C. Sauty et K. Tsinganos, NONRADIAL AND NONPOLYTROPIC ASTROPHYSICAL OUTFLOWS .3. A CRITERION FOR THE TRANSITION FROM JETS TO WINDS, Astronomy and astrophysics, 287(3), 1994, pp. 893-926
A new class of analytical solutions for rotating MHD outflows from the
gravitational potential of a central object is discussed; the outflow
s are driven by thermal pressure gradients arising from a non polytrop
ic heating, as well as by magnetic rotator forces. The solutions are o
btained by a separation of the variables, of the spherical distance R
and of the magnetic flux function alpha in several physical key quanti
ties. Thus, the solutions are magnetic flux self-similar and treat ful
ly the dynamics of the flow from its source to large distances. The to
pology and asymptotical behaviour of this broad class of solutions is
examined in detail. At the Alfvenic and X-type critical points which t
he transAlfvenic solution crosses, the appropriate criticality conditi
ons are applied. Attention is focused on the streamline shape which is
calculated exactly and consistently throughout the outflow and allows
us to formulate a criterion that distinguishes between collimated jet
s and non collimated winds. Thus, two classes of solutions with marked
ly different asymptotics are found. The first corresponds to outflows
wherein the streamlines obtain asymptotically a conical shape on the p
oloidal plane, while the second is constituted of collimated jet-type
outflows wherein the streamlines obtain asymptotically a cylindrical s
hape. Furthermore, it is shown that a basic feature of such collimated
flows is an oscillatory jet width, without the help of an external co
nfining pressure; an analytical formula is given for the wavelength of
these oscillations. Hence, the jet does not need to focalize complete
ly along the polar axis, but through successive contractions and expan
sions in its width, it naturally relaxes into a cylindrical pattern; i
t is argued that this is due to a consistent treatment of the current
flowing along the axis of the jet. The study is applied to the relevan
t problem of jets from young stellar objects; this preliminary applica
tion suggests that several observational constraints are satisfied if
we have a two-component outflow, one originating at the star while the
other at the surrounding disc. A simple criterion is given for the tr
ansition from a magnetic rotator with collimated jets to a slow magnet
ic rotator with a noncollimated wind, in terms of the meridional aniso
tropy in the available energy in the streamlines of the outflow; it es
sentially amounts to saying that if the magnetic rotator results in a
surplus of energy along any nonpolar streamline as compared to the ava
ilable energy along the polar streamline, then the flow collimates int
o a jet. It is suggested therefore that the shape of the streamlines o
f the outflow from a rotating object switches over from cylindrical to
conical asymptotics, as the central object looses angular momentum an
d passes successively from the stage of a pre-main sequence YSO to tha
t of a main sequence star.