Minor stars in plane graphs with minimum degree five

The weight of a subgraph $H$ in $G$ is the sum of the degrees in $G$ of vertices of $H$. The {\em height} of a subgraph $H$ in $G$ is the maximum degree of vertices of $H$ in $G$. A star in a given graph is minor if its center has degree at most five in the given graph. Lebesgue (1940) gave an approximate description of minor $5$-stars in the class of normal plane maps with minimum degree five. In this paper, we give two descriptions of minor $5$-stars in plane graphs with minimum degree five. By these descriptions, we can extend several results and give some new results on the weight and height for some special plane graphs with minimum degree five.Comment: 11 pages, 3 figure

The "True" Column Density Distribution in Star-Forming Molecular Clouds

We use the COMPLETE Survey's observations of the Perseus star-forming region to assess and intercompare three methods for measuring column density in molecular clouds: extinction mapping (NIR); thermal emission mapping (FIR); and mapping the intensity of CO isotopologues. The structures shown by all three tracers are morphologically similar, but important differences exist. Dust-based measures give similar, log-normal, distributions for the full Perseus region, once careful calibration corrections are made. We also compare dust- and gas-based column density distributions for physically-meaningful sub-regions of Perseus, and we find significant variations in the distributions for those regions. Even though we have used 12CO data to estimate excitation temperatures, and we have corrected for opacity, the 13CO maps seem unable to give column distributions that consistently resemble those from dust measures. We have edited out the effects of the shell around the B-star HD 278942. In that shell's interior and in the parts where it overlaps the molecular cloud, there appears to be a dearth of 13CO, likely due either to 13CO not yet having had time to form in this young structure, and/or destruction of 13CO in the molecular cloud. We conclude that the use of either dust or gas measures of column density without extreme attention to calibration and artifacts is more perilous than even experts might normally admit. And, the use of 13CO to trace total column density in detail, even after proper calibration, is unavoidably limited in utility due to threshold, depletion, and opacity effects. If one's main aim is to map column density, then dust extinction seems the best probe. Linear fits amongst column density tracers are given, quantifying the inherent uncertainties in using one tracer (when compared with others). [abridged]Comment: Accepted in ApJ. 13 pages, 6 color figures. It includes small changes to improve clarity. For a version with high-resolution figures see http://www.cfa.harvard.edu/COMPLETE/papers/Goodman_ColumnDensity.pd

Clustering of the Diffuse Infrared Light from the COBE DIRBE maps. III. Power spectrum analysis and excess isotropic component of fluctuations

The cosmic infrared background (CIB) radiation is the cosmic repository for energy release throughout the history of the universe. Using the all-sky data from the COBE DIRBE instrument at wavelengths 1.25 - 100 mic we attempt to measure the CIB fluctuations. In the near-IR, foreground emission is dominated by small scale structure due to stars in the Galaxy. There we find a strong correlation between the amplitude of the fluctuations and Galactic latitude after removing bright foreground stars. Using data outside the Galactic plane ($|b| > 20\deg$) and away from the center ($90\deg< l <270\deg$) we extrapolate the amplitude of the fluctuations to cosec$|b|=0$. We find a positive intercept of $\delta F_{\rm rms} = 15.5^{+3.7}_{-7.0},5.9^{+1.6}_{-3.7}, 2.4^{+0.5}_{-0.9}, 2.0^{+0.25}_{-0.5}$ nW/m2/sr at 1.25, 2.2,3.5 and 4.9 mic respectively, where the errors are the range of 92% confidence limits. For color subtracted maps between band 1 and 2 we find the isotropic part of the fluctuations at $7.6^{+1.2}_{-2.4}$ nW/m2/sr. Based on detailed numerical and analytic models, this residual is not likely to originate from the Galaxy, our clipping algorithm, or instrumental noise. We demonstrate that the residuals from the fit used in the extrapolation are distributed isotropically and suggest that this extra variance may result from structure in the CIB. For 2\deg< \theta < 15^\deg, a power-spectrum analysis yields firm upper limits of (\theta/5^\deg) \times\delta F_{\rm rms} (\theta) < 6, 2.5, 0.8, 0.5 nW/m2/sr at 1.25, 2.2, 3.5 and 4.9 mic respectively. From 10-100 mic, the upper limits <1 nW/m2/sr.Comment: Ap.J., in press. 69 pages including 24 fig

Monte Carlo simulations of dusty spiral galaxies: extinction and polarization properties

We present Monte Carlo simulations of dusty spiral galaxies, modelled as bulge + disk systems, aimed to study their extinction and polarization properties. The extinction parameters (absorption and scattering) of dust grains are calculated from Mie's theory for a full distribution of sizes and materials; the radiation transfer is carried on for the four Stokes parameters. Photometric and polarimetric maps of galaxies of different optical depths, inclinations and bulge-to-total ratios have been produced in the B and I bandpasses. As expected, the effect of scattering is to reduce substantially the extinction for a given optical depth, in particular for what concerns the obscuration of bright bulge cores. For the same reason, scattering reduces also the reddening, as evaluated from B-I maps. On the other hand the bluing directly due to forward scattering is hardly appreciable. Radial color gradients are often found. A comparison with ``sandwich'' models shows that they fail dramatically to reproduce the extinction - optical depth relation. The degree of linear polarization produced by scattering is usually of the order of a few percent; it increases with optical depth, and with inclination (less than 80 degrees). The polarization pattern is always perpendicular to the major axis, unless the dust distribution is drastically modified. There is little local correlation between extinction and polarization degree and there is a trend of increasing polarization from the B to the I band. We discuss implications and relevance of the results for studies of the structure and morphology of spiral galaxies and of their interstellar medium.Comment: 43 pages, 13 Postscript figures, Latex AAS manuscript substyle, Ap. J. Accepte

Clustering of the Diffuse Infrared Light from the COBE DIRBE maps. I. C(0)C(0) and limits on the near-IR background

This paper is devoted to studying the CIB through its correlation properties. We studied the limits on CIB anisotropy in the near IR (1.25, 2.2, and 3.5 \um, or $J,\;K,\;L$) bands at a scale of 0.7\deg\ using the COBE\footnote{ The National Aeronautics and Space Administration/Goddard Space Flight Center (NASA/GSFC) is responsible for the design, development, and operation of the {\it COBE}. Scientific guidance is provided by the {\it COBE} Science Working Group. GSFC is also responsible for the development of the analysis software and for the production of the mission data sets.} Diffuse Infrared Background Experiment (DIRBE) data. In single bands we obtain the upper limits on the zero-lag correlation signal $C(0)= \langle(\nu \delta I_\nu)^2\rangle < 3.6 \times 10^{-16},\; 5.1 \times 10^{-17},\; 5.7 \times 10^{-18}$ \w2m4sr2 for the $J,K,L$ bands respectively. The DIRBE data exhibit a clear color between the various bands with a small dispersion. On the other hand most of the CIB is expected to come from redshifted galaxies and thus should have different color properties. We use this observation to develop a `color subtraction' method of linear combinations of maps at two different bands. This method is expected to suppress the dominant fluctuations from foreground stars and nearby galaxies, while not reducing (or perhaps even amplifying) the extragalactic contribution to $C(0)$. Applying this technique gives significantly lower and more isotropic limits.Comment: 44 pages postcript; includes 5 tables, 14 figures. Astrophysical Journal, in pres

Ionized and neutral gas in the peculiar star/cluster complex in NGC 6946

The characteristics of ionized and HI gas in the peculiar star/cluster complex in NGC 6946, obtained with the 6-m telescope (BTA) SAO RAS, the Gemini North telescope, and the Westerbork Synthesis Radio Telescope (WSRT), are presented. The complex is unusual as hosting a super star cluster, the most massive known in an apparently non-interacting giant galaxy. It contains a number of smaller clusters and is bordered by a sharp C-shaped rim. We found that the complex is additionally unusual in having peculiar gas kinematics. The velocity field of the ionized gas reveals a deep oval minimum, ~300 pc in size, centered 7" east of the supercluster. The Vr of the ionized gas in the dip center is 100 km/s lower than in its surroundings, and emission lines within the dip appear to be shock excited. This dip is near the center of an HI hole and a semi-ring of HII regions. The HI (and less certainly, HII) velocity fields reveal expansion, with the velocity reaching ~30 km/s at a distance about 300 pc from the center of expansion, which is near the deep minimum position. The super star cluster is at the western rim of the minimum. The sharp western rim of the whole complex is plausibly a manifestation of a regular dust arc along the complex edge. Different hypotheses about the complex and the Vr depression origins are discussed, including a HVC/dark mini-halo impact, a BCD galaxy merging, and a gas outflow due to release of energy from the supercluster stars.Comment: MN RAS, accepte

The Magnetic Field of L1544: I. Near-Infrared Polarimetry and the Non-Uniform Envelope

The magnetic field (B-field) of the starless dark cloud L1544 has been studied using near-infrared (NIR) background starlight polarimetry (BSP) and archival data in order to characterize the properties of the plane-of-sky B-field. NIR linear polarization measurements of over 1,700 stars were obtained in the H-band and 201 of these were also measured in the K-band. The NIR BSP properties are correlated with reddening, as traced using the RJCE (H-M) method, and with thermal dust emission from the L1544 cloud and envelope seen in Herschel maps. The NIR polarization position angles change at the location of the cloud and exhibit their lowest dispersion of position angles there, offering strong evidence that NIR polarization traces the plane-of-sky B-field of L1544. In this paper, the uniformity of the plane-of-sky B-field in the envelope region of L1544 is quantitatively assessed. This allowed evaluating the approach of assuming uniform field geometry when measuring relative mass-to-flux ratios in the cloud envelope and core based on averaging of the envelope radio Zeeman observations, as in Crutcher et al. (2009). In L1544, the NIR BSP shows the envelope B-field to be significantly non-uniform and likely not suitable for averaging Zeeman properties without treating intrinsic variations. Deeper analyses of the NIR BSP and related data sets, including estimates of the B-field strength and testing how it varies with position and gas density, are the subjects of later papers in this series.Comment: 16 pages, 9 figures; accepted for publication in The Astrophysical Journa

A three dimensional extinction map of the Galactic Anticentre from multi-band photometry

We present a three dimensional extinction map in $r$ band. The map has a spatial angular resolution, depending on latitude, between 3 -- 9\,arcmin and covers the entire XSTPS-GAC survey area of over 6,000\,$\rm deg^2$ for Galactic longitude $\rm 140 \leq$ $l$ $\leq 220\deg$ and latitude $\rm -40\leq$ $b$ $\leq 40\deg$. By cross-matching the photometric catalog of the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anticentre (XSTPS-GAC) with those of 2MASS and WISE, we have built a multi-band photometric stellar sample of about 30 million stars and applied spectral energy distribution (SED) fitting to the sample. By combining photometric data from the optical to the near-infrared, we are able to break the degeneracy between the intrinsic stellar colours and the amounts of extinction by dust grains for stars with high photometric accuracy, and trace the extinction as a function of distance for low Galactic latitude and thus highly extincted regions. This has allowed us to derive the best-fit extinction and distance information of more than 13 million stars, which are used to construct the three dimensional extinction map. We have also applied a Rayleigh-Jeans colour excess (RJCE) method to the data using the 2MASS and WISE colour $(H-W2)$. The resulting RJCE extinction map is consistent with the integrated two dimensional map deduced using the best-fit SED algorithm. However for individual stars, the amounts of extinction yielded by the RJCE method suffer from larger errors than those given by the best-fit SED algorithm.Comment: 20 pages, 18 figures, accepted in MNRA