Hot stars in old stellar populations: a continuing need for intermediate ages

We present numerical investigations into the formation of massive stars from turbulent cores of density structure  ρ∝ r ^−1.5  . The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the formation of small clusters of protostars. We generate two different initial turbulent velocity fields corresponding to power-law spectra   P ∝ k ⁻⁴  and   P ∝ k ^−3.5  , and we apply two different initial core radii. Calculations are included for both completely isothermal collapse, and a non-isothermal equation of state above a critical density  (10⁻¹⁴ g cm⁻³)  . Our calculations reveal the preference of fragmentation over monolithic star formation in turbulent cores. Fragmentation was prevalent in all the isothermal cases. Although disc fragmentation was largely suppressed in the non-isothermal runs due to the small dynamic range between the initial density and the critical density, our results show that some fragmentation still persisted. This is inconsistent with previous suggestions that turbulent cores result in the formation of a single massive star. We conclude that turbulence cannot be measured as an isotropic pressure term.     

The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to 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 except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively.
We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system.
Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars.     

Episodic dust formation by HD 192641 (WR 137) – II

We present new infrared photometry of the WC7-type Wolf–Rayet star HD 192641 (WR 137) from 1985 to 1999. These data track the cooling of the dust cloud formed in the 1982–84 dust-formation episode from 1985 to 1991, the increase of the infrared flux from 1994.5 to a new dust-formation maximum in 1997 and its subsequent fading. From these and earlier data we derive a period of 4765±50 d (13.05±0.15 yr) for the dust-formation episodes. Between dust-emission episodes, the infrared spectral energy distribution has the form of a power law, λF _λ ∝ λ ^−1.86. The rising branch of the infrared light curve (1994–97) differs in form from that of the episodic dust-maker WR 125. Time-dependent modelling shows that this difference can be attributed to a different time dependence of dust formation in WR 137, which occurred approximately ∝ t ² until maximum, whereas that of WR 125 could be described by a step function, akin to a threshold effect. For an adopted distance of 1.6 kpc, the rate of dust formation was found to be 5.0×10⁻⁸ M_⊙ yr⁻¹ at maximum, accounting for a fraction f _C≈1.5×10⁻³ of the carbon flowing in the stellar wind. The fading branches of the light curves show evidence for secondary 'mini-eruptions' in 1987, 1988 and 1990, behaviour very different from that of the prototypical episodic dust-maker HD 193793 (WR 140), and suggesting the presence in the WR 137 stellar wind of large-scale structures that are crossed by the wind–wind collision region.     

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.     

Star-like activity from a very young 'isolated planet'

The discovery of isolated bodies of planetary mass has challenged the paradigm that planets form only as companions to stars. To determine whether 'isolated planets', brown dwarfs and stars can have a common origin, we have made deep submillimetre observations of part of the ρ Oph B star formation region. Spectroscopy of the 9-Jupiter-mass core Oph B-11 has revealed carbon monoxide line wings such as those of a protostar. Moreover, the estimated mass of outflowing gas lies on the force versus core-mass relation for protostars and protobrown dwarfs. This is evidence for a common process that can form any object between planetary and stellar masses in a molecular cloud. In a submillimetre continuum map, six compact cores in ρ Oph B were found to have masses presently below the deuterium-burning limit, extending the core mass function down to  0.01 M_⊙  with the approximate form  d N /d M ∝ M ^−3/2  . If these lowest-mass cores are not transient and can collapse under gravity, then isolated planets should be very common in ρ Oph in the future, as is the case in the Orion star formation region. In fact, the isolated planetary objects that may form from these cores would outnumber the massive planets that have been found as companions to stars.     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

Boundary layer on the surface of a neutron star

In an attempt to model the accretion on to a neutron star in low-mass X-ray binaries, we present 2D hydrodynamical models of the gas flow in close vicinity of the stellar surface. First, we consider a gas pressure-dominated case, assuming that the star is non-rotating. For the stellar mass we take   M _star= 1.4 × 10⁻² M_⊙  and for the gas temperature   T = 5 × 10⁶ K  . Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of T ≃ 10⁸ K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity.     

The violent past of Cygnus X-2

Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary (IMXB). Using Mazzitelli's stellar code we compute detailed evolutionary sequences for the system and find that its prehistory is sensitive to stellar input parameters, in particular the amount of core overshooting during the main-sequence phase. With standard assumptions for convective overshooting a case B mass transfer starting with a 3.5-M_⊙ donor star is the most likely evolutionary solution for Cygnus X-2. This makes the currently observed state rather short-lived, of order 3 Myr, and requires a formation rate > 10⁻⁷–10⁻⁶ yr⁻¹ of such systems in the Galaxy. Our calculations show that neutron star IMXBs with initially more massive donors (≳4 M_⊙) encounter a delayed dynamical instability; they are unlikely to survive this rapid mass transfer phase. We determine limits for the age and initial parameters of Cygnus X-2 and calculate possible dynamical orbits of the system in a realistic Galactic potential, given its observed radial velocity. We find trajectories which are consistent with a progenitor binary on a circular orbit in the Galactic plane inside the solar circle that received a kick velocity ≤200 km s⁻¹ at the birth of the neutron star. The simulations suggest that about 7 per cent of IMXBs receiving an arbitrary kick velocity from a standard kick velocity spectrum would end up in an orbit similar to Cygnus X-2, while about 10 per cent of them reach yet larger Galactocentric distances.     

Self-similar solutions for the dynamical condensation of a radiative gas layer

A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time  ∝ρ² T ^α  , where  ρ,  T   and α are the density, temperature and a free parameter, respectively. Given α, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows:  ρ( x = 0, t ) ∝ ( t _c− t )^{−η/(2−α)}  and   P ( x = 0, t ) ∝ ( t _c− t )^{(1−η)/(1−α)}  , where t _c is the epoch at which the central density becomes infinite. For  η∼ 0  the solution describes the isochoric mode, whereas for  η∼ 1  the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for  0 < η < 1  . No self-similar solution is found for  α > 1  . We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (H  i clouds and molecular clouds) by thermal instability.     

Optical and submillimetre observations of Bok globules – tracing the magnetic field from low to high density

Although the stellar initial mass function (IMF) has only been directly determined in star clusters, it has been manifoldly applied on galaxy-wide scales. But taking the clustered nature of star formation into account the galaxy-wide IMF is constructed by adding all IMFs of all young star clusters leading to an integrated galactic initial mass function (IGIMF). The IGIMF is top-light compared to the canonical IMF in star clusters and steepens with decreasing total star formation rate (SFR). This discrepancy is marginal for large disc galaxies but becomes significant for Small Magellanic Cloud type galaxies and less massive ones. We here construct IGIMF-based relations between the total far- and near-ultraviolet luminosities of galaxies and the underlying SFR. We make the prediction that the Hα luminosity of star-forming dwarf galaxies decreases faster with decreasing SFR than the ultraviolet (UV) luminosity. This turn-down of the Hα/UV-flux ratio should be evident below total SFRs of  10⁻² M_⊙ yr⁻¹  .     

A top-heavy stellar initial mass function in starbursts as an explanation for the high mass-to-light ratios of ultra-compact dwarf galaxies

It has been recently shown that the dynamical V -band mass-to-light ratios of compact stellar systems with masses from 10⁶ to  10⁸ M_⊙  are not consistent with the predictions from simple stellar population models. Top-heavy stellar initial mass functions (IMFs) in these so-called ultra-compact dwarf galaxies (UCDs) offer an attractive explanation for this finding, the stellar remnants and retained stellar envelopes providing the unseen mass. We therefore construct a model which quantifies by how much the IMFs of UCDs would have to deviate in the intermediate- and high-mass range from the canonical IMF in order to account for the enhanced   M / L_V   ratio of the UCDs. The deduced high-mass IMF in the UCDs depends on the age of the UCDs and the number of faint products of stellar evolution retained by them. Assuming that the IMF in the UCDs is a three-part power law equal to the canonical IMF in the low-mass range and taking 20 per cent as a plausible choice for the fraction of the remnants of high-mass stars retained by UCDs, the model suggests the exponent of the high-mass IMF to be ≈1.6 if the UCDs are  13 Gyr  old (i.e. almost as old as the Universe) or ≈1.0 if the UCDs are  7 Gyr  old, in contrast to 2.3 for the Salpeter–Massey IMF. If the IMF was as top heavy as suggested here, the stability of the UCDs might have been threatened by heavy mass loss induced by the radiation and evolution of massive stars. The central densities of UCDs must have been in the range  10⁶ to 10⁷ M_⊙ pc⁻³  when they formed with star formation rates of  10 to 100 M_⊙ yr⁻¹  .     

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M_⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R ⁻² distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.     

Sakurai's Object: characterizing the near-infrared CO ejecta between 2003 and 2007

We present observations of Sakurai's Object obtained at 1–5 μm between 2003 and 2007. By fitting a radiative transfer model to an echelle spectrum of CO fundamental absorption features around  4.7 μm  , we determine the excitation conditions in the line-forming region. We find  ¹²C/¹³C = 3.5^+2.0_−1.5  , consistent with CO originating in ejecta processed by the very late thermal pulse, rather than in the pre-existing planetary nebula. We demonstrate the existence of  2.2 × 10⁻⁶≤ M _CO≤ 2.7 × 10⁻⁶ M_⊙  of CO ejecta outside the dust, forming a high-velocity wind of  500 ± 80 km s⁻¹  . We find evidence for significant weakening of the CO band and cooling of the dust around the central star between 2003 and 2005. The gas and dust temperatures are implausibly high for stellar radiation to be the sole contributor.     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

Evolution of the phase-space density of dark matter haloes and mixing effects in merger events

Cosmological N -body simulations were performed to study the evolution of the phase-space density   Q =ρ/σ³  of dark matter haloes. No significant differences in the scale relations   Q ∝σ^−2.1  or   Q ∝ M ^−0.82  are seen for the 'cold' or 'warm' dark matter models. The follow-up of individual haloes from   z = 10  up to the present time indicate the existence of two main evolutionary phases: an early and fast one  (10 > z > 6.5)  , in which Q decreases on the average by a factor of 40 as a consequence of the randomization of bulk motions, and a late and long one  (6.5 > z ≥ 0)  , in which Q decreases by a factor of 20 because of mixing induced by merger events. The study of these haloes has also evidenced that rapid and positive variations of the velocity dispersion, induced by merger episodes, are related to a fast decrease of the phase-space density Q .     

Cygnus X-3 with ISO: investigating the wind

We have observed the energetic binary Cygnus X-3 in both quiescent and flaring states between 4 and 16 μm using the ISO satellite. We find that the quiescent source shows the thermal free–free spectrum typical of a hot, fast stellar wind, such as from a massive helium star. The quiescent mass-loss rate arising from a spherically symmetric, non-accelerating wind is found to be in the range (0.4–2.9)×10⁻⁴ M_⊙ yr⁻¹, consistent with other infrared and radio observations, but considerably larger than the 10⁻⁵ M_⊙ yr⁻¹ deduced from both the orbital change and the X-ray column density. There is rapid, large-amplitude flaring at 4.5 and 11.5 μm at the same time as enhanced radio and X-ray activity, with the infrared spectrum apparently becoming flatter in the flaring state. We believe that non-thermal processes are operating, perhaps along with enhanced thermal emission.     

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).     

Peering through the stellar wind of IGR J19140+0951 with simultaneous INTEGRAL/RXTE observations

We have used the RXTE and INTEGRAL satellites simultaneously to observe the high-mass X-ray binary (HMXB) IGR J19140+0951. The spectra obtained in the 3–80 keV range have allowed us to perform a precise spectral analysis of the system along its binary orbit. The spectral evolution confirms the supergiant nature of the companion star and the neutron star nature of the compact object. Using a simple stellar wind model to describe the evolution of the photoelectric absorption, we were able to restrict the orbital inclination angle in the range 38°–75°. This analysis leads to a wind mass-loss rate from the companion star of  ∼5 × 10⁻⁸ M_⊙ yr⁻¹  , consistent with an OB I spectral type. We have detected a soft excess in at least four observations, for the first time for this source. Such soft excesses have been reported in several HMXBs in the past. We discuss the possible origin of this excess, and suggest, based on its spectral properties and occurrences around the superior conjunction, that it may be explained as the reprocessing of the X-ray emission originating from the neutron star by the surrounding ionized gas.