Christopher A. Tout

The most magnetic stars

Observations of magnetic A, B and O stars show that the poloidal mag- netic flux per unit massp/M appears to have an upper bound of approximately 10 6.5 Gcm 2 g 1 . A similar upper bound to the total flux per unit mass is found for the magnetic white dwarfs even though the highest magnetic field strengths at their surfaces are much larger. For magnetic A and B stars there also appears to be a well defined lower bound below which the incidence of magnetism declines rapidly. Accord- ing to recent hypotheses, both groups of stars may result from merging stars and owe their strong magnetism to fields generated by a dynamo mechanism as they merge. We postulate a simple dynamo that generates magnetic field from differential rotation. We limit the growth of magnetic fields by the requirement that the poloidal field stabilizes the toroidal and vice versa. While magnetic torques dissipate the differential rotation, toroidal field is generated from poloidal by an dynamo. We further suppose that mechanisms that lead to the decay of toroidal field lead to the generation of poloidal. Both poloidal and toroidal fields reach a stable configuration which is independent of the size of small initial seed fields but proportional to the initial differential rotation. We pose the hypothesis that strongly magnetic stars form from the merging of two stellar objects. The highest fields are generated when the merge introduces differential rotation that amounts to critical break up velocity within the condensed object. Cali- bration of a simplistic dynamo model with the observed maximum flux per unit mass for main-sequence stars and white dwarfs indicates that about 1.5×10 4 of the decay- ing toroidal flux must appear as poloidal. The highest fields in single white dwarfs are generated when two degenerate cores merge inside a common envelope or when two white dwarfs merge by gravitational-radiation angular momentum loss. Magnetars are the most magnetic neutron stars. Though these are expected to form directly from single stars, their magnetic flux to mass ratio indicates that a similar dynamo, driven by differential rotation acquired at their birth, may also be the source of their strong magnetism.

A two-stream formalism for the convective Urca process

We derive a new formalism for convective motions involving two radial flows. This formalism provides a framework for convective models that guarantees consistency for the chemistry and the energy budget in the flows, allows time dependence and accounts for the interaction of the convective motions with the global contraction or expansion of the star. In the one-stream limit, the formalism reproduces several existing convective models and allows them to treat the chemistry in the flows. We suggest a version of the formalism that can be implemented easily in a stellar evolution code. We then apply the formalism to convective Urca cores in Chandrasekhar-mass white dwarfs and compare it to previous studies. We demonstrate that, in degenerate matter, nuclear reactions which change the number of electrons strongly influence the convective velocities, and we show that the net energy budget is sensitive to the mixing. We illustrate our model by computing stationary convective cores with Urca nuclei. Even a very small mass fraction of Urca nuclei (as little as 10 -8 ) strongly influences the convective velocities. We conclude that the proper modelling of the Urca process is essential for determining the ignition conditions for the thermonuclear runaway in Chandrasekhar-mass white dwarfs.

Merging binary stars and the magnetic white dwarfs

A magnetic dynamo driven by differential rotation generated when stars merge can explain strong fields in certain classes of magnetic stars, including the high field magnetic white dwarfs (HFMWDs). In their case the site of the differential rotation has been variously proposed to be within a common envelope, the massive hot outer regions of a merged degenerate core or an accretion disc formed by a tidally disrupted companion that is subsequently incorporated into a degenerate core. We synthesize a population of binary systems to investigate the stellar merging hypothesis for observed single HFMWDs. Our calculations provide mass distribution and the fractions of white dwarfs that merge during a common envelope phase or as double degenerate systems in a post common envelope phase. We vary the common envelope efficiency parameter alpha and compare with observations. We find that this hypothesis can explain both the observed incidence of magnetism and the mass distribution of HFMWDs for a wide range of alpha. In this model, the majority of the HFMWDs are of the Carbon Oxygen type and merge within a common envelope. Less than about a quarter of a per cent of HFMWDs originate from double degenerate stars that merge after common envelope evolution and these populate the high-mass tail of the HFMWD mass distribution.

The nature of millisecond pulsars with helium white dwarf companions

We examine the growing data set of binary millisecond pulsars that are thought to have a helium white dwarf companion. These systems are believed to form when a low- to intermediate-mass companion to a neutron star fills its Roche lobe between central hydrogen exhaustion and core helium ignition. We confirm that our own stellar models reproduce a well-defined period-companion mass relation irrespective of the details of the mass transfer process. With magnetic braking this relation extends to periods of less than 1d for a 1Msun giant donor. With this and the measured binary mass functions we calculate the orbital inclination of each system for a given pulsar mass. We expect these inclinations to be randomly oriented in space. If the masses of the pulsars were typically 1.35Msun then there would appear to be a distinct dearth of high-inclination systems. However if the pulsar masses are more typically 1.55 to 1.65Msun then the distribution of inclinations is indeed indistinguishable from random. If it were as much as 1.75Msun then there would appear to be an excess of high-inclination systems. Thus with the available data we can argue that the neutron star masses in binary millisecond pulsars recycled by mass transfer from a red giant typically lie around 1.6Msun and that there is no preferred inclination at which these systems are observed. Hence there is reason to believe that pulsar beams are either sufficiently broad or show no preferred direction relative to the pulsars spin axis which is aligned with the binary orbit. This is contrary to some previous claims, based on a subset of the data available today, that there might be a tendency for the pulsar beams to be perpendicular to their spin.

Does GD 356 have a terrestrial planetary companion

GD 356 is unique among magnetic white dwarfs because it shows Zeeman-split Balmer lines in pure emission. The lines originate from a region of nearly uniform field strength (δB/B≈ 0.1) that covers 10 per cent of the stellar surface in which there is a temperature inversion. The energy source that heats the photosphere remains a mystery but it is likely to be associated with the presence of a companion. Based on current models, we use archival Spitzer Infrared Array Camera (IRAC) observations to place a new and stringent upper limit of 12 MJ for the mass of such a companion. In the light of this result and the recent discovery of a 115-min photometric period for GD 356, we exclude previous models that invoke accretion and revisit the unipolar inductor model that has been proposed for this system. In this model, a highly conducting planet with a metallic core orbits the magnetic white dwarf and, as it cuts through field lines, a current is set flowing between the two bodies. This current dissipates in the photosphere of the white dwarf and causes a temperature inversion. Such a planet is unlikely to have survived both the red and asymptotic giant branch phases of evolution so we argue that it may have formed from the circumstellar disc of a disrupted He or CO core during a rare merger of two white dwarfs. GD 356 would then be a white dwarf counterpart of the millisecond binary pulsar PSR 1257+12 which is known to host a planetary system.

Formation of redbacks via accretion-induced collapse

We examine the growing class of binary millisecond pulsars known as redbacks. In these systems the pulsars companion has a mass between 0.1 and about 0.5 solar masses in an orbital period of less than 1.5 days. All show extended radio eclipses associated with circumbinary material. They do not lie on the period-companion mass relation expected from the canonical intermediate-mass X-ray binary evolution in which the companion filled its Roche lobe as a red giant and has now lost its envelope and cooled as a white dwarf. The redbacks lie closer to, but usually at higher period than, the period-companion mass relation followed by cataclysmic variables and low-mass X-ray binaries. In order to turn on as a pulsar mass accretion on to a neutron star must be sufficiently weak, considerably weaker than expected in systems with low-mass main-sequence companions driven together by magnetic braking or gravitational radiation. If a neutron star is formed by accretion induced collapse of a white dwarf as it approaches the Chandrasekhar limit some baryonic mass is abruptly lost to its binding energy so that its effective gravitational mass falls. We propose that redbacks form when accretion induced collapse of a white dwarf takes place during cataclysmic variable binary evolution because the loss of gravitational mass makes the orbit expand suddenly so that the companion no longer fills its Roche lobe. Once activated, the pulsar can ablate its companion and so further expand the orbit and also account for the extended eclipses in the radio emission of the pulsar that are characteristic of these systems. The whole period-companion mass space occupied by the redbacks can be populated in this way.

A Common Envelope Binary Star Origin of Long Gamma-ray Bursts

The stellar origin of γ-ray bursts can be explained by the rapid release of energy in a highly collimated, extremely relativistic jet. This in turn appears to require a rapidly spinning highly magnetized stellar core that collapses into a magnetic neutron star or a black hole within a relatively massive envelope. They appear to be associated with Type Ib/c supernovae but, with a birth rate of around 10- 6 to 10 -5 yr -1 per galaxy, they are considerably rarer than such supernovae in general. To satisfy all these requirements we hypothesize a binary star model that ends with the merging of an oxygen/neon white dwarf with the carbon/oxygen core of a naked helium star during a common envelope phase of evolution. The rapid spin and high magnetic field are natural consequences of such a merging. The evolution that leads to these progenitors is convoluted and so naturally occurs only very rarely. To test the hypothesis we evolve a population of progenitors and find that the rate is as required. At low metallicity we calculate that a similar fraction of stars evolve to this point and so would expect the γ-ray burst rate to correlate with the star formation rate in any galaxy. This too is consistent with observations. These progenitors, being of intermediate mass, differ radically from the usually postulated high-mass stars. Thus we can reconcile observations that the bursts occur close to but not within massive star associations.

Genesis of magnetic fields in isolated white dwarfs

A dynamo mechanism driven by differential rotation when stars merge has been proposed to explain the presence of strong fields in certain classes of magnetic stars. In the case of the high field magnetic white dwarfs (HFMWDs), the site of the differential rotation has been variously thought to be the common envelope, the hot outer regions of a merged degenerate core or an accretion disc formed by a tidally disrupted companion that is subsequently accreted by a degenerate core. We have shown previously that the observed incidence of magnetism and the mass distribution in HFMWDs are consistent with the hypothesis that they are the result of merging binaries during common envelope evolution. Here we calculate the magnetic field strengths generated by common envelope interactions for synthetic populations using a simple prescription for the generation of fields and find that the observed magnetic field distribution is also consistent with the stellar merging hypothesis. We use the Kolmogorov-Smirnov test to study the correlation between the calculated and the observed field strengths and find that it is consistent for low envelope ejection efficiency. We also suggest that field generation by the plunging of a giant gaseous planet on to a white dwarf may explain why magnetism among cool white dwarfs (including DZ white dwarfs) is higher than among hot white dwarfs. In this picture a super Jupiter residing in the outer regions of the planetary system of the white dwarf is perturbed into a highly eccentric orbit by a close stellar encounter and is later accreted by the white dwarf.

The convective Urca process

One possible fate of an accreting white dwarf is explosion in a type Ia supernova. However, the route to the thermonuclear runaway has always been uncertain owing to the lack of a convective model consistent with the Urca process. We derive a formalism for convective motions involving two radial flows. This formalism provides a framework for convective models that guarantees self-consistency for chemistry and energy budget, allows time-dependence and describes the interaction of convective motions with the global contraction or expansion of the star. In the one-stream limit, we reproduce several already existing convective models and allow them to treat chemistry. We also suggest as a model easy to implement in a stellar evolution code. We apply this formalism to convective Urca cores in Chandrasekhar mass white dwarfs. We stress that in degenerate matter, nuclear reactions that change the number of electrons strongly influence the convective velocities. We point out the sensitivity of the energy budget on the mixing. We illustrate our model by computing stationary convective cores with Urca nuclei. We show that even a very small mass fraction of Urca nuclei (10 −8 ) strongly influences the convective velocities. Finally, we present preliminary computations of the late evolution of a close to Chandrasekhar mass C+O white dwarf including the convective Urca process.

Accretion induced collapse of white dwarfs and the origin of Long Gamma‐Ray Bursts

The stellar origin of gamma‐ray bursts can be explained by the rapid release of energy in a highly collimated, extremely relativistic jet. This in turn appears to require a rapidly spinning highly magnetised stellar core that collapses into a magnetic neutron star or a black hole within a relatively massive envelope. We hypothesize a binary star model that ends with the merging of an oxygen neon white dwarf with the carbon‐oxygen core of a naked helium star during a common envelope phase of evolution, and subsequent accretion induced collapse into a neutron star. The rapid spin and high magnetic field are natural consequences of such a merging. These progenitors, being of intermediate mass, differ radically from the usually postulated high‐mass stars. Thus we can reconcile observations that the bursts occur close to but not within massive star associations.