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Register a new userEccentric Nuclear Disks with Self Gravity: Predictions for the Double Nucleus of M31
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We present a method for constructing models of weakly self-gravitating, finite dispersion eccentric stellar disks around central black holes. The disk is stationary in a frame rotating at a constant precession speed. The stars populate quasiperiodic orbits whose parents are numerically integrated periodic orbits in the total potential. We approximate the quasiperiodic orbits by distributions of Kepler orbits dispersed in eccentricity and orientation, using an approximate phase space distribution function written in terms of the Kepler integrals of motion. We show an example of a model with properties similar to those of the double nucleus of M31. The properties of our models are primarily determined by the behavior of the periodic orbits. Self-gravity in the disk causes these orbits to assume a characteristic radial eccentricity profile, which gives rise to distinctive multi-peaked line-of-sight velocity distributions (LOSVDs) along lines of sight near the black hole. The multi-peaked features should be observable in M31 at the resolution of STIS. These features provide the best means of identifying an eccentric nuclear disk in M31, and can be used to constrain the disk properties and black hole mass.
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We construct dynamical models of the ``double nucleus of M31 in which the nucleus consists of an eccentric disk of stars orbiting a central black hole. The principal approximation in these models is that the disk stars travel in a Kepler potential, i.e., we neglect the mass of the disk relative to the black hole. We consider both ``aligned models, in which the eccentric disk lies in the plane of the large-scale M31 disk, and ``non-aligned models, in which the orientation of the eccentric disk is fitted to the data. Both types of model can reproduce the double structure and overall morphology seen in Hubble Space Telescope photometry. In comparison with the best available ground-based spectroscopy, the models reproduce the asymmetric rotation curve, the peak height of the dispersion profile, and the qualitative behavior of the Gauss-Hermite coefficients h_3 and h_4. Aligned models fail to reproduce the observation that the surface brightness at P1 is higher than at P2 and yield significantly poorer fits to the kinematics; thus we favor non-aligned models. Eccentric-disk models fitted to ground-based spectroscopy are used to predict the kinematics observed at much higher resolution by the STIS instrument on the Hubble Space Telescope (Bender et al. 2003), and we find generally satisfactory agreement.
The double nucleus geometry of M31 is currently best explained by the eccentric disk hypothesis of Tremaine, but whether the eccentric disk resulted from the tidal disruption of an inbounding star cluster by a nuclear black hole, or by an m=1 perturbation of a native nuclear disk, remains debatable. I perform detailed 2-D decomposition of the M31 double nucleus in the Hubble Space Telescope V-band to study the bulge structure and to address competing formation scenarios of the eccentric disk. I deblend the double nucleus (P1 and P2) and the bulge simultaneously using five Sersic and one Nuker components. P1 and P2 appear to be embedded inside an intermediate component (r_e=3.2) that is nearly spherical (q=0.97+/-m0.02), while the main galaxy bulge is more elliptical (q=0.81+/-0.01). The spherical bulge mass of 2.8x10^7 M_sol is comparable to the supermassive black hole mass (3x10^7 M_sol). In the 2-D decomposition, the bulge is consistent with being centered near the UV peak of P2, but the exact position is difficult to pinpoint because of dust in the bulge. P1 and P2 are comparable in mass. Within a radius r=1arcsec of P2, the relative mass fraction of the nuclear components is M_BH:M_bulge:P1: P2 = 4.3:1.2:1:0.7, assuming the luminous components have a common mass-to-light ratio of 5.7. The eccentric disk as a whole (P1+P2) is massive, M ~ 2.1x10^7 M_sol, comparable to the black hole and the local bulge mass. As such, the eccentric disk could not have been formed entirely out of stars that were stripped from an inbounding star cluster. Hence, the more favored scenario is that of a disk formed in situ by an m=1 perturbation, caused possibly by the passing of a giant molecular cloud, or the passing/accretion of a small globular cluster.
Nuclear-structure effects often provide an irreducible theory error that prevents using precision atomic measurements to test fundamental theory. We apply newly developed effective field theory tools to Hydrogen atoms, and use them to show that (to the accuracy of present measurements) all nuclear finite-size effects (e.g. the charge radius, Friar moments, nuclear polarizabilities, recoil corrections, Zemach moments {it etc.}) only enter into atomic energies through exactly two parameters, independent of any nuclear-modelling uncertainties. Since precise measurements are available for more than two atomic levels in Hydrogen, this observation allows the use of precision atomic measurements to eliminate the theory error associated with nuclear matrix elements. We apply this reasoning to the seven atomic measurements whose experimental accuracy is smaller than 10 kHz to provide predictions for nuclear-size effects whose theoretical accuracy is not subject to nuclear-modelling uncertainties and so are much smaller than 1 kHz. Furthermore, the accuracy of these predictions can improve as atomic measurements improve, allowing precision fundamental tests to become possible well below the irreducible error floor of nuclear theory.
In some galaxies, the stars orbiting the supermassive black hole take the form of an eccentric nuclear disk, in which every star is on a coherent, apsidally-aligned orbit. The most famous example of an eccentric nuclear disk is the double nucleus of Andromeda, and there is strong evidence for many more in the local universe. Despite their apparent ubiquity however, a dynamical explanation for their longevity has remained a mystery: differential precession should wipe out large-scale apsidal-alignment on a short timescale. Here we identify a new dynamical mechanism which stabilizes eccentric nuclear disks, and explain for first time the negative eccentricity gradient seen in the Andromeda nucleus. The stabilizing mechanism drives oscillations of the eccentricity vectors of individual orbits, both in direction (about the mean body of the disk) and in magnitude. Combined with the negative eccentricity gradient, the eccentricity oscillations push some stars near the inner edge of the disk extremely close to the black hole, potentially leading to tidal disruption events. Order of magnitude calculations predict extremely high rates in recently-formed eccentric nuclear disks ($sim0.1 - 1$ ${rm yr}^{-1} {rm gal}^{-1}$). Unless the stellar disks are replenished, these rates should decrease with time as the disk depletes in mass. If eccentric nuclear disks form during gas-rich major mergers, this may explain the preferential occurrence of tidal disruption events in recently-merged and post-merger (E+A/K+A) galaxies.
In order to be in a long-lived configuration, the density in a fluid disk should be constant along streamlines to prevent compressional (PdV) work from being done cyclically around every orbit. In a pure Kepler potential, flow along aligned, elliptical streamlines of constant eccentricity will satisfy this condition. For most density profiles, differential precession driven by the pressure gradient will destroy the alignment; however, in the razor-thin approximation there is a family of simple equilibria in which the precession frequency is the same at all radii. These disks may therefore be long-lived at significant eccentricities. The density can be made axisymmetric as r goes to 0, while maintaining the precession rate, by relaxing the requirement of constancy along streamlines in an arbitrarily small transition region near the center. In the limit of small eccentricity, the models can be seen as acoustically perturbed axisymmetric disks, and the precession rate is shown to agree with linear theory. The perturbation is a traveling wave similar to an ocean wave, with the fluid rising and falling epicyclically in the gravitational field of the central mass. The expected emission line profiles from the eccentric disks are shown to be strongly asymmetric in general, and, in extreme cases, prone to misinterpretation as single narrow lines with significant velocity offsets.
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