## 2. Low-frequency electromagnetic waves generated at the wind frontOur mechanism for production of short pulses of low-frequency radio emission from relativistic, strongly magnetized wind-generated cosmological GRBs applies very generally. For the sake of concreteness, we consider wind parameters that are natural in a GRB model that involves a fast rotating compact object like a millisecond pulsar or dense transient accretion disc with a surface magnetic field G (Usov 1992; Blackman et al. 1996; Katz 1997; Kluzniak & Ruderman 1998; Spruit 1999; Wheeler 1999; Woosley 1999; Ruderman, Tao, & Kluzniak 2000). In this model the rotational energy of compact objects is the energy source of cosmological GRBs. The electromagnetic torque transfers this energy on a time scale of seconds to the energy of a Poynting flux-dominated wind that flows away from the object at relativistic speeds, (e.g., Usov 1994). The wind structure at a time is similar to a shell with radius and thickness of , where is the characteristic deceleration time of the compact object's rotation, or the dissipation time of a transient accretion disc. The strength of the magnetic field at the front of the wind may be as high as where cm is the radius of the
compact object, s The distance at which deceleration of the wind due to its interaction with an ambient gas becomes important is (Mészáros & Rees 1992; Piran 1999) where Substituting for where we have introduced a parameter
which gives the fraction of the wind
power remaining in the magnetic field at the deceleration radius. For
plausible parameters of cosmological
-ray bursters,
G,
s For consideration of the interaction between a relativistic
magnetized wind and an ambient gas, it is convenient to switch to the
co-moving frame of the outflowing plasma (the wind frame). While
changing the frame, the magnetic and electric fields in the wind are
reduced from In the wind frame, the ambient gas moves to the wind front with the Lorentz factor and interacts with it. The main parameter which describes the wind-ambient gas interaction is the ratio of the energy densities of the ambient gas and the magnetic field, , of the wind where is the density of the ambient gas in the wind frame and is the proton mass. At the initial stage of the wind outflow, , is , but it increases in the process of the wind expansion as decreases. At , when is more than , the interaction between the wind and the ambient gas is strongly nonstationary, and effective acceleration of electrons and generation of low-frequency waves at the wind front both begin (Smolsky & Usov 1996, 2000; Usov & Smolsky 1998). For , the mean Lorentz factor of outflowing high-energy electrons accelerated at the wind front and the mean field of low-frequency waves weakly depend on (see Table 1) and are approximately given by to within a factor of 2, where and are the magnetic and electric field components of the waves. The mechanism of generation of these waves is coherent and consists of the following: At the wind front there is a surface current that separates the wind matter with a very strong magnetic field and the ambient gas where the magnetic field strength is negligible. This current varies in time because of nonstationarity of the wind-ambient gas interaction and generates low-frequency waves.
Fig. 1 shows a typical spectrum of low-frequency waves generated at the wind front in the wind frame. This spectrum has a maximum at the frequency which is about three times higher than the proton gyrofrequency in the wind field :
© European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |