Jet formation is connected most probably with matter acceleration from the
vicinity of rotating magnetized bodies. It is usually related to the mass
outflows and ejection from accretion disks around black holes. Problem of jet
collimation is discussed. Collapse of a rotating magnetized body during star
formation or supernovae explosion may lead to a jet-like mass ejection for
certain angular velocity and magnetic field distributions at the beginning of
the collapse. Jet formation during magnetorotational explosion is discussed
basing on the numerical simulation of collapse of magnetized bodied with
quasi-dipole field.Comment: Will be published in the proc. of 20th Texas Symposium, Austin, Texas
  7 pages, 7 picture

Ardeljan, N. V.

Bisnovatyi-Kogan, G. S.

Moiseenko, S. G.

English

arXiv

G. S. Bisnovatyi-Kogan

Crossref

Jet formation from rotating magnetized objects

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1
Jet Formation from Rotating Magnetized Objects
G.S.Bisnovatyi-Kogan∗ N.V.Ardeljan†, S.G.Moiseenko ‡
Abstract
Jet formation is connected most probably with matter acceleration
from the vicinity of rotating magnetized bodies. It is usually related to
the mass outflows and ejection from accretion disks around black holes.
Problem of jet collimation is discussed. Collapse of a rotating magnetized
body during star formation or supernovae explosion may lead to a jet-like
mass ejection for certain angular velocity and magnetic field distributions
at the beginning of the collapse. Jet formation during magnetorotational
explosion is discussed basing on the numerical simulation of collapse of
magnetized bodied with quasi-dipole field.
1 Introduction
Matter outflow is observed in most astrophysical objects in the form of stel-
lar wind, or collimated outflow (ejection) from young stellar objects, AGN
and quasars, microquasars (galactic X-ray sources). Mechanisms of mass loss
are connected with a radiative and/or electromagnetic acceleration. The last
one, which is probably the best for producing collimated outflows, may work
quasi-stationary, or may be connected with explosive events. Rotation is always
present in compact objects, and formation of collimated jets results from the
action of magneto-rotational phenomena.
2 Problem of collimation
During accretion and outflow of matter the relative dynamical action of mag-
netic field increases for a given element of matter. As was shown in
[Schwartzman(1971)], the conservation of a magnetic flux during stationary ac-
cretion implies a dependence Br ∼ r
−2. At constant mass flux Ṁ = 4πρvrr
2
and free-fall velocity vr ∼ r
−1/2, the density increases as ρ ∼ r−3/2, and kinetic
energy density Ek ∼ r
−5/2. The growth of the magnetic energy density is faster
∗Space Research Institute, Profsoyuznaya str. 84/32, Moscow 117810, Russia, E-mail:
gkogan@mx.iki.rssi.ru
†Department of Computational Mathematics and Cybernetics, Moscow State University,
Vorobjevy Gory, Moscow B-234 119899, Russia, E-mail: ardel@redsun.cs.msu.su
‡Space Research Institute, Profsoyuznaya str. 84/32, Moscow 117810, Russia, E-mail:
moiseenko@mx.iki.rssi.ru
1
Em ∼ B
2
r ∼ r
−4. After equipartition Ek ∼ EM is reached, it cannot be violated
during subsequent accretion.
The outflow from rotating magnetized object contain azimuthal component
of the magnetic field, which energy density decreases not faster than the specific
kinetic energy of matter. For the outflow with constant velocity vr in stationary
spherical outflow the density ρ ∼ r−2, Bφ ∼ r
−1. In this conditions Ek ∼ Em,
and the trajectories of mass outflow become more tightly spiraled, and finally
the flow is becoming highly collimated with direction of the flow along the
rotational axis [Heyvaerts and Norman(1989)], [Bogovalov(1998)]. We may say
here about the universal magnetic collimation in the outflows from rotating
magnetized objects.
The outbursts may be collimated at the very beginning. When jets are
separated from the object of its origin the problem appears of preservation of
the jet against its spherization during a motion in a rarefied medium. One of the
plausible mechanism of jet preservation is a magnetic pinch collimation produced
by an axial electrical current, suggested in [Bisnovatyi-Kogan et al.(1969)].
3 Jet formation by matter outflow from magne-
tized accretion disk
Accretion of matter with a large scale magnetic field into a black hole leads to
formation of an accretion disk with a strong poloidal magnetic field. Models of
non-rotating accretion disks, supported by magnetic field had been constructed
in [Bisnovatyi-Kogan and Ruzmaikin(1974)],
[Bisnovatyi-Kogan and Ruzmaikin(1976)], see Figure 1.
Rotation of matter in such a disk is accompanied by generation of a strong
electrical field, leading to particle acceleration and ejection of matter along mag-
netic field lines. Qualitative and phenomenological models had been considered
in [Bisnovatyi-Kogan and Blinnikov(1976)],
[Blandford(1976)], [Lovelace(1976)]. Analytical self-similar solutions for jets and
winds produced by centrifugally and magnetically driven mechanisms had been
obtained in [Blandford and Payne(1982)], [Lovelace et al.(1991)].
Extensive numerical simulations have been done for construction of more re-
alistic models of quasi-stationary jet formation from magnetized accretion disks.
In the paper [Romanova et al.(1998)] numerical simulations have been done of
dynamics of magnetic loops in the coronae of accretion disks. It was obtained
that in presence of differential rotation the loops are opened in the inner parts
of the disk, and opening of loops is followed by magnetically driven outflow
from the disk. The outflow may be transient, consisting of small-scale outbursts
from different loop opening, or may be steady, corresponding to outflow along
the open field lines at the inner part of the disk, and showing some collima-
tion. Computations of magnetocentrifugally driven winds had been performed
in [Ustyugova et al.(1999)]. The stationary regime of the outflow was obtained
by solution of time-dependent MHD equations, with a split-monopole poloidal
2
B
v
disk
Figure 1: Schematic picture of magnetic field lines, obtained from the external
uniform field by accretion of a non-rotating gas with infinite conductivity into
a black hole. Dash lines are produced by the self-similar accretion flow with a
sink in the equatorial plane. In reality the accretion gas is forming a disk in the
equatorial plane, where matter is collected, and is moving into a black hole due
to non-perfect conductivity. This motion is generating additional azymuthal
currents in the disk, changing the external magnetic field. Solid lines give the
self-consistent magnetic field structure with account of currents in the disk, from
[Bisnovatyi-Kogan and Ruzmaikin(1976)].
3
field configuration frozen into the disk. Close to the disk the outflow is driven
by the centrifugal force, while at all larger distances the flow is driven by the
magnetic force, which is proportional to −∇(rBφ)
2, where Bφ is the toroidal
field. The collimation distance over which the flow becomes collimated is much
larger than the size of the sumulation region, so the obtained outflows are ap-
proximately spherical.
MHD simulation have been performed in [Ustyugova et al.(2000)] of Pointing
outflows, where the mass flux is negligible and energy and angular momentum
are carried predominantly by electromagnetic field in the form of MHD waves.
As a result of time-dependent simulations a quasi-stationary collimated Pointing
jet arises from the inner part of the disk and a steady uncollimated hydromag-
netic outflow from the outer disk for a case Keplerian disk initially threaded by
a dipole like poloidal magnetic field.
4 Magnetorotational explosions
Mechanism of magnetorotational explosion was suggested in
[Bisnovatyi-Kogan(1970)], where amplification of the toroidal component of
the magnetic field due to differential rotation leads to the transformation of
a part of the rotational energy to the energy of the ejection. First numer-
ical simulations devoted to the magnetorotational mechanism were made in
[Le Blanc and Wilson(1970)], and investigated analytically by
[Meier et.al.(1976)].
One of the most important parameters for this problem is relation of mag-
netic energy to the gravitational energy of the star: α =
Emag
|Egrav|
. 2-D simu-
lations have been done in [Ardeljan et al.(2000)] for the initial values of the
α = 10−2, 10−4, 10−6. The computations have been performed using implicit
Lagrangian scheme with triangle reconstructive grids, specially designed for as-
trophysical problems. Details of the definition of the initial magnetic field are
described in the paper [Ardeljan et al.(2000)].
Initial magnetic field chosen for our simulations has quadrupole-like kind of
symmetry (i.e. its ”z”- component is equal to zero at the equatorial plane). As
a result an ejection predominantly in the equatorial plane was obtained. The
toroidal magnetic field grows with time and produces MHD shock which moves
to the boundary of the star. Part of the matter of the envelope of the star
(about 7% of the mass of the star) has radial kinetic energy larger than its
potential energy and can be ejected. This ejected matter carries about 3.3% of
the total energy of the star (see also the previous contribution). When the ini-
tial magnetic field have a dipole-like symmetry jet formation is possible as was
first shown in calculations of [Le Blanc and Wilson(1970)]. Calculations with
the initial magnetic field structure, similar to [Le Blanc and Wilson(1970)] have
been performed using the same program as in [Ardeljan et al.(2000)]. The re-
sults are presented in Figures 2-4. The initial model (Fig.2, left) was constructed
as a differentially rotating star with a quasi-dipole magnetic field (Fig.2, right),
produced by toroidal currents ring situated at about 0.5 of the equatorial radius,
4
Figure 2: Lagrangian grid (left), and poloidal magnetic field distribution (right)
in a stationary equilibrium differentially rotating star at t1 = 18.918451, when
the magnetic field was included into calculations.
where density was less than 0.1 of the central density.
The time is given in non-dimensional units, one unit of time is roughly equal
to the time of crossing of stellar radius with the parabolic speed of the initial
model. Initial distributions of the density and angular velocity are represented
in Figure 3.
Magnetic field twisting produced strong toroidal magnetic field with local
energy density of the order of the one of the matter. Absence of the radial
component of the magnetic field in the equatorial plane led to formation of
toroidal field rings at higher latitudes. The excess of the magnetic pressure
produced a matter compression across the axis, and ejection of the matter in
the direction attached to the axis. Density distribution and velocity field in the
last calculational point with clear indication of formation of the ejection are
represented in Figure 4.
5 Mirror symmetry braking of magnetic field in
differentially rotating stars
There is a possibility of asymmetric MHD explosion, when we have asymmet-
ric magnetic field amplification. One example of development of asymmetric
picture was considered by [Bisnovatyi-Kogan and Moiseenko(1992)]. When the
collapsing and exploding star has initially toroidal and poloidal fields of different
symmetry: dipole poloidal and symmetric poloidal, or quadrupole poloidal and
antisymmetric toroidal fields, formation of an additional toroidal field from the
existing poloidal due to differential rotation leads to spontaneous breaking of
the symmetry. Due to the asymmetry of the toroidal field during the explosion
the outbursts could also become asymmetric, giving observational asymmetric
5
Figure 3: Density (left), and angular velocity (right) distributions at t1 =
18.918451.
Figure 4: Density distribution (left) and velocity field (right) at t = 30.947880,
when the mass ejection preferentially in the pole direction is formed.
6
or even one-side jets often observed in extragalactic jets, and may be in micro-
quasars [Mirabel et al.(1992)], [Fender(1999)]. Another possibility of the asym-
metry of the magnetic field was considered in [Wang et al.(1992)], where disk
with the mixture of dipole and quadrupole fields was considered. Asymmetric
magnetic field in the accretion disk may lead to appearance of asymmetric jets
in stationary and non-stationary variants. In transient accretion disks, formed
by tidal capture or destruction of the nearby star by a black hole, asymmetric
magnetic field may be formed, and magnetorotational explosion in such disk
may lead to the one side ejection.
Acknowledgments
This work was partially supported by RFBR grant 99-02-18180 and INTAS-
ESA grant 120. The authors are grateful to Prof. J.C.Wheeler and the Orga-
nizing Committee for support and hospitality, and to O.D.Toropina for help.
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