Extrapolating SMBH correlations down the mass scale: the case for IMBHs in globular clusters

Empirical evidence for both stellar mass black holes (M _•<10²  M _⊙) and supermassive black holes (SMBHs, M _•>10⁵  M _⊙) is well established. Moreover, every galaxy with a bulge appears to host a SMBH, whose mass is correlated with the bulge mass, and even more strongly with the central stellar velocity dispersion σ _c , the M _•–σ relation. On the other hand, evidence for “intermediate-mass” black holes (IMBHs, with masses in the range 100–10⁵ M _⊙) is relatively sparse, with only a few mass measurements reported in globular clusters (GCs), dwarf galaxies and low-mass AGNs. We explore the question of whether globular clusters extend the M _•–σ relationship for galaxies to lower black hole masses and find that available data for globular clusters are consistent with the extrapolation of this relationship. We use this extrapolated M _•–σ relationship to predict the putative black hole masses of those globular clusters where existence of central IMBH was proposed. We discuss how globular clusters can be used as a constraint on theories making specific predictions for the low-mass end of the M _•–σ relation.     

The Basic Building Blocks of Galaxies

Current cold dark matter models of structure formation make a clear prediction for cosmic structures in the Dark Ages. We discuss the formation and nature of the first collapsed and first luminous objects in the universe arising in these theories. The first virialized objects are dark matter halos at the free streaming length which depends on the mass and nature of the assumed weakly interacting massive particle. The first objects that also contain significant fractions of gas have masses of the cosmological Jeans scale ∼ 10^4M _⊙ at the redshifts of interest (z ∼ 30). The first pre-galactic objects that host stars have masses of 10⁶ M _⊙. This mass scale is given by the requirement of a sufficiently high virial temperature to enable the chemical reactions necessary to form molecular hydrogen which subsequently allows the gas to dissipate its gravitational energy and to collapse to form a star. An individual massive star is formed per such object and explodes in a supernova within a few Myrs. All these stages of the formation of the first objects are illustrated by fully resolved three dimensional cosmological hydrodynamic simulations. This revised version was published online in September 2006 with corrections to the Cover Date.     

On the Formation of Massive Primordial Stars

We investigate the formation by accretion of massive primordial protostars in the range 10 to 300 M _⊙. The high accretion rate used in the models (M _⊙ = 4.4 x 10^-3 M_⊙ yr^-1) causes the structure and evolution to differ significantly from those of both present-day protostars and primordial zero-age main sequence stars. The stellar surface is not visible throughout most of the main accretion phase, since a photosphere is formed in the in falling envelope. Significant nuclear burning does not take place until a protostellar mass of about 80 M _⊙. As the interior luminosity approaches the Eddington luminosity, the protostellar radius rapidly expands owing to the radiation pressure. Eventually, a final swelling occurs when the stellar mass reaches about 300 M _⊙. This expansion is likely to signal the end of the main accretion phase, thus setting an upper limit to the protostellar mass formed in these conditions. This revised version was published online in September 2006 with corrections to the Cover Date.     

The evolution of BD+60°2522: with mass loss and overshooting

The ionizing star BD+60°2522 is known as the central star of Bubble Nebulae NGC 7635—wind-blown bubble created by the interaction of the stellar wind of BD+60°2522 (O6.5 IIIef, V=8.7 mag, mass loss rate 10^−5.76 M _⊙/year) with the ambient interstellar medium. From the evolutionary calculations for the star with mass loss and overshooting, we find that the initial mass of the star is 60M _⊙, its present age is 2.5×10⁶ years, and the present mass is 45M _⊙.     

The Yields of r-Process Elements and Chemical Evolution of the Galaxy

The supernova yields of r-process elements are obtained as a function of the mass of their progenitor stars from the abundance patterns of extremely metal-poor stars on the left-side [{Ba/Mg}]--[{Mg/H}] boundary with a procedure proposed by Tsujimoto and Shigeyama. The ejected masses of r-process elements associated with stars of progenitor mass M _ms ≤ 18 M _⊙ are infertile sources and the SNe II with 20 M _⊙ ≤ M _ms ≤ 40 M _⊙ are the dominant source of r-process nucleosynthesis in the Galaxy. The ratio of these stars 20 M _⊙ ≤ M _ms ≤ 40 M _⊙ with compared to the all massive stars is about∼ 18%. In this paper, we present a simple model that describes a star's [r/Fe] in terms of the nucleosynthesis yields of r-process elements and the number of SN II explosions. Combined the r-process yields obtained by our procedure with the scatter model of the Galactic halo, the observed abundance patterns of the metal-poor stars can be well reproduced.     

Faint companions of isolated 2MIG galaxies

We present the results of a search for companions around the isolated galaxies from the 2MIG catalog. Among 3227 2MIG galaxies we detected 125 objects with a total of 214 neighbors having radial velocity differences of ΔV < 500 km/s and projected separations of R _p < 500 kpc relative to the 2MIG galaxies. The median luminosity of the companions is 1/25 of the luminosity of catalog galaxies, which has little effect on the dynamic isolation of the latter. The median ratio of the orbital mass to the K-luminosity determined from 60 companions of E and S0 2MIG galaxies, 63M _⊙/L _⊙, is significantly greater than that found from the spiral galaxy companions (17M _⊙/L _⊙). We note that a fraction of 2MIG galaxies with companions may be a part of low-contrast diffuse structures: clouds and filaments.     

Mass-luminosity relation for massive stars

A catalog of massive (⩾10 M _⊙) stars in binary and multiple systems with well-known masses and luminosities has been compiled. The catalog is analyzed using a theoretical mass-luminosity relation. This relation allows both normal main-sequence stars and stars with peculiarities: with clear manifestations of mass transfer, mass accretion, and axial rotation, to be identified. Least-squares fitting of the observational data in the range of stellar masses 10M _⊙ ⩽ M ≲ 50 M _⊙ yields the relation L ∼ M ^2.76. An erratum to this article is available at .     

Aq Psc – Analysis of New Light Curves

New BV light curves of the A-type W UMa star AQ Psc (P = 0.476d) have been observed and are described. A few times of minimum light are obtained and the ephemeris is improved. The light curves are analyzed for the binary parameters with a light curve synthesis method. Combining the results with Lu and Rucinski’s spectroscopic mass ratio we determined the masses and radii of the components: M ₁ = 1.69M _⊙, M ₂ = 0.38M _⊙, R ₁ = 1.77R _⊙, and R ₂ = 0.89R _⊙.     

Models for the formation of binary and millisecond radio pulsars

The peculiar combination of a relatively short pulse period and a relatively weak surface dipole magnetic field strength of binary radio pulsars finds a consistent explanation in terms of (i) decay of the surface dipole component of neutron-star magnetic fields on a timescale of (2–5) × 10⁶ yr, in combination with (ii) spin-up of the rotation of the neutron star during a subsequent mass-transfer phase. The four known binary radio pulsars appear to fall into two different categories. Two of them, PSR 0655 + 64 and PSR 1913 + 16, have short orbital periods (<25 h) and high mass functions, indicating companion masses 0.7M⊙ (∼1 (± 0.3) M⊙ and 1.4 M⊙, respectively). The other two, PSR 0820 + 02 and PSR 1953 + 29, have long orbital periods (117d), nearly circular orbits, and low, almost identical mass functions of about 3×10^-3 M⊙, suggesting companion masses of about 0.3M⊙. It is pointed out that these two classes of systems are expected to be formed by the later evolution of binaries consisting of a neutron star and a normal companion star, in which the companion was (considerably) more massive than the neutron star, or less massive than the neutron star, respectively. In the first case the companion of the neutron star in the final system will be a massive white dwarf, in a circular orbit, or a neutron star in an eccentric orbit. In the second case the final companion to the neutron star will be a low-mass (∼ 0.3 M⊙) helium white dwarf in a wide and nearly circular orbit. In systems of the second type the neutron star was most probably formed by the accretion-induced collapse of a white dwarf. This explains in a natural way why PSR 1953 + 29 has a millisecond rotation period and PSR 0820 + 02 has not. Among the binary models proposed for the formation of the 1.5-millisecond pulsar, the only ones that appear to be viable are those in which the companion disappeared by coalescence with the neutron star. In such models the companion may have been a red dwarf of mass 0.03M⊙, a neutron star, or a massive (>0.7M⊙) white dwarf. Only in the last-mentioned case is a position of the pulsar close to the galactic plane a natural consequence. In the first-mentioned case the progenitor system most probably was a cataclysmic-variable binary in which the white dwarf collapsed by accretion.     

Absolute parameters of the close binary BW Boo with a superasynchronous A2m primary component

Based on two high-dispersion spectra of the close binary BW Boo, we have detected lines of the secondary component whose contribution to the combined spectrum does not exceed 2%. We have determined the rotation velocities of the components and spectroscopic orbital elements. Numerous lines of neutral and ionized iron have been used to determine the effective temperature and surface gravity for the primary component. The photometric light curves for this binary have been solved for the first time. Its primary component is an A2Vm star with a mass of 2 ± 0.1M _⊙ and a radius of 1.9 ± 0.4R _⊙. Its rotation velocity is 2 km s⁻¹, which is a factor of 18 lower than the pseudo-synchronous velocity for this component. The G6 secondary component, a T Tau star, has a rotation velocity of 17 km s⁻¹, amass of 1.1M _⊙, and a radius of 1 R _⊙. The age of the binary has been estimated to be 10⁷ yr.     

Astrometric study of the relative motion of three stars with possible invisible companions based on homogeneous series obtained at Pulkovo with a 26-inch refractor

We investigate the relative motion of three stars, ADS 7446, 9346, and 9701, based on long-term observations with the Pulkovo 26-inch refractor. The relative motion of all three stars shows a perturbation that could be produced by the gravitational influence of an invisible companion. For ADS 7446, we have determined the orbit of the photocenter with a period of 7.9 yr; the mass of the companion is more than 0.4M _⊙. For ADS 9346, we have determined the radial velocities of the components: −14.60 km s⁻¹ for A and −13.94 km s⁻¹ for B. For ADS 9346 and 9701, we have determined the dynamical parallaxes, 24 and 20 mas, respectively, which are larger than those in the Hipparcos catalog by 5 mas, and calculated the orbits by the apparent motion parameter (AMP) method. The new orbit of ADS 9346 is: a = 5″.2, P = 2035 yr, and e = 0.46 at the system’s mass M = 2.5M _⊙. The new orbits of ADS 9701 are: (a = 2″.9, P = 829 yr, e = 0.54, M = 4.3M _⊙) and (a = 3″.8, P = 1157 yr, e = 0.53, M = 5.0M _⊙).     

A microscopic equation of state for protoneutron stars

We study the structure of protoneutron stars within the finite-temperature Brueckner–Bethe–Goldstone many-body theory. If nucleons, hyperons, and leptons are present in the stellar core, we find that neutrino trapping stiffens considerably the equation of state, because hyperon onsets are shifted to larger baryon density. However, the value of the critical mass turns out to be smaller than the “canonical” value 1.44M _⊙. We find that the inclusion of a hadron-quark phase transition increases the critical mass and stabilizes it at about 1.5–1.6M _⊙.      

Absolute dimensions of the close binary systems V453 Monocerotis and V523 Cassiopeiae

We present multi-colour CCD observations of the low-temperature contact binaries, V453 Mon and V523 Cas. Their light curves are modelled to determine a new set of stellar and orbital parameters. Analysis of mid-eclipse times yields a new linear ephemeris for both systems. A period decrease (dP/dt=2.3×10⁻⁷ days/yr) in V453 Mon is discovered. V523 Cas, however, is detected to show a period increase (dP/dt=9.8×10⁻⁸ days/yr) because of the mass transfer of a rate of 1.1×10⁻⁷ M_⊙ yr⁻¹, from a less massive donor. Using these findings we can determine the physical parameters of the components of V523 Cas to be M ₁=0.76 (3)M _⊙, M ₂=0.39 (2)M _⊙, R ₁=0.74 (2)R _⊙, R ₂=0.55 (2)R _⊙, L ₁=0.19 (3)L _⊙, L ₂=0.14 (3)L _⊙, and the distance of system as 46(9) pc.     

Neutron stars and general equation of nuclear matter

It has been shown that the mass of neutron stars obtained from equations of state based on nuclear theory depend upon the number of baryons assembled in it but not on the type of interactions considered. On examining the behaviour of different equations of state based on nuclear theories, a simple polytropic equation of state,P = (K/N)(p –p _s)^N is proposed. The results obtained forN=1.75 cover the entire range of neutron star masses obtained from the equations of state based on nuclear theories and give a maximum mass of 2.8M . Depending upon various mechanisms for energy output the mass of Crab pulsar is estimated to range from 0.32M to 1.5M . The relation connecting the coordinate mass,M, and the rest mass,M ₀, may be written asM/M 0.93 (M ₀/M)^0.9.     

The angular momentum loss of low-mass close binary systems

The detailed evolution of low-mass main-sequence stars (M < 1M ) with a compact companion is studied. For angular momentum loss associated with magnetic braking it is found that about 10^–11–10^–12 M yr^–1 in stellar wind loss would be required. This wind is 10²–10³ times stronger than the solar wind, so we believe here magnetic stellar wind is insufficient. It is well known that there is mass outflow in low-mass close binary systems. We believe here that these outflows are centrifugal driven winds from the outer parts of the accretion disks. The winds extract angular momentum from these systems and therefore drive secular evolution. Disk winds are preferred to winds from the secondary, because of the lower disk surface gravity.     

Production of dust by massive stars at high redshift

The large amounts of dust detected in sub-millimeter galaxies and quasars at high redshift pose a challenge to galaxy formation models and theories of cosmic dust formation. At z>6 only stars of relatively high mass (>3 M_⊙) are sufficiently short-lived to be potential stellar sources of dust. This review is devoted to identifying and quantifying the most important stellar channels of rapid dust formation. We ascertain the dust production efficiency of stars in the mass range 3–40 M_⊙ using both observed and theoretical dust yields of evolved massive stars and supernovae (SNe) and provide analytical expressions for the dust production efficiencies in various scenarios. We also address the strong sensitivity of the total dust productivity to the initial mass function. From simple considerations, we find that, in the early Universe, high-mass (>3 M_⊙) asymptotic giant branch stars can only be dominant dust producers if SNe generate ≲3×10⁻³ M_⊙ of dust whereas SNe prevail if they are more efficient. We address the challenges in inferring dust masses and star-formation rates from observations of high-redshift galaxies. We conclude that significant SN dust production at high redshift is likely required to reproduce current dust mass estimates, possibly coupled with rapid dust grain growth in the interstellar medium.     

Comparison of Star Formation Rate Estimates from Hα, FIR and Radio Data

We use three indicators of massive star formation, H_α, FIR and non-thermal radio luminosities, to compare estimates of the star formation rate (SFR) for a sample of 34 spiral galaxies. To adjust the SFR values obtained from these indicators, we considered the slope, α, and/or the upper mass limit M _up of the initial mass function (IMF) as free parameters. The best agreement between the indicators is found for M _up≈ 60-100 M⊙ and α ≈–3.1 at the high-mass end of the IMF (M>10 M⊙.Parallelwith the SFR we also estimated the FIR excess X _FIR, defined as the fraction of the observed FIR not directly related to young massive stars. X _FIR is found to be well correlated with types of spiral galaxies and their colours (B-V): the redder a galaxy, the higher its FIR excess. We conclude that for any parameters of the IMF the observed FIR flux of early-type spiral galaxies needs an additional source of energy apart from massive star radiation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of tidal evolution in determining the ages of eclipsing-variable early main sequence close binary systems

New Claret evolutionary model-tracks, constructed for the first time for studying close binary systems (CBS) including tidal evolution constants, are used to determine the age of 112 eclipsing-variable stars in the Svechnikov-Perevozkina catalog by the method of isochrones. There is some interest in comparing the calculated ages with previous estimates obtained for these same close binary systems using evolutionary modeltracks for individual stars taking their mass loss into account. A correlation of the ages of the principal and secondary components is noted, which is most marked for massive close binaries with principal components having masses M₁ ≥ 3 M_⊙. A rejuvenating effect is found to occur for the systems studied here as calculated on the new tracks; it is most distinct for low-mass close binaries with a total mass M₁ + M₂ ≤ 3.5 M_⊙ and is predicted theoretically in terms of magnetic braking. The calculated broadband grid of isochrones, from zero-age main-sequence (ZAMS) to the age of the galaxy, can be used for estimating the ages of close binaries from other catalogs. Ages are given for the 112 eclipsing-variable close binaries with detached components lying within the main sequence. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 299–312 (May 2007).     

Masses and Radii of Low-Mass Stars: Theory Versus Observations

Eclipsing binaries with M-type components are still rare objects. Strong observational biases have made that today only a few eclipsing binaries with component masses below 0.6 M_⊙ and well-determined fundamental properties are known. However, even in these small numbers the detailed comparison of the observed masses and radii with theoretical predictions has revealed large disagreements. Current models seem to predict radii of stars in the 0.4--0.8 M_⊙ range to be some 5--15% smaller than observed. Given the high accuracy of the empirical measurements (a few percent in both mass and radius), these differences are highly significant. I review all the observational evidence on the properties of M-type stars and discuss a possible scenario based on stellar activity to explain the observed discrepancies.     

Pulsational instability of yellow hypergiants

Instability of population I (X = 0.7, Z = 0.02) massive stars against radial oscillations during the post-main-sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range 65M _⊙ ≤ M _ZAMS ≤ 90M _⊙. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is T _eff > 6700 K for M _ZAMS = 65M _⊙ and T _eff > 7200 K for M _ZAMS = 90M _⊙. Pulsational instability is due to the κ-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed ≈200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is T _eff > 7300 K for M _ZAMS = 65M _⊙ and T _eff > 7600 K for M _ZAMS = 90M _⊙. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (T _eff > 7700 K for M _ZAMS = 65M _⊙ and T _eff > 8200 K for M _ZAMS = 90M _⊙). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed ≈130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.