My research interests

Ap stars

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 nom-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?

The magnetic field in magnetars

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 ~10^15 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 (~10^4 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.

INTEGRAL Picture Of the Month (POM): A giant outburst of the soft gamma-ray repeater SGR 1806-20

Above is an observational record of the most energetic of these SGR outbursts to be seen. This outburst released around 2x10^46 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..

Instability of a toroidal magnetic field, and a magnetic dynamo

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 would be able to eliminate differential rotation, perhaps on a time-scale of 10^3 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.

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