We investigate how the imprint of Faraday rotation on radio spectra can be used to determine the geometry of radio sources and the strength and structure of the surrounding magnetic fields. We model spectra of Stokes Q and U for frequencies between 2
00 MHz and 10 GHz for Faraday screens with large-scale or small-scale magnetic fields external to the source. These sources can be uniform or 2D Gaussians on the sky with transverse linear gradients in rotation measure (RM), or cylinders or spheroids with an azimuthal magnetic field. At high frequencies the spectra of all these models can be approximated by the spectrum of a Gaussian source; this is independent of whether the magnetic field is large-scale or small-scale. A sinc spectrum in polarized flux density is not a unique signature of a volume where synchrotron emission and Faraday rotation are mixed. A turbulent Faraday screen with a large field coherence length produces a spectrum which is similar to the spectrum of a partial coverage model. At low and intermediate frequencies, such a Faraday screen produces a significantly higher polarized signal than the depolarization model by Burn, as shown by a random walk model of the polarization vectors. We calculate RM spectra for four frequency windows. Sources are strongly depolarized at low frequencies, but RMs can be determined accurately if the sensitivity of the observations is sufficient. Finally, we show that RM spectra can be used to differentiate between turbulent foreground models and partial coverage models.
Many models for the pulsar radio and $gamma$-ray emissions have been developed. The tests for these models using observational data are very important. Tests for the pulsar radio emission models using frequency-altitude relation are presented in this
paper. In the radio band, the mean pulse profiles evolve with observing frequencies. There are various styles of pulsar profile - frequency evolutions (which we call as beam evolution figure), e.g. some pulsars show that mean pulse profiles are wider and core emission is higher at higher frequencies than that at lower frequencies, but some other pulsars show completely the contrary results. We show that all these beam evolution figures can be understood by the Inverse Compton Scattering(ICS) model (see Qiao at al.2001 also). An important observing test is that, for a certain observing frequency different emission components are radiated from the different heights. For the $gamma$-ray pulsars, the geometrical method (Wang et al. 2006) can be used to diagnose the radiation location for the $gamma$-ray radiation. As an example, Wang et al. (2006) constrain the $gamma$-ray radiation location of PSR B1055-52 to be the place near the null charge surface. Here we show that Wangs result matches the proposed radiation locations by the annular gap model as well as the outer gap models.
