −2 (10 keV-10 GeV) over the duration T 90 ≃ 25s of the prompt emission. These data give an isotropic energy E iso = (3.63 ± 0.05) × 10 54 erg, comparable to the energy in another bright GRB detected by Fermi, GRB 080916C (Abdo et al. 2009a). It was also detected by the Fermi LAT with extended high energy (> 100 MeV) emission up to 1000 s after the trigger, which includes a 33.4 GeV photon at 82s after the trigger, the highest energy yet detected from GRBs. The spectrum of this extended emission is consistent with a power law with photon index Γ = −2.1 ± 0.1, and its flux (>100 MeV) declines as t −1.5±0.1 over the interval from 25 to 1000 s after the trigger (Abdo et al. 2009b).
The optical-infrared afterglow of GRB 090902B has been observed by several instruments (Pandey et al. 2010;McBreen et al. 2010). The earliest optical detection by ROTSE-IIIa occurring at about 5000 s after the burst reveals a bright afterglow which decays faster than t −1.6 (Pandey et al. 2010). The temporal decay of the optical afterglow becomes flatter after ∼ 12.5 hours with a decaying index of −0.90 ± 0.08. The X-ray afterglow, detected by Swift XRT (Kennea & Stratta 2009), is consistent with a single power law decay with an index of ∼ 1.30 ± 0.04 from 12.5 hours to 17 days after the burst. In the radio band, the light curve remains flat until weeks after the burst and then starts to decline (Cenko et al. 2010).  modeled the the LAT, Xray and late-time (t 1days) optical data of GRB090902B 1 Department of Astronomy, Nanjing University, Nanjing, 210093, China 2 Key laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China with the forward shock synchrotron emission and find that one forward shock component can explain these data. However, their modeling does not include the early optical data at 5000 s and the long-term radio afterglow data. Cenko et al. (2010) model the late-time optical, X-ray and radio data of GRB090902b with one forward shock component. Following Pandey et al. (2010), they attribute the early optical flash to the reverse shock emission. They also calculated the expected high-energy emission using their best-fit parameters, but find that the expected 100 MeV flux at t = 50 s is a factor of 7 below the observed value. Given these incompleteness and inconsistency, we aim at modeling the broadband data of GRB090902B, including the LAT, optical, X-ray and radio data.
One interesting feature of GRB090902B is the fast temporal decay of the early optical emission, i.e. the power-law decay slope in F ν ∝ t −α is α 1.6. Analogous phenomenon has been observed in GRB 990123 and has been interpreted as arising from the reverse shock passing through the baryonic ejecta of the GRB outflow, which produces an optical flash with a steep decay (typically evolves as t −2 ) at the early time (Mészáros & Rees 1997Sari & Piran 1999a, b;Panaitescu & Kumar 2004;Nakar & Piran 2004. The reverse shock scenario has been also proposed for the early optical emission of GRB 090902B (Pandey et al. 2010;Cenko et al. 2010). With the high-energy afterglow data from Fermi LAT for GRB 090902B, the forward-reverse shock scenario for the all-band data can be further tested.
There are other scenarios that can possibly explain the early fast decay optical and high-energy emission, such as the fully or partially radiative blast wave model (Ghisellini et al 20010;Wu et al. 2005a). The radiation emitted by electrons accelerated in shocks may lead to energy loss of the shock. The adiabatic shock approximation will break down when the energy loss becomes important, which occurs when the equipartition factor for electrons (i.e. ǫ e ) and the radiation efficiency of electrons are high. In the extreme case when almost all the shock energy goes into electrons (i.e. ǫ e ≃ 1) and the electrons are in the fast-cooling regime, the shock becomes fully radiative. Although the fully radiative shock is in general unrealistic for GRBs, a partially radiative shock is possible when ǫ e is relatively high, especially during the early afterglow phase. Due to the decreasing energy remained in the forward shock, a faster decay of the afterglow than that predicted by the standard scenario is expected (Wu et al. 2005a). Motivated by this, we also consider whether this scenario can explain the early fast decay of the optical emission in GRB 090902B.
Numerical simulations show a structured outflow when the jet breaks out the collapsing stellar envelope of massive stars (Zhang et al. 2003). In the structured jet model, it is usually assumed that the energy per unit solid angle depends as a power-law or a Gaussian function on the angular distance from the axis (e.g. Mészáros , Rees, & Wijers 1998;Dai & Gou 2001;Rossi, Lazzati, & Rees 2002;Zhang & Mészáros 2002;Zhang et al. 2004). For the sake of calculation ease, the structured jet can be simplified as a two-component jet (Ramirez-Ruiz et al. 2002, Berger et al. 2003Peng et al. 2005;Huang et al. 2004), which consists of a narrow and bright jet component in the core and a surrounding wide and less energetic jet component. When observers view along the axis, one will see the afterglow emission produced by both the bright core and the broad wings surrounding the core. As the narrow component has a small opening angle, the jet break in the light curve can occur very early and the afterglow emission produced by the narrow component will have a fast decay after that time. This provides a potential mechanism to produce the early-time fast decaying optical emission of GRB 090902B, while the late radio, optical and X-ray afterglows that have normal light curves can arise from the wide component. We will study whether this two-component scenario can explain the broadband afterglow data of GRB 090902B.
We first study the reverse shock scenario in §2, and find that the reverse shock scenario for the early optical emission predicts a higher radio flux than the observed value. In §3, we study whether the partially radiative forward shock can explain the broadband data of GRB 090902B, but find a negative result. Then we propose a two-component jet model for the broadband afterglow data of GRB 090902B in §4. In §5, we discuss the origin of early-time high energy (> 100MeV) emission observed during the prompt bursting phase. Finally we give our conclusions and discussions in §6.

FORWARD SHOCK -REVERSE SHOCK (FS-RS) MODEL
When the ultrarelativistic cold baryon-dominated GRB ejecta encounters the cold ISM, a reverse shock that propagates back into the ejecta and a forward shock that propagates into the ISM will form, and as a result both the ejecta matter and the ISM matter are heated up. An optical flash is expected to be produced by the reverse shock synchrotron emission, which should decay quickly due to that the shocked ejecta is expanding adiabatically. The early optical flash from GRB 990123 with a 9th magnitude is believed to be such a good case (Sari & Piran 1999a;Mészáros & Rees 1999). It remains unclear why such optical flashes are lacked in general in GRBs as ground-based robotic telescope observations (Yost et al. 2007) and early Swift UV/Optical Telescope (UVOT) observations (Roming et al. 2006) yield non-detections down to a much lower limit.
A bright optical flash is detected by ROTSE from GRB 090902B with a magnitude of m R = 16.4 ± 0.5 at t = 5320 s after the burst. The optical non-detections at 2 × 10 4 s by ROTSE imply that the optical emission decays faster than t −1.6 . Pandey et al. (2010) and Cenko et al. (2010) argue that this rapid decay slope is suggestive of the reverse shock origin. With the rich multiwavelength observation data available for this burst, including the high-energy LAT data, the radio data, late-time optical and X-ray data, we aim at testing this reverse-shock origin possibility.
2.1. The forward shock emission The late-time optical and X-ray afterglow emission after half a day shows a normal decay, with a decay slope of α O = −0.90 ± 0.08 and α X ∼ −1.30 ± 0.04 respectively. They are broadly consistent with the synchrotron afterglow emission produced by a forward shock expanding into a constantdensity medium with an electron index of p ≃ 2.2 if the cooling frequency in the synchrotron spectrum is between the optical and X-ray frequencies Cenko et al. 2010). Following Sari et al. (1998) and Wijers & Galama (1999), we get the radius of forward shock at time T where E is the isotropic-equivalent kinetic energy of the burst and n is the number density of the circum-burst ISM. Throughout the paper, and we use c.g.s units and denote by Q x the value of the quantity Q in units of 10 x . Adopting R = 4γ 2 cT , the bulk Lorentz factor of the shocked matter can be described by Then we can obtain the characteristic frequencies of the afterglow synchrotron emission ν mf = 1.05 × 10 18 f 2 (p)ǫ 2 e,−1 E  (3) where f (p) = 6(p − 2)/(p − 1), ǫ ef and ǫ Bf are the equipartition factor for the energy in electrons and magnetic field in the shock, and ν cf = 1.13 × 10 24 E −1/2 is Compton parameter for electrons that produce the synchrotron photons at ν cf . Hereafter the superscripts/subscripts 'f' and 'r' are used to represent the quantities of the forward shock and reverse shock respectively. The peak flux density is Bf,−5 (1 + z)D −2 L,28 ergcm −2 s −1 (5) Then we get the flux density at a fixed frequency where Y (ν) is the Compton parameter for the electrons whose synchrotron frequency is ν. Due to Klein-Nishina scattering effect, Y (ν) is not a constant for the electrons that produce high energy photons ) and in fact is dependent of ν. Now we confront the above theory with the observed data to constrain the unknown parameters. From Abdo et al. (2009), Pandey et al. (2010, we take the observed flux for LAT data at 173s, R-band optical data at 1.30 × 10 5 s, X-ray data at 1.09 × 10 5 s and radio data at 4.67 × 10 5 s as below: where κ ≃ 0.85 is the extinction coefficient of the host galaxy in R band (Cenko et al. 2010). The spectral regime of each frequency is given in the parentheses. Although ν LAT and ν X belong to the same spectral regime, the X-ray flux and high-energy flux data can give two independent constraints due to two different Y parameters. For electrons that produce the X-ray synchrotron afterglow, the inverse-Compton scattering loss is in the Thompson regime and Y ∼ 74.3ǫ in the slow-cooling phase, while for high-energy gamma-ray photons, Y parameter is small due to the KN suppression effect on the scattering cross section, as we will show later.
So we obtain the constraints on the shock parameters where Y (100MeV) is the Compton parameter for the electrons whose synchrotron frequency is hν = 100MeV at t = 173s. In the calculation, a typical value of p = 2.2 for forward shock has been used. Solving the above equations, we obtain For the above set of parameters, we obtain . As Y (100MeV) ≪ 1, we can just omit Y (100MeV) in these expressions.

The reverse shock emission
As the reverse shock propagates into the fireball ejecta, the number of shocked electrons increases, which leads to an initial rise of the reverse shock flux. Once it has passed through the shell, no new electrons will be shocked and the flux will decrease due to adiabatic expansion of the radiating gas. The flux of reverse shock peaks at T i = max(T dec , T cross ) (hereafter, we use the subscript 'i' to represent quantities at the peak time). Here T dec ≡ (l/η 8/3 c)(1 + z) is the shell deceleration time, where l = (E/nm p c 2 ) 1/3 is the Sedov length and η is the initial Lorentz factor of the ejecta. T cross ≡ (∆/c)(1 + z) = T 90 , is the characteristic timescale within which the reverse shock crosses the shell, where ∆ is the thickness of the shell (Sari & Piran 1995, 1999b. When the shell is thick so that T cross > T dec , the reverse shock becomes relativistic early on, and we call it "thick shell" case, otherwise it belongs to the "thin shell" case. Evolution of bulk Lorentz factor, gas pressure and density of shocked electrons after crossing time follows γ ∝ T −7/16 , p ∝ T −13/12 and n ∝ T −13/16 (Sari & Piran 1999a, b;Meszaros & Rees 1999;Kobayashi 2000).
The bulk Lorentz factor of the shocked shell at the peak time is Then we can get the Lorentz factor of the reverse shock at the peak timē The minimum random Lorentz factor of electrons is given by where ǫ er is the fraction of thermal electrons carried by magnetic field in reverse shock, b ≡ (γ−1) η/γ (namely,γ − 1 = b η γ ) andt ≡ T /T i . We use this approximation forγ − 1 so that we can treat the calculation analytically. Usually, the value of b is taken to be 1 (Waxman & Draine 2000;Kobayashi et al. 2007) or 1 2 (Wang et al. 2005). A mildly relativistic reverse shock approximation withγ − 1 ≃ 1 is also sometimes used (see e.g. Sari & Piran 1999a). In this paper, we take b = 1 2 in the calculation, as η γ i . For a typical value of p = 2.5 for the reverse shock emission, f (p) = 2.
If we attribute the early optical emission at t ≃ 5000 s to the reverse shock synchrotron emission, we would have κF r opt (5000s) = 0.91mJy where κ ≃ 0.85 is the extinction coefficient of the host galaxy in R band (Cenko et al. 2010). The reverse shock emission can produce a radio flare as has been seen in GRB 990123 (Kulkarni et al. 1999). Although the radio emission in GRB 090902B drops after the first detection, it shows a flattening after the second detection at 4.67 × 10 5 s, so the forward shock emission should be dominated at this time. Thus, we expect that F r radio (4.67 × 10 5 s) < 1 2 F obs radio (4.67 × 10 5 s) At 5000 s, from equation (12) and (13) and using the constrained value of E and n from the forward shock emission, we get ν mr ∼ 6.39 × 10 8 η 2 3 ǫ 2 er,−1 ǫ 1/2 Br,−1 Hz and ν cr ∼ 3.29 × 10 17 ǫ −3/2 Br,−1 Hz, so the optical frequency ν opt (4.7 × 10 14 Hz) is expected to be in the regime ν mr < ν opt < ν cr and the flux density should decline with a temporal index of ≃ −2. If the radio frequency ν radio (8.5×10 9 Hz) also lies in the same regime (i.e. ν mr < ν radio < ν cr ) at 4.67 × 10 5 s, the radio flux then relates with the optical flux as Combining Eqs. (17) and (18), we obtain p < 1.5. Such a small p is inconsistent with the observed decay slope of the late-time optical and X-ray emission. As ν mr ∝ t −73/48 , we note that at 4.67 × 10 5 s, Br,−1 . Since such an initial Lorentz factor is too large, this spectral regime is unlikely (see c.f. Ioka 2010).
Radio flux from the reverse shock may be also affected by the synchrotron self absorption (SSA) of the radiating electrons. The SSA frequency in the slow cooling case is (Wu et al. 2005a) ν ar = a 3/5 ν mr , ν ar < ν mr , a 2/(p+4) ν mr , ν mr < ν ar , where is the column density of electrons heated by the reverse shock. The SSA effect leads to a different light curve in the radio band from that in the optical band if ν radio lies in one of the following regimes: ν radio < ν mr < ν ar ,ν mr < ν radio < ν ar , and ν radio < ν ar < ν mr . Among these three cases, the second one is the most likely case for GRB 090902B since we expect ν mr < ν radio for normal parameter values. So we just consider this case here and leave discussions on other cases in the Appendix. We find ν mr < ν radio < ν ar requires E 54 n −3 ǫ er,−1 ǫ Br,−1 10 4 at 4.67 × 10 5 s according to equations (3), (19) and (20). If we substitute E 54 = 2.0 and n −3 = 0.40, which are derived from the constraints by the forward shock emission, into this inequality, we obtain ǫ er,−1 ǫ Br,−1 1.25 × 10 4 , which is unlikely. Therefore we conclude that SSA effect can not solve the problem that the reverse shock scenario for the optical emission overpredicts the radio emission.

PARTIALLY RADIATIVE MODEL
It is usually assumed that the blast wave that produces the afterglow emission is nearly adiabatic (Mészáros & Rees 1997;Sari et al. 1998), i.e. the total kinetic energy of the relativistic shock is a constant. However, the energy loss of the blast wave could be significant under some circumstance.
The radiation efficiency of the blast wave is given by (Wu et al. 2005a As we can see from the above equation, the energy loss is especially important in the "fast-cooling" case (i.e. ν m > ν c ) with a large ǫ e . In this case, the decreasing blast wave energy at early times will result in a faster decay of the afterglow emission than the adiabatic case. At late time, as νm νc decreases with time, the radiation efficiency drops and the decay slope changes to the adiabatic case. We examine whether this scenario can explain the fast decay in the early optical and high-energy LAT emission. According to Huang et al. (1999) and Wu et al. (2005a), the isotropic-equivalent energy E of the blast wave evolve with time as .
The quantities describing the synchrotron spectrum in such a semi-radiative shock are similar to equations (3)- (5), except that the constant E in these equations should be replaced by a time-dependent E as described by Eq. (22). So the synchrotron emission flux decays as F ν ∝ T −3(p−1+ǫ)/(4−ǫ) for ν mf < ν < ν cf . To explain the decay slope α 1.6 of the early optical emission in GRB 090902B with this model, we need ǫ 0.6. Thus we need To explain the late optical, X-ray and radio observations, we also need: κF f opt (10 5 s) ≃ 0.01mJy, F f radio (10 5 s) ≃ 0.03mJy, and F f X (10 5 s) ≃ 0.2µJy (radio observations starts at about 1.3 × 10 5 s, we extrapolate it to 10 5 s). At 10 5 s, the two characteristic frequencies in the synchrotron spectrum are ν mf ≃ 2.0 × 10 12 E Bf,−5 Hz for ǫ e = 0.6 and p = 2.2. As ν opt , ν X , ν radio lie in three different frequency regimes, we have three independent constraints on the shock parameters. Finally we obtain n −3 ≃ 0.53, ǫ Bf,−5 ≃ 0.39, E 54 (10 5 s) ≃ 8.0 For these parameters, the deceleration time of the blast wave is T dec ≃ 120s, and we can obtain the blast wave kinetic energy at the deceleration time T dec according to Eq.(??), i.e. E 54 (T dec ) ≃ 50. This energy is extraordinary large. With such a high isotropic energy, we expect the flux density in LAT band at the deceleration time to be F f LAT (T dec ) ≃ 1µJy, which is one order of magnitude higher than the observed flux (≃ 0.1µJy). Therefore, we conclude that this model can not explain the broadband data of GRB 090902B.

TWO-COMPONENT JET MODEL
Jets from GRBs may have complex structure. For the sake of calculation ease, the structured jet can be simplified as a two-component jet. It assumes that the jet consists of two components: a narrow component with a relatively small halfopening angle (θ N ) and a large isotropic-equivalent energy in the center, and a wide component with a larger half-opening angle (θ W ) and a smaller isotropic-equivalent energy (hereafter, we use the superscripts/subscripts 'N' and 'W' represents the quantities of the narrow component and the wide component respectively). The energy distribution of the twocomponent jet can be parameterized as: The two components of the jet encounter the ISM and generate forward shock and reverse shock respectively. The observed afterglow emission is the superposition of the two component. Due to a higher kinetic energy, the contribution by the narrow component to the afterglow emission should dominate at the early time. As the bulk Lorentz factor γ N of the narrow component decreases, the light curves breaks to a steeper one once γ N < 1/θ N . After the break, the light curve of the narrow component declines much faster than that of the wide one, and the contribution by the wide component could dominate at late times. For the case of GRB 090902B, we can attribute the early optical emission around 5000s to the forward shock emission of the narrow component after the jet break, since the optical emission decays very fast. The extended high-energy emission detected by LAT can be attributed to the afterglow emission of the narrow component before the jet break and the late radio, optical and X-ray emission can be attributed to the afterglow emission of the wide component.
Considering the inverse Compton loss of electrons, the synchrotron flux density at frequency ν after the jet break is (Rhoads 1999;Sari, Piran & Halpern 1999) The jet break of the narrow component should occur after the last LAT detection (around 1000 s) and before the first ROTSE optical data at about 5000 s. Assuming a jet break time at, e.g.

T N
Break ∼ 4000s, the broadband data of GRB 090902B imply 4000s −p ≃ 9.06 × 10 −27 ergcm −2 s −1 κF W opt (1.3 × 10 5 s) ≃ 9.33 × 10 −29 ergcm −2 s −1 F W X (1.09 × 10 5 s) ≃ 1.82 × 10 −30 ergcm −2 s −1 F W radio (4.67 × 10 5 s) ≃ 6.83 × 10 −28 ergcm −2 s −1 By comparing the above flux data with the theory prediction of the two-component jet model, we get the constraints Solving this set of equations, we obtain  For the above parameter values, we find that Y (100MeV) ≪ 1 . Figures 1-4 show the fit result of the LAT, R band, Xray and radio data of GRB 090902B, respectively, and the fitting parameters are given in Table 1. In the LAT energy band (Fig. 1), we plot the forward shock emission for three different values of the initial Lorentz factor, i.e. η = 3000, 1800 and 1300 respectively. In the case of η = 3000, the shell crossing time T cross = T 90 = 25s is larger than the shell deceleration time T dec , so the reverse shock belongs to the thick shell case. In this case, the reverse shock will  transit from the Newtonian phase to the relativistic phase at time t N = l 3/2 (1+z) ∆ 1/2 η 4 c = 0.38E 1/2 54 n −1/2 −3 (η/3000) −4 (1 + z) 3/2 s. At time t N < t < T cross , the Lorentz factor of the forward shock evolves as Γ ∝ t −1/4 , and the radius of the shell evolves as R ∝ t 1/2 . Thus, the characteristic frequencies and the peak flux evolve as ν mf ∝ t −1 , ν cf ∝ t −1 and F f ν,max ∝ t. As a result, the flux of high energy emission evolves as F LAT ∝ t (−p+3)/2 in the regime ν mf < ν LAT < ν cf , and evolves as F LAT ∝ t (−p+2)/2 in the regime ν LAT > ν cf . For the inferred parameters of GRB090902B, ν LAT > ν cf , so F LAT ∝ t (−p+2)/2 ∝ t −0.1 before T cross (for p = 2.2). We can see that the η = 3000 case (the green solid line) can not account for the flux of the LAT peak at 10-20 s, although its light curve peaks at the right time. When η 1800, the reverse shock belongs to the thin shell case and light curve peaks after T 90 . In the thin shell case, the light curve rises initially as t 2 before the peak. For η = 1800, the forward shock emission can account for the LAT data after ∼ 50 s (the red solid line), but falls below the observed highenergy flux before ∼ 50 s. When η is smaller, the deceleration time is longer, as seen by the the case of η = 1300 (the blue lines).
In the optical band (Fig.2), the forward shock emission of the narrow component reproduces the early optical flash at ∼ 5000 s. The isotropic energy in the narrow jet component is E N,iso = 2.7 × 10 54 erg and its half opening-angle is θ N = 0.36 • . The afterglow emission of the wide component can also reproduce the late-time (t 1 days) optical data as well as the X-ray and radio data, if there is a jet break at ∼ 6 days (see Figs 2-4). The discrepancy between the model light curve and the first radio detection at ∼ 10 5 s could be due to strong interstellar scintillation of radio emission at early times (Cenko et al. 2010). In the fitting, the half opening-angle of the wide component is θ N = 2.8 • and the isotropic energy is E W,iso = 0.65 × 10 54 erg. The circum-burst density in the fitting is n = 0.28 × 10 −3 cm −3 , which is at the low end of the ISM density 3 . Our fitting parameters of the wide component agree well with that of Cenko et al. (2010), who modeled only the late-time optical, X-ray and radio afterglow emission. With the extra contribution by a narrow jet, our two-component jet model is able to fit also the early optical data and the LAT high-energy data after ∼ 50 s. Due to a relatively low ǫ e and a low circum-burst density n that lead to a low radiative efficiency, the radiative energy loss of the shock is unimportant, so the adiabatic shock approximation used in the calculation is valid. Ryde et al. (2010) argue that a thermal photosphere component is seen in the prompt burst emission of GRB 090902B. If this is true, the composition of the jet should be baryondominated. In this case, the reverse shock emission produced by the two components should also be present. We calculate the reverse shock emission produced by the two component jet, which are also shown in Figures 1-4. We find that the reverse shock emission is typically subdominant and that the parameters of the reverse shock are not well constrained. The parameter values given in Table 2 are just one illustration. EMISSION We have shown that the forward shock emission of the narrow jet component can account for the long-lived high-energy emission after ∼ 50 s, as shown in Fig.1, but it can not account for the early-time high-energy data. The early LAT data is inconsistent with a forward shock origin in the following aspects: 1)that the high-energy emission of GRB090902B starts to decay before T 90 is unexpected because before T 90 the shell is putting energy into the forward blast wave continuously to keep it from being decelerated quickly; 2) the LAT peak at 10-20 s is very sharp and the decay slope immediately after the peak is too steep while the forward shock emission model predicts a smooth and round peak; 3) the temporal variability of the LAT emission during the prompt bursting phase is correlated to some extent with the low-energy emission detected by GBM, while the the forward shock emission model predicts a smooth light curve. Therefore, there must be an extra component that produces the high-energy emission before ∼ 50 s in GRB 090902B. The same situation is seen in the modeling of GRB090510 , in which the forward shock emission can not account for the high-energy emission before ∼ 3 s. We first check whether the reverse shock can produce the peak at 10-20 s in the LAT light curve. Due to that the flux of reverse shock synchrotron emission rises rapidly with time before reaching its peak and that the reverse shock operates only once, the light curve of the reverse shock self inverse-Compton emission is expected to form a peak at the crossing time (Wang et al. 2001a,b;Kobayashi et al. 2007). However, due to the low density inferred for GRB 090902B from the broadband afterglow data, the scattering optical depth of electrons in the ejecta is low, so the IC flux is found to be weak. For the parameter values given by Eq.(29), the scattering optical depth in the reverse shock ejecta of the narrow component at the crossing time is

ORIGIN OF THE EARLY-TIME HIGH-ENERGY (> 100MEV)
where N r e,N = E N /ηm p c 2 is the number density of electrons in the narrow component jet. According to Eq.(14), the peak flux of the reverse shock synchrotron emission is F r,syn max,N ≈ 7.3η −1 3 ǫ 1/2 Br,−1 Jy, then we get the peak flux of the SSC emission from the reverse shock Br,−1 µJy.
Since this peak flux is lower than the observed high-energy flux, which is ∼ 3µJy (Abdo et al. 2009b), and the peak frequency of the SSC emission locates at low energy, the SSC emission from the reverse shock can not account for the LAT peak. Using the parameters constrained by the low-energy broadband afterglow data, we find that the synchrotron flux of the reverse shock at the LAT band is of the order of 10 −2 µJy, which is also much lower than the observed value. Therefore, the early LAT emission has to be attributed to some internal dissipation process that occurs at radius much smaller than the deceleration radius of the external shock. We note that there are pulses around 7.0s, 7.8s, 8.3s, 9.6s and 16s in LAT band, most of which have corresponding GBM pulses. The coincidence supports the viewpoint that the early-time LAT emission is due to internal dissipation within the outflow, such as internal shocks. Ryde et al. (2010) show that the timeresolved spectra of the prompt emission of GRB090902B from KeV to GeV can be decomposed into two components, one is the thermal multi-color blackbody component peaking at sub-MeV and another is a power-law component extending into GeV. Within this picture, the high-energy emission is attributed to the non-thermal emission (synchrotron emission, SSC or Comptonization of the thermal photons) produced by electrons in internal shocks (e.g. Ryde et al. 2010;Toma et al. 2009;Pe'er et al. 2010). Hadronic scenarios have also been proposed, including the proton synchrotron radiation (Razzaque et al. 2010) or photohadronic cascade radiation (Asano et al. 2009), which usually need a very large energy budget due to the low radiation efficiency of protons (Wang et al. 2009).
The highest-energy (33 GeV) photon is detected after the prompt burst, at 80 s after the trigger. In its local redshift (z = 1.822) frame, this energy is 94 GeV. Whether such a highenergy photon can originate from the synchrotron radiation of the forward shock is an interesting issue (Abdo et al. 2009b;Piran & Nakar 2010), as the maximum energy of electrons is limited by shock acceleration. At 80 s, the bulk Lorentz factor is γ ≃ 700 for the pa-rameter values constrained by the broadband afterglow data of GRB090902B. So the maximum synchrotron photon energy is ε max ≃ 40κ −1 (γ/700)GeV (32) according to Eq.(12) in Wang et al. (2009), where κ 1 is a parameter describing the efficiency of shock acceleration with κ = 1 corresponding to the fastest shock accelerationthe Bohm diffusive shock acceleration in which the scattering mean free path equals to the particle gyroradius. This means that the highest energy photons of GRB090902B can be marginally accommodated by the forward shock emission under the optimistic condition that particles are accelerated by the Bohm diffusive shock. Another possibility is that this highest energy photon belongs to the prompt component, although the detailed radiation mechanism is unknown. In the latter scenario, the deceleration time of the forward shock should be later than 80 s, such as the η = 1300 case (the blue lines) shown in Figure 1. Now we study the origin of the steep decay immediately after the LAT light curve peak at t = 10 − 20 s. A possible scenario for the steep decay of the high energy photons is the high-latitude emission of the jet at the end of the prompt emission phase. Because photons from high latitude regions with respect to the line of sight will arrive later than that from low latitude region due to the curved front surface of the jet, one observes a fast decreasing emission from the high-latitude region rather than an abrupt stop of the emission. The flux density of the high-latitude emission evolves with time as (Kumar & Panaitescu 2000;Wu et al. 2006;Toma et al. 2009) where ∆T is the duration of the last prompt pulse detected by LAT, T c is the LAT peak time and β is the spectral index of high-energy photons. According to Figure 1 of Abdo et al. (2009b), there is a LAT pulse around 16s. The variability time in the energy band above 100 MeV is not well-determined, although the sub-MeV emission detected by GBM shows variability timescale of ∼ 0.05 s. In some internal dissipation models, such as the residual internal shock model in which high-energy emissions arise from much larger radii (Li 2010), the variability time in high-energy emission could be longer than that of the low-energy emission. Thus, we take β = 1.1, T c = 16s and assume three different values for ∆T (i.e. ∆T =0.05s, 1s and 5s respectively) to test the highlatitude emission model. We calculate the high-latitude emission according to Eq.(33), which is shown by the black dotted lines in Fig.1. As we can see, only with a very large ∆T (i.e. ∆T 5s) can the peak-time data be fitted by this model. As such a long variability is inconsistent with the LAT data of GRB090902B, the steep decay may just reflect the tail of the on-axis prompt emission. We note that a similar conclusion has been reached for the early steeply decaying high-energy emission in GRB090510 ).

CONCLUSIONS AND DISCUSSIONS
With the broadband data from radio frequencies up to the LAT high-energy ( 100MeV) band available, GRB 090902B is a good case to examine the origin of the high-energy emission in GRBs detected by Fermi/LAT. This burst has a bright optical flash detected by ROTSE at ∼ 5000 s, which has been suspected to arise from the reverse shock (Pandey et al. 2009;Cenko et al. 2010). We first try to fit the broadband afterglow observations of GRB 090902B with the FS-RS model, with the reverse shock emission explaining the optical flash detected at 5000 s. We find that the optical and radio observations cannot be explained simultaneously by this model because a bright reverse shock optical emission will yield a much higher radio flux than observed. The self-absorption frequency of the reverse shock emission is found to be below the radio band under the constraints by the late-time forward shock optical and X-ray emission, so the self-absorption effect can not suppress the reverse shock radio emission.
Considering that the partially radiative blast wave scenario can induce a fast decay of the afterglow emission, we further test the partially radiative blast wave scenario, but find that it can not explain the broadband data of GRB 090902B either. This is mainly because that late-time optical and X-ray flux constraints in combination with the large energy loss in this scenario lead to a huge initial kinetic energy in the blast wave which overpredicts the early-time high-energy gammaray emission.
Then we propose that the two-component jet model, which consists of a narrow and bright jet component in the core and a surrounding wide and less-energetic jet component, is able to account for the broadband observations of GRB 090902B. The long-lived high-energy emission and early time optical emission can be attributed to the forward shock synchrotron emissions of the narrow component. The first optical detection at 5000 s should be later than the jet break time of the narrow component so that a fast decay optical afterglow is seen. From this, we derive that the half-opening angle of the narrow component is θ N ≃ 0.36 • . On the other hand, the late-time optical, radio and X-ray afterglows can be attributed to the wide component. To model the radio, X-ray and late-time optical light curve, a jet break at ∼ 5-10 days is needed. From this, we derive the initial half opening angle of the wide component, θ W ≃ 2.8 • . The probability of observing within the central bright core is only ∼ 10 −2 . This is consistent with the rare detection of bursts with energy as large as that of GRB090902B.
When observers view along the axis, the burst would be bright and one will see the afterglow emission produced by both the bright core and the broad wings surrounding the core. However, when observers view the burst off-axis, one would miss the bright core and will see the afterglow emission produced dominantly by the quasi-uniform wing. As a consequence, we expect that the two-component jet structure can be discerned more easily in brighter bursts, such as GRB 090902B, through afterglow observations. We note that the two-component jet model is favored in another strong, long burst -GRB 080319B (Racusin et al. 2008). A twocomponent model has also been invoked to explained the broadband data of a short GRB 090510 (Corsi et al. 2010), with the wide component explaining a mild excess in the optical band at late times 4 . Extended high-energy emission is especially useful to diagnose the narrow component, since at such early time, high-energy emission is predominantly produced by the narrow core component.
The early LAT emission of GRB090902B before ∼ 50 s after the trigger can not be explained by the external shock emission and should be due to an internal origin. This is consistent with the multiple-pulse structure of the high-energy emission and its temporal correlation with the sub-MeV emission seen during the prompt bursting phase. Modeling of the broadband data of GRB090510 also show that the external shock emission cannot account for the high-energy emission before ∼ 3 s after the trigger . The fact that one single Band function component can fit the spectrum of the prompt emission from 10 keV to GeV in GRB080916C also supports that the high-energy emission originate from the same internal dissipation process as that of the sub-MeV emission (Abdo et al. 2009a). Taken together, these results suggest that highenergy emission of GRBs detected by Fermi/LAT during the prompt bursting phase is dominated by the high-energy emission arising from the internal origin, rather than the onset of the external shock, although the external forward shock can readily account for the extended high-energy after the prompt phase (Kumar & Barniol Duran 2009Ghirlanda et al. 2010).
We would like to thank Zhuo Li for valuable comments and Zigao Dai, Yongfeng Huang and Haoning He for valuable discussions. This work is supported by the NSFC under grants 10973008 and 11033002, the 973 program under grants 2009CB824800 the Foundation for the Authors of National Excellent Doctoral Dissertations of China, the Program for New Century Excellent Talents in University, the Qing Lan Project and the Fok Ying Tung Education Foundation.

Appendix: The forward-reverse shock scenario in different spectral regimes
As we mentioned in §2, there are three different regimes in which the light curve in the radio band is affected by the synchrotron self-absorption effect and thus its behavior is different from that in the optical band at 4.67 × 10 5 s. In fact, these three cases can be categorized into two cases, i.e. (1) ν ar > ν mr and ν ar > ν radio , (2) ν ar < ν mr and ν ar > ν radio . We take E 54 = 2.0 and n −3 = 0.40, as constrained by the late radio, optical and X-ray emission and a typical value of p = 2.5 for the reverse shock is used here.

THICK SHELL CASE
The necessary condition for the thick shell is T 90 > T dec , so we get η 3 1.91. According to equations (3), (19) and (20) Table 2 Reverse-shock parameters in two-component jet model.