A theory of galactic mass and rotation curves

The goal of this paper is to account for the complete observed rotation curves of disk galaxies without dark matter. To attain that goal, use is made of a conservation law from stability theory of linear waves, leading to a vector-based theory of gravitation. In the theory, galactic centers are sites of strong gravitational fields. The new theory predicts extra matter at the center of disk galaxies, which is well-known to be consistent with intergalactic dynamics. For given disk radiusr ₀ and edge tangential speedv, the greater the deviation of a rotation curve from linear (solid disk rotation), the greater the mass of the galaxy as a multiple of Newtonian massr ₀v²/G, up to a factor of about 1000. In an approximate calculation it turns out that disk density (r) (in kg m^–2) is proportional to 1/r for typical rotation curves. Rotation is characterized by two constants which in turn are determined by the edge speed and mass distribution. Not just any curve shape can be so obtained; in fact, the theoretically possible curves correspond to observed curves.     

Gas,dust and molecules in the Galaxy

The relative abundances of cool neutral hydrogen, carbon monoxide and formaldehyde are studied using all the available observational data in the literature. The obtained mean valuesN _{H 1}/ ,N _{H 1}/N _CO,N _CO/ are approximately constant in the dark clouds of the solar neighbourhood and in the distant molecular clouds.The observed correlationsN _CO,A _v and ,A _v show that formaldehyde can also be used as an indicator of molecular hydrogen. The ratioN H₁/A _v depends on densities and decays considerably in the ranges of visual absorptions in which the molecules become detectable (A _v 2 mg); an average of /N _{H 1}10 is calculated for the dense dark clouds.Indications of systematic temperature gradiens T/A _v are found for formaldehyde and neutral hydrogen inside the dark clouds, and qualitative comparisons are made with theoretical quantum mechanics calculations.The observed carbon monoxide and formaldehyde abundances, the free electron layer in the Galaxy, the distribution of neutral hydrogen in different states are only compatible if an ionization rate of 10^–16 is accepted, provided presumably by 2 MeV protons of cosmic radiation.Three main states for neutral hydrogen and dust are identified from different kinds of observational data (21 cm line in emission, absorption in galactic radio sources and self-absorption in the hot gas background): (1) a homogeneous intercloud stratum of tenuous gas and dust with a galactic halfwidth of 350 pc and mean parametersn _H=0.2 atom cm^–3, spin temperatureT _s 10000 K andn _d 0.3 mg kpc^–1; (2) cool gas and dust concentrated in spiral features with a galactic half-width of less than 100 pc, probably forming clouds with diffuse and indefinite limits, with mean parametersn _H2 atom cm^–3,T _s <1100 K (probable average,T _s =135 K) andn _d 3 mg kpc^–1; (3) dense gas and dust clouds with a mean diameter of 7 pc and mean parametersn _H700 atom cm^–3 (90% in a molecular state),T _s 63 K andn _d 1 mg pc^–1 on which molecules as CO and H₂CO are formed.The application of the Jeans criteria for gravitational instability shows that the dense clouds are gravitationally bound while the gas in the intermediate state (2) can be protected against collapse by the total internal energy in the medium increasing due to cosmic rays and the magnetic field in the Galaxy.The observed velocity halfwidths and galacticZ-halfwidths in states (1) and (2) are compatible with a total mass density in the galactic layer of 90M pc^–2 (gas plus stars) according to the barometric equation.The relative abundancesN _{H 1}/N _CO, calculated from C¹²O and C¹³O data and comparisons with studies in the 21 cm emission line, show that the antenna temperatureT _A ⁺ in the 2.6 mm line of C¹²O is a good indicator of the cool gas densities in the Galaxy. The possible application of this for studies in galactic structure is discussed and hypothetical distributions of carbon monoxide in the zones outside the galactic planeB=0° are presented.From a synthesis based on the results obtained, a cycle is postulated for the neutral hydrogen in the Galaxy: condensation and cooling of gas molecular formation gravitational collapse and star formation gas dissipation and heating by cosmic rays and UV radiation.     

Quasi-static collapse of homogeneous spheroids within constrained halos

The virial theorem in tensor form for subsystems is used to determine equilibrium configurations of two-component, concentric and copolar, homogeneous spheroids, one completely lying within the other. Then the related total energy and angular momenta are expressed explicitly as functions of the mass ratio,m, the equatorial axis ratio,y, the polar to equatorial axis ratios, _U , the rotation parameters, _rotU , and the anisotropy parameters, _pecU . With assigned masses, angular momenta, total energy, rotation parameters, and anisotropy parameters, there remain three independent equations and four unknowns, i.e. equatorial semiaxes and (polar to equatorial) axis ratios. To get a unique solution, and then describe the quasi-static collapse (via energy dissipation) of the inner subsystem within the halo, a number of alternative additional conditions are taken into consideration. It is also argued that the true situation, involving neither homogeneous nor spheroidal halos, lies between two extreme cases, namely: (i) the two subsystems collapse together with coinciding boundaries, and (ii) halos depart only faintly, or not at all, from the related initial configurations. Starting from systems with coinciding boundaries and specific angular momenta, the related evolutionary sequences are derived by substantial improvement of previous attempts. Some limiting situations are also considered, where the mass of one subsystem tends to zero and/or the mass of the other one tends to infinite. An application of the theory to systems of galactic mass and plausible other parameters shows that (i) initial configurations depend on the total mass and final (with a flat inner component) configurations depend on the mass of the collapsing visible body; (ii) quasi-static collapse depends mainly on the mass ratio,m, for given total masses and angular momenta, while the action of different additional conditions is negligible; (iii) halos as massive as about ten visible bodies depart from the initial configuration by no more than a few percents, using different additional conditions, and yield (for fiduciary values related to the Galaxy, i.e. total mass 10¹² M , total angular momentum 10⁷⁵ g cm² s^–1) final configurations related to flat visible bodies with equatorial semiaxes of about 15 kpc, close to observations.     

The spiral structure in the inner parts of the Galaxy

The spiral structure of the inner parts of the Galaxy is studied using 21 cm line data and stellar data. To study the neutral hydrogen distribution in the galactic layer a parameter =(dV/dr) proportional to the mean densities is calculated using a first approximation for the velocity gradients due to differential rotation.The obtained distribution (R, Z) shows spiral features completely consistent with the early star distribution and with the Hii regions. The corrugation effect of the galactic layer is observed in all the studied zones in neutral hydrogen and in the distribution of the OB stars in the Carina zone.The pattern obtained indicates four spiral arms for the inner parts of the Galaxy, three of which are identified also in the stellar data (arms -I, -II, and -III) and the more distant -IV in Hii regions.The local arm according to the stellar data of Kilkennyet al. forms a feature completely similar to the arms -I and -II and there are no indications that this arm is a special material branch between two main spiral arms as has been supposed in order to conciliate the neutral hydrogen pattern with the stellar distribution.The pitch angles for the spiral arms are approximately 13°–17°.The observed wave form distribution of the hydrogen cloud layer is completely consistent with the theoretical predictions of Nelson (1976) but there are no indications of such an effect in the intercloud hydrogen. The corrugated cloud layer has a width of 100 pc, a wave amplitude of 70 pc, and a wavelength which grows with the galactic center distance (approx. 2 kpc in the zones next to the galactic nucleus and 2.6–3.0 kpc in the zones next to the Sun). To each wavelength correspond two spiral arms. The spiral features in our Galaxy show characteristics quite similar to the features in the Andromeda nebula, not only in the component materials (neutral hydrogen, Hii regions and possibly also dust and stars) but also in their kinematics.     

The galactic centre

An attempt is made to present all the relevant observations of our galactic centre and to explain them by means of a working scheme that involves a minimum number ofad hoc assumptions.In this scheme, the central engine is Sgr A^*, a supermassive star of some 10³ M and surface temperature 3.6×10⁴ K in Keplerian rotation, fuelled by the strongly magnetized disk. It drives both a non-thermal (pair-plasma) wind and a thermal wind. Interactions with the central star cluster and with the circumnuclear disk give rise to the thermal vortex Sgr A West and to the non-thermal spill-over bubble Sgr A East. The relativistic pair plasma escapes supersonically through the galactic chimney into the galactic twin jets, as in Seyfert galaxies.     

A galactic model with a pulsating active nucleus

The chemical evolution of the Galaxy with a pulsating active nucleus is investigated. The surface densities of gas, stellar remnants, stars and chemical species such as helium and heavy elements inZ6 are calculated as functions of the position in the Galaxy and of the evolutional time of the Galaxy. According to this model, the entire luminosity of the galactic disk becomes almost constant at some 2×10⁹ yr after the galactic formation, but the nuclear bulge, whose dimensions gradually diminishes, becomes more and more luminous with time. On the other hand, the abundance depletion of helium and heavy elements appears in the inner region of the disk after some 6×10⁹ yr of the galactic formation. It also becomes clear that the activity for the nucleosynthesis in the nucleus is limited only in the early history of the Galaxy and has been reduced rapidly with time. Using this model, we can account for the observed phenomena such as the smooth dependence of the elemental abundance in the halo population on the distance from the galactic center, the high abundance of heavy elements in quasar spectra and etc.     

UBVRI Photometry and Polarimetry of the Eclipsing Binary RY Per

Results are presented from multicolor photometric and polarimetric studies of the eclipsing binary RY Per during 2001-2003. Light curves in the UBVRI bands are shown. An analysis of the variations in the linear polarization makes it possible to separate it into interstellar and intrinsic components. The degree of intrinsic polarization of the system away from the eclipse attains a maximum (0.23%) in the B band and falls off rapidly with increasing wavelength. This dependence is indicative of the existence of optically thick gas in the system. An analysis of the polarimetric data also shows that: the total mass of optically thin gas in the system is about 2·10^-10 M , while the total mass of the shell must be several times that; and, the inclination of the orbital plane of the binary system relative to the galactic plane is 4° or 18°.     

30 Doradus as the active centre of the Large Magellanic Cloud

Evidence is presented for the hypothesis that the supergiantHii-complex 30 Doradus (NGC 2070) is the mildly active galactic nucleus of the Large Magellanic Cloud. For this purpose the general properties of galactic nuclei and the characteristics of active nuclei are reviewed (Section 2). Examination of 30 Doradus shows that it plasy the same exceptional role among allHii-regions of the LMC as Sgr A among those of our Galaxy, and has all the properties of a galactic nucleus (luminosity, emission spectrum, IR source, semistellar central object R 136, symmetry centre of an starting point of spiral structure). Evidence for the activity is given by the peculiar filamentary structure (Figure 1), the young spiral filaments superposed on old, broad and smooth near-circular arms (Figure 2), the splitting of the [Oiii] 5007 profile in two components corresponding to an expansion velocity of 50 km s^–1, and the strong non-thermal component (Section 3). The mass loss of 30 Dor is estimated at 0.05M /a. It is speculated that the nucleus of a galaxy may be wandering due to explosive events.     

Das ProduktAR 0 und Weitere Galaktische Parameter

According to the tangential method the productAR ₀ is determined with 145.7 km s^–1 from measurements of the line profiles of the 21-cm line of the neutral hydrogen by Weaver and Williams (1973). The recent individual measurements of Oort's constantA and of the distanceR ₀ of the Sun from the galactic centre yields 138.5 km s^–1. The mean value 142.1 kms^–1 leads toA=14.56 km s^–1 kpc^–1 andR ₀=9.76 kpc. At the galactocentric distanceR nearR ₀ the angular velocity is represented by (R)=25.84–2.98 (R–9.76)+0.075 (R–9.76)². The mass of the Galaxy amounts to 1-92×10¹¹ .

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Herrn Kollegen Prof. Dr W. Gleisberg zum 70. Geburtstag am 26.12.1973 gewidmet.

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Mitteilungen Serie A.     

Spiral structure of galaxies two alternatives

At present the wave theory of the spiral structure of the galaxies includes two alternative viewpoints. Two types of spiral waves—short-wave and long-wave modes—can be excited. According to Lin and Shu (1964) the short-wave modeK is responsible for the spiral structure of the galaxies and, according to Marochniket al. (1972), the long-wave mode (K ₀). In our Galaxy theK -mode corresponds to the wave with an angular rotation velocity _p =11–13 kms^–1 kps^–1 and a radial group velocity directed from the periphery to the center. TheK ₀-mode corresponds to the wave having an angular rotation velocity _p =23 ± 3 kms^–1 kps^–1 and a radial group velocity directed from the center of the Galaxy to its periphery. The theoretical and observational evidences in favour of Marochniket al.'s (1972) model are given.     

An analysis of the longitudinal distribution of gamma rays from SAS-II data

An analysis of the longitudinal distribution of gamma rays from SAS-II data has been carried out using the available information on the gas distribution in the Galaxy. The overall distribution of cosmic rays in the galactic plane can be represented by an exponential function in galactocentric distance with a scale length of 8 kpc upto the solar circle and 10 kpc beyond. There is no evidence for a large gradient of the cosmic ray intensity in the outer parts of the Galaxy. The local emissivities of gamma rays in the energy regionsE >100 MeV and 35 MeV<E <100 MeV are (1.73±0.27)×10^–25 photon/(cm³ s n_H) and (2.40±0.41)×10^–25 photon/(cm³ s n_H) respectively. The contribution of °-decay gamma rays is 80% forE >100 MeV and 20% at lower energies. The electron spectrum required by this analysis has a power law spectral index of about –2.7 below a few hundred MeV. The observed gas distribution towards the galactic centre would predict a gamma-ray flux larger than observed. It is suggested that the molecular gas in the central region may be in the form of dense coudlets, in which low evergy cosmic rays do not penetrate; in this case the centre should be seen as a strong source only at high energies. An analysis of the radio sky survey map of the Galaxy at 408 MHz shows thatB varies with a scale-length of 40 kpc; no significance can be attached to the apparent deviation from the equipartition of energy densities between cosmic rays and magnetic field. The derived local emissivity is (1.46±0.28)×10^–40 W/((m³ Hz), which corresponds toB 5 G. The surface brightness of radio and gamma-ray emissions in the Galaxy decreases from the centre with scale-lengths 6 kpc and 7 kpc respectively. No positive correlation can be noticed with either co-rotation radius or pattern speed, when compared with external spiral galaxies.     

The scale and strength of the galactic magnetic field according to the pulsar data

In accordance with the data on the Faraday rotation, angular coordinates, and dispersion measurements and distances of 38 pulsars, the strengthB=2.1±1.1 G and directionl=99°±24°,b0° of the large-scale galactic magnetic field and the mean electron density in the galactic discN _e=0.03±0.01 cm^–3 are determined. A comparison with the results of a study of the measures of rotation of extragalactic radio sources enabled us to estimate the characteristic half-width of the distribution of the electron density on the Z-coordinate (h400 ps). The characteristic size of galactic magnetic field flucturations is shown to be =100–150 ps.     

The structure of the spiral arm S4 in andromeda galaxy

TheUBV photometry of 690 stars in the spiral arm S4 and the U magnitudes of 120 stars in the spiral arm S6 with the help of the 2 m RCC telescope of the Rozhen Observatory at the Bulgarian Academy of Sciences, has been used to obtain the colour-magnitude and colour-colour diagrams across the arms. Our age estimations are compared with van den Bergh's (1964). The age gradient across the S4 arm has been found. The colour excessE _B-V is highest at the inner edge of the arm S4. From the age we have evaluated the velocity of star formation propagation across the arm S4 60 km s^–1 , pattern frequency _p 14 km s^–1 kpc^–1 and corotation radiusR _c20 kpc. The structure of S4 along the arm is complicated. In the OB 82 region an age gradient is absent. The young associationOB 79b is located near the outer edge of S4 and it has a large absorptionA _v2^m.5 contrary to the density wave prediction. This association bears no relation to the spiral density wave and it is probably, supernova events that stimulated the star formation in it. The colour excessE _R-V is randomly distributed and the youngest stars are concentrated in the middle of the S6 arm. A value of pattern frequency _p = 12km s^–1 kpc^–1 andR _c=12 kpc of our Galaxy has been obtained from the age distribution of the open clusters and cepheids across the Carina-Sagittarius arm. The spiral structure of M31 is compared with that of the galaxy. There is a similarity between S4 in M31 and Carina-Sagittarius in the Galaxy, and also between the S6 and Perseus arms. The Orion arm in the Galaxy bears no relation to the wave density.     

A new estimate of the galactic halo mass based on the kinematics of globular clusters

We calculated the energy distribution function for globular clusters in our Galaxy, using the inversion procedure first suggested by Eddington. If the halo mass distribution is of the formM _H=r ^1.21, then the observed data on the velocity dispersion of F-clusters can be explained, resulting an enclosed mass of 4.3×10¹¹ M within a galactocentric radius of 33 kpc.     

Faraday rotation and the turbulent structure of the Galaxy

We extend Jokipii and Lerche's analysis of the turbulent structure of our Galaxy by means of a study of the rotation measure of extragalactic sources. Like them we use a simple, statistically homogeneous and isotropic disc model of the Galaxy and assume that the magnetic field has both an average component and a fluctuating one. We assume that the electron density is proportional to some power of the magnetic field (N _eB ⁿ with 1n2). Using the rotation measure data on 242 extragalactic sources given by Vallée and Kronberg we consider both an exponential and a Gaussian two-point correlation function for the (Gaussian) fluctuating component of the magnetic field with a correlation lengthL. We find reasonable agreement between theory and observations for an average magnetic field of about 3 G, a fluctuating magnetic field component with an amplitude of about 2.6G, an average electron density of about 0.03 cm^–3, a fluctuating density component of about 0.05 cm^–3, and a correlation length of about 300 pc.     

Large-scale flow of interstellar gas in galactic spiral waves: Effects of thermal balance and self-gravitation

Using the recent observational data on atomic and molecular hydrogen in the Galaxy, we analyse the dynamics of the interstellar gas in a spiral density wave. Within the framework of Marochniket al.'s (1972) model of the galactic spiral structure, the gas flow is obtained, with self-gravitation and thermal processes taken into account.It is shown that: (1) the self-gravitation of gas does not practically affect the galactic shock if the dominant contribution into the gas density comes from atomic hydrogen; (2) the effects of self-gravitation could be essential for both the gas flow and the stellar spiral wave only if the density contribution of H₂ exceeded several times that ofHi, with molecular hydrogen as a continuous medium having the isothermal equation of state; (3) however, regardless of the estimates of H₂ abundance in the Galaxy, its reaction to the density wave is weak, since it forms a collisionless system not dragged by the intercloud gas.It has been found that, if we allow for thermal processes in the interstellar medium, new types of gas flow can develop alongside with a previously-known continuous flow and galactic shock. They are: (1) galactic shock with the phase transition leading to the formation of dense cold clouds; (2) a three-phase flow where hot cavities and dense cold clouds coexist with an initial, moderately dense and cold phase; (3) an accretion wave which is a specific type of nonlinear wave with an amplitude of 11/2 orders of magnitude larger than that of the isothermal galactic shock appearing under the same conditions, but without heating and cooling.     

The frequency of novae in the Galaxy

Recent statistics indicate that each year an average of 3.5 novae or nova-like objects are discovered in the Galaxy. With reasonable assumptions about the completeness of the surveys, we arrive at an overall galactic production rate of 76±38 y^–1. When recurrent novae are omitted, this rate drops to 60±30 y^–1. Hence, it seems that our Galaxy is more prolific than M31 in nova production. The total amount of material released into galactic space by novae each year is about one-tenth that ejected by supernovae.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

On the formation of superdense gaseous cores in the nuclei of disk galaxies — I

A model for the formation of superdense gaseous cores by accretion in the nuclei of disk galaxies has been proposed. Equations for radial flow of gas into the nucleus in the presence of aweak galactic magnetic field have been solved, and time scales for the accretion of an exploding mass in the nucleus (10⁹ M ) have been obtained under several different situations in the absence of any rotation. The time scales are found to lie in the range between a few times 10⁷ yr and 10⁸ yr. Such time scales have been proposed by some authors for repeated explosions in the nuclei of galaxies; they have also proposed that spiral arms in disk galaxies are repeatedly formed and destroyed over such time scales. It is shown that the presence of rotational velocities in the infalling gas practically destroys the efficiency of the accretion process unless such velocities are dissipated by frictional forces within the system. Viscosity of gas is the most obvious dissipative agent. The problem of accretion of a rotating viscous gas will be discussed in a subsequent paper.     

Orbital eccentricity study for the spherical component of our galaxy

An analysis of the data concerning high-velocity stars from Eggen's catalogue aimed at a determination of the approximate slope of the mass function for the spherical component of our Galaxy, and at estimating the local circular velocity, as well as the local rotation velocity, as by-products, has been performed. Our conclusions are that:

1. A linear dependence of the mass on the radius is very likely;
2. the value of the limiting radius is most likely equal to (40±10) kpc;
3. the two local velocities are approximately equal to each other, being both equal to (230±30) km s^?1;
4. the local escape velocity appears to be most likely equal to (520±30) km s^?1;
5. the total mass of a corona, obtained in this way, is (5±1)×10¹¹ M _⊙.

     

Galactic longitude dependence of the intensity ratio of the diffuse interstellar absorption bands at λλ6180 and 4430

Equivalent widths, as published by Seddon, for the diffuse interstellar absorption band at 6180 are compared with photoelectric 4430 indices for ten stars in the northern Milky Way. The intensity ratio is found to depend on galactic longitude in a way similar to that found by Johnson for the ratioA _V /E _B–V of total to selective interstellar absorption.The dependence found, combined with deductions from a tentative identification of the bands as due to negative hydrogen, points to a direction for the galactic magnetic field that is in better agreement with the direction derived from rotation measures of extragalactic sources than with that based on the dust-hypothesis interpretation of interstellar optical polarization.