The G‐dwarf problem in the solar neighbourhood: II. Halo subdwarfs

The oxygen abundance distribution in solar neighbourhood halo subdwarfs is deduced, using two alternative, known empirical relationships, involving the presence or the absence of [O/Fe] plateau for low [Fe/H] values, from a sample of 372 kinematically selected halo stars, for which the iron abundance distribution has been determined by Ryan & Norris (1991). The data are interpreted by a simple, either homogeneous or inhomogeneous model of chemical evolution, using an updated value of the solar oxygen abundance. The effect of changing the solar oxygen abundance, the power‐law exponent in the initial mass function, and the rate of oxygen nucleosyntesis, keeping the remaining input parameters unchanged, is investigated, and a theorem is stated. In all cases, part of the gas must necessarily be inhibited from forming stars, and no disk contamination has to be advocated for fitting the empirical oxygen abundance distribution in halo subdwarfs of the solar neighbourhood (EGD). Then a theorem is stated, which allows a one‐to‐one correspondence between simple, homogeneous models with and without inhibited gas, related to same independent parameters of chemical evolution, except lower stellar mass limit, real yield, and inhibition parameter. The mutual correlations between the latter parameters are also specified. In addition the starting point, and the point related to the first step, of the theoretical distribution of oxygen abundance (TGD) predicted by simple, inhomogeneous models, is calculated analytically. The mean oxygen abundance of the total and only inhibited gas, respectively, are also determined. Following the idea of a universal, initial mass function (IMF), a power‐law with both an exponent p = 2.9, which is acceptably close to Scalo IMF for m ≳ m_⊙, and an exponent p = 2.35, i.e. Salpeter IMF, have been considered. In general, both the age‐metallicity relationship and the empirical distribution of oxygen abundance in G dwarfs of the disk solar neighbourhood, are fitted by power‐law IMF exponents in the range 2.35 ≤ p ≤ 2.9. Acceptable models predict about 15% of the total mass in form of long‐lived stars and remnants, at the end of halo evolution, with a mean gas oxygen abundance which is substantially lower than the mean bulge and initial disk oxygen abundance. To avoid this discrepancy, either the existence of a still undetected, baryonic dark halo with about 15% of the total mass, or an equal amount of gas loss during bulge and disk formation, is necessary. The latter alternative implies a lower stellar mass limit close to 0.2 m_⊙, which is related to a power‐law IMF exponent close to 2.77. Acceptable models also imply a rapid halo formation, mainly during the first step, Δt = 0.5 Gyr, followed by a period (three steps) where small changes occur. Accordingly, statistical fluctuations are found to produce only minor effects on the evolution.     

The G-dwarf problem in the solar neighbourhood: a Lagrangian picture

Recent data on the empirical metallicity distribution of G dwarfs in the disk solar neighbourhood are fitted in two different ways. We use an extended Poisson distribution in the limit where the probability of star formation is small, and a Gauss distribution in the limit where a large number of physical variables is required to determine stellar metal abundance. Both are found to reproduce the data at the same (acceptable) extent, with a slight preference for the former. The emprirical, differential metallicity distribution of G dwarfs in the disk solar neighbourhood is compared with its theoretical counterpart, in the picture of a closed, comoving model of chemical evolution. The limits of the currently used infall models are discussed and a scenario of galactic formation and evolution is presented. The Galactic history is thought as made of two main phases: contraction (which produces the extended component) and equilibrium (which gives the disk). In this view, the stars observed within the solar cylinder did not necessarily arise from the primordial gas which later collapsed into the disk solar neighbourhood. It is found that the G-dwarf problem is strongly alleviated, with the possible exception of the low-metallicity and high-metallicity tail of the distribution. The best choice of parameters implies: (i) a metal yield in the contraction phase which is larger by a factor of about 5 with respect to the equilibrium phase; (ii) a model halo mass fraction of about 0.3; (iii) a model disk mass fraction of about 0.6. It provides additional support to the idea of a generalized Schmidt star formation law, which is different in different phases of evolution. The model, cumulative, G-dwarf metallicity distribution in the disk solar neighbourhood is found to predict too may low-metallicity stars with respect to its empirical counterpart, related to a Poissonian or Gaussian fit. The main resons for the occurrence of a G-dwarf problem are discussed. Finally, a stochastic process of star formation, related to a Poisson distribution, is briefly outlined.     

The SFR and IMF of the galactic disk

There is a long term dynamical heating of stellar populations with age observed in the age – velocity dispersion – relation (AVR). This effect allows a determination of the star formation history SFR(t) from local kinematical data of main sequence stars. Using a self-consistent disk model for the vertical structure of the disk, we find from the kinematics of the stars in the solar neighbourhood that the SFR shows a moderate star burst about 10 Gyr ago followed by a continuous decline to the present day value consistent with the observed number of OB stars. The gravitational potential of the gas component and of the Dark Matter Halo is included and the effect of chemical enrichment, finite lifetime of the stars and mass loss of the stellar component are taken into account. The scale heights for main sequence stars together with the SFR is then used to determine constistently the IMF from the observed local luminosity function. The main new result is that the power law break in the present day mass function (PDMF) around 1 M _⊙ is entirely due to evolutionary effects of the disk and does not appear in the IMF. This revised version was published online in August 2006 with corrections to the Cover Date.     

Age and Metallicity Distributions among Galactic Disk Stars

Observational studies of the relations between ages, metalicities and kinematics of disk stars in the solar neighbourhood are discussed with emphasis on the recent survey by Edvardsson et al. (1993), and galactic metallicity gradients inferred from these nearby stars are compared with gradients determined from distant B stars and open clusters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two-dimensional transport of solids in viscous protoplanetary disks

Large-scale radial transport of solids appears to be a fundamental consequence of protoplanetary disk evolution based on the presence of high temperature minerals in comets and the outer regions of protoplanetary disks around other stars. Further, inward transport of solids from the outer regions of the solar nebula has been postulated to be the manner in which short-lived radionuclides were introduced to the terrestrial planet region and the cause of the variations in oxygen isotope ratios in the primitive materials. Here, both outward and inward transport of solids are investigated in the context of a two-dimensional, viscously evolving protoplanetary disk. The dynamics of solids are investigated to determine how they depend on particle size and the particular stage of protoplanetary disk evolution, corresponding to different rates of mass transport. It is found that the outward flows that arise around the disk midplane of a protoplanetary disk aid in the outward transport of solids up to the size of CAIs s and can increase the crystallinity fraction of silicate dust at 10 AU around a solar mass star to as much as ∼40% in the case of rapidly evolving disks, decreasing as the accretion rate onto the star slows. High velocity, inward flows along the disk surface aid in the rapid transport of solids from the outer disk to the inner disk, particularly for small dust. Despite the diffusion that occurs throughout the disk, the large-scale, meridonal flows associated with mass transport prevent complete homogenization of the disk, allowing compositional gradients to develop that vary in intensity for a timescale of one million of years. The variations in the rates and the preferred direction of radial transport with height above the disk midplane thus have important implications for the dynamics and chemical evolution of primitive materials.     

Galactic scale gas flows in colliding galaxies: 3-Dimensional,N-body/hydrodynamics experiments

We present some results from three dimensional computer simulations of collisions between models of equal mass galaxies, one of which is a rotating, disk galaxy containing both gas and stars and the other is an elliptical containing stars only. We use fully self consistent models in which the halo mass is 2.5 times that of the disk. In the experiments we have varied the impact parameter between zero (head on) and 0.9R (whereR is the radius of the disk), for impacts perpendicular to the disk plane. The calculations were performed on a Cray 2 computer using a combined N-body/SPH program. The results show the development of complicated flows and shock structures in the direction perpendicular to the plane of the disk and the propagation outwards of a density wave in both the stars and the gas. The collisional nature of the gas results in a sharper ring than obtained for the star particles, and the development of high volume densities and shocks.     

Oxygen abundance in local disk and bulge: chemical evolution with a strictly universal IMF

This paper has two parts: one about observational constraints related to the empirical differential oxygen abundance distribution (EDOD), and the other about inhomogeneous models of chemical evolution, in particular the theoretical differential oxygen abundance distribution (TDOD). In the first part, the EDOD is deduced from subsamples related to two different samples involving (i) N=532 solar neighbourhood (SN) stars within the range, −1.5<[Fe/H]<0.5, for which the oxygen abundance has been determined both in presence and in absence of the local thermodynamical equilibrium (LTE) approximation (Ramirez et al. in Astron. Astrophys. 465:271, 2007); and (ii) N=64 SN thick disk, SN thin disk, and bulge K-giant stars within the range, −1.7<[Fe/H]<0.5, for which the oxygen abundance has been determined (Melendez et al. in Astron. Astrophys. 484:L21, 2008). A comparison is made with previous results implying use of [O/H]–[Fe/H] empirical relations (Caimmi in Astron. Nachr. 322:241, 2001b; New Astron. 12:289, 2007) related to (iii) 372 SN halo subdwarfs (Ryan and Norris in Astron. J. 101:1865, 1991); and (iv) 268 K-giant bulge stars (Sadler et al. in Astron. J. 112:171, 1996). The EDOD of the SN thick + thin disk is determined by weighting the mass, for assumed SN thick to thin disk mass ratio within the range, 0.1–0.9. In the second part, inhomogeneous models of chemical evolution for the SN thick disk, the SN thin disk, the SN thick + thin disk, the SN halo, and the bulge, are computed assuming the instantaneous recycling approximation. The EDOD data are fitted, to an acceptable extent, by their TDOD counterparts with the exception of the thin or thick + thin disk, where two additional restrictions are needed: (i) still undetected, low-oxygen abundance thin disk stars exist, and (ii) a single oxygen overabundant star is removed from a thin disk subsample. In any case, the (assumed power-law) stellar initial mass function (IMF) is universal but gas can be inhibited from, or enhanced in, forming stars at different rates with respect to a selected reference case. Models involving a strictly universal IMF (i.e. gas neither inhibited from, nor enhanced in, forming stars with respect to a selected reference case) can also reproduce the data to an acceptable extent. Our main conclusions are (1) different models are necessary to fit the (incomplete) halo sample, which is consistent with the idea of two distinct halo components: an inner, flattened halo in slow prograde rotation, and an outer, spherical halo in net retrograde rotation (Carollo et al. in Nature 450:1020, 2007); (2) the oxygen enrichment within the inner SN halo, the SN thick disk, and the bulge, was similar and coeval within the same metallicity range, as inferred from observations (Prochaska et al. in Astron. J. 120:2513, 2000); (3) the fit to thin disk data implies an oxygen abundance range similar to its thick disk counterpart, with the extension of conclusion (2) to the thin disk, and the evolution of the thick + thin disk as a whole (Haywood in Mon. Not. R. Astron. Soc. 388:1175, 2008) cannot be excluded; (4) leaving outside the outer halo, a fit to the data related to different environments is provided by models with a strictly universal IMF but different probabilities of a region being active, which implies different global efficiencies of the star formation rate; (5) a special case of stellar migration across the disk can be described by models with enhanced star formation, where a fraction of currently observed SN stars were born in situ and a comparable fraction is due to the net effect of stellar migration, according to recent results based on high-resolution N-body + smooth particle hydrodynamics simulations (Roškar et al. in Astrophys. J. Lett. 684:L79, 2008).     

Star formation history in the central region of the barred galaxy NGC 7177

Using the method of two-dimensional spectroscopy, we have investigated the kinematics and distribution of the gas and stars at the center of the early-type spiral galaxy NGC 7177 with a mediumscale bar as well as the change in the mean age of the stellar population along the radius. A classical picture of radial gas inflow to the galactic center along the shock fronts delineated by dust concentration at the leading edges of the bar has been revealed. The gas inflow is observed down to a radius R = 1″.5−2″, where the gas flows at the inner Lindblad resonance concentrate in an azimuthally highly inhomogeneous nuclear star formation ring. The bar in NGC 7177 is shown to be thick in z coordinate—basically, it has already turned into a pseudo-bulge as a result of secular dynamical evolution. The mean stellar age inside the star formation ring, in the galactic nucleus, is old, ∼10 Gyr.Outside, at a distance R = 6″−8″ from the nucleus, the mean age of the stellar population is ∼2 Gyr. If we agree that the bar in NGC 7177 is old, then, obviously, the star formation ring has migrated radially inward in the last 1–2 Gyr, in accordance with the predictions of some dynamical models.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

The metallicity distribution of stars in the galactic bulge and disc

The chemical evolution of the 3-component system of halo-bulge-disc is calculated. If the bulge accretes primordial halo matter quickly and forms stars rapidly before the gas is ejected by a galactic wind after 10⁹ yr, the metallicity distribution of the bulge K-giants (Rich, 1988) is reproduced. The metal-enriched matter in a wind from the bulge is mixed with the halo gas which is accreted into the disc. The metallicity distribution of the G-dwarfs and Twarog's age-metallicity relatin in the solar neighbourhood can be well reproduced by assuming reasonable bulge-to-disc mass ratio.     

Parameters of the Magnetic Flux inside Coronal Holes

The parameters of the magnetic flux distribution inside low-latitude coronal holes (CHs) were analyzed. A statistical study of 44 CHs based on Solar and Heliospheric Observatory (SOHO)/MDI full disk magnetograms and SOHO/EIT 284?Å images showed that the density of the net magnetic flux, B _net, does not correlate with the associated solar wind speeds, V _x . Both the area and net flux of CHs correlate with the solar wind speed and the corresponding spatial Pearson correlation coefficients are 0.75 and 0.71, respectively. A possible explanation for the low correlation between B _net and V _x is proposed. The observed non-correlation might be rooted in the structural complexity of the magnetic field. As a measure of the complexity of the magnetic field, the filling factor, f(r), was calculated as a function of spatial scales. In CHs, f(r) was found to be nearly constant at scales above 2 Mm, which indicates a monofractal structural organization and smooth temporal evolution. The magnitude of the filling factor is 0.04 from the Hinode SOT/SP data and 0.07 from the MDI/HR data. The Hinode data show that at scales smaller than 2 Mm, the filling factor decreases rapidly, which means a multifractal structure and highly intermittent, burst-like energy release regime. The absence of the necessary complexity in CH magnetic fields at scales above 2 Mm seems to be the most plausible reason why the net magnetic flux density does not seem to be related to the solar wind speed: the energy release dynamics, needed for solar wind acceleration, appears to occur at small scales below 1 Mm.     

Inhomogeneous Chemical Evolution of the Galaxy in the Solar Neighbourhood

N-body numerical simulations of an inhomogeneous Galactic Chemical Evolution (GCE) of the solar neighbourhood with a high temporal resolution are presented. The solar annular ring is divided into distinct spatial grids of area ~1–2 kpc². Each grid evolves distinctly in terms of star formation and nucleosynthetic yields from numerous generations of stars. The evolution of the galaxy is simulated by considering discrete episodes of star formation. Subsequent to the evolution of the simulated stars within each grid the stellar nucleosynthetic yields are homogenized within the grid rather than the traditionally adopted criteria of homogenizing over the entire solar annular ring. This provides a natural mechanism of generating heterogeneities in the elemental abundance distribution of stars. A complex chemical evolutionary history is inferred that registers episodes of time-dependent contributions from SN II+Ib/c with respect to SN Ia. It was observed that heterogeneities can remerge even after episodes of large scale homogenizations on scales larger than the grid size. However, a comparison of the deduced heterogeneities with the observed scatter in the elemental abundances of the dwarf stars suggest only a partial match, specifically, for [Fe/H] > ?0.5. The deduced heterogeneities in the case of carbon, oxygen, magnesium, silicon, sulphur, calcium and titanium can explain the observed heterogeneities for [Fe/H] < ?0.5. It may not be possible to explain the entire observed spread exclusively on the basis of the inhomogeneous GCE.     

Magnetic Star-Disk Interaction in Classical T Tauri Stars

We carry out 2.5D MHD simulations to study the interaction between a dipolar magnetic field of a T Tauri Star, a circumstellar accretion disk, and the halo above the disk. The initial disk is the result of 1D radiation hydrodynamics computations with opacities appropriate for low temperatures. The gas is assumed resistive, and inside the disk accretion is driven by a Shakura–Sunyaev-type eddy viscosity. Magnetocentrifugal forces due to the rotational shear between the star and the Keplerian disk cause the magnetic field to be stretched outwards and part of the field lines are opened. For a solar-mass central star and an accretion rate of 10^?8 solar masses per year a field strength of 100 G (measured on the surface of the star) launches a substantial outflow from the inner parts of the disk. For a field strength of 1 kG the inner parts of disk is disrupted. The truncation of the disk turns out to be temporary, but the magnetic field structure remains changed after the disk is rebuilt.     

A revision of the solar neighbourhood metallicity distribution

We present a revised metallicity distribution of dwarfs in the solar neighbourhood. This distribution is centred on solar metallicity. We show that previous metallicity distributions, selected on the basis of spectral type, are biased against stars with solar metallicity or higher. A selection of G-dwarf stars is inherently biased against metal-rich stars and is not representative of the solar neighbourhood metallicity distribution. Using a sample selected on colour, we obtain a distribution where approximately half the stars in the solar neighbourhood have metallicities higher than [Fe/H]=0 . The percentage of mid-metal-poor stars ([Fe/H]<−0.5) is approximately 4 per cent, in agreement with present estimates of the thick disc.
In order to have a metallicity distribution comparable to chemical evolution model predictions, we convert the star fraction to mass fraction, and show that another bias against metal-rich stars affects dwarf metallicity distributions, due to the colour (or spectral type) limits of the samples. Reconsidering the corrections resulting from the increasing thickness of the stellar disc with age, we show that the simple closed-box model with no instantaneous recycling approximation gives a reasonable fit to the observed distribution. Comparisons with the age–metallicity relation and abundance ratios suggest that the simple closed-box model may be a viable model of the chemical evolution of the Galaxy at solar radius.     

Peripheral Structures of Planetary Systems

We analyze the conditions for the formation and time evolution of peripheral comet structures of solar-type planetary systems. In the Solar system, these include the Kuiper belt, the Oort cloud, the comet spear, and the Galactic comet ring that marks the Galactic orbit of the Sun. We consider the role of the viscosity of a protoplanetary gas–dust disk, major planets, field stars, globular clusters, giant molecular clouds, and the Galactic gravitational field in the formation of these peripheral structures marked by comets and asteroids. We give a list of the closest past and future passages of neighboring stars through the solar Oort cloud that perturb the motion of its comets and, thus, contribute to the enhancement of its cometary activity, on the one hand, and to the replenishment of the solar comet spear with new members, on the other hand.     

Radial mixing and the transition between the thick and thin Galactic discs

The analysis of the kinematics of solar neighbourhood stars shows that the low- and high-metallicity tails of the thin disc are populated by objects which orbital properties suggest an origin in the outer and inner Galactic disc, respectively. Signatures of radial migration are identified in various recent samples, and are shown to be responsible for the high-metallicity dispersion in the age–metallicity distribution. Most importantly, it is shown that the population of low-metallicity wanderers of the thin disc (−0.7 < [Fe/H] < −0.3 dex) is also responsible for the apparent hiatus in metallicity with the thick disc (which terminal metallicity is about −0.2 dex). It implies that the thin disc at the solar circle has started to form stars at about this same metallicity. This is also consistent with the fact that 'transition' objects, which have α-element abundance intermediate between that of the thick and thin discs, are found in the range [−0.4, −0.2] dex. Once the metal-poor thin disc stars are recognized for what they are – wanderers from the outer thin disc – the parenthood between the two discs can be identified on stars genuinely formed at the solar circle through an evolutionary sequence in [α/Fe] and [Fe/H]. Another consequence is that stars that can be considered as truly resulting of the chemical evolution at the solar circle have a metallicity restricted to about [−0.2, +0.2] dex, confirming an old idea that most chemical evolution in the Milky Way have preceded the thin disc formation.     

Relativistic and Newtonian diskoseismology

The normal mode oscillations of thin accretion disks around black holes and other compact objects are analyzed and contrasted with those in stars. For black holes, the most robust modes are gravitationally trapped near the radius at which the radial epicyclic frequency is maximum. Their eigenfrequencies depend mainly on the mass and angular momentum of the black hole. The fundamental g-mode has recently been seen in numerical simulations of black hole accretion disks. For stars such as white dwarfs, the modes are trapped near the inner boundary (magnetospheric or stellar) of the accretion disk. Their eigenfrequencies are approximately multiples of the (Keplerian) angular velocity of the inner edge of the disk. The relevance of these modes to the high frequency quasi-periodic oscillations observed in the power spectra of accreting binaries will be discussed. In contrast to most stellar oscillations, most of these modes are unstable in the presence of viscosity (if the turbulent viscosity induced by the magnetorotational instability acts hydrodynamically).     

Local Stars as Tracers of Galactic Evolution

We describe the overall properties of a new catalogue of metallicities, ages, and galactic orbits for a large, complete sample of F and G dwarfs in the solar neighbourhood. Based on a magnitude-limited sample of ∼ 14000 stars, it is volume-complete to ∼ 40 pc. Together with the astrophysical parameters of direct relevance to models of the evolution of the disk, it will contain the basic photometric, astrometric, and radial velocity data from which they are derived. Information on duplicity is also included. The full exploitation of the data will require a lengthy analysis, in particular to assess the degree of completeness of subsamples of stars of different population types. An early result on the effects of diffusion of galactic orbits in the disk – essential for understanding the scatter in the age-metallicity diagram and estimating the birth radius of stars – is briefly illustrated. This revised version was published online in July 2006 with corrections to the Cover Date.     

A coupled model of magnetic flux generation and transport in stars

We present a combined model for magnetic field generation and transport in cool stars with outer convection zones. The mean toroidal magnetic field, which is generated by a cyclic thin-layer α Ω dynamo at the bottom of the convection zone is taken to determine the emergence probability of magnetic flux tubes in the photosphere. Following the nonlinear rise of the unstable thin flux tubes, emergence latitudes and tilt angles of bipolar magnetic regions are determined. These quantities are put into a surface flux transport model, which simulates the surface evolution of magnetic flux under the effects of large-scale flows and turbulent diffusion. First results are discussed for the case of the Sun and for more rapidly rotating solar-type stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)