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The paradox of the scale-free discs
Scale-free discs have no preferred length or time-scale. The questionhas been raised whether such discs have a continuum of unstable linearmodes or perhaps no unstable modes at all. We resolve this paradox byanalysing the particular case of a gaseous, isentropic disc with acompletely flat rotation curve (the Mestel disc) exactly. The heart ofthe matter is this: what are the correct boundary conditions to imposeat the origin or central cusp? We argue that the linear stabilityproblem is ill-posed and that similar ambiguities may afflict generaldisc models with power-law central cusps. From any finite radius, wavesreach the origin after finite time but with logarithmically divergentphase. Instabilities exist, but their pattern speeds depend upon anundetermined phase with which waves are reflected from the origin. Forany definite choice of this phase, there is an infinite but discrete setof growing modes. The ratio of growth rate to pattern speed isindependent of the central phase. This ratio is derived in closed formfor non-self-gravitating normal modes and is shown to agree withapproximate results obtained from the shearing sheet in theshort-wavelength limit. This provides the first exact, analyticallysolved stability analysis for a differentially rotating disc. Forself-gravitating normal modes, the ratio of growth rate to pattern isfound numerically by solving recurrence relations in Mellin-transformspace.
| An image database. II. Catalogue between δ=-30deg and δ=70deg.
A preliminary list of 68.040 galaxies was built from extraction of35.841 digitized images of the Palomar Sky Survey (Paper I). For eachgalaxy, the basic parameters are obtained: coordinates, diameter, axisratio, total magnitude, position angle. On this preliminary list, weapply severe selection rules to get a catalog of 28.000 galaxies, wellidentified and well documented. For each parameter, a comparison is madewith standard measurements. The accuracy of the raw photometricparameters is quite good despite of the simplicity of the method.Without any local correction, the standard error on the total magnitudeis about 0.5 magnitude up to a total magnitude of B_T_=17. Significantsecondary effects are detected concerning the magnitudes: distance toplate center effect and air-mass effect.
| The CfA Redshift Survey: Data for the NGP +36 Zone
We have assembled redshifts for a complete sample of 719 galaxies withm_zw_ <= 15.5 in the declination range 32.5^deg^ <= δ <=38.5^deg^ and right ascension range 8^h^ <= α <= 17^h^. Wehave determined morphological types for all galaxies in the magnitudelimited sample by direct inspection of the POSS-O plates. 576 of theredshifts are measurements from Mount Hopkins, and 405 are newredshifts. We also include new redshifts for 77 fainter galaxies in thesame strip.
| Galaxy Properties at the North Galactic Pole. I. Photometric Properties on Large Spatial Scales
A two-color study of the galaxies detected on POSS-I in a 289 squaredegree region centered on the North Galactic Pole is presented. We use avariety of mapping techniques to characterize the large-scale spatialdistribution of galaxies. The depth and sample size of this new surveyallows, for the first time, the isolation of large photometricsubsamples of galaxies in high- and low-density environments on thescale of superclusters. Our principal finding is a statisticallysignificant difference between the mean photometric properties of thesesubsamples in the sense that galaxies in the high-density Coma andfilament environments have redder colors and larger concentrationindices than galaxies drawn from low-density interfilament regions.These results are in accord with the known morphology-density relation.Thus, appropriately chosen photometric and morphological parameters, inconcert with a galaxy surface density map, can be used to selectstructures from the projected galaxy distribution which correspond toregions of high density. An illustration of this point is our discoveryof a concentration of blue galaxies identified in our maps near the coreof the Coma cluster. This feature is comprised of early-type galaxieswhich exhibit signs of current or recent star formation. These resultsare predicated on relations between morphological type and photometricparameters derived from APS scans of POSS-I. We therefore discuss theimage calibration procedures used to compile our catalog of physicallysignificant photometric parameters. We demonstrate the morphologicaltype dependence among quantities such as mean color and imageconcentration index, and the lack of such a dependence for mean surfacebrightness.
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