Group-theoretic models of the inversion process in bacterial genomes

The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog

The supermassive black hole in NGC4486a detected with SINFONI at the VLT

The near-infrared integral field spectrograph SINFONI at the ESO VLT opens a new window for the study of central supermassive black holes. With a near-IR spatial resolution similar to HST optical and the ability to penetrate dust it provides the possibility to explore the low-mass end of the M-sigma relation (sigma<120km/s) where so far very few black hole masses were measured with stellar dynamics. With SINFONI we observed the central region of the low-luminosity elliptical galaxy NGC4486a at a spatial resolution of ~0.1arcsec in the K band. The stellar kinematics was measured with a maximum penalised likelihood method considering the region around the CO absorption band heads. We determined a black hole mass of M_BH=1.25^{+0.75}_{-0.79} x 10^7 M_sun (90% C.L.) using the Schwarzschild orbit superposition method including the full 2-dimensional spatial information. This mass agrees with the predictions of the M-sigma relation, strengthening its validity at the lower sigma end.Comment: 7 pages, 7 figures. Accepted by MNRA

Dynamical Measurements of Black Hole Masses in Four Brightest Cluster Galaxies at 100 Mpc

We present stellar kinematics and orbit superposition models for the central regions of four Brightest Cluster Galaxies (BCGs), based upon integral-field spectroscopy at Gemini, Keck, and McDonald Observatories. Our integral-field data span radii from < 100 pc to tens of kpc. We report black hole masses, M_BH, of 2.1 +/- 1.6 x 10^10 M_Sun for NGC 4889, 9.7 + 3.0 - 2.6 x 10^9 M_Sun for NGC 3842, and 1.3 + 0.5 - 0.4 x 10^9 M_Sun for NGC 7768. For NGC 2832 we report an upper limit of M_BH < 9 x 10^9 M_Sun. Stellar orbits near the center of each galaxy are tangentially biased, on comparable spatial scales to the galaxies' photometric cores. We find possible photometric and kinematic evidence for an eccentric torus of stars in NGC 4889, with a radius of nearly 1 kpc. We compare our measurements of M_BH to the predicted black hole masses from various fits to the relations between M_BH and stellar velocity dispersion, luminosity, or stellar mass. The black holes in NGC 4889 and NGC 3842 are significantly more massive than all dispersion-based predictions and most luminosity-based predictions. The black hole in NGC 7768 is consistent with a broader range of predictions.Comment: 24 pages, 18 figures. Accepted for publication in Ap

A 20 Thousand Solar Mass Black Hole in the Stellar Cluster G1

We present the detection of a 2.0(+1.4,-0.8)x10^4 solar mass black hole (BH) in the stellar cluster G1 (Mayall II), based on data taken with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope. G1 is one of the most massive stellar clusters in M31. The central velocity dispersion (25 kms) and the measured BH mass of G1 places it on a linear extrapolation of the correlation between BH mass and bulge velocity dispersion established for nearby galaxies. The detection of a BH in this low-mass stellar system suggests that (1) the most likely candidates for seed massive BHs come from stellar clusters, (2) there is a direct link between massive stellar clusters and normal galaxies, and (3) the formation process of both bulges and massive clusters is similar due to their concordance in the M_BH/sigma relation. Globular clusters in our Galaxy should be searched for central BHs.Comment: 4 pages, accepted in The Astrophysical Journal Letters, October 200

The Black Hole Mass in Brightest Cluster Galaxy NGC 6086

We present the first direct measurement of the central black hole mass, M_BH, in NGC 6086, the Brightest Cluster Galaxy (BCG) in Abell 2162. Our investigation demonstrates for the first time that stellar dynamical measurements of M_BH in BCGs are possible beyond the nearest few galaxy clusters. We observed NGC 6086 with laser guide star adaptive optics and the integral-field spectrograph (IFS) OSIRIS at the W.M. Keck Observatory, and with the seeing-limited IFS GMOS-N at Gemini Observatory North. We combined the two IFS data sets with existing major-axis kinematics, and used axisymmetric stellar orbit models to determine M_BH and the R-band stellar mass-to-light ratio, M*/L_R. We find M_BH = 3.6(+1.7)(-1.1) x 10^9 M_Sun and M*/L_R = 4.6(+0.3)(-0.7) M_Sun/L_Sun (68% confidence), from models using the most massive dark matter halo allowed within the gravitational potential of the host cluster. Models fitting only IFS data confirm M_BH ~ 3 x 10^9 M_Sun and M*/L_R ~ 4 M_Sun/L_Sun, with weak dependence on the dark matter halo structure. When data out to 19 kpc are included, the unrealistic omission of dark matter causes the best-fit black hole mass to decrease dramatically, to 0.6 x 10^9 M_Sun, and the best-fit stellar mass-to-light ratio to increase to 6.7 M_Sun/L_Sun. The latter value is at further odds with stellar population studies favoring M*/L ~ 2 M_Sun/L_Sun,R. Biases from dark matter omission could extend to dynamical models of other galaxies with central stellar cores, and new measurements of M_BH from models with dark matter could steepen the empirical scaling relationships between black holes and their host galaxies.Comment: 22 pages, 19 figures; accepted for publication in Ap

Orbit-Based Dynamical Models of the Sombrero Galaxy (NGC 4594)

We present axisymmetric, orbit-based models to study the central black hole, stellar mass-to-light ratio, and dark matter halo of NGC 4594 (M104, the Sombrero Galaxy). For stellar kinematics, we use published high-resolution kinematics of the central region taken with the Hubble Space Telescope, newly obtained Gemini long-slit spectra of the major axis, and integral field kinematics from the SAURON instrument. At large radii, we use globular cluster kinematics to trace the mass profile and apply extra leverage to recovering the dark matter halo parameters. We find a black hole of mass M_{\bullet}=(6.6 +/- 0.4) x 10^8 M_{\odot}, and determine the stellar M/L_I=3.4 +/- 0.05 (uncertainties are the 68% confidence band marginalized over the other parameters). Our best fit dark matter halo is a cored logarithmic model with asymptotic circular speed V_c=376 +/- 12 km/s and core radius r_c= 4.7 +/- 0.6 kpc. The fraction of dark to total mass contained within the half-light radius is 0.52. Taking the bulge and disk components into account in our calculation of \sigma_e puts NGC 4594 squarely on the M-\sigma relation. We also determine that NGC 4594 lies directly on the M-L relation.Comment: 13 pages, 10 figures, accepted for publication in Ap

The Effect of Spatial Gradients in Stellar Mass-to-Light Ratio on Black Hole Mass Measurements

We have tested the effect of spatial gradients in stellar mass-to-light ratio (Y) on measurements of black hole masses (MBH) derived from stellar orbit superposition models. Such models construct a static gravitational potential for a galaxy and its central black hole, but typically assume spatially uniform Y. We have modeled three giant elliptical galaxies with gradients alpha = d(log Y)/d(log r) from -0.2 to +0.1. Color and line strength gradients suggest mildly negative alpha in these galaxies. Introducing a negative (positive) gradient in Y increases (decreases) the enclosed stellar mass near the center of the galaxy and leads to systematically smaller (larger) MBH measurements. For models with alpha = -0.2, the best-fit values of MBH are 28%, 27%, and 17% lower than the constant-Y case, in NGC 3842, NGC 6086, and NGC 7768, respectively. For alpha = +0.1, MBH are 14%, 22%, and 17% higher than the constant-Y case for the three respective galaxies. For NGC 3842 and NGC 6086, this bias is comparable to the statistical errors from individual modeling trials. At larger radii, negative (positive) gradients in Y cause the total stellar mass to decrease (increase) and the dark matter fraction within one effective radius to increase (decrease).Comment: 6 pages, 4 figures, 1 table. To appear in ApJ