We analyze the orbits of stars and dark matter particles in the halo of a disk galaxy formed in a cosmological hydrodynamical simulation. The halo is oblate within the inner ~20 kpc and triaxial beyond this radius. About 43% of orbits are short axis
tubes - the rest belong to orbit families that characterize triaxial potentials (boxes, long-axis tubes and chaotic orbits), but their shapes are close to axisymmetric. We find no evidence that the self-consistent distribution function of the nearly oblate inner halo is comprised primarily of axisymmetric short-axis tube orbits. Orbits of all families, and both types of particles are highly eccentric with mean eccentricity >0.6. We find that randomly selected samples of halo stars show no substructure in integrals of motion space. However individual accretion events can be clearly identified in plots of metallicity versus formation time. Dynamically young tidal debris is found primarily on a single type of orbit. However, stars associated with older satellites become chaotically mixed during the formation process (possibly due to scattering by the central bulge and disk, and baryonic processes), and appear on all four types of orbits. We find that the tidal debris in cosmological hydrodynamical simulations experiences significantly more chaotic evolution than in collisionless simulations, making it much harder to identify individual progenitors using phase space coordinates alone. However by combining information on stellar ages and chemical abundances with the orbital properties of halo stars in the underlying self-consistent potential, the identification of progenitors is likely to be possible.
Resolved surveys of the Milky Ways stellar halo can obtain all 6 phase space coordinates of tens of thousands of individual stars, making it possible to compute their 3-dimensional orbits. Spectral analysis of large numbers of halo orbits can be used
to construct frequency maps which are a compact, yet informative representation of their phase space distribution function (DF). Such maps can be used to infer the major types of orbit families that constitute the DF of stellar halo and their relative abundances. The structure of the frequency maps, especially the resonant orbits, reflects the formation history and shape of the dark matter potential and its orientation relative to the disk. The application of frequency analysis to cosmological hydrodynamic simulations of disk galaxies shows that the orbital families occupied by halo stars and dark matter particles are very similar, implying that stellar halo orbits can be used to constrain the DF of the dark matter halo, possibly impacting future direct dark matter detection experiments. An application of these methods to a sample of sim 16,000 Milky Way halo and thick disk stars from the SDSS-SEGUE survey yields a frequency map with strong evidence for resonant trapping of halo stars by the Milky Way disk, in a manner predicted by controlled simulations in which the disk grows adiabatically. The application of frequency analysis methods to current and future phase space data for Milky Way halo stars will provide new insights into the formation history of the dierent components of the Galaxy and the DF of the halo.
The phase space coordinates of individual halo stars obtained by Galactic surveys enable the computation of their full 3-dimensional orbits. Spectral analysis of halo orbits can be used to construct frequency maps which provide a compact representati
on of the 6-dimensional phase space distribution function. Frequency maps identify important major orbit families, and the orbital abundances reflect the shape and orientation of the dark matter halo relative to the disk. We apply spectral analysis to halo orbits in a series of controlled simulations of disk galaxies. Although the shape of the simulated halo varies with radius, frequency maps of local samples of halo orbits confined to the inner halo contain most of the information about the global shape of the halo and its major orbit families. Quiescent or adiabatic disk formation results in significant trapping of halo orbits in resonant orbit families (i.e. orbits with commensurable frequencies). If a good estimate of the Galactic potential in the inner halo (within ~50kpc) is available, the appearance of strong, stable resonances in frequency maps of halo orbits will allow us to determine the degree of resonant trapping induced by the disk potential. The locations and strengths of these resonant families are determined both by the global shape of the halo and its distribution function. Identification of such resonances in the Milky Ways stellar halo would therefore provide evidence of an extended period of adiabatic disk growth. If the Galactic potential is not known exactly, a measure of the diffusion rate of large sample of 10^4 halo orbits can help distinguish between the true potential and an incorrect potential. The orbital spectral analysis methods described in this paper provide a strong complementarity to existing methods for constraining the potential of the Milky Way halo and its stellar distribution function (ABRIDGED).
We summarize recent developments in the use of spectral methods for analyzing large numbers of orbits in N-body simulations to obtain insights into the global phase space structure of dark matter halos. The fundamental frequencies of oscillation of o
rbits can be used to understand the physical mechanism by which the shapes of dark matter halos evolve in response to the growth of central baryonic components. Halos change shape primarily because individual orbits change their shapes adiabatically in response to the growth of a baryonic component, with those at small radii become preferentially rounder. Chaotic scattering of orbits occurs only when the central point mass is very compact and is equally effective for centrophobic long-axis tube orbits as it is for centrophilic box orbits.
We study the evolution of phase-space density during the hierarchical structure formation of LCDM halos. We compute both a spherically-averaged surrogate for phase-space density (Q) and the coarse-grained distribution function f(x,v) for dark matter
particles that lie within~2 virial radii of four Milky-Way-sized dark matter halos. The estimated f(x,v) spans over four decades at any radius. Dark matter particles that end up within two virial radii of a Milky-Way-sized DM halo at $z=0$ have an approximately Gaussian distribution in log(f) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by a power-law in (1+z). The highest values of f are found at the centers of dark matter halos and subhalos, where f can be an order of magnitude higher than in the center of the main halo. The power-law Q(r) profile likely reflects the distribution of entropy (K = sigma^2/rho^{2/3} propto r^{1.2}), which dark matter acquires as it is accreted onto a growing halo. The estimated f(x, v), on the other hand, exhibits a more complicated behavior. Although the median coarse-grained phase-space density profile F(r) can be approximated by a power-law in the inner regions of halos and at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high-f material associated with surviving subhalos, as well as relatively unmixed material (probably in streams) resulting from disrupted subhalos, which contribute a sizable fraction of matter at large radii. (ABRIDGED)
We present a stellar dynamical estimate of the black hole (BH) mass in the Seyfert 1 galaxy, NGC 4151. We analyze ground-based spectroscopy as well as imaging data from the ground and space, and we construct 3-integral axisymmetric models in order to
constrain the BH mass and mass-to-light ratio. The dynamical models depend on the assumed inclination of the kinematic symmetry axis of the stellar bulge. In the case where the bulge is assumed to be viewed edge-on, the kinematical data give only an upper limit to the mass of the BH of ~4e7 M_sun (1 sigma). If the bulge kinematic axis is assumed to have the same inclination as the symmetry axis of the large-scale galaxy disk (i.e., 23 degrees relative to the line of sight), a best-fit dynamical mass between 4-5e7 M_sun is obtained. However, because of the poor quality of the fit when the bulge is assumed to be inclined (as determined by the noisiness of the chi^2 surface and its minimum value), and because we lack spectroscopic data that clearly resolves the BH sphere of influence, we consider our measurements to be tentative estimates of the dynamical BH mass. With this preliminary result, NGC 4151 is now among the small sample of galaxies in which the BH mass has been constrained from two independent techniques, and the mass values we find for both bulge inclinations are in reasonable agreement with the recent estimate from reverberation mapping (4.57[+0.57/-0.47]e7 M_sun) published by Bentz et al.
