Synchrotron self-absorption in pulsar magnetospheres: Implications for optical emission

Nonthermal optical emission from pulsars has been observed definitively from five objects. The model that most accurately predicts the luminosity of such emissions is that of Pacini and Salvati, a model based on synchrotron radiation originating at a constant fraction of the light cylinder. We parameterize optical emission in a similar way, obtaining the solution to the radiative transfer equation that yields expressions for the expected monochromatic luminosity and synchrotron self-absorption frequency. If due to synchrotron self-absorption, we investigate whether the rollover at IR wavelengths observed for the Crab pulsar is a process likely to be common to all the synchrotron active pulsars. Although the low-frequency turnover in the Crab pulsar spectrum may be due to a low-energy cutoff in the underlying emitting particle population or to particles emitting below their critical frequency, a test of the current self-absorption model is provided by PSR B0540-69 and the 16 ms "Crab-like" pulsar J0537-69. Our model, scaled relative to the Crab pulsar, predicts that PSR B0540-69 should exhibit a rollover between the L and I bands and that PSR J0537-69 may be self-absorbed at optical wavelengths with m_v ∼ 24 (dependent on the spectral index, a, where F _v ∼ v^-α). Our model is applicable to frequency regions well outside the optical and is limited to "young," "fast" (<100 ms) pulsars.