The formation of a bound star cluster: from the Orion nebula cluster to the Pleiades

Direct N -body calculations are presented of the formation of Galactic clusters using GasEx , which is a variant of the code Nbody6 . The calculations focus on the possible evolution of the Orion nebula cluster (ONC) by assuming that the embedded OB stars explosively drove out 2/3 of its mass in the form of gas about 0.4 Myr ago. A bound cluster forms readily and survives for 150 Myr despite additional mass loss from the large number of massive stars, and the Galactic tidal field. This is the very first time that cluster formation is obtained under such realistic conditions. The cluster contains about 1/3 of the initial 10⁴ stars, and resembles the Pleiades cluster to a remarkable degree, implying that an ONC-like cluster may have been a precursor of the Pleiades. This scenario predicts the present expansion velocity of the ONC, which will be measurable by upcoming astrometric space missions. These missions should also detect the original Pleiades members as an associated expanding young Galactic-field subpopulation. The results arrived at here suggest that Galactic clusters form as the nuclei of expanding OB associations.
The results have wide implications, also for the formation of globular clusters and the Galactic-field and halo stellar populations. In view of this, the distribution of binary orbital periods and the mass function within and outside the model ONC and Pleiades is quantified, finding consistency with observational constraints. Advanced mass segregation is evident in one of the ONC models. The calculations show that the primordial binary population of both clusters could have been much the same as is observed in the Taurus–Auriga star-forming region. The computations also demonstrate that the binary proportion of brown dwarfs is depleted significantly for all periods, whereas massive stars attain a high binary fraction.     

Primordial substructure in the Orion Nebula Cluster

We use numerical N -body simulations of the Orion Nebula Cluster (ONC) to investigate the possibility of substructure in its formation. There is no substructure apparent in the ONC today. However, unless there was a remarkable degree of homogeneity in the molecular cloud from which it formed, it seems unlikely that this would have been true of the cluster in its earliest phase. More plausibly, the early structure of the cluster would have consisted of groups or clumps of subclusters, following the structure of the cloud itself. We have explored the extent to which such subclusters could subsequently have merged, and find that the age of the cluster is a critical factor. The most inhomogeneous initial conditions, comprising a small number of subclusters with many members, are ruled out by an age of 2 Myr or less. There is a considerable amount of freedom in the other direction, however, which suggests that fragmentation in the original cloud is more likely to have been on the scale of small clumps, each producing fewer than 100 stars. These initial subclusters could have been very dense – perhaps two or three orders of magnitude more dense than the core of the ONC today.     

Using the minimum spanning tree to trace mass segregation

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected.
We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a 'mass segregation ratio (MSR)'  Λ_MSR= 8.0 ± 3.5  (where  Λ_MSR= 1  is no mass segregation) down to  16 M_⊙  , and also that the ONC is mass segregated at a lower level  (∼2.0 ± 0.5)  down to  5 M_⊙  . Below  5 M_⊙  we find no evidence for any further mass segregation in the ONC.     

A highly abnormal massive star mass function in the Orion Nebula cluster and the dynamical decay of trapezium systems

The Orion Nebula cluster (ONC) appears to be unusual on two grounds: the observed constellation of the OB stars of the entire ONC and its Trapezium at its centre implies a time-scale problem given the age of the Trapezium, and an initial mass function (IMF) problem for the whole OB star population in the ONC. Given the estimated crossing time of the Trapezium, it ought to have totally dynamically decayed by now. Furthermore, by combining the lower limit of the ONC mass with a standard IMF it emerges that the ONC should have formed at least about 40 stars heavier than  5 M_⊙  while only 10 are observed. Using the N -body experiments we (i) confirm the expected instability of the Trapezium and (ii) show that beginning with a compact OB-star configuration of about 40 stars both the number of observed OB stars after 1 Myr within 1 pc radius and a compact trapezium configuration can be reproduced. These two empirical constraints thus support our estimate of 40 initial OB stars in the cluster. Interestingly, a more-evolved version of the ONC resembles the Upper Scorpius OB association. The N -body experiments are performed with the new C-code catena by integrating the equations of motion using the chain-multiple-regularization method. In addition, we present a new numerical formulation of the IMF.     

The photoevaporation of discs around young stars in massive clusters

We present models in which the photoevaporation of discs around young stars by an external ultraviolet source (as computed by Adams et al.) is coupled with the internal viscous evolution of the discs. These models are applied to the case of the Orion Nebula Cluster (ONC), where the presence of a strong ultraviolet field from the central OB stars, together with a detailed census of circumstellar discs and photoevaporative flows, is well established. In particular we investigate the constraints that are placed on the initial disc properties in the ONC by the twin requirement that most stars possess a disc on a scale of a few astronomical unit (au), but that only a minority (<20 per cent) are resolved by Hubble Space Telescope ( HST ) at a scale of 50 au. We find that these requirements place very weak constraints on the initial radius distribution of circumstellar discs: the resulting size distribution readily forgets the initial radius distribution, owing to the strong positive dependence of the photoevaporation rate on disc radius. Instead, the scarcity of large discs reflects the relative scarcity of initially massive discs (with mass  >0.1 M_⊙  ). The ubiquity of discs on a small scale, on the other hand, mainly constrains the time-span over which the discs have been exposed to the ultraviolet field (<2 Myr). We argue that the discs that are resolved by HST represent a population of discs in which self-gravity was important at the time that the dominant central OB star switched on, but that, according to our models, self-gravity is unlikely to be important in these discs at the present time. We discuss the implications of our results for the so-called proplyd lifetime problem.     

The Monitor project: rotation of low-mass stars in NGC 2362 – testing the disc regulation paradigm at 5 Myr

We report on the results of a time-series photometric survey of NGC 2362, carried out using the CTIO 4-m Blanco telescope and Mosaic-II detector as part of the Monitor project. Rotation periods were derived for 271 candidate cluster members over the mass range  0.1 ≲ M /M_⊙≲ 1.2  . The rotation period distributions show a clear mass-dependent morphology, qualitatively similar to that in NGC 2264, as would be expected from the age of this cluster. Using models of angular momentum evolution, we show that angular momentum losses over the ∼1–5 Myr age range appear to be needed in order to reproduce the evolution of the slowest rotators in the sample from the ONC to NGC 2362, as found by many previous studies. By incorporating Spitzer IRAC mid-infrared (mid-IR) measurements, we found that three to four objects showing mid-IR excesses indicative of the presence of circumstellar discs were all slow rotators, as would be expected in the disc regulation paradigm for early pre-main-sequence angular momentum evolution, but this result is not statistically significant at present, given the extremely limited sample size.     

The distance to the Orion Nebula cluster

The distance to the Orion Nebula cluster (ONC) is estimated using the rotational properties of its low-mass pre-main-sequence (PMS) stars. Rotation periods, projected equatorial velocities and distance-dependent radius estimates are used to form an observational sin  i distribution (where i is the axial inclination), which is modelled to obtain the distance estimate. A distance of  440 ± 34 pc  is found from a sample of 74 PMS stars with spectral types between G6 and M2, but this falls to  392 ± 32 pc  when PMS stars with accretion discs are excluded on the basis of their near-infrared excess. Since the radii of accreting stars are more uncertain and probably systematically underestimated, then this closer distance is preferred. The quoted uncertainties include statistical errors and uncertainties due to a number of systematic effects including binarity and inclination bias. This method is geometric and independent of stellar evolution models, though does rely on the assumption of random axial orientations and the Cohen & Kuhi effective temperature scale for PMS stars. The new distance is consistent with, although lower and more precise, than most previous ONC distance estimates. A closer ONC distance implies smaller luminosities and an increased age based on the positions of PMS stars in the Hertzsprung–Russell diagram.     

Fitting the young main-sequence: distances, ages and age spreads

We use several main-sequence models to derive distances (and extinctions), with statistically meaningful uncertainties for 11 star-forming regions and young clusters. The model dependency is shown to be small, allowing us to adopt the distances derived using one model. Using these distances, we have revised the age order for some of the clusters of Mayne et al. The new nominal ages are: ≈2 Myr for NGC 6530 and the ONC, ≈3 Myr for λ Orionis, NGC 2264 and σ Orionis, ≈4–5 Myr for NGC 2362, ≈13 Myr for h and χ Per, ≈20 Myr for NGC 1960 and ≈40 Myr for NGC 2547. In cases of significantly variable extinction, we have derived individual extinctions using a revised Q-method. These new data show that the largest remaining uncertainty in deriving an age ordering (and necessarily ages) is metallicity. We also discuss the use of a feature we term the radiative–convective gap overlap to provide a diagnostic of isochronal age spreads or varying accretion histories within a given star formation region. Finally, recent derivations of the distance to the ONC lie in two groups. Our new more precise distance of 391⁺¹²₋₉ pc allows us to decisively reject the further distance; we adopt 400 pc as a convenient value.     

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.     

Effects of errors in the solar radius on helioseismic inferences

Frequencies of intermediate-degree f modes of the Sun seem to indicate that the solar radius is smaller than what is normally used in constructing solar models. We investigate the possible consequences of an error in radius on results for solar structure obtained using helioseismic inversions. It is shown that solar sound speed will be overestimated if oscillation frequencies are inverted using reference models with a larger radius. Using solar models with a radius of 695.78 Mm and new data sets, the base of the solar convection zone is estimated to be at a radial distance of 0.7135 ± 0.0005 of the solar radius. The helium abundance in the convection zone as determined using models with an OPAL equation of state is 0.248 ± 0.001, where the errors reflect the estimated systematic errors in the calculation, the statistical errors being much smaller. Assuming that the OPAL opacities used in the construction of the solar models are correct, the surface Z / X is estimated to be 0.0245 ± 0.0006.     

Binary formation in stellar clusters

We consider how the tidal potential of a stellar cluster or a dense molecular cloud affects the fragmentation of gravitationally unstable molecular cloud cores. We find that molecular cloud cores which would collapse to form a single star in the absence of tidal shear, can be forced to fragment if they are subjected to tides. This may enhance the frequency of binaries in star-forming regions such as Ophiuchus and the frequency of binaries with separations ≲100 au in the Orion Trapezium Cluster. We also find that clouds which collapse to form binary systems in the absence of a tidal potential will form bound binary systems if exposed to weak tidal shear. However, if the tidal shear is sufficiently strong, even though the cloud still collapses to form two fragments, the fragments are pulled apart while they are forming by the tidal shear and two single stars are formed. This sets an upper limit for the separation of binaries that form near dense molecular clouds or in stellar clusters.     

Do accretion discs regulate the rotation of young stars?

We present a photometric study of I -band variability in the young cluster IC 348. The main purpose of the study was to identify periodic stars. In all, we find 50 periodic stars, of which 32 were previously unknown. For the first time in IC 348, we discover periods in significant numbers of lower-mass stars  ( M < 0.25 M_⊙)  and classical T Tauri stars. This increased sensitivity to periodicities is a result of the enhanced depth and temporal density of our observations, compared with previous studies. The period distribution is at first glance similar to that seen in the Orion nebula cluster (ONC), with the higher-mass stars  ( M > 0.25 M_⊙)  showing a bi-modal period distribution concentrated around periods of 2 and 8 d, and the lower-mass stars showing a uni-modal distribution, heavily biased towards fast rotators. Closer inspection of the period distribution shows that the higher-mass stars show a significant dearth of fast rotators, compared to the ONC, whilst the low-mass stars are rotating significantly faster than those in Orion. We find no correlation between rotation period and K – L colour or Hα equivalent width.
We also present a discussion of our own IC 348 data in the context of previously published period distributions for the ONC, the Orion flanking fields and NGC 2264. We find that the previously claimed correlation between infrared excess and rotation period in the ONC might, in fact, result from a correlation between infrared excess and mass. We also find a marked difference in period distributions between NGC 2264 and IC 348, which presents a serious challenge to the disc-locking paradigm, given the similarity in ages and disc fractions between the two clusters.     

Predicting the clustering of X-ray selected galaxy clusters in flux-limited surveys

We present a model to predict the clustering properties of X-ray selected clusters in flux-limited surveys. Our technique correctly accounts for past light-cone effects on the observed clustering and follows the non-linear evolution in redshift of the underlying dark matter correlation function and cluster bias factor. The conversion of the limiting flux of a survey into the corresponding minimum mass of the hosting dark matter haloes is obtained by using theoretical and empirical relations between mass, temperature and X-ray luminosity of galaxy clusters. Finally, our model is calibrated to reproduce the observed cluster counts adopting a temperature–luminosity relation moderately evolving with redshift. We apply our technique to three existing catalogues: the ROSAT Brightest Cluster Sample (BCS); the X-ray Brightest Abell-type Cluster sample (XBACs); and the ROSAT –ESO Flux-Limited X-ray sample (REFLEX). Moreover, we consider an example of possible future space missions with fainter limiting flux. In general, we find that the amplitude of the spatial correlation function is a decreasing function of the limiting flux and that the Einstein–de Sitter models always give smaller correlation amplitudes than open or flat models with low matter density parameter Ω_0m. In the case of the XBACs catalogue, the comparison with previous estimates of the observational spatial correlation shows that only the predictions of models with Ω_0m=0.3 are in good agreement with the data, while the Einstein–de Sitter models have too low a correlation strength. Finally, we use our technique to discuss the best strategy for future surveys. Our results show that, to study the clustering properties of X-ray selected clusters, the choice of a wide area catalogue, even with a brighter limiting flux, is preferable to a deeper, but smaller area, survey.     

Models of Very-High-Energy Gamma-Ray Emission from the Jets of Microquasars: Orbital Modulation

The recent detection of very-high-energy (GeV – TeV) γ-ray emission from the Galactic black-hole candidate and microquasar LS 5039 has sparked renewed interest in jet models for the high-energy emission in those objects. In this work, we have focused on models in which the high-energy emission results from synchrotron and Compton emission by relativistic electrons in the jet (leptonic jet models). Particular attention has been paid to a possible orbital modulation of the high-energy emission due to azimuthal asymmetries caused by the presence of the companion star. Both orbital-phase dependentγγ absorption and Compton scattering of optical/UV photons from the companion star may lead to an orbital modulation of the gamma-ray emission. We make specific predictions which should be testable with refined data from HESS and the upcoming GLAST mission.     

Abundances in intermediate-mass AGB stars undergoing third dredge-up and hot-bottom burning

High-dispersion near-infrared spectra have been taken of seven highly evolved, variable, intermediate-mass (4–6 M_⊙) asymptotic giant branch (AGB) stars in the Large Magellanic Cloud and Small Magellanic Cloud in order to look for C, N and O variations that are expected to arise from third dredge-up and hot-bottom burning. The pulsation of the objects has been modelled, yielding stellar masses, and spectral synthesis calculations have been performed in order to derive abundances from the observed spectra. For two stars, abundances of C, N, O, Na, Al, Ti, Sc and Fe were derived and compared with the abundances predicted by detailed AGB models. Both stars show very large N enhancements and C deficiencies. These results provide the first observational confirmation of the long-predicted production of primary nitrogen by the combination of third dredge-up and hot-bottom burning in intermediate-mass AGB stars. It was not possible to derive abundances for the remaining five stars: three were too cool to model, while another two had strong shocks in their atmospheres which caused strong emission to fill the line cores and made abundance determination impossible. The latter occurrence allows us to predict the pulsation phase interval during which observations should be made if successful abundance analysis is to be possible.     

Photometric constraints on white dwarfs and the identification of extreme objects

It is possible to reliably identify white dwarfs (WDs) without recourse to spectra, instead using photometric and astrometric measurements to distinguish them from main-sequence stars and quasars. WDs' colours can also be used to infer their intrinsic properties (effective temperature, surface gravity, etc.), but the results obtained must be interpreted with care. The difficulties stem from the existence of a solid angle degeneracy, as revealed by a full exploration of the likelihood, although this can be masked if a simple best-fitting approach is used. Conversely, this degeneracy can be broken if a Bayesian approach is adopted, as it is then possible to utilize the prior information on the surface gravities of WDs implied by spectroscopic fitting. The benefits of such an approach are particularly strong when applied to outliers, such as the candidate halo and ultracool WDs identified by Vidrih et al. A reanalysis of these samples confirms their results for the latter sample, but suggests that most of the halo candidates are thick-disc WDs in the tails of the photometric noise distribution.     

Non-emission-line young stars of intermediate mass

We present optical spectra of four intermediate-mass candidate young stellar objects that have often been classified as Herbig Ae/Be stars. Typical Herbig Ae/Be emission features are not present in the spectra of these stars. Three of them, HD 36917, HD 36982 and HD 37062, are members of the young Orion nebula cluster (ONC). This association constrains their ages to be ≲1 Myr. The lack of appreciable near-infrared excess in them suggests the absence of hot dust close to the central star. However, they do possess significant amounts of cold and extended dust as revealed by the large excess emission observed at far-infrared wavelengths. The fractional infrared luminosities  ( L _ir/ L _★)  and the dust masses computed from IRAS fluxes are systematically lower than those found for Herbig Ae/Be stars but higher than those for Vega-like stars. These stars may thus represent the youngest examples of the Vega phenomenon known so far. In contrast, the other star in our sample, HD 58647, is more likely to be a classical Be star, as is evident from the low   L _ir/ L _★  , the scarcity of circumstellar dust, the low polarization, the presence of H α emission and near-infrared excess, and the far-infrared spectral energy distribution consistent with free–free emission similar to other well-known classical Be stars.     

Probing quintessence: reconstruction and parameter estimation from supernovae

We explore the prospects for using future supernova observations to probe the dark energy. We focus on quintessence, an evolving scalar field that has been suggested as a candidate for the dark energy. After simulating the observations that would be expected from the proposed SuperNova / Acceleration Probe satellite ( SNAP ), we investigate two methods for extracting information concerning quintessence from such data. First, by expanding the quintessence equation of state as   w _Q ( z ) = w _Q (0) −α ln(1 + z )  , to fit the data, it is possible to reconstruct the quintessence potential for a wide range of smoothly varying potentials. Secondly, it will be possible to test the basic properties of the dark energy by constraining the parameters  Ω _Q , w _Q   and α. We show that it may be possible, for example, to distinguish between quintessence and the cosmological constant in this way. Furthermore, when supernova data are combined with other planned cosmological observations, the precision of reconstructions and parameter constraints is significantly improved, allowing a wider range of dark energy models to be distinguished.     

A possible detection mechanism for pre-low-mass X-ray binaries

This work presents a possible detection mechanism for close, detached, neutron star–red dwarf binaries, which are expected to be the evolutionary precursors of low-mass X-ray binaries (LMXBs). Although this pre-low-mass X-ray binary (pre-LMXB) phase of evolution is predicted theoretically, as yet no such systems have been identified observationally. The calculations presented here suggest that the X-ray luminosity of neutron star wind accretion in a pre-LMXB system can be expected to exceed the intrinsic X-ray luminosity of the red dwarf secondary star. Furthermore, the temperature of the radiation emitted from the neutron star wind accretion process is expected, within the confines of a reasonable set of conditions, to lie within the detection range of X-ray satellites. Sources with X-ray luminosities greater than that expected for a red dwarf star, but the positions of which coincide with that of a red dwarf star, are then candidate pre-LMXB systems. These candidate systems should be surveyed for the radial velocity shifts that would occur as a result of the orbital motion of a red dwarf star within a close binary system containing a high-mass compact object.