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Дата изменения: Tue Feb 25 19:20:00 1997 Дата индексирования: Tue Oct 2 14:40:00 2012 Кодировка: Поисковые слова: manicouagan crater |
Next: The
Stopping Radius in Up: ``Ecology''
of Magnetic Rotators Previous: The
Environment of the
Now we consider qualitatively the effect of the electromagnetic field
of a magnetic rotator on the accreting plasma. Consider a magnetic rotator
with a dipole magnetic moment
, rotational frequency
and mass M. At distances
the surrounding plasma is characterized by the following parameters: density
, sound velocity
and/or velocity
relative to the star. The plasma will tend to accrete on to the star under
the action of gravitation. The electromagnetic field, however, will obstruct
this process, and the accreting matter will come to a stop at a certain
distance.
Basically, two different cases can be considered: (1) when the interaction
takes place beyond the light cylinder,
, and (2) the accreting plasma penetrates the light cylinder
.
(1) Case (1)
was first considered by Schwartzman (1970b,c)[175,
174]. In this case the magnetic rotator
generates a relativistic wind consisting of a flux of different kinds of
electromagnetic waves and relativistic particles. The form in which the
major part of the rotational energy of the star is ejected is not important
at this stage. What is important is that both relativistic particles and
magnetic dipole radiation will transfer their momentum and hence exert
pressure on the accreting plasma. Indeed, random magnetic fields are always
present in the accreting plasma. The Larmor radius of a particle with energy
eV moving in the lowest interstellar magnetic field
G is much smaller than the characteristic values of radius of interaction,
so the relativistic wind will be trapped by the magnetic field of the accreting
plasma and thus will transfer its momentum to it.
Thus, a relativistic wind can effectively impede the accretion of matter.
A cavern is formed around the magnetic rotator,
and the pressure of the ejected wind
at its boundary balances the ram pressure of the accreting plasma
:
This equality defines a characteristic size of the stopping radius,
which we call the Schwartzman radius
.
(2) The pressure of the accreting plasma is high enough to permit the
plasma to enter the light cylinder
. Since the magnetic field inside the light cylinder decreases as a dipole
field, the magnetic pressure is given by
Matching this pressure to the ram pressure of the accreting plasma yields
the AlfvИn radius
.
The magnetic pressure and the pressure of the relativistic wind can be written in the following convenient form:
We introduce a dimensionless factor
such that the power of the ejected wind is
Assuming
, we get for
a continuous function
whose qualitative behavior is shown in Figure 4.
The accreting pressure of plasma outside the capture radius
is nearly constant, and hence gravitation does not affect the medium parameters
significantly. In contrast, at distances inside the gravitational capture
radius
the matter falls almost freely and exerts pressure on the ``wall'' equal
to the dynamical pressure. For spherically symmetric accretion
we obtain
Here we used the continuity equation
. When presented in this form, the pressure
is a continuous function of distance (Figure 4).
Summarizing, for the stopping radius we get
The expressions for the AlfvИn radius are:
and for the Schwartzman radius: