Astron. Astrophys. 322, 242-255 (1997)
6. Emission from AE Aquarii
Having outlined the acceleration mechanism and found the regimes in
which it may operate, we now proceeed to see whether it can explain
the radio emission which we observe in AE Aqr.
6.1. Quiescent radio emission
Can acceleration by magnetic compressions power the quiescent radio
emission from AE Aqr? Since the radio spectrum is observed to increase
with frequency up to at least 394 GHz
(Abada-Simon et al. 1995a) we shall assume that the majority of
quiescent emission is output around this frequency. Assuming that the
emission is synchrotron radiation, the characteristic individual
particle energy is (Pacholczyk 1970)
![[EQUATION]](img207.gif)
or (91 in a T
field). The particles would have to be accelerated to this energy and
then kept there by pumping, balancing out with synchrotron and Coulomb
energy losses in a steady-state situation. The loss of energy in
synchrotron radiation of each particle is given by Eq. (27), and
inserting the value for the Lorentz factors of emitting particles
gives the total synchrotron power for a volume V of particles at
density ,
![[EQUATION]](img211.gif)
(integrating over solid angle, assuming an isotropic distribution
and an optically thin cloud). From Fig. 5 we see that the
magnetic field must be T for a net
acceleration to appropriate energy to take place (determined by
). Therefore we need
emitting electrons to explain the quiescent emission at
W. Acceleration can occur (giving a
sustainable emission of synchrotron radiation) in cold plasma
densities . Also, for a steady source the
particle energy density should remain smaller than the energy density
of the magnetic field, which leads to an upper
limit on the fast particle density of
m-3 (for a Lorentz factor and a
field strength T). Then the source volume is
at least m3. If the white dwarf
surface field at the poles is 100 T, this corresponds to a spherical
shell of minimum thickness m at the distance
at which the field equals T
( m). As detailed in the previous section
precipitation losses increase this distance further.
It therefore seems possible that the quiescent radio emission can
be explained by continuous energisation of the particles by the
large-scale standing field oscillations.
6.2. Flare radio emission
To produce flares, we would envisage a situation in which enough
particles are trapped on the field lines of the white dwarf and
subsequently take part in the acceleration process. As the energy
density in fast particles becomes too large with respect to that in
the field, a MHD instability sets in and a magnetic cloud containing
accelerated particles is expelled.
The number of energetic particles that may be stored in the white
dwarf magnetosphere depends both on the magnetic field geometry and on
where the energetic particles are produced. If they are deposited
within a narrow flux tube a ballooning instability is likely, leading
to an outward expansion of the flux tube releasing a cloud of
energetic particles. To find the conditions for this it is necessary
to specify the size and location of the region where the particles are
deposited.
If the energy of stored particles ,
deposited at a radius , is comparable to the
magnetic energy required to open the field
beyond , the closed field lines will open up
releasing them. Approximating the open field
by a uniform radial field which reverses direction at a current sheet
in the equatorial plane, with a flux given by a dipole magnetic flux
at , we have .
Neglecting the change in magnetic energy for ,
the condition for releasing the stored particles is,
. If we take T,
m as canonical values for the white dwarf
magnetic field and radius this maximum stored energy is
J. For example if the minimum radius at which
energisation dominates over losses is , we
expect the stored particles to be released if their energy exceeds
J.
Once the cloud of trapped particles has been released from the
magnetosphere much of the particle energy will go towards expanding
the plasmoid. The individual particle energy will decrease as
as the source radius
increases. For an observed luminosity of W, a
source size , and a bandwidth
the brightness temperature at 400 GHz is given
by
![[EQUATION]](img238.gif)
and the source is initially optically thin for
. Therefore at this frequency the brightness
temperature decreases as the plasmoid expands. However at lower
frequencies, taking into account the observed average positive slope
of the spectrum (index ), the brightness
temperature increases and the source is
initially optically thick. In fact the observed positive frequency
slope of the quiescent average radio flux and the transition from
optically thick to thin emission in a flare (Bastian et al. 1988) can
be understood if a constant number of electrons are gradually
accelerated to larger and larger energies within the same loop
structure until it bursts open.
Finally, note that the emission at the time of the outbreak of the
plasmoid is rather efficient as the synchrotron loss-time equals the
acceleration time.
6.3. Hard X-ray emission by trapped and precipitating particles
To determine if trapped particles would emit observable quantities
of X-rays we calculate the hard X-ray luminosity from:
![[EQUATION]](img242.gif)
where L is the hard X-ray luminosity, T is the
temperature of the emitting plasma, and
are the electron and ion densities with
electric charge Z, and V is the volume of the emitting plasma.
The term in brackets is the so-called emission measure (EM) which can
be simplified as V. The above equation can
therefore be re-written as:
![[EQUATION]](img246.gif)
From § 5.1 and § 6.1 we take
m-3, V
m3, (the thermal electron velocity)
= m s-1 (which implies an electron
temperature of K) and find
W. This figure is many orders of magnitude
less than the observed hard X-ray flux, W
(Eracleous et al. 1991). We conclude that the particles energised by
magnetic pumping would not contribute a significant proportion to the
observed hard X-ray flux.
If we assume that a small fraction of these energised particles
(say 1%) can escape from the magnetosphere (see x4) and generate thick
target emission near the stellar surface, the hard X-ray emission from
these particles would be W for
and
hour. If the hard X-rays are generated from
tall accretion curtains of the sort described by Eracleous et al
(1995), it is clear that the emission from the accelerated particles
would not contribute a significant amount to the overall X-ray flux
and are not the origin of the X-rays seen in AE Aqr (Clayton &
Osborne 1995).
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998
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