5.3 One dimensional simulations
5.3.4 Spectral evolution
Figures 5.18, 5.19 and 5.20 show the spectral evolution of the observed light curves. The color coded contour plots show the logarithm of the light curve, i.e., the luminosity in the observer frame seen at 21 frequencies logarithmi- cally spaced between 1016 and 1019 Hz for different observation times. The horizontal lines denote the frequency limits of the two light curve integra- tion bands: S (soft from 0.1 to 1keV) and H (hard from 2 to 10keV). The overplotted black line shows the temporal evolution of the spectral maxi- mum.
Figure 5.15: Light curves (top) and observer-xy plots (bottom) of models emissivity for the G0E (upper panel) and G0N (lower panel), respectively. Both light curves and the emissivity have been integrated in the frequency band 1016−1019 Hz. zis the distance
along the jet axis andT is the time measured in the laboratory frame. tobs is the time
measured by the observer.
type-E models. This is because the spectral maximum of type-N models is generally a bit lower than in type-E models, so that the radiation is “lost” from the observational bands (soft and hard). The exception are models
Figure 5.16: Same as Fig. 5.15, but for modelsG1E andG1N, respectively.
evolution has a similar behavior as in their type-E counterparts. These models have in common the Lorentz factors of the shells (Γ1 = 5, Γ2 = 15). Models G0N, G3N and G4N (Γ1 = 3, Γ2 = 15) are the most luminous, although their spectral maxima always lie below 1016 Hz.
This can be explained by the property of the type-N model of accelerat- ing only a fixed number of electrons (proportional to fluid density). Since the relative velocity between the shells in models G0N, G3N and G4N is higher than in G2N, G5N and G6N, there is more dissipation and, conse-
Figure 5.17: Same as Fig. 5.15, but for modelsG2E andG2N, respectively.
quently, electrons are being accelerated for longer time, i.e., the net effect is that more electrons have been accelerated than in the other three mod- els. However, the Lorentz factor of the fluid in the region of interaction is higher in case ofG2N,G5N andG6N, so that the radiation is more Doppler blueshifted than in the case ofG0N,G3N andG4N. A rough estimate can be done by comparing the effective Doppler factors δ = [Γeff(1−βeff)]−1 (where Γeff =√Γ1Γ2) in both cases: δ= 13 (forG0N,G3N and G4N) and
Figure 5.18: Spectral evolution of the light curves of models G0, G1 and G2, respectively. A color-coded contour plot of the logarithm ofνL(ν, t) (whereL(ν, t) is the luminosity in the observer frame, at a frequencyν at a timet) is shown. Four horizontal lines denote the two light curve integration bands, S (soft from 0.1 to 1keV) and H (hard from 2 to 10 keV). The overplotted black line shows the frequency of spectral maximum for a given time of observations. In case of models G0N and G1N the maximum in the frequency band under consideration has a frequency of 1016Hz at all times. The line exhibits sharp
jumps which are due to the finite number of frequency bins used in a simulation.
is being shifted by at least this factor (and probably by a larger factor since the region of interaction has a larger Lorentz factor than the slower shell), so that the ratio of the frequency maxima between models G2N, G5N, G6N
and G0N, G3N and G4N is > 1.3, consistent with what is seen of Figs. 5.18, 5.19 and 5.20. For similar reasons the light curves ofG1N, G7N and
G8N are very weak in the frequency band 1016-1019 Hz.
Looking at the light curves of type-E models, we can see that the rise of the spectral maximum seems to be well correlated with the rise of the ob- served intensity. This is not surprising since, in type-E models, the increase of dissipation means that the number of electrons injected increases. Since their energy distribution has always the same limits, the frequency of the spectral maximum rises as the pressure (and thus magnetic field) rises in
Figure 5.19: Same as Fig. 5.18, but for models G3, G4 and G5, respectively.
the region where a lot of kinetic energy is dissipated into thermal energy. However, the time of the observed maximum of the observed light curve does not coincide exactly with the time at which the maximum frequency of the spectral maximum is observed. This is due to the fact that, as the emitting region expands the magnetic field decreases, thus decreasing the frequency of the maximum. However, due to the expansion, more radiation arrives to the observer simultaneously. This means that the time at which the global spectral maximum is observed should be slightly ahead of the time when the global light curve maximum is observed, which is the case for all type-E models in Figs. 5.18, 5.19 and 5.20.