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.     

Spectroscopic solution of the star QX Cas

High-resolution spectroscopic observations around the Hα line of the binary star QX Cas covering the whole orbital period are presented. Our radial velocity solution, the first ever determined, requires an eccentric orbit with the following orbital parameters: eccentricity,   e = 0.22 ± 0.01  ; longitude of periastron,  ω= 45°± 5°  ; semi-amplitudes of the radial velocity curves of the primary and secondary stars,   K ₁ sin  i = 125.8 ± 0.9 km s⁻¹  and   K ₂ sin  i = 144.8 ± 1.1 km s⁻¹  ; gamma velocity,   V ₀= 65.1 ± 0.5 km s⁻¹  ; and mass ratio,   q = 0.869 ± 0.013  . The corresponding lower limits of the masses of the components and their separation are         , and   a sin  i = 31.34 ± 0.48 R_⊙  .     

The discovery of a low-mass, pre-main-sequence stellar association around γ Velorum

We report the serendipitous discovery of a population of low-mass, pre-main-sequence (PMS) stars in the direction of the Wolf–Rayet/O-star binary system γ ²  Vel and the Vela OB2 association. We argue that γ ²  Vel and the low-mass stars are truly associated and approximately coeval, and that both are at distances between 360 and 490 pc, disagreeing at the 2 σ level with the recent Hipparcos parallax of γ ²  Vel, but consistent with older distance estimates. Our results clearly have implications for the physical parameters of the γ ²  Vel system, but also offer an exciting opportunity to investigate the influence of high-mass stars on the mass function and circumstellar disc lifetimes of their lower mass PMS siblings.     

Constraints on Jupiters from observations of Galactic bulge microlensing events during 2000

We present observations of eight Galactic bulge microlensing events taken with the 1.0-m Jacobus Kapteyn Telescope (JKT) on La Palma during 2000 June and July. The JKT observing schedule was optimized using a prioritizing algorithm to automatically update the target list. For most of these events we have sampled the light curves at times where no information was available from the OGLE alert team. We assume a point-source point-lens (PSPL) model and perform a maximum likelihood fit to both our data and the OGLE data to constrain the event parameters of the fit. We then refit the data assuming a binary lens and proceed to calculate the probability of detecting planets with mass ratio   q = 10⁻³  . We have seen no clear signatures of planetary deviations on any of the eight events and we quantify constraints on the presence of planetary companions to the lensing stars. For two well-observed events, 2000BUL31 and 2000BUL33, our detection probabilities peak at ∼30 and ∼20 per cent respectively for   q = 10⁻³  and   a ∼ R _E  for a  Δχ²  threshold value of 60.     

The Hubble flow around the Local Group

We use updated data on distances and velocities of galaxies in the proximity of the Local Group (LG) in order to establish properties of the local Hubble flow. For 30 neighbouring galaxies with distances  0.7 < D _LG < 3.0  Mpc, the local flow is characterized by the Hubble parameter   H _loc= (78 ± 2) km s⁻¹ Mpc⁻¹  , the mean-square peculiar velocity  σ_v= 25 km s⁻¹  , corrected for errors of radial velocity measurements  (∼4 km s⁻¹)  and distance measurements  (∼10 km s⁻¹)  , as well as the radius of the zero-velocity surface   R ₀= (0.96 ± 0.03)  Mpc. The minimum value for σ_v is achieved when the barycentre of the LG is located at the distance   D_c = (0.55 ± 0.05) D _M31  towards Andromeda galaxy (M31) corresponding to the Milky Way (MW)-to-M31 mass ratio   M _MW/ M _M31≃ 4/5  . In the reference frame of the 30 galaxies at 0.7–3.0 Mpc, the LG barycentre has a small peculiar velocity  ∼(24 ± 4) km s⁻¹  towards the Sculptor constellation. The derived value of R ₀ corresponds to the total mass   M _T(LG) = (1.9 ± 0.2) 10¹² M_⊙  with  Ω_m= 0.24  and a topologically flat universe, a value in good agreement with the sum of virial mass estimates for the MW and M31.     

Do binaries in clusters form in the same way as in the field?

We examine the dynamical destruction of binary systems in star clusters of different densities. We find that at high densities  (10⁴– 10⁵ M_⊙ pc⁻³)  almost all binaries with separations  >10³  au are destroyed after a few crossing times. At low densities [     ], many binaries with separations  >10³  au are destroyed, and no binaries with separations  >10⁴  au survive after a few crossing times. Therefore, the binary separations in clusters can be used as a tracer of the dynamical age and past density of a cluster.
We argue that the central region of the Orion nebula cluster was ∼100 times denser in the past with a half-mass radius of only 0.1–0.2 pc as (i) it is expanding, (ii) it has very few binaries with separations  >10³  au and (iii) it is well mixed and therefore dynamically old.
We also examine the origin of the field binary population. Binaries with separations  <10²  au are not significantly modified in any cluster, therefore at these separations the field reflects the sum of all star formation. Binaries with separations in the range  10²– 10⁴  au are progressively more and more heavily affected by dynamical disruption in increasingly dense clusters. If most star formation is clustered, these binaries must be overproduced relative to the field. Finally, no binary with a separation  >10⁴  au can survive in any cluster and so must be produced by isolated star formation, but only if all isolated star formation produces extremely wide binaries.     

Flare variability in the close binary FL Vir

The results of U -filter flare monitoring of the binary flare star FL Vir = Wolf 424 is presented. 57 flares with energies between  2 × 10²⁸  and  2 × 10³¹ erg  were recorded in 20 h of observation. The properties of flare occurrence and flare time-scales are analysed, and the flare activity level in 1980 April is determined to be   L _f( U ) = 8.0 × 10²⁶ erg s⁻¹  . This is larger than previously published results and may indicate a variation in the flare activity level on a time-scale of years. An analysis of existing data indicates that the flare activity level correlates with the relative orbital positions of the stars.     

Multiwavelength study of the transient X-ray binary IGR J01583+6713

We have investigated multiband optical photometric variability and stability of the Hα line profile of the transient X-ray binary IGR J01583+6713. We set an upper limit of 0.05 mag on photometric variations in the V band over a time-scale of three months. The Hα line is found to consist of non-Gaussian profile and quite stable for a duration of two months. We have identified the spectral type of the companion star to be B2 IVe while the distance to the source is estimated to be ∼4.0 kpc. Along with the optical observations, we have also carried out analysis of X-ray data from three short observations of the source, two with the Swift –XRT and one with the RXTE –PCA. We have detected a variation in the absorption column density, from a value of  22.0 × 10²² cm⁻²  immediately after the outburst down to  2.6 × 10²² cm⁻²  four months afterwards. In the quiescent state, the X-ray absorption is consistent with the optical reddening measurement of   E ( B − V ) = 1.46  mag. From one of the Swift observations, during which the X-ray intensity was higher, we have a possible pulse detection with a period of 469.2 s. For a Be X-ray binary, this indicates an orbital period in the range of 216–561 d for this binary system.     

Supernova kicks and misaligned Be star binaries

Be stars are rapidly spinning B stars surrounded by an outflowing disc of gas in Keplerian rotation. Be star/X-ray binary systems contain a Be star and a neutron star. They are found to have non-zero eccentricities and there is evidence that some systems have a misalignment between the spin axis of the star and the spin axis of the binary orbit. The eccentricities in these systems are caused by a kick to the neutron star during the supernova that formed it. Such kicks would also give rise to misalignments. In this paper, we investigate the extent to which the same kick distribution can give rise to both the observed eccentricity distribution and the observed misalignments. We find that a Maxwellian distribution of velocity kicks with a low velocity dispersion,  σ_k≈ 15 km s⁻¹  , is consistent with the observed eccentricity distribution but is hard to reconcile with the observed misalignments, typically   i ≥ 25°  . Alternatively, a higher velocity kick distribution,  σ_k= 265 km s⁻¹  , is consistent with the observed misalignments but not with the observed eccentricities, unless post-supernova circularization of the binary orbits has taken place. We discuss briefly how this might be achieved.     

Excitation of oscillation modes by tides in close binaries: constraints on stellar and orbital parameters

The parameter space favourable for the resonant excitation of free oscillation modes by dynamic tides in close binary components is explored using qualitative considerations to estimate the order of magnitude of the tidal force and the frequency range covered by the tidally induced oscillations. The investigation is valid for slowly rotating stars with masses in the interval between 2 and  20 M_⊙  , and an evolutionary stage ranging from the beginning to the end of the main sequence. Oscillation modes with eigenfrequencies of the order of five times the inverse of the dynamical time-scale  τ_dyn  of the star, i.e. the lowest-order p -modes, the f -mode and the lowest-order g ⁺-modes, are found to be outside the favourable parameter space since their resonant excitation requires orbital eccentricities that are too high for the binary to stay detached when the components pass through the periastron of their relative orbit. Resonances between dynamic tides and g ⁺-modes with frequencies of the order of half of the inverse of the dynamical time-scale of the star on the other hand are found to be favourable for orbital periods up to  ∼200τ_dyn  , provided that the binary mass ratio q is larger than 1/3, and the orbital eccentricity e is larger than ∼0.25. This favourable range comes down to orbital periods of up to 5–12 d in the case of  2–20 M_⊙  zero-age main-sequence binary components, and orbital periods of up to 21–70 d in the case of terminal main-sequence binary components.     

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.     

Optical evolution of Nova Ophiuchi 2007 = V2615 Oph

The moderately fast Nova Oph 2007 reached maximum brightness on 2007 March 28 at   V = 8.52, B − V =+1.12, V − R _C=+0.76, V − I _C=+1.59  and   R _C− I _C=+0.83  , after fast initial rise and a pre-maximum halt lasting a week. Decline times were   t ^V ₂= 26.5, t ^B ₂= 30, t ^V ₃= 48.5  and   t ^B ₃= 56.5  d. The distance to the nova is   d = 3.7 ± 0.2 kpc  , the height above the Galactic plane is   z = 215 pc  , the reddening is   E ( B − V ) = 0.90  and the absolute magnitude at maximum is   M ^max _V =−7.2  and   M ^max _B =−7.0  . The spectrum four days before maximum resembled a F6 supergiant, in an agreement with broad-band colours. It later developed into that of a standard 'Fe  ii '-class nova. Nine days past maximum, the expansion velocity estimated from the width of Hα emission component was  ∼730 km s⁻¹  , and the displacement from it of the principal and diffuse-enhanced absorption systems was ∼650 and  1380 km s⁻¹  , respectively. Dust probably formed and disappeared during the period from 82 to 100 d past maximum, causing (at peak dust concentration) an extinction of  Δ B = 1.8  mag and an extra  Δ E ( B − V ) = 0.44  reddening.     

On a time-symmetric Hermite integrator for planetary N-body simulation

We describe a P(EC) ⁿ Hermite scheme for planetary N -body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N -body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N -body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC) ⁿ Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)² Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N  = 100,  m  = 10²⁵ g planetesimal system with the rms eccentricity 〈 e ²〉^1/2 ≲0.03.     

Inflow and outflow from the accretion disc of the microquasar SS 433: UKIRT spectroscopy

A succession of near-infrared (near-IR) spectroscopic observations, taken nightly throughout an entire cycle of SS 433's orbit, reveal (i) the persistent signature of SS 433's accretion disc, having a rotation speed of  ∼500 km s⁻¹  , (ii) the presence of circumbinary disc recently discovered at optical wavelengths by Blundell, Bowler & Schmidtobreick (2008) and (iii) a much faster outflow than has previously been measured for the disc wind, with a terminal velocity of  ∼1500 km s⁻¹  . The increased wind terminal velocity results in a mass-loss rate of  ∼10⁻⁴ M_⊙ yr⁻¹  . These, together with the newly (upwardly) determined masses for the components of the SS 433 system, result in an accurate diagnosis of the extent to which SS 433 has super-Eddington flows. Our observations imply that the size of the companion star is comparable with the semiminor axis of the orbit which is given by     , where e is the eccentricity. Our relatively spectral resolution at these near-IR wavelengths has enabled us to deconstruct the different components that comprise the Brackett-γ (Brγ) line in this binary system, and their physical origins. With this line being dominated throughout our series of observations by the disc wind, and the accretion disc itself being only a minority (∼15 per cent) contribution, we caution against use of the unresolved Brγ line intensity as an 'accretion signature' in X-ray binaries or microquasars in any quantitative way.     

The problem of the critical inclination revisited

The behaviour of the argument of the pericentre is investigated for the orbit of an artificial satellite which is moving under the potential when the inclination of the orbit is close to thecritical value tan^?1 2. The theory is developed to first order and it is applicable to all values of the eccentricity, with the exception of those in the neighbourhood of zero and unity. Four principal types of behaviour are noted and these are illustrated in appropriate phase-plane diagrams. It is shown that the two types which exhibit double libration in the argument of the pericentre are restricted to a relatively small domain in the (a, e)-plane of possible motions. Moreover, it is demonstrated that for double libration to occur it is necessary, but not sufficient, that \(e > \sqrt 6/13\) . The ranges of values of the inclination for which libration of the pericentre is a possibility are given for the more important cases. The general results are applied to the specific case of artificial Earth satellites whose orbits are inclined to the equator at angles close to the value of the critical inclination.     

Investigating the Andromeda stream – II. Orbital fits and properties of the progenitor

We construct test-particle orbits and simple N -body models that match the properties of the giant stellar stream observed to the south of M31, using the model of M31's potential derived in the companion paper by Geehan et al. We introduce a simple approximation to account for the difference in position between the stream and the orbit of the progenitor; this significantly affects the best-fitting orbits. The progenitor orbits we derive have orbital apocentre  ∼60 kpc  and pericentre  ∼3 kpc  , though these quantities vary somewhat with the current orbital phase of the progenitor which is as yet unknown. Our best combined fit to the stream and galaxy properties implies a mass within 125 kpc of M31 of  (7.4 ± 1.2) × 10¹¹ M_⊙  . Based on its length, width, luminosity, and velocity dispersion, we conclude that the stream originates from a progenitor satellite with mass   M _s∼ 10⁹ M_⊙  , and at most modest amounts of dark matter; the estimate of M _s is again correlated with the phase of the progenitor. M31 displays a large number of faint features in its inner halo which may be progenitors or continuations of the stream. While the orbital fits are not constrained enough for us to conclusively identify the progenitor, we can identify several plausible candidates, of which a feature in the planetary nebula distribution found by Merrett et al. is the most plausible, and rule out several others. We make predictions for the kinematic properties of the successful candidates. These may aid in observational identification of the progenitor object, which would greatly constrain the allowed models of the stream.     

RR Pic (1925): a Chandra X-ray view

We present the Chandra ACIS-S3 data of the old classical nova RR Pic (1925). The source has a count rate of 0.067 ± 0.002 count s⁻¹ in the 0.3–5.0 keV energy range. We detect the orbital period of the underlying binary system in the X-ray wavelengths. We also find that the neutral hydrogen column density differs for orbital minimum and orbital maximum spectra with values  0.25^+0.23_−0.18× 10²²  and  0.64^+0.13_−0.14× 10²² cm⁻²  at 3σ confidence level. The X-ray spectrum of RR Pic can be represented by a composite model of bremsstrahlung with a photoelectric absorption, two absorption lines centered around 1.1–1.4 keV and five Gaussian lines centered at emission lines around 0.3–1.1 keV corresponding to various transitions of S, N, O, C, Ne and Fe. The bremsstrahlung temperature derived from the fits ranges from 0.99 to 1.60 keV and the unabsorbed X-ray flux is found to be  2.5^+0.4_−1.2× 10⁻¹³ erg  cm⁻² s⁻¹  in the 0.3–5.0 keV range with a luminosity of 1.1 ± 0.2  10³¹ erg s⁻¹  at 600 pc. We also detect excess emission in the spectrum possibly originating from the reverse shock in the ejecta. A fit with a cooling flow plasma emission model shows enhanced abundances of He, C, N, O and Ne in the X-ray emitting region indicating existence of diffusive mixing.     

Peculiar nature of hard X-ray eclipse in SS433 from INTEGRAL observations

The analysis of hard X-ray INTEGRAL observations (2003–2008) of superaccreting Galactic microquasar SS433 at precessional phases of the source with the maximum disc opening angle is carried out. It is found that the shape and width of the primary X-ray eclipse are strongly variable, suggesting additional absorption in dense stellar wind and gas outflows from the optical A7I component and the wind–wind collision region. The independence of the observed hard X-ray spectrum on the accretion disc precessional phase suggests that hard X-ray emission (20–100 keV) is formed in an extended, hot, quasi-isothermal corona, probably heated by interaction of relativistic jet with inhomogeneous wind outflow from the precessing supercritical accretion disc. A joint modelling of X-ray eclipsing and precessional hard X-ray variability of SS433 revealed by INTEGRAL by a geometrical model suggests the binary mass ratio   q = m_x / m _v ≃  0.25–0.5. The absolute minimum of joint orbital and precessional  χ²  residuals is reached at   q ≃ 0.3  . The found binary mass ratio range allows us to explain the substantial precessional variability of the minimum brightness at the middle of the primary optical eclipse. For the mass function of the optical star   f _v = 0.268 M_⊙  as derived from Hillwig & Gies data, the obtained value of   q ≃ 0.3  yields the masses of the components   m_x ≃ 5.3 M_⊙, m _v ≃ 17.7 M_⊙  , confirming the black hole nature of the compact object in SS433.     

PSR J1012+5307: younger than it looks?

Lorimer et al. have recently reported that the spin-down age (∼7 × 10⁹ yr) of the low-mass binary pulsar PSR J1012+5307 is much higher than the cooling age (3 × 10⁸ yr) of its white dwarf companion. The proposed solutions for this discrepancy are outlined and discussed. In particular, the revised cooling age estimate proposed by Alberts et al. agrees with data from other low-mass binary pulsar systems if a transition to the 'classical' cooling regime occurs between ∼0.14 and ∼0.28 M_⊙. If this transition is excluded, PSR J1012+5307 seems to have finished its accretion phase far from the spin-up line.     

Optical spectroscopy and photometry of SAX J1808.4−3658 in outburst

We present phase resolved optical spectroscopy and photometry of V4580 Sagittarii, the optical counterpart to the accretion powered millisecond pulsar SAX J1808.4−3658, obtained during the 2008 September/October outburst. Doppler tomography of the N  iii λ4640.64 Bowen blend emission line reveals a focused spot of emission at a location consistent with the secondary star. The velocity of this emission occurs at  324 ± 15 km s⁻¹  ; applying a ' K -correction', we find the velocity of the secondary star projected on to the line of sight to be  370 ± 40 km s⁻¹  . Based on existing pulse timing measurements, this constrains the mass ratio of the system to be  0.044^+0.005_−0.004  , and the mass function for the pulsar to be  0.44^+0.16_−0.13 M_⊙  . Combining this mass function with various inclination estimates from other authors, we find no evidence to suggest that the neutron star in SAX J1808.4−3658 is more massive than the canonical value of  1.4 M_⊙  . Our optical light curves exhibit a possible superhump modulation, expected for a system with such a low mass ratio. The equivalent width of the Ca  ii H and K interstellar absorption lines suggest that the distance to the source is ∼2.5 kpc. This is consistent with previous distance estimates based on type-I X-ray bursts which assume cosmic abundances of hydrogen, but lower than more recent estimates which assume helium-rich bursts.