3. Expansion of the plasmon
The plasmon after escaping from the cool disk of the Be star enters the region of the hot wind and will expand. The expansion of a relativistic plasma bubble in a gas was considered by van der Laan (1963). The time t taken by the relativistic gas bubble with an energy Er in the relativistic particles to expand to a radius r in a gas with a density n0 is given by
in seconds. The above expression is valid when the energy density of the relativistic particles is larger than the magnetic field energy density and when the dimension of the plasmon is much larger than its initial size. With the values of Er and B given in Sect. 2, the first condition is satisfied; in any case the decrease in radio emission with time implies the expansion of the plasma, which in turn implies that this condition is satisfied. The second condition is valid when rm is compared to the value of the initial size of the plasmon assumed here near the periastron.
The strength of the wind of the Be star, from UV observations is between 310-11 and 310-9 yr-1 (Snow 1982). The wind velocity V varies between about 600 km s-1 near the Be star to a terminal velocity of about 1000 km s-1. If we use yr-1 and V=600 km s-1 at a distance of 31012 cm from the Be star then the particle density in the wind at this point is n02107 cm-3. Using this value and the values of the plasmon size (rm) and energy in relativistic particles given above (Er), the delay time t can be calculated using Eq. (3). We find that t3.7 days, which is approximately the delay observed. Thus the time delay of the observed peak emission from the time of the periastron passage can be explained as the time taken by the plasmon to become optically thin as it expands in the Be star wind. The radio bursts of the lower intensity will take a longer time to reach the optically thin stage as is seen from Eq. (3). The lowest energy bursts are about a factor of about six lower in intensity than the highest energy burst, leading to a time delay of about 2.5 times the delay for the high energy burst, which is in approximate agreement with observations in view of the variability of the various parameters involved.
© European Southern Observatory (ESO) 1999
Online publication: November 3, 1999