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Register a new userSelf-consistent potential-density pairs of thick disks and flattened galaxies
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J. An
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We analyze the Miyamoto--Nagai substitution, which was introduced over forty years ago to build models of thick disks and flattened elliptical galaxies. Through it, any spherical potential can be converted to an axisymmetric potential via the replacement of spherical polar $r^2$ with $R^2 + ( a + !sqrt{z^2+b^2} )^2$, where ($R,z$) are cylindrical coordinates and $a$ and $b$ are constants. We show that if the spherical potential has everywhere positive density, and satisfies some straightforward constraints, then the transformed model also corresponds to positive density everywhere. This is in sharp contradistinction to substitutions like $r^2 rightarrow R^2 + z^2/q^2$, which leads to simple potentials but can give negative densities. We use the Miyamoto--Nagai substitution to generate a number of new flattened models with analytic potential--density pairs. These include (i) a flattened model with an asymptotically flat rotation curve, which (unlike Binneys logarithmic model) is always non-negative for a wide-range of axis ratios, (ii) flattened generalizations of the hypervirial models which include Satohs disk as a limiting case and (iii) a flattened analogue of the Navarro--Frenk--White halo which has the cosmologically interesting density fall-off of (distance)$^{-3}$. Finally, we discuss properties of the prolate and triaxial generalizations of the Miyamoto-Nagai substitution.
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We present accurate models of the gravitational potential produced by a radially exponential disk mass distribution. The models are produced by combining three separate Miyamoto-Nagai disks. Such models have been used previously to model the disk of the Milky Way, but here we extend this framework to allow its application to disks of any mass, scalelength, and a wide range of thickness from infinitely thin to near spherical (ellipticities from 0 to 0.9). The models have the advantage of simplicity of implementation, and we expect faster run speeds over a double exponential disk treatment. The potentials are fully analytical, and differentiable at all points. The mass distribution of our models deviates from the radial mass distribution of a pure exponential disk by <0.4% out to 4 disk scalelengths, and <1.9% out to 10 disk scalelengths. We tabulate fitting parameters which facilitate construction of exponential disks for any scalelength, and a wide range of disk thickness (a user-friendly, web-based interface is also available). Our recipe is well suited for numerical modelling of the tidal effects of a giant disk galaxy on star clusters or dwarf galaxies. We consider three worked examples; the Milky Way thin and thick disk, and a disky dwarf galaxy.
Thick disks are faint and extended stellar components found around several disk galaxies including our Milky Way. The Milky Way thick disk, the only one studied in detail, contains mostly old disk stars (~10 Gyr), so that thick disks are likely to trace the early stages of disk evolution. Previous detections of thick disk stellar light in external galaxies have been originally made for early-type, edge-on galaxies but detailed 2D thick/thin disk decompositions have been reported for only a scant handful of mostly late-type disk galaxies. We present in this paper for the first time explicit 3D thick/thin disk decompositions characterising the presence and properties (eg scalelength and scaleheight) for a sample of eight lenticular galaxies by fitting 3D disk models to the data. For six out of the eight galaxies we were able to derive a consistent thin/thick disk model. The mean scaleheight of the thick disk is 3.6 times larger than that of the thin disk. The scalelength of the thick disk is about twice, and its central luminosity density between 3-10% of, the thin disk value. Both thin and thick disk are truncated at similar radii. This implies that thick disks extend over fewer scalelengths than thin disks, and turning a thin disk into a thick one requires therefore vertical but little radial heating. All these structural parameters are similar to thick disk parameters for later Hubble-type galaxies previously studied. We discuss our data in respect to present models for the origin of thick disks, either as pre- or post-thin-disk structures, providing new observational constraints.
We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous pair (a closed form expression) corresponding to a uniform disk, and a ``residual pair. This residual component is converted into an infinite series of integrals over the radial extent of the disk. For a certain class of surface density distributions (like power laws of the radius), this series is fully analytical. The extraction of the homogeneous pair is equivalent to a convergence acceleration technique, in a matematical sense. In the case of power law distributions, the convergence rate of the residual series is shown to be cubic inside the source. As a consequence, very accurate potential values are obtained by low order truncation of the series. At zero order, relative errors on potential values do not exceed a few percent typically, and scale with the order N of truncation as 1/N**3. This method is superior to the classical multipole expansion whose very slow convergence is often critical for most practical applications.
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We discuss the dense molecular gas in central regions of nearby Seyfert galaxies, and report new arcsec resolution observations of HCN(1-0) and HCO$^+$(1-0) for 3 objects. In NGC 3079 the lines show complex profiles as a result of self-absorption and saturated continuum absorption. H$^{13}$CN reveals the continuum absorption profile, with a peak close to the galaxys systemic velocity that traces disk rotation, and a second feature with a blue wing extending to $-350$km s$^{-1}$ that most likely traces a nuclear outflow. The morphological and spectral properties of the emission lines allow us to constrain the dense gas dynamics. We combine our kinematic analysis for these 3 objects, as well as another with archival data, with a previous comparable analysis of 4 other objects, to create a sample of 8 Seyferts. In 7 of these, the emission line kinematics imply thick disk structures on radial scales of $sim$100pc, suggesting such structures are a common occurrence. We find a relation between the circumnuclear LHCN and Mdyn that can be explained by a gas fraction of 10% and a conversion factor {alpha}HCN $sim$ 10 between gas mass and HCN luminosity. Finally, adopting a different perspective to probe the physical properties of the gas around AGN, we report on an analysis of molecular line ratios which indicates that the clouds in this region are not self-gravitating.
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