Above: a polar system. The white dwarf remnant is pulling a stream of matter off its Roche-lobe filling
main sequence dwarf star companion as in a typical cataclysmic variable. In many cases this would lead
to a more-or-less complete accretion disc around the white dwarf star. However, in white dwarfs with very
strong magnetic fields the situation becomes somewhat different. White dwarfs, being compact stellar
remanants, often have very strong magnetic fields. For example the white dwarf in AR UMa has a
magnetic field of strength 230 MGauss (230 million Gauss) or 23 000 Tesla at its surface. This is much
stronger than any magnetic field ever created on Earth! Such stars are super-magnets!
Stars consist principally of plasma - gas in which many or all of
The electrons have been stripped from the atoms by extreme
high temperatures. This results in a mixture of a gas of
positively charged ions and a gas of negatively charged
electrons. Magnetic fields can accelerate moving charges (see
particle paths and energetic processes. In particle charges
moving across magnetic field lines are turned, causing them to
spiral along the field lines. In effect, if the magnetic field is
strong enough to overcome the momentum of the particles
then they become trapped by the magnetic field which then
steers the particles. The magnetic field and the particle motion
are then frozen together - particles can travel along the field
lines but cannot easily cross them.
When gas leaves the donor star it levels at the 'Lagrangian point' nearest the white dwarf. As soon as it
leaves the Lagrangian point it is now dominated by the gravity of the white dwarf rather than by the
donor star. This accretion stream or jet may be moving with sufficient velocity and kinetic energy to
overcome the outer weaker magnetic field of the white dwarf. In this situation we can ignore the effects of
the magnetic field - the particles simply travel on as if the magnetic field did not exist (and bulk motion of
the plasma actually drags the field-lines around with it). However, since the magnetic field increases
towards the white dwarf, there comes a point at which the jet has insufficient 'ram pressure' and over a
short distance there is a switch from motion dominated by the kinetic energy of the jet to motion
dominated by the magnetic field. The particles no longer have sufficient momentum to simply cross the
magnetic field lines and instead matter flows along them (with the particles spiralling as they go). The
transition from kinetic-energy dominated flow to magnetic-dominated flow is mathematically complex,
however, elsewhere we can use the simplifying assumptions just described. First, if the kinetic energy
dominates then we can ignore the effects of the magnetic field (without losing much accuracy) and the
matter drags magnetic field lines along with it. However, if the magnetic field dominates then we can
ignore the initial kinetic motion of the plasma and model it as flowing along the magnetic field lines.
At this point the accretion stream or jet generally splits into two, with one arm travelling in an arc toward
one pole of the white dwarf and the other stream travelling in an arc to the other pole. If the white dwarf
is significantly tilted on its axis, then matter will flow preferentially towards the nearest magnetic pole,
though some will still make it to the other pole. Indeed, the magnetic field itself generally seems to tilt, so
that one magnetic pole is nearer the accretion stream as a way of lowering the system's energy or
increasing its stability. These arcs are simply lines on a torus: the white dwarf acts like a bar magnet,
much as the Earth does, with a toroidal belt of magnetic field lines around the equator. Look at the
depiction of the Earth's magnetic field and you should be able to visualise why the plasma flows along
arcs to both poles. As the plasma streams into these two arcs, it breaks up into blobs or globules,
surrounded by a finer mist. As it nears the white dwarf, this matter is squeezed as the field lines
converge on the pole, compressing it into a narrow cylinder only about 1% the diameter of the dwarf.
Several globules a second will impact on the thin atmosphere of the white dwarf, just above the
photosphere (visible surface or region of the atmosphere at which light escapes) at the pole.
The in-falling mist of less dense material forms an accretion column. More exactly, the material arrives in
an arc, just to one side of the magnetic pole. The accreting material, having fallen through the
gravitational field of the white dwarf is now traveling at supersonic velocities. As the relatively cool
plasma, descending in free fall, slams into the atmosphere, a supersonic shock zone forms as the matter
abruptly decelerates to subsonic velocities. Some of the lost kinetic energy is converted into heat and
the plasma is heated to about 200 million kelvins (20 keV). This raises the thermal kinetic energy of the
particles and as they jostle about frequent collisions result in the loss of energy, which is radiated away
as X-rays. (These 'collisions' involve negative electrons passing close to positively charged ions, which
causes the electrons to turn and slow, releasing energy as they accelerate (decelerate) in the form of
X-ray photons; the energy being called bremsstrahlung radiation or 'breaking radiation').
The radiation of X-rays carries away energy and the material cools, and so becomes denser and sinks
onto the surface of the white dwarf - it has been accreted. The X-ray photons emitted are 'hard X-rays'
meaning they are high-energy X-rays (with energies around 10 keV). Some of these X-rays will hit the
surface of the white dwarf and be reflected, whilst others will be absorbed by the dwarf and gases
around the column, heating the column until it glows white or blue-hot. Dense in-falling blobs of plasma
may not be decelerated sufficiently to undergo shock and may instead plunge straight into the white
dwarf, heating it, causing it to emit soft X-rays (lower energy X-rays). If most of the matter is accreted as
dense blobs then most of the X-ray emission will be as soft X-rays. In polars, most of the radiation
emitted comes from the accretion column.
Why are polars called polars?
Polars are so-called because they also emit polarised light. As the particles spiral around the magnetic
field lines, during their journey to the pole, they radiate photons (cyclotron radiation). If a field line is
viewed side-on, then the spiralling photons will move predominantly up and down and so release
vertically polarised light. However, if a field-line is viewed head-on, then the photons will carry information
about the rotating electric field and will be circularly polarised. Thus, linearly polarised light is radiated
away to the sides of the accretion arc trajectory, circularly polarised light ahead of it. Polars are also
called AM Her stars, after their prototype star.
The magnetic field of AR UMa is so intense, that even near the point at which the accretion stream
emerges from the donor star it is strong enough to split the matter stream, so that two arcs of material
emerge from the Lagrangian point. At the other end of the spectrum, we have white dwarfs with weaker
magnetic fields. In this case the in-falling accretion stream moves much closer to the white dwarf, by
virtue of its momentum. If it moves close enough to reach the orbit which matches its angular momentum
then it begins to orbit the white dwarf at that distance, the so-called circularisation radius, and here an
accretion disc is born as the material spreads, with some of it losing angular momentum and spirally
slowly inwards, whilst a small amount gains angular momentum and spins away. However, there comes a
point when the material in the disc spirals in close enough for the magnetic field to dominate and the disc
cannot go any closer to the white dwarf. Instead, materials sweeps off the inner edge of the disc, travels
along magnetic field lines, and accretes onto both poles of the white dwarf as an accretion curtain. Such
a system is not quite a polar, but is instead referred to as an intermediate polar.
Another phenomenon to note is that of orbital synchronicity. The strong magnetic field of the white
dwarf interacts with the magnetic field of the donor star as the white dwarf spins - the two fields become
tangled, with their field lines crossing over and tugging at one-another. Breaking magnetic field lines
takes a lot of energy and instead the field lines usually 'wind up' and store a lot of energy as tension.
This creates a drag force on the rotating white dwarf, slowing its rate of spin until it rotates on its axis
once per orbital period. This means that the orbit is locked or synchronous - both stars will always
present the same face toward one-another (tidal forces can achieve a similar locking between planets,
such as the Earth and Moon). However, about 10% of polars are asynchronous, meaning that there is a
small difference between the white dwarf's spine period and the orbital period (as the two stars orbit
their common centre of mass). This difference is only about 1% can cause the accretion stream to
periodically switch poles since the white dwarf orbits relative to the donor star and if it's magnetic field is
tilted on its axis then each pole will take turns being closest to the accretion stream. This period of pole
switching is called the beat period and leaves characteristic tell-tale signs in the star's light-curve.
Coming soon - propeller systems and magnetars ...