Statistical survey of planetary nebulae: Distances,masses, and distribution in the galaxy

On the basis of empirical (D)-dependency at the frequency of 5 GHz constructed using 15 planetary nebulae with the independently measured distances (10^–171×10^–20 W m^–2 Hz^–1 ster^–1), we evaluated distances of 335 objects. Independent evidence of the correctness of the accepted scale are given. Then(D)-dependency is constructed and it is shown that atD<0.08 pc the mean electron density is higher than the one determined by the Seaton method. We showed that the filling factor diminishes with the increase of the PN diameter (1 atD0.08 pc and 0.2 atD0.4 pc). the ionized mass of 33 PNs is determined. With the diameter increase the ionized mass grows and atD0.4 pc reaches the valueM0.07M . We used the new distance scale when investigating the space distribution of PNs. The mean scale height =130±15 pc and the mean gradient of the change of surface densitym=0.37, which allowed us to estimate the total number of nebulae in the GalaxyN4×10⁴. We divided the PNs according to their velocities (withV _LSR>35 km s^–1 andV _LSR<35 km s^–1) and permitted us to confirm that the PN belong to different sub-systems of the Galaxy. The estimated local formation rate of PNs [=(4.6±2.2)×10^–12 pc^–3 yr^–1] is a little higher than the one of the white dwarfs. That can be explained by a large number of PNs having binary cores, which used in our sample. The statistical estimation of PN expansion velocity showed thatV _ex increases from 5–7 km s^–1 (atD0.03 pc) to 40–50 km s^–1 (atD0.8 pc).     

On the acceleration of interstellar grains

Dust grains of radiir _g 3×10^–6 cm, injected into the intercloud medium at speeds in the range 10⁷–10⁸ cm s^–1, may be stochastically accelerated to speeds 0.1c due to scattering by irregularities in the galactic magnetic field.     

General-relativistic hierarchical cosmology: An exact model

An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R ^–2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R ^–, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.     

Compact,variable sources on the Sun at 2 centimeter wavelength

Very Large Array (VLA) observations of compact transient sources on the Sun at 2 cm wavelength are presented. These sources have angular sizes of 5–25, brightness temperatures of T _B 1–3 × 10⁵ K, and lifetimes ranging between a few minutes to several hours. The emission originates in regions of diffuse plage and quiet Sun, where the photospheric magnetic fields are relatively weak (H 100 G). In some cases the 2 cm radiation may be explained as the thermal bremsstrahlung of a dense (N _e 10¹⁰ cm^-3) plasma in the transition region. For other sources, the relatively high circular polarization ( _c 40–50 %) suggests a nonthermal emission mechanism, such as the gyrosynchrotron radiation of mildly relativistic electron with a power-law spectrum.     

A Molecular Ring in the Liner Ngc 5218

High resolution OVRO CO 1–0 observations of the inner 30 in the LINER galaxy NGC 5218 reveal the presence of a double centrally peaked molecular concentration with extensions out to a radius of 12. The molecular mass detected is 2.4 × 10⁹ M and the gas surface density is high, 3000 M pc square in the inner 500 pc. The SFR is 2–3 M yr^–1 and the SFE is 13, which are low or moderate values for that gas surface density. We interpret the inner feature as a rotating molecular ring with a radius of 200 pc. We furthermore suggest that the LINER activity in NGC 5218 is not caused by an aging starburst, but by a buried AGN.     

A study of the wavelength dependence of interstellar polarization using a scanning spectropolarimeter

A scanning spectropolarimeter has been constructed and used in a preliminary search for conspicuous features of the interstellar polarization curve between ^–1 = 1.58 ^–1 and 2.50 ^–1. The instrument was used at thef/4.5 prime focus of the 36 telescope of the Cambridge University Observatories. Scans were made on HD2905, HD21389, And and Tau with slitwidths of 50 Å and 100 Å.The commonly adopted method of correcting for instrumental polarisation by using observations of unpolarized stars has been applied. The normalized polarization curves corrected for instrumental polarization for HD2905 and HD21389 reveal a feature near ^–1 = 1.68 ^–1 which is most probably of insterstellar rather than instrumental origin.     

Almost stable regions for an area-preserving mapping

The area preserving mapping x = x + a(y – y ³), y = y – a(x – x³), for 0.3 a 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).     

Spectrum of the galactic magnetic fields

The magnetic fields observed in the galactic disc are generated by the differential rotation and the helical turbulent motions of interstellar gas. On the scalesl=2k ^–1 which lie in the intervall ₀<l<l _e (l ₀100 pc is the energy-range scale of the galactic turbulence), the spectral density of the kinetic energy of turbulence (k ^–5/3) exceeds the magnetic energy spectral density (k ^–1). The equipartition between magnetic and kinetic energies is reached atl=l _e 6 pc in the intercloud medium and is maintained down to the scalel=l _d 0.03 pc. In dense interstellar cloudsl _e is determined by the individual cloud size andl _d 0.1 pc.The internal turbulent velocities in Hi clouds (cloud size is assumed to be 10 pc) lie in the range from 1.8 to 5.6km s^–1, fitting well within the observed range of internal rms velocities. Dissipation of the interstellar MHD turbulence leads to creation of temperature fluctuations with amplitudes of 150 K and 65 K in dense clouds and intercloud medium, respectively. The small-scale fluctuations observed in the interstellar medium may arise from such perturbations due to the thermal instability, for instance. Dissipation of the MHD turbulence energy provides nearly half of the energy supply needed to maintain the thermal balance of the interstellar medium.     

Annihilation radiation from a power-law distributed electron-positron plasma on the ground Landau level: the case of low magnetic fields

Intensity, polarization, and cooling rate of the two-photon annihilation radiation are studied in detail in the case of one-dimensional power-law distributions of electrons and positrons, assuming that they occupy the ground Landau level in a strong magnetic fieldB10¹⁰–10¹² G. Simple analytical expressions for limiting cases are obtained and results of numerical calculations of radiation characteristics are presented. Power-lawe ^± distributions _{± ±} ^–k are shown to generate power-law spectra of the annihilation radiation atEmc ² andEmc ², with indices depending on the direction of radiation. The annihilation spectra at =0 show the largest blue-shifts of their maxima and the hardest high-energy tailsI(Emc ², =0)E ^–(k–1). The blue-shifts reduce, and the hard tials steepen, with increasing . At >(2mc ²/E)^1/2 the slopes of the high-energy tails rapidly transform to that at =2,I(Emc ², =/2)E ^–(2k+3). The direction-integrated spectraS(E) also display the power-law tials at low and high energies,S(Emc ²)E ^–(k+1). The total annihilation rate and energy losses decrease with decreasingk, being higher than for the isotropice ^± power-law distributions at the samek. The radiation is linearly polarized in the plane formed by the magnetic field and wave-vector. The polarization degreeP is maximum atEmc ²:P _max0.6 for =/2. Annihilation features and power-law-like hard tails observed in many gamma-ray burst spectra may be associated with the annihilation radiation of the magnetized power-law distributed plasma near neutron stars. Comparison of the observed and theoretical spectra allows one to estimate the power-law index of thee ^– e ⁺-distribution and the gravitational redshift factor in the radiating region.     

On the inability of magnetically constricted transition regions to account for the 105 to 106 K plasma in the quiet solar atmosphere

Although back conduction from the corona has been shown to be inadequate for powering EUV emission below T 2 × 10⁵ K, it is thought to be adequate in the temperature range 2 × 10⁵ K < T < 10⁶ K. No models to date, however, have included the large magnetic constriction which should occur in the legs of coronal loops where conductive transition regions, hitherto thought to contain the bulk of the plasma in this higher temperature range, are located. On the basis of fine scale magnetograms, Dowdy et al. (1986) have estimated that these magnetic flux tubes are constricted from end to end by an areal factor of approximately 100. Furthermore, on the basis of simple steady-state conductive models, Dowdy et al. (1985) have shown that the large constriction can inhibit the conductive flow of heat by an order of magnitude. We are thus led to re-examine static models of this region of the atmosphere which incorporate not only conduction and radiation but also the effects of large magnetic constrictions. We find that the structure of this plasma depends not only on the magnitude of the constriction but also on the tube's shape.Our results show that no model with a constriction of order 100 can simultaneously (a) produce the variation of differential emission measure with temperature derived from measured line intensities and (b) satisfy the observed constraint (Reeves, 1976) that EUV emission from below T 7 × 10⁵ K be confined to the supergranular network, covering no more than 0.45 of the solar surface. The failure of the models suggests that the bulk of the 10⁵–10⁶ K plasma in the quiet solar atmosphere is not in transition region structures, but is instead magnetically isolated from the corona and heated internally. Even though the transition region component of 10⁵–10⁶ K plasma in the legs of coronal loops should exist, it comprises only a small fraction of the total 10⁵–10⁶ K plasma and, hence, produces only a small fraction of the observed EUV emission from this temperature range.We also find that for any permitted tube shape, constriction factors of order 100 reduce the coronal conductive energy losses to the transition region to a value which is less than a third of the value for an unconstricted field, i.e., to less than 2 × 10⁵ erg cm ^–2 s ^–1. In particular, if the magnetic geometry of the upper transition region is extremely concave (i.e., horn-shaped geometry with most of the areal divergence near the hot end), then a constriction of order 100 results in a conductive loss of less than 1 × 10⁴ erg cm^–2 s^–1 and, hence, much less than the coronal radiative energy loss. For such geometries, the constriction in the magnetic field hence provides an effective thermal insulation of the corona from the cooler parts of the solar atmosphere.Presidential Young Investigator.     

The spatial distribution and birth-rate of pulsars

The distribution of pulsars in the wide range of observed luminosities has been obtained. It is shown that the function of luminosity (FL) within 3×10²⁶L2×10³⁰ erg s^–1 conforms to the power law dN/dL–c ₁ L ^–, where =1.76±0.06. ForL3×10²⁶ erg s^–1, FL changes its inclination and may be approximated as , where ₁ = 0.7±0.2. On the basis of statistical selection, including all pulsars withL>3×10²⁸ erg s^–1, the distribution of pulsars has been investigated as a function of the distance to the centreR and galactic planeZ.The obtained laws of the radial andZ-distribution of pulsars and galactic supernova remnants and also the radial distribution of types I and II supernovae in the models Sb and Sc support the hypothesis of their origin from the objects of the flat subsystem of Population I. Since there are some arguments in favour of a possible connection between supernovae I and the objects of the intermediate component of the Galaxy, one cannot exclude the possibility of supernovae explosions at the end of the evolution of stars with masses of 1.5–2M . It is also shown that pulsars and supernovae are evidently objects that are connected genetically, and, within the limits of statistical error, they have a similar birth-rate.The empirical law of the evolution of a pulsar's luminosity as a function of its true age has been obtained, according to whichL=c ₂ t ^–, wherec ₂=(3.69±3.4)×10³⁵, =1.32±0.11.     

CH3CN J = 8 − 7 and CS J = 3 − 2 emission in orion KL

The data of the line series CH₃CN 8(K) – 7(K) K = 0 – 7 and line CS J = 3 – 2 were taken simultaneously. At beam size of 16 the emissions of CH₃CN and CS have a common center position located near IRc2 with deviations -8 and 5. The observed data show that in Orion KL core the integrated intensities of the two species have double peaks separated by a space of 14. The 2-dimension Gaussian fitting plots (FWHM) are ellipses ofD _maj = 26 andD _min = 22 for CH₃CN 8(K) – 7(K) K = 3 – 6 andD_maj = 39 D_min = 31 for CS J = 3 – 2 at a distance about 450 pc. Towards the multiple line emission region of CH₃CN 8(K) – 7(K) K = 3 – 6, using a simplified very large velocity gradient model to solve the statistical equilibrium and radiative transfer equations, we find to fit the observed results, the optimum physical parameters and kinetic temperatureT _k 120 K, densityn(H _a) 1.2 × 10⁵ cm^–3, velocity gradientV _gr 92 km s^–1 pc^–1 and the local abundance of CH₃CNF _ab 3 × 10^–8. However towards the region of single line emission of CS J = 3 – 2 we have to use LTE and the optical thin approximation on the assumption ofT _k= 120 K to obtain the lower limits of column density and then, an averaged abundance of CS of 6 × 10^–8.     

The densest prestellar condensations: H2CO Studies ofρ Oph B1

We present new images of the well-known molecular outflow and Herbig-Haro complex L 1551-IRS 5. Deep, high-resolution images of the central region of the flow in [SII] 6716,6731 and H (6565 Å) are complemented by a mosaic of much of the CO outflow in H₂ v=1-0 S(1). While the optical data trace the intermediate-to-high excitation shocks in the flow (v _shock > 30 – 50 km s^–1), the near-IR data reveal the lower-excitation, molecular shocks (v _shock 10–50 km s^–1). In particular, the H₂ data highlight the regions where the flow impacts and shocks ambient molecular gas.     

r-Centroids and Franck-Condon factors of the CP,SiC, and CO+ molecules

Ther-centroids and Franck-Condon factors for the bands of theA ² –X ²⁺ of CP,C ³ –X ³ of SiC, andB ²⁺ –X ²⁺ of CO⁺ molecules have been determined. The Franck-Condon factors are evaluated by the approximate analytical method of Jarmain and Fraser. The absence of the bands in these systems is explained.     

The solar continuum from 900 to 130 000 Å and the photospheric temperature model

In order to obtain a better agreement between observed and computed values of the solar intensity, an improved temperature distribution is deduced for the range 0.02<0< 10. The intensity observations here considered refer to the wavelength region between 1980 and 129 500, and the center-limb variations generally go down to cos = 0.1. The improved model, given in Figure 4 and Table II, differs rather little from the Utrecht 1964 model, used here as a reference.It appears necessary to introduce an empirical correction function to be applied to the continuous absorption coefficient. This function was derived for the spectral region between 2000 and 130000 Å; it is shown in Figure 5.Furthermore, an extension of the model (1.10^–7<0< 2.10^–2) is deduced (see Table III and Figure 8), which reasonably well represents the observations of the ultraviolet solar flux ( 900–1700 Å).     

An Erupting Active Region Filament: Three-Dimensional Trajectory and Hydrogen Column Density

From 15:33 through 16:02 UT on 13 June 1998, observations of an erupting filament as it crossed solar disk center were obtained with the NSO/KPVT and SOHO/CDS instruments as part of the SOHO Joint Observing Program 70. Context observations show that this event was the eruption of the north-east section of a small active region filament associated with NOAA 8237, that the photospheric magnetic field was changing in this active region between 12–14 June 1998, and that a coronal Moreton-wave disk event occurred, as well as a white-light CME off the south-west solar limb. The NSO/KPVT imaging spectroscopy data covered 512 × 512 arc sec of the disk center and were spectrally centered at the Hei 1083 nm line and captured ±1.0 nm of surrounding solar spectrum. The Hei absorption line is seen blue-shifted to velocities of between 200 and 300 km s^–1. The true solar trajectory of the eruption is obtained by using the projected solar coordinates and by integrating the Doppler velocity. The filament travels with a total velocity of about 300 km s^–1 along a path inclined roughly 49 deg to the solar surface and rises to a height of just over 1.5 solar radii before it becomes too diffuse to follow. The filament also shows internal motions with multiple Doppler components shifted by ±25 km s^–1. Finally, the KPVT data show no Stokes V profiles in the Doppler-shifted Hei 1083.03 nm absorption to a limit of roughly 3×10^–3 times the continuum intensity. The SOHO/CDS scanned the center of the KPVT FOV using seven EUV lines; Doppler-shifted filament emission is seen in lines from Hei 58.4 nm, Heii 30.4 nm, Oiv 55.5 nm, Ov 63.0 nm, Nevi 56.3 nm, and Mgx 61.0 nm representing temperatures from about 2×10⁴K through 1×10⁶K. Bound-free continuum absorption from Hi, without confusion from foreground emission and line emission, is seen as the filament obscures underlying chromospheric emission. A fit to the wavelength dependence of the absorption from five lines between 55.5 to 63.0 nm yields a column density _H I =4.8±2.5×10¹⁷ cm^–2. Spatial maps show that this filament absorption is more confined than the regions which show emission.     

Pulsar dispersion measures and the mean and mean-squared interstellar electron density

Theoretical distributions of pulsar dispersion measures (times sinb ^II) are computed for various assumed pulsar spatial distributions above (and below) the galactic plane, assuming a distribution for the ionized gas. The statistics on the twelve high-latitude pulsars lead to the conclusion that the pulsar distribution inz is at least as broad as the distribution of the ionized gas. The value derived for the local mean interstellar electron density in the galactic plane is 0.12 cm^–3 and is interpreted to be due to a uniform ionized intercloud medium.Interstellar absorption of radio waves at low frequencies and cosmic X-rays at low energies are considered with regard to irregularities in the distribution of ionized gas. It is shown that if the obervations are made with a wide angle receiver the effective absorption optical deph is –²/2 where is the mean value and is the dispersion in . This relation assumes is much larger than . Analysis of recent low-frequency radio measurements from a satellite-borne receiver, however, leads to the conclusion that effects of irregulatirities are large.     

Anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R , the major axis scattering angle is 0.7 at =6 cm and it varies with heliocentric distance asR ^–1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to =20 cm, has a value 20±7 at 5R and varies with heliocentric distance asR ^–3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scales sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R and 4 km at 13R . These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times t between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail (t) for large waiting times (t>10hours). It is shown that the power-law index varies with the solar cycle. For the minimum phase of the cycle the index is =–1.4±0.1, and for the maximum phase of the cycle the index is –3.2±0.2. For all years 1975–2001, the index is –2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate (t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(), the time distribution of the rate . If f() has a power-law form for low rates, the waiting time-distribution is predicted to have a power-law tail (t)^–(3+) (>–3). Distributions f() are constructed from the GOES data. For the entire catalog a power-law index =–0.9±0.1 is found in the time distribution of rates for low rates (<0.1hours ^–1). For the maximum and minimum phases power-law indices =–0.1±0.5 and =–1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices –2.2±0.1 (1975–2001), –2.9±0.5 (maximum phase) and –1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.     

Thermal bifurcation in the upper photosphere inferred from heterodyne spectroscopy of OH rotational lines

We have obtained low noise (S/N > 10³), high spectral resolution (/ 10 ⁶) observations of two pure rotation transitions of OH from the solar photosphere. The observations were obtained using the technique of optically null-balanced infrared heterodyne spectroscopy, and consist of center-to-limb line profiles of a = 1 and a = 0 transition near 12 m. These lines should be formed in local thermodynamic equilibrium (LTE), and are diagnostics of the thermal structure of the upper photosphere. We find that the = 0R22(24.5)e line strengthens at the solar limb, in contradiction to the predictions of current one-dimensional photospheric models. Our data for this line support a two-dimensional model in which horizontal thermal fluctuations of order ±800 K occur in the region ₅₀₀₀ 10^–3–10^–2. This thermal bifurcation may be maintained by the presence of magnetic flux tubes, and may be related to the solar limb extensions observed in the 30–200 m region.Observations of the = 1R11(29.5)f line, at 885.643 cm^–1, show that it is anomalously weak in the photospheric spectrum. We argue that the source function in the core of this line has been substantially increased by interaction with the 9j-7i transition of Mgi at 885.524 cm^–1, which is itself too weak to appear in the disk center spectrum.Visiting Astronomer, Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation.