arXiv subjects
Publications and source records attributed to H. C. Spruit.
In this lecture the basic theory of accretion disks is reviewed, with emphasis on aspects relevant for X-ray binaries and Cataclysmic Variables. The text gives a general introduction as well as a selective discussion of a number of more recent topics.
A rapid timing analysis of VLT/ULTRACAM and RXTE observations of the black hole binary GX 339-4 in its 2007 low/hard state is presented. The optical light curves in the r', g' and u' filters show slow (~20 s) quasi-periodic variability. Upon this is superposed fast flaring activity on times approaching the best time resolution probed (~50 ms) and with maximum strengths of more than twice the local mean. Power spectral analysis over ~0.004-10 Hz is presented, and shows that although the average optical variability amplitude is lower than that in X-rays, the peak variability power emerges at a higher Fourier frequency in the optical. Energetically, we measure a large optical vs. X-ray flux ratio, higher than that seen when the source was fully jet-dominated. Such a large ratio cannot be easily explained with a disc alone. The optical:X-ray cross-spectrum shows a markedly different behaviour above and below ~0.2 Hz. The peak of the coherence function above this threshold is associated with a short optical time lag, also seen as the dominant feature in the time-domain cross-correlation at ~150 ms. The rms energy spectrum of these fast variations is best described by distinct physical components over the optical and X-ray regimes, and also suggests a maximal disc fraction of 20% at ~5000 A. If the constant time delay is due to propagation of fluctuations to (or within) the jet, this is the clearest optical evidence to date of the location of this component. The low-frequency QPO is seen in the optical but not in X-rays. Evidence of reprocessing emerges at the lowest Fourier frequencies, with optical lags at ~10 s and strong coherence in the blue u' filter. Simultaneous optical spectroscopy also shows the Bowen fluorescence blend, though its emission location is unclear. But canonical disc reprocessing cannot dominate the optical power easily, nor explain the fast variability. (abridged)
Some established views of the solar magnetic cycle are discussed critically, with focus on two aspects at the core of most models: the role of convective turbulence, and the role of the `tachocline' at the base of the convection zone. The standard view which treats the solar cycle as a manifestation of the interaction between convection and magnetic fields is shown to be misplaced. The main ingredient of the solar cycle, apart from differential rotation, is instead buoyant instability of the magnetic field itself. This view of the physics of the solar cycle was already established in the 1950s, but has been eclipsed mathematically by mean field turbulence formalisms which make poor contact with observations and have serious theoretical problems. The history of this development in the literature is discussed critically. The source of the magnetic field of the solar cycle is currently assumed to be located in the `tachocline': the shear zone at the base of the convection zone. While the azimuthal field of the cycle is indeed most likely located at the base of the convection zone, it cannot be powered by the radial shear of the tachocline as assumed in these models, since the radiative interior does not support significant shear stresses. Instead, it must be the powered by the latitudinal gradient in rotation rate in the convection zone, as in early models of the solar cycle. Possible future directions for research are briefly discussed.
The Sun supports a rich spectrum of internal waves that are continuously excited by turbulent convection. The GONG network and the MDI/SOHO space instrument provide an exceptional data base of spatially-resolved observations of solar oscillations, covering an entire sunspot cycle (11 years). Local helioseismology is a set of tools for probing the solar interior in three dimensions using measurements of wave travel times and local mode frequencies. Local helioseismology has discovered (i) near-surface vector flows associated with convection (ii) 250 m/s subsurface horizontal outflows around sunspots (iii) ~50 m/s extended horizontal flows around active regions (converging near the surface and diverging below), (iv) the effect of the Coriolis force on convective flows and active region flows (v) the subsurface signature of the 15 m/s poleward meridional flow, (vi) a +/-5 m/s time-varying depth-dependent component of the meridional circulation around the mean latitude of activity, and (vii) magnetic activity on the far side of the Sun.
The magnetic theory for the production of jets by accreting objects is reviewed with emphasis on outstanding problem areas. An effort is made to show the connections behind the occasionally diverging nomenclature in the literature, to contrast the different points of view about basic mechanisms, and to highlight concepts for interpreting the results of numerical simulations. The role of dissipation of magnetic energy in accelerating the flow is discussed, and its importance for explaining high Lorentz factors. The collimation of jets to the observed narrow angles is discussed, including a critical discussion of the role of `hoop stress'. The transition between disk and outflow is one of the least understood parts of the magnetic theory; its role in setting the mass flux in the wind, in possible modulations of the mass flux, and the uncertainties in treating it realistically are discussed. Current views on most of these problems are still strongly influenced by the restriction to 2 dimensions (axisymmetry) in previous analytical and numerical work; 3-D effects likely to be important are suggested. An interesting problem area is the nature and origin of the strong, preferably highly ordered magnetic fields known to work best for jet production. The observational evidence for such fields and their behavior in numerical simulations is discussed. I argue that the presence or absence of such fields may well be the `second parameter' governing not only the presence of jets but also the X-ray spectra and timing behavior of X-ray binaries.
We have performed 2.5D and 3D simulations of conical jets driven by the rotation of an ordered, large-scale magnetic field in a stratified atmosphere. The simulations cover about three orders of magnitude in distance to capture the centrifugal acceleration as well as the evolution past the Alfven surface. We find that the jets develop kink instabilities, the characteristics of which depend on the velocity profile imposed at the base of the flow. The instabilities are especially pronounced with a rigid rotation profile, which induces a shearless magnetic field. The jet's expansion appears to be limiting the growth of Alfven mode instabilities.
We present the discovery of optical/X-ray flux correlations on rapid timescales in the low/hard state of the Galactic black hole GX 339-4. The source had recently emerged from outburst and was associated with a relatively-faint counterpart with mag V~17. The optical (VLT/ULTRACAM) and X-ray (RXTE/PCA) data show a clear positive cross-correlation function (CCF) signal, with the optical peak lagging X-rays by ~ 150 ms, preceded by a shallow rise and followed by a steep decline along with broad anti-correlation dips. Examination of the light curves shows that the main CCF features are reproduced in superpositions of flares and dips. The CCF peak is narrow and the X-ray auto-correlation function (ACF) is broader than the optical ACF, arguing against reprocessing as the origin for the rapid optical emission. X-ray flaring is associated with spectral hardening, but no corresponding changes are detected around optical peaks and dips. The variability may be explained in the context of synchrotron emission with interaction between a jet and a corona. The complex CCF structure in GX 339-4 has similarities to that of another remarkable X-ray binary XTE J1118+480, in spite of showing a weaker maximum strength. Such simultaneous multi-wavelength, rapid timing studies provide key constraints for modeling the inner regions of accreting stellar sources.
Possible origins of the magnetic fields of neutron stars include inheritance from the main sequence progenitor and dynamo action at some stage of evolution of progenitor. Inheritance is not sufficient to explain the fields of magnetars. Energetic considerations point to differential rotation in the final stages of core collapse process as the most likely source of field generation, at least for magnetars. A runaway phase of exponential growth is needed to achieve sufficient field amplification during relevant phase of core collapse; it can probably be provided by a some form of magnetorotational instability. Once formed in core collapse, the field is in danger of decaying again by magnetic instabilities. The evolution of a magnetic field in a newly formed neutron star is discussed, with emphasis on the existence of stable equilibrium configurations as end products of this evolution, and the role of magnetic helicity in their existence.
We present results of numerical 3D MHD simulations with radiative energy transfer of fine structure in a small sunspot of about 4 Mm width. The simulations show the development of filamentary structures and flow patterns that are, except for the lengths of the filaments, very similar to those observed. The filamentary structures consist of gaps with reduced field strength relative to their surroundings. Calculated synthetic images show dark cores like those seen in the observations; the dark cores are the result of a locally elevated $τ=1$ surface. The magnetic field in these cores is weaker and more horizontal than for adjacent brighter structures, and the core support a systematic outflow. Movies show migration of the dark-cored structures towards the umbra, and fragments of magnetic flux that are carried away from the spot by a large scale `moat flow'. We conclude that the simulations are in qualitative agreement with observed penumbra filamentary structures, Evershed flows and moving magnetic features.
We present numerical 2D magnetostatic models for sunspot penumbrae consisting of radially aligned field-free gaps in a potential magnetic field, as proposed by Spruit and Scharmer (2006). The shape of the gaps and the field configurations around them are computed consistently from the condition of magnetostatic pressure balance between the gap and the magnetic field. The results show that field-free gaps in the {\it inner} penumbra are cusp-shaped and bounded by a magnetic field inclined by about $70^\circ$ from the vertical. Here, the magnetic component has a Wilson depression on the order 200--300 km relative to the top of the field-free gap; the gaps should thus appear as noticeably elevated features. This structure explains the large variations in field strength in the inner penumbra inferred from magnetograms and two-component inversions, and the varying appearance of the inner penumbra with viewing angle. In the {\it outer} penumbra, on the other hand, the gaps are flat-topped with a horizontal magnetic field above the middle of the gap. The magnetic field has large inclination variations horizontally, but only small fluctuations in field strength, in agreement with observations.
Instabilities in magnetic fields wound up by differential rotation as reviewed in Spruit (1999) are discussed with some detail and new developments added. In stellar models which include magnetic torques, the differential rotation tends to accumulate in the gradients in composition. In view of this, instability in a $μ$-gradient is studied in more detail here, resulting in the detection of a second instability. Its relevance for angular momentum transport is uncertain, however, since it requires high horizontal field gradients and would not operate near the pole. Finally, the possibility is discussed that magnetic instability in a $μ$-gradient will lead to {\em layer formation}: the gradients breaking up into small steps of uniform composition and rotation rate. This would enhance the angular momentum transport across inhomogeneous zones, and decrease the rotation rates of the end products of stellar evolution. A recent {\tt astro-ph} submission by Dennisenkov and Pinsonneault proposing a modification of the instability conditions is shown to contain a mathematical error.
We use numerical MHD to look at the stability of a possible poloidal field in neutron stars (Flowers & Ruderman 1977), and follow its unstable evolution, which leads to the complete decay of the field. We then model a neutron star after the formation of a solid crust of high conductivity. As the initial magnetic field we use the stable `twisted torus' field which was the result of our earlier work (Braithwaite & Nordlund 2005), since this field is likely to exist in the interior of the star at the time of crust formation. We follow the evolution of the field under the influence of diffusion, and find that large stresses build up in the crust, which will presumably lead to cracking. We put this forward as a model for outbursts in soft gamma repeaters.
We present numerical simulations of a self-sustaining magnetic field in a differentially rotating non-convective stellar interior. A weak initial field is wound up by the differential rotation; the resulting azimuthal field becomes unstable and produces a new meridional field component, which is then wound up anew, thus completing the `dynamo loop'. This effect is observed both with and without a stable stratification. A self-sustained field is actually obtained more easily in the presence of a stable stratification. The results confirm the analytical expectations of the role of Tayler instability.
We interpret penumbral filaments as due to convection in field-free, radially aligned gaps just below the visible surface of the penumbra, intruding into a nearly potential field above. This solves the classical discrepancy between the large heat flux and the low vertical velocities observed in the penumbra. The presence of the gaps causes strong small-scale fluctuations in inclination, azimuth angle and field strength, but without strong forces acting on the gas. The field is nearly horizontal in a region around the cusp-shaped top of the gap, thereby providing an environment for Evershed flows. We identify this region with the recently discovered dark penumbral cores. Its darkness has the same cause as the dark lanes in umbral light-bridges, reproduced in numerical simulations by Nordlund and Stein (2005). We predict that the large vertical and horizontal gradients of the magnetic field inclination and azimuth in the potential field model will produce the net circular polarization seen in observations. The model also explains the significant elevation of bright filaments above their surroundings. It predicts that dark areas in the penumbra are of two different kinds: dark filament cores containing the most inclined (horizontal) fields, and regions between bright filaments, containing the least inclined field lines.
We suggest a possible mechanism of efficient transport of the large-scale external magnetic flux inward through a turbulent accretion disk. The outward drift by turbulent diffusion which limits the effectiveness of this process is reduced if the external flux passes through the disk in concentrated patches. Angular momentum loss by a magnetocentrifugal wind from these patches of strong field adds to the inward drift. We propose that magnetic flux accumulating in this way at the center of the disk provides the `second parameter' determining X-ray spectral states of black hole binaries, and the presence of relativistic outflows.
Some main-sequence stars of spectral type A are observed to have a strong (300-30000 G), static, large-scale magnetic field, of a chiefly dipolar shape -- the `Ap stars' (for example Alioth, the fifth star in the Big Dipper). Following their discovery fifty years ago, it was speculated that these fields a remnants of the star's formation, a `fossil' field. Alternatively, they could be generated by a dynamo process in the star's convective core. The dynamo hypothesis has difficulty explaining high field strengths and the lack of a correlation with rotation. The weakness of the fossil-field theory has been the absence of known field configurations stable enough to survive in a star over its lifetime. We demonstrate here the formation of stable magnetic field configurations, with properties agreeing with those observed, by evolution from arbitrary, unstable initial fields. The results are applicable equally to Ap stars, magnetic white dwarfs and some highly magnetised neutron stars known as magnetars. This establishes fossil fields as the natural, unifying explanation for the magnetism of all these stars.
We calculate the evaporation of a cool accretion disk around a black hole due to the ion-bombardment by an ion supported accretion flow (here ISAF, or optically thin ADAF). As first suggested by Spruit & Deufel (2002), this evaporation takes place in two stages: ion bombardment of the cool disk (Shakura-Sunyaev disk: SSD) produces an intermediate-temperature layer on top of the disk (`warm layer') which constitutes an independent accretion flow on both sides of the SSD. As this warm material accretes inward of the inner radius of the SSD, it becomes thermally unstable by lack of cooling of photons, and evaporates into the ISAF, thereby feeding the latter. Angular momentum conservation forces a certain fraction of the ISAF material to move outward, where it can bombard the SSD with its hot ions. The flow geometry is derived by computing stationary solutions of the continuity- and angular momentum equations for the three components (ISAF, warm flow and SSD). The overall radiative output is dominated by hard X-rays. They are produced mostly from the warm component, rather than the ISAF. The expected time dependence and stability of the flow, not computed here, is discussed briefly.
We investigate the production of the gamma-ray spectrum of a Poynting-flux dominated GRB ouflow. The very high magnetic field strengths (super-equipartition) in such a flow lead to very efficient synchrotron emission. In contrast with internal shocks, dissipation of magnetic energy by reconnection is gradual and does not produce the spectrum of cooling electrons associated with shock acceleration.We show that a spectrum with a break in the BATSE energy range is produced, instead, if the magnetic dissipation heats a small (\sim 10^{-4}) population of electrons.