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Synchrotron X-rays can be a useful tool to investigate electron accelerationat young supernova remnants (SNRs). At present, since the magnetic fieldconfiguration around the shocks of SNRs is uncertain, it is not clear whetherelectron acceleration is limited by SNR age, synchrotron cooling, or evenescape from the acceleration region. We study whether the accelerationmechanism can be constrained by the cutoff shape of the electron spectrumaround the maximum energy. We derive analytical formulae of the cutoff shape ineach case where the maximum electron energy is determined by SNR age,synchrotron cooling and escape from the shock. They are related to the energydependence of the electron diffusion coefficient. Next, we discuss whetherinformation on the cutoff shape can be provided by observations in the nearfuture which will simply give the photon indices and the flux ratios in thesoft and hard X-ray bands. We find that if the power-law index of the electronspectrum is independently determined by other observations, then we canconstrain the cutoff shape by comparing theoretical predictions of the photonindices and/or the flux ratios with observed data which will be measured byNuSTAR and/or ASTRO-H. Such study is helpful in understanding the accelerationmechanism. In particular, it will supply another independent constraint on themagnetic field strength around the shocks of SNRs.

Synchrotron X-ray diagnostics of cutoff shape of nonthermal electron spectrum at young supernova remnants