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Register a new userEffects of Relativistic Expansion on the Late-time Supernova Light Curves
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Koichi Iwamoto
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The effects of relativistic expansion on the late-time supernova light curves are investigated analytically, and a correction term to the (quasi-)exponential decay is obtained by expanding the observed flux in terms of (beta), where (beta) is the maximum velocity of the ejecta divided by the speed of light (c). It is shown that the Doppler effect brightens the light curve owing to the delayed decay of radioactive nuclei as well as to the Lorentz boosting of the photon energies. The leading correction term is quadratic in (beta), thus being proportional to (E_{rm k}/(M_{rm ej} c^2)), where (E_{rm k}) and (M_{rm ej}) are the kinetic energy of explosion and the ejecta mass. It is also shown that the correction term evolves as a quadratic function of time since the explosion. The relativistic effect is negligibly small at early phases, but becomes of considerable size at late phases. In particular, for supernove having a very large energy(hypernova) or exploding in a jet-like or whatever non-spherical geometry, (^{56})Ni is likely to be boosted to higher velocities and then we might see an appreciable change in flux. However, the actual size of deviation from the (quasi-)exponential decay will be uncertain, depending on other possible effects such as ionization freeze-out and contributions from other energy sources that power the light curve.
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The light curves of type-II supernovae (SNe) are believed to be highly affected by recombination of hydrogen that takes place in their envelopes. In this work, we analytically investigate the transition from a fully ionized envelope to a partially recombined one and its effects on the SN light curve. The motivation is to establish the underlying processes that dominate the evolution at late times when recombination takes place in the envelope, yet early enough so that $^{56}$Ni decay is a negligible source of energy. We consider the diffusion of photons through the envelope while analyzing the ionization fraction and the coupling between radiation and gas, and find that the main effect of recombination is on the evolution of the observed temperature. Before recombination the temperature decreases relatively fast, while after recombination starts it significantly reduces the rate at which the observed temperature drops with time. This behaviour is the main cause for the observed flattening in the optical bands, where for a typical red supergiant explosion, the recombination wave affects the bolometric luminosity only mildly during most of the photospheric phase. Moreover, the plateau phase observed in some type-II SNe is not a generic result of recombination, and it also depends on the density structure of the progenitor. This is one possible explanation to the different light curve decay rates observed in type II (P and L) SNe.
Compact object mergers can produce a thermal electromagnetic counterpart (a kilonova) powered by the decay of freshly synthesized radioactive isotopes. The luminosity of kilonova light curves depends on the efficiency with which beta-decay electrons are thermalized in the ejecta. Here we derive a simple analytic solution for thermalization by calculating how electrons accumulate in the ejecta and lose energy adiabatically and via plasma losses. We find that the time-dependent thermalization efficiency is well described by $f(t) approx (1 + t/t_e)^{-n}$ where $n approx 1$ and the timescale $t_e$ is a function of the ejecta mass and velocity. For a statistical distribution of r-process isotopes with radioactive power $dot{Q} propto t^{-4/3}$, the late time kilonova luminosity asymptotes to $L propto t^{-7/3}$ and depends super-linearly on the ejecta mass, $L propto M^{5/3}$. If a kilonova is instead powered by a single dominate isotope, we show that the late time luminosity can deviate substantially from the underlying exponential decay and eventually become brighter than the instantaneous radioactivity due to the accumulation of trapped electrons. Applied to the kilonova associated with the gravitational wave source GW170817, these results imply that a possible steepening of the observed light curve at $gtrsim 7$ days is unrelated to thermalization effects and instead could mark the onset of translucency in a high opacity component of ejecta. The analytic results should be convenient for estimating the properties of observed kilonovae and assessing the potential late time detectability of future events.
The very nearby Type Ia supernova 2014J in M82 offers a rare opportunity to study the physics of thermonuclear supernovae at extremely late phases ($gtrsim$800 days). Using the Hubble Space Telescope (HST), we obtained six epochs of high precision photometry for SN 2014J from 277 days to 1181 days past the $B-$band maximum light. The reprocessing of electrons and X-rays emitted by the radioactive decay chain $^{57}$Co$rightarrow ^{57}$Fe are needed to explain the significant flattening of both the $F606W$-band and the pseudo-bolometric light curves. The flattening confirms previous predictions that the late-time evolution of type Ia supernova luminosities requires additional energy input from the decay of $^{57}$Co (Seitenzahl et al. 2009). By assuming the $F606W$-band luminosity scales with the bolometric luminosity at $sim$500 days after the $B-$band maximum light, a mass ratio $^{57}$Ni/$^{56}$Ni$sim$0.065$_{-0.004}^{+0.005}$ is required. This mass ratio is roughly $sim$3 times the solar ratio and favors a progenitor white dwarf with a mass near the Chandrasekhar limit. A similar fit using the constructed pseudo-bolometric luminosity gives a mass ratio $^{57}$Ni/$^{56}$Ni$sim$0.066$_{-0.008}^{+0.009}$. Astrometric tests based on the multi-epoch HST ACS/WFC images reveal no significant circumstellar light echoes in between 0.3 pc and 100 pc (Yang et al. 2017) from the supernova.
We have conducted a systematic and comprehensive monitoring programme of the Type Ia supernova 2000cx at late phases using the VLT and HST. The VLT observations cover phases 360 to 480 days past maximum brightness and include photometry in the BVRIJH bands, together with a single epoch in each of U and Ks. While the optical bands decay by about 1.4 mag per 100 days, we find that the near-IR magnitudes stay virtually constant during the observed period. This means that the importance of the near-IR to the bolometric light curve increases with time. The finding is also in agreement with our detailed modeling of a Type Ia supernova in the nebular phase. In these models, the increased importance of the near-IR is a temperature effect. We note that this complicates late-time studies where often only the V band is well monitored. In particular, it is not correct to assume that any optical band follows the bolometric light curve at these phases, and any conclusions based on such assumptions, e.g., regarding positron-escape, must be regarded as premature. A very simple model where all positrons are trapped can reasonably well account for the observations. The nickel mass deduced from the positron tail of this light curve is lower than found from the peak brightness, providing an estimate of the fraction of late-time emission that is outside of the observed wavelength range. Our detailed models show the signature of an infrared catastrophe at these epochs, which is not supported by the observations.
We present late-time optical $R$-band imaging data from the Palomar Transient Factory (PTF) for the nearby type Ia supernova SN 2011fe. The stacked PTF light curve provides densely sampled coverage down to $Rsimeq22$ mag over 200 to 620 days past explosion. Combining with literature data, we estimate the pseudo-bolometric light curve for this event from 200 to 1600 days after explosion, and constrain the likely near-infrared contribution. This light curve shows a smooth decline consistent with radioactive decay, except over ~450 to ~600 days where the light curve appears to decrease faster than expected based on the radioactive isotopes presumed to be present, before flattening at around 600 days. We model the 200-1600d pseudo-bolometric light curve with the luminosity generated by the radioactive decay chains of $^{56}$Ni, $^{57}$Ni and $^{55}$Co, and find it is not consistent with models that have full positron trapping and no infrared catastrophe (IRC); some additional energy escape other than optical/near-IR photons is required. However, the light curve is consistent with models that allow for positron escape (reaching 75% by day 500) and/or an IRC (with 85% of the flux emerging in non-optical wavelengths by day 600). The presence of the $^{57}$Ni decay chain is robustly detected, but the $^{55}$Co decay chain is not formally required, with an upper mass limit estimated at 0.014 M$_{odot}$. The measurement of the $^{57}$Ni/$^{56}$Ni mass ratio is subject to significant systematic uncertainties, but all of our fits require a high ratio >0.031 (>1.3 in solar abundances).
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