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Acta Polytechnica CTU Proceedings 2(1): 60–65, 2015

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doi: 10.14311/APP.2015.02.0060

On the Influence of Magnetic Field on Accretion Processes in CVs

D. V. Bisikalo1, A. G. Zhilkin1

1Institute of Astronomy RAS, Moscow, Russia

Corresponding author: bisikalo@inasan.ru

Abstract

We consider the influence of such parameters as the value of the proper magnetic field Ba and the spin-rotation velocity
of the white dwarf on accretion processes in CVs. The results of 3D MHD simulations have shown that the accretion
rate is a non-monotonic function of Ba: with growing Ba it raises in the intermediate polars and decreases in the polars.
The maximal accretion rate occurs in the systems, transiting from the stage of intermediate polars to polars; it’s value
reaches ∼60% of the initially set mass transfer rate. We have also shown that the acretion rate decreases with the growing
spin-rotation velocity of the white dwarf.

Keywords: cataclysmic variables - intermediate polars - polars - accretion - MHD simulations.

1 Introduction

Two main classes of CVs where magnetic field signif-
icantly influences accretion processes are the interme-
diate polars and polars [1]. These are semi-detached
binary systems, consisting of a low-mass late type star
(donor-star) and a white dwarf (accretor).

In the polars, white dwarfs possess strong magnetic
fields (Ba ≈ 107–108 G on the surface). Observations
show that no accretion disks form in polars. Instead,
the material, issuing from the L1 point, forms a col-
limated stream, that flows onto one of the magnetic
poles of the accretor along magnetic field lines[1, 2].
In the intermediate polars, white dwarfs possess rela-
tively weak magnetic fields (Ba ≈ 104–106 G on the
surface). These systems occupy an intermediate stage
between the polars and non-magnetic CVs. We should
note that in these systems the spin-rotation periods of
the primaries may be significantly shorter than the or-
bital periods [3].

In our previous works [4, 5] we, by means of 3D
MHD simulations, studied the flow structure of the in-
termediate polars and polars, having various surface
magnetic fields of the accretors Ba, ranging from 10

5

to 108 G. This allowed us to investigate conditions of
accretion disk formation and to find a criterion, sepa-
rating two types of the flow, corresponding to the in-
termediate polars and polars. Besides, in [5] we also in-
vestigated how the spin-rotation velocity of the accretor
influences the MHD flow structure in the system.In this
paper we summarize the results of our previous research
and show how the accretion rate varies, depending on
two parameters as the magnetic induction on the sur-
face of the white dwarf and its spin-rotation velocity.

2 What Happens with the Flow
Structure if Ba Grows

To investigate how the value of the accretor’s surface
magnetic field influences MHD flow structure in a close
binary system we have conducted 7 computational runs
with various Ba: 10

5 G (model 1); 5 × 105 G (model 2);
106 G (model 3); 5 × 106 G (model 4); 107 G (model
5); 5 × 107 G (model 6); and 108 G (model 7). We
suppose that the accretor’s magnetic field is of dipole
type and the axis of the field is inclined with respect to
the accretor’s rotation axis by θ = 30◦.

For the computations we used our method of inves-
tigations of mass transfer processes in semi-detached bi-
nary systems where the accretors possess strong mag-
netic fields [4, 5]. The method is based on the idea
that plasma dynamics is determined by the relatively
slow average motion of plasma against a background
of which very rapid MHD waves propagate. The equa-
tions, describing the slow motion of plasma, are derived
via a procedure of averaging over the rapidly propagat-
ing pulsations. Strong external magnetic field in this
approach plays a role of an effective liquid interact-
ing with plasma. In the equation of motion the mean
electromagnetic force is analogous to the friction force
working in multi-component plasma. In our numerical
model we take into account processes of the magnetic
field diffusion caused by the currents’ dissipation in tur-
bulent vortices and magnetic buoyancy. Besides, when
averaging the induction equation over the rapidly prop-
agating MHD waves we introduce an additional source
of magnetic field dissipation (wave dissipation).

In order to see how namely the magnetic induc-
tion influences the solution we fix all the other param-

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http://dx.doi.org/10.14311/APP.2015.02.0060


On the Influence of Magnetic Field on Accretion Processes in CVs

eters. The computations have been conducted for a
close binary system, having parameters of the SS Cygni
(see [6]). The donor-star (red dwarf) in this system has
the mass Md = 0.56M� and the effective temperature
of 4000 K. The accretor (white dwarf) has the mass
Ma = 0.97M� and the temperature of 37000 K. The
orbital period of the system is Porb = 6.6 hours and
its binary separation is A = 2.05R�. We have sup-
posed that the accretion disk forms in the system for the
first time so the accretor’s spin-rotation is synchronous,
i.e. Pspin = Porb. The influence of the accretor’s spin-
rotation on a formed accretion disk is considered in the
next section.

The obtained solutions can be divided into two
groups. The first group contains models 1, 2, and 3 with
relatively weak magnetic fields where accretion disks
form. These models correspond to the intermediate po-
lars. In the models of the second group (models 4–7)
magnetic fields are strong and there are no accretion
disks formed. These models represent the polars.

The typical flow structure in the intermediate po-
lars is shown in Fig. 1, where we plotted an iso-surface
of density logarithm lgρ = −4.5 (in units of ρ(L1)) ob-
tained in the model 1 (Ba = 10

5 G). In Figure we also
show the magnetic flow lines originating on the accre-
tor’s surface, accretor’s rotation axis (thin straight line)
and magnetic axis (bold inclined line). We note that
all the gas dynamic structures found in our previous
studies [7, 8, 5], including the accretion disk and shock
waves exist in the obtained solution. Near the accretor
the magnetosphere forms and material is accreted via
funnel flows.

With growing magnetic field the outer radius of
the disk significantly decreases. The efficiency of the
magnetic breaking and angular momentum transfer in-
creases. The region of the magnetosphere becomes sig-
nificantly larger. Finally, when Ba = 10

6 G (model 3,
Fig. 2) the accretion disk almost degenerates. The ma-
terial makes only 1–2 cycles before falling onto the ac-
cretor. To describe this flow structure a term ”spiralo-
disk” is more appropriate, since the velocity distribu-
tion in this structure strongly differs from the Keple-
rian. The outer radius of this ”spiralo-disk” is approxi-
mately 0.1A and the inner radius is determined by the
size of the magnetosphere. A significant part of the
”spiralo-disk” is accretion funnel flows. We can state
that this solution is an ultimate case of the intermedi-
ate polars.

To determine a criterion, separating the intermedi-
ate polars and polars let us consider behavior of the gas
stream, issuing from the L1 point into the Roche lobe

of the accretor. Taking into account that the gas in the
stream moves with supersonic velocity we can consider
its behavior using the ballistic approach and omitting
the effects of pressure and magnetic field [9, 10].

Figure 1: 3D flow structure for the model 1 with
Ba = 10

5 G. Iso-surface of density (lgρ = −4.5 in units
of ρ(L1)) and magnetic field lines are shown. The ac-
cretor’s rotation axis is shown by the thin straight line,
magnetic axis — by the bold inclined line.

Figure 2: The same as in Fig. 1 for the model 3 with
Ba = 10

6 G.

Figure 3: The same as in Fig. 1 for the model 5 with
Ba = 10

7 G.

61



D. V. Bisikalo, A. G. Zhilkin

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Figure 4: The dependence of the accretion rate Ṁa on value of the magnetic field Ba (left row) in absolute
values (top panel) and in % from the mass transfer rate Ṁ (bottom panel). The vertical lines limit the specific
amplitudes of the accretion rate variations. In the upper-right panel we show the mass transfer rate as a function
of the value of magnetic field. In the lower-right panel we show the mass transfer rate as a function of the
accretor’s spin velocity in the model with Ba = 10

5 G.

Analysis of the trajectories [11] shows that the
stream comes very close to the accretor’s surface at a
distance Rmin. If Rmin is larger than the radius of the
magnetosphere rm the magnetic field does not strongly
influence the motion of material. The stream rounds
the star and intersects itself at a certain point. The
further evolution of this flow results in the formation of
an accretion disk in the system. If Rmin is smaller than
rm then the magnetic field starts to strongly influence
the stream at a certain part of its trajectory. The action
of electromagnetic forces in this region slows the stream
down and causes loss of the angular momentum.

As a result the stream can not round the star and
form an accretion disk. Thus, the boundary between
the intermediate polars (with accretion disks) and po-
lars (no accretion disks) is determined by the relation
rm = Rmin. If we calculate both the radii using the
parameters of the SS Cygni we see that this relation is
satisfied at Ba ≈ 106 G separating the two regimes of
the flow. We should note that this estimate of magnetic

field induction, separating the intermediate polars and
polars, is more or less general for CVs, since the value
of q there varies insignificantly.

The typical flow structure in the polars is shown in
Fig. 3, where, like in Figures 1 and 2, we plotted an
iso-surface of density logarithm lgρ = −4.5 (in units of
ρ(L1)) for the model 4 (10

7 G). In the models 4–7 no
accretion disks form and material is accreted via funnel
flows. In the models 4 and 5 the stream, starting at
L1 point, splits into two flows when approaching the
accretor’s surface. Then the first flows falls onto the
northern magnetic pole of the accretor, the second —
onto the southern. With growing magnetic field the dif-
ference between the two poles becomes more obvious.
In the model 6, for example, only one accretion flow
occurs that then ends up at the southern pole. In the
model 7 the magnetic field is so strong that it almost
entirely controls the flow structure in the Roche lobe of
the accretor. The field captures material in the immedi-
ate vicinity of the inner Lagrangian point and, splitting

62



On the Influence of Magnetic Field on Accretion Processes in CVs

it into two flows — more powerful southern and weaker
northern, — transports it onto the accretor’s surface
along the field lines.

Let us now consider how the described variations
of the flow structure influence the accretion rate. In
the upper-left panel of Fig. 4 we plot the computed
accretion rate Ṁa as a function of Ba. The vertical
lines show specific values of the accretion rate varia-
tions. The main feature of this function is that it is
non-monotonic. For the values Ba < 10

6 G the accre-
tion rate increases with increasing magnetic field and
the amplitude of its variations decreases. At the point
Ba = 10

6 G the accretion rate approaches its max-
imal value. This can be explained by the fact that
in the solutions with accretion disks the accretion rate
is controlled by processes of angular momentum trans-
fer. The growing magnetic field in intermediate polars
makes magnetic breaking more effective and, hence, in-
creases Ṁa. After the point of maximum the accretion
rate starts to decrease while Ba continues to grow. As
we have shown above starting at the point Ba = 10

6 G
no accretion disk forms in the system and the material
is accreted via funnel flows. In this case the accretion
rate is determined by the throughput of the stream.
When the magnetic field grows the width of the stream
decreases and the accretion rate falls.

Dependence of the accretion efficiency Ṁa/Ṁ on the
induction of magnetic field is shown in the lower-left
panel of Fig. 4. With growing Ba this value increases
monotonically. In a transit range of magnetic field val-
ues (near Ba ≈ 106 G) this dependence has an inflection
point. The lowest effectiveness of accretion (30–40%) is
approached for intermediate polars with weak magnetic
fields. This may be explained by the fact that their
disks are large and a portion of material may leave the
accretor’s Roche lobe and form a common envelope of
the binary system [12]. In the polars (with strong mag-
netic fields) almost all the material, flowing from the L1
point onto the accretor, is accumulated and ”enclosed”
in the stream. Thus, in such systems the effectiveness
of accretion reaches almost 100%.

The non-monotonic shape of the Ṁa(Ba) curve,
obtained in our calculations, does not contradict the
monotonic character of the dependence of the accretion
effectiveness on Ba. The point is that the mass trans-
fer rate Ṁ also depends on the value of magnetic field.
This dependence is shown in the upper-right diagram of
Fig. 4. In Figure one can see that with growing Ba the
value of Ṁ monotonically decreases. In a range of weak
fields (Ba < 10

6 G, intermediate polars) this decrease is
almost invisible. However in strong fields (Ba > 10

6 G,
polars) the value of the mass transfer rate sharply drops
(by almost an order of magnitude). This behavior may
be explained by the fact that the strong magnetic field
of the accretor generates extra-pressure in the vicinity

of the L1 point, which prevents the outflow of the ma-
terial from the donor’s envelope. Thus, with growing
Ba the throughput of the accretion stream decreases.

3 Influence of the Asynchronous
Rotation of the White Dwarf on the
Accretion Rate

The influence of the accretor’s spin-rotation on MHD
flow structure in CVs can be characterized by a rela-
tion between the radius of the magnetosphere rm and
the co-rotation radius rc that is a distance at which
the velocity of rotation of the field lines is equal to the
rotation velocity of material in the accretion disk. If
the accretor rotates relatively slow (rc > rm) then the
rotation velocity of the field lines at the boundary of
the magnetosphere is lower than the Keplerian. So the
material, captured by the magnetic field can freely fall
onto the accretor’s surface. This regime may be called
the ”accretor” regime. When the accretor’s rotation is
fast enough (rc < rm) a centrifugal barrier occurs at
the boundary of the magnetosphere. This barrier pre-
vents material from free falling onto the surface. This
regime we may call the ”propeller”. In systems of AE
Aqr type the rotation of the white dwarf is so fast that
no accretion disk can form. Thus, for this regime we
can use a term ”super-propeller” [5].

To investigate how the asynchronous rotation of the
accretor influences the flow structure in a close binary
system we conducted four runs of 3D numerical simula-
tions for the period relation of Pspin/Porb: 0.1 (”ac-
cretor”); 0.033 (”equilibrium rotation”); 0.01 (”pro-
peller”); and 0.001 (”super-propeller”) [5]. To preserve
the generality we again use the parameters of the SS
Cygni. In all the runs the magnetic induction was set
equal to 105 G and the magnetic axis is inclined by
θ = 30◦.

In the models ”accretor” and ”equilibrium rotation”
the flow structure is analogous to the model 1, consid-
ered in previous section. In the ”propeller” regime, in
the inner regions of the disk a magnetospheric cavity
forms. Its radius is 0.05–0.1A. At the boundary of
this cavity the Kelvin–Helmholtz instability develops.
Since there is almost no material in the cavity, the ac-
cretion rate in the ”propeller” model is close to zero.
On the other hand the mass transfer continues and the
mass of the disk grows. In the systems with an ap-
propriate combination of parameters (disk mass, value
of magnetic field and rotation velocity) the material at
the boundary of the cavity at a certain moment can
push the magnetosphere down and initiate a short pe-
riod of accretion. After the exceptional mass has been
removed the system returns into the ”propeller” regime.
In the ”super-propeller” regime the material, issuing
from the inner Lagrangian point, is captured by the

63



D. V. Bisikalo, A. G. Zhilkin

rapidly rotating accretor’s magnetosphere, acquires ad-
ditional angular momentum and gets ejected out of the
accretor’s Roche lobe. The accretion rate in this case
is almost zero.

In the lower-right panel of Fig. 4 we show depen-
dence of the accretion rate on the parameter Porb/Pspin
that characterizes the spin velocity of the accretor. The
data shown are for the case of Ba = 10

5 G. In Figure
one can see that with the growing accretor’s spin ve-
locity the accretion rate decreases. If the white dwarf
rotates relatively slow, which corresponds to the ”ac-
cretor” regime, the accretion rate decrease is not sig-
nificant in comparison with the case of synchronous
rotation. However, when the spin velocity overcomes
an equilibrium value the system enters the ”¡propeller”
regime and the accretion rate sharply drops. In fact, in
the ”propeller” and ”super-propeller” regimes the ac-
cretion rate is determined by the accretion of material
from the common envelope but not of the material, is-
suing from the inner Lagrangian point.

4 Conclusions

Using the results of 3D numerical MHD simulations, we
have considered the influence of the magnetic field value
Ba and the spin-rotation velocity of the white dwarf on
accretion processes in CVs. Analyzing the results of
seven computational runs for models with Ba equal to
105 G, 5 × 105 G, 106 G, 5 × 106 G, 107 G, 5 × 107 G
and 108 G, we have found that the accretion rate Ṁa
is a non-monotonic function of Ba. In the intermedi-
ate polars the growing Ba makes the magnetic breaking
more effective and, hence, increases Ṁa. In the polars,
where the accretion rate is determined by the through-
put of the funnel flow the accretion rate decreases with
growing Ba. The maximal value of the accretion rate
occurs in the systems at a stage of transit between the
intermediate polars and polars. This value is ∼60% of
the initially set mass transfer rate.

We should note that unlike the absolute value of Ṁa
the accretion efficiency Ṁa/Ṁ monotonically increases
with the increasing induction of magnetic field. In the
polars it approaches the value of almost 100%. This
is because the mass transfer rate decreases with grow-
ing Ba, since strong magnetic field prevents the inflow
of material into the accretor’s Roche lobe through the
inner Lagrangian point.

Analyzing the results of four computational runs of
3D MHD simulations with various values of the period
ratio (Pspin/Porb = 0.1, 0.033, 0.01 0.001) and fixed
Ba = 10

5 G we found that the accretion rate decreases
with the increasing spin-rotation velocity. It is interest-
ing to note that even in a system, living in the ”pro-
peller” regime, the average accretion rate may be not
equal to zero if the combination of such parameters as

the disk mass, value of magnetic field and rotation ve-
locity can cause quasi-periodic accretion bursts (falling
of the portion of the disk mass onto the accreting star).

Acknowledgement

This work was supported by the Basic Research Pro-
gram of the Presidium of the Russian Academy of Sci-
ences, the Russian Foundation for Basic Research Re-
search (projects 11-02-00076, 12-02-00047, 13-02-00077,
13-02-00939), the Federal Targeted Program ”Science
and Science Education for Innovation in Russia 2009–
2013”.

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http://dx.doi.org/10.1017/CBO9780511586491
http://dx.doi.org/10.1086/423333
http://dx.doi.org/10.1016/j.asr.2009.09.006
http://dx.doi.org/10.1086/153614
http://dx.doi.org/10.1134/S1063772907100083


On the Influence of Magnetic Field on Accretion Processes in CVs

DISCUSSION

CHRISTIAN KNIGGE: You seemed to use SS Cyg
as a prototype of DN intermediate polar, out what is
the empirical evidence for this?

DMITRY BISIKALO: We just used SS Cyg as a
DN illustrative example. The parameters of the SS Cyg
(components masses, radii, separation, etc.) are quite
typical for intermediate polars, so we can consider these
numerical results as a good illustration of the flow struc-
ture in the intermediate polars.

GIORA SHAVIV: If I saw right, you do not have ra-
diative transfer, only local energy sinks. How it works
when the disk is optically thick?

DMITRY BISIKALO:Yes, this approach is strictly
applicable for optically thin disks. If you consider op-
tically thick disks it is necessary to add the radiative
transfer in some form to the model, and we are work-
ing on this. Fortunately, we can use the assumption of
optically thin disks for a significant sample of CVs.

65


	Introduction
	What Happens with the Flow Structure if Ba Grows
	Influence of the Asynchronous Rotation of the White Dwarf on the Accretion Rate
	Conclusions