Interstellar extinction and diffuse absorption features

The equivalent width of the 2175 Å band,W ₂₁₇₅, well known as the big bump in the interstellar extinction curves, has been found to be closely correlated with the colour excessE _B-V as well as with the extinction differencesE _8–6 andE _9–7 defined to characterize quantitatively the steep slopes of the extinction curves in the far ultraviolet.The equivalent widths of the 5780 and 5797 Å diffuse lines show good correlation withE _B-V. The correlations ofW ₅₇₈₀ andW ₅₇₉₇ withE _8–6 resp.E _9–7 are, however, rather weak. Correlations betweenW ₂₁₇₅ andW ₅₇₈₀ and betweenW ₂₁₇₅ andW ₅₇₉₇ are indicated.The results have been qualitatively interpreted in favour of the dust model consisting of a mixture of small silicate grains and larger silicate grains coated by molecular mantles.Paper presented at the Symposium on Solid State Astrophysics, held at the University College, Cardiff, Wales, between 9–12 July 1974.     

Schmidt survey in the Galactic anticentre direction. 1. Investigation of open clusters

A study of four open clusters in the direction of the Galactic anticentre (l = 186°, b = +2°) is presented. In a field of 8.32 square degrees proper motions and B magnitudes for about 79 000 stars down to 19.5 were determined on Tautenburg Schmidt plates. For more than 15 500 of them U magnitudes down to 17.3 could be obtained. Additionally, OCA Schmidt plates were used to determine V, R magnitudes in a larger field of 24.45 square degrees for 271 000 stars down to V = 18.2. For stars brighter than V = 15.5 an accuracy of about 1.5 mas/yr has been estimated for proper motions. The rms errors of stellar magnitudes and colour indices are 0.09 – 0.12 mag. Several open clusters have been already known in this direction of the sky, e.g. NGC 2168 or M 35 (C 0605+243), NGC 2158 (C 0604+241) and IC 2157 (C 0601+240). Inspecting the plates and analysing the colour-magnitude diagrams and published data, we could identify an additional anonymous cluster C 0605+242 with a projection on the sky near the centre of M 35 but at a larger distance from the Sun. The cluster membership determination was carried out using information on spatial and proper motion distributions of stars in the field. The colour-magnitude diagrams were derived down to the limiting stellar magnitude. For each cluster the interstellar extinction A_v, the diameters of the core and corona, the ages and spatial velocity components (V,W) relative to the LSR in the Y,Z – Galactic directions were determined. The distances to the clusters of 960 pc, 2 600 pc, 2 520 pc and 3 700 pc were obtained for M 35, IC 2157, C 0605+242 and NGC 2158. They show the loci of the clusters in the Local and Perseus spiral arms and at external border of Perseus arm, respectively.     

Refinement of the geopotential scale factorR 0 on

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.     

Hydrodynamic and turbulent motions in the galactic disk

Statistics in absorption 21-cm data show two main types of clouds at low galactic latitudes: dense small clouds, many of them with molecular cores, with dispersions σ≈1.5 km s⁻¹ and large clouds forming the fine features of the spiral arms (the shingle like features) with a dispersion range α≈3–4 km s⁻¹. Sizes and dispersions of both types of clouds are compatible with the Kolmogorov law of turbulence: σ∞d ^1/3. The large clouds forming the shingle-like features can be considered as the largest clouds of a Kolmogorov spectrum (the initial vortices), or as the hydrodynamic features with minimum sizes in the Galaxy. In order to define hydrodynamic motions in the same sense as given by Ogrodnikov (1965) we use here the tensorial form of the Helmholtz theorem to obtain an approximation for the hydrodynamic motions depending on distances and seen from the local standard of rest:V _r ∞r. The intermediate range of sizes between turbulent motions and hydrodynamic motions is 100<d<300 pc which is also the range of sizes of the large clouds forming the fine features of the spiral arms. A classification on of motions in the Galaxy is postulated: (a) a basic rotation motion given by an smooth unperturbed curveΘ _b (R) associated to the old disk population. (b) Systematic motions of the spiral arms. (c) Systematic motions in the fine structure of the arms. For scale sizes smaller than these fine features one has turbulent motions according to the Kolmogorov law. The densities and sizes of the turbulent clouds behave asn _H ∝d ⁻² in a range of sizes 7 pc<d<300 pc. The obtained gas densities of the clouds are confirmed with the dust densities from photometric studies. The conditions for gravitational binding of the clouds are analyzed. Factors as the geometry and the magnetic field within the clouds increases the critic densities for gravitational binding. When we consider these factors we find that the wide component clouds have densities below such a critical value. The narrow component clouds have densities similar or above the critical value; but the real fraction of collapsing clouds remains unknown as far as the factor of geometry and the inner magnetic field of each cloud are not determinated.     

Motions in wide pairs at various galactocentric distances

The motions of the components of wide binary stars in the regular Galactic gravitational field on time scales ~10¹⁰ yr at various Galactocentric distances R ₀ have been studied numerically. Near the Galactic center, the influence of the bar has been taken into account. The regions of restricted motions of the components in wide pairs have been found depending on the initial conditions: the magnitude of the relative velocity of the components, their mutual distance, and the inclination of the relative velocity vector to the Galactic plane. The shape and sizes of these regions are shown to depend significantly on R ₀: the sizes of the region of initial conditions corresponding to restricted motions increase with R ₀. Profound changes in the eccentricity of the binary orbit occur at inclinations close to 90?, which can lead to close approaches of the stars with a pericenter distance less than 1 AU. For retrograde motions (the binary rotates in a direction opposite to the Galactic rotation), there are elongated branches of the region of restricted motions in all cases, which extend at least to 10 pc in some cases.     

An electron temperature distribution derived from optical and radio measurements of HII regions

Radio measurements of the electron temperature ofHii regions are obtained from the ratio of the brightness temperature of a hydrogen recombination line to that of the adjacent continuum, while optical measurements are obtained from the ratio of [Oiii] forbidden-line intensities. The radio and optical measurements made under the assumption of an isothermalHii region,T _R andT _opt respectively, are combined to derive a temperature distribution for an entire nebula. A sphericalHii region in local thermodynamic equilibrium with constant density which is optically thin in both the line and the continuum is used as a model. Assuming linear temperature gradients withT _R=6000K andT _opt=10000K, it is found thatT=12000K (1–0.74r/R), wherer is the distance from the center andR is the radius of the nebula.     

The <Emphasis Type="Italic">z</Emphasis> distribution of hydrogen clouds and masers with kinematic distances

Data on HII regions, molecular clouds, and methanol masers have been used to estimate the Sun’s distance from the symmetry plane z _⊙ and the vertical disk scale height h. Kinematic distance estimates are available for all objects in these samples. The Local-arm (Orion-arm) objects are shown to affect noticeably the pattern of the z distribution. The deviations from the distribution symmetry are particularly pronounced for the sample of masers with measured trigonometric parallaxes, where the fraction of Local-arm masers is large. The situation with the sample of HII regions in the solar neighborhood is similar. We have concluded that it is better to exclude the Local arm from consideration. Based on the model of a self-gravitating isothermal disk, we have obtained the following estimates from objects located in the inner region of the Galaxy (R ≤ R ₀): z _⊙ = ?5.7 ± 0.5 pc and h ₂ = 24.1 ± 0.9 pc from the sample of 639 methanol masers, z _⊙ = ?7.6±0.4 pc and h ₂ = 28.6±0.5 pc from 878HII regions, z _⊙ = ?10.1 ± 0.5 pc and h ₂ = 28.2 ± 0.6 pc from 538 giant molecular clouds.     

Schmidt plate survey in the galactic centre direction. 1. Investigation of open clusters in the Sagittarius-Carina spiral arm

A study of four open clusters on Tautenburg Schmidt plates in the direction to the Galactic Centre (l = 17.0°, b = +0.8°) is presented. In a field of 8.95 square degrees proper motions and B, V magnitudes were determined for about 36 500 stars up to the limiting magnitudes B = 17^m.9, V = 16^m.8. For stars brighter than B = 16^m an accuracy of about 3 mas/year has been estimated for proper motions. The rms errors of stellar magnitudes and (B—V) colours is about 0.1 mag. There are two open clusters already known in this sky area: Trumpler 32 (C 1814-133) and NGC 6611 (C 1816-138). By the inspection of the plates two additional anonymous clusters were identified near the double star ADS 11285 or BD −14°5014 (C 1819-146) and near the star BD −14°5016 (C 1820-146). The cluster membership determination was carried out using information on spatial and proper motion distributions of stars in the field. The colour-magnitude diagrams up to the limiting stellar magnitude were constructed. For each cluster interstellar extinction A_V, diameters of the core and corona, ages and spatial velocity components (V, W) relative to the LSR in the Y, Z-galactic directions were derived. The distances to the clusters were obtained to 1720 pc, 2260 pc, 2130 pc and 2130 pc for Trumpler 32, NGC 6611, C 1819-146 and C 1820-146, respectively. All clusters are situated in the Sagittarius-Carina spiral arm. Their spatial location confirms the assumption that galactic spiral arms are close to logarithmic spirals with a characteristic angle of about 20 degrees.     

Hα emission objects in Circinus

We present a new survey for Hα emission objects in the Circinus cloud complex and introduce an efficient photometric method for detecting Hα emission via observations in a narrow‐band filter. The observed flux is compared to a blackbody fit of the continuum. Our search strategy reveals 20 stars with strong Hα emission (EW > 10 Å), eight of them being new detections. All Hα stars display infrared excess corroborating their youth. On the other hand, the region contains a number of infrared excess objects that do not show Hα emission. Our results support the picture that accretion – as witnessed by Hα emission – is a highly variable phenomenon. Therefore, Hα surveys can only trace the temporarily active objects. In contrast, infrared excess is a more robust tracer that reveals most of the population of young stellar objects in a star forming region. Our analysis of the general stellar content of the region yields a reliable distance of 450 pc for the Circinus cloud. Moreover, we find a ratio of total‐to‐selective extinction of R^V = 2.8 suggesting that smaller‐than‐normal dust grains may be present. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Is the Entropy S q Extensive or Nonextensive?

The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the entropies S _BG ≡ −k ∑ _{i = 1} ^W p _i ln p _i and S _q ≡ k (1−∑ _{i = 1} ^W p _i ^q )/(q−1) (q∊ℜ S ₁ = S _BG ). Through them we revisit the concept of additivity, and illustrate the (not always clearly perceived) fact that (thermodynamical) extensivity has a well defined sense only if we specify the composition law that is being assumed for the subsystems (say A and B). If the composition law is not explicitly indicated, it is tacitly assumed that A and B are statistically independent. In this case, it immediately follows that S _BG (A+B) = S _BG (A)+S _BG (B), hence extensive, whereas S _q (A+B)/k = [S _q (A)/k]+[S _q (B)/k]+(1−q)[S _q (A)/k][S _q (B)/k], hence nonextensive for q ≠ 1. In the present paper we illustrate the remarkable changes that occur when A and B are specially correlated. Indeed, we show that, in such case, S _q (A+B) = S _q (A)+S _q (B) for the appropriate value of q (hence extensive), whereas S _BG (A+B) ≠ S _BG (A)+S _BG (B) (hence nonextensive). We believe that these facts substantially improve the understanding of the mathematical need and physical origin of nonextensive statistical mechanics, and its interpretation in terms of effective occupation of the W a priori available microstates of the full phase space. In particular, we can appreciate the origin of the following important fact. In order to have entropic extensivity (i.e., lim _N→∞ S(N)/N < ∞, where N≡ numberof elements of the system), we must use (i) S _BG , if the number W ^eff of effectively occupied microstates increases with N like W ^{{eff}}∼ W ∼ μ ^N (μ ≥ 1); (ii) S _q with q = 1−1/ρ, if W ^{{eff}}∼ N^ρ < W (ρ ≥ 0). We had previously conjectured the existence of these two markedly different classes. The contribution of the present paper is to illustrate, for the first time as far as we can tell, the derivation of these facts directly from the set of probabilities of the W microstates.     

Molecular cores of the high-latitude cloud MBM 40

Towards the high-latitude cloud MBM 40, we identify 3 dense molecular cores of M0.2–0.5 M, and sizes of 0.2 pc in diameter embedded in the H I cloud of 8 M which is observed to be extended along the northeast–southwest direction. The molecular cloud is located almost perpendicularly to the H I emission. We confirm the previous result of Magnani et al. that MBM 40 is not a site for new star formations. We found a very poor correlation between the H I and the IRAS 100 μm emissions, but the CO (1–0) and 100 μm emissions show a better correlation of W_CO/I₁₀₀=1±0.2 K km s⁻¹ (MJy sr⁻¹)⁻¹. This ratio is larger by a factor of ≥5 than in dense dark clouds, which may indicate that the CO is less depleted in MBM 40 than in dense dark clouds.     

A colour-agnitude diagram of the Pisces dwarf galaxy

We present B, V and R band CCD images of the dwarf galaxy LGS-3 (Pisces dwarf). About 180 stars and diffuse objects were found and processed in these frames. The colour-magnitude diagram shows a prominent red giant branch and a few blue stars only. Details of the morphological properties and colour-agnitude diagram indicate to an intermediate (between dIrr and dSph) type of LGS-3. We estimate the galaxy distance modulus to be about (m - M)₀ = 23.9 ± 0.3 mag on the basis of the tip of the red giant branch. We measured the galaxy colour to be about B–V = 0.8 mag and the linear diameter 700 pc, which is the smallest one in the Local group.     

Cr 135 revisited

In this paper we combine information on photometry, radial velocities and proper motions to study the nature of the suspected open cluster Cr 135. For the first time we introduce proper motions of a large number of stars in the region of Cr 135 into the discussion. The proper motions taken from the PPM catalogue favour the hypothesis that Cr 135 is a real open cluster with at least 12 members at a distance of 300 pc having a space motion U, V, W of (−11, −13, −15) km s⁻¹. But still more accurate observations are needed to separate it from the field stars without any doubt.     

The significance of observed rotational magnetic hysteresis in lunar samples

Rotational Magnetic hysteresis (W _R ) curves for lunar soils 10084, 12070, 14259, and rock 14053, have been published. There is no adequate explanation to date for the observed largeW _R at high fields. Lunar rock magnetism researchers consider fine particle iron to be the primary source of stable magnetic remanence in lunar samples. Iron has cubic anisotropy with added shape anisotropy for extreme particle shapes. The observed high fieldW _R must have its source in uniaxial or unidirectional anisotropy. This implies the existence of minerals with uniaxial anisotropy or exchange coupled spin states. Therefore, the source of this observed high fieldW _R must be identified and understood before serious paleointensity studies are made. It is probable that the exchange coupled spin states and/or the source of uniaxial anisotropy responsible for the high fieldW _R might be influenced by the lunar surface diurnal temperature cycling. The possible sources of high fieldW _R in lunar samples are presented and considered.     

The radial distribution function in planetary nebulae

We have investigated the variation of planetary nebula number densities as a function of nebular radius, taking account of uncertainties arising from interstellar extinction. We find that the trend is composed of two components: one (a “spike” component) located at radii R < 0.035 pc, and the other (a “plateau” component) extending to larger radii. The plateau component appears to follow a Gaussian fall‐off law with scale radius R₀ = 0.28 pc. It is shown that this latter trend is not consistent with the assumption that larger shells are optically thin and density bounded. Rather, it seems likely thatmany of the larger sources have appreciable Lyman continuum optical depths and are ionization bounded. The deduced variation in N(R) then suggests that the velocities of the ionization fronts increase with radius. The nature of the spike component is less easy to fathom, and this may arise as a result of sharply lower ionization front velocities at radii R < 0.035 pc, or through contraction of the shells following a down‐turn in central star luminosities.     

Estimation of the solar galactocentric distance and galactic rotation velocity from near-solar-circle objects

We have tested the method of determining the solar Galactocentric distance R ₀ and Galactic rotation velocity V ₀ modified by Sofue et al. using near-solar-circle objects. The motion of objects relative to the local standard of rest has been properly taken into account. We show that when such young objects as star-forming regions or Cepheids are analyzed, allowance for the perturbations produced by the Galactic spiral density wave improves the statistical significance of the estimates. The estimate of R ₀ = 7.25 ± 0.32 kpc has been obtained from 19 star-forming regions. The following estimates have been obtained from a sample of 14 Cepheids (with pulsation periods P > 5 ^d ): R ₀ = 7.66 ± 0.36 kpc and V ₀ = 267 ± 17 km s^?1. We consider the influence of the adopted Oort constant A and the character of stellar proper motions (Hipparcos or UCAC4). The following estimates have been obtained from a sample of 18 Cepheids with stellar proper motions from the UCAC4 catalog: R ₀ = 7.64 ± 0.32 kpc and V ₀ = 217 ± 11 km s^?1.     

Remarks on statistical errors in equivalent widths

Equivalent width measurements for rapid line variability in atomic spectral lines are degraded by increasing error bars with shorter exposure times.We derive an expression for the error of the line equivalent width σ (W _λ ) with respect to pure photon noise statistics and provide a correction value for previous calculations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM ^–5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M ^5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M ², predicted by some more complex considerations.The distribution functionf(q=M ₂/M₁) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.