Equilibrium configurations of strongly magnetized neutron stars with realistic equations of state

We investigate equilibrium sequences of magnetized rotating stars with four kinds of realistic equations of state (EOSs) of SLy, FPS, Shen and LS, employing the Tomimura–Eriguchi scheme to construct the equilibrium configurations. We study the basic physical properties of the sequences in the framework of Newtonian gravity. In addition, we take a new step by taking into account a general relativistic effect to the magnetized rotating configurations. With these computations, we find that the properties of the Newtonian magnetized stars, e.g. structure of magnetic field, highly depends on the EOSs. The toroidal magnetic fields concentrate rather near the surface for Shen and LS EOSs than those for SLy and FPS EOSs. The poloidal fields are also affected by the toroidal configurations. Paying attention to the stiffness of the EOSs, we analyse this tendency in detail. In the general relativistic stars, we find that the difference due to the EOSs becomes small because all the employed EOSs become sufficiently stiff for the large maximum density, typically greater than  10¹⁵ g cm⁻³  . The maximum baryon mass of the magnetized stars with axis ratio   q ∼ 0.7  increases about up to 20 per cent for that of spherical stars. We furthermore compute equilibrium sequences at finite temperature, which should serve as an initial condition for the hydrodynamic study of newly born magnetars. Our results suggest that we may obtain information about the EOSs from the observation of the masses of magnetars.     

Metallicity and photospheric abundances in field K and M dwarfs

Elemental abundances in late-type stars are of interest in several ways: they determine the location of the stars in the HR diagram and therefore their ages, as well as the atmospheric structure in their middle and upper photospheres. Especially in the case of chromospherically active late-type stars the question arises to what degree the upper photosphere is influenced by the nearby chromosphere. Analysing S/N ∼ 200 and Δλ/λ ∼ 20 000 data, we found a mean metallicity index [M/H] = −0.2 for programme K and M field stars based on an analysis of spectra in the region 5500–9000 Å. We also found that the Ca  I 6162-Å transition is a potential surface gravity indicator for K-type stars. For the chromospheric activity interval 4.4 < log  F _{Mg II}  < 6.6 we did not find any chromospheric activity impact on photospheric and upper photospheric transitions. With the derived metallicity, we confirmed the Li abundance from our previous paper and thus its dependence on the Mg  II chromospheric activity index. The nature of the spectrum for the active M-type star Gl 896A is explained by pure rotation of 14 km s⁻¹. As far as the lithium–rotation relation is concerned, the spectrum of Gl 517 is rotationally broadened as well, by 12 km s⁻¹, and the Li abundance is the second highest in our sample of stars. However, there is no link between very high Li abundance, 2.2 dex, in the K dwarf star Gl 5 and stellar rotation.     

Destabilization of hydrodynamically stable rotation laws by azimuthal magnetic fields

We consider the effect of toroidal magnetic fields on hydrodynamically stable Taylor–Couette differential rotation flows. For current-free magnetic fields a non-axisymmetric   m = 1  magnetorotational instability arises when the magnetic Reynolds number exceeds   O (100)  . We then consider how this 'azimuthal magnetorotational instability' (AMRI) is modified if the magnetic field is not current-free, but also has an associated electric current throughout the fluid. This gives rise to current-driven Tayler instabilities (TIs) that exist even without any differential rotation at all. The interaction of the AMRI and the TI is then considered when both electric currents and differential rotation are present simultaneously. The magnetic Prandtl number Pm turns out to be crucial in this case. Large Pm have a destabilizing influence, and lead to a smooth transition between the AMRI and the TI. In contrast, small Pm have a stabilizing influence, with a broad stable zone separating the AMRI and the TI. In this region the differential rotation is acting to stabilize the TIs, with possible astrophysical applications (Ap stars). The growth rates of both the AMRI and the TI are largely independent of Pm , with the TI acting on the time-scale of a single rotation period, and the AMRI slightly slower, but still on the basic rotational time-scale. The azimuthal drift time-scale is ∼20 rotations, and may thus be a (flip-flop) time-scale of stellar activity between the rotation period and the diffusion time.     

Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models

We show that the mass–radius  ( M – R )  relation corresponding to the stiffest equation of state (EOS) does not provide the necessary and sufficient condition of dynamical stability for equilibrium configurations, because such configurations cannot satisfy the 'compatibility criterion'. In this regard, we construct sequences composed of core–envelope models such that, like the central condition belonging to the stiffest EOS, each member of these sequences satisfies the extreme case of the causality condition,   v = c = 1  , at the centre. We thereafter show that the M – R relation corresponding to the said core–envelope model sequences can provide the necessary and sufficient condition of dynamical stability only when the 'compatibility criterion' for these sequences is 'appropriately' satisfied. However, the 'compatibility criterion' can remain satisfied even when the M – R relation does not provide the necessary and sufficient condition of dynamical stability for the equilibrium configurations. In continuation of the results of a previous study, these results explicitly show that the 'compatibility criterion' independently provides, in general, the necessary and sufficient condition of hydrostatic equilibrium for any regular sequence. In addition to its fundamental result, this study can explain simultaneously the higher and the lower values of the glitch healing parameter observed for the Crab-like and Vela-like pulsars respectively, on the basis of the starquake model of glitch generation.     

Full evolution of low-mass white dwarfs with helium and oxygen cores

We study the full evolution of low-mass white dwarfs with helium and oxygen cores. We revisit the age dichotomy observed in many white dwarf companions to millisecond pulsar on the basis of white dwarf configurations derived from binary evolution computations. We evolve 11 dwarf sequences for helium cores with final masses of 0.1604, 0.1869, 0.2026, 0.2495, 0.3056, 0.3333, 0.3515, 0.3844, 0.3986, 0.4160 and  0.4481 M_⊙  . In addition, we compute the evolution of five sequences for oxygen cores with final masses of 0.3515, 0.3844, 0.3986, 0.4160 and  0.4481 M_⊙  . A metallicity of   Z = 0.02  is assumed. Gravitational settling, chemical and thermal diffusion are accounted for during the white dwarf regime. Our study reinforces the result that diffusion processes are a key ingredient in explaining the observed age and envelope dichotomy in low-mass helium-core white dwarfs, a conclusion we arrived at earlier on the basis of a simplified treatment for the binary evolution of progenitor stars. We determine the mass threshold where the age dichotomy occurs. For the oxygen white dwarf sequences, we report the occurrence of diffusion-induced, hydrogen-shell flashes, which, as in the case of their helium counterparts, strongly influence the late stages of white dwarf cooling. Finally, we present our results as a set of white dwarf mass–radius relations for helium and oxygen cores.     

The eclipsing binary PV Cas: a case of strong differential rotation in depth

In this study, we show that only models with differential rotation, as opposed to non-rotation or solid-body rotation for the components of PV Cas, are in satisfactory agreement with the observations (including constraints on the apsidal advance rate and the synchronous rotation of the components in addition to their luminosities and radii). Internal rotation profiles found for solar and metal-rich chemical compositions are similar to each other in that only a small part of the outermost regions is rotating very slowly  ( v _eq∼ 65 km s ⁻¹)  and the rest is rotating very rapidly. Confirmation of Ap-like variations in the light curve of the system leads us to search for a connection between this type (and similar types) of internal rotation and chemically peculiar stars. The temperature difference between the blue sides of the main sequence for the normal and for the magnetic Ap stars may arise from such a connection, since we find a similar difference between the models with this kind of rotation and the non-rotating models of somewhat lower mass.     

Stellar differential rotation from direct star-spot tracking

On the Sun, the rotation periods of individual sunspots not only trace the latitude-dependence of the surface rotation rate, but also provide clues as to the amount of subsurface fluid shear. In this paper we present the first measurements of stellar differential rotation made by tracking the rotation of individual star-spots with sizes comparable to the largest sunspots. To achieve this we re-analyse four sequences of densely sampled, high signal-to-noise ratio echelle spectra of AB Doradus spanning several stellar rotations in 1996 December. Using spectral subtraction, least-squares deconvolution and matched-filter analysis, we demonstrate that it is possible to measure directly the velocity amplitudes and rotation periods of large numbers of individual star-spots at low to intermediate latitude. We derive values for the equatorial rotation rate and the magnitude of the surface differential rotation, both of which are in excellent agreement with those obtained by Donati & Collier Cameron from cross-correlation of Doppler images derived a year earlier in 1995 December, and with a re-analysis of the 1996 data by the χ ² landscape method. The differences between the rotation rates of individual spots and the fitted differential rotation law are substantially greater than the observational errors. The smaller spots show a greater scatter about the mean relation than the larger ones, which suggests that buffeting by turbulent supergranular flows could be responsible.     

Spot patterns and differential rotation in the eclipsing pre-cataclysmic variable binary, V471 Tau

We present surface spot maps of the K2V primary star in the pre-cataclysmic variable binary system, V471 Tau. The spot maps show the presence of large high-latitude spots located at the sub-white dwarf longitude region. By tracking the relative movement of spot groups over the course of four nights (eight rotation cycles), we measure the surface differential rotation rate of the system. Our results reveal that the star is rotating rigidly with a surface shear rate,  dΩ= 1.6 ± 6 mrad d⁻¹  . The single active star AB Dor has a similar spectral type, rotation period and activity level as the K star in V471 Tau, but displays much stronger surface shear  (46 < dΩ < 58 mrad d⁻¹)  . Our results suggest that tidal locking may inhibit differential rotation; this reduced shear, however, does not affect the overall magnetic activity levels in active K dwarfs.     

Oscillations of rapidly rotating superfluid stars

Using time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.     

Modelling surface magnetic field evolution on AB Doradûs due to diffusion and surface differential rotation

From Zeeman–Doppler images of the young, rapidly-rotating K0 dwarf AB Doradûs, we have created a potential approximation to the observed radial magnetic field and have evolved it over 30 d subject to the observed surface differential rotation , meridional flow and various diffusion rates. Assuming that the dark polar cap seen in Doppler images of this star is caused by the presence of a unipolar field, we have shown that the observed differential rotation will shear this field to produce the observed high-latitude band of unidirectional azimuthal field. By cross-correlating the evolved fields with the initial field each day we have followed the decay with time of the cross-correlation function. Over 30 d it decays by only 10 per cent. This contrasts with the results of Barnes et al. , who show that on this time-scale the spot distribution of He699 is uncorrelated. We propose that this is due to the effects of flux emergence changing the spot distributions.     

Doin' the twist: secular changes in the surface differential rotation on AB Doradus

We present measurements of the rotation rates of individual starspots on the rapidly rotating young K0 dwarf AB Doradus, at six epochs between 1988 December and 1996 December. The equatorial rotation period of the star decreased from 0.5137 to 0.5129 d between 1988 December and 1992 January. It then increased steadily, attaining a value of 0.5133 d by 1996 December. The latitude dependence of the rotation rate mirrored the changes in the equatorial rotation rate. The beat period between the equatorial and polar rotation periods dropped from 140 to 70 d initially, then rose steadily. The most rigid rotation, in 1988 December, occurred when the starspot coverage was at a maximum. The time-dependent part of the differential rotation is found to have     , which should alter the oblateness of the star enough to explain the period changes observed in several close binaries via the Applegate mechanism.     

Differential rotation of cool active stars: the case of intermediate rotators

In this paper, we present a new method for measuring the surface differential rotation of cool stars with rotation periods of a few days, for which the sparse phase coverage achievable from single-site observations generally prevents the use of more conventional techniques. The basic idea underlying this new analysis is to obtain the surface differential rotation pattern that minimizes the information content of the reconstructed Doppler image through a simultaneous fit of all available data.
Simulations demonstrate that the performance of this new method in the case of cool stars is satisfactory for a variety of observing strategies. Differential rotation parameters can be recovered reliably as long as the total data set spans at least 4 per cent of the time for the equator to lap the pole by approximately one complete cycle. We find in particular that these results hold for potentially complex spot distributions (as long as they include a mixture of low- and high-latitude features), and for various stellar inclination angles and rotation velocities. Such measurements can be obtained from either unpolarized or polarized data sets, provided their signal-to-noise ratio is larger than approximately 500 and 5000 per 2 km s⁻¹ spectral bin, respectively.
This method should therefore be very useful for investigating differential rotation in a much larger sample of objects than what has been possible up to now, and should hence give us the opportunity of studying how differential rotation reacts to various phenomena operating in stellar convective zones, such as tidal effects or dynamo magnetic field generation.     

A new numerical scheme for structures of rotating magnetic stars

We have developed a new numerical scheme for obtaining structures of rapidly rotating stars with strong magnetic fields. In our scheme, both poloidal and toroidal magnetic fields can be treated for stars with compressibility and infinite conductivity. By introducing the vector potential and its integral representation, we can treat the boundary condition for the magnetic fields across the surface properly. We show structures and distributions of magnetic fields as well as the distributions of the currents of rotating magnetic polytropic stars with polytropic index   N = 1.5  . The shapes of magnetic stars are oblate as long as the magnetic vector potential decreases as 1/ r when   r →∞  . For extremely strong magnetic fields, equilibrium configurations can be of toroidal shapes.     

Differential rotation on both components of the pre-main-sequence binary system HD 155555

We present the first measurements of surface differential rotation on a pre-main-sequence binary system. Using intensity (Stokes I) and circularly polarized (Stokes V) time-series spectra, taken over 11 nights at the Anglo-Australian Telescope (AAT), we incorporate a solar-like differential rotation law into the surface imaging process. We find that both components of the young, 18 Myr, HD 155555 (V824 Ara, G5IV + K0IV) binary system show significant differential rotation. The equator–pole lap times as determined from the intensity spectra are 80 d for the primary star and 163 d for the secondary. Similarly, for the magnetic spectra we obtain equator–pole lap times of 44 and 71 d, respectively, showing that the shearing time-scale of magnetic regions is approximately half of that found for stellar spots. Both components are therefore found to have rates of differential rotation similar to those of the same spectral-type main-sequence single stars. The results for HD 155555 are therefore in contrast to those found in other, more evolved, binary systems where negligible or weak differential rotation has been discovered. We discuss two possible explanations for this: first that at the age of HD 155555 binary tidal forces have not yet had time to suppress differential rotation and secondly that the weak differential rotation previously observed on evolved binaries is a consequence of their large convection zone depths. We suggest that the latter is the more likely solution and show that both temperature and convection zone depth (from evolutionary models) are good predictors of differential rotation strength. Finally, we also examine the possible consequences of the measured differential rotation on the interaction of binary star coronae.     

LO Peg in 1998: star-spot patterns and differential rotation

We present Doppler images of the young K5V–K7V rapid rotator LO Peg from seven nights of continuous spectroscopy obtained in 1998 from July 04 to July 10. The images reveal the presence of a strong polar cap with appendages extending to mid-latitudes, but no star-spots are seen below 15°. We briefly discuss the distribution of spots in light of recent flux transport simulations, which are able to reproduce the observed latitude dependence. With the full time series of spectra, of which 314 are useful, many phases are observed three times over the seven nights of observations. Using star-spots as tracers of a solar-like latitudinal differential rotation in our image reconstructions, we find that the equatorial regions complete one more rotation than the polar regions every  181 ± 35 d  . LO Peg is the second coolest star for which such a measurement has been made using indirect imaging methods. The degree of latitudinal shear is less than that seen in G and early K dwarfs, suggesting a trend in which differential rotation decreases with stellar mass in (pre-)main-sequence objects.     

Sounding stellar cycles with Kepler – I. Strategy for selecting targets

The long-term monitoring and high photometric precision of the Kepler satellite will provide a unique opportunity to sound the stellar cycles of many solar-type stars using asteroseismology. This can be achieved by studying periodic changes in the amplitudes and frequencies of the oscillation modes observed in these stars. By comparing these measurements with conventional ground-based chromospheric activity indices, we can improve our understanding of the relationship between chromospheric changes and those taking place deep in the interior throughout the stellar activity cycle. In addition, asteroseismic measurements of the convection zone depth and differential rotation may help us determine whether stellar cycles are driven at the top or at the base of the convection zone. In this paper, we analyse the precision that will be possible using Kepler to measure stellar cycles, convection zone depths and differential rotation. Based on this analysis, we describe a strategy for selecting specific targets to be observed by the Kepler Asteroseismic Investigation for the full length of the mission, to optimize their suitability for probing stellar cycles in a wide variety of solar-type stars.     

Multiperiodic semiregular variable stars in the ASAS data base: A pilot study

Based on a search for multi‐periodic variability among the semi‐regular red variable stars in the database of the All Sky Automated Survey (ASAS), a sample of 72 typical examples is presented. Their period analysis was performed using the Discrete Fourier Transform. In 41 stars we identified two significant periods each, simultaneously present, while the remaining 31 cases revealed even three such periods per star. They occur in a range roughly between 50 and 3000 days. Inter‐relationships between these periods were analyzed using the “double period diagram” which compares adjacent periods, and the so‐called “Petersen diagram”, the period ratio vs. the shorter period. In both diagrams we could identify six sequences of accumulation of the period values. For five of these sequences (containing 97 % of all data points) we found an almost perfect coincidence with those of previous studies which were based on very different samples of semiregular red variables. Therefore, existence and locations of these sequences in the diagrams seem to be universal features, which appear in any data set of semi‐regularly variable red giants of the AGB; we conclude that they are caused by different pulsation modes as the typical and consistent properties of similar stellar AGB configurations. Stellar pulsations can be considered as the principal cause of the observed periodic variability of these stars, and not binary, rotation of a spotted surface or other possible reasons suggested in the literature. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiperiodic variations in the last 104-yr light curve of the symbiotic star BF Cyg

We analyse a light curve (LC) of the symbiotic star BF Cyg, covering 114 yr of its photometric history. The star had a major outburst around the year 1894. Since then the mean optical brightness of the system is in steady decline, reaching only in the last few years its pre-outburst value. Superposed on this general decline are some six less intense outbursts of 1–2 mag and duration of 2000–5000 d. We find a cycle of 6376 d, or possibly twice this period, in the occurrence of these outbursts. We suggest that the origin of the system outbursts is in some magnetic cycle in the outer layers of the giant star of the system, akin to the less intense 8000-d magnetic cycle of our Sun. We further find, that in addition to its well-known binary period of 757.3 d, BF Cyg possesses also another photometric period of 798.8 d. This could be the rotation period of the giant star of the system. If it is, the beat period of these two periodicities, 14 580 d, is the rotation period of a tidal wave on the surface of the giant. A fourth period of 4436 d, the beat period of the 14 580-d and the 6376-d cycles is possibly also present in the LC. We predict that BF Cyg will be at the peak of its next outburst around the month of May in the year 2007. The newly discovered 798.8-d period explains the disappearance of the orbital modulation at some epochs in the LC. The 757.3-d oscillations will be damped again around the year 2013.     

Multiple stellar populations in the Sextans dwarf spheroidal galaxy?

We present wide-field     multiband ( BVI ) CCD photometry (down to     of the very low surface brightness dwarf spheroidal galaxy Sextans. In the derived colour–magnitude diagrams we find evidence suggesting the presence of multiple stellar populations in this dwarf spheroidal. In particular, we discover (i) a blue horizontal branch tail that appears to lie on a brighter sequence with respect to the prominent red horizontal branch and the RR Lyrae stars, very similar to what was found by Majewski et al. for the Sculptor dwarf spheroidal, (ii) hints of a bimodal distribution in colour of the red giant branch stars, (iii) a double red giant branch bump. All of these features suggest that (at least) two components are present in the old stellar population of this galaxy: the main one with     and a minor component around     . The similarity to the Sculptor case may indicate that multiple star formation episodes are also common in the most nearby dwarf spheroidals that ceased their star formation activity at very early epochs.     

Magnetic cycle of LQ Hydrae: observational indications and dynamo model

We present a model for the differential rotation and dynamo activity of the young rapidly rotating K0 dwarf LQ Hya ( P _rot=1.6 d). As might be expected from observations of the similar rapid rotator AB Dor, the predicted differential rotation is small (≃0.8 per cent) but extremely efficient in generating magnetic fields. The dynamo, which is of a distributed type, produces a globally axisymmetric field with radial and azimuthal components that are of the same magnitude and display a phase-lag in their evolution of about π/2. This is consistent with the long-term Zeeman–Doppler imaging study by Donati. The latitudinal distribution of flux is, however, a little different from that observed and the cycle period of 3.2 yr is somewhat shorter than suggested by the observations.