## 2. BackgroundIn what follows we will assume that RFM exists. In other words, the radiation received at a particular frequency, , can be clearly mapped to a certain altitude above the neutron star surface, , where the emission takes place. We are interested in the absolute value of the emission altitude as well as its dependence on frequency, generally assumed to be a power law, Under this assumption, we might be able to observe a difference in the times-of-arrival (TOAs) of a pulse profile observed at different frequencies. Several contributions to this time difference are possible. Following Phillips (1991b; 1992, hereafter P92), we take four major effects into account.
Here we have chosen the sign in the sense that is positive if is fulfilled.
with as the electron column density along
the path to the pulsar, which is called
In this expression, is the inclination angle
between spin and magnetic axis and where the sign is chosen in the sense of Eq. (3). In the case that the emission region is located well inside the light cylinder, i.e. , the relation simplifies to
which gives rise to a time delay of approximately Adding these major contributions we obtain for the total time difference Within the canonical model that high frequency emission originates from closer to the neutron star than low frequency emission, i.e. validity of relation Eq.(3), the first and third term are positive while the second and last contribution are negative. In other words, while retardation and aberration effects are delaying the high frequency emission (with respect to low frequency emission), dispersion and magnetic field sweep back act in just the opposite way. Since previous results indicate that even the low frequency emission takes place well inside the light cylinder (e.g. Cordes 1978, Matese & Whitmire 1980, BCW, P92 or Kijak & Gil 1996), we make use of the simpler expression for the aberration delay and obtain where we have introduced and used
© European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |