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OCR for page 46
Manifestations of Dynamo Driven Large-Scale
Magnetic Field in Accretion Disks of Compact Objects
G. D. CHAGELISHVILI, R.G . CHANISHVILT, J.G. LOMINADZE,
AND Z.A. SOKHADZE
Abastumani Astrophysical Observatory
ABSTRACT
Many observations, as well as the possible theoretical explanations
of these observations, indicate that the existence of mean (large-scale)
magnetic fields in the majority of astrophysical objects is determined by
the turbulent dynamo action. The magnetic field generation sources in the
turbulent dynamo mechanism are the differential rotation of the medium
and the gyrotropic character of the turbulence, existing in this medium
(Moflatt 1978; Vainstein et al. 198~, Krause and Radler 1980~. In the
accretion disks of the compact objects the matter is moving due to the
Kepler law, i.e. the rotation has a strong differential character. That
is why one can suppose that in the convect~vely active regions of these
objects the especially favorable conditions for the large-scale magnetic
field generation are realized. In fact, the generation of the large-scale
magnetic field in turbulent dynamo theory depends on the value of the so-
called dynamo number (Moflatt 1978), determined by the parameters of the
medium and turbulence. In the case of the accretion disk, these parameters
have such values that when there is a thermal convection, the large-scale
magnetic field is generated without any difficulties. The maximum value
reached by the magnetic field is determined by nonlinear phenomena, i.e.
by suppression of the sources of generation by the magnetic field itself (in
the case of the accretion disk it is a suppression of the helical character
of turbulence (Chagelishvili et al. 19863. The turbulent dynamo nonlinear
theory developed by us (Chagelishvili et al. 1986, 1988) shows that in the
compact objects of accretion disks, the generated large-scale magnetic field
(when the generation takes place) has a practically toroidal configuration.
46
OCR for page 47
HIGH-ENERGY ASTROPHYSICS
47
Its energy density can be much higher than turbulent pulsations energy
density, and it becomes comparable with the thermal energy density of the
medium. On the basis of these constantations the manifestations to which
the large-scale magnetic field can lead at the accretion onto black holes
and gravimagnetic rotators respectively are presented.
In particular, it is shown below that at the accretion onto the black
holes, the dynamical activity of the strong toroidal, large-scale magnetic
field as a result of the Parker instability development, in the disk, max-
imum energy release region, can create such formations (hot, optically
thin coronaes3 which can explain, for example, the Cyg X-1 spectrum and
radiation specifications in the low state of this source.
It is also shown below that at the disk accretion of the magnetized
plasma onto an aligned grav~nagnet~c rotator, the existence of two magnetic
fields of different origin in the system leads to the asymmetric accretion of
the matter. The accretion mainly takes place selectively onto one of the
magnetic poles depending on the co-rotation and Alfven radii ratio.
BIMODAL ACCRETION ON CYGNUS X-1
Turbulence in accretion disks may be caused by the differential char-
acter of matter rotation on Keplerian orbits and/or by the existence of a
superadiabatic pressure gradient across the disk (when it does exist). The
kinds of turbulence corresponding to these two factors are called shear and
convective turbulence, respectively. Both kinds of turbulence can create
an anomalous nscositr, transporting angular momentum outwards through
the disk and thus causing an accretion. However, there is a basic difference
between these kinds of turbulence, which account for the bimodal character
of accretion in Cyg X-1. This difference is the following: shear turbulence
is mainly two~imensional and has no gyrotropic character, while convec-
tive turbulence is especially three-dimensional and of gyrotropic character.
Therefore, convective turbulence in a differentially rotating accretion disk
generates helicity and leads to amplification of large-scale magnetic fields
(Chagelishvili e! al. 1986~. Thus, unlike shear turbulence, convective tur-
bulence may make an accretion disk magnetically active, but only if there
exists a large-scale magnetic seed field which is not too small. On this
property of convective turbulence along the bimodal ac~edon, the model
for Cyg X-1 (Chagelishvili et al. 1986, 1988) is founded. It predicts, for a
"low" state, the formation of hot magnetic arcs: the very inhomogeneities
which are able to create MV for this source.
The model assumes (Chagelishvili et al. 1986, 1988) a variation of the
.
accretion rate M in a certain interval (M1, M2) and the existence of some
critical rate MA in it (Here MCr has nothing in common with the critical
Eddington accretion rate). Shear turbulence definitely exists in the whole
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48
AMERICAN AND SOY7ET PERSPECTIVES
accretion disk (Chagelishvili et al. 1988), but convective turbulence is only
inherent to the inner t radiation-dominated region of the accretion disk and
is always absent In the outer region. Thermal convection is also absent in
the middle region if M > Mcr' and for M < MCr the parameters of the
region are such that it becomes unstable against thermal convection; that
is, the middle region becomes connectively active.
This is the very circumstance that makes the accretion disk magnetically
active and switches Cyg X-1 to the "low" state. But how does it actually
happen?
Originally a magnetic field is camed to the disk by the matter coming
from the optical component of the binary system. A part of this field,
being large-scale, may be considered as a seed field for the processes
described by the turbulent dynamo equations. In the outer region where
helical turbulence is absent (there is no thermal convection), the large-scale
magnetic field decreases because of the turbulent diffusion arising from the
shear turbulence. If thermal convection in the middle region is still absent
(M > Mcr), the decrease of the large-scale field transported through by the
matter is not able to supply the inner region of the disk with a sufflcientl`,r
strong large-scale magnetic field. As a result, in spite of the fact that
the large-scale magnetic field is generated in the inner, convectivetr active
region of the disk, estimations show (Chagelishvili e! al. 1986) that it does
not have time to increase up to perceptible values, and accretion goes on
without a large-scale magnetic field, mainly in accordance with the standard
model Thus, we can say that when M > M=, Cyg X-1 is in a "high" state.
When M < Mar, thermal convection appears in the middle region
of the disk and the generation of a large-scale magnetic field has already
begun here long before the matter comes to the inner region. It should
be emphasized that the generated large-scale magnetic field is virtually
azimuthal (Chagelishvili e! al. 19863. Under such conditions, the magnetic
forces become stronger in the region of the main energy release of the
disk and have a real influence on the matter dynamics. Namely they give
rise to a Parker instabilit~rather oblonged parts of some magnetic tubes
emerge out of the main volume of the disk, forming arcs of decreased
density above it. At the same time the greater part of the magnetic tube
matter sinks toward the central plane, forming "clots" situated between the
arcs (see Figure 1~. The study of Parker instability in the inner region of an
accretion disk made by Chagelishvili ~ al. (1988) shows that in the process
~ It is well known that depending on the nature of opanDr (complon scauenng Ke ,, or free-free
transitions Kff ~ and on the ratio of the gas pressure to the radiation pressure Pg/Pr), there may
be three regions in an accretion disk (Shakura and Sunyaev 1973~: an outer region (ems << Kf I;
P,/Pr ~ 1), a middle region (ReS ~ Kff; Pg/Pr ~ 1), and an inner region (Ken ~ Kff;
Pg/Pr << 1).
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HIGH-ENERGY ASTROPHYSICS
A_
_:
;Z'
:'\-
49
FIGURE 1 Schematic geometry of the disl: inner region in the cross section r = const
at the Parker instability development. Shaded regions present clustem of concentrated gas.
Solid Attires with arrows are magnetic lines folded from the initial azimuthal magnetic
field.
of instability development, mainly with maximum growth rate perturbations
that have no Z ~ -Z reflection symmetry are amplified (see Figure 1).
The action of Parker instability described above must be considered as
a quasiperiodical process. We assume that magnetic flux tubes emerging in
the region of the main energy release are heated, forming a hot, optically
thin corona. The latter is made up of several magnetic arcs which are
connected with the main disk and are sweeping inward in the process of
matter accretion. Then the magnetic flux tubes emerge once again and
the Cycle continues. At any subsequent time, the magnetic flux tube may
emerge at a different distance from the black hole.
Thus we propose that a number of these magnetic arcs of decreased
density form, due to heating, the hot, optically thin corona so necessary for
explaining the power-law spectrum of Cyg X-1 in the "low" state. Such a
spectrum is generated in the arcs by comptoni~tion of soft X-ray photons
emitted by dense clusters of relatives cold plasma between and under the
arcs in the vicinity of the equatorial plane of the disk (see Figure 1~. The
corona made up of these magnetic arcs will cover only a part of the colder
"core" which, in fact, is indirectly confirmed by some observations of C;yg
X-1 (Sunyaev and lluemper 1979~.
We hold that macroscopic magnetic arcs rapidly rotating in the region
of the main energy release are the very "hot spots" necessary to explain
millisecond variation phenomena in a "low" state.
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50
AMERICAN AND SOVIET PERSPECTIVES
ASYMMETRIC DISK ACCRETION ONTO MAGNETIZED
ROTATING COMPACT STARS
The phenomena, occurnog at disk accretion onto magnetized rotating
compact stars in all their diversity, have been studied since the early
1970s. They have been collected and classified in the books of Shapiro and
Teukosly (1983) and Lipunov (1987~. The completeness of the research is
limited as they considered only the non-magnetized disks, i.e., the cases of
the accretion disks without Me magnetic field, which can really influence
the interaction processes of the accredng gas and compact star's magnetic
field. First of all it is relevant to the processes taldug place on the Even
surface. In fact, as the researchers say, under certain conditions (the
existence of the convective turbulence of hyrotropic nature in the larger
part of the disk) the case where the disk has the large-scale magnetic field
generated as a result of the turbulent dynamo action is realized. The field
obtained thus is mainly of toroidal configuration (Chagelishvili e' al. 1986)
and is capable of mounting to the meaning where the magnetic pressure
of the disk becomes comparable with its thermal pressure (Chagelishvili e'
al. 1986~. In other words, it becomes comparable with the compact star
magnetic pressure on the Alden surface. It is easy to understand that this
circumstance will radically change the Secreting gas penetration ways and
means into the star magnetic pole. To be more specific, the strong toroidal
magnetic field of a disk will prevent the interchange instability and thus
will exclude the scenario of plasma penetration into the magnetosphere
developed in papers by Ghosh and Lamb (1979a,b).
The peculiarities of the accretion at a magnetized disk are revealed in
the most simple and, consequently, the most easily obsene~d case which we
are going to consider: a compact star, whose rotation and magnetic axes
coincide (let us direct these axes along z-coordinate). We shall idealize a
compact magnetized star as a gravimagnetic rotator with three character-
istics: mass, magnetic dipole moment, and rotational moment Such an
object can seine as the model for absolutely different astophysical objects:
neutron stars, white dwarfs, magnetic stars and spinars-the supermassive
stars. Let us consider that this magnetized thin accretion disk is in the
equatorial plane of the star. Moreover, let us suppose the equilibrium
rotation of the compact star to be almost achieved (Lipunov 1987~: on the
Alden surface the Secreting plasma almost corotates with the field lines of
the star's magnetic field. This occurs when the Alfven (RA) and corotation
(Rc) radii are close to each other: RA ~ RC. AS iS known (Lipunov
1987) the similar corelation between these radii is quite widespread and
that is why when considering it, one can hope that we encompass the most
interesting cases Besides, it is especially easy to describe the field lines
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HIGH-ENERGY ASTROPHYSICS
51
reconnection process of the rotator and the accretion disk magnetic fields
while obse~v~g the above-mentioned ratio.
Let us note that the change of the dipole magnetic field direction
into the opposite one, in the case of non-magnetized plasma disk accretion
in the align rotator, does not influence the accretion physics: the physical
processes are symmetrical relatives to the equatorial plane. But in our case
the existence of two magnetic fields of different origin, the accretion disk
toroidal field (Be) and the rotator dipole field (BD), in the system leads
to the occurrence of asymmetry (relative to z-axis) in the direction of the
physical phenomena, and this asymmetry is determined by the B.<,, and BD
mutual orientation. Namely, the manifestation of this asymmetry is such a
circumstance when the plasma accretion will take place mainly to one of the
rotator magnetic poles and not to both. The accretion will be asymmetrical
in the case discussed by us and that, by all means, should adequately
describe the observational manifestations of such systems. Concretely, the
reason for this asymmetry is the following: the star and the accretion disk
magnetic fields are crossed. This fact promotes their reconnection on the
Eleven surface and the latter promotes the formation of the "channels"
(see Figure 4~. The accreting plasma "slips" along the "channels" mainly
to one of the two magnetic poles of the rotator.
Let us discuss the reconnection process in detail. The reconnection
of the magnetic field lines takes place as a result of the tearing-mode
instability development (Furth et al. 1963; Lee and Fu 1985; Southwood et
al. 1986) in solar situations. In our case the dissipative effects are insured
by the disk turbulence (Chagelishvili et al. 1986) that leads to the Reynolds
magnetic numbers Rm ~ 102 . 103. The mathematic methods of the tearing
mode instability research are quite non-trivial. However, the information
necessary for the qualitative description of the field lines behavior during
the reconnections on the Alfven surface can be extracted from the papers
(Furth et al. 1963; Lee and Fu 1985; Southwood et al. 19863. In accordance
with them the field line dynamics can be schematically presented as follows.
Figure 2 presents the align rotator ~D) and the accretion disk (B¢)
field lines on the Alfven surface separately from each other. The bold
lines present the regions, which are magnified in Figure 3 and where the
reconnection physics is described. The reconnection of the crossed field
lines occurs at the nodal points (Figure 3a) during the characteristic tome
(r ~ Rmi/2/Q) where Q is the star rotation angular velocity (Furth et al.
1963), which is less than the accretion time. The further dynamics of the
field lines, resulting in paths formation, is presented in Figures 3(b) and
3(c). Figure 4 shows one of the field tubes, formed as a result of the above
processes. The configuration of the given field lines in the equatorial region
is such that the matter, included and frozen into it, receives the impulse
in the z-direction and "slips" to the upper magnetic pole if the Kepler
OCR for page 52
52
Q
AMERICAN AND SOVIET PERSPECTIVES
BD
l ~
Bv
FIGURE 2 The align rotator ~D) and the accretion disk (13~) field lines on the Albren
surface separately from each other. The bold lines present the regions, which in Figure 3
are magnified and where the reconnection physics is dubbed.
~ -> ~ -) ~
a b c
FIGURE 3 1-he c~ field lines reconnection dynamics
rotation velocity of the matter in a disk is higher than BRA on the Alden
radius. In other words, it occurs when RC > RA tie. when RC/RA-1 >
O). NaturaLly, the "slip" of me matter to the lower magnetic pole will take
place at RC < RA observance (see Figure 4~. We want to reiterate that we
discuss the case when RA and RC are close to each other, as only in this
case the Kepler rotation of the matter does not change the teanng-mode
Instability development, described in papers by Furth e' al. (1963~; Lee and
Fu (1985~; and Southwood e! al. (1986~.
This paper has carried out the qualitative analysis of the accretion
onto the align gravimagnetic rotator. But it is easy to understand that
the main character of the accretion- the asymmetry- will be preserved at
the disk accretion of the magnetized plasma (Bf ~ 0) onto the oblique
gravimagnetic rotator as well.
Finally we enumerate those observational manifestations to which the
above-described accretion can lead due to the asymmetry:
· if such a system is capable of generating jets, Men they will be
observed only in one direction;
· even the slightest change of the accretion rate can lead to the
RC/RA-1 sign change. That will lead to the fact that the other pole
will become accreting. Eking into account that the Alfven radius may
OCR for page 53
HIGH-ENERGY ASTROPHYSICS
-
-
-
Q~
l ~
_ ~-
FIGURE 4 One of the field tubes, formed as a result of the connection passes.
53
be hundreds of times bigger than the radius of the star itself, the above-
mentioned will significantly effect the radiation of the given source directed
towards the observer. It may become, for example, the explanation of the
variability of some transients;
· even a weak quasispheric component always exists in the accreting
flow, even at disk accretion on compact objects. That is why in the case
considered by us, at least a weak flow of matter is always directed at the
non-accreting magnetic pole. Supposing the neutron star to be a compact
object, if the pressure of the electromagnetic radiation and the one of the
relativistic particles ejected from the polar cap are sufficient high, then
the accreting matter from the above-mentioned quasispheric component is
"swept" out of the capture region or out of the light cylinder limits. Then
the non-accreting magnetic pole will be an ejector, similar to the single
magnetized neutron star.
REFERENCES
Chagelishv~li, G.D ., ERG. Chanishnli, and J. G. Lam inadze. 1986. Pages 563-568. J. G. Proc.
Of Joint Varenna-Abastumani Intern. School and Workshop. Sukhumi, USSR (ESA
SP-253~.
Chagelishvili, GD., J.G Lominadze, and Zip Sokhadze. 1986. Pages 523 529. Proceed.
Of Joint Varenna-Abastumani Intern. School and Workshop. Sukhumi, USSR (ESA
SP-251~.
Chagelishivili, G.D., G. D. Chan Vile, and R.G. Lominadze. 1 988. Advanced Space
Research. 8~2~:216.
Chagelish~ili, G.D., G.D. Chanishvili, and J.G. Lominadze. 1~8. Ap. Space Sci. 141:361.
Furth, H.P., J. Killen, and M.N. Rosenbluth. 1963. Phys. F1. 6: 459.
Ghosh, P., and Fed Lamb. 1979. Ap. J. 2~256.
Ghosh, P., and F.K Lamb. 1979. Ap. J. 234:296.
Krause, F., and RH. Radler. 1980. Mean field magnetohyd~dynamics and dynamo theory,
Pergamon Press.
Lee, L.C, and Z.F. Fu. Geophysical Research Lett. 1985. 12: 105.
Iipunov, V.M. 1987. Astrophysics of neutron stem. Nauka, Moscow.
OCR for page 54
54
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~~ Pa.
Sba~, N.I., and ~^ Suit. 1~. Ago Ha. ~:~7.
Shape, S.L, and S.^ Nuked 19~. Black holed Wile Bat "d neuron saw. Abe
~1~ and ~= ~ ~
Sou , D), at Sowed, ~.W Dunlop, ARC ~ie~d=~i=, and R.R
Gnat 1~. Pit. Sit. ad. :.
SO 1~ ~.
Representative terms from entire chapter:
accretion disk
