Stellar Velocity Dispersion and Black Hole Mass in the Blazar Markarian 501

The recently discovered correlation between black hole mass and stellar velocity dispersion provides a new method to determine the masses of black holes in active galaxies. We have obtained optical spectra of Markarian 501, a nearby gamma-ray blazar with emission extending to TeV energies. The stellar velocity dispersion of the host galaxy, measured from the calcium triplet lines in a 2"x3.7" aperture, is 372 +/- 18 km/s. If Mrk 501 follows the M-sigma correlation defined for local galaxies, then its central black hole has a mass of (0.9-3.4)x10^9 solar masses. This is significantly larger than some previous estimates for the central mass in Mrk 501 that have been based on models for its nonthermal emission. The host galaxy luminosity implies a black hole of 6x10^8 solar masses, but this is not in severe conflict with the mass derived from the M-sigma relation because the M_BH-L_bulge correlation has a large intrinsic scatter. Using the emission-line luminosity to estimate the bolometric luminosity of the central engine, we find that Mrk 501 radiates at an extremely sub-Eddington level of L/L_Edd ~ 10^-4. Further applications of the M-sigma relation to radio-loud active galactic nuclei may be useful for interpreting unified models and understanding the relationship between radio galaxies and BL Lac objects.Comment: To appear in ApJ Letters. 5 pages, 2 figure

Manufactured analytical solutions for isothermal full-Stokes ice sheet models

We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. <br><br> The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions

Effects of spatial non-uniformity on laser dynamics

Semiclassical equations of lasing dynamics are re-derived for a lasing medium in a cavity with a spatially non-uniform dielectric constant. It is shown that the non-uniformity causes a radiative coupling between modes of the empty cavity. This coupling results in a renormalization of self- and cross-saturation coefficients, which acquire a non-trivial dependence on the pumping intensity. Possible manifestations of these effects in random lasers are discussed.Comment: 4 pages, 1 figure, LaTex. Introduction is significantly rewritten, and the results is placed in the context of random lasin

The structure and dynamics of the dense cores in the Perseus molecular cloud complex

We have produced wide-field (≳ 0.1 deg^2) images of the molecular gas around the dense cores observed by Ladd et al. (1994) in the Perseus cloud complex in various CO (CO(1-0), ^(13)CO(1-0), C^(18)O(1-0)) and CS (CS(2-1), C^(34)S(2-1)) isotopomers, and N_2H^+(1-0), using the 16-element focal plane array operating at a wavelength of 3 mm at the Five College Radio Astronomy Observatory. We also performed mosaic observations in the N_2H^+(1-0) line and in the adjacent 3 mm continuum with the OVRO interferometer. Only within one of the observed cores we unambiguously detected a 3 mm continuum compact source with the interferometer. The single-dish large-scale maps of the densest gas, which in Perseus is concentrated within two large filamentary structures roughly aligned along a NE-SW axis, allowed us to analyse the spatial and kinematical properties of the cores and of the surrounding ambient gas. In the PER4/PER5 and PER7 regions we find that the large-scale and core velocity gradients have the same sign and similar magnitudes. In at least three cases we then find pairs of nearby cores with differences in the CS and N_2H^+ emission and in the line profile, which may have been caused by evolutionary effects. The small fraction of cores with compact continuum sources, the chemical differentiation and the inward motions observed suggest that we are observing objects in a phase preceeding the collapse and the formation of stars