We present the results from a detailed analysis of photometric and spectrophotometric data on five Seyfert 1 galaxies observed as a part of a recent reverberation mapping program. The data were collected at several observatories over a 140-day span beginning in 2010 August and ending in 2011 January. We obtained high sampling-rate light curves for Mrk 335, Mrk 1501, 3C 120, Mrk 6, and PG 2130+099, from which we have measured the time lag between variations in the 5100Å continuum and the Hβ broad emission line. We then used these measurements to calculate the mass of the supermassive black hole at the center of each of these galaxies. Our new measurements substantially improve previous measurements of M BH and the size of the broad line-emitting region for four sources and add a measurement for one new object. Our new measurements are consistent with photoionization physics regulating the location of the broad line region in active galactic nuclei.

We present velocity-resolved reverberation results for five active galactic nuclei. We recovered velocity-delay maps using the maximum entropy method for four objects: Mrk 335, Mrk 1501, 3C 120, and PG 2130+099. For the fifth, Mrk 6, we were only able to measure mean time delays in different velocity bins of the Hβ emission line. The four velocity-delay maps show unique dynamical signatures for each object. For 3C 120, the Balmer lines show kinematic signatures consistent with both an inclined disk and infalling gas, but the He ii λ4686 emission line is suggestive only of inflow. The Balmer lines in Mrk 335, Mrk 1501, and PG 2130+099 show signs of infalling gas, but the He ii emission in Mrk 335 is consistent with an inclined disk. We also see tentative evidence of combined virial motion and infalling gas from the velocity-binned analysis of Mrk 6. The maps for 3C 120 and Mrk 335 are two of the most clearly defined velocity-delay maps to date. These maps constitute a large increase in the number of objects for which we have resolved velocity-delay maps and provide evidence supporting the reliability of reverberation-based black hole mass measurements.

We investigate the timescales for stochasticity and chaotic mixing in a family of triaxial potentials that mimic the distribution of light in elliptical galaxies. Some of the models include central point masses designed to represent nuclear black holes. Most of the boxlike orbits are found to be stochastic, with mean Liapunov times that are 3È6 times the period of the long-axis orbit. In models with large cores or small black holes, the stochastic orbits mimic regular box orbits for at least hundreds of oscillations. However, a small core radius or signiÐcant black hole mass causes most of the stochastic orbits to di †use through phase space on the same timescale, visiting a signiÐcant fraction of the volume beneath the equipotential surface. Some stochastic orbits, with initial conditions lying close to those of regular orbits, remain trapped in all models.We estimate timescales for chaotic mixing in the more strongly stochastic models by evolving ensembles of 104 points until their distribution reaches a nearly steady state. Mixing initially takes place rapidly, with characteristic times of 10È30 dynamical times, as the phase points Ðll a region similar in shape to that of a box orbit. Subsequent mixing is slower, with characteristic times of hundreds of orbital periods. Mixing rates were found to be enhanced by the addition of modest force perturbations, and we propose that the stochastic parts of phase space might be efficiently mixed during the early phases of galaxy formation when such perturbations are large. The consequences for the structure and evolution of elliptical galaxies are discussed.

We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of 10^4 orbits, we numerically compute the three fundamental frequencies of the motion, allowing us to map out the Arnold web. We also compute diffusion rates of stochastic orbits in frequency space. The objects of fundamental importance in structuring phase space are found to be the 3-dimensional resonant tori; even when stable, such tori are not necessarily associated with periodic orbits as in systems with only two degrees of freedom. Boxlike orbits are generically stochastic, but some tube orbits are stochastic as well. The spectrum of diffusion rates for box-like orbits at a given energy is well approximated as a power law over at least six decades. Models with high central concentrations -- steep central cusps or massive black holes -- exhibit the most stochasticity. A black hole with a mass of 0.3% the mass of the galaxy is as effective as the steepest central density cusp at inducing stochastic diffusion. There is a transition to global stochasticity in box-like phase space when the mass of a central black hole exceeds 2% the galaxy mass. We predict a greater average degree of dynamical evolution in faint ellipticals, due to their high central densities and short crossing times. The evolution time is estimated to be shorter than a galaxy lifetime for absolute magnitudes fainter than about -19 or -20, consistent with the observed change in many elliptical galaxy properties at this luminosity.Comment: Revised version to appear in the Astrophysical Journal, vol 498, Oct 20 1998. Minor changes to text. References and 1 new figure added. 28 Latex pages, 22 Postscript figures, style file include

We present kinematics of 35 highly r-process-enhanced ([Eu/Fe] ≥ +0.7) metal-poor (−3.8 < [Fe/H] < −1.4) field stars. We calculate six-dimensional positions and velocities, evaluate energies and integrals of motion, and compute orbits for each of these stars using parallaxes and proper motions from the second Gaia data release and published radial velocities. All of these stars have halo kinematics. Most stars (66%) remain in the inner regions of the halo (< 13 kpc), and many (51%) have orbits that pass within 2.6 kpc of the Galactic center. Several stars (20%) have orbits that extend beyond 20 kpc, including one with an orbital apocenter larger than the Milky Way virial radius. We apply three clustering methods to search for structure in phase space, and we identify eight groups. No abundances are considered in the clustering process, but the [Fe/H] dispersions of the groups are smaller than would be expected by random chance. The orbital properties, clustering in phase space and metallicity, and lack of highly r-process-enhanced stars on disk-like orbits indicate that such stars likely were accreted from disrupted satellites. Comparison with the galaxy luminosity-metallicity relation suggests M V −9 for most of the progenitor satellites, characteristic of ultra-faint or low-luminosity classical dwarf spheroidal galaxies. Environments with low rates of star formation and Fe production, rather than the nature of the r-process site, may be key to obtaining the [Eu/Fe] ratios found in highly r-process-enhanced stars.

We investigate the ability of three-integral, axisymmetric, orbit-based modeling algorithms to recover the parameters defining the gravitational potential (mass-to-light ratio Ç and black hole mass M . ) in spheroidal stellar systems using stellar kinematical data. We show that the potential estimation problem is generically underdetermined when applied to long-slit kinematical data of the kind used for most black hole mass determinations to date. A range of parameters (Ç, M . ) can provide equally good fits to the data, making it impossible to assign bestfit values. The indeterminacy arises from the large variety of orbital solutions that are consistent with a given mass model. We demonstrate the indeterminacy using a variety of data sets derived from realistic models, as well as published observations of the galaxy M32. The indeterminacy becomes apparent only when a sufficiently large number of distinct orbits are supplied to the modeling algorithm; if too few orbits are used, spurious minima appear in the 2 ðÇ; M Þ contours, and these minima do not necessarily coincide with the parameters defining the gravitational potential. We show that the range of degeneracy in M . depends on the degree to which the data resolve the radius of influence r h of the black hole. For FWHM=2r h k 0:5, where FWHM refers to the instrumental resolution, we find that only very weak constraints can be placed on M . . In the case of M32, our reanalysis demonstrates that when a large orbit library is used, data published prior to 2000 (FWHM=2r h % 0:25) are equally consistent with black hole masses in the range 1:5  10 6 M < M < 5  10 6 M , with no preferred value in that range. Exactly the same data can reproduce previous published results with smaller orbit libraries. While the Hubble Space Telescope (HST ) Space Telescope Imaging Spectrograph (STIS) data for this galaxy (FWHM=2r h % 0:06) may overcome the degeneracy in M . , HST data for most galaxies do not resolve the black hole's sphere of influence and in these galaxies the degree of degeneracy allowed by the data may be greater than previously believed. We investigate the effect of regularization, or smoothness constraints, on the degree of degeneracy of the solutions. Enforcing smoothness reduces the range of acceptable models, but we find no indication that the true potential can be recovered simply by enforcing smoothing. For a given smoothing level, all solutions in the minimum 2 valley exhibit similar levels of noise; as the smoothing is increased, there is a systematic shift in the midpoint of the 2 valley, until at a high level of smoothing the solution is biased with respect to the true solution. These experiments suggest both that the indeterminacy is real (i.e., that it is not an artifact associated with nonsmooth solutions) and that there is no known empirical way to choose the smoothing parameter to ensure that the correct solution is selected.

The rotation curve of the Milky Way is commonly used to estimate the local dark matter density ρDM, . However, the estimates are subject to the choice of the distribution of baryons needed in this type of studies. In this work we explore several Galactic mass models that differ in the distribution of baryons and dark matter, in order to determine ρDM, . For this purpose we analyze the precise rotation curve measurements of the Milky Way up to ∼ 25 kpc from the Galactic centre obtained from Gaia DR2 [1]. We find that the estimated value of ρDM, stays robust to reasonable changes in the spherical dark matter halo. However, we show that ρDM, is affected by the choice of the model for the underlying baryonic components. In particular, we find that ρDM, is mostly sensitive to uncertainties in the disk components of the Galaxy. We also show that, when choosing one particular baryonic model, the estimate of ρDM, has an uncertainty of only about 10% of its best-fit value, but this uncertainty gets much bigger when we also consider the variation of the baryonic model. In particular, the rotation curve method does not allow to exclude the presence of an additional very thin component, that can increase ρDM, by more than a factor of 8. Therefore, we conclude that exclusively using the rotation curve of the Galaxy is not enough to provide a robust estimate of ρDM, . For all the models that we study without the presence of an additional thin component, our resulting estimates of the local dark matter density take values in the range ρDM, 0.3-0.4 GeV/cm 3 , consistent with many of the estimates in the literature.

Hubble Space Telescope (HST ) images and spectra of the nucleated dwarf elliptical galaxy NGC 205 are combined with three-integral axisymmetric dynamical models to constrain the mass M BH of a putative nuclear black hole. This is only the second attempt, after M33, to use resolved stellar kinematics to search for a nuclear black hole with mass below 10 6 solar masses. We are unable to identify a best-fit value of M BH in NGC 205; however, the data impose a upper limit of 2:2 ; 10 4 M (1 confidence) and an upper limit of 3:8 ; 10 4 M (3 confidence). This upper limit is consistent with the extrapolation of the M BH -relation to the M BH <10 6 M regime. If we assume that NGC 205 and M33 both contain nuclear black holes, the upper limits on M BH in the two galaxies imply a slope of $5.5 or greater for the M BH -relation. We use our three-integral models to evaluate the relaxation time and stellar collision time in NGC 205; T r is $10 8 yr or less in the nucleus, and T coll % 10 11 yr. The low value of T r is consistent with core collapse having already occurred, but we are unable to draw conclusions from nuclear morphology about the presence or absence of a massive black hole.