<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Dear All,<div class=""><br class=""></div><div class="">as promised in the telecon, here are some thoughts to perhaps include in the discussion of the low-frequency turnover.</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">There is the ‘Beskin-school’ which relates the turn-over, or ‘low-frequency cut-off’ (as they call it), is due to</div><div class="">mode propagation in the magnetosphere. Here the ‘ordinary wave has a refractive index which prevents</div><div class="">it to propagate below a certain frequency. I attach a recent review of Vasilii for your convenience. Have a</div><div class="">look at Eq. 118, which he compares with existing data in Figure 24. One could easily produce a new</div><div class="">figure with the new LOFAR data. This is certainly meat for discussion as it would be interesting to see how</div><div class="">this hold up.</div><div class=""><br class=""></div><div class="">There is work by Petrova (2002), which is along similar lines, but she concentrates more on the power-law</div><div class="">behaviour above the low-frequency turn-over. Nevertheless she summarised that the is indeed attributed</div><div class="">to propagation effects e.g. to free-free
absorption (Malov 1979) or induced scattering (Lyubarskii
& Petrova 1996).</div><div class=""><br class=""></div><div class="">The synchrotron self-absorption that I mentioned is probably the oldest model, as I find the first reference to it</div><div class="">by Sturrock (1971). But perhaps the Beskin explanation is the most commonly cited these days.</div><div class=""><br class=""></div><div class="">There is also a paper that I have been involved in (Loehmer et al. 2008), which concentrates on the</div><div class="">high-frequency part of the spectrum, but where we model the radio emission in general as a superposition</div><div class="">of short pulses. We derive the spectrum for the superposition of such pulses (Eq 3). This produces a </div><div class="">flattening of the spectrum at low frequency, but not a real turn-over. Having said this, the spectrum’s </div><div class="">formula has only three (physical) parameters (see end of section 5.2) and it may be interesting to</div><div class="">see if you can get a fit done. Perhaps, it is a combination of this plus the propagation effects mentioned</div><div class="">above.</div><div class=""><br class=""></div><div class="">I hope this is useful.</div><div class=""><br class=""></div><div class="">Cheers, Michael</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""></div></body></html>