Ewan D. Barr edited minres2.tex  over 8 years ago

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Now, it It  is reasonable to assume that more extreme pulsars with faster spin periods than are  currently known will be found given the sensitivity of SKA1. Taking the example of If we assume  a sub-millisecond J0437$-$4715-like  pulsar with a 500-$\mu$s spin period that requires 2048 phase bins period, it would require \sim200~ns time resolution observations to be able  to full  resolve all the structure in its pulse profile, we find that this implies a maximum time resolution of 200~ns. profile.  Na\"ively speaking 200~ns time resolution would imply 5~MHz frequency channels via a reciprocal bandwidth argument. However due to the nature of the temporal response of polyphase filterbanks, we suggest that the required channel width here is actually closer to 10~MHz (the true required channel bandwidth here depends on the exact nature of the polyphase filter applied to the data). The 200~ns resolution described above is only required for high-precision pulsar timing, where we need to resolve the highest spin harmonics in the pulsars we observe. Due to the deleterious effects of the interstellar medium (ISM), we consider 200~ns time resolution to be unnecessarily high for SKA1\_Low. For the pulsar-related science goals of SKA1\_Low, a coarser resolution would be acceptable. Currently the SKA1\_Low LFAA design implies channel widths of 800~kHz being delivered to the CSP for processing. By the same arguments as above, this would provide roughly 1.6~$\mu$s effective time resolution. This is roughly 4 times better than the resolution achievable with LOFAR. We consider this resolution to be acceptable for achieving pulsar science goals with SAK1\_Low. 

\indent\textit{Definition: }\textbf{Effective Time Resolution for Pulsar Timing with SKA1}\\  Definition to follow...  While the above requirements would appear to satisfy the needs of the pulsar community, the practicality of these requirements is seriously undermined by the computational burden of performing coherent dedispersion at low frequencies on 10 MHz channels. This burden only becomes more difficult to manage as we move to larger dispersion measures (DMs). As such, the requirements suggested above need a modifier that allows them to change with DM. This modifier is provided by the physical limitations that interstellar scattering places on the minimum resolvable feature width in a pulse profile. This is discussed in detail below.