Magnetic Fields in Stars
Magnetic Fields in Stars
Magnetism—the force that deflects the needle of a
compass—and magnetic fields have been found in some
hundreds of stars during the past 50 yr. Magnetic fields
have been detected in T Tauri stars and other pre-mainsequence stars, several types of main sequence stars, white
dwarfs and neutron stars. We now know a number of
methods by which such magnetic fields may be detected,
we are in the process of learning more about how they are
distributed over stellar surfaces, and we understand some
of the ways in which these fields reflect—and sometimes
influence—the evolution of the stars which possess them.
The first stellar magnetic fields were detected in
sunspots (see SUNSPOT MAGNETIC FIELDS) in the Sun by George
Ellery Hale in 1908. Almost forty years later, in 1947, the
first magnetic field in a star other than the Sun was found
by Horace W Babcock, who discovered a magnetic field in
the star 78 Virginis, a ‘chemically peculiar’ main sequence
star (see STELLAR EVOLUTION) about twice as massive as the
Sun. Magnetic fields are now known in perhaps 200 other
A and B stars of the middle main sequence, all of which
are, like 78 Vir, chemically peculiar (which means that
they have very unusual surface chemical compositions).
In such stars the fields are generally found to be roughly
dipolar in form; in other words, they have an overall
structure reminiscent of that of a simple bar magnet or of
the Earth’s magnetic field, with a north and a south pole,
between which the the magnetic force (as represented by
magnetic lines of force) points along loops connecting one
pole to the other. The typical field strength of such stars—
over the whole stellar surface—is of the order of 1000 G
(0.1 T), some 3000 times greater than the strength of the
Earth’s surface field, and about as strong as the magnetic
field of a good permanent horseshoe magnet.
The discovery of PULSARS in 1967 by Jocelyn Bell
Burnell and Anthony Hewish was soon recognized to
be both the discovery of NEUTRON STARS and of magnetic
fields in such stars. The pulsed radio radiation emitted
by these spinning, magnetized neutron stars is still almost
the only means for detecting single neutron stars. The
roughly dipolar fields of neutron stars are initially of the
order of 1012 –1013 G (108 –109 T) and then seem to decay
in strength by about a factor of 100. Most or all neutron
stars thus appear to be formed initially with fields about
1010 times stronger than are found in the magnetic middle
main sequence stars.
Three years later the first magnetic field was detected
in a WHITE DWARF by James Kemp, John Swedlund, John
Landstreet and Roger Angel. Fields are now known in
about 50 other white dwarfs. These fields range from about
105 to 109 G (10–105 T) in strength, roughly a factor of 104
stronger than those of middle main sequence stars. The
white dwarf fields also appear to be approximately dipolar
in structure. Unlike neutron stars, only a few per cent of
all white dwarfs have detectable magnetic fields.
The first magnetic fields in stars of the lower main
sequence were detected in 1980 by Richard Robinson, Pete
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
Worden and Jack Harvey. Fields are now known in more
than 50 cool stars, mostly rather young, active stars, or
in stars in which a companion enforces rapid rotation
(see the SOLAR–STELLAR CONNECTION). Recently, fields have
been found in a few PRE-MAIN-SEQUENCE STARS and T TAURI
STARS. In cool stars, the fields detected have very different
distributions over the stellar surface from those of the
stellar types already described. Instead of simple, roughly
dipolar structure, these fields seem to occur in forms more
like giant sunspots, or in patches on the stellar surface that
may resemble solar active regions. The field strengths are
typically of the order of 103 G (0.1 T), while the fraction
of the stellar surface covered is typically only of order
20–50%.
Unlike the fields of middle main sequence stars,
white dwarfs and neutron stars, all of which are observed
to change in structure only very slowly with time, the
distribution of magnetic flux on the surface of a lower main
sequence star usually changes substantially in a period of
weeks or months. It is generally supposed that, in the
cool stars, the fields observed are generated by a dynamo
process operating in the convective outer envelope of
the star, while the more stable fields of middle main
sequence stars, white dwarfs and neutron stars are ‘fossil
fields’—large-scale fields produced during an earlier stage
of evolution, and subsequently frozen into the highly
electrically conductive matter of the star. In this article
we will focus on the fields of middle main sequence stars
and of white dwarfs, leaving those of solar-type stars and
of neutron stars to other articles.
Methods of detecting stellar magnetic fields
Basic physics
Most of the magnetic fields detected in main sequence
and white dwarf stars are found by detecting the ZEEMAN
EFFECT in the stellar spectrum.
This effect splits each
energy level of an atom in a magnetic field into several
magnetic substates, leading to a number of effects that can
in favorable cases be detected.
When placed in an external magnetic field, a state i
of an atom with energy Ei and total angular momentum
quantum number J splits into 2J + 1 magnetic substates
equally spaced in energy, with a spacing which varies from
one atomic level to another. Transitions between level i
and another level f of energy Ef are characterized by the
frequency νif = (Ef − Ei )/ h when no magnetic field is
present. When a field B is applied, the splitting of the
lower and upper energy levels by the magnetic field leads
to the splitting of the spectral line associated with this
transition into three closely spaced group of lines. These
groups arise because most atomic transitions allow the
magnetic quantum number M to change by −1, 0, or 1.
The M = Mf − Mi = 0 group, called π components,
are distributed symmetrically about νif . The two groups
of lines with M = ±1, called σ components, are shifted
systematically to frequencies above and below νif , with
the M = +1 group on one side and the M = −1 group
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Magnetic Fields in Stars
on the other. The typical separation between the π and
one of the σ groups is
λB = ḡeBλ2 /4πmc2
where ḡ is a number of order 1 which varies from one
transition to another. In familiar units, the splitting is
λB (nm) = 4.67 × 10−3 ḡB(kG)λ(µm)2 .
Thus a field of 1 kG (0.1 T) leads to a π –σ separation of the
order of 0.001 nm at 500 nm = 0.5 µm.
The π and σ groups of lines are polarized. If the
magnetic field is transverse to the line of sight, the π
components (in emission) are linearly polarized parallel
to the applied field and the σ components are linearly
polarized in the orthogonal direction. If the field is parallel
to the line of sight, the π components are suppressed and
the two groups of σ components have opposite circular
polarizations.
When the magnetic field strength is strong enough (of
order 105 G) that the perturbation of the atom by the field
is larger than the spin–orbit perturbation, the relatively
complex Zeeman effect is superseded by the Paschen–Back
effect, which leads essentially to splitting of all lines into
simple triplets. A field of order 106 G results in a significant
quadratic Zeeman effect, which systematically shifts lines
of large upper principal quantum number nf relative to
lines of smaller nf . As a field of order 107 G is reached
and the magnetic interaction energy becomes comparable
with the Coulomb energy of the atomic electrical field, the
atomic spectrum of any atom, even H, becomes extremely
complicated.
At fields above about 106 G, another magnetic effect
occurs that is very useful for detection of fields in white
dwarfs: polarization of continuum radiation. The broadband light from a star with a field strength of this order
is circularly polarized, essentially because the field forces
electrons to spiral about field lines in a preferred direction.
For still larger fields, broad-band linear polarization can
also occur.
Field measurement methods
The splitting, shifting and polarization of spectral lines
by the Zeeman, Paschen–Back and quadratic Zeeman
effects, and the occurrence of continuum polarization
for sufficiently large fields, have provided astrophysicists
with a number of methods of detecting and measuring
magnetic fields in stars.
The most straightforward of these methods is useful
for stars that have a very small projected equatorial
rotational velocity veq sin i and hence sharp spectral lines.
In this case, one can directly observe the splitting of
spectral lines into components if the field is of the order of
a few kilogauss or more in main sequence stars, or about
106 G in white dwarfs. The separation of the observed
line components provides a direct measurement of the
modulus of the magnetic field averaged over the surface
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
of the star, a quantity called the mean field modulus, Bs ,
as shown in figure 1.
The polarization introduced into spectral lines by
magnetic splitting provides a second powerful method of
field detection. This method depends on the fact that, in
a magnetic field with a significant component along the
line of sight, the σ components on one side of the line
center absorb circularly polarized light of one sense of
polarization, while the σ components on the other side
of line center absorb the opposite circular polarization. If
we observe the stellar spectrum through polarizers that
pass each of the two senses of circular polarization, the
absorption lines in one of the two circularly polarized
spectra are not at precisely the same wavelengths as the
same lines in the other polarized spectrum, because of the
small wavelength difference between the two sets of σ
components. The presence of a field can be detected by
this shift in the position of spectral lines between spectra
observed in right- and left-circularly polarized light, or
equivalently in the spectrum formed by the difference of
the two spectra divided by their sum, as shown in the lefthand panel in figure 2.
The fact that, in the presence of a magnetic field
transverse to the line of sight, the absorption by the
π components is orthogonally polarized with respect
to the polarization of the σ components leads to a
similar effect when a spectrum is observed through linear
polarizers oriented parallel to and perpendicular to the
field direction, as seen in the right-hand panel of figure 2.
In general, the observable effect in linear polarization is
considerably smaller than in circular polarization.
Detection of the polarization effects from a stellar
magnetic field is possible only if there are substantial
regions on the stellar surface over which the field does
not change direction too much. Clearly, a field structure in
which many small tubes of magnetic flux directed out of
the star are closely mixed in with small tubes of inwarddirected flux will lead to no net polarization, as the effects
of adjacent oppositely directed flux tubes will cancel. On
the other hand, the detection of circular polarization,
which is not readily produced in line profiles by other
mechanisms, is a very robust indicator of the presence of a
field. Furthermore, very small levels of polarization (0.1%
or even 0.01%) can be measured reliably. The result is
that circular polarization methods, which measure what is
called the ‘mean longitudinal field’ B , provide much more
sensitivity to weak but geometrically simple magnetic
fields than methods that depend on studying line profiles.
In the best cases, B values as small as tens of gauss can
presently be detected.
Magnetic fields in middle main sequence
(‘peculiar A’) stars
The oblique rotator
Magnetic fields are detected in middle main sequence
stars (stars of between about 2 and 10 times the mass
of the Sun, which are burning hydrogen in their cores)
both by the detection of circular polarization in spectral
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Magnetic Fields in Stars
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
Figure 1. A portion of the spectrum of the very slowly rotating magnetic Ap star HD 94660 (the spectrum at the top of the figure),
showing splitting of spectral lines by a magnetic field of Bs ≈ 6400 G. Below the stellar spectrum is a schematic diagram of the Zeeman
splitting pattern of several strong stellar spectral lines. Each of the vertical lines above and below the line at intensity 0.4 (respectively
π and σ components) represents one Zeeman component; the position of each component is calculated for a field of 6400 G, and the
height of each line is proportional to the strength of that component. The ion responsible for each strong line is identified at the bottom
of the figure. (From G Mathys 1990 Astron. Astrophys. 232 151, reproduced by permission of Astronomy and Astrophysics.)
lines and by observing Zeeman splitting of spectral lines
in stars with small veq sin i values. All well-confirmed
detections of fields in middle main sequence stars are in
members of a class of stars known as ‘chemically peculiar
A stars’, often called Ap (or Bp) stars (see also PULSATING
AND CHEMICALLY PECULIAR UPPER MAIN SEQUENCE STARS). These
stars have long been known to have (sometimes very)
anomalous atmospheric chemical composition compared
with the Sun. Their chemistry is typically characterized
by unusually large amounts of chemical elements such
as Sr, Cr, Eu and other rare earths, Si and (only in the
most massive Bp stars) He. Most of these stars also have
unusually small amounts of a few elements as well, often
He and O. The elements which are anomalous depend
systematically on the mass of the star. It appears that
all chemically peculiar stars having the same general
chemical anomalies as the known magnetic stars probably
have fields.
A first question about the magnetic middle main sequence stars (I will call them ‘magnetic Ap stars’) is that of
determining the geometry of the magnetic field over the
stellar surface. This cannot be determined by directly observing the disks of such stars, of course; they are much too
small in angular size for direct imaging. We must use other
kinds of information to deduce the magnetic geometry.
The magnetic Ap stars are in most cases observed to
vary periodically in apparent brightness, in the strengths
and profiles of some or most spectral lines, and in the
measured components of the magnetic field. All these
quantities are generally observed to vary with the same
period. The period of variations is typically in the range
1–10 days, although periods as short as 0.5 days and as
long as some decades or known. An example is shown in
figure 3.
An important clue to the origin of the variations
is furnished by the observed fact that the value of the
projected rotational velocity veq sin i is closely correlated
with the period of variation. Large values of veq sin i are
only found for stars with short periods and, the longer the
period, the smaller the values of veq sin i are. The facts
that the observed periods are found with an enormous
range of values and that the periods are closely related to
the projected rotational velocities clearly indicate that the
observed variations are due to the rotation of the magnetic
Ap star. Variation in the average magnetic field indicates
that the star must have a magnetic field that varies from
one place to another at the surface, either in strength
or in inclination or both. Thus, when we see mainly
magnetic field lines directed towards the observer, we
measure a large value of B , but, when the field lines
are mainly perpendicular to the line of sight, B is small.
The variations in spectral line intensity and shape indicate
that the relative abundances of various chemical elements
vary from one place on the star to another. When we are
looking at a part of the star in which some element (such
as He) is relatively abundant, the spectral lines are strong
and deep; when we look at a different part of the star
which has relatively less He, the spectral lines are weaker.
The variations in surface chemistry in turn influence the
amount of light emitted at various wavelengths and lead
to the variations observed in brightness as the star rotates.
We observe that the value of B of a magnetic Ap star
generally varies in a fairly sinusoidal fashion. When we
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Magnetic Fields in Stars
Figure 2. Effects of a magnetic field on the line profile and
polarization of stellar spectral lines. The panels show
schematically the effect of a magnetic field with the Zeeman
pattern displayed in (a) for a field parallel to the line of sight
(left) and perpendicular to it (right). (b) The change in the line
from the non-magnetic case (dotted) to the magnetic case (solid)
for Zeeman splitting comparable with the Doppler width of the
spectral line. (c) The absorption line in left- and right-circular
polarization (left) and in linear polarization parallel to and
perpendicular to the stellar field (right). (d) The net circular (left)
and linear (right) polarization in the line. (From D J Landstreet
1980 Astron. J. 85 611, reproduced by permission of the American
Astronomical Society.)
try to reproduce this behavior by calculating the variations
expected from various simple models of the field geometry,
we find that this observation is consistent with the idea
that the structure of the magnetic field over the surface of
the star is in the general form of a dipole, typically inclined
(oblique) to the rotation axis of the star by some fairly large
angle. As the star rotates, we thus usually see one pole of
the dipolar distribution, and then the other. This model is
known as the ‘oblique rotator model’.
Astronomers are also actively working to use
observed spectrum variations to deduce the distributions
of different chemical elements over the surface of the
star. Often the models that fit the observations have a
distribution of the elements that is roughly axisymmetric
around the axis of the magnetic dipole. It is not uncommon
to find very large differences in the fractional abundances
of some elements over the stellar surface; in some cases
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
Figure 3. Variations of the massive magnetic Bp star HD 184927
(whose most striking abundance peculiarity is a considerable
excess of atmospheric He) with a period of 9.53 days. The
horizontal axis gives time in phase units (fractions of one cycle
from the periodically repeating time when the helium spectral
line intensities are strongest). The three panels show (from top to
bottom) the mean longitudinal field in kilogauss, the strength of
one helium line in arbitrary units and the brightness of the star
(in magnitudes) seen through a narrow (Strömgren) ultraviolet
filter. (From G A Wade et al 1997 Astron. Astrophys. 320 172,
reproduced by permission of Astronomy and Astrophysics.)
there may be more than 100 times more atoms of some
elements per unit volume of gas in one part of the star’s
atmosphere than in another part.
Origin of the observed magnetic fields and of the chemical
anomalies
Astronomers generally accept two possible origins for
observed stellar fields. One is that a field may be generated
by the interplay between convection (boiling motions of
the gas) in the outer layers of a star and the overall
rotation of the star. These motions may act as a dynamo
in the highly conducting outer layers of a star, producing
a complex and time-varying field. This mechanism seems
to be the cause of the magnetic field observed in the Sun.
In spite of much theoretical effort, such dynamo fields are
still not well understood.
The second possible origin is that the field is the result
of the collapse of a huge gas cloud to form a tiny star,
trapping in the partly ionized, electrically conducting gas
some small fraction of the weak galactic magnetic field. As
the field lines of the galactic field are squeezed together, the
strength of the entrained field is amplified by a very large
factor. Thus, the observed fields of the magnetic Ap stars
may be ‘fossil’ magnetic fields. This is not as unreasonable
an idea as may at first appear. Owing to the very large bulk
and high electrical conductivity of a star, a field formed in
this way would take a very long time, of the order of 1010 yr,
to decay. This is longer than the main sequence lifetime
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Magnetic Fields in Stars
of a middle main sequence star, and so a fossil field could
easily persist throughout the life of such a star.
The absence of any long-term changes in the observed
magnetic field strengths of magnetic Ap stars (such as
the solar activity cycle), other than the periodic variations
caused by stellar rotation, and the simple overall geometry
deduced for these fields, suggests that they are probably
fossil fields rather than dynamo-generated ones. This
view is supported by the lack of any obvious means of
generating a large dynamo field in a star that may be
rotating 100 times slower than the Sun and that has almost
no convection in its outer layers.
The presence of remarkable chemical peculiarities in
these magnetic stars also requires an explanation. In fact,
this is not quite as anomalous as it seems. The lowermass stars of the main sequence (M ≤ 2M ) show quite
homogeneous abundance patterns, with overall content
of ‘heavy elements’ (everything heavier than He) that
depends only on the age of the star. (Older low-mass
stars, formed when the universe was less rich in the
elements synthesized in many generations of supernova
explosions, have less of all heavy elements than younger
stars.) Very massive main sequence stars (M ≥ 10M )
lose mass rapidly, and this ensures that their surfaces
reveal their bulk composition which, because of their
very short main sequence lifetimes, is essentially that of
the contemporary interstellar material from which they
form. The intermediate-mass stars, among which the
magnetic Ap stars are found, almost all exhibit some
degree of chemical individuality. In most A and B stars
the variations are no more than some tens of per cent of
excess or deficiency compared with other similar stars,
but several other families of stars (mostly slowly rotating
and apparently non-magnetic stars) are known in which
certain deficiencies or enhancements can reach much
larger values. ‘Metallic-line A’ (Am) stars often have 10
times less Ca and Sc than other main sequence stars of
similar mass, and 10 times more of some rare earths.
‘Mercury–manganese’ (HgMn) stars have enhancements
of some elements by factors of from order 102 (V, Mn, Ga)
up to 105 or more (Eu, Pt, Hg). The abundance anomalies
of the magnetic Ap stars are simply some of the most
spectacular types of anomaly in a mass range filled with
variety.
These chemical abundance anomalies are generally
believed to be confined to the atmospheres and outer
envelopes of intermediate-mass stars, rather than being
representative of the bulk chemical composition of these
stars, for several reasons. First, the wide variety of
observed compositions, in stars all of which formed
relatively recently in galactic history, does not correspond
to any similar variety of compositions in the interstellar
clouds which form stars, or in other young stars of low
or high mass. Furthermore, the extremes of anomaly are
so great (factors of 105 or more) that it is not possible to
imagine any way in which star formation could have led
to gas clouds with such peculiar composition. Instead,
we believe that the observed chemical anomalies are
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
essentially surface phenomena, due to powerful processes
that separate elements, raising some into the atmosphere
while others sink out of sight.
The main sorting process leading to chemical
anomalies is microscopic diffusion of atoms of lowabundance elements, relative to the dominant hydrogen
of the stellar gas. Under the influence of gravity, elements
with higher atomic mass than hydrogen tend to sink into
the interior of the star. In a sufficiently stable atmosphere,
this process would eventually lead to an exterior layer
made up only of hydrogen, as is actually observed in many
white dwarfs. However, there are competing processes.
One of the most important is the outward force felt
by atoms and ions which can absorb photons of many
wavelengths from the outward flow of radiation through
the star. This absorption imparts an outward acceleration
to such ions and lifts them up to higher levels in the
stellar envelope. Thus, the overall effect of diffusion is
to allow some elements to sink in the atmosphere under
the dominant influence of gravity, while others are lifted
towards the surface by radiation.
These sorting processes compete with various mixing
processes such as convection. Thus, because the outer
layers of low-mass main sequence stars are strongly
convective, all sorting processes are strongly inhibited,
and these Sun-like stars exhibit very similar compositions.
In contrast, the main sequence stars of intermediate
mass are precisely the stars with sufficiently stable
atmospheres to allow diffusion to sort the chemical
elements, at least to some extent. Rapid rotation is capable
of generating slow mixing currents, and so the more
rapidly rotating A and B stars have only modestly sorted
surface chemistries. Most of the more peculiar middle
main sequence stars are slowly rotating. The magnetic Ap
stars have the additional feature that the presence of the
magnetic field rather strongly inhibits mixing motions in
the outer layers. The chemical peculiarities of the magnetic
Ap stars are simply a particularly strongly developed
aspect of a characteristic found in all stars in this mass
range.
Magnetic fields in white dwarfs
Observations and modelling
Magnetic fields are detected in white dwarfs by the same
methods used for magnetic Ap stars, namely by direct
observation of magnetic splitting of spectral lines and by
observation of circular polarization in line wings. Fields
are also detected by means of the continuum polarization
produced by fields of more than about 106 G. The deduced
fields range in strength from about 105 up to 109 G. At the
low end of this range, the spectrum of a white dwarf is
hardly perturbed at all by the field. For fields in the range
from about 106 to 3 × 107 G, splitting of familiar spectral
lines is easily seen. For still larger fields, the wavelengths
and shapes of spectral lines are so strongly altered by the
field that the spectrum is not recognizably related to that
of any non-magnetic white dwarf. The spectrum of one
magnetic white dwarf is shown in figure 4.
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Magnetic Fields in Stars
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
more than about 3 × 107 G. Modelling of such fields leads
to deduced magnetic field geometries that are roughly
dipolar, like the fields of magnetic Ap stars. For stronger
fields, the main difficulties come from the complex and
uncertain behavior of even simple atoms such as H in the
presence of fields so strong that they influence the motion
of the electron(s) as strongly as the central Coulomb
attraction of the atomic nucleus. The observations of
spectra of white dwarfs with fields of 108 G or more are
in reasonable accord with the results of atomic physics
calculations, but no detailed modelling has yet been
possible.
Fields as small as about 10 kG could be detected
in most white dwarfs. Surveys of many white dwarfs
to about this level of precision have shown that the
great majority of white dwarfs do not possess detectable
magnetic fields. About 4% of the total population of
white dwarfs have fields, with about equal probabilities
per decade of field strength over the range 105 –109 G.
Figure 4. The flux and polarization spectrum of the magnetic
white dwarf GD 229, which has a field of order 109 G. The
lowest curve shows the wavelength variation of the flux, the
second lowest of circular polarization, the third lowest the
percentage linear polarization and the top the position angle of
linear polarization.
The polarization and/or line splitting is observed to
be variable in about one-quarter of the known magnetic
white dwarfs. Observed variations are periodic, with
periods in the range from about 1 h to 20 days. These
periods are so long compared with any reasonable
oscillation period of a white dwarf that they must be
rotation periods, and so we are again quickly led to the
oblique rotator model for the variations. The observed
variations in the magnetic field strength and in spectral line
shapes are again interpreted as simply being due to the fact
that we see a magnetic field that is inclined to the stellar
rotation axis from different directions as the star rotates.
The fact that most magnetic white dwarfs do not vary may
imply that, in most magnetic white dwarfs, the magnetic
field is axisymmetric about the rotation axis or possibly
that most magnetic white dwarfs rotate with periods of
decades or more.
Modelling of observed spectra and their variations
is possible if the fields are not too large, say not much
Origin of white dwarf fields
Trying to understand the origin of the fields observed
in white dwarfs presents us with substantial challenges.
There are no obvious mechanisms for producing largescale, ordered, static fields in either magnetic Ap stars or
white dwarfs after they are formed. We observe that a
small fraction of middle main sequence stars, and of white
dwarfs, have magnetic fields large enough to detect, in
the range 102 –105 G on the main sequence and 105 –109 G
in white dwarfs. The observed magnetic Ap fields may
be due to magnetic flux retention during star formation,
and the fields of white dwarfs could be due to the further
retention of that same flux as magnetic Ap stars collapse
to become white dwarfs. This hypothesis is consistent
to some extent with the relative values of observed field
strength, since, if the magnetic flux threading a star’s
equator is retained during a collapse, the magnetic field
strength will increase as
B ∝ /R 2
where R is the stellar radius. Thus the decrease in radius
by a factor of 102 as a star becomes a white dwarf could
lead to a field strength increase by a factor of 104 , about the
difference observed between the ranges of field strength on
the main sequence and among white dwarfs. However,
this does not explain how that magnetic flux is retained
in the evolution stages between the main sequence and
white dwarf stages; the intervening giant state is expected
to be largely convective, which might be expected to expel
much of the magnetic flux in a star. Furthermore, this idea
does not explain why the largest (108 –109 G) fields are as
common as fields 103 times smaller; on the main sequence
the largest fields are a modest tail on a distribution that is
very strongly peaked around fields of less than 103 G.
Magnetic fields in neutron stars present us with
further challenges. It appears that almost all neutron stars
have fields of the order of 1010 –1013 G. Again, these are
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Magnetic Fields in Stars
E N C Y C LO P E D IA O F A S T R O N O M Y AN D A S T R O P H Y S I C S
about the fields that would be expected by magnetic flux
retention from the main sequence. However, if this is the
origin of magnetic fields in neutron stars, why do almost all
neutron stars have large fields, while only a small fraction
of white dwarfs have large fields? This question is made
still more puzzling by the fact that virtually no magnetic
main sequence stars are known in the mass range that is
expected to evolve eventually to neutron stars.
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