Predictions for triple stars with and without a pulsar in star clusters

Though about 80 pulsar binaries have been detected in globular clusters so far, no pulsar has been found in a triple system in which all three objects are of comparable mass. Here, we present predictions for the abundance of such triple systems, and for the most likely characteristics of these systems. Our predictions are based on an extensive set of more than 500 direct simulations of star clusters with primordial binaries, and a number of additional runs containing primordial triples. Our simulations employ a number N _tot of equal-mass stars from   N _tot= 512  to  19 661  and a primordial binary fraction from 0 to 50 per cent. In addition, we validate our results against simulations with   N = 19 661  that include a mass spectrum with a turn-off mass at  0.8 M_⊙  , appropriate to describe the old stellar populations of Galactic globular clusters. Based on our simulations, we expect that typical triple abundances in the core of a dense cluster are two orders of magnitude lower than the binary abundances, which in itself already suggests that we do not have to wait too long for the first comparable-mass triple with a pulsar to be detected.     

On the origin of high-velocity runaway stars

We explore the hypothesis that some high-velocity runaway stars attain their peculiar velocities in the course of exchange encounters between hard massive binaries and a very massive star (either an ordinary  50–100 M_⊙  star or a more massive one, formed through runaway mergers of ordinary stars in the core of a young massive star cluster). In this process, one of the binary components becomes gravitationally bound to the very massive star, while the second one is ejected, sometimes with a high speed. We performed three-body scattering experiments and found that early B-type stars (the progenitors of the majority of neutron stars) can be ejected with velocities of  ≳200–400 km s⁻¹  (typical of pulsars), while  3–4 M_⊙  stars can attain velocities of  ≳300–400 km s⁻¹  (typical of the bound population of halo late B-type stars). We also found that the ejected stars can occasionally attain velocities exceeding the Milky Ways's escape velocity.     

Black holes and core expansion in massive star clusters

In this study we present the results from realistic N -body modelling of massive star clusters in the Magellanic Clouds. We have computed eight simulations with   N ∼ 10⁵  particles; six of these were evolved for at least a Hubble time. The aim of this modelling is to examine in detail the possibility of large-scale core expansion in massive star clusters, and search for a viable dynamical origin for the radius–age trend observed for such objects in the Magellanic Clouds. We identify two physical processes which can lead to significant and prolonged cluster core expansion – mass-loss due to rapid stellar evolution in a primordially mass-segregated cluster, and heating due to a retained population of stellar mass black holes, formed in the supernova explosions of the most massive cluster stars. These two processes operate over different time-scales and during different periods of a cluster's life. The former occurs only at early times and cannot drive core expansion for longer than a few hundred Myr, while the latter typically does not begin until several hundred Myr have passed, but can result in core expansion lasting for many Gyr. We investigate the behaviour of each of these expansion mechanisms under different circumstances – in clusters with varying degrees of primordial mass segregation, and in clusters with varying black hole retention fractions. In combination, the two processes can lead to a wide variety of evolutionary paths on the radius–age plane, which fully cover the observed cluster distribution and hence define a dynamical origin for the radius–age trend in the Magellanic Clouds. We discuss in some detail the implications of core expansion for various aspects of globular cluster research, as well as the possibility of observationally inferring the presence of a significant population of stellar mass black holes in a cluster.     

Limits on initial mass segregation in young clusters

Mass segregation is observed in many star clusters, including several that are less than a few Myr old. Time-scale arguments are frequently used to argue that these clusters must be displaying primordial segregation, because they are too young to be dynamically relaxed. Looking at this argument from the other side, the youth of these clusters and the limited time available to mix spatially distinct populations of stars can provide constraints on the amount of initial segregation that is consistent with current observations. We present n -body experiments testing this idea, and discuss the implications of our results for theories of star formation. For system ages less than a few crossing times, we show that star formation scenarios predicting general primordial mass segregation are inconsistent with observed segregation levels.     

The possible companions of young radio pulsars

We discuss the formation of pulsars with massive companions in eccentric orbits. We demonstrate that the probability for a non-recycled radio pulsar to have a white dwarf as a companion is comparable to that of having an old neutron star as a companion. Special emphasis is given to PSR B1820−11 and PSR B2303+46. Based on population synthesis calculations we argue that PSR B1820−11 and PSR B2303+46 could very well be accompanied by white dwarfs with mass ≳1.1 M_⊙. For PSR B1820−11, however, we cannot exclude the possibility that its companion is a main-sequence star with a mass between ∼0.7 M_⊙ and ∼5 M_⊙.     

Effects of external tidal field on the evolution of the outer regions of multi-mass star clusters

We present N -body simulations (including an initial mass function) of globular clusters in the Galaxy in order to study effects of the tidal field systematically on the properties of the outer parts of globular clusters. Using nbody6 , which correctly takes into account the two-body relaxation, we investigate the development of tidal tails of globular clusters in the Galactic tidal field. For simplicity, we have employed only the spherical components (bulge and halo) of the Galaxy, and ignored the effects of stellar evolution which could have been important in the very early phase of the cluster evolution. The total number of stars in our simulations is about 20 000, which is much smaller than the realistic number of stars. All simulations had been done for several orbital periods in order to understand the development of the tidal tails. In our scaled-down models, the relaxation time is sufficiently short to show the mass segregation effect, but we did not go far enough to see the core collapse, and the fraction of stars lost from the cluster at the end of the simulations is only ∼10 per cent. The radial distribution of extra-tidal stars can be described by a power law with a slope around −3 in surface density. The directions of tidal tails are determined by the orbits and locations of the clusters. We find that the length of tidal tails increases towards the apogalacticon and decreases towards the perigalacticon. This is an anti-correlation with the strength of the tidal field, caused by the fact that the time-scale for the stars to respond to the potential is similar to the orbital time-scale of the cluster. The escape of stars in the tidal tails towards the pericentre could be another reason for the decrease of the length of tidal tails. We find that the rotational angular velocity of tidally induced clusters shows quite different behaviour from that of initially rotating clusters.     

Discovery of three new pulsars in a 610-MHz pulsar survey with the GMRT

We report on the discovery of three new pulsars in the first blind survey of the north Galactic plane  (45° < l < 135°; | b | < 1°)  with the Giant Meterwave Radio telescope (GMRT) at an intermediate frequency of 610 MHz. The survey covered 106 deg² with a sensitivity of roughly 1 mJy to long-period pulsars (pulsars with period longer than 1 s). The three new pulsars have periods of 318, 933 and 1056 ms. Their timing parameters and flux densities, obtained in follow-up observations with the Lovell Telescope at Jodrell Bank and the GMRT, are presented. We also report on pulse nulling behaviour in one of the newly discovered pulsars, PSR J2208+5500.     

Resonant cyclotron scattering in pulsar magnetospheres and its application to isolated neutron stars

Resonant cyclotron scattering(RCS)in pulsar magnetospheres is considered.The photon diffusion equation(Kompaneets equation)for RCS is derived.The photon system is modeled three dimensionally.Numerical calculations show that there exist not only up scattering but also down scattering of RCS,depending on the parameter space.RCS's possible applications to spectral energy distributions of magnetar candidates and radio quiet isolated neutron stars(INSs)are pointed out.The optical/UV excess of INSs may be caused by the down scattering of RCS.The calculations for RX J1856.5-3754 and RX J0720.4-3125 are presented and compared with their observational data.In our model,the INSs are proposed to be normal neutron stars,although the quark star hypothesis is still possible.The low pulsation amplitude of INSs is a natural consequence in the RCS model.     

Freely precessing neutron stars: model and observations

We present a model of a freely precessing neutron star, which is then compared against pulsar observations. The aim is to draw conclusions regarding the structure of the star, and to test theoretical ideas of crust–core coupling and superfluidity. We argue that, on theoretical grounds, it is likely that the core neutron superfluid does not participate in the free precession of the crust. We apply our model to the handful of proposed observations of free precession that have appeared in the literature. Assuming crust-only precession, we find that all but one of the observations are consistent with there being no pinned crustal superfluid at all; the maximum amount of pinned superfluid consistent with the observations is about 10⁻¹⁰ of the total stellar moment of inertia. However, the observations do not rule out the possibility that the crust and neutron superfluid core precess as a single unit. In this case the maximum amount of pinned superfluid consistent with the observations is about 10⁻⁸ of the total stellar moment of inertia. Both of these values are many orders of magnitude less than the 10⁻² value predicted by many theories of pulsar glitches. We conclude that superfluid pinning, at least as it affects free precession, needs to be reconsidered.     

A timing formula for main-sequence star binary pulsars

In binary radio pulsars with a main-sequence star companion, the spin-induced quadrupole moment of the companion gives rise to a precession of the binary orbit. As a first approximation one can model the secular evolution caused by this classical spin-orbit coupling by linear-in-time changes of the longitude of periastron and the projected semi-major axis of the pulsar orbit. This simple representation of the precession of the orbit neglects two important aspects of the orbital dynamics of a binary pulsar with an oblate companion. First, the quasiperiodic effects along the orbit, owing to the anisotropic 1/ r ³ nature of the quadrupole potential. Secondly, the long-term secular evolution of the binary orbit, which leads to an evolution of the longitude of periastron and the projected semi-major axis, which is non-linear in time.   In this paper a simple timing formula for binary radio pulsars with a main-sequence star companion is presented which models the short-term secular and most of the short-term periodic effects caused by the classical spin-orbit coupling. I also give extensions of the timing formula that account for long-term secular changes in the binary pulsar motion. It is shown that the short-term periodic effects are important for the timing observations of the binary pulsar PSR B1259–63. The long-term secular effects are likely to become important in the next few years of timing observations of the binary pulsar PSR J0045–7319. They could help to restrict or even determine the moments of inertia of the companion star and thus probe its internal structure.   Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR J0045–7319 since the analysis given in the literature is based on an incorrect expression for the precession of the longitude of periastron. A lower limit of 20° for the inclination of the B star with respect to the orbital plane is derived.     

The influence of gas expulsion and initial mass segregation on the stellar mass function of globular star clusters

Recently, De Marchi, Paresce & Pulone studied a sample of 20 globular clusters and found that all clusters with high concentrations have steep stellar mass functions while clusters with low concentration have comparatively shallow mass functions. No globular clusters were found with a flat mass function and high concentration. This seems curious since more concentrated star clusters are believed to be dynamically more evolved and should have lost more low-mass stars via evaporation, which would result in a shallower mass function in the low-mass part.
We show that this effect can be explained by residual-gas expulsion from initially mass segregated star clusters, and is enhanced further through unresolved binaries. If gas expulsion is the correct mechanism to produce the observed trend in the   c –α  -plane, then observation of these parameters would allow to constrain cluster starting conditions such as star formation efficiency and the time-scale of gas expulsion.     

Ratios of star cluster core and half-mass radii: a cautionary note on intermediate-mass black holes in star clusters

There is currently much interest in the possible presence of intermediate-mass black holes (IMBHs) in the cores of globular clusters (GCs). Based on theoretical arguments and simulation results it has previously been suggested that a large core radius – or particularly a large ratio of the core radius to half-mass radius – is a promising indicator for finding such a black hole (BH) in a star cluster. In this study N -body models of 100 000 stars with and without primordial binaries are used to investigate the long-term structural evolution of star clusters. Importantly, the simulation data are analysed using the same processes by which structural parameters are extracted from observed star clusters. This gives a ratio of the core and half-mass (or half-light) radii that are directly comparable to the Galactic GC sample. As a result, it is shown that the ratios observed for the bulk of this sample can be explained without the need for an IMBH. Furthermore, it is possible that clusters with large core to half-light radius ratios harbour a BH binary (comprising stellar mass BHs) rather than a single massive BH. This work does not rule out the existence of IMBHs in the cores of at least some star clusters.     

Captured older stars as the reason for apparently prolonged star formation in young star clusters

The existence of older stars within a young star cluster can be interpreted to imply that star formation occurs on time-scales longer than a free-fall time of a pre-cluster cloud core. Here, the idea is explored that these older stars are not related to the star formation process forming the young star cluster but rather that the orbits of older field stars are focused by the collapsing pre-cluster cloud core. Two effects appear: the focusing of stellar orbits leads to an enhancement of the density of field stars in the vicinity of the centre of the young star cluster; and due to the time-dependent potential of the forming cluster some of these stars can get bound gravitationally to the cluster. These stars exhibit similar kinematical properties to the newly formed stars and cannot be distinguished from them on the basis of radial velocity or proper motion surveys. Such contaminations may lead to a wrong apparent star formation history of a young cluster. In the case of the ONC, the theoretical number of gravitationally bound older low-mass field stars agrees with the number of observed older low-mass stars.