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Register a new userThree-dimensional Keplerian orbit-superposition models of the nucleus of M31
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We present three-dimensional eccentric disc models of the nucleus of M31, modelling the disc as a linear combination of thick rings of massless stars orbiting in the potential of a central black hole. Our models are nonparametric generalisations of the parametric models of Peiris & Tremaine. The models reproduce well the observed WFPC2 photometry, the detailed line-of-sight velocity distributions from STIS observations along P1 and P2, together with the qualitative features of the OASIS kinematic maps. We confirm Peiris & Tremaines finding that nuclear discs aligned with the larger disc of M31 are strongly ruled out. Our optimal model is inclined at 57 degrees with respect to the line of sight of M31 and has a position angle of 55 degrees. It has a central black hole of mass 10^8 solar masses, and, when viewed in three dimensions, shows a clear enhancement in the density of stars around the black hole. The distribution of orbit eccentricities in our models is similar to Peiris & Tremaines model, but we find significantly different inclination distributions, which might provide valuable clues to the origin of the disc.
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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.
We present a method for fitting orbit-superposition models to the kinematics of discrete stellar systems when the available stellar sample has been filtered by a known selection function. The fitting method can be applied to any model in which the distribution function is represented as a linear superposition of basis elements with unknown weights. As an example, we apply it to Fritz et al.s kinematics of the innermost regions of the Milky Ways nuclear stellar cluster. Assuming spherical symmetry, our models fit a black hole of mass $M_bullet=(3.76pm0.22)times10^6,M_odot$, surrounded by an extended mass $M_star=(6.57pm0.54)times10^6,M_odot$ within 4 pc. Within 1 pc the best-fitting mass models have an approximate power-law density cusp $rhopropto r^{-gamma}$ with $gamma=1.3pm0.3$. We carry out an extensive investigation of how our modelling assumptions might bias these estimates: $M_bullet$ is the most robust parameter and $gamma$ the least. Internally the best-fitting models have broadly isotropic orbit distributions, apart from a bias towards circular orbits between 0.1 and 0.3 parsec.
We present HST spectroscopy of the nucleus of M31 obtained with STIS. Spectra taken around the CaT lines at 8500 see only the red giants in the double bright- ness peaks P1 and P2. In contrast, spectra taken at 3600-5100 A are sensitive to the tiny blue nucleus embedded in P2, the lower surface brightness red nucleus. P2 has a K-type spectrum, but the embedded blue nucleus has an A-type spectrum with strong Balmer absorption lines. Given the small likelihood for stellar collisions, a 200 Myr old starburst appears to be the most plausible origin of the blue nucleus. In stellar population, size, and velocity dispersion, the blue nucleus is so different from P1 and P2 that we call it P3. The line-of-sight velocity distributions of the red stars in P1+P2 strengthen the support for Tremaine s eccentric disk model. The kinematics of P3 is consistent with a circular stellar disk in Keplerian rotation around a super-massive black hole with M_bh = 1.4 x 10^8 M_sun. The P3 and the P1+P2 disks rotate in the same sense and are almost coplanar. The observed velocity dispersion of P3 is due to blurred rotation and has a maximum value of sigma = 1183+-201 km/s. The observed peak rotation velocity of P3 is V = 618+-81 km/s at radius 0.05 = 0.19 pc corresponding to a circular rotation velocity at this radius of ~1700 km/s. Any dark star cluster alternative to a black hole must have a half-mass radius <= 0.03 = 0.11 pc. We show that this excludes clusters of brown dwarfs or dead stars on astrophysical grounds.
With high-resolution infrared data becoming available that can probe the formation of high-mass stellar clusters for the first time, models that make testable predictions of these objects are necessary. We utilize a three-dimensional radiative transfer code, including a hierarchically clumped medium, to study the earliest stages of super star cluster evolution. We explore a range of parameter space in geometric sequences that mimic the evolution of an embedded super star cluster. The inclusion of a hierarchically clumped medium can make the envelope porous, in accordance with previous models and supporting observational evidence. The infrared luminosity inferred from observations can differ by a factor of two from the true value in the clumpiest envelopes depending on the viewing angle. The infrared spectral energy distribution also varies with viewing angle for clumpy envelopes, creating a range in possible observable infrared colors and magnitudes, silicate feature depths and dust continua. General observable features of cluster evolution differ between envelopes that are relatively opaque or transparent to mid-infrared photons. The [70]-[160] color can be used to determine star formation efficiency; the Spitzer IRAC/MIPS [8.0]-[24] color is able to constrain Rin and Rout values; and the IRAC [3.6]-[5.8] color is sensitive to the fraction of the dust distributed in clumps. Finally, in a comparison of these models to data of ultracompact HII regions, we find good agreement, suggesting that these models are physically relevant, and will provide useful diagnostic ability for datasets of resolved, embedded SSCs with the advent of high-resolution infrared telescopes like JWST.
We show that orbit-superposition dynamical models (Schwarzschilds method) provide reliable estimates of nuclear black hole masses and errors when constructed from adequate orbit libraries and kinematic data. We thus rebut two recent papers that argue that BH masses obtained from this method are unreliable. These papers claim to demonstrate that the range of allowable BH masses derived from a given dataset is artificially too narrow as a result of an inadequate number of orbits in the library used to construct dynamical models. This is an elementary error that is easily avoided. We describe a method to estimate the number and nature of orbits needed for the library. We provide an example that shows that this prescription is adequate, in the sense that the range of allowable BH masses is not artificially narrowed by use of too few orbits. A second point raised by critics is that kinematic data are generally obtained with insufficient spatial resolution to obtain a reliable mass. We make the distinction between unreliable determinations and imprecise ones. We show that there are several different properties of a kinematic dataset that can lead to imprecise BH determinations, but none of the attributes we have investigated leads to an unreliable determination. In short, the degree to which the BH radius of influence is resolved by spectroscopic observations is already reflected in the BH-mass error envelope, and is not a hidden source of error. The BH masses published by our group and the Leiden group are reliable.
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