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Systematic Study of Acceleration Efficiency in Young Supernova Remnants with Nonthermal X-ray Observations

Cutoff energy in a synchrotron radiation spectrum of a supernova remnant (SNR) contains a key parameter of ongoing particle acceleration. We systematically analyze 11 young SNRs, including all historical SNRs, to measure the cutoff energy, thus shedding light on the nature of particle acceleration at the early stage of SNR evolution. The nonthermal (synchrotron) dominated spectra in filament-like outer rims are selectively extracted and used for spectral fitting because our model assumes that accelerated electrons are concentrated in the vicinity of the shock front due to synchrotron cooling. The cutoff energy parameter ($\varepsilon_0$) and shock speed ($v_{\rm sh}$) are related as $ \varepsilon_0 \propto v_{\rm sh}^2 η^{-1}$ with a Bohm factor of $η$. Five SNRs provide us with spatially resolved $\varepsilon_0$-$v_{\rm sh}$ plots across the remnants, indicating a variety of particle acceleration. With all SNRs considered together, the systematic tendency of $η$ clarifies a correlation between $η$ and an age of $t$ (or an expansion parameter of $m$) as $η\propto t^{-0.4}$ ($η\propto m^{4}$). This might be interpreted as the magnetic field becomes more turbulent and self-generated, as particles are accelerated at a greater rate with time. The maximum energy achieved in SNRs can be higher if we consider the newly observed time dependence on $η$.