Stellar disruption by a supermassive black hole: is the light curve really proportional to t−5/3?

In this paper, we revisit the arguments for the basis of the time evolution of the flares expected to arise when a star is disrupted by a supermassive black hole. We present a simple analytic model relating the light curve to the internal density structure of the star. We thus show that the standard light curve proportional to   t ^−5/3  only holds at late times. Close to the peak luminosity the light curve is shallower, deviating more strongly from   t ^−5/3  for more centrally concentrated (e.g. solar type) stars. We test our model numerically by simulating the tidal disruption of several stellar models, described by simple polytropic spheres with index γ. The simulations agree with the analytical model given two considerations. First, the stars are somewhat inflated on reaching pericentre because of the effective reduction of gravity in the tidal field of the black hole. This is well described by a homologous expansion by a factor which becomes smaller as the polytropic index becomes larger. Secondly, for large polytropic indices wings appear in the tails of the energy distribution, indicating that some material is pushed further away from parabolic orbits by shocks in the tidal tails. In all our simulations, the   t ^−5/3  light curve is achieved only at late stages. In particular, we predict that for solar-type stars, this happens only after the luminosity has dropped by at least 2 mag from the peak. We discuss our results in the light of recent observations of flares in otherwise quiescent galaxies and note the dependence of these results on further parameters, such as the star/hole mass ratio and the stellar orbit.     

Metal-rich carbon stars in the Sagittarius dwarf spheroidal galaxy

We present spectroscopic observations from the Spitzer Space Telescope of six carbon-rich asymptotic giant branch (AGB) stars in the Sagittarius dwarf spheroidal galaxy (Sgr dSph) and two foreground Galactic carbon stars. The band strengths of the observed C₂H₂ and SiC features are very similar to those observed in Galactic AGB stars. The metallicities are estimated from an empirical relation between the acetylene optical depth and the strength of the SiC feature. The metallicities are higher than those of the Large Magellanic Cloud, and close to Galactic values. While the high metallicity could imply an age of around 1 Gyr, for the dusty AGB stars, the pulsation periods suggest ages in excess of 2 or 3 Gyr. We fit the spectra of the observed stars using the dusty radiative transfer model and determine their dust mass-loss rates to be in the range  1.0–3.3 × 10⁻⁸ M_⊙ yr⁻¹  . The two Galactic foreground carbon-rich AGB stars are located at the far side of the solar circle, beyond the Galactic Centre. One of these two stars shows the strongest SiC feature in our present Local Group sample.     

Burial of the polar magnetic field of an accreting neutron star – II. Hydromagnetic stability of axisymmetric equilibria

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad–Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as   M _a= 6 × 10⁻⁴ M_⊙  , by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to   M _a < 10⁻⁴ M_⊙  ) into the time-dependent, ideal-magnetohydrodynamic code zeus-3d and loading additional mass on to the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in zeus-3d . Surprisingly, it is observed that the equilibria are marginally stable for all   M _a≤ 6 × 10⁻⁴ M_⊙  ; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels <1 per cent of the mass and magnetic flux).     

Simulations of the formation of stellar discs in the Galactic Centre via cloud–cloud collisions

Young massive stars in the central parsec of our Galaxy are best explained by star formation within at least one, and possibly two, massive self-gravitating gaseous discs. With help of numerical simulations, we here consider whether the observed population of young stars could have originated from a large angle collision of two massive gaseous clouds at   R ≃ 1 pc  from Sgr A*. In all the simulations performed, the post-collision gas flow forms an inner, nearly circular gaseous disc and one or two eccentric outer filaments, consistent with the observations. Furthermore, the radial stellar mass distribution is always very steep,  Σ_*∝ R ⁻²  , again consistent with the observations. All of our simulations produce discs that are warped by between 30° and 60°, in accordance with the most recent observations. The three-dimensional velocity structure of the stellar distribution is sensitive to initial conditions (e.g. the impact parameter of the clouds) and gas cooling details. For example, the runs in which the inner disc is fed intermittently with material possessing fluctuating angular momentum result in multiple stellar discs with different orbital orientations, contradicting the observed data. In all the cases the amount of gas accreted by our inner boundary condition is large, enough to allow Sgr A* to radiate near its Eddington limit over ∼10⁵ yr. This suggests that a refined model would have physically larger clouds (or a cloud and a disc such as the circumnuclear disc) colliding at a distance of a few parsecs rather than 1 pc as in our simulations.     

Seismological studies of ZZ Ceti stars – II. Application to the ZZ Ceti class

We used the detected pulsation modes and adiabatic pulsation models to do seismology of the class of ZZ Ceti stars and measure the H layer mass for 83 stars. We found the surface hydrogen layer to be within the range  10^−9.5≥ M _H/ M _*≥ 10⁻⁴  , with an average of   M _H/ M _*= 10^−6.3  , which is thinner than the predicted value of   M _H/ M _*= 10⁻⁴  , indicating that the stars lose more mass during their evolution than previously expected. These results are preliminary and do not include the possible effects of realistic C/O profiles on the fits.     

Unresolved emission and ionized gas in the bulge of M31

We study the origin of unresolved X-ray emission from the bulge of M31 based on archival Chandra and XMM–Newton observations. We demonstrate that three different components are present. (i) Broad-band emission from a large number of faint sources – mainly accreting white dwarfs and active binaries, associated with the old stellar population, similar to the Galactic ridge X-ray emission of the Milky Way. The X-ray to K -band luminosity ratios are compatible with those for the Milky Way and for M32; in the 2–10 keV band, the ratio is  (3.6 ± 0.2) × 10²⁷ erg s⁻¹ L⁻¹_⊙  . (ii) Soft emission from ionized gas with a temperature of about ∼300 eV and a mass of  ∼2 × 10⁶ M_⊙  . The gas distribution is significantly extended along the minor axis of the galaxy, suggesting that it may be outflowing in the direction perpendicular to the galactic disc. The mass and energy supply from evolved stars and Type Ia supernovae is sufficient to sustain the outflow. We also detect a shadow cast on the gas emission by spiral arms and the 10-kpc star-forming ring, confirming significant extent of the gas in the 'vertical' direction. (iii) Hard extended emission from spiral arms, most likely associated with young stellar objects and young stars located in the star-forming regions. The   L _X/SFR  (star formation rate) ratio equals  ∼9 × 10³⁸ (erg s⁻¹)(M_⊙ yr⁻¹)⁻¹  , which is about ∼1/3 of the high-mass X-ray binary contribution, determined earlier from Chandra observations of other nearby galaxies.     

X-ray emission by a shocked fast wind from the central stars of planetary nebulae

We calculate the X-ray emission from the shocked fast wind blown by the central stars of planetary nebulae (PNe) and compare with observations. Using spherically symmetric self-similar solutions, we calculate the flow structure and X-ray temperature for a fast wind slamming into a previously ejected slow wind. We find that the observed X-ray emission of six PNe can be accounted for by shocked wind segments that were expelled during the early-PN phase, if the fast wind speed is moderate,   v ₂∼ 400–600 km s⁻¹  , and the mass-loss rate is a few times  10⁻⁷ M_⊙ yr⁻¹  . We find, as proposed previously, that the morphology of the X-ray emission is in the form of a narrow ring inner to the optical bright part of the nebula. The bipolar X-ray morphology of several observed PNe, which indicates an important role of jets, rather than a spherical fast wind, cannot be explained by the flow studied here.     

Primordial magnetic fields and formation of molecular hydrogen

We study the implications of primordial magnetic fields for the thermal and ionization history of the post-recombination era. In particular, we compute the effects of dissipation of primordial magnetic fields owing to ambipolar diffusion and decaying turbulence in the intergalactic medium (IGM) and the collapsing haloes, and compute the effects of the altered thermal and ionization history on the formation of molecular hydrogen. We show that, for magnetic field strengths in the range  2 × 10⁻¹⁰≲ B ₀≲ 2 × 10⁻⁹ G  , the molecular hydrogen fraction in IGM and collapsing halo can increase by a factor of 5 to 1000 over the case with no magnetic fields. We discuss the implication of the increased molecular hydrogen fraction on the radiative transfer of ultraviolet photons and the formation of first structures in the universe.     

TeV gamma-rays from accreting magnetars in massive binaries

This paper focuses on neutron stars (NS) of the magnetar type inside massive binary systems. We determine the conditions under which the matter from the stellar wind can penetrate the inner magnetosphere of the magnetar. At a certain distance from the NS surface, the magnetic pressure can balance the gravitational pressure of the accreting matter, creating a very turbulent, magnetized transition region. It is suggested that this region provides good conditions for the acceleration of electrons to relativistic energies. These electrons lose energy due to the synchrotron process and inverse Compton (IC) scattering of the radiation from the nearby massive stellar companion, producing high-energy radiation from X-rays up to ∼TeV γ-rays. The primary γ-rays can be further absorbed in the stellar radiation field, developing an IC  e^±  pair cascade. We calculate the synchrotron X-ray emission from primary electrons and secondary  e^±  pairs and the IC γ-ray emission from the cascade process. It is shown that quasi-simultaneous observations of the TeV γ-ray binary system LSI +61 303 in the X-ray and TeV γ-ray energy ranges can be explained with such an accreting magnetar model.     

Relativistic models of magnetars: structure and deformations

We find numerical solutions of the coupled system of Einstein–Maxwell equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass   M = 1.4 M_⊙  and surface magnetic fields of the order of 10¹⁵ G, a quadrupole ellipticity of the order of 10⁻⁶ to 10⁻⁵ should be expected. Low-mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10⁻³ in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.     

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement.
Our results show that for a primary black hole mass of  ∼10⁶–10⁷ M_⊙  , the black hole mass-ratio   q > 10⁻²  , cusp size ∼1 pc, the tidal disruption rate can be as large as  ∼10⁻²–1 M_⊙ yr⁻¹  . This is at least 10²–10⁴ times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: ∼10⁵ yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.     

Detecting the first objects in the mid-infrared with the Next Generation Space Telescope

We calculate the expected mid-infrared (MIR) molecular hydrogen line emission from the first objects in the Universe. As a result of their low masses, the stellar feedback from massive stars is able to blow away their gas content and collect it into a cooling shell where H₂ rapidly forms and IR roto-vibrational (as for example the rest-frame 2.12 μm) lines carry away a large fraction (up to 10 per cent) of the explosion energy. The fluxes from these sources are in the range 10⁻²¹–10⁻¹⁷ erg s⁻¹ cm⁻² . The highest number counts are expected in the 20-μm band, where about 10⁵ sources deg⁻² are predicted at the limiting flux of 3×10⁻¹⁸ erg s⁻¹ cm⁻². Among the planned observational facilities, we find that the best detection perspectives are offered by the Next Generation Space Telescope ( NGST ), which should be able to reveal about 200 first objects in one hour observation time at its limiting flux in the above band. Therefore, mid-IR instruments appear to represent perfect tools to trace star formation and stellar feedback in the high ( z ≳5) redshift Universe.     

The dependence of star formation on initial conditions and molecular cloud structure

We investigate the dependence of stellar properties on the initial kinematic structure of the gas in star-forming molecular clouds. We compare the results from two large-scale hydrodynamical simulations of star cluster formation that resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical, but in the new simulation the power spectrum of the velocity field imposed on the cloud initially and allowed to decay is biased in favour of large-scale motions. Whereas the calculation of Bate et al. began with a power spectrum   P ( k ) ∝ k ⁻⁴  to match the Larson scaling relations for the turbulent motions observed in molecular clouds, the new calculation begins with a power spectrum   P ( k ) ∝ k ⁻⁶  .
Despite this change to the initial motions in the cloud and the resulting density structure of the molecular cloud, the stellar properties resulting from the two calculations are indistinguishable. This demonstrates that the results of such hydrodynamical calculations of star cluster formation are relatively insensitive to the initial conditions. It is also consistent with the fact that the statistical properties of stars and brown dwarfs (e.g. the stellar initial mass function) are observed to be relatively invariant within our Galaxy and do not appear to depend on environment.     

Emergence of magnetic field due to spin-polarized baryon matter in neutron stars

A model of the ferromagnetic origin of magnetic fields of neutron stars is considered. In this model, the magnetic phase transition occurs inside the core of neutron stars soon after formation. However, owing to the high electrical conductivity the core magnetic field is initially fully screened. We study how this magnetic field emerges for an outside observer. After some time, the induced field that screens the ferromagnetic field decays enough to uncover a detectable fraction of the ferromagnetic field. We calculate the time-scale of decay of the screening field and study how it depends on the size of the ferromagnetic core. We find that the same fractional decay of the screening field occurs earlier for larger cores. We conjecture that weak fields of millisecond pulsars, B ∼10⁸–10⁹ G, could be identified with ferromagnetic fields of unshielded fraction ε ∼10⁻⁴–10⁻³ resulting from the decay of screening fields by a factor 1− ε in ∼10⁸ yr since their birth.     

Parameters of core collapse

This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple,  ξ⁻¹  , of the central relaxation time, and produces a density profile in which  ρ∝ r ^−α  , where α is a constant. The parameters α and ξ have usually been determined from simplified models, such as gas and Fokker–Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N -body simulations carried out using the newly completed GRAPE-6.     

A systematic study of variability in a sample of ultraluminous X-ray sources

We present results from a study of short-term variability in 19 archival observations by XMM–Newton of 16 ultraluminous X-ray sources (ULXs). Eight observations (six sources) showed intrinsic variability with power spectra in the form of either a power-law or broken power-law-like continuum and in some cases quasi-periodic oscillations (QPOs). The remaining observations were used to place upper limits on the strength of possible variability hidden within. Seven observations (seven sources) yielded upper limits comparable to, or higher than, the values measured from those observations with detectable variations. These represented the seven faintest sources, all with   f_x < 3 × 10⁻¹² erg cm⁻² s⁻¹  . In contrast, there are four observations (three sources) that gave upper limits significantly lower than both the values measured from the ULX observations with detectable variations, and the values expected by comparison with luminous Galactic black hole X-ray binaries (BHBs) and active galactic nuclei (AGN) in the observed frequency bandpass (10⁻³–1 Hz). This is the case irrespective of whether one assumes characteristic frequencies appropriate for a stellar mass  (10 M_⊙)  or an intermediate mass  (1000 M_⊙)  black hole, and means that in some ULXs the variability is significantly suppressed compared to bright BHBs and AGN. We discuss ways to account for this unusual suppression in terms of both observational and intrinsic effects and whether these solutions are supported by our results.     

The expansion of the giant filamentary shell, DEM 171, in the Magellanic Bridge

The giant filamentary shell, DEM 171, is found to be expanding at approximately 37 km s⁻¹. A supernova and stellar wind origin are both explored as possible causes for the expanding shell. A stellar wind origin would imply a mass-loss rate of the order of 10⁻⁵ M_⊙ yr⁻¹, indicating that it could be caused by a Wolf–Rayet star. A number of blue stars are found to lie within the shell and one is identified as a Wolf–Rayet candidate.     

Population III stars: hidden or disappeared?

A Population III/Population II transition from massive to normal stars is predicted to occur when the metallicity of the star-forming gas crosses the critical range   Z _cr= 10^−5±1 Z_⊙  . To investigate the cosmic implications of such a process, we use numerical simulations which follow the evolution, metal enrichment and energy deposition of both Population II and Population III stars. We find that: (i) due to inefficient heavy element transport by outflows and slow 'genetic' transmission during hierarchical growth, large fluctuations around the average metallicity arise; as a result, Population III star formation continues down to   z = 2.5  , but at a low peak rate of  10⁻⁵ M_⊙ yr⁻¹ Mpc⁻³  occurring at   z ≈ 6  (about 10⁻⁴ of the Population II one); and (ii) Population III star formation proceeds in an 'inside–out' mode in which formation sites are progressively confined to the periphery of collapsed structures, where the low gas density and correspondingly long free-fall time-scales result in a very inefficient astration. These conclusions strongly encourage deep searches for pristine star formation sites at moderate  (2 < z < 5)  redshifts where metal-free stars are likely to be hidden.     

Magnetically collimated jets with high mass flux

We present HST /WFPC2 observations of UGC 4483, an irregular galaxy in the M81/NGC 2403 complex. Stellar photometry was carried out with HSTphot, and is complete to V ≃26.0 and I ≃24.7. We measure the red giant branch tip at I =23.56±0.10, and calculate a distance modulus of μ ₀=27.53±0.12 (corresponding to a distance of 3.2±0.2 Mpc), placing UGC 4483 within the NGC 2403 subgroup. We were able to measure properties of a previously known young star cluster in UGC 4483, finding integrated magnitudes of V =18.66±0.21 and I =18.54±0.10 for the stellar contribution (integrated light minus H α and [O  iii ] contribution), corresponding to an age of ∼10–15 Myr and an initial mass of ∼10⁴ M_⊙. This is consistent with the properties of the cluster's brightest stars, which were resolved in the data for the first time. Finally, a numerical analysis of the galaxy's stellar content yields a roughly constant star formation rate of 1.3×10⁻³ M_⊙ yr⁻¹ and mean metallicity of [Fe/H]=−1.3 dex from 15 Gyr ago to the present.     

The micro-glitch in PSR B1821−24: a case for a strange pulsar?

The single glitch observed in PSR B1821−24, a millisecond pulsar in M28, is unusual on two counts. First, the magnitude of this glitch is at least an order of magnitude smaller  (Δν/ν∼ 10⁻¹¹)  than the smallest glitch observed to date. Secondly, all other glitching pulsars have strong magnetic fields with   B ≳ 10¹¹ G  and are young, whereas PSR B1821−24 is an old recycled pulsar with a field strength of  2.25 × 10⁹ G  . We have earlier suggested that some of the recycled pulsars could actually be strange quark stars. In this work, we argue that the crustal properties of such a strange pulsar are just right to give rise to a glitch of this magnitude, explaining the scarcity of larger glitches in millisecond pulsars.