Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei
The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when “twisting” the torus by radiation or wind transforms it into a dipole toroidal vortex which in turn can be the source of matter replenishing the accre...
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Bannikova, E.Yu. Kontorovich, V.M. 2015-05-11T19:23:57Z 2015-05-11T19:23:57Z 2006 Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei / E.Yu. Bannikova, V.M. Kontorovich // Вопросы атомной науки и техники. — 2006. — № 5. — С. 146-151. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 94.30.Tz https://nasplib.isofts.kiev.ua/handle/123456789/81160 The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when “twisting” the torus by radiation or wind transforms it into a dipole toroidal vortex which in turn can be the source of matter replenishing the accretion disk. Thus originating instability which can be responsible for quasar radiation flares accompanied by matter outbursts is also discussed. A “matreshka” scheme for obscuring vortex torus structure that could explain the AGN variability and evolution is proposed. The model parameters estimated numerically for the luminosity close to the Eddington limit agree well with the observations. Принята концепция тора как неотъемлемая структурная компонента ядра активной галактики (ЯАГ). Здесь обсуждается ситуация, когда «вращающийся» тор благодаря излучению или ветру трансформируется в тороидальный вихрь, который может быть источником вещества, пополняющего акреационный диск. Таким образом обсуждено также, что исходная неустойчивость может быть ответственна за вспышки излучения квазаров, сопровождающиеся выбросами вещества. Предложена схема “матрешка” для структуры н блюдающегося тороидального вихря, которая может объяснить изменчивость и эволюцию ЯАГ. Параметры модели оценены численно для яркости, близкой к Эддингтоновскому пределу и хорошо согласуются с наблюдениями. Прийнята концепція тора як невід’ємної структурної компоненти ядра активної галактики (ЯАГ). Тут обговорюється ситуація, коли «твістуючий» тор завдяки випромінюванню або вітрові трансформується в тороїдальний вихор, котрий може бути джерелом речовини, що поповнює акреаційний диск. Таким чином обговорено також, що первісна нестійкість може бути відповідальна за спалахи випромінювання квазарів, які супроводжуються викидами речовини. Запропонована схема “матрьошка” для структури тороїдального вихорю, яка може пояснити змінність та еволюцію ЯАГ. Параметри моделі оцінені чисельно для яскравості, близької до Едингтонівської межі та добре узгоджуються зі спостереженнями. This work is partly supported by the Ukraine President grant ГП/Ф8/0051. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Космическая плазма Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei Дипольные тороидальные вихри и ветрово-акpеационная неустойчивость в ядре активной галактики Дипольні тороїдальні вихорі та вітрово-акpеаційна нестійкість у ядрі активної галактики Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei |
| spellingShingle |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei Bannikova, E.Yu. Kontorovich, V.M. Космическая плазма |
| title_short |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei |
| title_full |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei |
| title_fullStr |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei |
| title_full_unstemmed |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei |
| title_sort |
dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei |
| author |
Bannikova, E.Yu. Kontorovich, V.M. |
| author_facet |
Bannikova, E.Yu. Kontorovich, V.M. |
| topic |
Космическая плазма |
| topic_facet |
Космическая плазма |
| publishDate |
2006 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Дипольные тороидальные вихри и ветрово-акpеационная неустойчивость в ядре активной галактики Дипольні тороїдальні вихорі та вітрово-акpеаційна нестійкість у ядрі активної галактики |
| description |
The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here,
the situation is discussed when “twisting” the torus by radiation or wind transforms it into a dipole toroidal vortex
which in turn can be the source of matter replenishing the accretion disk. Thus originating instability which can be responsible
for quasar radiation flares accompanied by matter outbursts is also discussed. A “matreshka” scheme for obscuring
vortex torus structure that could explain the AGN variability and evolution is proposed. The model parameters
estimated numerically for the luminosity close to the Eddington limit agree well with the observations.
Принята концепция тора как неотъемлемая структурная компонента ядра активной галактики (ЯАГ). Здесь обсуждается ситуация, когда «вращающийся» тор благодаря излучению или ветру трансформируется в тороидальный вихрь, который может быть источником вещества, пополняющего акреационный диск. Таким образом обсуждено также, что исходная неустойчивость может быть ответственна за вспышки излучения квазаров, сопровождающиеся выбросами вещества. Предложена схема “матрешка” для структуры н блюдающегося тороидального вихря, которая может объяснить изменчивость и эволюцию ЯАГ. Параметры модели оценены численно для яркости, близкой к Эддингтоновскому пределу и хорошо согласуются с наблюдениями.
Прийнята концепція тора як невід’ємної структурної компоненти ядра активної галактики (ЯАГ). Тут
обговорюється ситуація, коли «твістуючий» тор завдяки випромінюванню або вітрові трансформується в
тороїдальний вихор, котрий може бути джерелом речовини, що поповнює акреаційний диск. Таким чином
обговорено також, що первісна нестійкість може бути відповідальна за спалахи випромінювання квазарів,
які супроводжуються викидами речовини. Запропонована схема “матрьошка” для структури тороїдального
вихорю, яка може пояснити змінність та еволюцію ЯАГ. Параметри моделі оцінені чисельно для яскравості,
близької до Едингтонівської межі та добре узгоджуються зі спостереженнями.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/81160 |
| citation_txt |
Dipole toroidal vortexes and wind-accretion instability in active galaxy nuclei / E.Yu. Bannikova, V.M. Kontorovich // Вопросы атомной науки и техники. — 2006. — № 5. — С. 146-151. — Бібліогр.: 12 назв. — англ. |
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2025-11-26T23:30:39Z |
| last_indexed |
2025-11-26T23:30:39Z |
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1850781261969227776 |
| fulltext |
DIPOLE TOROIDAL VORTEXES AND WIND-ACCRETION INSTABILI-
TY IN ACTIVE GALAXY NUCLEI
E.Yu. Bannikova, V.M. Kontorovich
Kharkov National University, Kharkov, Ukraine
E-mail: bannikova@astron.kharkov.ua
Institute of Radio Astronomy NAS of Ukraine, Kharkov, Ukraine
E-mail: vkont@ira. kharkov.ua
The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here,
the situation is discussed when “twisting” the torus by radiation or wind transforms it into a dipole toroidal vortex
which in turn can be the source of matter replenishing the accretion disk. Thus originating instability which can be re-
sponsible for quasar radiation flares accompanied by matter outbursts is also discussed. A “matreshka” scheme for ob-
scuring vortex torus structure that could explain the AGN variability and evolution is proposed. The model parameters
estimated numerically for the luminosity close to the Eddington limit agree well with the observations.
PACS: 94.30.Tz
1. INTRODUCTION
Starting with the Antonucci and Miller’s outstanding
work, tori have been considered as an AGN-structure
necessary element forming the basis of the AGN unified
model [1]. A brilliant achievement was the first direct
observation of the obscuring tori described by Jaffe and
his colleagues [2]. Tori were positively confirmed exist-
ing when observed with the Hubble telescope and the
MIDI IR-camera equiped VLT optical interferometer,
though the efforts to reveal their structure detail and in-
ternal motion are yet to come. Many papers are devoted
to tori as embodiments of thick accretion disks, and also
investigate their stability defined by the orbital motion
gradients. However, within the AGN structure they are
mainly considered purely geometrically.
We offer to consider a torus as a dynamic object
with its proper vortex motion. As is well known, a torus
allows two independent rotations: “orbital” over the
torus periphery and “vortical” over its inner-radius cir-
cle (our terms). This latter will be of our major interest.
The vortical motion in a self-gravitating torus (see dis-
cussion in [3]) is vitally different from the orbital one,
which in an oversimplified case merely means rotation
of a torus as a single whole about the axis of symmetry.
For the near Eddington limit luminosity EddL L≈ ,
when the gravitation is largely balanced by light pres-
sure, this motion in AGN is not so essential. Though it
is necessary to stabilize self-gravitation of a compact
toroidal vortex [4], as used here, it can be quite neglect-
ed at first.
The vortical torus motion, which makes the torus the
vortex, will be of most importance in the following.
Originating or being sustained by the central source ra-
diation or wind «twist» it is capable of «replenishing»
the accretion disk mass, thereby adjusting the process of
accretion and introducing a feedback (Fig.1). Here, the
dipole structure of a toroidal vortex defined by the sym-
metry of radial-outflowing wind and radiation is of im-
portance. Note that the streamline structure across such
a dipole vortex resembles the structure and topology of
streamlines in the well-studied hydrodynamic models,
such as Hill and Lamb’s vortices [5], Larichev-Reznik
solitons, and others. At the same time, each component
of a toroidal dipole taken separately resembles the
Maxwell vortex, though with the opposite direction of
rotation.
Fig.1. Dipole toroidal vortex in the center of AGN – 3D
picture. Conic sections sketch out the wind and radiation
2. TWISTING A VORTEX BY RADIATION
At the torus large radius distance R, the central
source emitted light pressure is L/(4πcR2). The equation
for a vortical motion momentum takes the form:
2
2 ( )
4twist
dp L
R r r
dt cR
ϕ π π ς θ
π
= Ч Ч Ч
ж ц
з ч
и ш
, (2.1)
where the right-hand side is the modulus of a force
twisting moment with the arm of about a torus small
radius r, which appears due to the radiation pressure on
the inner torus surface ( 2 R rπ π≈ Ч ). Factor ( ) 1ς θ Ј
takes into account the torus shape effect and the radiant
flux angular dependence. The momentum [3] is related
with circulation and mass as / 2ringp Mϕ π= Γ , where
Mring is the torus mass and 2 vd r jp=G Ч=т v rС is the
torus inner circle velocity circulation. Twisting, which
turns the torus into a toroidal (ring) vortex and sustains
its vortical motion (the velocity circulation), by virtue of
the symmetry should result in a “dipole” vortex whose
“northern” and “southern” components rotate in oppo-
site directions (Fig.2).
________________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.146-151.
146
Fig.2. Schematic of a central source wind- and radia-
tion-twisted vortex
The streamline cross-section should resemble a pair
of vortices of different signs. Such a system, as is
known, moves as a whole with the velocity
/(4 )ringV rπ= Γ . As Lamb notes [5, p.300] this motion
can be interpreted as the necessity to compensate the at-
traction of vortices induced by the Bernoulli effect aris-
ing due to a flow of a moving vortex pair. In our case,
such a flow should result from the central source wind
with the velocity Uwind. As the torus and wind have dif-
ferent densities, the balance condition, as it is easy to as-
certain, takes the form
2 2
wind wind ringU Vρ ρ= . (2.2)
The fact that both components of a dipole-vortex torus
gravitate towards each other should be taken into ac-
count too.
Using the known result for the attraction of two elec-
trically charged rings [6], we may rewrite the gravita-
tional force between the two rings with masses aM and
bM , with the distance of 2r between them in the form:
3 2
2 ( )
4 1
a b
g
GM M r k E k
F
R kπ
Ч Ч
=
−
,
where 2 2k R r R= + , E(k) is the elliptic function.
If r R= , then 21 1 2 ( )k r R≈ − Ч , 2 21 ( )k r R− ≈
and in this case ( ) (1) 1E k E≈ = . The gravitational
force between the two components of a dipole toroidal
vortex (for r R= ) takes the form
2
2
ring
g
GM
F
R rπ
= . (2.3)
This attraction will also be balanced by wind flow.
Therefore, in the equality (2.2) an additional addend ap-
pears:
2 2 2
wind wind ring escU V Vρ ρ ρ= + , (2.4)
where 2 (2 )esc ringV GM R= . Below it will be shown that
for the numerical parameters chosen, the gravity contri-
bution (i.e. the second addend in the right-hand side of
equality (2.4)) exceeds the hydrodynamic one and is
about of the same order as the radiation twist contribu-
tion. Therefore in this work, the wind effect is neglect-
ed. At the same time it will be observed that unlike for
the “unipolar” self-gravitating vortices, where the envi-
ronment is not a governing factor, for the dipole toroidal
vortex, according to (2.4), the environment − similar to
vortices in an incompressible fluid − is required in prin-
ciple. At the same time, a flow generated «lifting force»
can explain the existence of «thick» cold tori that caus-
es per se a serious problem now [7].
In the luminosity, let us single out the contribution
to the accretion disk of matter from a torus and the
“background” torus unrelated luminosity L0:
2
0L L Mcξ= + & , (2.5)
where M dM dtє& is the accretion rate, and 0.1x :
means accretion related energy conversion into radia-
tion. The magnitude L will be considered close to the
Eddington limit, which is typical of the AGN luminosi-
ty. The toroidal vortex luminosity contribution is de-
scribed by the second addend connected with the accre-
tion disk vortex “twist”.
3. ACCRETION DISK REPLENISHMENT
BY VORTEX
For the problem considered, the vortex matter inflow
into the accretion disk due to partiсle detachment in the
region of contact of dipole components is essential. This
process is similar to that considered in [3] of the origin
of a jet in a compact-vortex hole. This process will be
described phenomenologically by introducing the
effective «height» h of a belt through which the toroidal
vortex matter flows into a disk. Then the mass flow
towards the disk per unity of time is equal to
2M v R hϕρ π= Ч Ч& , (3.1)
where the vortex density ρ is
22
ring
H
M
m n
R r
ρ
π π
=є
Ч
, (3.2)
and the vortex velocity vϕ is expressed through circula-
tion Γ as
2
v
rϕ π
Γ
= . (3.3)
The particle detachment parameters enter into the ex-
pression for the area 2 R hπ Ч through the belt height
Fig.3. Schematic of a vortex fed accretion disk. The belt
effective height h is amenable to particle intake in a
disk
which will be taken equal to the torus minor radius part
1h rξ= . (3.4)
The major and minor radii relate as [3]
r Rλ= , (3.5)
where 2 (4 )ringGMλ π= Γ is the Jeans scale. This rela-
tion is a direct consequence of coordinate dependencies
of gravitational and centrifugal forces connected to a
vortical motion in a torus. By substituting (3.2)-(3.5) in
________________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. № 5.
Серия: Плазменная электроника и новые методы ускорения (5), с.146-151.
147
(3.1) we obtain the accretion rate expression
2
12 ringMG
M
R
ξ
π
=
Γ
& . (3.6)
The magnitude of M& determines the accretion rate
defining the central source luminosity and connected to
the replenishment from a toroidal vortex.
Generally speaking, by virtue of nonstationarity of
the process under investigation, the time delay between
the mass intake into a disk at the distance of a torus ma-
jor radius R and its “irradiation” in the central engine
(i.e. in the disk inner part) may become essential. The
effect of this irradiation, as well as of the time lag be-
tween the moment of radiation and the vortex twist (due
to the light and wind velocity finiteness), will be dis-
cussed more below.
Now let us substitute the accretion rate expression
(3.6) into the luminosity formula (2.5)
22
1
0
2 ringMGc
L L
R
ξ ξ
π
= +
Γ
. (3.7)
Hence, using the relation of Γ with pφ and taking
(3.5) into account yield the following formula for the
rate of momentum change (2.1) due to twisting:
0 1
2
2
3
( ) ( )
2 2ringtwist
dp L c
p p
dt GM c R
ϕ
ϕ ϕ
π ζ θ ζ θ ξ ξ
= +
ж ц
з ч
и ш
. (3.8)
The torus mass loss in replenishing the disk results,
however, in the loss of the momentum carried away by
the escaping (pulled inward a disk) mass. The corre-
sponding momentum losses are described by
21
2 ring
repl
dp G
M
dt R
ϕ ξ
π
= −
ж ц
з ч
и ш
. (3.9)
Actually, the momentum carried away from the torus
per time unit is equal to
2
repl
dp
v rv Rh
dt
ϕ
ϕ ϕρ π= − Ч Ч
ж ц
з ч
и ш
, (3.10)
whence follows (3.9).
4. ACCRETION-WIND INSTABILITY
Let us first neglect the losses, assuming that the
inequality providing the angular momentum growth is
fulfilled:
twist repl
dp dp
dt dt
ϕ ϕ>
ж ц ж ц
з ч з ч
и ш и ш
. (4.1)
Nevertheless, the time evolution of inequality depends
essentially on how the torus mass ringM varies. If the
torus illuminated side subjects to wind and radiation,
there is no radiation pressure on its shadowed side and
the mass inflow is possible from a more distant environ-
ment. In particular, one of the variants of the discussed
scenario corresponds to the steady-state mass inflow
which allows considering ringM& as one of the slowly
varying parameters for the times of “fast” variations.
Substitution of (3.8) at 0 0L = and (3.9) in (4.1) yields
momentum restriction from below
2
2
4
( )
ringGM
p
cϕ π ξ ς θ
> . (4.2)
The angular momentum which satisfies it on the order
of magnitude is equal to
2
( )
ringGM
p
cϕ ξ ς θ
∗ ≈ . (4.3)
This might be amenable to the fact that the contribution
of the “background” addend with 0 0L № into vortex
twisting can be of fundamental importance [6]. The ac-
cretion rate and luminosity magnitudes corresponding to
pϕ
∗ are of the form
2 3
1 1
2 2
( ) ( )
,ring ringM c M c
M L
R R
ξ ξ ς θ ξ ξ ς θ
π π
∗ ∗= =& . (4.4)
The possibility for AGN instability connected both with
the accretion from a torus and with the central source
wind (the photon wind included) is obvious from (3.8).
The nature of such accretion-wind instability, as it could
possibly be named, is that the growing L increases pϕ& ,
while this in turn increases M& , that again increases L,
i.e.
, ,p L L Mϕ ∝ ∝ && . (4.5)
The linear increment of accretion-wind instability at
0 0L = should result in the exponential growth with the
slowly rising (due to the decrease of R) parameter α :
1 ( )
,
2
dp c
p
dt R
ϕ
ϕ
ξ ξ ς θ
α α= =Ч . (4.6)
The complete analysis of instability may appear rather
complicated and is not meant here in this paper.
Nevertheless, in its character and behavior the
instability is similar to the observable quasar radiation
bursts [8] that can testify to the discussed dynamic role
of AGN toroidal vortices (see Fig.6 and discussion
further in this paper).
5. THE DELAY EFFECT ON THE INCRE-
MENT
The feedforward and feedback circuit, which causes the
accretion-wind instability, has the delay which in the
oversimplified case is described by the equation
( )
( )
dp t
p t
dt
ϕ
ϕα τ= − , (5.1)
where 1 2τ τ τ= + (see Fig.4).
Fig.4. Schematic of time delay in a feedback circuit of
accretion-wind instability, where τ1 is the time of mass
transfer along the disk radius, τ2 is the time of centre-to-
torus radiation propagation
148
The evolutionary differential equation with the time
delay
( )
( )
dx t
x t
dt
α τ= − (5.2)
allows the exact solution and results, as earlier in the
system with no delay, in the exponentially growing so-
lution
( )( ) (0) f tx t x e α α τ− ⋅= ⋅ , (5.3)
but with the increment depending on the dimensionless
delay α τ , where the universal function f(α τ ) is the
solution of the transcendental equation
exp( )f fα τ= − or
ln /f f α τ= − . (5.4)
The form of this function is shown in Fig.5 and is
obtained by the inversion of function (5.4).
Fig.5. The dependence ( )f α τ obtained as graphic so-
lution of the functional equation (5.4)
It is seen that 1f Ј (see Fig.5), 1 (1 )f α τ= + for the
weak delay 1at = . Thus, the delay present reduces
the increment of accretion-wind instability
( )fα α α τ→ Ч . With the vortex compression and thin-
to-compact evolution, the delay becomes less important
and the increment rises.
6. DISCUSSION
The aforesaid proves that in the considered system
the positive feedback and related instability are possible.
We have considered the instability in its simplest case
with least parameters: no background radiation uncon-
nected with a toroidal vortex, insignificant wind contri-
bution to twisting vs. radiation, rather slow motion
(compression) over the torus major radius. Then, ac-
cording to (4.7), the accretion-wind instability incre-
ment is equal to 1 ( ) (2 )c Rα ξ ξ ς θ= and determines the
characteristic time scale of its development. In case we
want to compare the 3.5-year time scale of the observ-
able burst duration in quasar 3C 345, see Fig.6 from [8],
we should take the space scale 1610R : cm (1/300 light
year). Here we have taken into account that 0.1x : ,
and 1ξ is taken of the same infinitesimal order. The last
estimation may essentially differ from reality, therefore
1ξ should be sooner treated as a scale factor which vari-
ation may considerably change the system parameters.
As the preliminary observed data [1] point to signifi-
cantly larger torus sizes, a question - which one of the
answers results in the “matreshka” scheme (Fig.7) - may
naturally arise. The inner toroidal vortex may be respon-
sible for the variability of AGN, the development of in-
stability, etc. In the shadow of a close minor-radius
torus there exists a preference for the centre-falling mat-
ter because of less interfering radiation (this latter being
weaker due to absorption) and of wind screened by the
inner torus.
Fig.6. Correlation between the optical bursts of quasars
3C345 and arising the super luminal components of
radio jet ( according to [8])
Therefore the interstellar gas clouds will move to-
wards the centre in the nearby torus shadow.
Fig7. The possible obscuring structure of AGN in the
form of the “matreshka” sequence of tori
Orbital motion causes the falling clouds to flatten into
tori and disks. Though the outer tori cannot add to the
development of accretion-wind instability due to this
latter extremely slow development at large scales (cf.
the estimate (4.7)) and, in addition, being weakened by
the increment-slowing delay.
Thus, the instability is determined by the inner cen-
tre-closest torus. The torus distribution increment is de-
termined by the accretion process on the scales consid-
erably exceeding those considered here and is beyond
the discussed scenario. Detailed studying of the process-
es which occur in the evolution of toroidal vortices in
the centres of active galaxies is a highly to intricate
problem. Nevertheless, it is possible already now distin-
guish some features of these processes. Under the near
Eddington’s conditions, due to the radiation pressure
compensated centre attraction, the evolution of vortices
should largely resemble their evolution without the cen-
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149
tral mass [3]. At the compact vortex phase, the ejection
of particles along the torus axis is possible, that might
explain the correlation between the quasar optical bursts
and the formation of new jet components [8].
The expressions obtained above may allow to esti-
mate the features of the outer (obscuring) torus for the
Seyfert galaxies (see Table 1) and quasars (see Table 2).
Table 1. Obscuring torus parameters for the Seyfert galaxies
Model param-
eters Chosen values Calculated
AGN values Obtained values
BHM 76.6 10 MЧ e [9] α 125 10−Ч CGS
ringM 0.1 BHMЧ [9] pϕ
643.8 10Ч CGS
R 1pc (see [3]) Γ 251.8 10Ч CGS
r/R 0.5 (see [10]) vϕ
62 10Ч cm/s
ξ 0.1 n 75.4 10Ч cm-3
1ξ ; ς 0.1 2
ringnV 202 10Ч CGS
2
wind windn U
2210 CGS
( 610windn = cm-3, 810windU = cm/s)
2
escnV 217.7 10Ч CGS
EddL 458.6 10Ч erg/s *L
481.2 10Ч erg/s
(see the text)
Table 2. Obscuring torus parameters for the quasars
Model parame-
ters
Chosen values Calculated
AGN values
Obtained values
BHM 910 Me
α 125 10−Ч CGS
ringM 0.1 BHMЧ pϕ
668.8 10Ч CGS
R 1pc Γ 262.8 10Ч CGS
r/R 0.5 vϕ
73 10Ч cm/s
ξ 0.1 n 91.4 10Ч cm-3
1ξ ; ς 0.1 2
ringnV 236.7 10Ч CGS
2
wind windn U 245 10Ч CGS, [11] 2
escnV 241.8 10Ч CGS
EddL 471.3 10Ч erg/s *L 491.8 10Ч erg/s
(see the text)
Note that in [9] the dust mass of a obscuring torus is
estimated on the order of magnitude of 0.01 BHM , where
BHM is the central black hole mass. In our estimations
we assume the dust making 10% of the total torus mass.
The discrepancy between the characteristic L* and
Eddington luminosities EddL can be easily eliminated by
assuming a smaller efficiency replenishment of the ac-
cretion disk by a toroidal vortex. Thus, taking 1
310ξ −=
yields 47* 10EddL L: : erg/s for the other parameters
unchanged. However, the delay affected decrease of L*
may appear to be essential as well. The luminosity L*
(4.5) can be represented as
2 2* 2 ringL M cξ α π= , (6.1)
where α is the accretion-wind instability increment. As
is shown above (item 5), the τ -time delay decreases the
increment by a factor of f, where ( )f α τ is the solution
of equation (5.4). As a matter of fact, the time delay es-
sentiality means that the detail description needs using
the theory of a nonstationary disk accretion with the
“boundary conditions” determined by the interaction of
a toroidal dipole vortex with a disk, that exceeds the
bounds of this paper.
For the luminosity near to the Eddington one the
torus mass ringM have to be near to the value
( )ring cM R Mη= , where ( )Rη is estimated from the
relation * 381.3 10 c
Edd
ML L
M
ж цчз ч< = Ч з чз чзи шe
erg/s, that led to
inequality 6
1
1( ) 3.7 10
( ) 1
RR
pc
η
ξ ς θ
− ж ц
< Ч з ч
и ш
. In particu-
lar, in the case 210R −= pc for 910cM M= e and
1 0.1ξ ς= = we receive the value 34 10ringM M» ґ e .
The decrease of the torus mass with decreasing the torus
radius naturally to link with a departure of the mass to
the accretion disk and/or with a blowing off the part of
the mass under the action of the wind.
The torus twisting by wind rather than by radiation
150
may appear essential. In this case, the magnitude
2
wind windUρ will play the role of the pressure on a torus in
(2.1). Closing a feedback circuit requires the knowledge
about the connection between the wind parameters and
the central source luminosity. The magnetic field which
impacts the parameters of wind and its angular distribu-
tion, and accordingly the torus twisting, can be of im-
portance too. Despite of these problems unsolved, the
described scheme already now yields the reasonable
correspondence with the data observed until recently.
A short description of some items of this work is pub-
lished in authors’ paper [12].
CONCLUSIONS
1) A dipole toroidal vortex may be an essential
AGN-structure element which “replenishes” the accre-
tion disk.
2) In the feedback circuit, which includes twisting
the vortex by radiation and wind and replenishment of
the accretion disk by a vortex, the instability causing the
bursts in active nuclei may develop.
3) The presence of a “lifting force” due to wind may
allow the existence of a “thick” and cold torus.
4) The “matreshka” scheme of AGN toroidal struc-
ture which may explain the evolution effects is pro-
posed.
This work is partly supported by the Ukraine President
grant ГП/Ф8/0051.
REFERENCES
1. R. Antonucci. Unified models for active galactic
nuclei and quasars // Ann. Rev. Astron. Astrophys.
1993, v.31, p.473-521
2. W. Jaffe, K. Meisenheimer, H.J.A. Rottgering, et
al. The central dusty torus in the active nucleus of
NGC 1068 // Nature. 2004, v.429, p.47-49.
3. K.Yu. Bliokh, V.M. Kontorovich. On the evolution
and gravitational collapse of toroidal vortex //
JETP. 2003, v.123, №6, p.1123-1130. .
4. E.Yu. Bannikova, K.Yu. Bliokh, V.M. Kontorovich.
The dynamics of self-gravitating toroidal vortex.
Wave transformation, coherent structures and turbu-
lence. M.: URSS, 2004, p 249-254.
5. G. Lamb. Hydrodynamics. Moscow-Leningrad:
“Ogiz – Gostehizdat”, 1947, p.928.
6. B.B. Batygin, I.N. Toptygin. Contemporary elec-
tro-dynamics, Part 1. Moscow-Izhevsk: “R & C
dyna-mics”, 2003, p.736 (in Russian).
7. J.H. Krolik. Dust-filled Doughnuts in the Space //
Nature. 2004, v.429, №1, p.29-30.
8. M.K. Babadzhanyants, E.T. Belokon. The optical
manifestation of a superluminal outflow of the
quasar 3C345 millisecond radio structure // As-
trofizika. 1985, v.23, №3, p.459-471.
9. M. Schartmann, K. Meisenheimer, M. Camenzind,
et al. Towards a physical model of dust tori in Ac-
tive Galactic Nuclei // astro-ph / 0504105.
10. J.H. Krolik, M.C. Begelman. Molecular tori in
seyfert galaxies: feeding monster and hiding it //
Astrophys.J. 1988, v.329, №1, p.702-711.
11. S. Mathur, M. Elvis, W. Belinda. Testing Unified
X-Ray/Ultraviolet Absorber Models with
NGC 5548 // Astrophys. J. 1995, v.452, №1, p.230-
237.
12. E.Yu. Bannikova, V.M. Kontorovich. Toroidal vor-
tex as an active galactic nuclei structure element //
Radio Physics and Radio Astronomy. 2006, v.11,
№1, p.42-48.
ДИПОЛЬНЫЕ ТОРОИДАЛЬНЫЕ ВИХРИ И ВЕТРОВО-АКPЕАЦИОННАЯ НЕУСТОЙЧИВОСТЬ
В ЯДРЕ АКТИВНОЙ ГАЛАКТИКИ
Е.Ю. Банникова, В.М. Конторович
Принята концепция тора как неотъемлемая структурная компонента ядра активной галактики (ЯАГ).
Здесь обсуждается ситуация, когда «вращающийся» тор благодаря излучению или ветру трансформируется
в тороидальный вихрь, который может быть источником вещества, пополняющего акреационный диск. Та-
ким образом обсуждено также, что исходная неустойчивость может быть ответственна за вспышки излуче-
ния квазаров, сопровождающиеся выбросами вещества. Предложена схема “матрешка” для структуры на-
блюдающегося тороидального вихря, которая может объяснить изменчивость и эволюцию ЯАГ. Параметры
модели оценены численно для яркости, близкой к Эддингтоновскому пределу и хорошо согласуются с на-
блюдениями.
ДИПОЛЬНІ ТОРОЇДАЛЬНІ ВИХОРІ ТА ВІТРОВО-АКPЕАЦІЙНА НЕСТІЙКІСТЬ У ЯДРІ
АКТИВНОЇ ГАЛАКТИКИ
Є.Ю. Банникова, В.М. Конторович
Прийнята концепція тора як невід’ємної структурної компоненти ядра активної галактики (ЯАГ). Тут
обговорюється ситуація, коли «твістуючий» тор завдяки випромінюванню або вітрові трансформується в
тороїдальний вихор, котрий може бути джерелом речовини, що поповнює акреаційний диск. Таким чином
обговорено також, що первісна нестійкість може бути відповідальна за спалахи випромінювання квазарів,
які супроводжуються викидами речовини. Запропонована схема “матрьошка” для структури тороїдального
вихорю, яка може пояснити змінність та еволюцію ЯАГ. Параметри моделі оцінені чисельно для яскравості,
близької до Едингтонівської межі та добре узгоджуються зі спостереженнями.
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151
Obtained values
|