About 5% of main-sequence A stars fall into the category of Ap stars (`peculiar A'). They differ from normal A stars in their metal abundances, and it was discovered around sixty years ago (the first discovery of magnetic fields outside the solar system) that they have strong (300 to 30,000 gauss) large-scale magnetic fields. It has been known for a long time that the magnetic field affects the transport of metals and thus causes the peculiar spectrum. The reason that these stars have such a magnetic field, however, has been something of a mystery. On the surface of the star we observe a roughly dipolar field, but what shape does the field have inside the star? How does this field survive for so long? Why does the observed field not change, even over a period of decades? It is these questions which I have been addressing over the last few years. The figure on the right (from Bagnulo et al. 2001) shows the form of the magnetic field observed on the surface of the Ap star 53 Cam. The main result from these studies is the existence of a stable field configuration which can survive in a star for the whole of the main-sequence lifetime. This result was obtained by numerically simulating a star containing an arbitrary magnetic field, and watching the field fall into a stable equilibrium, an energy minimum. The field finds its way into a twisted torus configuration (see figure below).
The figure is of the stereographic type. Stare through the computer screen and the two images will become one, the 3D structure visible. The red and blue lines represent the magnetic field, the grey circle the core of the torus shape and the yellow lines the surface of the star.
For a hand-waving explanation of why a stable field has to be this
shape, click here.
This stable field configuration is presumably also present in magnetic
white dwarfs. According to observations of magnetic white dwarfs, the
fields are very similar in shape and total flux to those seen on Ap
stars, and there is lots of evidence that Ap stars are indeed the
progenitors of magnetic white dwarfs. The animated figure shows the
spectrum and infered surface field of REJ 0317-853 (from Barstow,
Jordan, O'Donoghue, Burleigh, Napiwotzki, Harrop-Allin et al.,
1995). Click on the image to see a larger version.
The observed spectra were binned into 12 phases (0-11) covering the
total rotational period of 725 seconds (making REJ 0317-853 the
fastest rotating known isolated white dwarf).
The model was calculated with the program for the radiative transport
through the magnetized stellar atmosphere of a white dwarf written by
Stefan Jordan.
The magnetic field geometry was chosen to match the observed spectra
best. A configuration was assumed, in which the magnetic field was
expanded into spherical harmonics up to l=2 (15 parameters). However,
only the three latitude dependent parameters for m=0 were
significantly different from zero, so that the model shown here is
almost cylindrically symmetric.
The animation shows the variation of the visible hemisphere relative
to the observer from the earth showing different parts of the star at
different times. The brighter the areas are, the larger the magnetic
field is (the steps in greyscale correspond to steps of 100 MG).
The magnetic field of REJ 0317-853 is extremely non-dipolar. A
centered dipole varies by a factor of two between the poles and the
equator, while the configuration shown here varies between 170 (the
darkest grey) and 800 Megagauss (the bright spot).
The dipole field strength is 413 MG, but the contribution of the
quadrupole and octupole relative to the dipole amounts 60% and 38%,
respectively.
I am currently investigating the effect of rotation on the magnetic
field and vice versa. Various questions remain to be answered, for
instance: do we expect the magnetic and rotation axes to be aligned
with one another, or that they are orthogonal? In what way could the magnetic
field cause the rotation axis to precess or nutate? What effect would
the magnetic fields of binary stars have upon each other?
Stability analysis of fields in Duez and Mathis 2009
Analytic methods can also be used to find stable equilibria. As a check, it is useful to put these configurations into a simulations and evolve the magnetic field in time, to see whether the field suffers any obvious instability.
To see some animations of these simulations, Click here
On larger scales, I am also interested in the intergalactic medium, the gas which resides in the gravitational potential well of a cluster of galaxies.
The gas in a galaxy cluster is hot (around 10^8 K) and emits X rays via the process of thermal Bremsstrahlung. Pointing an X-ray telescope at a cluster, we see brighter emission from the dense central region and fainter emission further out. Often, we see "bubbles" of apparently less dense material. These bubbles are thought to consist of material ejected from an Active Galactic Nucleus (AGN) which are often found at the centre of large galaxies in clusters.
In essence, an AGN is a supermassive black hole which accretes surrounding gas. Because of the angular momentum of the accreted gas, an "accretion disc" forms around the hole. A by-product of this spinning accretion is the formation of jets, where material is ejected along the spin axes of the hole. The properties of this ejected material are not very well understood except that it will probably be both hot and magnetised. This would explain how these bubbles can be less dense than the surrounding intracluster gas, although the internal pressure of the bubble must be the same as the pressure of the surroundings - the ejecta has a higher temperature and/or has significant pressure from a magnetic field. Cosmic rays (energetic particles) may also play an important role. In fact, we know that the bubbles do contain at least some cosmic rays and at least some magnetic field, because we see the resulting synchrotron emission in the radio part of the spectrum.
Galaxy cluster MS 0735.6+7421. On the left, an X-ray image taken with the Chandra telescope. In the middle, a radio image taken with the VLA. On the right, a composite image combining X-ray, radio and optical. In X rays we see the hot intracluster medium, which is denser in the centre of the cluster. On either side of the centre are underdense bubbles. Sychrotron (radio) emission from the bubbles confirms the presence of magnetic fields. Note the large galaxy at the centre, which hosts the supermassive black hole responsible for inflating the bubbles.
Now, imagine how a bubble is inflated by the AGN, detaches and rises upwards through the surrounding intracluster medium. There is a buoyant upwards force on the bubble equal to the weight of displaced external medium minus the bubble's own weight, and a detached bubble will reach a terminal velocity where this force is balanced by aerodynamic drag. While the bubble is being inflated, if its volume is increasing at a constant rate then bubble's radius will increase in time as t^(1/3), so that the 'expansion velocity' goes at t^(-2/3), i.e. the expansion slows down. Once the expansion velocity drops below the terminal velocity, the bubble detaches from the parent AGN and floats upwards.
The Perseus galaxy cluster in X rays. Bubbles can reach a significant distance from their origin without breaking up.
It is seen in hydro simulations of rising bubbles that the velocity shear at the bubble boundary is unstable, and that the top of the bubble is subject to the Rayleigh-Tayler instability as the less dense gas is pushed against the denser surroundings. This results in disintegration of the bubble once the bubble has risen by a distance equal to its own radius. This, however, is contrary to observations of intact bubbles located at larges distances from their parent AGN. An obvious candidate for preventing this bubble shredding is a magnetic field, which could inhibit these instabilities.
One might expect the bubble to contain an initially disordered magnetic field which reconnects to form a `helical ball' which stabilises the bubble. Preliminary calculations suggest that the formation of a helical ball takes place on somewhat less than the buoyant-rise timescale of the bubble. Numerical simulations can be used to resolve this problem, first without and then with gravity and an accompanying stratification of the external intergalactic medium. This should shed some light on, amongst other things, the process of chemical and magnetic enrichment of the primordial gas and more generally on the formation and evolution of galaxy clusters and on the history of star formation. Moreover, this work should answer a more fundamental question: what happens to a magnetised region embedded in a non-magnetised region, how does the magnetic reconnection process proceed and what is the end result?
The rotation of a star will generally affect the stability of the magnetic field configuration inside it. In fact, rotation has a tendency to stabilise a magnetic field. Poloidal magnetic fields are known to be unstable in non-rotating stars, and I have recently been working on their stability in rotating stars. It seems that the rotation is able to slow down the decay of the field, but that the field will still decay on a very short timescale compared to the star's lifetime.
To see some animations of these simulations, Click here
The Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) emit X-rays continuously and, in the case of the SGRs, in energetic outbursts. These objects are believed to be isolated neutron stars. But since, unlike in classical pulsars, the rate of loss of rotational kinetic energy is nowhere near enough to account for the energy emitted, it is thought that the emission is powered instead by the gradual decay of a strong magnetic field of ~1015 gauss (the `magnetar model'). A neutron star has a solid crust, and the weaker field of a classical radio pulsar could be confined by this crust, even if it were in an otherwise dynamically unstable form. The field in a magnetar, however, is too strong to be held in place by the crust and must be stable on a dynamic (Alfven) time-scale if it is to survive for the lifetimes (~104 years) of these objects. An obvious candidate for the configuration of this magnetic field is the stable configuration found from the research on A stars mentioned above - if this magnetic field can exist in an A star, why not also in a neutron star? I am working on the application of this stable A-star field in magnetars, and have found that as the field slowly looses energy, owing to finite conductivity, stress builds up in the crust of the star. Just as stress in the Earth's crust leads to earthquakes, this magnetic stress could cause starquakes which we observe as SGR outbursts. Investigation of these phenomena could also help to towards a better understanding of the neutron stars' equation of state, its physical properties and conductivity, and in general, the behaviour of matter in extreme circumstances.
Above is an observational record of the most energetic of these SGR outbursts to be seen. This outburst released around 2x1046 erg, and it is now thought possible that events of this nature may account for some proportion of Short Gamma-ray Bursts. It is also very possible that nearby events of this type have been responsible for mass extinctions on Earth. Have a look at Robert Duncan's magnetar website for more info..
Differential rotation in a star will lead to the `winding up' of any magnetic field present. What properties will this magnetic field have? Will it be unstable? Numerical simulations have demonstrated that a toroidal field of this type will be unstable to the so-called Tayler instability and decay on the dynamic (Alfven) time-scale. This has the interesting consequence that as the resulting decayed field is wound up anew by the differential rotation, a dynamo cycle is created. This `Tayler-Spruit' dynamo would effectively remove any residual differential rotation from the radiative zone of a star, and could therefore explain, for instance, the uniform rotation of the solar core. This also has a possible application in neutron stars - it could have something to say about the mysterious lack of newly formed pulsars with rotational periods of anywhere close to the theoretical break-up limit, which is a little less than one millisecond. There are various theories to explain rapid spindown after neutron-star birth; gravitational waves and viscous damping have been suggested as well as a range of magnetohydrodynamic phenomena. This magnetic dynamo could be able to eliminate differential rotation, perhaps on a time-scale of 103 seconds. Whether this could have any relevance for this spindown of neutron stars remains to be seen and is the topic of research I intend to undertake in the future.