Surface trapping and leakage of low-frequency g modes in rotating early-type stars – II. Global analysis

A global analysis of the surface trapping of low-frequency non-radial g modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. The dimensionless pulsation equations governing these modes are reviewed, and the boundary conditions necessary for solution of the equations are considered; in particular, an outer mechanical boundary condition, which does not enforce complete wave trapping at the stellar surface, is derived and discussed in detail. The pulsation equations are solved for a 7-M_⊙ model star over a range of rotation rates, using a numerical approach.
The results of the calculations confirm the findings of the preceding paper in the series: modes with eigenfrequencies below a cut-off cannot be fully trapped within the star, and exhibit leakage in the form of outwardly propagating waves at the surface. The damping rates resulting from leakage are calculated for such 'virtual' modes, and found to be appreciably larger than typical growth rates associated with opacity-driven pulsation. Furthermore, it is demonstrated that the surface perturbations generated by virtual modes are significantly changed from those caused by fully trapped modes; the latter result suggests differences in the line-profile variations exhibited by these two types of mode.
The findings are discussed in the context of the 53 Per, SPB and pulsating Be classes of variable star. Whilst wave leakage will probably not occur for overstable g modes in the 53 Per and slowly rotating SPB stars, the adoption of the new outer mechanical boundary condition may still affect the pulsational stability of these systems. Wave leakage for overstable modes remains a possibility in Be stars and the more rapidly rotating SPB stars.     

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.     

Absolute magnitudes of OB and Be stars based on Hipparcos parallaxes – II

A new method of determining absolute visual magnitudes of early-type stars, based on averaging Hipparcos parallaxes ( ESA 1997 ) inside samples of the same spectrum and luminosity (Sp/L) classes, is proposed. The used sample consists of 6262 unreddened and reddened OB stars as well as 430 Be stars of luminosity classes Ia, Iab, Ib, II, III, IV and V. The colour excesses of the reddened stars have been calculated using the mean colour indices, according to the SIMBAD data base and the intrinsic ( B − V ) values calibrated for given Sp/L classes by Papaj, Wegner & Krełowski . The values of the total-to-selective extinction   R_V = A_V / E ( B − V )  for all reddened stars were calculated from the published near-infrared photometric measurements. The calculated visual magnitudes M_V of OB and Be stars are compared to those published by Wegner in Paper I, and the earlier determinations of Schmidt-Kaler. Generally, the new values of M_V agree well with those given in Paper I, except those for O stars which are systematically brighter than the earlier estimates. The mean absolute magnitudes published by Schmidt-Kaler are generally brighter (except OB stars of luminosity class V) than those determined in this paper.     

Quasi-radial modes of rotating stars in general relativity

By using the Cowling approximation, quasi-radial modes of rotating general relativistic stars are computed along equilibrium sequences from non-rotating to maximally rotating models. The eigenfrequencies of these modes are decreasing functions of the rotational frequency. The eigenfrequency curve of each mode as a function of the rotational frequency has discontinuities, which arise from the avoided crossing with other curves of axisymmetric modes.     

The continuum re-processing efficiency of Be‐star circumstellar discs

We have calculated the total flux emitted in H α , P α and Br α by the circumstellar envelope of both an early Be star, γ Cas, and a late Be star, 1 Delphini, assuming the central star is the only source of energy input into the circumstellar envelope. These estimates are based on the Be-star models of Millar & Marlborough which have self-consistent temperature distributions determined by equating the local rates of energy gain and energy loss in the envelopes. We find that an additional source of ionizing photons, as argued by Apparao, is not necessary to account for the observed emission.     

Oscillations of rapidly rotating superfluid stars

Using time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.     

Spectroscopic analysis of southern B and Be stars

Spectroscopic monitoring of 141 southern field B-type stars, 114 of them known to exhibit the Be phenomenon, allowed the estimation of their projected rotational velocities, effective temperatures and superficial gravities from both line and equivalent width fitting procedures. Stellar ages, masses and bolometric luminosities were derived from internal structure models. Without taking into account the effects of gravity darkening, we note the occurrence of the Be phenomenon in later stages of main-sequence phase.     

Secular instability of g-modes in rotating neutron stars

Gravitational radiation tends to drive gravity modes in rotating neutron stars to become unstable. For an inviscid star, the instability sets in when the rotation frequency is about 0.7 times the corresponding mode frequency of the non-rotating star. Neutron stars with spin frequencies ≳100 Hz are susceptible to this instability, with a growth time of the order of years. However, it is likely that viscous dissipation suppresses the instability except for a narrow range of temperatures around 10⁹ K. We also show that the viscosity-driven instability of g-modes is absent.     

Circumstellar disc geometry constrained by infrared line fluxes

Lenorzer et al. introduce ratios of hydrogen infrared recombination lines as a diagnostic tool to constrain the spatial distribution and physical condition of circumstellar material around hot massive stars. They demonstrate that the observed line flux ratios Hu14/Brα and Hu14/Pfγ from different types of objects associated with circumstellar material, such as Be stars, B[e] stars, and Luminous Blue Variable (LBV) stars are well separated in a diagnostic diagram. In this paper, we investigate this diagnostic tool using a non-LTE disc code developed by Sigut & Jones focusing on Be discs. We find good agreement between the empirical and predicted locations of Be stars in the Hu14/Brα versus Hu14/Pfγ diagram and show that indeed this diagnostic tool can be used to constrain basic properties of the discs of these stars.     

Oscillations of rapidly rotating stratified neutron stars

We use time evolutions of the linear perturbation equations to study the oscillations of rapidly rotating neutrons stars. Our models account for the buoyancy due to composition gradients and we study, for the first time, the nature of the resultant g modes in a fast spinning star. We provide detailed comparisons of non-stratified and stratified models. This leads to an improved understanding of the relationship between the inertial modes of a non-stratified star and the g modes of a stratified system. In particular, we demonstrate that each g mode becomes rotation dominated, i.e. approaches a particular inertial mode, as the rotation rate of the star is increased. We also discuss issues relating to the gravitational wave driven instability of the various classes of oscillation modes.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

Be phenomenon in open clusters: results from a survey of emission-line stars in young open clusters

Emission-line stars in young open clusters are identified to study their properties, as a function of age, spectral type and evolutionary state. 207 open star clusters were observed using the slitless spectroscopy method and 157 emission stars were identified in 42 clusters. We have found 54 new emission-line stars in 24 open clusters, out of which 19 clusters are found to house emission stars for the first time. About 20 per cent clusters harbour emission stars. The fraction of clusters housing emission stars is maximum in both the 0–10 and 20–30 Myr age bin (∼40 per cent each). Most of the emission stars in our survey belong to Classical Be class (∼92 per cent) while a few are Herbig Be stars (∼6 per cent) and Herbig Ae stars (∼2 per cent). The youngest clusters to have Classical Be stars are IC 1590, NGC 637 and 1624 (all 4 Myr old) while NGC 6756 (125–150 Myr) is the oldest cluster to have Classical Be stars. The Classical Be stars are located all along the main sequence (MS) in the optical colour–magnitude diagrams (CMDs) of clusters of all ages, which indicates that the Be phenomenon is unlikely due to core contraction near the turn-off. The distribution of Classical Be stars as a function of spectral type shows peaks at B1–B2 and B6–B7 spectral types. The Be star fraction [N(Be)/N(B+Be)] is found to be less than 10 per cent for most of the clusters and NGC 2345 is found to have the largest fraction (∼26 per cent). Our results indicate there could be two mechanisms responsible for the Classical Be phenomenon. Some are born Classical Be stars (fast rotators), as indicated by their presence in clusters younger than 10 Myr. Some stars evolve to Classical Be stars, within the MS lifetime, as indicated by the enhancement in the fraction of clusters with Classical Be stars in the 20–30 Myr age bin.