On the number of young stellar discs in the Galactic Centre

Observations of the Galactic Centre show evidence of disc-like structures of very young stars orbiting the central supermassive black hole within a distance of a few 0.1 pc. While it is widely accepted that about half of the stars form a relatively flat disc rotating clockwise on the sky, there is a substantial ongoing debate on whether there is a second, counter-clockwise disc of stars.
By means of N -body simulations using our bhint code, we show that two highly inclined stellar discs with the observed properties cannot be recognized as two flat circular discs after 5 Myr of mutual interaction. Instead, our calculations predict a significant warping of the two discs, which we show to be apparent among the structures observed in the Galactic Centre. While the high eccentricities of the observed counter-clockwise orbits suggest an eccentric origin of this system, we show the eccentricity distribution in the inner part of the more massive clockwise disc to be perfectly consistent with an initially circular disc in which stellar eccentricities increase due to both non-resonant and resonant relaxation.
We conclude that the relevant question to ask is therefore not whether there are two discs of young stars, but whether there were two such discs to begin with.     

X-rays from cusps of compact remnants near galactic centres

Compact remnants – stellar mass black holes and neutron stars formed in the inner few parsec of galactic centres are predicted to sink into the central parsec due to dynamical friction on low-mass stars, forming a high concentration cusp. Same physical region may also contain very high-density molecular clouds and accretion discs that are needed to fuel supermassive black hole (SMBH) activity. Here we estimate gas capture rates on to the cusp of stellar remnants, and the resulting X-ray luminosity, as a function of the accretion disc mass. At low disc masses, most compact objects are too dim to be observable, whereas in the high disc case most of them are accreting at their Eddington rates. We find that for low accretion disc masses, compact remnant cusps may be more luminous than the central SMBHs. This 'diffuse' emission may be of importance for local moderately bright active galactic nuclei (AGNs), especially low-luminosity AGNs. We also briefly discuss how this expected emission can be used to put constraints on the black hole cusp near our Galactic Centre.     

Regular black hole motion and stellar orbital resonances

The motion of a black hole about the centre of gravity of its host galaxy induces a strong response from the surrounding stellar population. We treat the case of a harmonic potential analytically and show that half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f ( E ). We show that this effect is operative out to a radius of approximately three to four times the hole's influence radius, R _bh. We use numerical integration to explore more fully the response of a stellar distribution to black hole motion. We consider orbits in a logarithmic potential and compare the response of stars on circular orbits, to the situation of a 'warm' and 'hot' (isotropic) stellar velocity field. While features seen in density maps are now wiped out, the kinematic signature of black hole motion still imprints the stellar line-of-sight mean velocity to a magnitude ≃13 per cent the local rms velocity dispersion σ. A study in three dimensions suggests a reduced effect for polar orbits.     

The effectiveness of the Kozai mechanism in the Galactic Centre

I examine the effectiveness of Kozai oscillations in the centres of galaxies and in particular the Galactic Centre (GC) using standard techniques from celestial mechanics. In particular, I study the effects of a stellar bulge potential and general relativity on Kozai oscillations, which are induced by stellar discs. Löckmann et al. recently suggested that Kozai oscillations induced by the two young massive stellar discs in the GC drive the orbits of the young stars to large eccentricity  ( e ≈ 1)  . If some of these young eccentric stars are in binaries, they would be disrupted near pericentre, leaving one star in a tight orbit around the central supermassive black hole and producing the S-star population. I find that the spherical stellar bulge suppresses Kozai oscillations, when its enclosed mass inside a test body is of the order of the mass in the stellar disc(s). Since the stellar bulge in the GC is much larger than the stellar discs, Kozai oscillations due to the stellar discs are likely suppressed. Whether Kozai oscillations are induced from other non-spherical components to the potential (e.g. a flattened stellar bulge) is yet to be determined.     

Gravitational loss-cone instability in stellar systems with retrograde orbit precession

We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics   l ≥ 3  . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems.     

Weighing the cusp at the Galactic Centre

As stars close to the galactic centre have short orbital periods it has been possible to trace large fractions of their orbits in the recent years. Previously the data of the orbit of the star S2 have been fitted with Keplerian orbits corresponding to a massive black hole (MBH) with a mass of M_BH = 3–4 × 10⁶M_⊙ implying an insignificant cusp mass. However, it has also been shown that the central black hole resides in a ∼1″ diameter stellar cluster of a priori unknown mass. In a spherical potential which is neither Keplerian nor harmonic, orbits will precess resulting in inclined rosetta shaped trajectories on the sky. In this case, the assumption of non‐Keplerian orbits is a more physical approach. It is also the only approach through which cusp mass information can be obtained via stellar dynamics of the cusp members. This paper presents the first exemplary modelling efforts in this direction. Using positional and radial data of star S2, we find that there could exist an unobserved extended mass component of several 10⁵M_⊙ forming a so‐called ‘cusp’ centered on the black hole position. Considering only the fraction of the cusp mass Mequation/tex2gif-inf-4.gif within the apo‐center of the S2 orbit we find as an upper limit that Mequation/tex2gif-inf-6.gif/(M_BH + Mequation/tex2gif-inf-9.gif) ≤ 0.05. A large extended cusp mass, if present, is unlikely to be composed of sub‐solar mass constituents, but could be explained rather well by a cluster of high M/L stellar remnants, which we find to form a stable configuration. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

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.     

Effect of angular momentum distribution on gravitational loss-cone instability in stellar clusters around a massive black hole

We study the small perturbations in spherical and thin disc stellar clusters surrounding a massive black hole. Because of the black hole, stars with sufficiently low angular momentum escape from the system through the loss cone. We show that the stability properties of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time, instability in disc clusters is possible for both types of distribution.     

Numerical simulations of protostellar encounters — I. Star–disc encounters

It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key role in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars.   We have carried out a series of simulations of star–disc interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism.   A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars and substellar objects. When the disc spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20 per cent of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically triggered star formation, then new companions are formed in approximately 50 per cent of encounters.     

Gas-driven evolution of stellar orbits in barred galaxies

We carry out a detailed orbit analysis of gravitational potentials selected at different times from an evolving self-consistent model galaxy consisting of a two-component disc (stars+gas) and a live halo. The results are compared with a pure stellar model, subject to nearly identical initial conditions, which are chosen so as to make the models develop a large-scale stellar bar. The bars are also subject to hose-pipe (buckling) instability which modifies the vertical structure of the disc. The diverging morphological evolution of both models is explained in terms of gas radial inflow, the resulting change in the gravitational potential at smaller radii, and the subsequent modification of the main families of orbits, both in and out of the disc plane.   We find that dynamical instabilities become milder in the presence of the gas component, and that the stability of planar and 3D stellar orbits is strongly affected by the related changes in the potential — both are destabilized, with the gas accumulation at the centre. This is reflected in the overall lower amplitude of the bar mode and in the substantial weakening of the bar, which appears to be a gradual process. The vertical buckling of the bar is much less pronounced and the characteristic peanut shape of the galactic bulge almost disappears when there is a substantial gas inflow towards the centre. Milder instability results in a smaller bulge, the basic parameters of which are in agreement with observations. We also find that the overall evolution in the model with a gas component is accelerated because of the larger central mass concentration and the resulting decrease in the characteristic dynamical time.     

The origin of the light distribution in spiral galaxies

We analyse a high-resolution, fully cosmological, hydrodynamical disc galaxy simulation, to study the source of the double-exponential light profiles seen in many stellar discs, and the effects of stellar radial migration upon the spatiotemporal evolution of both the disc age and metallicity distributions. We find a 'break' in the pure exponential stellar surface brightness profile, and trace its origin to a sharp decrease in the star formation per unit surface area, itself produced by a decrease in the gas volume density due to a warping of the gas disc. Star formation in the disc continues well beyond the break. We find that the break is more pronounced in bluer wavebands. By contrast, we find little or no break in the mass density profile. This is, in part, due to the net radial migration of stars towards the external parts of the disc. Beyond the break radius, we find that ∼60 per cent of the resident stars migrated from the inner disc, while ∼25 per cent formed in situ . Our simulated galaxy also has a minimum in the age profile at the break radius but, in disagreement with some previous studies, migration is not the main mechanism producing this shape. In our simulation, the disc metallicity gradient flattens with time, consistent with an 'inside-out' formation scenario. We do not find any difference in the intensity or the position of the break with inclination, suggesting that perhaps the differences found in empirical studies are driven by dust extinction.     

Red giant stellar collisions in the Galactic Centre

We show that collisions with stellar-mass black holes can partially explain the absence of bright giant stars in the Galactic Centre, first noted by Genzel et al. We show that the missing objects are low-mass giants and asymptotic giant branch stars in the range  1–3 M_⊙  . Using detailed stellar evolution calculations, we find that to prevent these objects from evolving to become visible in the depleted K bands, we require that they suffer collisions on the red giant branch, and we calculate the fractional envelope mass losses required. Using a combination of smoothed particle hydrodynamic calculations, restricted three-body analysis and Monte Carlo simulations, we compute the expected collision rates between giants and black holes, and between giants and main-sequence stars in the Galactic Centre. We show that collisions can plausibly explain the missing giants in the  10.5 < K < 12  band. However, depleting the brighter  ( K < 10.5)  objects out to the required radius would require a large population of black hole impactors which would in turn deplete the  10.5 < K < 12  giants in a region much larger than is observed. We conclude that collisions with stellar-mass black holes cannot account for the depletion of the very brightest giants, and we use our results to place limits on the population of stellar-mass black holes in the Galactic Centre.     

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.     

Early star formation and the evolution of the stellar initial mass function in galaxies

It has frequently been suggested in the literature that the stellar IMF in galaxies was top-heavy at early times. This would be plausible physically if the IMF depended on a mass-scale such as the Jeans mass that was higher at earlier times because of the generally higher temperatures that were present then. In this paper it is suggested, on the basis of current evidence and theory, that the IMF has a universal Salpeter-like form at the upper end, but flattens below a characteristic stellar mass that may vary with time. Much of the evidence that has been attributed to a top-heavy early IMF, including the ubiquitous G-dwarf problem, the high abundance of heavy elements in clusters of galaxies, and the high rate of formation of massive stars in high-redshift galaxies, can be accounted for with such an IMF if the characteristic stellar mass was several times higher during the early stages of galaxy evolution. However, significant variations in the mass-to-light ratios of galaxies and large amounts of dark matter in stellar remnants are not as easily explained in this way, because they require more extreme and less plausible assumptions about the form and variability of the IMF. Metal-free 'population III' stars are predicted to have an IMF that consists exclusively of massive stars, and they could help to account for some of the evidence that has been attributed to a top-heavy early IMF, as well as contributing importantly to the energetics and chemical enrichment of the early Universe.     

Nuclear stellar discs in early-type galaxies — II. Photometric properties

Hubble Space Telescope images of two early-type galaxies harbouring both nuclear and outer stellar discs are studied in detail. By means of a photometric decomposition, the images of NGC 4342 and 4570 are analysed and the photometric properties of the nuclear discs investigated. We find a continuity of properties in the parameter space defined by the central surface brightness μ₀ and the scalelength R _d of discs in spirals, S0s and embedded discs in ellipticals, in the sense that the nuclear discs extend the observed disc properties even further towards smaller scalelengths and brighter central surface brightnesses. When including the nuclear discs, disc properties span more than four orders of magnitude in both scalelength and central surface brightness. The nuclear discs studied here are the smallest and brightest stellar discs known, and as such, they are as extreme in their photometric properties as Malin I, when compared with typical galactic discs that obey Freeman's law. We discuss a possible formation scenario in which the double-disc structure observed in these galaxies has been shaped by now dissolved bars. Based on the fact that the black holes known to exist in some of these galaxies have masses comparable to those of the nuclear discs, we explore a possible link between the black holes and the nuclear discs.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

Variable accretion and emission from the stellar winds in the Galactic Centre

We present numerical simulations of stellar wind dynamics in the central parsec of the Galactic Centre, studying in particular the accretion of gas on to Sgr A*, the supermassive black hole. Unlike our previous work, here we use state-of-the-art observational data on orbits and wind properties of individual wind-producing stars. Since wind velocities were revised upwards and non-zero eccentricities were considered, our new simulations show fewer clumps of cold gas and no conspicuous disc-like structure. The accretion rate is dominated by a few close 'slow-wind stars' ( v _w≤ 750 km s⁻¹), and is consistent with the Bondi estimate, but variable on time-scales of tens to hundreds of years. This variability is due to the stochastic infall of cold clumps of gas, as in earlier simulations, and to the eccentric orbits of stars. The present models fail to explain the high luminosity of Sgr A* a few hundred years ago implied by Integral observations, but we argue that the accretion of a cold clump with a small impact parameter could have caused it. Finally, we show the possibility of constraining the total mass-loss rate of the 'slow-wind stars' using near infrared observations of gas in the central few arcseconds.     

An analytic model for disc disruption by strong stellar magnetic fields

An analytic model is presented for the inner structure of an accretion disc in the presence of a strong stellar magnetic field. The model is valid inside the radius at which the electron scattering opacity starts to exceed the Kramers opacity. It illustrates how the increasing stellar poloidal field leads to an elevated disc temperature, ultimately causing a breakdown in the vertical equilibrium owing to rapidly increasing radiation pressure which cannot be balanced by the vertical stellar gravity. Viscous instability also occurs. The solution gives an accurate representation of numerical results, and enables useful expressions to be derived for the radius at which the disc is marginally thin and the radius at which viscous instability occurs. The disruption mechanism appears to have general validity for accretion discs around strongly magnetic stars.     

On the effects of the stellar magnetic field on the structure of T Tauri accretion discs

The structure of accretion discs around magnetic T Tauri stars is calculated numerically using a particle hydrodynamical code, in which magnetic interaction is included in the framework of King's diamagnetic blob accretion model. Setting up the calculation so as to simulate the density structure of a quasi-steady disc in the equatorial plane of a T Tauri star, we find that the central star's magnetic field typically produces a central hole in the disc and spreads out the surface density distribution. We argue that this result suggets a promising mechanism for explaining the unusual flatness (IR excess) of T Tauri accretion disc spectra.