The frequency dependence of scattering imprints on pulsar observations

Observations of pulsars across the radio spectrum are revealing a dependence of the characteristic scattering time ($\tau$) on frequency, which is more complex than the simple power law with a theoretically predicted power law index. In this paper we investigate these effects using simulated pulsar data at frequencies below 300 MHz. We investigate different scattering mechanisms, namely isotropic and anisotropic scattering, by thin screens along the line of sight, and the particular frequency dependent impact on pulsar profiles and scattering time scales of each. We also consider how the screen shape, location and offset along the line of sight lead to specific observable effects. We evaluate how well forward fitting techniques perform in determining $\tau$. We investigate the systematic errors in $\tau$ associated with the use of an incorrect fitting method and with the determination of an off-pulse baseline. Our simulations provide examples of average pulse profiles at various frequencies. Using these we compute spectra of $\tau$ and mean flux for different scattering setups. We identify setups that lead to deviations from the simple theoretical picture. This work provides a framework for interpretation of upcoming low frequency data, both in terms of modelling the interstellar medium and understanding intrinsic emission properties of pulsars.