Afterglow Light Curves Research Articles

A Millimeter Rebrightening in GRB 210702A

We present X-ray to radio frequency observations of the bright long gamma-ray burst GRB 210702A. Our Atacama Large Millimeter/submillimeter Array 97.5 GHz observations show a significant rebrightening by a factor of ≈2 beginning at 8.2 days post-burst and rising to peak brightness at 18.1 days before declining again. This is the first such rebrightening seen in a millimeter afterglow light curve. A standard forward shock model in a stellar wind circumburst medium can explain most of our X-ray, optical, and millimeter observations prior to the rebrightening, but significantly overpredicts the self-absorbed radio emission, and cannot explain the millimeter rebrightening. We investigate possible explanations for the millimeter rebrightening, and find that energy injection or a reverse shock from a late-time shell collision are plausible causes. Similar to other bursts, our radio data may require alternative scenarios such as a thermal electron population or a structured jet to explain the data. Our observations demonstrate that millimeter light curves can exhibit some of the rich features more commonly seen in optical and X-ray afterglow light curves, motivating further millimeter wavelength studies of GRB afterglows.

Unveiling the Multifaceted GRB 200613A: Prompt Emission Dynamics, Afterglow Evolution, and the Host Galaxy’s Properties

We present our optical observations and multiwavelength analysis of the GRB 200613A detected by the Fermi satellite. Time-resolved spectral analysis of the prompt gamma-ray emission was conducted utilizing the Bayesian block method to determine statistically optimal time bins. Based on the Bayesian Information Criterion, the data generally favor the Band+blackbody (BB) model. We speculate that the main Band component comes from the Blandford–Znajek mechanism, while the additional BB component comes from the neutrino annihilation process. The BB component becomes significant for a low-spin, high-accretion-rate black hole central engine, as evidenced by our model comparison with the data. The afterglow light curve exhibits typical power-law decay, and its behavior can be explained by the collision between the ejecta and the constant interstellar medium. Model fitting yields the following parameters: EK,iso=(2.04−1.50+11.8)×1053 erg, Γ0=354−217+578 , p=2.09−0.03+0.02 , n18=(2.04−1.87+9.71)×102 cm−3, θj=24.0−5.54+6.50 degree, ϵe=1.66−1.39+4.09)×10−1 and ϵB=(7.76−5.9+48.5)×10−6 . In addition, we employed the public Python package Prospector to perform a spectral energy distribution modeling of the host galaxy. The results suggest that the host galaxy is a massive galaxy ( log(M*/M⊙)=11.75−0.09+0.10 ) with a moderate star formation rate ( SFR=22.58−7.22+13.63M⊙ yr−1). This SFR is consistent with the SFR of ∼34.2M ⊙ yr−1 derived from the [O ii] emission line in the observed spectrum.

Afterglow Linear Polarization Signatures from Shallow GRB Jets: Implications for Energetic GRBs

Gamma-ray bursts (GRBs) are powered by ultrarelativistic jets. The launching sites of these jets are surrounded by dense media, which the jets must cross before they can accelerate and release high-energy emission. Interaction with the medium leads to the formation of a mildly relativistic sheath around the jet, resulting in an angular structure to the jet’s asymptotic Lorentz factor and energy per solid angle, which modifies the afterglow emission. We build a semi-analytical tool to analyze the afterglow light curve and polarization signatures of jets observed from a wide range of viewing angles, and focus on ones with slowly declining energy profiles known as shallow jets. We find overall lower polarization compared to the classical top hat jet model. We provide an analytical expression for the peak polarization degree as a function of the energy profile power-law index, magnetic field configuration, and viewing angle, and show that it occurs near the light-curve break time for all viewers. When applying our tool to GRB 221009A, suspected to originate from a shallow jet, we find that the suggested jet structures for this event agree with the upper limits placed on the afterglow polarization in the optical and X-ray bands. We also find that at early times the polarization levels may be significantly higher, allowing for a potential distinction between different jet structure models and possibly constraining the magnetization in both forward and reverse shocks at that stage.

X-ray Afterglow limits on the viewing angles of short gamma-ray bursts

Abstract The behavior of a short gamma-ray burst (sGRB) afterglow lightcurve can reveal the angular structure of the relativistic jet and constrain the observer’s viewing angle θobs. The observed deceleration time of the jet, and, therefore, the time of the afterglow peak, depends on the observer’s viewing angle. A larger viewing angle leads to a later peak of the afterglow and a lower flux at peak. We utilize the earliest afterglow detections of 58 sGRBs detected with the Neil Gehrels Swift Observatory X-ray Telescope to constrain the ratio of the viewing angle θobs to the jet’s core θc. We adopt a power-law angular jet structure in both energy E(θ)∝θ−a and Lorentz factor Γ(θ)∝θ−b beyond the core. We find that either sGRBs are viewed within θobs/θc < 1 or the initial Lorentz factor of material in their jet’s core is extremely high (Γ0 > 500). If we consider tophat jets, we constrain 90% of our sample to be viewed within θobs/θc < 1.06 and 1.15 for our canonical and conservative afterglow scenarios. For a subset of events with measurements of the jet break, we can constrain Γ0θc ≳ 30. This confirmation that cosmological sGRBs are viewed either on-axis or very close to their jet’s core has significant implications for the nature of the prompt gamma-ray production mechanism and for the rate of future sGRB detections coincident with gravitational waves (GWs), implying that they are extremely rare.

Klein–Nishina Corrections to the Spectra and Light Curves of Gamma-Ray Burst Afterglows

Multiwavelength modeling of the synchrotron radiation from relativistic transients such as gamma-ray burst (GRB) afterglows is a powerful means of exploring the physics of relativistic shocks and of deriving properties of the explosion, such as the kinetic energy of the associated relativistic outflows. Capturing the location and evolution of the synchrotron cooling break is critical to break parameter degeneracies associated with such modeling. However, the shape of the spectrum above the cooling break, as well as the location and evolution of the break itself can be significantly altered by synchrotron self-Compton (SSC) cooling. We present an observer’s guide to applying SSC cooling with and without Klein–Nishina (KN) corrections to GRB afterglow modeling. We provide a publicly available Python code to calculate the Compton Y-parameter as a function of electron Lorentz factor, from which we compute changes to the electron distribution, along with KN-corrected afterglow spectra and light curves. In this framework, the canonical synchrotron spectral shapes split into multiple subregimes. We summarize each new spectral shape and describe its observational significance. We discuss how KN corrections can account for harder spectra and shallower decline rates observed in some GRB X-ray afterglows. Our overall aim is to provide an easy application of SSC+KN corrections into analytical multiwavelength modeling frameworks for relativistic transients.

Multiwavelength Modeling for the Shallow Decay Phase of Gamma-Ray Burst Afterglows

We simulate the emission in the shallow decay phase of gamma-ray burst afterglows using a time-dependent code. We test four models: the energy injection model, evolving the injection efficiency of nonthermal electrons, evolving the amplification of the magnetic field, and the wind model with a relatively low bulk Lorentz factor. All of the four models can reproduce the typical X-ray afterglow lightcurve. The spectral shape depends on not only the parameter values at the time corresponding to the observer time but also the past evolution of the parameters. The model differences appear in the evolution of the broadband spectrum, especially in the inverse Compton component. Future gamma-ray observations with imaging atmospheric Cherenkov telescopes such as the Cherenkov Telescope Array will reveal the mechanism of the shallow decay phase.

Multi-messenger prospects for black hole – neutron star mergers in the O4 and O5 runs

The existence of merging black hole-neutron star (BHNS) binaries has been ascertained through the observation of their gravitational wave (GW) signals. However, to date, no definitive electromagnetic (EM) emission has been confidently associated with these mergers. Such an association could help unravel crucial information on these systems, for example, their BH spin distribution, the equation of state (EoS) of the neutron star and the rate of heavy element production. We modeled the multi-messenger (MM) emission from BHNS mergers detectable during the fourth (O4) and fifth (O5) observing runs of the LIGO-Virgo-KAGRA (LVK) GW detector network in order to provide detailed predictions that can help enhance the effectiveness of observational efforts and extract the highest possible scientific information from such remarkable events. Our methodology is based on a population synthesis approach, which includes the modeling of the signal-to-noise ratio of the GW signal in the detectors, the GW-inferred sky localization of the source, the kilonova (KN) optical and near-infrared light curves, the relativistic jet gamma-ray burst (GRB) prompt emission peak photon flux, and the GRB afterglow light curves in the radio, optical, and X-ray bands. The resulting prospects for BHNS MM detections during O4 are not promising, with an LVK GW detection rate of 15.0−8.8+15.4 yr−1, but joint MM rates of ∼10−1 yr−1 for the KN and ∼10−2 yr−1 for the jet-related emission. In O5, we found an overall increase in expected detection rates by around an order of magnitude, owing to both the enhanced sensitivity of the GW detector network and the coming online of future EM facilities. Considering variations in the NS EoS and BH spin distribution, we find that the detection rates can increase further by up to a factor of several tens. Finally, we discuss direct searches for the GRB radio afterglow with large field-of-view instruments during O5 and beyond as a new possible follow-up strategy in the context of ever-dimming prospects for KN detection due to the recession of the GW horizon.

Insights into the physics of gamma-ray bursts from the high-energy extension of their prompt emission spectra

The study of the high-energy part (MeV-GeV) of the spectrum of gamma-ray bursts (GRBs) can play a crucial role in investigating the physics of prompt emission, but it is often hampered by low statistics and the paucity of GeV observations. In this work, we analyze the prompt emission spectra of the 22 brightest GRBs which have been simultaneously observed by Fermi/GBM and Fermi/LAT, spanning six orders of magnitude in energy. The high-energy photon spectra can be modeled with a power-law N(E)∝E−β possibly featuring an exponential cutoff. We find that, with the inclusion of the LAT data, the spectral index β is softer than what is typically inferred from the analysis of Fermi/GBM data alone. Under the assumption that the emission is synchrotron, we derived a median value of the index p ∼ 2.79 of the power-law energy distribution of accelerated particles (N(γ)∝γ−p). In nine out of 22 GRB spectra, we find a significant presence of an exponential cutoff at high energy, ranging between 14 and 298 MeV. By interpreting the observed cutoff as a sign of pair-production opacity, we estimate the jet bulk Lorentz factor Γ, finding values in the range 130–330. These values are consistent with those inferred from the afterglow light curve onset time. Finally, by combining the information from the high-energy prompt emission spectrum with the afterglow light curve, we exploited a promising method to derive the distance R from the central engine where the prompt emission occurs. The distances (R > 1013 − 15 cm) inferred for the only two GRBs in our sample that are suitable for the application of this method, which have only lower limits on their cutoff energies, suggest large emitting regions, although they are still compatible with the standard model. Larger samples of GRBs with measured cutoff energies and afterglow deceleration time will allow for more informative values to be derived. These results highlight the importance of including high-energy data, when available, in the study of prompt spectra and their role in addressing the current challenges of the GRB standard model.

Cascade Radiations of e ± from γγ-annihilation Process as an Extra Component of the Early Optical/X-Ray Afterglows of Gamma-Ray Bursts

Chromatic break and/or plateau observed in the early optical and X-ray afterglow lightcurves challenge the conventional external shock models of gamma-ray bursts (GRBs). Detection of TeV gamma-ray afterglows indicates strong gamma-ray production within the afterglow jets. We investigate the cascade radiations of the e ± production via the γ γ interaction in the jets. Our numerical calculations show that the cascade synchrotron emission can make a significant contribution to the early optical/X-ray afterglows. The combination of the primary and cascade emission fluxes can shape a chromatic break and/or plateau in the early optical/X-ray lightcurves, depending on the jet properties. Applying our model to GRBs 050801 and 080310, we found that their optical plateaus and the late X-ray/optical lightcurves can be explained with our model in reasonable parameter values. We suggest that such a chromatic optical plateau could be a signature of strong e ± production in GRB afterglow jets. The TeV gamma-ray flux of such GRBs should be significantly reduced and hence tends to be detectable for those GRBs that have a single power-law decaying optical afterglow lightcurve.

Scaling relations for gamma-ray burst afterglow light curves and centroid motion independent of jet structure and dynamics

ABSTRACT Models for gamma-ray burst afterglow dynamics and synchrotron spectra are known to exhibit various scale invariances, owing to the scale-free nature of fluid dynamics and the power-law shape of synchrotron spectra. Since GRB 170817A, off-axis jet models including a lateral energy structure in the initial outflow geometry have gained in prominence. Here, we demonstrate how the scale invariance for arbitrary jet structure and dynamical stage can be expressed locally as a function of jet temporal light-curve slope. We provide afterglow flux expressions and demonstrate their use to quickly assess the physical implications of observations. We apply the scaling expressions to the Swift X-ray Telescope sample, which shows a spread in observed fluxes, binned by light-curve slope at time of observation, that increases with increasing light-curve slope. According to the scaling relations, this pattern is inconsistent with a large spread in environment densities if these were the dominant factor determining the variability of light curves. We further show how the late deep Newtonian afterglow stage remains scale-invariant but adds distinct spectral scaling regimes. Finally, we show that for given jet structure a universal curve can be constructed of the centroid offset, image size, and ellipticity (that can be measured using very large baseline interferometry) versus observer angle, in a manner independent of explosion energy and circumburst density. Our results apply to any synchrotron transient characterized by a release of energy in an external medium, including supernova remnants, kilonova afterglows, and soft gamma-repeater flares.

A comparative study of outflow structures of two classes of gamma-ray bursts

ABSTRACT The outflow structures of gamma-ray bursts (GRBs) can provide insights into the origins and radiation mechanisms of these cosmic explosions. We systematically study the GRB outflow structures by modelling their afterglow light curves and check if the structures of long gamma-ray bursts (LGRBs) and short gamma-ray bursts (SGRBs) are different. The sample consists of Swift-XRT afterglows with sufficient coverage and known redshift, which includes 195 well-fit LGRBs and 13 well-fit SGRBs. The model we use is a two-parameter ‘boosted fireball’ model, which consists of a family of outflows, with shapes varying smoothly from a quasi-spherical outflow to a highly collimated jet. We use the jetfit package to fit afterglow light curves and obtain the jet parameters. We find that there are no statistical differences in the distributions of jet parameters between LGRBs and SGRBs by performing K–S test and 74 per cent of the ratios of the observer angle to jet opening angle are in the range of 0.2 to 1. Our analysis indicates that the majority of GRB afterglows are viewed off-axis and there has no statistical difference between LGRBs and SGRBs. We also find that both the LGRBs and SGRBs exhibit two similar correlations: the jet opening angle is positively correlated with the observer angle, with the correlation coefficient 0.61 for LGRBs and 0.63 for SGRBs; the circumburst density is inversely correlated with the explosion energy with the correlation coefficient −0.89 for LGRBs and −0.69 for SGRBs. Our results suggest that the outflow structures are similar for the LGRBs and SGRBs.

GRB 200612A: An Ultralong Gamma-Ray Burst Powered by Magnetar Spinning Down

GRB 200612A could be classified as an ultralong gamma-ray burst due to its prompt emission lasting up to ∼1020 s and the true timescale of the central engine activity t burst ≥ 4 × 104 s. The late X-ray light curve with a decay index of α = 7.53 is steeper than the steepest possible decay from an external shock model. We propose that this X-ray afterglow can be driven by dipolar radiation from the magnetar spindown during its early stage, while the magnetar collapsed into the black hole before its spindown, resulting in a very steep decay of the late X-ray light curve. The optical data show that the light curve is still rising after 1.1 ks, suggesting a late onset. We show that GRB 200612A’s optical afterglow light curve is fitted with the forward shock model by Gaussian structured off-axis jet. This is a special case among GRBs, as it may be an ultralong gamma-ray burst powered by a magnetar in an off-axis observation scenario.

Potential biases and prospects for the Hubble constant estimation via electromagnetic and gravitational-wave joint analyses

ABSTRACT GW170817 is a binary neutron star merger that exhibited a gravitational wave (GW) and a gamma-ray burst, followed by an afterglow. In this work, we estimate the Hubble constant (H0) using broad-band afterglow emission and relativistic jet motion from the Very Long Baseline Interferometry and HST images of GW170817. Compared to previous attempts, we combine these messengers with GW in a simultaneous Bayesian fit. We probe the H0 measurement robustness depending on the data set used, the assumed jet model, the possible presence of a late time flux excess. Using the sole GW leads to a 20 per cent error ($77^{+21}_{-10}$ $\rm km\, s^{-1}\, Mpc^{-1}$, medians, 16th–84th percentiles), because of the degeneracy between viewing angle (θv) and luminosity distance (dL). The latter is reduced by the inclusion in the fit of the afterglow light curve, leading to $H_0=96^{+13}_{-10}$ $\rm km\, s^{-1}\, Mpc^{-1}$, a large value, caused by the fit preference for high viewing angles due to the possible presence of a late-time excess in the afterglow flux. Accounting for the latter by including a constant flux component at late times brings $H_0=78.5^{+7.9}_{-6.4}$$\rm km\, s^{-1}\, Mpc^{-1}$. Adding the centroid motion in the analysis efficiently breaks, the dL − θv degeneracy and overcome the late-time deviations, giving $H_0 = 69.0^{+4.4}_{-4.3}$ $\rm km\, s^{-1}\, Mpc^{-1}$ (in agreement with Planck and SH0ES measurements) and $\theta _{\rm v} = 18.2^{+1.2}_{-1.5}$°. This is valid regardless of the jet structure assumption. Our simulations show that for next GW runs radio observations are expected to provide at most few other similar events.

Magnetar Central Engine Powering the Energetic GRB 210610B?

The bright GRB 210610B was discovered simultaneously by Fermi and Swift missions at redshift 1.13. We utilized broadband Fermi-GBM observations to perform a detailed prompt emission spectral analysis and to understand the radiation physics of the burst. Our analysis displayed that the low energy spectral index (αpt) exceeds boundaries expected from the typical synchrotron emission spectrum (-1.5,-0.67), suggesting additional emission signature. We added an additional thermal model with the typical Band or CPL function and found that CPL + BB function is better fitting to the data, suggesting a hybrid jet composition for the burst. Further, we found that the beaming corrected energy (Eγ,θj = 1.06 × 1051 erg) of the burst is less than the total energy budget of the magnetar. Additionally, the X-ray afterglow light curve of this burst exhibits achromatic plateaus, adding another layer of complexity to the explosion’s behavior. Interestingly, we noted that the X-ray energy release during the plateau phase (EX,iso = 1.94 × 1051 erg) is also less than the total energy budget of the magnetar. Our results indicate the possibility that a magnetar could be the central engine for this burst.

GRB 080710: A narrow, structured jet showing a late, achromatic peak in the optical and infrared afterglow?

We present a possible theoretical interpretation of the observed afterglow emission of long gamma-ray burst GRB 080710. While its prompt GRB emission properties are normal, the afterglow light curves in the optical and infrared bands are exceptional in two respects. One is that the observed light curves of different wavelengths have maximum at the same time, and that the achromatic peak time, 2.2×103 s after the burst trigger, is about an order of magnitude later than typical events. The other is that the observed flux before the peak increases more slowly than theoretically expected so far. Assuming that the angular distribution of the outflow energy is top-hat or Gaussian-shaped, we calculate the observed light curves of the synchrotron emission from the relativistic jets and explore the model parameters that explain the observed data. It is found that a narrowly collimated Gaussian-shaped jet with large isotropic-equivalent energy is the most plausible model for reproducing the observed afterglow behavior. Namely, an off-axis afterglow scenario to the achromatic peak is unlikely. The inferred values of the opening angle and the isotropic equivalent energy of the jet are possibly similar to those of GRB 221009A, but the jet of GRB 080710 has a much smaller efficiency of the prompt gamma-ray emission. Our results indicate a greater diversity of the GRB jet properties than previously thought.

Impact of anisotropic ejecta on jet dynamics and afterglow emission in binary neutron-star mergers

ABSTRACT Binary neutron-stars mergers widely accepted as potential progenitors of short gamma-ray bursts. After the remnant of the merger has collapsed to a black hole, a jet is powered and may breakout from the the matter expelled during the collision and the subsequent wind emission. The interaction of the jet with the ejecta may affect its dynamics and the resulting electromagnetic counterparts. We here examine how an inhomogeneous and anisotropic distribution of ejecta affects such dynamics, dictating the properties of the jet-ejecta cocoon and of the afterglow radiated by the jet upon deceleration. More specifically, we carry out general-relativistic hydrodynamical simulations of relativistic jets launched within a variety of geometrically inhomogeneous and anisotropic distributions of ejected matter. We find that different anisotropies impact the variance of the afterglow light curves as a function of the jet luminosity and ejected mass. A considerable amount of the jet energy is deposited in the cocoon through the jet-ejecta interaction with a small but important dependence on the properties of the ejecta. Furthermore, all configurations show a two-component behaviour for the polar structure of the jet, with a narrow core at large energies and Lorentz factors and a shallow segment at high latitudes from the jet axis. Hence, afterglows measured on off-axis lines of sight could be used to deduce the properties of the ejected matter, but also that the latter need to be properly accounted for when modelling the afterglow signal and the jet-launching mechanisms.

Unraveling parameter degeneracy in GRB data analysis

ABSTRACT Gamma-ray burst (GRB) afterglow light curves and spectra provide information about the density of the environment, the energy of the explosion, the properties of the particle acceleration process, and the structure of the decelerating jet. Due to the large number of parameters involved, the model can present a certain degree of parameter degeneracy. In this paper, we generated synthetic photometric data points using a standard GRB afterglow model and fit them using the Markov chain Monte Carlo (MCMC) method. This method has emerged as the preferred approach for analysing and interpreting data in astronomy. We show that, depending on the choice of priors, the parameter degeneracy can go unnoticed by the MCMC method. Furthermore, we apply the MCMC method to analyse the GRB 170817A afterglow. We find that there is a complete degeneracy between the energy of the explosion E, the density of the environment n, and the microphysical parameters describing the particle acceleration process (e.g. ϵe and ϵB), which cannot be determined by the afterglow light curve alone. Our results emphasize the importance of gaining a deep understanding of the degeneracy properties which can be present in GRB afterglows models, as well as the limitations of the MCMC method. In the case of GRB 170817, we get the following values for the physical parameters: E = 8 × 1050–1 × 1053 erg, n = 7 × 10−5–9 × 10−3, ϵe = 10−3–0.3, ϵB = 10−10–0.3.

On the Theory of Ring Afterglows

Synchrotron and inverse Compton emission successfully explain the observed spectra of gamma-ray burst (GRB) afterglows. It is thought that most GRBs are products of extremely relativistic outflows and the afterglow marks the interaction of that ejecta with the surrounding matter. A faster decay of afterglow light curves at late times is indicative of nonspherical geometries, and is usually interpreted as evidence for jet geometry. Recent numerical simulations have shown that ring-like geometries are also permissible for relativistic outflows. We therefore extend the standard theory of afterglow evolution to ring geometries. An analytic prescription for the light curves and spectra produced by relativistic toroidal blast waves is presented. We compare these to their spherical and jet-like counterparts, and show that ring afterglows decay faster than spherical outflows but not as fast as jets.

GRB 221009A: Revealing a Hidden Afterglow during the Prompt Emission Phase with Fermi-GBM Observations

Recently, LHAASO reported the detection of the brightest-of-all-time GRB 221009A, revealing the early onset of a TeV afterglow. We analyze the spectral evolution of the X-ray/gamma-ray emission of GRB 221009A measured by the Fermi Gamma-ray Burst Monitor (GBM) during the dips of two prompt emission pulses (i.e., intervals T 0 + [300–328] s and T 0 + [338–378] s, where T 0 is the GBM trigger time). We find that the spectra at the dips transit from the Band function to a power-law function, indicating a transition from the prompt emission to the afterglow. After ∼T 0 + 660 s, the spectrum is well described by a power-law function, and the afterglow becomes dominant. Remarkably, the underlying afterglow emission at the dips smoothly connect with the afterglow after ∼T 0 + 660 s. The entire afterglow emission measured by GBM can be fitted by a power-law function F ∼ t −0.95±0.05, where t is the time since the first main pulse at T* = T 0 + 226 s, consistent with the TeV afterglow decay measured by LHAASO. The start time of this power-law decay indicates that the afterglow peak of GRB 221009A should be earlier than T 0 + 300 s. We also test the possible presence of a jet break in the early afterglow light curve, finding that both the jet break model and single power-law decay model are consistent with the GBM data. The two models cannot be distinguished with the GBM data alone because the inferred jet break time is quite close to the end of the GBM observations.

The signature of refreshed shocks in the afterglow of GRB 030329

ABSTRACT GRB 030329 displays one clear and, possibly, multiple less intense fast-rising (Δt/t ∼ 0.3) jumps in its optical afterglow light curve. The decay rate of the optical light curve remains the same before and after the flux jumps. This may be the signature of energy injection into the shocked material at the front of the jet. In this study, we model the Gamma-ray Burst (GRB) ejecta as a series of shells. We follow the dynamical evolution of the ejecta as it interacts with itself (i.e. internal shocks) and with the circumburst medium (i.e. external forward and reverse shocks), and calculate the emission from each shock event assuming synchrotron emission. We confirm the viability of the proposed model in which the jumps in the optical afterglow light curve of GRB 030329 are produced via refreshed shocks. The refreshed shocks may be the signatures of collisions between earlier ejected material with an average Lorentz factor $\bar{\Gamma }\gtrsim 100$ and later ejected material with $\bar{\Gamma } \sim 10$ once the early material has decelerated due to interaction with the circumburst medium. We show that even if the late material is ejected with a spread of Lorentz factors, internal shocks naturally produce a narrow distribution of Lorentz factors (ΔΓ/Γ ≲ 0.1), which is a necessary condition to produce the observed quick rise times of the jumps. These results imply a phase of internal shocks at some point in the dynamical evolution of the ejecta, which requires a low magnetization in the outflow.